Mass Transport in Magmatic Systems 0128212012, 9780128212011

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Mass Transport in Magmatic Systems

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Mass Transport in Magmatic Systems Bjorn O. Mysen

Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC, United States

Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States Copyright © 2023 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. ISBN: 978-0-12-821201-1 For information on all Elsevier publications visit our website at https://www.elsevier.com/books-and-journals Publisher: Candice Janco Acquisitions Editor: Amy Shapiro Editorial Project Manager: Chris Hockaday Production Project Manager: Sreejith Viswanathan Cover Designer: Matthew Limbert Typeset by TNQ Technologies

Contents Preface .................................................................................................................................................. xi

CHAPTER 1 Melting in the Earth’s interior: solidus and liquidus relations........... 1 1.1 Introduction.................................................................................................................1 1.2 Premelting ...................................................................................................................1 1.3 Melting of peridotite...................................................................................................2 1.3.1 Peridotite melting without volatiles ................................................................. 3 1.3.2 Solidus phase assemblage and pressure........................................................... 6 1.3.3 Peridotite melting with volatiles ...................................................................... 7 1.4 Melting of basalt .......................................................................................................21 1.4.1 Basalt/gabbro melting without volatiles ........................................................ 21 1.4.2 Basalt/gabbro-H2O ......................................................................................... 22 1.4.3 Basalt/gabbro-CO2.......................................................................................... 28 1.4.4 Basalt with multicomponent fluid.................................................................. 29 1.5 Melting of andesite ...................................................................................................33 1.5.1 AndesiteeH2O................................................................................................ 33 1.5.2 Andesite melting and H2O activity................................................................ 34 1.5.3 Melting of sediment ....................................................................................... 36 1.5.4 The role of oxygen fugacity........................................................................... 37 1.6 Rhyolite melting .......................................................................................................38 1.6.1 Rhyolite-H2O.................................................................................................. 39 1.6.2 H2O-undersaturated rhyolite/granite melting................................................. 39 1.6.3 The role of oxygen fugacity........................................................................... 41 1.7 Concluding remarks..................................................................................................42 References.........................................................................................................................42

CHAPTER 2 Melting in the Earth’s interior: melting phase relations between the solidus and liquidus ...................................................... 53 2.1 Introduction...............................................................................................................53 2.2 Melting interval of mantle peridotite without volatiles ...........................................53 2.2.1 Degree of melting........................................................................................... 56 2.2.2 Melt composition in the melting interval ...................................................... 60 2.2.3 Upper mantle magma genesis without volatiles............................................ 63 2.3 Melting interval of mantle peridotite with volatiles ................................................65 2.3.1 Degree of melting: PeridotitedH2O.............................................................. 65 2.3.2 Melt composition in the peridotitedH2O melting interval .......................... 67 2.3.3 Upper mantle magma genesis with H2O ....................................................... 72 2.3.4 Degree of melting: PeridotitedCO2 .............................................................. 74 2.3.5 Melt composition in the peridotiteeCO2 melting interval............................ 76

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2.3.6 Melting of peridotite with halogens, CO2 and/or H2O.................................. 83 2.3.7 Peridotite-CO2 melting and upper mantle magma genesis ........................... 83 2.3.8 PeridotiteeCeOeH melting and melt compositions.................................... 84 2.4 Melting interval of basalt..........................................................................................87 2.4.1 Redox variations at ambient pressure ............................................................ 87 2.4.2 High-pressure melting without volatiles........................................................ 89 2.4.3 Melting of basalt with volatiles ..................................................................... 90 2.5 Melting interval of andesite......................................................................................96 2.6 Melting interval of granite......................................................................................100 2.6.1 H2O-undersaturated melting......................................................................... 102 2.6.2 Melting with variable redox conditions ....................................................... 102 2.7 Concluding remarks................................................................................................103 References.......................................................................................................................104

CHAPTER 3

Element distribution during melting and crystallization................. 113 3.1 Introduction.............................................................................................................113 3.2 Principles.................................................................................................................113 3.3 Trace element substitution in melts and minerals..................................................115 3.3.1 Trace element substitution in minerals ........................................................ 116 3.3.2 Trace element substitution in melts ............................................................. 120 3.4 Element partitioning, intensive, and extensive variables .......................................130 3.4.1 Olivine-melt.................................................................................................. 130 3.4.2 Plagioclase-melt ........................................................................................... 141 3.4.3 Clinopyroxene-melt ...................................................................................... 154 3.4.4 Orthopyroxene-melt...................................................................................... 171 3.4.5 Garnet-melt................................................................................................... 182 3.4.6 Amphibole-melt............................................................................................ 189 3.4.7 Other mineral-melt pairs .............................................................................. 199 3.5 Mineral-melt partitioning and igneous processes ..................................................200 3.5.1 Melting models............................................................................................. 200 3.5.2 Variable partition coefficients ...................................................................... 200 3.6 Concluding remarks................................................................................................201 References.......................................................................................................................202

CHAPTER 4

Energetics of melts and melting in magmatic systems .................. 213 4.1 Introduction.............................................................................................................213 4.2 Energetics of melting..............................................................................................214 4.2.1 Thermodynamics of premelting ................................................................... 214 4.2.2 Enthalpy and entropy of fusion.................................................................... 225 4.3 Heat content, heat capacity, and entropy of silicate melts and magma ................233 4.3.1 Heat capacity and entropy of magmatic liquids .......................................... 237

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4.3.2 Heat capacity, entropy, and silicate melt polymerization in metal oxide-SiO2 systems ...................................................................................... 243 4.3.3 Heat capacity and entropy in Al-bearing systems....................................... 246 4.3.4 Heat capacity and entropy in Fe- and Ti-bearing melt systems.................. 247 4.3.5 Thermodynamics of mixing and solution .................................................... 252 4.4 Thermodynamics of melts and liquidus phase relations........................................262 4.5 Concluding remarks................................................................................................266 References.......................................................................................................................267

CHAPTER 5 Structure of magmatic liquids.......................................................... 275 5.1 Introduction.............................................................................................................275 5.2 Glass versus melt and glass transition....................................................................275 5.3 Silicate melt and glass structure .............................................................................278 5.3.1 Degree of silicate polymerization, NBO/T................................................... 279 5.3.2 SieOeAl bonding and charge-balance of tetrahedrally coordinated Al3þ .......................................................................................... 287 5.3.3 Silicate speciation (Qn-species).................................................................... 292 5.3.4 Al3þ substitution for Si4þ in magmatic systems ......................................... 304 5.3.5 Other tetrahedrally coordinated cations (P5þ and Ti4þ).............................. 309 5.4 Iron in magmatic liquids.........................................................................................310 5.4.1 Redox relations of Fe3þ and Fe2þ ............................................................... 311 5.4.2 Structural role of iron in magmatic systems................................................ 315 5.4.3 Magma properties and redox ratio of iron................................................... 317 5.5 Concluding remarks................................................................................................318 References.......................................................................................................................319

CHAPTER 6 Structure and properties of fluids .................................................... 331 6.1 Introduction.............................................................................................................331 6.2 Fluid/melt partitioning of volatile components......................................................332 6.2.1 Fluid/melt partitioning of H2O..................................................................... 333 6.2.2 Fluid/melt partitioning of CO2 ..................................................................... 334 6.2.3 Fluid/melt partitioning of chlorine............................................................... 336 6.2.4 Fluid/melt partitioning of fluorine ............................................................... 344 6.2.5 Fluid/melt partitioning of bromine and iodine ............................................ 345 6.2.6 Fluid/melt partitioning of sulfur................................................................... 347 6.3 Structure and properties of H2O in fluids ..............................................................349 6.3.1 Structure of liquid and supercritical H2O .................................................... 351 6.3.2 Properties of liquid and supercritical H2O .................................................. 363 6.3.3 H2OeNaCl.................................................................................................... 375 6.3.4 H2OeCeOeH.............................................................................................. 383 6.3.5 H2OeSeOeH .............................................................................................. 390

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6.4 Solubility behavior in fluid: H2OeSiO2.................................................................393 6.4.1 Solubility of SiO2 in H2O ............................................................................ 393 6.4.2 Solubility mechanism of SiO2 in H2O......................................................... 400 6.4.3 Properties of H2OeSiO2 fluid...................................................................... 406 6.4.4 H2OeSiO2eNaCl......................................................................................... 410 6.5 Solubility behavior in fluid: H2OeSiO2eMgO .....................................................413 6.5.1 Solubility of MgOeSiO2 in H2O................................................................. 413 6.5.2 Solubility mechanism of MgOeSiO2 in H2O ............................................. 415 6.5.3 MgOeSiO2 solubility in saline solutions .................................................... 418 6.5.4 Properties of MgOeSiO2eH2O fluid .......................................................... 421 6.6 Solubility behavior in fluid: H2OeAl2O3(eNaCleKOHeSiO2) ..........................422 6.6.1 Al2O3eH2O with and without halogens ...................................................... 422 6.6.2 H2OeAl2O3-alkali aluminosilicate with and without halogens .................. 426 6.7 Minor and trace elements in aqueous fluid ............................................................433 6.7.1 Ti solubility .................................................................................................. 434 6.7.2 Zr solubility .................................................................................................. 436 6.7.3 Salinity of aqueous solutions and trace element solubility ......................... 440 6.7.4 Sulfur in aqueous solutions and trace element solubility............................ 450 6.8 Concluding remarks................................................................................................463 References.......................................................................................................................463

CHAPTER 7

7.1 7.2 7.3 7.4

Water in magma................................................................................ 483

Introduction.............................................................................................................483 Speciation and abundance ......................................................................................483 Principles of solubility............................................................................................484 H2O solubility .........................................................................................................485 7.4.1 H2O solubility in simple system melts ........................................................ 486 7.4.2 Miscibility between hydrous melts and aqueous fluids............................... 493 7.4.3 Water solubility and mixed volatiles ........................................................... 493 7.4.4 Water solubility in natural magmatic liquids .............................................. 496 7.4.5 H2O solubility models for natural magma................................................... 496 7.4.6 Water solution mechanisms in magma ........................................................ 501 7.4.7 H2O in magmatic liquids.............................................................................. 511 7.4.8 Properties and processes of hydrous magmatic liquids............................... 513 7.5 Concluding remarks................................................................................................525 References.......................................................................................................................526

CHAPTER 8

Volatiles in magmatic liquids........................................................... 535

8.1 Introduction.............................................................................................................535 8.2 Oxidized carbon species .........................................................................................536 8.2.1 Solubility of CO2 in magma ........................................................................ 536 8.2.2 Solubility mechanisms of CO2 in magma ................................................... 539 8.2.3 Oxidized carbon (CO2) in magmatic processes........................................... 542

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8.3 Reduced carbon (CH4, CO, and carbide) ...............................................................548 8.3.1 Carbon monoxide (CO)................................................................................ 550 8.3.2 Carbide (C) ................................................................................................... 551 8.3.3 Methane (CH4) ............................................................................................. 551 8.3.4 Magma properties and CH4-induced melt depolymerization...................... 554 8.4 Sulfur solubility ......................................................................................................555 8.4.1 Oxidized sulfur (SO2 and SO3).................................................................... 558 8.4.2 Reduced sulfur (S2).................................................................................... 561 8.5 Nitrogen solubility and solution mechanisms ........................................................567 8.5.1 Oxidized nitrogen ......................................................................................... 568 8.5.2 Reduced nitrogen.......................................................................................... 569 8.5.3 Nitrogen in the Earth’s interior .................................................................... 572 8.6 Hydrogen solubility and solution mechanisms ......................................................573 8.6.1 Hydrogen in the Earth’s mantle ................................................................... 574 8.7 Halogen solubility and solution mechanisms.........................................................575 8.7.1 Fluorine solubility ........................................................................................ 575 8.7.2 Fluorine solution mechanisms...................................................................... 576 8.7.3 Chlorine solubility........................................................................................ 579 8.7.4 Chlorine solution mechanisms ..................................................................... 582 8.7.5 Bromine and iodine ...................................................................................... 582 8.7.6 Halogens in magma...................................................................................... 582 8.8 Noble gas solubility and solution mechanisms ......................................................585 8.8.1 Noble gases in fully polymerized silicate melt structure ............................ 585 8.8.2 Noble gases in depolymerized silicate melt structure ................................. 588 8.8.3 Noble gases in magmatic systems ............................................................... 589 8.9 Concluding remarks................................................................................................590 References.......................................................................................................................591

CHAPTER 9 Transport properties.......................................................................... 605 9.1 Introduction.............................................................................................................605 9.2 Relationships among transport properties ..............................................................606 9.3 Viscosity of magmatic liquids ................................................................................607 9.3.1 Magma viscosity, composition, and temperature ........................................ 608 9.3.2 Viscosity and structure of magmatic liquids ............................................... 614 9.3.3 Viscosity, iron content, and Fe3þ/SFe of magmatic liquids ....................... 617 9.3.4 Effect of pressure on viscosity of magma ................................................... 619 9.3.5 Viscosity and volatiles in magmatic liquids ................................................ 626 9.4 Viscosity of model system silicate melts ...............................................................633 nþ 9.4.1 Viscosity of melts and glasses in the M2=n O  SiO2 system...................... 634 nþ 9.4.2 Viscosity of melts and glasses in the M2=n O  Al2 O3  SiO2 system....... 651 9.4.3 Viscosity of iron-bearing silicate melts ....................................................... 670 9.5 Modeling melt viscosity .........................................................................................673

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9.6 Diffusion .................................................................................................................676 9.6.1 Diffusion, composition, and temperature..................................................... 677 9.6.2 Diffusion, composition, and pressure .......................................................... 684 9.6.3 Volatiles and diffusion.................................................................................. 694 9.7 Electrical conductivity ............................................................................................717 9.7.1 Electrical conductivity, composition, and temperature ............................... 719 9.7.2 Electrical conductivity and pressure ............................................................ 724 9.7.3 Electrical conductivity and volatiles............................................................ 725 9.8 Concluding remarks................................................................................................731 References.......................................................................................................................732

CHAPTER 10

Equation-of-state of magmatic liquids........................................... 755 Introduction...........................................................................................................755 Equation-of-state (EOS) of glass versus melt......................................................757 Functional relationships........................................................................................762 Equation-of-state of magmatic liquids .................................................................766 10.4.1 EOS of natural magma, composition, and temperature...........................766 10.4.2 EOS of natural magma and pressure .......................................................776 10.4.3 Volatiles and their influence on the EOS of magmatic liquids ...............784 10.5 Equation-of-state of simple system model liquids...............................................799 nþ 10.5.1 EOS of melts in the M2=n O  SiO2 system .............................................799 nþ 10.5.2 EOS of melts in the M2=n O  Al2 O3  SiO2 system..............................803 4þ 10.5.3 EOS of melts with Ti and Fe3þ ............................................................807 10.6 Concluding remarks..............................................................................................810 References.......................................................................................................................811 10.1 10.2 10.3 10.4

CHAPTER 11

Mass transport ................................................................................ 821 11.1 Introduction...........................................................................................................821 11.2 Porosity, permeability, and transport....................................................................822 11.2.1 Porosity and permeability of aqueous fluids and silicate melts ..............822 11.2.2 Equilibrium texture and wetting angle ....................................................826 11.2.3 Dihedral angles and H2O distribution in the earth ..................................841 11.2.4 Wetting angles and partial melts..............................................................849 11.2.5 Melt/mineral dihedral angle, porosity, and properties.............................854 11.2.6 Permeability and porosity in carbonate and sulfide-bearing silicate systems......................................................................................................859 11.3 Concluding remarks..............................................................................................865 References.......................................................................................................................866

Index .................................................................................................................................................. 877

Preface The formation and evolution of the Earth and planets depend on transfer of mass and energy. Magma and fluid are integral parts of the transport processes that govern the mass and energy transfer. Mass transport property data are central to describe those processes. Mass transport is accomplished by transfer of fluids and magma and typically takes place at high temperature and pressure. Mass transport typically occurs along temperature and pressure gradients, which means that energy transport also associates with mass transport, although in this book, energy transfer is not explicitly discussed. A structure-based understanding of how transport properties reflect changes in composition, temperature, and pressure greatly enhances our ability to use property data to characterize transport and transfer processes. This knowledge not only is helpful for the materials characterization needed to describe mass transport processes in nature, it also contributes to the knowledge base of adjoining scientific disciplines including glass and materials science. The focus of this book is to describe and discuss transport properties of magma together with aspects of transport properties of fluids, and to employ such data to characterize mass transport in the interior of Earth, its moon, and the terrestrial planets. The principal aim of this Book, therefore, is to describe mass transport by magma and fluids, what and how melt and fluid properties govern those processes, and how understanding of the structure of those transport agents, and, therefore, their chemical composition, temperature, and pressure, can be used to characterize the properties. Linkage of transport properties to structure of the transport agents is important because this understanding provides a basis for quantitative modeling of property behavior without otherwise more comprehensive and extensive experimental study of each and every composition and conditions. The latter efforts require more human and financial resources than often are available. The main focus of this book is on transport by magma with lesser emphasis on mass transfer by fluids. Some of the reasons for this selection is that fluid property data such as density and viscosity, for example, differ greatly from those of surrounding crystalline materials to the extent that variations of those properties of fluids do not impact greatly fluid-mediated mass transport. Of course, fluid compositions, pressures, and temperatures do. These property variations, therefore, are the subject of a major chapter of the book, but have not been isolated into individual chapters as was done for silicate melt and magma properties. The variables causing petrogenetically important changes in properties of fluids also affect migration efficiency. These variables have been discussed in the last Chapter of the Book (Chapter 11). That Chapter is centered on mass transfer by fluids and magma through crystalline rock matrix together with a number of examples from natural observations that can be, or have been, interpreted in terms of the passage of melts or fluids in a rock matrix. The transport properties of magmatic liquids, often substantiated with information from compositionally simpler model system, are the main focus of this Book. For this purpose, the Book is organized in a petrogenetically evolutionary sense beginning with melting and crystallization of rock-forming materials to form and evolve magma (Chapters 1 and 2). Within this evolution, which leads to a wide variety of magma compositions and greatly variable transport properties, we follow the melting and crystallization behavior from the most primitive magma created by partial melting of peridotitic parental rocks in the Earth’s mantle to a finish where melting and crystallization of the most evolved magmatic liquids, such as those of rhyolite and granite composition, are presented. Roles of volatiles, in particular H2O and CO2, were incorporated as appropriate. The compositional variations of the

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magmatic liquids in those environments can cause their transport properties to vary over many orders of magnitude. Element distribution among melts, fluids, and minerals, and how this distribution is affected by their composition and structure, is central to characterization of mass transport in the Earth. Bulk composition of magma and crystalline minerals together with element, oxide, and isotopic solubility in and partitioning between these phases are sensitive to temperature, pressure, and redox conditions of the formation and evolution of magmatic liquids and the environment in which partitioning occurs. Element partitioning is described and discussed in Chapter 3, which follow naturally, therefore, from phase equilibrium melting and crystallization behavior presented in Chapters 1 and 2. The focus of Chapter 4 is thermodynamic data needed for characterization of the properties and processes discussed in Chapters 1e3. This chapter highlights existing thermodynamic data and how such information aids our understanding of the behavior of magmatic systems. This includes melting and crystallization behavior, element partitioning, and how thermodynamic data can be employed to characterize transport properties (viscosity, diffusion, and electrical conductivity) of silicate melts and magmatic liquids. Thermodynamics, therefore, not only help us to understand melting, crystallization, and element distribution behavior, such information can be employed directly to model transport properties of magma. Of course, ultimately, thermodynamic data and other melt and fluid property data are manifestations of the structure of the materials of interest. Structural information forms the basis, therefore, for characterization of transport properties of magmatic liquids and of fluids. Structural data and how those data are linked to transport and associated properties such as described in Chapters 1e4, obtained for the most part from experimental studies, are contained in Chapters 5e8. Those four chapters are separated into a basic description of structural principles necessary to describe silicate melt structure and can be found in Chapter 5 for melt and in Chapter 6 for fluid structure. In Chapter 6, in addition to structure discussions, other properties of fluids, including partitioning of the fluid components (H2O, CO2, CH4, H2, halogen-, N-, and S-containing fluid species, both reduced and oxidized) between fluids and melts fill out the initial sections of the discussion. This is followed by description of solubility behavior of major, minor, and trace compositions in fluids of various relevant compositions. The solubility and solution mechanisms of volatiles in magmatic liquids and model simple-system silicate melts are discussed in Chapters 7 and 8. This presentation was intended to follow naturally from the structure data provided in Chapters 5 and 6. Many facets of melt and fluid structure affect their transport properties, some of which also can be found in these chapters. The remaining chapters (Chapters 9e11), focus directly on how mass transport (properties and processes governed by properties) by magma and fluid and of magma- and fluid-bearing systems depends on intensive and extensive parameters. Transport properties such as viscosity, diffusion, and conductivity together with how these may be linked together, can be found in Chapter 9. This chapter also offers several examples of how transport properties affect mass transport processes in the Earth and terrestrial planets. Mass transport in planetary interiors is affected critically by the equation-of-state (EOS) of magmatic liquids as discussed in Chapter 10. The EOS information includes density, volumes, thermal expansion, and compressibility of chemically complex magmatic liquids. Similar data reported for the simpler model system are employed for a more thorough understanding of EOS of magma and (fluid) at high temperature and pressure.

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The last chapter (Chapter 11) deals with actual movement of fluids and magma through rock matrices at pressures and temperatures exceeding those above which open cracks can be supported by the rock strength. Characterization of these properties and how they are affected by intensive and extensive parameters are critical for characterization of mass transport in planetary interiors. In this chapter, there not only is a discussion of some of the main variables governing fluid and melt migration, Chapter 11 also includes assessment of which melt and fluid properties can affect movement of those liquids through a crystalline matrix. Moreover, this chapter contains summaries of how liquid distribution and composition in a crystalline matrix affects geophysically and geochemically important properties of rocks often with small volume fractions of magma or fluid, and how such knowledge helps interpretation of natural geochemical and geophysical data. The creation of a book such as this requires input from a wide range of specialties, many of which might not always have been in the center of the author’s research activities. It has been very important, therefore, to garner input from friends and colleagues and, perhaps, most important of all, access and help in accessing published literature from a wide variety of scientific disciplines and subdisciplines. The assistance from our library and its two members, Shaun Hardy and M. O. O’Donnell, has been invaluable in this regard. This book could not have been produced without their exceptional professionalism, efficiency, and cheerful assistance. This is particularly so as this book was written while the COVID-19 pandemic was raging here and elsewhere in the world. Hence, much of the work was carried out electronically because person-to-person contact was difficult. Moreover, COVID-19-related technical problems such as, for example, production of graphics were overcome thanks in no little part to the assistance and support of my wife, Susana, who assisted in the generation of many of the diagrams used in the text. There is, of course, much more data and understanding needed before we can claim an understanding of all transport processes governing the mass and energy transfer associated with the formation and evolution of Earth, its moon, and the terrestrial planets. I hope, however, that the information that is offered in this book will help pointing not only to what we believe we know, but also, and perhaps more importantly, what we do not know. It provides, therefore, an overview of current understanding of mass transport in petrogenetic processes. A major aim also is to develop suggestions for where future research activities might be the most useful. Those objectives can be reached not by what may be the fancy of the day, but with concerted and integrated efforts and inputs from natural observations, from systematic laboratory experiments, and by numeric modeling and integration.

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CHAPTER

Melting in the Earth’s interior: solidus and liquidus relations

1

1.1 Introduction Mass transport in the Earth and terrestrial planets is by magma (silicate melts) and by fluids compositionally in the system CeOeHeNeS. Generation of magma is the focus of this chapter. Magma exists from ambient pressure and high temperature to the pressures and temperatures corresponding to the core/mantle boundary (Labrosse et al., 2007; Andrault et al., 2014; French and Romanowicz, 2015). Magma can, therefore, serve as a mass (and energy) transport medium throughout the pressure range of the silicate Earth (136 GPa). Details of magma transport are presented in Chapter 9. In this chapter, we will discuss how to generate magma in the Earth with a focus on the variables that govern the melting (solidus) and crystallization (liquidus) temperature/pressure coordinates. The phase relations that describe equilibria between minerals and melt the temperature interval between initial melting and complete melting will be discussed in Chapter 2. Here, after a brief discussion of premelting phenomena, we will describe the relationships at or near the solidus and the liquidus of the dominant silicate rocks in the Earth.

1.2 Premelting A phenomenon known as “premelting” is detected by discontinuities in heat capacity versus temperature trajectories (Fig. 1.1). To date premelting has been observed only in laboratory experiments using endmember minerals (Richet and Fiquet, 1991; Courtial et al., 2000; Richet et al., 1996, 1998). The lack of information from chemically complex natural systems may simply be because the relevant experiments have not been carried out. Macroscopically, premelting is represented by a rapid increase of the heat capacity as the melting temperature of a crystal is approached (Fig. 1.1). The heat capacity discontinuity begins from 80 to 250
C below actual melting temperatures. Enthalpy and entropy effects representi from 7% to 22% of the enthalpies and entropies of fusion (Richet and Fiquet, 1991; Thie´blot et al., 1999; Courtial et al., 2000; Nera´d et al., 2013). Premelting has been reported in synthetic diopside, CaMgSi2O6, together with other synthetic metasilicates (Richet et al., 1996). For diopside, the onset of premelting coincides with discontinuous changes in properties such as Ca diffusion (Dimanov and Ingrin, 1995) and electrical conductivity (Bouhifd et al., 2002). In this case, premelting has been inferred to be a reflection of Mass Transport in Magmatic Systems. https://doi.org/10.1016/B978-0-12-821201-1.00005-5 Copyright © 2023 Elsevier Inc. All rights reserved.

1

Chapter 1 Melting in the Earth’s interior

27 26 25 24

premelting interval

(C ano aA rt l S hite iO )

di (Ca opsid e Mg Si O )

Mean heat capacity, J/g atom K

2

premelting interval

23 22 1000

1200

1400

1600

1800

2000

Temperature, K FIGURE 1.1 Mean heat capacity of crystalline diopside (CaMgSi2O6) and anorthite (CaAl2Si2O8) as a function of temperature. Shaded region shows temperature interval of actual temperature range of premelting. Modified after Richet et al. (1996).

temperature-dependent (Ca, Mg) structural disorder as the structural mechanism for the premelting phenomenon (Richet et al., 1996). In other metasilicates, incipient breakup of the silicate chain structure has been proposed (Richet et al., 1998; Nesbitt et al., 2017). For aluminosilicate crystals such as anorthite (CaAl2Si2O8), (Al,Si) disordering accounts for the premelting effect (Richet et al., 1994). Possible effects of solid solutions such as diopside-hedenbergite and anorthite-albite on premelting have not been addressed as yet.

1.3 Melting of peridotite Partial melting of peridotite in the Earth’s mantle is the principal source of primary magma. Following melting, magma aggregates and ascends toward the surface of the Earth either to form shallow-depth magma chambers, perhaps governed by the principle of neutral buoyancy (Ryan, 1987), where crystal fractionation can alter the magma composition, or magma ascends directly ascent to or near the Earth’s surface. Peridotite melting may take place under essentially volatile-free conditions (e.g., Kushiro, 1969; Falloon et al., 1988; Zhang and Herzberg, 1994; Walter, 1998) or it occurs in the presence of volatiles such as H2O (Grove et al., 2006; Kawamoto and Holloway, 1997), CO2 (Canil and Scarfe, 1990; Brey et al., 2008), or mixtures of CO2 and H2O (Mysen and Boettcher 1975a,b; Wyllie, 1977; Ulmer and Sweeney, 2002). Under redox conditions equal to or more reducing than that corresponding to the iron-wu¨stite (IW) oxygen buffer1 reduced species such as H2 and CH4 can also play important roles 1 In this and following chapters, oxygen fugacity is often referred to with reference to common oxygen buffers. These are HM (hematite-magnetite), NNO (nickel-nickel oxide), QFM (quartz-fayalite-magnetite), MW (magnetite-wu¨stite) and IW (ironwu¨stite).

1.3 Melting of peridotite

3

during melting (Eggler and Baker, 1982; Luth and Boettcher, 1986; Taylor and Green, 1988). Such conditions likely were more common during the Earth’s early history.

1.3.1 Peridotite melting without volatiles Notwithstanding the common occurrence of mantle melting with volatiles such as either H2O or CO2, or both, melting of a peridotite lithosphere also takes place without volatiles (Herzberg et al., 1990; Hirose and Kushiro, 1993; Asimow et al., 2001). Early experimental studies on peridotite melting using natural peridotite starting material were those of Green and Ringwood (1967) and Kushiro et al. (1968). As can be seen in Fig. 1.2, the ambient pressure solidus of a typical peridotite is near 1150
C. The solidus temperature increases with increasing pressure at a rate of about 150
C/GPa. Within experimental error of the Kushiro et al. (1968) study, the solidus curve is linear. However, given the change of solidus mineral assemblage from olivine þ orthopyroxene þ clinopyroxene þ spinel to olivine þ orthopyroxene þ clinopyroxene þ garnet at pressures between 2 and 3 GPa, one would expect a change of the slope of the solidus curve. From the Claussius-Clapeyron expression vP=vT ¼ DS=DV;

(1.1)

the volume change, DV, will change as the mineral assemblage changes with increasing pressure. Such a volume change would be expected near 3 GPa at the solidus temperature shown in Fig. 1.2 as this is approximately where the garnet-to-spinel transition is located. Evidently, this kink is within 0

Pressure, GPa

1

2

3

4

5 1000 1300 1600 Temperature, ˚C

FIGURE 1.2 Pressure/temperature of peridotite melting (solidus) in the absence of volatiles. Modified after Kushiro et al. (1968).

Chapter 1 Melting in the Earth’s interior

Temperature, ˚C

2400 2200

ol: olivine cpx: clinopyroxene gt: garnet b: β-Mg SiO g: γ-Mg SiO gt: garnet MgPv: Mg-perovskite CaPv: Ca-pervskite Mw: magnesiowüstite

2000

i

sol

t

β+g

v gP +M v w P M a +C

t

ol+

soli

1600 1400 0

dus

+g

cpx

1800

us

lid

so

γ+gt +CaPv

2600

dus

4

5

10 15 20 Pressure, GPa

25

30

FIGURE 1.3 Pressure/temperature trajectory of peridotite melting to pressures near the interface of the transition zone to the lower mantle. Modified after Herzberg and Zhang (1996).

experimental error in the early data shown in Fig. 1.2. In more recent experimental studies, there are distinctive kinks of the solidus curve as a phase transformation is encountered although no kinks in the solidus were reported where the spinel-to-garnet is located (Herzberg et al., 2000; see also Fig. 1.3). The results summarized in Fig. 1.3 do, however, show kinks of the solidus near 15, 20, and 23 GPa. These kinks and change in solidus slope reflect transformation from olivine to b-spinel phase (b-Mg2SiO4), Ca-perovskite (CaSiO3), to magnesiowu¨stite þ Mg-perovskite (MgO and MgSiO3). Obviously, these changes in phase assemblages will also affect the composition of the melts on the solidus. These latter issues will be discussed in detail in Chapter 2. Although there is little disagreement as to the general nature of solidus phase assemblages of peridotite in the Earth’s mantle, details of these phase assemblages as well as the pressure/temperature coordinates of the solidus curve and of the phase changes remain open to some discussion (see, for example, a review of those data by Herzberg et al., 2000). Some of the differences, seen, for example, in the various solidus temperatures reported in the literature (Fig. 1.4) are the result of different peridotite compositions. The most obvious compositional effect on the peridotite solidus temperature is from changes in the Mg/(Mg þ Fe) ratio of the peridotite. This ratio ranges from near 0.95 to less than 0.85 in mantle peridotite. From a compilation of 3 GPa data from various experimentally determined peridotite solidus temperatures, Hirschmann (2000) found there to be a 90e100
C range in temperatures as a function of the bulk melt Mg/(Mg þ Fe) of the peridotite (Fig. 1.5). This effect is not surprising given the relationship between Mg/(Mg þ Fe) and solidus temperatures of the peridotite mineral phases (olivine, pyroxenes, spinel, and garnet). The Mg/(Mg þ Fe) ratio also affects the pressure of the spinelto-garnet transformation garnet on the peridotite solidus (Mysen and Boettcher, 1975a). Another composition variable affecting solidus temperatures of terrestrial mantle peridotite is the alkali content (Na þ K) (Fig. 1.6). This probably happens because alkali elements are incompatible in peridotite mineral assemblages and, therefore, enters the melt phase almost exclusively, at least under upper mantle conditions. Increasing Na and K, or both, results in solidus temperature depression.

1600

6]

98

Temperature, ˚C

1500 on

s bin

Ro

1400

se

d

an

et

Ku

al.

[1

iro sh

i [1

sh

ha

] aka 98 T

9

3]

99

[1

ro

Hi

1300

]

94

19

y[

wa

o oll

1200

nd

H

aa

r tk

Be

1100 0

1

2 Pressure, GPa

3

4

FIGURE 1.4 Pressure/temperature trajectories of various peridotite solidii in the absence of volatiles. Modified after Herzberg et al. (2000) with the sources of individual curves indicated on individual solidii.

Solidus temperature, ˚C

1520 1500 1480 1460 1440

1420 0.85

0.86

0.87 0.88 0.89 Mg/(Mg+Fe)

0.90

0.91

FIGURE 1.5 Solidus temperature of volatile-free peridotite as a function of their Mg/(Mg þ Fe). Modified after Hirschmann et al. (2000).

Solidus temperature, ˚C

1520 1500 1480 1460 1440 1420 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Na2O + K2O, wt%

FIGURE 1.6 Solidus temperature of volatile-free peridotite as a function of their total alkali content. Modified after Hirschmann et al. (2000).

6

Chapter 1 Melting in the Earth’s interior

1.3.2 Solidus phase assemblage and pressure The peridotite solidus mineral assemblage governs the composition of initial melts. This assemblage and, therefore, the melt composition on the peridotite solidus, is a function of pressure (see also Chapter 2 for discussion of melting and crystallization mineral assemblages). Up to pressures near 15 GPa, olivine, orthopyroxene, clinopyroxene, and one or more aluminous phases (plagioclase, spinel, and garnet) form the solidus mineral assemblage. At pressures below approximately 1 GPa, plagioclase is the principal aluminous phase and initial melt is similar to midocean ridge basalt (Yoder and Tilley, 1962; Presnall et al., 2002). For typical terrestrial peridotite, aluminous spinel is on the solidus from near 1 GPa to somewhere between 2 and 3 GPa above which pressure garnet becomes the aluminous phase on the solidus of volatile-free peridotite. Garnet and aluminous spinel can coexist over a pressure range up to as much as 1.5 GPa for the most Fe-rich peridotites (Bertka and Holloway, 1994; Walter, 1998; Grove et al., 2013). There is also a pressure range between about 1 and 1.5 GPa where spinel and plagioclase coexist. In this pressure range, plagioclase becomes increasingly anorthite-rich as pressure increases until the plagioclase endmember, anorthite, finally disappears via the melting reaction (Presnall et al., 2002): olivine þ anorthite ¼ orthopyroxene þ clinopyroxene þ spinel þ melt.

(1.2)

At pressures near 2 GPa, spinel begins to react out to form a garnet þ spinel peridotite mineral assemblage with spinel finally disappearing at pressures near 2.5 GPa for typical peridotite compositions such as illustrated in Fig. 1.7. The pressure range with only garnet on the solidus can sometimes be as wide as 10 GPa, which corresponds to the depth range w300 km in the upper mantle (Takahashi, 1986; Herzberg and Zhang, 1996). The garnet in this pressure range not only changes its Mg/ (Mg þ Fe) but also its Al/(Al þ Si) ratio because the concentration of the silicate perovskite component in garnet increases with increasing pressure (Irifune, 1994; Okamoto and Maruyama, 2004). 1900

field net

stab

ility

1700

el+

gar

1600

spin

Temperature, ˚C

1800

1500 1400

2

us

id

l So

garnet stability field

3

5 4 Pressure, GPa

6

FIGURE 1.7 Pressure and temperature ranges of spinel and garnet peridotite mineralogy on the peridotite solidus. Modified after Walter (1998).

1.3 Melting of peridotite

7

At pressures near 15 GPa, olivine on both the solidus and liquidus of peridotite compositions undergoes a transformation to denser b-(Mg, Fe)2SiO4 (Fei et al., 1992). This phase is transformed to g-(Mg,Fe)2SiO4 with a further pressure increase before silicate perovskite is stabilized at pressures near 20 GPa. Magnesiowu¨stite [(Mg, Fe)O] becomes the solidus phase at even higher pressures (Irifune, 1994; Herzberg and Zhang, 1996). The composition of the initial melt at these latter very high pressures (>20 GPa) is not well known. Most likely, this lack of information results from challenges associated with temperature-quenching of melt without crystallization of quench phases at these very high pressures. As noted earlier in the description of the results in Fig. 1.3, the pressure/temperature trajectory of the solidus curve shows a distinctive changes or kinks in slope as changes in solidus phase assemblages take place. These kinks reflect the volume change of melting as new mineral phases appear on the solidus.

1.3.3 Peridotite melting with volatiles The principles that describe congruent melting of any rock in the presence of H2O or any other volatile in the CeOeHeNeS system are illustrated in the isobaric, low-pressure schematic representation in Fig. 1.8. In this figure, the solidus temperature, f-d, is fixed regardless of the amount of H2O in the system unless all the H2O is bound in hydrated minerals such as chlorite phases, amphiboles, mica minerals, or epidote. The solidus terminates at d because there is a finite solubility of rock materials in the H2O fluid (see Chapter 6). The liquidus topology, on the other hand, depends on the amount of H2O c

c

Rock-saturated H2O fluid

urat -sat

Melt a

Va p

oro

us

H2O-saturated liquidus

iquid ed l

Rock+melt+H2O vapor

us

Temperature

H 2O

Melt+H2O vapor

ed

at s

du ui

liq

Rock +melt f

b

Solidus: Rock+H2O

d

Subsolidus: Rock+H2O vapor Rock

Composition

H2 O

FIGURE 1.8 Schematic representation of rock-H2O phase relations from temperatures above their vaporous to subsolidus conditions at low pressure (see text for detailed discussion).

8

Chapter 1 Melting in the Earth’s interior

present in the system. For any bulk composition between f and b, the initial melt is at b. This melt is saturated with H2O. By increasing temperature above the undersaturated liquidus, a-b, an H2Oundersaturated melt will form. As drawn in Fig. 1.8, it is assumed that the H2O solubility in the melt decreases with increasing temperature, a feature commonly observed in experiments (Holtz et al., 1995; see also Chapter 7 for discussion of H2O solubility behavior in magmatic liquids). This means that by increasing the temperature until the H2O-saturated liquidus, c-b, is reached, H2O will exsolve. It is even possible to reach a condition below the H2O-saturated liquidus where the melt will exsolve H2O and will also partially crystallize. A further increase will eventually reach the vaporous. Details on solubility of silicate (rock) in the vapor (or fluid) can be found in Chapter 6.

1.3.3.1 Peridotite-H2O Melting of peridotite in the presence of H2O at high pressure such as the deep crust, upper mantle, and beyond occurs at lower temperature than melting of peridotite in the absence of H2O (Fig. 1.9). When there is excess H2O over that which may be bound in hydrous minerals (amphibole, phlogopite, and chlorite, for example) or if temperatures and pressures are outside the stability field of hydrous phases in a peridotite-H2O system (Mysen and Boettcher, 1975a; Grove et al., 2006; Till et al., 2012), the isobaric hydrous solidus temperature is the same regardless of total H2O content. As is always the case for melting of rocks in the presence of H2O, its solidus temperature decreases from its coincidence with H2O-free melting at ambient pressure to minimum temperature at pressures

3.5 peridotite-H2 O solidii

{ A

C

D B

A B C D

}

Mysen and Boettcher (1975a)

(196

8)

3.0

et al. hiro te so

lidus

[Kus

2.0

ridoti

1.5

s pe

Pressure, GPa

2.5

Gro

ve

0.5

anhy drou

1.0 et a

l. (2

006 )

0 600

800

1000 Temperature, ˚C

1200

1400

FIGURE 1.9 Solidus pressure/temperature trajectories of different peridotite compositions in the presence of excess H2O. The individual curves are from peridotite with varying Mg/(Mg þ Fe) and total alkali content. Modified after Mysen and Boettcher (1975a) and Grove et al. (2006). Also shown in the solidus trajectory of volatile-free peridotite from Kushiro et al. (1968).

1.3 Melting of peridotite

9

in the 2e4 GPa range (Fig. 1.9). The coincidence at ambient pressure occurs because the H2O solubility in magma at ambient pressure is only a small fraction of wt% (see Chapter 7) and does, therefore, have no discernible effects on the solidus temperature. The exact pressure/temperature trajectory of the H2O-saturated solidus depends on the particular bulk composition of the peridotite. Mysen and Boettcher (1975a) found, for example, that depending of Mg/(Mg þ Fe) ratio and alkali content, the hydrous peridotite temperature can vary by as much as 150
C at pressures near 3 GPa (Fig. 1.9). The temperature/pressure trajectory of the hydrous peridotite differs significantly among various published experimental studies. At the minimum temperature between 2 and 4 GPa, solidus temperatures have been reported to be from 1000
C (Hirose and Kawamoto, 1995; Kawamoto and Holloway, 1997) to less than 800
C (Mysen and Boettcher, 1975a; Grove et al., 2006; Till et al., 2012). The reason for such a large variation in experimentally determined solidus temperatures is not clear. It is even further puzzling in light of the fact that for other rock types ranging from basalt/gabbro þ H2O to granite/rhyolite þ H2O, there is little disagreement between the published experimental data (see discussion of those experimental data below). A w200
C difference in reported solidus temperatures for hydrous peridotite is important as this affects the depth in the mantle where melting of hydrous peridotite may take place by perhaps 25 km depending on the geotherm. The mineral assemblages on the hydrous peridotite solidus in the continental lithosphere are the same as for anhydrous peridotite except that the pressures at which the transformation of plagioclase to spinel and spinel-to-garnet occurs on the H2O-saturated solidus is lower because the pressures and temperatures of the hydrous solidus is lower than for anhydrous peridotite and the spinel-to-garnet transformation as a positive dT/dP slope (see Fig. 1.9, for example). Garnet appears near and below 2 GPa, for example (Taylor and Green, 1988), whereas for anhydrous melting, garnet on the peridotite solidus appears above 2.5e3.0 GPa (Takahashi et al., 1993; Walter, 1998). The stability relations of hydrous phases in continental lithosphere are profoundly different from their stability relations in the peridotite wedge in subduction zones. This difference is governed by the release of hydrous fluids saturated in silicate components from the descending slab in subduction zones, whereas no such source of H2O and silicate components can be found in lithospheric mantle. Hydrous phases such as amphibole, mica, and chlorite on the hydrous peridotite solidus wedge in subduction zones can occur over a range of pressures and temperatures (Mysen and Boettcher, 1975a; Grove et al., 2006; Till et al., 2012). During melting of continental lithosphere, on the other hand, the near absence of H2O in the melting region results in lack of significant contribution of hydrous phases to the peridotite melting. It is generally agreed that at least to pressures near 2 GPa, the initial melt on the solidus of hydrous peridotite is quartz normative and resembles andesitic compositions (Kushiro, 1972; Grove et al., 2006). It is less well known how that melt composition may change at higher pressures. It seems reasonable to assume that the melt compositions may eventually take on an olivine normative character (Condamine et al., 2016).

1.3.3.2 Dehydration on the peridotite solidus Whenever the total H2O of hydrous peridotite is contained in hydrous phases, initial melting in limited pressure ranges could be controlled by the dehydration of the hydrous mineral(s). This may be the situation in the continental lithosphere where the H2O contents are on the order of hundreds of ppm (Jambon, 1994). This H2O likely is contained in a few hydrous phases and in nominally anhydrous phases. Among these hydrous phases, their detailed stability field depends on the peridotite

10

Chapter 1 Melting in the Earth’s interior

6

H O saturated solidus

5

by

3

us lid so

lidus

n io at dr hy de

o rite s chlo

Pressure, GPa

4

2

am

ph

ib

ol

e

so

lid

us

1

0 7 00

H

800

O sa so tura lidu ted s

900 1000 1100 Temperature. ˚C

1200

FIGURE 1.10 Example of solidus pressure/temperature trajectory with all H2O bound in hydrous phases (amphibole and chlorite) in their stability range on the solidus. Modified after Fig. 1.5: Solidus temperature of volatile-free peridotite as a function of their Mg/(Mg þ Fe) (Modified after Till et al. (2012).

composition. For the Hart and Zindler (1986) primitive peridotite used in the experiments by Till et al. (2012), the relationships between hydrous phase stability and dehydration melting are shown in Fig. 1.10. The Mg/(Mg þ Fe) of mantle peridotite is in the range 0.85e0.94 and total alkali concentrations ranging between, 0.1 and 0.9 wt%. A range in amphibole stability over about 75
C and 0.3e0.4 GPa temperature and pressure range is the result (Fig. 1.11). The alkali concentration, which is important for the amphibole stability (Allen et al., 1975), is uncertain in the peridotite wedge above descending plates in subduction zones as dehydration of the plate materials likely will release an aqueous fluid enriched in alkali metals (Mysen, 2002; Manning, 2004). Alkali metal concentration also is important in defining mica stability field as a K-rich phase such as phengite can be stable to pressures near 10 GPa, for example (Poli and Schmidt, 1998; Tro¨nnes, 2002). K-rich amphiboles have been reported stable to near 10 GPa at temperatures near the hydrous peridotite solidus (Sudo and Tatsumi, 1990; Tro¨nnes, 2002). Such amphiboles and micas may not be found in typical upper mantle, but can be stable in metasomatized peridotite wedge above subducting slabs. In the deeper mantle of subduction zones, the H2O content likely is so low that all H2O is bound in such hydrous phases. The peridotite solidus under this circumstances can then be governed by dehydration of these phases (Fig. 1.12).

1.3 Melting of peridotite

11

3.5 Green [1973]

3.0

a b c d

}

Mysen and Boettcher (1975a)

Pressure, GPa

2.5 b a

2.0

d c

1.5

1.0

0.5

800

1000 1200 Temperature, ˚C

1400

FIGURE 1.11 Pressure/temperature trajectories of amphibole dehydration solidi of peridotite with all H2O bound in amphibole when stable on the solidus. Modified after Green (1973) and Mysen and Boettcher (1975a).

16

6

ridotite

phlogopite

4 Na-amphibole

2

a deh pproxi m ydra tion ate soli dus

8

K-richterite

ted pe

10

H O-sa tura

Pressure, GPa

12

solidus

14

0 800

900

1000 1100 1200 1300 1400 1500 Temperature,˚C

FIGURE 1.12 Pressure/temperature trajectory of dehydration solidus of peridotite with K-richterite and phlogopite as dehydration phases. Modified after Tro¨nnes (2002). H2O-saturated solidus with extrapolation to high pressure in dashed lines from Mysen and Boettcher (1975a).

12

Chapter 1 Melting in the Earth’s interior

Another important variable in peridotite mantle is the oxygen fugacity. This will affect not only amphibole stability, but likely also pressure/temperature stability range of biotite (Ernst, 1968; Niida and Green, 1999; Fumagali and Poli, 2005). Unfortunately, less is known about the relationship between bulk composition and biotite stability than of the amphibole stability. We do know, however, the phlogopite stability tends to exceed that of amphibole (Fig. 1.12; see also Kushiro et al., 1967; Tro¨nnes, 2002; Frost, 2006; Condamine et al., 2016). However, in certain circumstances K-richterite stability can exceed that of phlogopite (Konzett et al., 1997; Konzett and Ulmer, 1999; Konzett and Fei, 2000; Tro¨nnes, 2002). Note that in Fig. 1.12, the stability ranges of dense, hydrous magnesian phases (DHMS) are not included (see Ulmer and Trommsdorf, 1995,1998). Some of these may indeed be stable to temperatures above the H2O-saturated solidus at pressures exceeding 25 GPa. It is important to note, however, that the stability field of some of these phases depend on their Mg/ (Mg þ Fe) (Konzett and Ulmer, 1999). Such phases may be found along the hydrous peridotite solidus at least to the bottom of the transition zone. The stability range of hydrous phases as a function of bulk composition, not to mention fluid composition and fluid abundance, is important for peridotite melting because with all H2O tied up in one or more hydrous phases, their pressure/temperature breakdown curves also define the solidus pressure and temperature conditions of peridotite hydrated in this manner. Those relations, in addition to the local geotherm, will then govern the pressure stability and, therefore, the depth of peridotite melting. For the situation illustrated in Fig. 1.12, melting in the presence of H2O will occur at pressures above about 14 GPa if all H2O were contained in K-richterite. However, for most mantle situations, the K-concentration of the peridotite is such that phlogopite would be the highest-pressure stable H2O-bearing phase on the hydrous mantle solidus. This corresponds to a depth of about 180 km. The relationship between this maximum pressure and the stability of DHMS will govern whether or not H2O might be transported to greater depth in the mantle.

1.3.3.3 Peridotite-CO2 melting Carbon dioxide is the dominant C-species in the mantle to depth of perhaps the bottom of the upper mantle (up to w15 GPa). At greater depths, the mantle appears sufficiently reducing (Wood et al., 1990; Frost and McCammon, 2008; Kaminsky et al., 2015) so that reduced carbon species are stable. Melting phase relations of the mantle under these conditions are, therefore, governed by carbon species different from CO2. This difference, in turn, results in changed melting phase relations (Litasov et al., 2014; see also further discussion of melting in a reduced mantle later in the chapter). Melting in a CO2-bearing mantle is distinctly dependent on depth of melting because the solidus has a pronounced kink at pressure/temperature conditions approximately those of the decarbonation reaction (Eggler, 1976, 1978); enstatite þ dolomite ¼ diopside þ forsterite þ CO2

(1.3)

This feature originally was noted (Eggler, 1978) from simple system experiments in the system CaOeMgOeSiO2eCO2 (Fig. 1.13) where the relationship between the solidus temperature depression and the univariant equilibrium (1.3) is illustrated. In this system, the melting temperature at pressures below about 2.5 GPa is so high that instead of diopside þ enstatite, pigeonite is stable. At higher pressure, the temperature of the peridotite-CO2 solidus decreases by nearly 400
C over a w0.5 GPa pressure interval (Fig. 1.13). In his groundbreaking study of the role of CO2 in upper mantle melting processes, Eggler (1976) also found, for example, that in the simple system model mantle,

1.3 Melting of peridotite

O Di+Dol+C En+Liq

Dol En+ O o+C F Di+ En+Liq Di+Fo +CO

2.0

1.5

Di: diopside Fo: forsterite En: enstatite Pig: pigeonite Dol: dolomite Liq: liquid CO : CO vapor

1000

1200

+CO Pig+L iq

2.5

Di+Fo

Pressure, GPa

3.0

Di+En Pig

3.5

13

1400

1600

Temperature, ˚C FIGURE 1.13 Pressure/temperature trajectory of the solidus in the system CaOeMgOeSiO2eCO2. Modified after Eggler (1978).

CaMgSi2O6 e Mg2SiO4 e SiO2, the pressure/temperature coordinates of the melt in equilibrium forterite þ enstatite shifts from near 3.5 GPa at 1800
C absent CO2 to near 1.7 GPa and 1650
C in the presence of CO2 (Fig. 1.14). The effect of CO2 on melting relationships in simple model mantle systems later was demonstrated also to operate in chemically more complex natural peridotite systems (Falloon and Green, 1989, Canil and Scarfe, 1990; Brey et al., 2008; Ghosh et al., 2009; see also Fig. 1.15). Several of those studies also extended the experiments to pressures near the bottom of the upper mantle (Canil and Scarfe, 1990; Ghosh et al., 2009). In these experimental studies, the nature and composition of the carbonate phase at the solidus also were monitored (Dasgupta et al., 2007) as well as the CO2 concentration in the melt at the solidus (Brey et al., 2008; Ghosh et al., 2014). From his experimental data in the model mantle system CaOeMgOeSiO2eCO2, Eggler (1978) observed that with increasing pressure, the carbonate phase changed from calcite to dolomite and finally magnesite. This is the same trend as reported by Dasgupta et al. (2007) from their experiments with natural peridotite compositions where, however, the absolute Ca/(Ca þ Mg) in the carbonate from natural peridotite þ CO2 is lower (Fig. 1.16). A linear fit to the experimental data from Dasgupta et al. (2007) yielded the relationship for the carbonate phase as a function of pressure: Ca=ðCa þ MgÞ ¼ 0:0258ðGPaÞ þ 0:5817:

(1.4)

1900

Temperature, ˚C

1800

Liq

Fo+

q

+Li En q i n+L

q

Li

E

Fo+

1700 O

+C

Liq

1600

Composition Di Fo {SiO ) Di: diopside Fo: forsterite En: enstatite Liq: liquid CO : CO vapor

CO

iq+

+L

Fo

CO

Liq+

En+

Fo+En+Liq+CO

1.5

2.0

2.5 Pressure, GPa

3.0

3.5

FIGURE 1.14 Phase relations in pressure/temperature space in the system CaOeMgOeSiO2 with and without CO2 near the invariant point, forsterite þ enstatite þ liquid þ vapor.

So

lidu

s

Modified after Eggler (1976).

3.5 ag

+M

Di

l

Do

+ En

2.5

1.5

1000

Solidus

us

ag +M O C o+ +F Di Di: diopside Fo: forsterite En: enstatite Mag: Magnesite Dol: dolomite CO : CO vapor En

lid

2.0

So

Pressure, GPa

3.0

1100 1200 Temperature, ˚C

1300

FIGURE 1.15 Pressure/temperature trajectory of the peridotite-CO2 solidus. Modified from Falloon and Green (1989).

Ca/(Ca+Mg) of carbonate (mole)

1.3 Melting of peridotite

15

0.60 Ca

O-

Mg

O-

Al

0.55

O

-S

iO

-C

O

0.50

pe

rid

oti

te-

CO

0.45

0.40 2

3

4 5 6 Pressure, GPa

7

8

FIGURE 1.16 Ca/(Ca þ Mg) of carbonate mineral in peridotite-CO2 and CaOeMgOeAl2O3eSiO2eCO2. Modified after Dasgupta et al. (2007).

1.3.3.4 Peridotite-C-O-H melting Fluid in the CeOeH system under oxidizing conditions are H2OeCO2. This redox regime extends to oxygen fugacity conditions near or slightly below that corresponding to the magnetite-wu¨stite oxygen buffer (MW). At lower oxygen fugacity conditions, the dominant C-bearing species in the CeOeH is CH4 (see discussion of these relationships in Chapter 8). Absent hydrogen, the carbon is stored as graphite to pressures near 200 km or diamond at greater depth (see also Kennedy and Kennedy, 1976; for data on the graphite-to-diamond transition). Under extremely reducing conditions, it has been suggested that carbon may substitute for oxygen in silicate polyhedra. This phenomenon has been reported in simple system silicate þ C and in crystalline solid solutions between metal nitride and metal carbonate (Renlund et al., 1991).

1.3.3.4.1 Peridotite: H2OeCO2 As noted above, under oxidizing conditions, H2O and CO2 are the two fluid species in the CeOeH system. These are the conditions in the uppermost 100e150 km in the modern Earth. At greater depth, the redox conditions are such that reduced carbon species may be stable (Stagno et al., 2013; Hammouda and Keshav, 2015). By adding CO2 to the peridotite-H2O environment, the solidus temperature increases in a systematic manner (Fig. 1.17; see also Mysen and Boettcher, 1975a). The transformation of spinel-togarnet peridotite at the solidus also increased as the CO2/H2O ratio increases because the temperature of intersection of the spinel-to-garnet transformation with the solidus increases with increasing CO2/ (CO þ H2O) ratio. In analyses of the solidus phase relations in peridotite-H2eCO2 (Eggler, 1976, 1978; Wylllie, 1977), it was demonstrated that at higher pressures, above the of the intersection of the reaction (1.3) with the vapor-saturated peridotiteeH2OeCO2 solidus, the initial melt remains carbonatitic to at least where the mol fraction in the vapor, CO2/(H2O þ CO2), reaches 0.25. This melt composition remained even though the temperatures of the solidus may change significantly (Wyllie, 1977).

16

Chapter 1 Melting in the Earth’s interior

4.0 0.25

0.50

1.0

3.5

0.75

H O/(H O+CO ) (molar)

ΔT(No Volatiles - H O/(H O+CO =0.25) site

ΔT(No Volatiles - H O/(H O+CO =0.5) ΔT(No Volatiles - H O/(H O+CO =0.75) ΔT(No Volatiles - H O/(H O+CO =1.0)

19 68 )

e agn e+m ite d i s m p olo dio e+d atit t s en

Ku sh iro

et al. ,

2.5

2.0

olid us (

t rne ga l e n i sp

tile -fre es

Pressure, GPa

3.0

Vo la

1.5

1.0

0.5

0 800

900

1600

1100 1200 1300 Temperature, ˚C

1400

1500

1600

FIGURE 1.17 Pressure/temperature trajectories of peridotteeH2OeCO2 solidii as a function of H2O/(H2O þ CO2) of the system. Modified from Mysen and Boettcher (1975a). The volatile-free solidus is from Kushiro et al. (1968).

Melting of an upper mantle with both CO2 and H2O depends significantly on whether the volatiles are contained completely in a crystalline phase such as amphibole, phlogopite, or carbonate, or whether there is excess volatiles over that which can be contained in crystalline phases (Eggler, 1978). With excess fluid, the composition of partial melt at 2e3 GPa total pressure varies continuously from basanite or nephelinite in an H2O-free environment and then changes gradually ending up as andesitic melt in a CO2-free environment (see also Mysen and Boettcher, 1975a, and the topological analysis of this situation by Eggler, 1978; see also Fig. 1.18A). However, with only a small amount of fluid such that all H2O is contained in amphibole (less than about 0.4 wt% fluid for a typical peridotite upper mantle), this amphibole is present in the solid assemblage over a CO2/(CO2þH2O)-range of 0e0.8. in this CO2/(CO2 þ H2O)-range, the melt composition, of melilitic composition, is invariant (Mysen and Boettcher, 1975b; Eggler, 1978). This fluid region was termed Zone of Invariant Composition (ZIVC) (Fig. 1.18B). Analogous analyses may be carried out with other hydrated phases such as, for example, phlogopite. In such cases, however, the pressures and melt compositions of the zone of invariant melting would be different.

1.3 Melting of peridotite

1300

1300 A

Temperature, ˚C

Temperature, ˚C

ol+ cpx+ +sp+ Vap

800 0.0 CO2

1200

ol+opx+cpx+ +sp+Liq+Vap

1100 opx+

900

B

ol+opx+ +sp+Liq+Vap

1200

1000

17

ol+opx+cpx+ +sp+amph+Liq+Vap

ol+opx+cpx+ +sp+amph+Vap

1100

ol+opx+cpx+ +sp+Liq+Vap ol+ opx+ cpx+ +sp+ Vap

900

0.2

0.4 06 mol fraction

0.8

1 .0 H2O

800 0.0 CO2

ol+opx+cpx+ +sp+amph+Liq ZIVC

ol+opx+cpx+ +sp+amph+Vap

1000

ol+opx+cpx+ +sp+amph+dol+Vap

ol+opx+cpx+ +sp+Liq

ol+opx+cpx+ +sp+amph+dol+Vap

0.2

0.4 06 mol fraction

0.8

1.0 H2O

FIGURE 1.18 Melting phase relations in the system CaOeMgOeAl2O3eSiO2eH2OeCO2 as a function of CO2/(CO2þH2O). (A) Phase relations with excess fluid. (B) Phase relations with all H2O bound in amphibole to create the Zone of Invariant Vapor Composition (ZIVC). Modified after Eggler (1978).

1.3.3.4.2 Peridotite-C-O-H under reducing conditions Experiments under reducing conditions involve equilibria between peridotite mineral assemblages and CH4-rich vapor (see also Chapter 8). The first attempt to determine melting of silicates in the presence of CH4 was that of Eggler and Baker (1982) where it was shown that CH4 reduced the melting temperature of diopside (CaMgSi2O6) by about 100
C at pressures near 2 GPa. Taylor and Green (1988) reported what appears to be the first experimental data on peridotiteeCH4eH2O melting at oxygen fugacity conditions defined by the tungsten-tungsten oxide buffer (which is about one log unit more oxidizing than the more commonly used iron-wu¨stite buffer). They reported a solidus temperature depression in the 1e3.5 GPa to be in the 100e150
C range (Fig. 1.19). The spinel-to-garnet transition occurs near 2 GPa on the solidus. The solidus mineral assemblage in the Taylor and Green (1988) study showed amphibole-bearing spinel lherzolite to maximum pressures of about 3 GPa and phlogopite-bearing garnet lherzolite at higher pressures. Amphibole was not stable on the solidus with the activity of H2O in aH2O, less than about 0.5. The maximum pressure of amphibole stability decreased as aH2O decreased. Litasov et al. (2014) extended the pressure range of peridotite-CH4 melting to about 20 GPa. They found that, compared with the volatile-free melting curve, CH4 depressed the peridotite solidus by between 100 and 400
C in this pressure range (Fig. 1.20). The solidus mineral assemblage from about 3 GPa to near 13 GPa is olivine þ orthopyroxene þ clinopyroxene þ garnet. At pressures below w3 GPa, garnet is replaced by spinel. From about 13 GPa to near 18 GPa, olivine on the solidus is replaced by wadsleyite (b-Mg2SiO4). At pressures above w18 GPa, wadsleyite is replaced by ringwoodite (g-Mg2SiO4). To the extent it was possible to determine the melt composition on the solidus, Litasov et al. (2014) reported it to be of basaltic composition.

7.0

Pressure, GPa

2.5 s

u

lid

so te

d

ri

3.0

lid

-O

-C

e

tit

o

oti

1.5

-H

et garn el in sp

so

us

2.0

aH O= 0.70 aH O =0. 3 5 aH O =0

otite

rid o

5.0

pe

Pressure, GPa

3.0

ti te

-H

O

perid

so li

du

3.5

0.85

-H O 2

B s

A

aH O=

4.0

1.5

rid

e

ee

pe

p

Vo

lat

ile

-fr

1.0

0.5 1000

1100 1200 Temperature, ˚C

1300

900

1000 1100 1200 Temperature, ˚C

FIGURE 1.19 Melting phase relations of peridotite-C-O-H under redox conditions at IWþ1. A. Comparison of the reduced peridotite-C-O-H solidus with the volatile-free and the peridotite-H2O solidus. B. Peridotite-C-O-H solidi as a function of the activity of H2O, aH2O. Modified after Taylor and Green (1988).

20 rw w

d+r

wad ol+wad ol

f = IW )

ΔT

er

-H

sol

ido tite

idu

10

so li

s(

du s

wa

pe

rid

5

ee p -fr Vo lat ile

otit

e-C -O

Pressure, GPa

15

Taylor and Green (1988)

0 1000

1200

1400 1600 1800 2000 Temperature, ˚C

2200

FIGURE 1.20 Melting phase relations of peridotite-C-O-H under redox conditions at IW oxygen buffer to pressures in the transition zone of the mantle. Note that this solidus does not show a change in dT/dP slope when the olivineto-wadsleyite and wadsleyite-to-ringwoodite univariant lines are crossed. This probably reflects lack of experimental precision when determining the solidus curve under these high-pressure conditions. Modified after Litasov et al. (2014).

1.3 Melting of peridotite

19

1.3.3.5 Magmatic processes in peridotite-C-O-H environments The dominant fluid in most tectonic settings of the upper mantle where peridotite melting occurs, likely is dominated by C-bearing volatiles (Zhang and Duan, 2009). The bulk C content of the silicate Earth is, however, only on the order of 200 ppm (Jambon, 1994). Low-degree partial melt at the depth of melt separation from its mantle residue, suggested to be at 30e50 km depth (Presnall et al., 2002), could then yield a tholeiitic to alkali basaltic magma with less than a few wt% CO2 (Brooker et al., 2001; Iacono-Marziano et al., 2012). Melting of a CO2-rich upper mantle, on the other hand, will result in alkali basalt (Mysen and Boettcher, 1975b). The exception to the statement above that CO2 tends to be the most abundant volatile in the melting region of the upper mantle can be found in island arcs. Here H2O concentrations in the mantle wedge can reach upwards of 1 wt% (Scambelluri and Philippot, 2001; Grove et al., 2002; Till et al., 2012). This H2O is stored in hydrous phases such as amphibole, mica, chlorite, and DHMS (Konzett and Ulmer, 1999; Fumagalli and Poli, 2005; Melekhova et al., 2015). Dehydration of these minerals with migration of this H2O into the overlying mantle wedge can result in H2O contents in the initial partial melts between 5 and 10 wt%. The composition of melt on the hydrous peridotite solidus to depths near 100 km is quartz normative and has been considered andesitic by many experimentalists (Kushiro, 1972; Mysen and Boettcher, 1975b; Grove et al., 2002, 2006). This conclusion would not be significantly affected by addition of some CO2 to the H2O fluid least at depth less than 100 km because the CO2 is retained in the solidus mineral assemblage as carbonate (Kerrick and Connolly, 2001; Poli et al., 2009). The CO2/ H2O ratio of the released fluid does, however, increase with additional depth so that melting beneath back arc regions would yield nepheline-normative magma (Mysen and Boettcher, 1995b; Eggler, 1978; Dasgupta et al., 2007). The oxygen fugacity (fO2) is a variable that can affect melting phase relations in the upper mantle significantly mostly because it affects the speciation of the CeOeH volatiles. The fO2 is, however, a function of depth in the mantle, as concluded, for example, by Frost and McCammon (2008). The fO2values in the uppermost 100þ km of the mantle are near those corresponding to the QFM oxygen buffer. These latter oxygen fugacity conditions are those under which midocean basalt last equilibrates with upper mantle mineral assemblages (Davis and Cottrell, 2018). As the pressure increases with a further increase of mantle depth, the oxygen fugacity decreases to about four orders of magnitude below QFM at 7 GPa (about 250 km depth) (Frost and McCammon, 2008; see also Fig. 1.21). Melting of peridotite-CO2 in a cratonic mantle begins at depths near 150 km (Sleep, 2009; see also Fig. 1.22). The initial melt at this depth would be carbonatitic under oxidizing conditions. However, if the conditions were sufficiently reducing so that the C will exist as CH4, melting along the continental platform geotherm will take place at slightly greater at depths, near 200 km (Fig. 1.22). These melting conditions yield a melt of basaltic composition (Falloon and Green, 1989). This contrasts with melt compositions under oxidizing conditions where the melt on the CO2 and CO2 þ H2O solidus is carbonatitic at this depth. Of course, any warmer geotherm will be consistent with melting in either peridotite-CO2 or peridotite-CH4 environments depending on whether the depth at which the geotherm and the peridotite solidus intersect. Moreover, if H2O is present, the solidus temperatures, whether with CO2eH2O or CH4eH2O, may decrease by as much as 200
C depending on C/H ratio (Mysen and Boettcher, 1975a; Taylor and Green, 1989). This will also result in melting at shallower depth and, therefore, possibly under more oxidizing conditions with the attending oxidation of the CeOeH fluid phase and consequent changes in solidus mineral assemblages and chemical composition of partial melts.

20

Chapter 1 Melting in the Earth’s interior

1

Log fO2 relative to QFM

0 -1 -2

-3 -4

-5

0

1

2

3 4 5 Pressure, GPa

6

7

FIGURE 1.21 Oxygen fugacities for a range of different peridotite samples from different depth (pressure) in the upper mantle. Modified after Frost and McCammon (2008).

0

1350˚C adiab

150

C iteidot per

200

depth, km

us solid

Pressure, GPa

at -CH otite perid

rm

rm

he ot

he

ot

ge

6

8

50

100

ge

on

4

rm

at

cr

tfo

la

lp

ta

en

in

nt

co

2

O dus soli

10

250

300 12 400

800 1200 Temperature, ˚C

1600

FIGURE 1.22 Pressure/temperature trajectories of solidii of peridotite-CH4 and peridotite-CO2. Modified after Sleep (2009).

1.4 Melting of basalt

21

1.4 Melting of basalt In this section, we will cover basalt sensu strictu as well gabbro, which is, of course, the intrusive form of basalt. In addition, basalt can be metamorphosed to eclogite in the deep continental crust and upper mantle. Eclogite melting will, therefore, also be discussed in this section. The mineral assemblage of eclogite is garnet þ clinophroxene  quartz  olivine, whereas at lower pressure in the crust, the mineral assemblage that will undergo initial melting is that of gabbro (plagioclase þ olivine þ pyroxene  quartz). With H2O, rocks of basaltic composition could be amphibolite with various amphiboles as the dominant solidus mineral. Basalt at or near the surface typically has olivine þ plagioclase as liquidus phases. Melting of basalt/gabbro takes place in the continental crust. In subduction zone settings, basalt melting (or its metamorphic equivalents, amphibolite and eclogite) occurs in upper portions of descending slabs. Melting of amphibolite occurs to depth near 75e100 km. Below this depth (equivalent to 2.5e3 GPa), amphibole (hornblende) breaks down and the rock is transformed to eclogite with or without hydrous minerals that are stable to higher pressures than amphibole (Ernst, 1968; Allen et al., 1975). The exact depth where this occurs is, however, significantly dependent on the amphibole composition and redox conditions. In this latter environment, the basaltic compositions often are those that were metamorphosed in the presence of recirculating ground water at high temperature when the basaltic magma was intruded or extruded near their original setting at midocean ridges (Poli and Schmidt, 2002).

1.4.1 Basalt/gabbro melting without volatiles At or near ambient pressure, basalt typically melts between about 1050
C and 1350
C. The primary control on the melting temperature is the Mg/(Mg þ Fe) of the rock (Yoder and Tilley, 1961; see also Fig. 1.23). Many more recent data could be added to the results summarized in Fig. 1.23. However, 1450 1400 1350

Temperature, ˚C

1300 1250 1200 1150 1100 1050 1000 950

0.1

0.2

0.3 Mg/(Mg+Fe)

0.4

0.5

0.6

FIGURE 1.23 Relationship between liquidus temperatures of basalt and their Mg/(Mg þ Fe). Modified after Tilley et al. (1964).

22

Chapter 1 Melting in the Earth’s interior

none of this would affect the general conclusion that links the bulk Mg/(Mg þ Fe) of basalts to their melting temperatures. The relationship illustrated in Fig. 1.23 is because the dominant minerals in basalt are olivine, orthopyroxene, and clinopyroxene, the melting temperatures of which are dominated by their Mg/ (Mg þ Fe) (Bowen and Schairer, 1935). For olivine, which is also the first phase to crystallize from most basaltic magmas upon cooling at crustal depths, there is a simple solid solution from the highesttemperature forsterite endmember melting near 1890
C to the lowest-temperature melting fayalite with a melting point near 1200
C (Bowen and Schairer, 1935). Of course, this endmember behavior is not directly applicable to the more complex basaltic magma where, for example, olivine is in a reaction relationship with orthopyroxene (Bowen and Anderson, 1914). Moreover, the plagioclase composition, which is the common second phase to crystallize from tholeiitic magma and the first to crystallize from high-alumina basalt magma, also is quite variable. The plagioclase crystallization temperature in basaltic composition environment can cover a wide range temperatures depending on the Na/ (Na þ Ca) (albite-anorthite solid solution of plagioclase) with melting temperatures from w1120
C for albite to w1550
C for anorthite (Tuttle and Bowen, 1950). The liquidus temperatures of pyroxenes can be more complex because of several possible reaction relations. However, this is not directly relevant to liquidus temperatures of basalt because at and near ambient pressure, pyroxenes do not crystallize on the liquidus. Pyroxene reaction relations will, however, affect the solidus conditions as well as high-pressure melting relations. Details of reaction relations such as those, as well as more complex relationships, will be discussed in more detail in Chapter 2. With increasing pressure, olivine as the solidus phase found in most basalts is replaced by clinopyroxene (cpx) over a rather narrow pressure interval (Fig. 1.24A). At pressure near 1 GPa there is a near-invariant point with olivine, orthopyroxene, clinopyroxene, and an aluminous phase (spinel or plagioclase) appearing with a few degrees of the liquidus (see Bender et al., 1978; Fuji and Bougalt, 1983; Draper et al., 1992; see also Fig. 1.24A). Clinopyroxene is the liquidus phase at high pressure followed by garnet. Interestingly, it is high-alumina basalt melts that crytallize the four-phase assemblage, olivine þ orthopyroxene þ clinopyroxene þ spinel and/or plagioclas in the 1e1.2 GPa pressure range (Yoder and Tilley, 1962; Fujii and Kushiro, 1977; Johnson, 1986), whereas what is referred to as “primitive tholeiite” does not show this near-invariant behavior at any pressure (Fig. 1.24B). On the other hand, Yoder and Tilley (1962) in their seminal paper on phase relations of basalt did indeed observe near-invariant crystallization of the mineral assemblage olivine þ orthopyroxene þ clinoppyroxee þ spinel þ plagioclase on the tholeiite liquidus at 1.1  0.05. GPa. These differences leave open the question as to whether merely crystallizing a fourphase peridotite-type mineral assemblage means that this rock was in fact equilibrated with upper mantle peridotite under relevant pressure and temperature conditions. In addition, there is also the question whether volatiles such as CO2 and/or H2O might play a role. Finally, we need to remember that the variations in chemical compositions are not great and the different small variations may be within experimental error.

1.4.2 Basalt/gabbro-H2O The high water content of igneous rocks found at or near convergent plate boundary commonly is ascribed to partial melting of descending oceanic sediments, of hydrated oceanic basalt (amphibolite), and/or to H2O-triggered partial melting of the overlying peridotite wedge (Mysen and Boettcher, 1975b; Poli and Schmidt, 2002; Mitchell and Grove, 2015). In general, the great majority of subducted and altered crust samples has H2O/CO2 > 1 (Fig. 1.25). The depth of devolatilization and the

B

iq

1.6 ol+

cp

1100

us

Liq

0.8

0.4

liquidu

s

liquidus

0.5

x+

liquid

s

cpx ol+Liq

1.0

1.2

ol+Liq

px+

1.5

Pressure, GPa

cpx pla

g+

Liq

2.0

+o

Pressure, GPa

2.5

23

cpx+L

A

liquid u

3.0

+L iq ga+ cpx +L iq liq uid ga us +Liq

1.4 Melting of basalt

1200 1300 1400 Temperature, ˚C

1500

1100

1200 1300 Temperature, ˚C

FIGURE 1.24 Examples of phase relations near the liquidus of “primitive basalt” (A) High-alumina basalt. (B) Olivine tholeiite. (A) Modified after Fujii and Bougault (1983), (B) See Gust and Perfit (1987).

concentration of the volatiles together with their H2O/CO2 abundance ratio reflect the pressuretemperature stability fields of the individual hydrous and carbonated minerals (Kerrick and Connolly, 2001; Poli and Schmidt, 2002). In general, the H2O-rich hydrous minerals epidote, chlorite, and amphibole tend to dehydrate at lesser depth than that at which decarbonation of carbonate minerals takes place (Poli and Schmidt, 2002). In fact, even in a water-rich CO2eH2O environment, CO2 is retained in the crystalline carbonate phases such as calcite and dolomite while the released fluid is quite H2O-enriched (Eggler, 1978; Yaxley and Green, 1994; Molina and Poli, 2000). The melting phase relations to depth near 100 km may, therefore, be illustrated by phase relations in hydrous basalt (Fig. 1.26). Those phase relations are the basis for the H2O budget in subduction zones as a function of depth (Fig. 1.27). Melting of subducting oceanic crust involves melting of hydrous basalt, overlying altered sediments, and perhaps a combination of the two. Melting of basalt with excess H2O results in a solidus temperature depression of 600
Ce700
C compared with the basalt solidus in the absence of volatiles [For an early review of experimental data, Lambert and Wyllie (1972, 1974) and summary in Fig. 1.28]. More recent data than those of Lambert and Wyllie (1972) and the papers references therein do not show significant differences from their original data source for hydrous melting of basalt.

24

Chapter 1 Melting in the Earth’s interior

Bulk H2O content, wt%

14 12 10 1:1

O 2=

8

:C HO 2

6 4 2 0 0

10 20 Bulk CO2 content, wt%

30

FIGURE 1.25 Estimate H2O and CO2 abundance of crustal materials being subducted in various subduction zones. Modified after Poli and Schmidt (2002). See this reference for original sources of data.

zo is

1

ite

ou

t

2 out

100

ba

ph

sa

en

gi

lt-

4

H

O

law

5

te

ou

t

so

lid

us

ut

eo

nit

so

6

su

200

r rc

pe

Pressure, GPa

2

itic

7 coesite stishovit e

9

laws

al?

8

t

e ou

onit

phengite K-hollandite

10 600

depth, km

3

amphibole out zoisite

700

800 900 Temperature, ˚C

300 1000

1100

FIGURE 1.26 Pressure/temperature trajectory of melting relations of Mid-Ocean Ridge Basalt-H2O and stability hydrous phases near the solidus. Modified after Poli and Schmidt (2002). See this reference for original sources of data.

1.4 Melting of basalt

25

50

Depth to slab, km

initial chlorite dehydration initial amphibole dehydration

100 initial lawsonite dehydration

150

initial phengite dehydration

200 0

5 10 15 H2O in fluid, % (100%=6.2 wt% H2O)

20

FIGURE 1.27 H2O content available for release from subducting slab beginning with 6.2 wt% H2O of the slab at the onset of subduction.

3.0

2.0

ua

gr os

s

lidu

so

0 0

O -H

lt sa

ba

0.5

rtz ua +q e it te de albi ja

la r an +ky or an th ite ite + q

1.0

rtz

1.5

su

Pressure, GPa

2.5

anhydrous ba

basalt-H O so lidus

3.5

salt solidus

Modified from Poli and Schmidt (2002).

500

1000 Temperature, ˚C

1500

FIGURE 1.28 Pressure/temperature trajectory of basalt with excess H2O and under anhydrous conditions. Modified after Hill and Boettcher (1970).

26

Chapter 1 Melting in the Earth’s interior

A striking feature of the data in Fig. 1.28, and also in other published experimental data, is the observation that the magnitude of the temperature depression of basalt þ H2O is near 50% greater than for peridotite þ H2O. In fact, in general the extent of the temperature depression of the solidus caused by H2O at any pressure increases as the magma becomes more (SiO2þAl2O3)-rich. An interesting feature of the H2O-saturated solidus curve of basalt (as well those of more felsic rocks, see below) is the kink of the solidus near 1.5 GPa. This pressure/temperature regime corresponds to the pressure/temperature conditions near the albite ¼ jadeite þ quartz and anorthite ¼ grossular þ kyanite þ quartz phase transition at the solidus of basalt þ H2O. These transformations change the volume of melting and, therefore, is the explanation for the change in slope (kink) in the melting curve. This feature often is not seen under anhydrous melting conditions because the intersection of the solidus will take place between 3.5 and 4 GPa, and there are few, if any, experimentally determined melting curves of volatile-free magmatic liquids in this temperature/ pressure regime. In the review and summary of basalt and sediment melting with excess H2O (Fig. 1.29), the hydrous minerals zoisite and phengite occur together on the solidus of both basalt and oceanic sediments (greywacke). For both minerals, these are stable to slightly higher temperatures in the greywacke composition. Amphibole is the mafic hydrous phase on the basalt solidus whereas biotite takes on this role in greywacke compositions. The mica, phengite, is the hydrous phase with the widest pressure/ temperature stability field in both basalt and greywacke compositions. It breaks down to K-hollandite þ H2O at pressures between 8 and 10 GPa and is stable to slightly higher pressures in the basalt composition compared with greywacke composition (see also Vielzeuf and Schmidt, 2001).

1.4.2.1 Dehydration melting on the basalt solidus The principles that were described above for the breakdown of hydrous phases to form the peridotite solidus also apply to the breakdown of hydrous phases to form the basalt solidus. In all such situations where all H2O is contained in hydrous phases, whenever the stability field of the hydrous phase exceeds that of the hydrous solidus, the temperature/pressure trajectory of the breakdown of the hydrous phase defines the solidus. For example, Blatter et al. (2013) reported experimental results with hornblende as that solidus-defining phase for a basalt from Mount Ranier basalt composition from about 0.1 GPa to more than 1 GPa. Somewhat similar experimental data were reported by Beard and Lofgren (1991) reporting also that high-Al granodiorite melts are formed on the solidus as amphibole melts out. Several experimental studies show an amphibole (hornblende) to be the solidus phase of basalt compositions to pressures as high as 2e2.5 GPa with the upper pressure breakdown followed closely by stabilization of garnet (Hill and Boettcher, 1970; Allen et al., 1972; Rapp and Watson, 1995). It must also be kept in mind, however, that amphibole and other iron-rich mineral stability fields can be significantly dependent of the redox conditions during melting and crystallization (Allen et al., 1972; Ernst, 1968; Ernst and Liu, 1998). In principle, the presence of amphibole is the governing factor of hydrous melting of basalt looks like the example in Fig. 1.30 (Stern et al., 1975). It is to be remembered, though, that the exact range of the amphibole stability field also varies somewhat with H2O content (see, for example, Rushmer, 1991). Qualitatively, there are similar variations in phlogopite stability as a function of H2O content. However, the experimental data for micas are more limited, so there is a less precise understanding of phlogopite melting under H2O-undersaturated conditions.

1.4 Melting of basalt

27

black: MORB grey: greywacke

10

8

law

nit

nit

eo

eo

ut

ut K-hollan dite phengite

vite stisho ite s e o c

7 6 5

gr

ut

2

ole ou t

ite o

zoisite out

amphib

biot

3

zoisite out

4

ey

wa

Pressure, GPa

so

so

K-hollan dite phengite

law son ck ite o ba e-H ut sa 2O ph ltl a en s wso H2 ol git nite O idu e out so s ou lid t us ph en git eo ut

9

law

1 600

700

800 900 1000 Temperature, ˚C

1100

FIGURE 1.29 Pressure/temperature trajectories of the solidus of basalt (MORB)-H2O and greywacke-H2O (grayed curve) together with phase relations of relevant hydrous phases near their respective solidii. Phase relations of MORB-H2O in black lines and greywacke-H2O in grayed lines. Modified after Poli and Schmidt (2002).

1.4.2.2 Basaltic magma and redox conditions Basaltic magma can be quite iron-rich with an average iron concentration between 9 and 11 wt% (see Earthchem.org). This high iron content makes the basaltic magma properties sensitive to redox conditions during initial melting as well as during ascent and final crystallization (Cottrell and Kelley, 2011; Gaillard et al., 2015; O’Neill et al., 2018). In order to characterize the role of oxygen fugacity, it is necessary to calibrate the relationship between redox ratio of iron oxides, magma composition, and oxygen fugacity. Such calibrations were reported by Kennedy (1948) and Fudali (1965) and more recently by Kilinc et al. (1983), Mysen (1987), and Kress and Carmichael (1988). Pressure is also a factor because the partial molar volume of

28

Chapter 1 Melting in the Earth’s interior

sH ces : Ex dus

Solidus temperature difference

Soli

Pressure, GPa

2

1

0 400

600

800

1000

Solidus: amphibole breakdown

O

3

1200

1400

Temperature, ˚C FIGURE 1.30 Pressure/temperature of the solidus of basalt with all H2O bound in amphibole. Modified after Stern et al. (1975).

FeO is less than that of FeO1.5 (Lange and Carmichael, 1989). The pressure variable was incorporated in the formulation proposed by Kress and Carmichael (1991). More details of these relationships are discussed in Chapter 5. The redox relations of iron in magmatic liquids not only have been used to deduce fO2 conditions, it has also been employed to describe relationships between melting and crystallization phase relations and fO2 (Tuthill and Sato, 1970; Botcharnikov et al., 2008; Moussallem et al., 2019). Tuthill and Sato (1970), in what appears to be among the first experimental study of this kind, examined the liquidus relations of simulated lunar basalt melt and found that at oxygen fugacity conditions higher than approximately that of the magnetite-wu¨stite oxygen buffer (MW), the liquidus stability fields of ferropseudobrookite and ferropseudobrookite þ olivine were affected. In a more recent experimental study with what was presumed to be parental Skaergaard magma (Brooks and Nielsen, 1978) at 200 MPa water pressure, Botcharnikov et al. (2008) noted that the stability relations of iron oxides and amphibole were affected by fO2.

1.4.3 Basalt/gabbro-CO2 Experiments in basalteCO2 systems have been conducted at more than 2 GPa at which pressure the basalt is converted to a carbonated eclogite assemblage (Yaxley and Green, 1994; Hammouda, 2003; Dasgupta et al., 2004; see also Fig. 1.31). The melting curves in such systems exhibit a large temperature decrease in the 4e6 GPa range resembling the topology of the pressure/temperature trajectory of peridotite-CO2 (Fig. 1.15). There is some difference in the pressure where this occurs between the results by Hammouda (2003) and Dasgupta et al. (2004), but overall the published topologies of the melting curves resemble one another.

1.4 Melting of basalt

29

10 9 O2

e-C

8

s:

du oli

it log

ec

s

Pressure, GPa

7 6 5

u+mag ga+cpx+r lm+dol ga+cpx+i

4 sol idu

3

s: e clo gite

2

-CO

1 900

1000

1100 Temperature, ˚C

1200

1300

FIGURE 1.31 Pressure/temperature of the solidus of basalteCO2. Data from Yaxley and Green (1994), Hammouda (2003), and Dasgupta et al. (2004).

Carbonate is the solidus phase together with the garnet þ clinopyroxene eclogite mineral assemblage. The melt on the solidus is carbonatitic with an increased Mg/(Mg þ Ca) as pressure is increased just as for the peridotite-CO2 system discussed earlier.

1.4.4 Basalt with multicomponent fluid In the CeOeH system, most igneous activity involving basalt takes place under conditions sufficiently oxidizing for the volatiles to be H2OeCO2 (Molina and Poli, 2000; Poli et al., 2009). However, experimental results from melting of basalteH2OeCO2 systems are not common and only a few examples have been published (Hill and Boettcher, 1970; Holloway and Burnham, 1972; Pichavant et al., 2009; see also Fig. 1.32). This scarcity of experimental data is surprising in light of the fact that H2O and CO2 commonly occur together in basaltic magma. In the experimental study of K-rich basalt from Stromboli, Italy, by Pichavant et al. (2009) with melt coexisting with CO2-rich H2O þ CO2 fluid, olivine and clinopyroxene were liquidus phases at

30

Chapter 1 Melting in the Earth’s interior

3.0

am

ph

2.5

ibo

le

ou

t:

ba

sa

H

OCO

am

ph

ibo

le

1.5

ou

t:

so

lt-

s:

O

2O lt-H

sa 2

asalt

CO

us: b -H2O

0.5

0 500

H2

ba

solid

1.0

ba

sa

u lid

Pressure, GPa

lt-

2.0

600

700

800

900

1000

1100

Temperature, ˚C

FIGURE 1.32 Pressure/temperature of the solidus of basalteH2OeCO2 compared with basalt-H2O. Also shown are the stability fields of amphibole in the same environments. The pressure/temperature trajectories of the upper stability of amphibole in these two environments would be the approximate solidus trajectory if all H2O was bound in the amphibole. Modified after Hill and Boettcher (1970).

100 MPa. At higher pressure, clinopyroxene was the sole liquidus phase. This comparatively low-pressure appearance of clinopyroxene on the liquidus differs from the phase relations of volatilefree basalt where clinopyroxene does not appear on the liquidus until about 1 GPa (Bartels et al., 1991; Draper et al., 1992). Halogens are another group of elements that can affect melting and crystallization activity. Halogens in this role are found primarily in island arc environments (Lukkari and Holtz, 2007; Filiberto and Treiman, 2009; Condamine et al., 2016). In this environment, halogens and H2O occur together (Skjerlie and Johnston, 1993; Filiberto et al., 2012). There is, however, also evidence for halogens during melting and crystallization in other portions of the Earth’s upper mantle (Schilling et al., 1980; Brey et al., 2008; Kawamoto et al., 2013). In fact, it has been suggested that liquid immiscibility in metasomatized lithosphere resulted in fluoride melts (Klemme, 2004). Significant fluorine contents in mantle-derived magma also have been reported (Signorelli et al., 1999). Fluorine and chlorine are the two halogens most commonly examined in experimental studies of basalt melting and crystallization (Holloway et al., 1975; Luth, 1988; Filiberto and Treiman, 2009;

1.4 Melting of basalt

31

Filiberto et al., 2012). In experiments with excess fluid, both fluorine and chlorine affect melting and crystallization relations (Wyllie and Tuttle, 1964; Van Groos and Wyllie, 1967; Luth, 1988; Filiberto et al., 2012). For example, a basalt from Gustav Crater (Mars) was examined experimentally with 0.7% Cl added (Fig. 1.33A). The liquidus temperature is depressed by 50
C and the pressure/temperature coordinates of the saturation of olivine þ orthopyroxene is shifted by 0.4 GPa and 50
C. Addition of fluorine to the hydrous basalt system conceptually resembles that of chlorine except the shifts in pressure and temperature coordinates are greater (Fig. 1.33B; see also Filiberto et al., 2012).

1.5

volatile-free basalt phase relations basalt-H O phase relations Cl-basalt phase relations

2.0

A liq uid us

2.0

B

1.5

pigeonite+liquid

0.5

liq

uid

us

olivine+liquid

olivine+liquid

s

olivine+ pigeonite+liquid

1.0

idu

olivine+ pigeonite+liquid

liqu

1.0

Pressure, GPa

Pressure, GPa

pigeonite+liquid

volatile-free basalt phase relations F-basalt phase relations

liq

uid

us

0.5

0

0 1250

1300 1350 Temperature, ˚C

1400

1200

1250

1300 1350 Temperature, ˚C

1400

C

SiO

wt %

Quartz

Alkali feldspar NaAlSi O

KAlSi O

FIGURE 1.33 Effect of halogens in liquidus phase relations of basalt-H2O and in the system NaAlSi3O8eKAlSi3O8eH2O. (A) Effect of adding chlorine to basalt-H2O. (B) Effect of adding fluorine to basalt-H2O. (C) Effect of fluorine on the relative stabilities of feldspar and quartz on the liquidus with fluorine added to the system NaAlSi3O8eKAlSi3O8eH2O. Modified after (A) Filiberto and Treiman, 2009, (B) Filiberto et al., 2012, and (C) Manning (1981).

32

Chapter 1 Melting in the Earth’s interior

By adding HF to SiO2eKAlSi3O8eNaAlSi3O8eH2O at high pressure, the solidus temperature is depressed significantly and the quartz stability volume on the liquidus is expanded significantly compared with the situation without HF (Wyllie and Tuttle, 1964; Manning, 1981, Fig. 1.33C). In an experimental study of the effects of Cl and F on melting temperature depressions in hydrous systems, the difference between the temperature depression caused by F and Cl increases with increasing F and Cl concentration (Wyllie and Tuttle, 1964). There are also different effects of fluorine and chlorine on liquidus phase relations. Wyllie and Tuttle (1964) determined, for example, that the liquidus volume of quartz in the NaAlSi3O8eH2OeHF system is considerably larger than in the equivalent NaAlSi3O8eH2OeHCl system. The effects of halogens on the phase relations are, however, considerably complex and also depend on the silicate composition (Luth, 1988). This complexity reflects complex solubility mechanisms of F and Cl in silicate melts (see Chapter 8). In a comparison of H, F, and Cl on a molar basis, Filiberto et al. (2012) found that the effects on liquidus temperature increased in the order, H < Cl < F. In situations where all fluorine, chlorine, or H2O are contained in crystalline phases, the effects on solidus temperatures will increase in a similar manner. A few experimental studies have been carried out on the influence of Cl and F on melting behavior of relevant hydroxylated minerals such as amphibole and phlogopite (Holloway et al., 1975; Condamine et al., 2016). Under conditions where all H2O and F are dissolved in crystalline phases, for basalt-type systems, these phases are phlogopite and pargasite (amphibole). For both minerals, substitution of F for OH expands their stability field (Fig. 1.34).

l ph

og

op

ite

am ph

F/(F+O)

0.08

ibo

le

0.10

0.06 0.04 0.02 950

1000 1050 1100 1150 1200

Temperature, ˚C FIGURE 1.34 Effect of F/(F þ O) on upper temperature stability of amphibole and phlogopite. Modified after Condamine et al. (2016).

1.5 Melting of andesite

33

1.5 Melting of andesite In this section, we will address the solidus and liquidus behavior under the heading of “andesite.” As was done for basalt, under this heading we also incorporate intrusive equivalents (tonalite) as well as dacite (diorite). Ocean floor sediments and their metamorphic equivalents descending together with underlying mafic rocks in subduction zones will also be included in this section because overall their bulk compositions do not differ greatly from andesite composition. Andesitic magma is dominating in subduction zone settings. This magma characteristically is quite H2O-rich with water concentrations typically in the 4e10 wt% range (Proteau et al., 1999; Grove et al., 2003; Blatter et al., 2017). Essentially all published information on andesite melting have, therefore, been carried out in the presence of H2O. Exception to this is the fractional crystallization modeling of basalt to yield andesite by Osborn (1959) and dry melting of eclogite mineral assemblages (Green and Ringwood, 1968). Experiments have been conducted with excess H2O over that which can dissolve in the magma (Stern et al., 1975; Carroll and Wyllie, 1990; Alonso-Perez et al., 2009). Significant efforts also have been on H2O-undersaturated melting conditions (no free vapor phase) (Eggler and Burnham, 1973; Patino Douce and Beard, 1995; Hermann and Green, 2001). Given the importance of hydrous minerals such as mica minerals and amphibole, major experimental efforts have been devoted to melting of andesite under conditions where all H2O was bound in these hydrous phases and, therefore, where dehydration of such phases can coincide with the melting temperature of the andesite (Allen et al., 1972; Eggler, 1974; Vielzeuf and Holloway, 1998). Finally, given the importance of iron-rich minerals, the role of oxygen fugacity during melting and crystallization has been a frequent focus in the experimental literature (Allen et al., 1972; Eggler and Burnham, 1973).

1.5.1 AndesiteeH2O All experiments on andesite melting with excess H2O broadly show the same solidus features (Eggler and Burnham, 1973; Lambert and Wyllie, 1974; Stern et al., 1975; Tatsumi, 1982). The amount of H2O is irrelevant provided that there is sufficient H2O to saturate potential hydrous minerals, as discussed later in the chapter. The melting curve of andesite þ excess H2O resembles that of basalt þ excess H2O (Fig. 1.35). The minimum on the melting curve coincides with the transformation of solidus mineral assemblage below w1.5 GPa being plagioclase þ quartz þ biotie þ hornblende þ H2O fluid to the denser mineral assemblage, quartz þ hornblende þ clinopyroxeene þ garnet þ kyanite þ H2O fluid. That volume change causes the dT/dP slope changing from negative below w1.5 GPa to positive at higher pressures. The hydrous phases, biotite and hornblende, coexist on the solidus to about 1.7e2.5 GPa, with hornblende being the only phase in the higher pressure range (Fig. 1.35). In typical andesite þ H2O environments, there is a w0.5 GPa pressure range of coexisting hornblende and garnet before hornblende disappears, typically between 2 and 3 GPa (Stern et al., 1975; Hermann and Spandler, 2008). The exact pressures where this transformation occurs varies with Mg/(Mg þ Fe) and alkali/alkaline earth abundance ratio. Increasing Mg/(Mg þ Fe) tends to expand the hornblende stability to higher pressures (Patino Douce and Beard, 1996). The other major hydrous solidus phase, biotite, disappears at slightly lower pressures than the incoming of solidus garnet under excess H2O conditions (Fig. 1.35).

34

Chapter 1 Melting in the Earth’s interior

hornb

2.0

lende

bas

esi

alt l

and

)

dus

s

us

lid

s

so

du

idu

e

oli

iqu

sit

lt s

iqui

te l

sa

de

an

ba

)

ndesite

1.0

ndesite

out (a

out (a

biotite

Pressure, GPa

3.0

400

600

800 1000 Temperature, ˚C

1200

FIGURE 1.35 Comparison of pressure/temperature trajectory of solidus and liquidus andesite-H2O and basalt-H2O. Modified after Lambert and Wyllie (1974) and Stern et al. (1975).

The liquidus of andesite magma with excess H2O typically is at about 300
C higher temperature than the solidus temperature (Lambert and Wyllie, 1974; Stern et al., 1975; see also Fig. 1.35). Moreover, the temperature difference between hydrous and volatile-free melting is significantly smaller than the difference between the anhydrous and H2O-bearing basalt. The low-pressure plagioclase þ pyroxene mineral assemblage in andesite magma is replaced by hornblende at pressures near 1 GPa, often followed by clinopyroxene at slightly higher pressures, and then garnet(þkyanite) at even higher pressures (Lambert and Wyllie, 1974; Proteau et al., 1999). Magnetite can also be a liquidus phase below 1 GPa under oxidizing conditions (Martel et al., 1999). In certain silicate-rich andesites (perhaps dacite?), orthopyroxene is the sole liquidus phase at low pressure (Blatter and Carmichael, 2001).

1.5.2 Andesite melting and H2O activity As also noted above, as long as the concentration of H2O in a rock exceeds that which can be contained in hydrous minerals, the solidus temperature at any pressure is not dependent on the H2O concentration. However, the liquidus temperature and the liquidus mineralogy is dependent on the H2O concentration (Eggler and Burnham, 1973; Carroll and Wyllie, 1990; Blatter et al., 2017). In this case, pressure is also an important variable because the solubility of H2O in the magma depends on pressure (see Chapter 7). Notably, at low H2O contents, plagioclase or clinopyroxene, depending on bulk composition, tend to be the singular liquidus mineral to H2O contents in the five to seven wt% range, followed by hornblende at higher H2O concentrations (Eggler and Burnham, 1973; Blatter et al., 2017; see also Fig. 1.36). There

Temperature, ˚C

1.5 Melting of andesite

35

400 MPa

1100 1000 900 800

Temperature, ˚C

0

3 6 Total H2O content, wt%

9

900 MPa

1100 1000

clin opy

rox e

900

ne+

liq u id

800

0

3 6 Total H2O content, wt%

9

FIGURE 1.36 Effect of H2O abundance and pressure on the relative stabilities of plagioclase and orthopyroxene on the liquidus of dacite from Mount St. Helens. Modified after Blatter et al. (2017).

can also be a very narrow H2O concentration range at lower crustal pressures (w0.7 GPa) where dacite magma can be multiply saturated in plagioclase þ pyroxene þ hornblande þ titanomagnetite (Blatter et al., 2017). With water concentration insufficient to oversaturate the system, available H2O will be tied up in hydrous phases. In the andesite compositional environment, these phases are hornblende, zoisite, biotite, and phengite (Proteau et al., 1999; Hermann and Green, 2001; Patino Douce, 2005; AlonsoPerez et al., 2009). Oxygen fugacity also plays a role (Eggler and Burnham, 1973; Patino Douce and Beard, 1996). Hornblende is the solidus phase during dehydration melting of hornblende in andesitic compositions in the pressure range between about 0.2 and 0.3 and about 2.5 GPa (See compilation by Patino Douce and Beard, 1995; and also Fig. 1.37). Above this pressure, to about 3.5 GPa, zoisite is the liquidus phase, followed by phengite at higher pressure.

36

Chapter 1 Melting in the Earth’s interior

ngi

so te out lid us

4.0

phe

3.5

le ou t

so

0.5

600

us

le o ut

solid

hibo

1.0

amp

exc lite+

1.5

0

hibo

ess

2.0

amp

s

zo oli d ou isit us t e t ou te s i u is zo lid

s H O solid u

2.5

tona

Pressure, GPa

3.0

800 1000 Temperature, ˚C

1200

FIGURE 1.37 Pressure/temperature trajectories hydration melting of hydrous phases (amphibole, zoisite, and phengite) in andesite-H2O with all H2O bound in the hydrous phases. Modified from Patino Douce and Beard (1995).

Zoisite has not been seen as a liquidus phase in more mafic compositions than that summarized in Fig. 1.37. Phengite is not a liquidus phase for basaltic andesite and more mafic composition. Instead, hornblende is replaced by garnet at about 2.5 GPa (Allen et al., 1972).

1.5.3 Melting of sediment The bulk chemical composition of oceanic sediment near the top of the descending slab in subduction zones typically is CO2-rich greywacke and pelite (Montel and Vielzeuf, 1997; Paoli et al., 2009). The greywacke transforms to hornblende and biotite gneiss before it undergoes melting (Pickering and Johnston, 1998; Hermann and Spandler, 2008; Schmidt et al., 2004). The solidus of subducted sediment (pelite and greywacke) was determined by Herman and Spandler (2008) in the 2.5e4.5 GPa pressure range. As can be seen in Fig. 1.38, those authors placed the solidus of sediment near that of andesite þ H2O. Interestingly, the solidus mineral assemblage was stated to be amphibole þ quartz þ phengite below about 2.5e2.7 GPa. At higher pressure, the solidus phase assemblage was reported to be garnet þ clinopyroxene þ coesite þ phengite. At pressures above about 3 GPa, Hermann (2002) and Hermann and Spandler (2008) referred to the presence of a “nonquenchable fluid.” This very likely is a region of supercritical fluid (see also Fig. 1.8). It is not clear how this material could be distinguished from quenched hydrous melt. In fact, Schmidt et al. (2004) in their experimental study of a greywacke and pelite starting compositions could

1.5 Melting of andesite

e-

H

O

so

lid

us

3

sit

2 an

de

Pressure, GPa

sup

ercr

tica

l

4

37

pelite s

solidu

1

600

700

800

900

1000

Temperature, ˚C FIGURE 1.38 Compariosn of pressure/temperature trajectories of andesite-H2O and greywacke-H2O. The dashed line is likely the temperature regime above the critical endpoint in these systems wherein there is complete miscibility between melt and fluid (see Chapter 7 for more discussion of this phenomenon). Modified from Hermann and Spandler (2008).

not detect melting at pressure above about 5.5 GPa. In this environment, hydrous melt cannot be distinguished from silicate-saturated aqueous fluid. Although the compositions used in Fig. 1.38 are not exactly those employed in experiments examining the pressure/temperature coordinates of the melt þ vapor field, from experiments with more mafic compositions (Kessel et al., 2005), it would seem very likely that the solvus for the systems under discussion here would be at lower pressures and temperatures than basalt þ H2O. The estimation results from the fact that the solubility of silicate components in fluid coexisting with pelite is greater than in fluid in equilibrium with a basalt composition, for example (see also Chapter 6).

1.5.4 The role of oxygen fugacity Oxygen fugacity (fO2) can be an important factor governing igneous rock evolution in island arcs. This is so because with iron oxides as liquidus phase during fractional crystallization of basalt, melt of andesitic composition can become the result (Osborn, 1959; Osborn and Arculus, 1975). The stability

38

Chapter 1 Melting in the Earth’s interior

-3

plag: plagioclase opx: orthopyroxene qtz: quartz mag: magnetite gnt: garnet

900˚C

tz

+q ag pl t g+ gn

-7 a

.4

-11

opx+plag

.55

=0 Mg Fe + Mg

qtz g+ ma opx z qt g+ la tz +p nt g+q g g a pla m g+ t a n g m gnt+qtz

-9

M Mg g+ Fe = 0

log fO 2 (MPa)

m

-13

-15 0

0.8 1.2 0.4 Pressure, GPa

1.6

FIGURE 1.39 Phase relations near the solidus of andesite as a function of oxygen fugacity (fO2) and Mg/(Mg þ Fe). Modified after Patino Douce and Beard (1996).

relations of Fe-rich silicate minerals also can be affected by oxygen fugacirty (Ernst, 1968; Allen et al., 1972; Eggler and Burnham, 1973; Patino Douce and Beard, 1996). Eggler and Burnham (1973) in their experimental study of Mt. Hood andesite, concluded that silicate mineral stability is not sensitive to fO2 until the oxygen fugacity conditions near those defined by the magnetitie-hematite oxygen buffer are reached, which are at least a couple of magnitude higher than that defined by the NNO oxygen buffer. Eggler and Burnham (1973) suggested that such conditions are unrealistic. However, more recent considerations by Carmichael and Ghiorso (1990) seem to imply that such oxygen fugacity conditions indeed can be encountered in subduction zone environments. Iron oxides such as ilmenite and magnetite are more sensitive to fO2 at ambient pressure with ilmenite as a liquidus phase at fO2 conditions above those corresponding to the quartz-magnetitefayalite (QFM) oxygen buffer (Eggler and Burnham, 1973). Patino Doce and Beard (1996) concluded, from their experiments to about 1.5 GPa pressure, that the garnet stability on the solidus was sensitive to both its Mg/(Mg þ Fe) and oxygen fugacity (Fig. 1.39). The dP/dfO2 slope describing breakdown reaction for garnet garnet þ O2 ¼ magnetite þ plagioclase þ quartz;

(1.5)

is positive. Furthermore, reaction (1.5) occurs at higher fO2 conditions the higher the Mg/(Mg þ Fe) of the garnet. In other words, at fixed fO2, the breakdown of garnet occurs at higher pressure the higher the pyrope content of the garnet.

1.6 Rhyolite melting Under this heading, as for andesite and basalt, both the extrusive and intrusive variants will be discussed. In fact, under the heading “rhyolite melting” most experimental data have focused on the

1.6 Rhyolite melting

39

intrusive variant, granite. Moreover, we will include compositionally associated rock types such as rhyodacite and granodiorite. It appears that all experiments with felsic rocks such as rhyolite or granite have been conducted in the presence of H2O. The lack of experimental data conducted without volatiles probably reflects the very low diffusivity of components in such magma composition making attainment of equilibrium extremely difficult on a laboratory time scale. For example, NaAlSi3O8 melt, with diffusivity similar to typical meta-aluminous granite, does not crystallize on a laboratory time scale. In the presence of H2O, magma fluidity and diffusion increases by many orders of magnitude (see Chapter 9). In contrast to andesite and basalt magma discussed above, rhyolitic (or granitic) magma cannot be formed by direct melting of mantle peridotite (Stern and Wyllie, 1981). The origin of rhyolitic magma may be either by very extensive crystal fractionation (>90%) from an original basaltic magma (Yoder, 1973) or by partial melting of basalt or sedimentary rocks typically with several wt% H2O (Montel and Vielzeuf, 1997; Schmidt et al., 2004). Granite may be subdivided into peraluminous, meta-aluminous and peralkaline. This division is based on whether there is excess Al3þover alkali metals þ alkaline earths, equal proportion of Al3þ to alkali metals þ akaline earths, or an excess of alkali metals þ alkaline earths over Al3þ. It has been suggested that peraluminous granitic magma is formed by partial melting of sediment (or, more accurately, gneiss) with several wt% H2O (Montel and Vielzeuf, 1997; Scaillet et al., 2016), whereas meta-aluminous and peralkaline magma was formed by fractional crystallization or partial melting of precursor igneous rocks such as andesite and basalt (Martel et al., 1999; Scaillet et al., 2016). The H2O concentration in the latter cases typically was less, perhaps less than 1.5% H2O. Whether or not the magmas thus formed are H2O-saturated depends both on the source rock of melting or fractional crystallization and depth of formation. However, any amount of H2O not bound in water-bearing minerals at given pressure will result in rocks melting at the same temperature at given pressure. The mineral assemblage at both the solidus and liquidus will depend on the amount of H2O present (Bogaerts et al., 2006). The assemblage may also vary with oxygen fugacity (Berndt et al., 2005).

1.6.1 Rhyolite-H2O Melting of rhyolitic (or granitic) composition with excess H2O results in solidus curves resembling those of less silica-rich rocks such as discussed in previous sections (Wyllie and Tuttle, 1959; Boettcher and Wyllie, 1968; Piwinskii, 1968; Stern et al., 1975; see also Fig. 1.40). The temperatures generally increasing in the order granite < tonalite < gabbro at pressures above about 0.5 GPa (Fig. 1.40).

1.6.2 H2O-undersaturated rhyolite/granite melting The liquidus temperature of the rhyolite/granite often is reported to increase systematically with decreasing H2O content of the melt. It has also been suggested that the solidus temperature decreases with increasing H2O content (Holtz and Johannes, 1991; Dall’Agnol et al., 1999; Bogaerts et al., 2006; Almeev et al., 2012). It is not clear, however, how this is possible unless all H2O is contained in one or more hydrous phases and the solidus temperature is defined by the dehydration of such phases. The original sources do not mention this, so it may be that the experiments did not reach equilibrium when it is reported that decreasing solidus temperature with increasing H2O content.

40

Chapter 1 Melting in the Earth’s interior

e-H O solidu

s

4

tonalite-H O solidus

granit

basalt-H O solidus

2

olid -H O s

granite

Pressure, GPa

3

1

tonalite-H O solidus

us

basalt-H O solidus

0 400

600

800

1000

Temperature, ˚C FIGURE 1.40 Comparison of pressure/temperature trajectories of granite, tonalite, and basalt with excess H2O. Modified after Stern et al. (1975).

The experimental results reported by Huang and Wyllie (1973) are among the few where the solidus temperature was reported to be independent of H2O content at constant pressure (Fig. 1.41A). The experimental data by Holtz and Johannes (1991) also could be made consistent with constant solidus temperature (Fig. 1.41B). 1400

[Holtz

ui

du

liquidus crystals + liquid

800

]

s

750

B

, 1991 annes

liquid + Vapor

liq

1000

Temperature, ˚C

liquid

h and Jo

Temperature, ˚C

1200

alternative solidus

s solidu

800

A

700

crystals + liquid + Vapor solidus

600

300 MPa

1.5 GPa

0

10

20 30 H2O content, wt%

40

50

650 0

1

2 3 4 5 H2O content, wt%

6

7

FIGURE 1.41 Solidus and liquidus phase relations of granite-H2O from Huang and Wyllie (1973) (A) and Holtz and Johannes (1991) (B). See text for discussion of Fig. 1.41B. Diagrams modified after Huang and Wyllie (1973) and Holtz and Johannes (1991).

1.6 Rhyolite melting

41

e+ id nit qu eo +li pig gite au

Temperature, ˚C

1050

1000

950

au

git

liqu idu s e+ liqu id

900 0

0.5

1.0 1.5 H2O content, wt%

2.0

2.5

FIGURE 1.42 Liquidus phase relations in granite-H2O as a function of H2O content. Modified after Klimm et al. (2008).

The solidus mineral assemblage from experimental determination depends on the bulk chemical composition of the starting material. The main solidus phases at pressures below about 0.5 GPa typically are quartz þ plagioclase þ orthoclase (Holtz and Johannes, 1991; Lukkari and Holtz, 2007). Pigeonite can appear near 0.2 GPa under H2O-undersaturated conditions (Almeev et al., 2012). With granodiorite starting materials, biotite and amphibole appear in the same pressure and temperature rage (Bogaerts et al., 2006). However, the liquidus mineral phase varies significantly with bulk composition of the magma. In muscovite granite, an Al2SiO5 polymorph can be liquidus phase. The exact polymorph depends on pressure and temperature (Johannes et al., 1971). The liquidus pressure/temperature path is significantly dependent on H2O content in the magma under H2O-undersaturated conditions (Almeev et al., 2012; Scaillet et al., 2016). Augite, possibly together with an iron oxide, are liquidus phases in the experiments shown in Fig. 1.42. The presence or absence of oxide phases is significantly dependent on oxygen fugacity (Klimm et al., 2008). In peraluminous granite magma, biotite is a liquidus phase at least in the 0.2e0.5 GPa pressure range under oxidizing conditions (Scaillet et al., 1995; Clemens and Birch, 2012). Feldspars dominate the liquidus of meta-aluminous and peralkaline granite magma (Clements et al., 1986; Klimm et al., 2008). Quartz becomes the liquidus phase in many peralkaline granite magma (Scaillet and Macdonald, 2001, 2006).

1.6.3 The role of oxygen fugacity Variations in oxygen fugacity primarily effect the type and abundance of iron oxide coupled with changes in ferromagnesian mineral stability (Dall’Agnol et al., 1999; Bogaerts et al., 2006). Dall’Agnol et al. (1999) found, for example, that by changing the fO2 from 2.5 orders of magnitude above the NNO buffer to 1.5 order of magnitude below, the oxide liquidus mineral(s) changed from ilmenite þ magnetite to magnetite only. The relative stability of clinopyroxene and hornblende also changed from clinopyroxene at high fO2 to hornblende at low fO2.

42

Chapter 1 Melting in the Earth’s interior

1.7 Concluding remarks Magma is the dominant mass transport agent in the Earth and likely also terrestrial planets. Following formation of the magma ocean during the Earth’s early history, which is not a subject of this discussion, primary magma was and is formed by partial melting of peridotite mantle. The melting temperature of a volatile-free peridotite mantle ranges from about 1350
C near the interface with the bottom of a continental crust to near 2000
C at the top of the transition zone. The partial melt formed at the solidus of peridotite in this pressure range is, broadly speaking, basaltic. At greater depth, there are discontinuities in the pressure/temperature slope of the solidus resulting from phase transitions such as olivine to spinel and pyroxene to perovskite. The composition of the initial melt in this greater pressure range is not well known. Addition of volatiles such as H2O or CO2 to the melting regime of peridotite can have major impact on the pressure/temperature trajectory of the solidus. The peridotite-H2O solidus decreases to between 800 and 900
C at 1e2 GPa pressure followed by a gradual temperature increase at greater pressure (depth). The melt in this initial pressure range is andesitic and gradually becomes increasingly mafic with increasing depth. There is a maximum pressure near 5e6 GPa beyond which there is complete miscibility between H2O and peridotite melt. The peridotite-CO2 solidus can be profoundly different from that of volatile-free peridotite. At pressures less than w2.5 GPa, CO2 only has a minor impact on melting temperature, and the melt is alkali basaltic. However, at greater pressures, the solidus temperature decreases very rapidly by as much as about 400
C. The solidus magma under these pressure conditions is carbonatitic. Derivative magmas are those formed upon melting or crystallization of primary magma. Melting of basalt and its intrusive equivalent, gabbro, under volatile-free conditions takes place at temperatures about 200e250
C lower than melting of peridotite. The exact melting temperature is a systematic function of its Mg/(Mg þ Fe). The pressure/temperature slope of the basalt solidus resembles that of peridotite. The solidus melt is more silica-rich than the basalt source, but its exact composition is significantly dependent on the redox conditions. The basalt-H2O solidus temperature reaches a minimum at pressures near 1.5 GPa with temperature values near 600
C. This temperature is about 500
C lower than the basalt solidus without volatiles. At higher pressures, the solidus temperature decreases by about 50
C/GPa. The solidus melt at these pressures is a silica-rich andesite. Rhyolite and its intrusive equivalent, granite, has been studied experimentally only in the presence of H2O. The granite-H2O melting curve is within 50
C that of hydrous andesite and hydrous basalt. The mass transport capacity of magma depends on magma viscosity and magma density. These variables vary greatly with magma composition and volatile type and content and will be discussed in greater detail in Chapter 9. Here we merely note that regardless of volatile content, transport capacity of magma increases in the order rhyolite < andesite < basalt. Magma density and compressibility increases in the same order.

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Martel, C., Pichavant, M., Holtz, F., Scaillet, B., Bourdier, J.L., Traineau, H., 1999. Effects of f O 2 and H2O on andesite phase relations between 2 and 4 kbar. J. Geophys. Res. Solid Earth 104 (12), 29453e29470. Melekhova, E., Blundy, J.D., Robertson, R., Humphreys, M.C.S., 2015. Experimental evidence for polybaric differentiation of primitive arc basalt beneath St. Vincent. Lesser Antilles, J. Petrol. 56, 161e192. Michell, A.L.G., Grove, T.L., 2015. Melting the hydrous, sub-arc mantle; the origin of primitive andesites. Contrib. Mineral. Petrol. 171. https://doi.org/10.1007/s00410-015-1161-4. Molina, J.F., Poli, S., 2000. Carbonate stability and fluid composition in subducted oceanic crust: an experimental study on H2O-CO2-bearing basalts. Earth Planet. Sci. Lett. 176, 295e310. Montel, J.-M., Vielzeuf, D., 1997. Partial melting of metagreywackes, Part II. Compositions of minerals and melts. Contrib. Mineral. Petrol. 128, 176e196. Moussallam, Y., Edmonds, M., Scaillet, B., Peters, N., Gennaro, E., Sides, I., Oppenheimer, C., 2019. The impact of degassing on the oxidation state of basaltic magmas: a case study of Klauea volcano. Earth Planet. Sci. Lett. 450, 317e325. Mysen, B.O., 1987. Magmatic silicate melts: relations between bulk composition, structure and properties. In: Mysen, B.O. (Ed.), Magmatic Processes: Physicochemical Principles. Elsevier, pp. 375e400. Mysen, B.O., 2002. Solubility of alkaline earth and alkali aluminosilicate components in aqueous fluids in the Earth’s upper mantle. Geochem. Cosmochim. Acta 66, 2421e2438. Mysen, B.O., Boettcher, A.L., 1975a. Melting of a hydrous mantle. I. Phase relations of natural peridotite at high pressures and temperatures with controlled activities of water, carbon dioxide and hydrogen. J. Petrol. 16, 520e548. Mysen, B.O., Boettcher, A.L., 1975b. Melting of a hydrous mantle. II. Geochemistry of crystals and liquids formed by anatexis of mantle peridotite at high pressures and high temperatures as a function of controlled activities of water, hydrogen and carbon dioxide. J. Petrol. 16, 549e590. Nerad, I., Miksokova, E., Kosa, L., Adamkovicikova, K., 2013. Premelting at fusion of titanite CaTiSiO5; a calorimetric study. Phys. Chem. Miner. 40. https://doi.org/10.1007/s00269-013-0597-1. Nesbitt, H.W., Bancrft, G.M., Henderson, G.S., Richet, P., O’Shaughnessy, C., 2017. Melting, crystallization, and the glass transition: toward a unified description for silicate phase transitions. Am. Mineral. 102, 412e420. Niida, K., Green, D.H., 1999. Stability and chemical composition of pargasitic amphibole in MORB pyrolite under upper mantle conditions. Contrib. Mineral. Petrol. 135, 18e40. O’Neill, H.S.C., Berry, A.J., Mallmann, G., 2018. The oxidation state of iron in mid-ocean ridge basaltic (MORB) glasses; implications for their petrogenesis and oxygen fugacities. Earth Planet. Sci. Lett. 504, 152e162. Okamoto, K., Maruyama, S., 2004. The eclogite-gametite transformation in the MORBþH2O system. Phys. Earth Planet. Int. 146, 283e296. Osborn, E.F., 1959. The role of oxygen pressure in the crystallization and differentiation of basaltic magma. Am. J. Sci. 257, 609e647. Osborn, E.F., Arculus, R.J., 1975. Phase relations in the system Mg2SiO4-iron oxide-CaAl2Si2O8-SiO2 at 10 kbar and their bearing on the origin of andesite. Carnegie Inst. Wash. Year Book 74, 504e507. Patino Douce, A.E., 2005. Vapor-absent melting of tonalite at 15e32 kbar. J. Petrol. 46, 275e290. Patino Douce, A.E., Beard, J.E., 1995. Dehydration-melting of biotite gneiss and quartz amphibolite from 3 to 15 kbar. J. Petrol. 36, 707e738. Patino Douce, A.E., Beard, J.S., 1996. Effects of P, fO2 and Mg/Fe ratio on dehydration-melting of model metagreywackes. J. Petrol. 37, 999e1024. Pichavant, M., Di Carlo, I., Le Gac, Y., Rotolo, S.G., Scaillet, B., 2009. Experimental constraints on the deep magma feeding system at Stromboli volcano, Italy. J. Petrol. 50, 601e624. Pickering, J.M., Johnston, A.D., 1998. Fluid-absent melting behavior of a two-mica metapelite: experimental constraints on the origin of black hills granite. J. Petrol. 39, 1787e1804.

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Piwinskii, A.J., 1968. Experimental studies of igneous rock series Central Nevada batholith California. J. Geol. 76, 548e570. https://doi.org/10.1086/627359. Poli, S., Franzolin, E., Fumagalli, P., Crottini, A., 2009. The transport of carbon and hydrogen in subducted oceanic crust: an experimental study to 5 GPa Earth Planet. Sci. Lett. 278, 350e360. Poli, S., Schmidt, M.W., 1998. The high-pressure stability of zoisite and phase relationships of zoisite-bearing assemblages. Contrib. Mineral. Petrol. 130, 162e175. Poli, S., Schmidt, M.W., 2002. Petrology of subducted slabs. Annu. Rev. Earth Planet. Sci. 30, 207e235. Presnall, D.C., Gudfinnsson, G.H., Walter, M.J., 2002. Generation of mid-ocean ridge basalts at pressures from 1 to 7 GPa. Geochem. Cosmochim. Acta 66, 2073e2090. Prouteau, G., Scaillet, B., Pichavant, M., Maury, m.R.C., 1999. Fluid-present melting of ocean crust in subduction zones. Geology 27, 1111e1114. Rapp, R.P., Watson, E.B., 1995. Dehydration melting of metabasalt at 8-32 kbar; implications for continental growth and crust-mantle recycling. J. Petrol. 36, 891e931. Renlund, G.M., Prochazka, S., Doremus, R.H., 1991. Silicon oxycarbide glasses. 2. Structure and properties. J. Mater. Res. 6, 2723e2734. Richet, P., Fiquet, G., 1991. High-temperature heat capacity and premelting of minerals in the system MgO-CaOAl2O3 -SiO2. J. Geophys. Res. B 96, 445e456. Richet, P., Ingrin, J., Mysen, B.O., Courtial, P., Gillet, P., 1994. Premelting effects in minerals; an experimental study. Earth Planet. Sci. Lett. 121, 589e600. Richet, P., Mysen, B.O., Andrault, D., 1996. Melting and premelting in alkali metasilicates: Raman spectroscopy and x-ray diffraction. Phys. Chem. Miner. 23, 157e172. Richet, P., Mysen, B.O., Ingrin, J., 1998. High-temperature X-ray diffraction and Raman spectroscopy of diopside and pseudowollastonite. Phys. Chem. Miner. 25, 401e414. Rushmer, T., 1991. Partial melting of two amphibolites: contrasting experimental results under fluid-absent conditions. Contrib. Mineral. Petrol. 107, 41e59. Ryan, M.P., 1987. Neutral buoyancy and the mechanical evolution of magmatic systems. In: Mysen)s, B.O. (Ed.), Magmatic Processes: Physicochemical Principle, Geol. Soc. Amer. Spec. Paper, vol. 1. Scaillet, B., Holtz, F., Pichavant, M., 2016. Experimental constraints on the formation of silicic magmas. Elements 12. Scaillet, B., Macdonald, R., 2001. Phase relations of peralkaline silicic magmas and petrogenetic implications. J. Petrol. 42, 825e845. Scaillet, B., Macdonald, R., 2006. Experimental constraints on pre-eruption conditions of pantelleritic magmas: evidence from the Eburru complex, Kenya Rift. Lithos 91, 95e108. Scaillet, B., Pichavant, M., Roux, J., 1995. Experimental crystallization of leucogranite magmas. J. Petrol. 36, 663e705. Scambelluri, M., Phillippot, P., 2001. Deep fluids in subduction zones. Lithos 55, 213e227. Schilling, J.G., Bergeron, M.B., Evans, R., 1980. Halogens in the mantle beneath the North Atlantic. In: Paper presented at Phil. Trans. R. Soc. Lond., 267m, pp. 148e178. Schmidt, M.W., Vielzeuf, D., Auzanneau, E., 2004. Melting and dissolution of subducting crust at high pressures: the key role of white mica. Earth Planet. Sci. Lett. 228, 65e84. Signorelli, S., Vaggelli, G., Romano, C., 1999. Pre-eruptive volatile (H2O, F, Cl and S) contents of phonolitic magmas feeding the 3550-year old Avellino eruption from Vesuvius, southern Italy. J. Volcanol. Geoth. Res. 93, 237e256. Skjerlie, K., Johnston, A.D., 1993. Fluid-absent melting behavior of an F-rich tonalitic gneiss at mid-crustal pressures; implications for the generation of anorogenic granites. J. Petrol. 34, 785e815. Sleep, N.H., 2009. Stagnant lid convection and carbonate metasomatism of the deep continental lithosphere. Geochem. Geophys. Geosyst. 10. https://doi.org/10.1029/2009GC002702.

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Stagno, V., Ojwang, D.O., McCammon, C.A., Frost, D.J., 2013. The oxidation state of the mantle and the extraction of carbon from Earth’s interior. Nature 493, 84e88. Stern, C.R., Huang, W.-L., Wyllie, P.J., 1975. Basalt-andesite-rhyolite-H2O: crystallization intervals with excess H2O and H2O-undersaturated liquidus surfaces to 35 kilobars, with implications for magma genesis. Earth Planet. Sci. Lett. 28, 189e196. Stern, C.R., Wyllie, P.J., 1981. Phase relationships of I-type granite with H2O to 35 kilobars; the Dinkey Lakes biotite-granite from the Sierra Nevada Batholith. J. Geophys. Res. 86, 10412e10422. https://doi.org/10.1029/ JB086iB11p10412. Sudo, A., Tatsumi, Y., 1990. Phlogopite and K-amphibole in the upper mantle: implications for magma genesis in subduction zones. Geophys. Res. Lett. 17, 29e32. Takahashi, E., 1986. Melting of a dry peridotite KLB-1 up to 14 GPa: implications on the origin of peridotitic upper mantle. J. Geophys. Res. 91, 9367e9382. Takahashi, E., Shimazaki, T., Tsuzaki, Y., Yoshida, H., 1993. Melting study of a peridotite KLB-1 to 6.5 GPa, and the origin of basaltic magmas. Phis. Trans. Roy. Soc. A. 342. https://doi.org/10.1098/rsta.1993.0008. Tatsumi, Y., 1982. Origin of high-magnesian andesites in the Setouchi volcanic belt, southwest Japan, II. Melting phase relations at high pressures. Earth Planet. Sci. Lett. 60, 305e317. Taylor, W.R., GReen, D.H., 1988. Measurement of reduced peridotite-C-O-H solidus and implications for redox melting of the mantle. Nature 332, 349e352. Taylor, W.R., Green, D.H., 1989. The role of reduced C-O-H fluids in mantle partial melting. In: Ross, J. (Ed.), Kimverlites and Related Rocks e Their Composition, Occurrence, Origin, and Emplacement. Blackwell Scientific Publishers, Carlton, pp. 592e602. Thieblot, L., Tequi, C., Richet, P., 1999. High-temperature heat capacity of grossular (Ca3Al2Si3O12), enstatite (MgSiO3), and titanite (CaTiSiO5). Am. Mineral. 84, 848e855. Till, C.B., Grove, T.L., Withers, A.C., 2012. The beginnings of hydrous mantle wedge melting. Contrib. Mineral. Petrol. 163, 669e688. Tilley, C.E., Yoder, H.S., Schairer, J.F., 1964. New relations on melting of basalt. Carnegie Inst. Wash. Year Book 63, 92e97. Trønnes, R., 2002. Stability range and decomposition of potassic richterite and phlogopite end members at 5e15 GPa. Contrib. Mineral. Petrol. 74, 129e148. Tuthill, R.S., Sato, M., 1970. Phase relations of a simulated lunar basalt as a function of oxygen fugacity and their bearing on the genesis of Apollo 11 basalts. Geochem. Cosmochim. Acta 34, 1293e1303. Tuttle, O.F., Bowen, N.L., 1950. High-temperature albite and contiguous feldspars. J. Geol. 58, 572e583. Ulmer, P., Trommsdorff, V., 1995. Serpentine stability to mantle depths and subduction-related magmatism. Science 268, 858e861. Ulmer, P., Trommsdorff, V., 1998. Phase relations of hydrous mantle subducting to 300 km. In: Fei, Y.-W., Bertka, C., Mysen, B.O. (Eds.), Mantle Petrology: Field Observations and High-Pressure Experimentation. Geochemical Society (in press). Ulmer, P., Sweeney, R.J., 2002. Generation and differentiation of group II kimberlites: constraints from a highpressure experimental study to 10 GPa. Geochem. Cosmochim. Acta 66, 2139e2153. Van Groos, K., Wyllie, P.J., 1967. Melting relationships in the system NaAlSi3O8-NaF-H2O to 4 kb pressure. J. Geol. 76, 50e70. Vielzeuf, D., Holloway, J.R., 1998. Experimental determination of the fluid-absent melting relations in the pelitic system. Contrib. Mineral. Petrol. 98, 257e276. Vielzeuf, D., Schmidt, M.W., 2001. Melting relations in hydrous systems revisited: application to metapelites, metagreywackes and metabasalts. Contrib. Mineral. Petrol. 141, 251e267. Walter, M.J., 1998. Melting of garnet peridotite and the origin of komatiite and depleted lithosphere. J. Petrol. 39, 29e60.

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Wood, B.J., Bryndzia, L.T., Johnson, K.E., 1990. Mantle oxidation state and its relationship to tectonic environment and fluid speciation. Science 248 (4953), 337e345. Wyllie, P.J., 1977. Peridotite-CO2-H2O, and carbonatitic liquids in the upper asthenosphere. Nature 266, 45e47. Wyllie, P.J., Tuttle, O.F., 1959. Effect of carbon dioxide on the melting of granite and feldspars. Amer. J. Sci. 257, 648e655. Wyllie, P.J., Tuttle, O.F., 1964. Experimental investigation of silicate systems containing two volatile components. III. The effects of SO3, P2O5, HCl, and Li2O in addition to H2O on the melting temperatures of albite and granite. Am. J. Sci. 262, 930e939. Yaxley, G.M., Green, D.H., Klapova, H., 1994. The refractory nature of carbonate during partial melting of eclogite: evidence from high pressure experiments and natural carbonate-bearing eclogites. Mineral. Mag. 58A, 996e997. Yoder, H.S., 1973. Contemporaneous basaltic and rhyolitic magmas. Amer. Mineral 58, 153e171. Yoder Jr., H.S., Tilley, C.E., 1961. Derivation of magma types from a primary magma. J. Geophys. Res. 66 (8), 2571. Yoder Jr., H.S., Tilley, C.E., 1962. Origin of basalt magmas; an experimental study of natural and synthetic rock systems. J. Petrol. 3 (Part 3), 342e532. Zhang, C., Duan, Z., 2009. A model for C-O-H fluid in the Earth’s mantle. Geochem. Cosmochim. Acta 73, 2089e2102. Zhang, J., Herzberg, C.T., 1994. Melting experiments on anhydrous peridotite KLB-1 from 5.0 to 22.5 GPa. J. Geophys. Res. 99, 17729. https://doi.org/10.1029/94JB01406.

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CHAPTER

Melting in the Earth’s interior: melting phase relations between the solidus and liquidus

2

2.1 Introduction Aggregation and transport of magmatic liquids at and from its source regions require sufficient extent of melting so that the magma forms a three-dimensionally interconnected mass.1 This magma is formed in the interval between the solidus and liquidus of a source rock. The bulk chemistry of this melt governs the composition of magmatic liquids whether during partial melting or fractional and equilibrium crystallization. During partial melting, the degree of melting and the equilibrium between melt and crystallizing mineral phases are major factors governing the magma composition and, therefore, also magma properties. Similarly, during equilibrium or fractional crystallization, the phase relations in the temperature interval between the solidus and liquidus governs the compositional and property evolution of magmatic liquids. In both environments, pressure, temperature, composition of source rock of melting, amount and proportions of volatiles, and redox conditions are the principal variables. These features are the topic of this chapter.

2.2 Melting interval of mantle peridotite without volatiles Characterization of melting behavior of peridotite and magma thus formed provides a basis for understanding formation of primary melts in the Earth’s interior. Crystallization or remelting of primary melts lead to evolved magmatic liquids such as broadly speaking andesite and rhyolite. Melting of peridotite in the Earth’s mantle has, therefore, been the subject of more experimental examination than the melting and crystallization behavior of more evolved magma. Experimental examination of the melting interval between the solidus and liquidus of peridotite under pressure conditions corresponding to the upper mantle reveals a systematic evolution of magma composition with increasing temperature (Mysen and Kushiro, 1977; Jaques and Green, 1980; Bertka and Holloway, 1994; Kushiro, 1996). For example, for a natural lherzolite composition, Jaques and Green (1980) found that during melting, the first phase to disappear with increasing temperature is the aluminous phase (plagioclase, spinel, or garnet). This is followed by disappearance of clinopyroxene (likely pigeonite), then orthopyroxene, and finally, olivine (Fig. 2.1). Plagioclase is the stable aluminous phase at pressures below about 1 GPa. In the 1e2.5 GPa pressure range, spinel is the aluminous phase, with garnet replacing spinel at pressures near 2.5 GPa. 1

Details of the physics and chemistry of this process are discussed in Chapter 11.

Mass Transport in Magmatic Systems. https://doi.org/10.1016/B978-0-12-821201-1.00004-3 Copyright © 2023 Elsevier Inc. All rights reserved.

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Chapter 2 Melting in the Earth’s interior

FIGURE 2.1 Pressure-temperature melting phase relations of Tinaquillo lherzolite. Redrawn from Jaques and Green (1980).

For more Fe-rich compositions such as, for example, the Fe-rich model martian mantle examined by Bertka and Holloway (1994), there is a wide pressure range from about 1.5 to more than 3 GPa where garnet and spinel coexist in the melting interval. At pressures above about 4 GPa, the stability field of garnet in the peridotite melting interval expands rapidly and approaches that of the liquidus as the pressure increases further (Walter, 1998; see also Fig. 2.2A). Garnet is the liquidus phase at pressures near and above 15 GPa (Herzberg and Zhang, 1966; Tro¨nnes and Frost, 2002). Garnet is replaced by magnesiowu¨stite [(Mg,Fe)O] and majorite

2.2 Melting interval of mantle peridotite without volatiles

55

FIGURE 2.2 Pressure-temperature melting phase relations of peridotite to very high pressure. (A) Melting relations in the 3e8 GPa pressure range, (B) Melting relations in the 0e30 GPa pressure range. (C) Melting relations in the 22e25 GPa pressure range. Abbreviations: Ca-Pv, Calcium perovskite; cpx, clinopyroxene; Mg-Pv, Magnesium perovskite; mw, magnesiowustite. (A) Redrawn from Walter (1998), (B) Herzberg and Zhang (1996), and (C) Tro¨nnes and Frost (2002).

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Chapter 2 Melting in the Earth’s interior

garnet [(Mg,Fe)4Si4O12] on the liquidus as pressures are increased further and finally by magnesiowu¨stite together with Mg-perovskite [(Mg,Fe)SiO3] at pressures corresponding to the transition to the lower mantle near 25 GPa (Fig. 2.2B). In this environment, olivine initially is replaced by the high-pressure form, wadsleyite, in the 15e18 GPa pressure range and by ringwoodite at even higher pressure (Fig. 2.2B). It should be noted, however, that in the study by Tro¨nnes and Frost (2002), which in many ways was similar to that of Herzberg and Zhang (1996), slightly different phase relations in the highest pressure range were noted (see Fig. 2.2C). They found, for example, that at pressures below about 25 GPa, the liquidus temperatures are lower than those reported in the Herzberg and Zhang (1996) study (see also Zhang and Herzberg, 1994). Moreover, Tro¨nnes and Frost (2002) reported the garnet þ melt stability field at the highest pressures less sensitive to pressure than Herzberg and Zhang (1996). Tro¨nnes and Frost (2002) also reported a much larger pressure-temperature stability field of magnesiowu¨stite þ garnet þ melt than reported by Herzberg and Zhang (1996).2 Notably, the temperature interval between the solidus and liquidus of peridotite mantle at the pressures above about 15 GPa is considerably narrower (150e200 C) compared with the lower pressures (>400 C). In fact, at 25 GPa, for example, 80% melting is obtained over less than 100 C from the solidus (Kuwahara et al., 2018).

2.2.1 Degree of melting Melting and crystallization behavior in the simple system Mg2SiO4(Fo)dCaMgSi2O6(Di)dSiO2 commonly has been employed to model the melting behavior of peridotite in the Earth’s upper mantle beginning with the original experimental results reported by Kushiro (1964). In this system, there is an invariant point, I, where forsterite, enstatite, and diopside coexist with melt at 2 GPa and 1650 C (Fig. 2.33). The proportion of melt that can be formed at this invariant point depends on the composition of the starting material. The melt composition is, of course, the same. For a composition representing typical peridotite modal abundances, about 20% melt will form at invariant point, I. The system becomes univariant once clinopyroxene melts out and the degree of melting is correlated with increasing temperature with forsterite and orthopyroxene coexisting with melt. At even higher temperature, orthopyroxene is exhausted and only olivine coexists with melt until the liquidus temperature finally is reached (Fig. 2.3). A number of experimental studies report degree of melting of natural peridotite as a function of temperature at various pressures (Mysen and Kushiro, 1977; Kushiro, 1996; Pickering-Witter and Johnston 2000; Bernard et al., 2018). In most such experimental studies, mass-balance calculations based on composition of coexisting phases were used to extract proportion of melt. The cumulative error in the melt fraction thus obtained reflects the errors in the analyses of each of the coexisting phases. Mysen and Kushiro (1977) employed a different method. They used a small amount of CO2 doped with radioactive 14C and then mapped the density of emitted b-particles by using photographic emulsion that were sensitive to the energy of the b-particles emitted from 14C. Essentially all of the

2 Note that Trønnes and Frost (2002) referred to the oxide phase as ferropericlase. However, for convenience, here I call it magnesiowustite. 3 The dashed lines in Fig. 2.3 represent the phase relations at ambient pressure and high temperature.

2.2 Melting interval of mantle peridotite without volatiles

57

FIGURE 2.3 2 GPa pressure liquidus phase relations in the model mantle system, Mg2SiO4 e SiO2 e CaMgSi2O6. Abbreviations: Di, diopside; En, enstatite; Fo, forsterite. Notice how the invariant point, I (Foss þ Enss þ Diss) at high pressure is on the forsterite side of the MgSiO3eCaMgSi2O6 join. This situation differs from the ambient-pressure liquidus phase relations where I is on the SiO2-excess side of the MgSiO3eCaMgSi2O6 join. Redrawn after Kushiro (1964).

CO2 would be dissolved in the melt because the carbon solubility in olivine, orthopyroxene, clinopyroxene, and spinel is less than 0.01% of that in the melt (Scheka et al., 2006). Therefore, the only source of error is in the counting statistics and b-particle density in the melt recorded in the photographic emulsions. Mysen and Kushiro (1977) chose the model composition Fo55En30Di154 as this is similar to the modal mineralogy of typical mantle peridotite, to illustrate the principles of how degree of melting evolves in a simple system (Fig. 2.4). At 2 GPa pressure, this composition yields about 20% melting at fixed temperature (w1650 C). At 20% melting, all diopside is exhausted and further melting is univariant with orthopyroxene, olivine and melt coexisting until about 45% melting is reached near 1700 C. At this point, orthopyroxene is exhausted and further temperature increase yields forsterite coexisting with melt.

4

Di, diopside (CaMgSi2O6); En, enstatite (MgSiO3); Fo, forsterite (Mg2SiO4). Subscripts in Fo55 En30Di15 indicate mol% of component.

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Chapter 2 Melting in the Earth’s interior

FIGURE 2.4 Degree of melting as a function of temperature at 2 GPa for composition forsterite55enstatite30dioside15 from the system Mg2SiO4 e SiO2 e CaMgSi2O6 (Fig. 2.3). Redrawn from Mysen and Kushiro (1977).

During melting of natural peridotite, compared with degree of melting versus temperature in simple systems such as shown in Fig. 2.4, there are differences in the degree of melting versus temperature mostly because in natural peridotite, there is Fe, Mg solid solutions. Moreover, there is an aluminous phase present (plagioclase, spinel, or garnet depending on pressure). These differences notwithstanding, relationships between degree of melting and temperature of natural systems resemble the simple system behavior (Fig. 2.5). This initial melting range in Fig. 2.5 generates melt of tholeiitic composition by the reaction (Mysen and Kushiro, 1977)5: cpx þ opx þ sp ¼ ol þ melt.

(2.1)

At higher temperature, following the exhaustion of spinel, the clinopyroxene is pigeonite (Ca-poor cpx), and the melting reaction is: cpx þ ol ¼ opx þ melt.

(2.2)

In the third and even higher-temperature melting interval, the melting reaction is: opx ¼ ol þ melt.

5

Abbreviations: cpx, clinopyroxene; ol, olivine; opx, orthopyroxene; sp, spinel.

(2.3)

FIGURE 2.5 Degree of melting and volatile-free, natural peridotite as a function of temperature. (A) Degree of melting of compositions 1611 at 2 GPa (Nixon and Boyd, 1973) and 66SAL-1 (Mysen and Boettcher, 1975a). (B) Degree of melting of composition, 1611, as a function of pressure. (C) Degree of melting of composition, 1611, as a function of temperature at 2 and 3.5 GPa. Compositions of 66SAL-1 and 1611, respectively, SiO2; 44.82 and 43.70 wt%, TiO2; 0.52 and 0.25 wt%, Al2O3; 8.21 and 2.75 wt%, O3; 2.07 and 1.38 wt%, FeO; 7.91 and, MnO; 0.19 and 0.13 wt%, MgO; 26.53 and 37.22 wt%,CaO; 8.12 and 3.26 wt%, Na2O; 0.89 and 0.33 wt%, K2O; 0.03 and 0.14 wt%. Analytical data from Nixon and Boyd (1973) (1611) and Mysen and Boettcher (1975a) (66SAL-1). (A) Redrawn after Mysen and Kushiro (1977), (B) Kushiro (1996), and (C) Mysen and Kushiro (1977).

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Kushiro (1996) noted a significant pressure effect on the relationship between degree of melting and temperature (Fig. 2.5B). The initial melting interval becomes narrower as pressure increases. The distinction between the first and second temperature interval also becomes less pronounced. In fact, at 3 GPa where garnet is the aluminous phase, Kushiro (1996) did not report a separation of the first and second melting interval. That observation differs, however, from that reported by Mysen and Kushiro (1977) who reported qualitatively similar topology of the degree of melting curves at 2 and 3.5 GPa (Fig. 2.5C). They inferred from the experimental data of Kushiro and Yoder (1974) that at the highest pressure(3.5 GPa) the melting reaction involves garnet6: cpx þ opx þ ga ¼ ol þ melt.

(2.4)

Although the experimental results from degree of melting versus temperature qualitatively resemble those from the simple system, Mg2SiO4(Fo)dCaMgSi2O6(Di)dSiO2 (Fig. 2.4), there are some important differences First, in the melting interval of natural peridotite, there is a narrow melting interval near the solidus where the temperature drops significantly. In fact, in the study of Mysen and Kushiro (1977), it was difficult to determine exactly where the solidus is located. Mysen and Kushiro (1977) suggested that this rapid temperature decrease might be because of all alkali metals in the peridotite source entered the melt. This suggestion was documented in a more recent experimental study by Hirschmann (2000), where initial melt shows very high alkali concentration. This alkali content decreased rapidly with increasing degree of melting (Fig. 2.6). The extent to which the solidus temperature is depressed because of alkali content of the initial partial melt is directly correlated with the alkali content of the starting material (see, for example, Hirose and Kushiro, 1993; Kushiro, 1996; Hirschmann, 2000). The width of the individual melting intervals also varies with peridotite bulk composition. This is illustrated with the two trends shown in Fig. 2.5. Composition 66SAL-1 is considerably more alkalirich, has higher Al2O3, and lower Mg/(Mg þ Fe) compared with composition 1611 (see Caption to Fig. 2.5). This difference results in lower melting temperatures and significantly wider melting intervals for peridotite 66SAL-1.

2.2.2 Melt composition in the melting interval The changes in melting phase relations in the melting intervals discussed in the previous section (Fig. 2.5) result in variations in melt composition (Mysen and Kushiro, 1977; Baker et al., 1995; Kushiro, 1996; Kogiso et al., 1998; Pickering-Witter and Johnston, 2000). In general, at any pressure, the concentration of the two dominant oxides, SiO2 and Al2O3, decrease with increasing degree of melting of peridotite, at least in the upper mantle pressure range to about 3 GPa (Fig. 2.7). In particular at low pressures such as 0.5 and 1 GPa, the initial melt has SiO2 contents that may reach more than 56e57 wt% with Al2O3 near 20 wt%. Such melts might be considered andesitic (Baker et al., 1995; Kushiro, 1996; Schwab and Johnston, 2001; see also Fig. 2.7). However, with increasing temperature in this pressure range, the SiO2 and Al2O3 concentrations decrease rapidly to values more like those of quartz tholeiite (Fig. 2.7).

6

ga, garnet.

2.2 Melting interval of mantle peridotite without volatiles

61

FIGURE 2.6 Total alkali concentration (Na2O þ K2O) in melt from peridotite composition as a function of degree of melting of various peridotite compositions at various pressures (see Hirschmann, 2000, for details). Redrawn after Hirschmann (2000).

Both SiO2 and Al2O3 abundance in partial melt from volatile-free peridotite decreases with increasing pressure. Notably, there may be a minimum SiO2 content between 10% and 15% melting in melts in the 2e3 GPa range (Kushiro, 1996). This minimum may coincide with the degree of melting where garnet disappears. Interestingly, the oxide compositions of the melts do not seem significantly dependent on the starting peridotite composition. This is as would be expected given that the melting phase relations are the same regardless of bulk composition of the peridotite. Schwab and Johnston (2001) did find, however, that the rate of melt production is a function of peridotite composition. Expressed in terms of normative components, it is clear that partial melts become increasingly olivine þ plagioclase normative with increasing pressure (Figs. 2.8 and 2.9). This behavior is consistent with partial melting at low pressure (3 GPa), komatiite and even kimberlite melts may have been formed by hydrous melting of peridotite (Mysen and Boettcher, 1975b; Mitchell and Grove, 2015). The bulk composition of the partial melts also depends significantly on total H2O content (Tenner et al., 2012; Kawamoto and Holloway, 1997; see also Figs. 2.17 and 2.18). Komatiitic magma may have been formed by peridotite-H2O partial melting near 3e4 GPa, whereas kimberlitic magma by this model would have been formed at higher pressure. Whether the high potassium content typical for kimberlite could be formed in this manner without addition of potassium to the source region is not clear. Melting of K-rich peridotite has been addressed experimentally in order to ascertain effects on melt composition of metasomatized hydrous upper mantle peridotite (Condamine and Medard, 2014; Condamine et al., 2016). Experiments have been carried out to 3 GPa where melting of phlogopitebearing peridotite gave rise to K-rich magma (Condamine et al., 2016): phlogopite þ clinopyroxene þ garnet ¼ olivine þ orthopyroxene þ melt

(2.6)

At 3 GPa, the magma composition evolved from foiditic to trachybasaltic with increasing degree of melting (Condamine et al., 2016; see Fig. 2.19). It is notable that the melting data even in the K-rich system show how the magma becomes increasingly silica-undersaturated with increasing pressure as the compositions shift from quartz-normative at 1 GPa to nepheline-normative at 3 GPa (Fig. 2.19).

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FIGURE 2.17 Evolution of SiO2 and Al2O3 abundance in partial melt from peridotite with various mounts of H2O and pressure. Redrawn from Tenner et al. (2012).

2.3.3 Upper mantle magma genesis with H2O Partial melting of hydrous peridotite in the Earth’s interior occurs predominantly in the mantle wedge in subduction zones. In this environment, the H2O to a large extent is derived from dehydration of hydrous phases in the descending slab (see also discussion of the dehydration phenomena in Chapter 1 and in particular Figs. 1.27 and 1.29 and also Chapter 6). However, the amount of H2O thus released decreases with increasing depth (Poli and Schmidt, 2002; Poli et al., 2009).

2.3 Melting interval of mantle peridotite with volatiles

73

FIGURE 2.18 Relationship between MgO and SiO2 abundance in H2O-saturated melts from garnet peridotite as a function of pressure. Redrawn from Kawamoto and Holloway (1997).

FIGURE 2.19 Evolution of melt composition with pressure from partial melting of K-rich lherzolite expressed in terms of endmembers as indicated. Redrawn from Condamine et al. (2016).

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The extent to which this alteration of the peridotite source of melting takes place has been the subject of several studies. These involve both the rate of transfer of H2O-rich fluid and the rate and extent to which the peridotite wedge is altered by incoming fluid (Mysen 1978; Iizuka and Mysen, 1998). In their experiments, Iizuka and Mysen (1998) determined the rate of orthopyroxene layer thickness on the boundary with enstatite by allowing H2O released by dehydrating an amphibole to filtrate through the adjoining forsterite þ enstatite layer. As discussed in detail in Chapter 6, this fluid is enriched in SiO2 as well as other major, minor, and trace elements (Zhang and Frantz, 2000; Manning, 2004) resulting in alteration in the peridotite wedge.7 This SiO2 will, for example, convert some of the olivine in the peridotite to orthopyroxene. Till et al. (2012) combined available data on peridotite-H2O melting, including the stability of hydrous phases on and near the solidus, to create sections of melting in subduction zones with warm and cold subduction. In this model, melting of hydrous peridotite involves melting in equilibrium with amphibole (likely pargasite) at shallow depth between 50 and 80 km. Here, the magma is andesitic. This observation agrees with the suggestion by Tatsumi (1989) that the volcanic front in Japan coincides with the dehydration of amphibole in the underlying mantle wedge. Interestingly, at greater depth, less H2O is available and, as discussed above, the magma during partial melting becomes basaltic. The melting model of Till et al. (2012) (and most other melting models of the mantle wedge) does not take into consideration how the wetting angle of a hydrated peridotite may control the H2O transport. These features will be discussed in more detail Chapter 11. Briefly, under hydrostatic conditions, the wetting angle needs to be less than 60 to permit interconnectivity of fluid and, therefore, movement of aqueous fluid (Smith, 1948). From experiments to determine wetting angle in peridotite minerals, Mibe et al. (1999) mapped the region of the upper mantle peridotite wedge where H2O is interconnected (angle less than 60 ) and fluid transport and consequent alteration of the peridotite source of melting is possible (Fig. 2.20). In this model, widespread magma formation via partial melting of hydrated peridotite may occur in the peridotite wedge above the subducting slab at depths less than about 100 km. At pressures less than those corresponding to w100 km depth (200 km depth), the oxygen fugacity is so low that the CeOeH fluids comprise hydrocarbons and H2O (Sokol et al., 2018). Under these conditions, experimental data (Litasov et al., 2014) indicate that the partial melts of peridotite-C-O-H would yield magma compositions resembling basalt. This, therefore, is the probable reasons why basalt magmatism rather than carbonatite magmatism is common in cratonic settings.

2.4 Melting interval of basalt Melting and crystallization of magma of basaltic composition for the most part take place under crustal pressure, temperature, and redox conditions.

2.4.1 Redox variations at ambient pressure Basaltic magma can be the parent magma of more evolved magma compositions. For example, andesitic magma may be formed by crystallization of iron oxide at near ambient pressures depending on the oxygen fugacity (Osborn, 1959). A few additional experimental studies have been carried out on basalt compositions, therefore, to further our understanding of how oxygen fugacity conditions may

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affect crystallization and crystal fractionation (Osborn, 1959; Fudali, 1965; Gust and Perfit, 1987; Juster et al., 1989). Osborn (1959) in what was probably the first in-depth discussion of the role of oxygen fugacity (fO2) during crystallization of basaltic magma, used melting phase relations in the system MgOeFeOeFe2O3eSiO2 at ambient pressure to point out that during fractional crystallization of basalt, the fractionation trend is that commonly observed for tholeiitic magma. However, if fractional crystallization takes place at constant oxygen fugacity, the magma composition becomes increasingly SiO2 rich and once the magnetite crystallization surface is reached, the iron oxide content of the residual magma decreases. Osborn (1959) suggested that this mechanism would result in a calcalkaline fractionation trends from basalt to andesitic magma. In more recent experimental studies, the focus has been on relationships between the redox conditions and the stability field of mafic minerals in equilibrium with magma. Gust and Perfit (1987) demonstrated, for example, that whereas olivine is the liquidus phase of high-Mg basalt under reducing conditions (fO2250 C at pressures less than 3 PGa to less than 100 C near 20 GPa. This evolution reflects changes in the mineral assemblages in this temperature interval with increasing pressure (Fig. 2.34). The silica phase is transformed to stishovite and clinopyroxene disappears as majorite garnet is formed (Yasuda et al., 1994). As a result of this change, the partial melts become nepheline-normative (Kogiso and Hirschmann, 2006).

2.4.3 Melting of basalt with volatiles Melting and crystallization phase equilibrium experiments with volatiles for the most part have been carried out with H2O (Beard and Lofgren, 1991; Sisson and Grove, 1993; Barklay and Carmichael, 2004; Di Carlo et al., 2006; Blatter et al., 2013; Melekhova et al., 2015). Characterization of melting and crystallization of basalt with other volatiles such as CO2, CH4, and halogens has been the subject to less experimental activity (but see Hammouda, 2003; Dasgupta et al., 2005; Filiberto and Treiman, 2009; Filiberto et al., 2012; Litasov et al., 2014).

2.4.3.1 Basalt-H2O Determination of melting and crystallization behavior basalt-H2O systems for the most part has been driven by our need to characterize magmatic processes in island arc settings where H2O plays a dominant role (Beard and Lofgren, 1991; Barclay and Carmichael, 2004; DiCarlo et al., 2006; Blatter et al., 2013). However, H2O can also be a contributor to magmatic processes in other tectonic settings (Medard and Grove, 2008; Husen et al., 2016).

FIGURE 2.34 Pressure and temperature relations to 20 GPa of melting phase relations of volatile-free MORB. Redrawn from Yasuda et al. (1994).

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91

The three major effects of H2O on basalt melting relations compared with melting without volatiles are (1) the substantial temperature depression of the basalt þ H2O solidus and liquidus, (2) the great expansion of stability fields of olivine (Me´dard and Grove, 2008), and (3) the presence of a second critical endpoint in basalt-H2O systems in the pressure/temperature region (w5 GPa/w1100 C) where on might otherwise expect partial melting and crystallization (Kessel et al., 2005). The consequences of the presence of H2O are common to all systems of magmatic interest, but the extent of the effects of H2O is significantly dependent on the silicate composition. For example, from a thermodynamic treatment of existing data on the effect of H2O on the liquidus temperature depression of basalt Me´dard and Grove (2008) arrived at the expression to describe this effect:     2 3 melt melt DTðCÞ ¼ 40:4 Cmelt þ 0:791 C (2.11)  2:97 C H2 O H2 O H2 O ; where Cmelt H2 O is the concentration of H2O in the magma (wt%). As can be seen in Fig. 2.35, the model fits experimental data reasonably well and does seem to do a better job than several other models.

FIGURE 2.35 Temperature depression, DT, of the olivine in the melting interval of basalt as a function of H2O content from the model of Medard and Grove (2008) (see also discussion in text) compared with results from other melting models as indicated on figure. Redrawn from Medard and Grove (2008).

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Chapter 2 Melting in the Earth’s interior

The behavior of a second critical endpoint in silicatedH2O systems is discussed in some detail in Chapter 7 [section (7.3.2)]. Here, we will describe only briefly the specific situation for basalt-H2O. In this system, with increasing temperature (and pressure) there is a gradual closure of the melt þ fluid field along the basaltdH2O join, which eventually leads to closure of the melt þ fluid immiscibility gap between 4 and 6 GPa (Fig. 2.36; see also Kessel et al., 2005). In terms of melt and fluid compositions, this closure is reflected in a transition from discontinuous to continuous evolution of oxide compositions with increasing temperature (Fig. 2.37). In the basalt-H2O system, these features occur are at considerably greater pressure and temperature than in more felsic systems such as, for example, rhyolitedH2O (Sowerby and Keppler, 1999) and at lower pressures and temperatures than in the peridotitedH2O (Mibe et al., 2007). In qualitative terms, there is a negative correlation between the pressure/temperature coordinates of the (fluid, melt) closure and the SiO2 þ Al2O3 content the system. It also is likely that the ratio of alkali metals to alkaline earths play a role. Absent the complexities of immiscibility between fluid and melt, the evolution of the solidus and liquidus as well as the phase relations in the melt region in between in basalt-H2O systems resemble that seen for other igneous systems (Lambert and Wylie, 1972; Stern and Wyllie, 1978; see also Fig. 2.38). The temperature minimum of the hydrous solidus near 1.5 GPa and 600 C reflects the plagioclase-to-jadeite þ quartz transformation. There is also a wide stability field of amphibole (hornblende) between the solidus to temperatures near the liquidus (Fig. 2.38). The upper pressure stability of amphibole, near 2.5 GPa, nearly coincides with the appearance of garnet, a feature originally reported by Allen et al. (1972). We note, however,

FIGURE 2.36 Phase relations in basalt rock-H2O space at 4 and 6 GPa illustrating how the system transforms to one with complete miscibility between H2O and silicate at pressures between 4 and 6 GPa. Redrawn from Kessel et al. (2005).

2.4 Melting interval of basalt

93

FIGURE 2.37 Evolution of SiO2 and Al2O3 concentrations in fluid, melts and supercritical fluid as a function of temperature at pressures below 4 GPa and above 6 GPa between which is the second critical endpoint (see also Fig. 2.36). Redrawn from Kessel et al. (2005).

that the stability field of amphibole also is sensitive to its magma composition (Allen et al., 1972), H2O activity (Huang and Wyllie, 1986; Beard and Lofgren, 1991; Di Carlo et al., 2006; Melekhova et al., 2015), and redox conditions (Allen et al., 1972; Barclay and Carmichael, 2004). The H2O content not only affects the stability range of hydrous phases such as amphibole, the rest of the mineral assemblage also is affected by the activity of H2O. For example, Melekhova et al. (2015) found that with 4.5 wt% H2O added to what was referred to primitive arc basalt, this magma was multiply saturated (olivine þ orthopyroxene þ clinopyroxene þ spinel), whereas with lower H2O content, this multiple saturation was no longer observed. Melekhova et al. (2015) also noted that the stability field of hornblende shrank and that of plagioclase expanded with decreasing H2O content. The oxygen fugacity affects melting phase relations of basalt þ H2O (Barclay and Carmichael, 2004; Botcharnikov et al., 2008). As also observed at ambient pressure (see earlier), the stability field

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Chapter 2 Melting in the Earth’s interior

FIGURE 2.38 Melting phase relations of basalt with excess H2O as a function of temperature and pressure. Abbreviations: coe, coesite; cpx, clinopyroxene; ga, garnet; hb, hornblende; ol, olivine; plag, plagioclase; qtz, quartz. Redrawn from Lambert and Wyllie (1972).

and composition of iron oxide are significantly affected by fO2. For example, the stability fields of ilmenite and magnetite expand with decreasing oxygen fugacity below that of the QFM oxygen buffer. For Skaergaard gabbro, for example, hematite is unstable at oxygen fugacity lower than about three orders of magnitude above the QFM buffer. The stability fields of clinopyroxene and plagioclase expand with decreasing fO2.

2.4.3.2 Magma genesis in hydrous basalt systems During fractional crystallization of basalt, whether this involves crystallization of olivine, clinopyroxene, plagioclase, or iron oxides, such crystallization has a major effect on the evolution of basaltic magma (Osborn, 1959; Mu¨ntner et al., 2001; Grove et al., 2003; Blatter et al., 2013). Pressure, activity of H2O, and oxygen fugacity are critical parameters in these processes. Strikingly, clinopyroxene is an important phase during crystallization at pressures corresponding to the deep crust and the uppermost continental mantle (Mu¨ntner et al., 2001; Grove et al., 2003; Alonzo-Perez, 2009). At pressures near 1 GPa (w30 km depth), augite is the dominating clinopyroxene. The magma composition resulting from the clinopyroxene (augite) fractional crystallization

2.4 Melting interval of basalt

95

trends toward peraluminous9 and silicate rich. The SiO2 at which the magma becomes peraluminous appears to increase with decreasing pressure. At lower crustal pressures ( 1. In other words, the proportion of Al3þ is greater than that for which charge-balancing cations are available. See also Chapter 6 for further discussion of this feature and its effect on the structure and properties of magma. 9

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Chapter 2 Melting in the Earth’s interior

FIGURE 2.39 Melting phase relations of eclogite-CO2 as a function of temperature and pressure. Notice how the carbonate phase near the solidus changes from calcite, via dolomite to magnesite with increasing pressure. Abbreviations: cpx, clinopyroxene; ga, garnet. Redrawn from Hammouda (2003).

Given the suggestion that the redox conditions at pressures near 5 GPa and more in the cratonic upper mantle is so reducing that fluids in the CeOeH system likely comprise hydrocarbons and H2O (Sokol et al., 2018), Litasov et al. (2014) conducted experiments with eclogite-C-O-H with the oxygen fugacity buffered with the MoeMoCO2 (MMO)10 and FeeFeO (IW) oxygen buffers. In contrast to results from experiments under oxidizing conditions where the partial melt is carbonatitic, under reducing conditions, the partial melt from basalt þ CH4 þ H2 þ H2O melt is basaltic. This result leaves open the question, therefore, whether carbonatite magma can be formed under these conditions in the upper mantle.

2.5 Melting interval of andesite With the exception of the fractional crystallization model of Osborn (1959) where ambient-pressure crystallization of iron oxides from a basaltic parent under anhydrous conditions would lead to 10 The oxygen fugacity governed by the MMO buffer (where H2O, CH4, and H2 dominate in a CeOeH fluid) is near an order of magnitude higher than that of the IW buffer, but nearly four orders of magnitude more reducing that that of the MW (magnetite-wustite) buffer (where CO2 and H2O dominate in a CeOeH fluid).

2.5 Melting interval of andesite

97

andesitic magma, all more recent models of andesite formation involve H2O (Tatsumi, 1982; Blatter and Carmichael, 2001; Hermann and Green, 2001; Grove et al., 2003; Spandler et al., 2010). This conclusion follows whether the melting model involves hydrous basalt (Luhr, 1992) or hydrous pelitic sediments (Schmidt et al., 2004). Huang and Wyllie (1986) in their study of melting of tonalite (which has andesitic composition) with variable H2O content found that this composition could not have been in equilibrium with a peridotite mineral assemblage because the liquidus phase assemblage under upper mantle conditions was clinopyroxene þ kyanite þ hornblende (Fig. 2.40). However, fractional crystallization of such minerals in the melting interval would yield a calc-alkaline trend (Huang and Wyllie, 1986). There are, however, other andesitic magma the melting phase relations of which could be consistent with equilibration with a peridotite mantle source. Tatsumi (1982) observed, for example, that a high-Mg andesite from the Satuchi volcanic belt, Japan, is in equilibrium with olivine þ orthopyroxene þ clinpyroxene near 1.5 GPa and 1030 C in the presence of excess H2O (Fig. 2.41). Characterization of the devolatilization and melting phase relations of the sedimentary layer of the subducting is central to our understanding of the how dehydration of this layer affects the mantle

FIGURE 2.40 Melting phase relations of tonalite as a function of H2O content at 1.5 GPa. Abbreviations: bi, bioite; cpx, clinopyroxene; ga, garnet; hbl, hornblende; Ky, kyanite; plag, plagioclase; qtz, quartz; V, H2O-rich vapor (silicate saturated). Redrawn from Huang and Wyllie (1986).

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Chapter 2 Melting in the Earth’s interior

FIGURE 2.41 Melting phase relations of H2O-saturated, high-Mg andesite as a function of temperature and pressure. Abbreviations: amph, amphibole; cpx, clinopyroxene; ol, olivine; opx, orthopyroxene; V, silicate-saturated H2O fluid. Notice how cpx, opx, and ol, coexist on the liquidus at 1.5 GPa and 1030 C suggesting, therefore, that this high-Mg andesite may be in equilibrium with mantle peridotite under H2O-saturated conditions at 1.5 GP and 1030 C. Redrawn from Tatsumi (1982).

source of magma in the overlying peridotite wedge. Spandler et al. (2010) conducted, for example, melting experiments from 3 to 5 GPa to further our understanding of the melting phase relations of these rocks. In their experiments, quartz or coesite (depending on pressure) is the liquidus phase. Crystallization of the silica phase is followed by garnet as the second mineral to crystallize upon cooling followed by clinopyroxene and finally feldspar (Fig. 2.42). The Na/K ratio of the feldspar decreases with increasing pressure and is nearly pure K-feldspar at 5 GPa. The partial melt is dacitic at all pressures with its Na/K abundance ratio governed by feldspar þ quartz at low pressure and clinyporoxene composition at higher pressures. Hydrous phases such as hornblende and mica can be critical for melting phase relations as well as minor and trace element patterns of magma formed in subduction zones (Rapp et al., 1995; Vielzeuf and Holloway, 1998; Brenan et al., 1998). As discussed earlier, provided that the H2O content is contained in hydrous phases; their breakdown defines the solidus. Typically, hornblende is the lowestpressure hydrous phase to define such a solidus followed by mica (biotite and phengite) at higher pressure. Dehydration melting of amphibole in the low-pressure regime between 0.5 and 2.0 GPa, can be described with the reaction (Douce and Alberto, 2005): amphibole þ biotite þ quartz þ plagioclase ¼ clinopyroxene þ garnet þ K  feldspar þ melt. (2.13)

2.5 Melting interval of andesite

99

FIGURE 2.42 Melting phase relations of volatile-free pelite as a function of temperature and pressure. Abbreviations: ap, apatite; coe, coesite; cpx, clinopyroxene; ga, garnet; K-spar, K-feldspar; ky, kyanite; qtz, quartz; rt, rutile. Redrawn from Spandler et al. (2010).

Above about 1.5 GPa, reaction (2.13) is replaced by: amphibole þ quartz ¼ clinopyroxene þ garnet þ melt

(2.14)

There can be a narrow pressure interval between 2.5 and 3.0 GPa where zoisite is the hydrous phase that defines dehydration melting (Douce and Alberto, 2005; see also Fig. 1.26). At higher pressure, biotite and phengite describes the dehydration melting phengite þ clinopyroxene þ quartz ¼ garnet þ K  feldspar þ melt

(2.15)

zoisite þ garnet þ quartz ¼ clinopyroxene þ kyanite þ melt.

(2.16)

and The magma compositions formed in all these melting reactions is leuocogranitic (Douce and Alberto, 2005; Hermann and Spandler, 2008). There is, nevertheless a systematic evolution of composition with pressure. The granitic magma becomes increasingly enriched in normative orthoclase component with increasing pressure (Fig. 2.43). This Na/K variation reflects the influence of pressure on the clinopyroxene composition, which buffers the Na concentration in the melt, and the stabilities of phengite and K-feldspar, which buffer K composition. We must note, however, that in this kind of system at lower crustal and upper mantle conditions, supercritical fluids my replace melt (Schmidt et al., 2004). This effect can be seen, for example, in the evolution of the Na2O/Al2O3 illustrated in Fig. 2.44.

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FIGURE 2.43 Composition of partial melt, expressed in terms of normative feldspar compositions, from tonalite-H2O with all H2O contained in biotite and amphibole as a function of pressure between 1.5 and 3.2 GPa. Redrawn from Douce and Alberto (2005).

2.6 Melting interval of granite The melting interval of granitic rocks and their near-surface equivalent, rhyolite, for the most part has been examined experimentally in the presence of H2O (Jahns and Burnham, 1958; Boettcher and Wyllie, 1968; Clemens and Holloway, 1986; Scaillet and Macdonald, 2003). The use of H2O in these experiments is in part because the diffusivity in these felsic magmas in the absence of H2O is so slow that it is essentially impossible to reach equilibrium conditions on a laboratory time scale. This restriction notwithstanding, there is at least one experimental study aimed at the determination of anhydrous melting conditions (Huang and Wylllie, 1973). However, even in this study, there was a small amount of H2O tied up in muscovite (Fig. 2.45). It appears unlikely, however, that the lowtemperature, near-solidus experiments reached equilibrium. This is because the solidus curve does not reflect the volume effects associated with. the crossing of the plagioclase ¼ jadeite þ quartz and quartz-coesite transformations otherwise observed in other experimental studies of hydrous melting of granite composition (Boettcher and Wyllie, 1968; Stern et al., 1975; see also Fig. 1.40).

2.6 Melting interval of granite

101

FIGURE 2.44 Evolution with temperature of SiO2/Al2O3 ratio of melt and aqueous fluid from pelite-H2O. Redrawn from Herman and Spandler (2008).

FIGURE 2.45 Melting phase relations of muscovite granite without additional H2O as a function of temperature and pressure. Abbreviations: co, corundum; coe, coesite; fsp, feldspar; ga, garnet; jd, jadeite; ky, kyanite; ms, muscovite; or, orthoclase; plag, plagioclase; qtz, quartz; sil, sillimanite. Redrawn from Huang and Wyllie (1973).

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Chapter 2 Melting in the Earth’s interior

FIGURE 2.46 Melting phase relations of muscovite granite as a function of H2O content at 1.5 GPa total pressure. Abbreviations: co, corundum; ga, garnet; ky, kyanite; ms, muscovite; or, orthoclase; plag, plagioclase; qtz, quartz; vap, silicate-saturated H2O fluid. Redrawn from Huang and Wyllie (1973).

2.6.1 H2O-undersaturated melting Most melting experiments that involve hydrous granite/rhyolite composition have been carried out under H2O-undersaturated conditions (Dall’Agnol et al., 1999; Costa et al., 2004; Holtz et al., 2005; see also Fig. 2.46). As is also the case for less silica-rich compositions, the stability fields of hydrous phases, mica and amphibole, are sensitive to the activity of H2O (Scaillet and MacDonald, 2001). Moreover, the temperature stability field of quartz diminishes with increasing activity of H2O while that of pyroxene expands (Fig. 2.46). The upper temperature stability of feldspar also decreases with increasing activity of H2O. Again, this feature is qualitatively similar to that seen in less felsic magma compositions such as andesite/tonalite (Fig. 2.40) and is a direct result of the solution mechanism of H2O in silicate melts (see also Chapter 7).

2.6.2 Melting with variable redox conditions The melting phase relations of granite/rhyolite also are sensitive to redox conditions (Scaillet and Evans, 1999; Scaillet and MacDonald, 2001; Costa et al., 2004; Scaillet et al., 2016) just as the phase

2.7 Concluding remarks

103

FIGURE 2.47 Melting phase relations of granite with variable H2O contents at 300 MPa and two different oxygen fugacities as indicated on figures. Abbreviations: bi, biotite; cpx, clinopyroxene; hbl, hornblende; K-fsp, K-feldspar; opx, orthopyroxene; qtz, quartz. Notice how, in particular, the stability relations of hydrous phases, hornblende and biotite, are sensitive to oxygen fugacity. Redrawn from Dall’agnol et al. (1999).

relations of less silica-rich magma (Martel et al., 1999; Berndt et al., 2005; Gaillard et al., 2015). Increasing oxygen fugacity results in diminished temperature stability of biotite and hornblende. This decreased temperature stability is associated with increased temperature stability of ortho- and clinopyroxene. Notably, the stability of field of iron oxides such as magnetite also expands as the oxygen fugacity is increased (Fig. 2.47). In contrast, the stability fields of quartz and feldspars in the melting interval of hydrous granite/rhyolite are less sensitive to the redox conditions (Fig. 2.47).

2.7 Concluding remarks Melting in the Earth’s mantle is dominated by melting of peridotite with and without volatiles. The dominant volatiles are in the CeOeH system. In subduction zone settings, the main volatiles are H2O and CO2, whereas elsewhere in the Earth’s deep upper mantle and below, redox conditions are such that the dominant volatiles are H2O and CH4 with a small proportion of H2. Peridotite melting without volatiles in the uppermost portions of the upper mantle yields tholeiite magma resembling MORB. With increasing depth, the magma becomes in increasingly alkalic so that the partial melts are alkali basaltic at depths near 100 km. Partial melting of peridotite-H2O affects solidus temperatures, phase equilibria in the melting interval, and the bulk chemical composition of the partial melts. These changes reflect the influence of

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H2O on silicate melt structure, which, governs decreased activity coefficients of silicate components. The result is partial melts from peridotite þ H2O resembling high-Mg andesite to depths of at least 50 km in settings such as the peridotite wedge in subduction zones. Increasing pressure results in gradual transition of magma composition toward alkali basaltic. Partial melting of peridotite-CO2 at 50e55 km depth yields magma compositions resembling those formed in the absence of volatiles with magma composition similar to olivine tholeiite in the uppermost mantle. The magma composition changes gradually to nepheline-normative magma as the pressure approaches 2 GPa. At greater depth, the solidus temperature decreases rapidly by more than 200 C and the magma composition on the CO2-saturated solidus changes to carbonatite. As the temperature is increased under these pressure conditions, this magma gradually changes to CO2-rich silicate melt. Fractional crystallization of basalt/gabbro without volatiles is dominated by crystallization of olivine, which results in significant iron-enrichment. However, the extent to which this takes place can be governed by how the stability of iron oxides may be affected by redox conditions. The redox conditions, in turn, govern, whether or not the calc-alkaline crystallization trends may be the result. However, melting and crystallization behavior of basalt/gabbro also is significantly dependent on the activity of H2O. With increasing H2O activity, partial melting results in silica-enriched magma such as andesite and dacite. Fractional crystallization of hydrous basalt will also lead to silica-enriched melt products. Partial melting and fractional crystallization of andesitic and more silica-rich composition in the presence of H2O yields magma compositions not greatly different from those of hydrous basalt and tends to yield granitic magma compositions. Peraluminous granitic composition can be the ultimate result.

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Mu¨ntener, O., Kelemen, P., G, T.L., 2001. The role of H2O during crystallization of primitive arc magmas under uppermost mantle conditions and genesis of igneous pyroxenites: an experimental study. Contrib. Mineral. Petrol. 141, 643e658. Mysen, B.O., 1978. The role of descending plates in the formation of andesite melts beneath island arcs. Carnegie Inst. Wash. Year Book 77, 797e801. Mysen, B.O., 2015. Carbon speciation in silicate-C-O-H as a function of redox conditions: An experimental study, in-situ to 1.7 GPa and 900C. Am. Miner. 100, 872e882. Mysen, B.O., Boettcher, A.L., 1975a. Melting of a hydrous mantle. I. Phase relations of natural peridotite at high pressures and temperatures with controlled activities of water, carbon dioxide and hydrogen. J. Petrol. 16, 520e548. Mysen, B.O., Boettcher, A.L., 1975b. Melting of a hydrous mantle. II. Geochemistry of crystals and liquids formed by anatexis of mantle peridotite at high pressures and high temperatures as a function of controlled activities of water, hydrogen and carbon dioxide. J. Petrol. 16, 549e590. Mysen, B.O., Kushiro, I., 1977. Compositional variations of coexisting phases with degree of melting of peridotite in the upper mantle. Am. Mineral. 62, 843e865. Mysen, B.O., Kushiro, I., Nicholls, I.A., Ringwood, A.E., 1974. A possible mantle origin of andesitic magmas: Discussion of a paper by Nicholls and Ringwood. Earth Planet. Sci. Lett. 21, 221e229. Mysen, B.O., Virgo, D., 1986. The structure of melts in the system Na2O-CaO-Al2O3-SiO2-H2O quenched from high temperature at high pressure. Chem. Geol. 57, 333e358. Nebel, O., Sossi, P.A., Bernard, A., Wille, M., Vroon, P.Z., 2015. Redox-variability and controls in subduction zones from an iron-isotope perspective. Earth Planet. Sci. Lett. 432, 14e151. Nicholls, I.A., Ringwood, A.E., 1973. Production of silica-saturated tholeiitic magmas in island arcs. Earth Planet. Sci. Lett. 17, 243e246. Nixon, P.H., Boyd, F.R., 1973. Petrogenesis of the granular and sheared ultrabasic nodule suite in kimberlites. In: Nixon, P.H. (Ed.), Lesotho Kimberlites. Cape and Transvaal Printer Ltd, Cape Town, pp. 48e56. Osborn, E.F., 1959. The role of oxygen pressure in the crystallization and differentiation of basaltic magma. Am. J. Sci. 257, 609e647. Parman, S.W., Grove, T.L., 2004. Harzburgite melting with and without H2O: Experimental data and predictive modeling. J. Geophys. Res. 109. Pickering-Witter, J., Johnston, A.D., 2000. The effects of variable bulk composition on the melting systematics of fertile peridotitic assemblages. Contrib. Mineral. Petrol. 140, 190e211. Poli, S., Franzolin, E., Fumagalli, P., Crottini, A., 2009. The transport of carbon and hydrogen in subducted oceanic crust: an experimental study to 5 GPa Earth Planet. Sci. Lett. 278, 350e360. Poli, S., Schmidt, M.W., 2002. Petrology of subducted slabs. Annu. Rev. Earth Planet Sci. 30, 207e235. Presnall, D.C., Gudfinnsson, G.H., Walter, M.J., 2002. Generation of mid-ocean ridge basalts at pressures from 1 to 7 GPa. Geochem. Cosmochim. Acta 66, 2073e2090. Rapp, R.P., Watson, E.B., 1995. Dehydration melting of metabasalt at 8-32 kbar; implications for continental growth and crust-mantle recycling. J. Petrol. 36, 891e931. Roder, P.L., Emslie, R.F., 1970. Olivine-liquid equilibrium. Contrib. Mineral. Petrol. 29, 275e289. Rohrbach, A., Schmidt, M.W., 2011. Redox freezing and melting in the Earth’s deep mantle resulting from carbon-iron redox coupling. Nature 472, 209e212. Rushmer, T., 1991. Partial melting of two amphibolites: contrasting experimental results under fluid-absent conditions. Contrib. Mineral. Petrol. 107, 41e59. Safonov, O.G., Butvina, V.G., 2013. Interaction of model peridotite with H2O-KCl fluid; experiment at 1.9 GPa and its implications for upper mantle metasomatism. Petrology 21, 599e615. https://doi.org/10.1134/ S0869591113060076.

References

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Scaillet, B., Evans, B.W., 1999. The 15 June 1991 Eruption of Mount Pinatubo. I. Phase equilibria and preeruption PeTefCO2efH2O conditions of the Dacite Magma. J. Petrol. 40, 381e411. Scaillet, B., Macdonald, R., 2001. Phase relations of peralkaline silicic magmas and petrogenetic implications. J. Petrol. 42, 825e845. Scaillet, B., Macdonald, R., 2003. Experimental constraints on the relationships between peralkaline rhyolites of the Kenya rift valley. J. Petrol. 44, 1867e1894. Scaillet, B., Holtz, F., Pichavant, M., 2016. Experimental constraints on the formation of silicic magmas. Elements 12, 109e114. Scheka, S.S., Wiedenbeck, M., Frost, D.J., Keppler, H., 2006. Carbon solubility in mantle minerals. Earth Planet. Sci. Lett. 245, 730e742. Sisson, T.W., Grove, T.L., 1993. Experimental investigations of the role of H2O in calc-alkaline differentiation and subduction zone magmatism. Contrib. Mineral. Petrol. 113, 143e166. Schmidt, M.W., Vielzeuf, D., Auzanneau, E., 2004. Melting and dissolution of subducting crust at high pressures: the key role of white mica. Earth Planet Sci. Lett. 228, 65e84. Schwab, B.E., Johnson, A.D., 2001. Melting systematics of modally variable, compositionally intermediate peridotites and the effects of mineral fertility. J. Petrol. 42, 1789e1811. Smith, C.S., 1948. Grains, phases, and interfaces: an introduction of microstructure. Trans Metall. Soc. AIME 175, 15e52. Sokol, A.G., Tomilanko, A.A., Bul’bak, T.A., Kruk, A.N., Sokol, I.A., 2018. Fate of fluids at the base of subcratonic lithosphere; experimental constraints at 5.5e7.8 GPa and 1150e1350 degrees C. Lithos 318e319, 419e433. Sowerby, J.R., Keppler, H., 1999. Water speciation in rhyolitic melt determined by in-situ infrared spectroscopy. Am. Mineral. 84, 1843e1849. Spandler, C., Yaxley, G.M., Green, D.H., Scott, D., 2010. Experimental phase and melting relations of metapelite in the upper mantle: implications for the petrogenesis of intraplate magmas. Contrib. Mineral. Petrol. 160, 569e589. Stern, C.R., Wyllie, P.J., 1978. Phase compositions through crystallization intervals in basalt-andesite-H2O with implications for subduction zone magmas. Am. Mineral. 63, 641e663. Stern, C.R., Huang, W.-L., Wyllie, P.J., 1975. Basalt-andesite-rhyolite-H2O: crystallization intervals with excess H2O and H2O-undersaturated liquidus surfaces to 35 kilobars, with implications for magma genesis. Earth Planet. Sci. Lett. 28, 189e196. Takahashi, E., Kushiro, I., 1983. Melting of a dry peridotite at high pressures and basalt magma genesis. Am. Mineral. 68, 859e879. Tateno, S., Hirose, K., Ohishi, Y., 2014. Melting experiments on peridotite to lowermost mantle conditions. J. Geophys. Res. 119, 4684e4469. Tatsumi, Y., 1982. Origin of high-magnesian andesites in the Setouchi volcanic belt, southwest Japan, II. Melting phase relations at high pressures. Earth Planet. Sci. Lett. 60, 305e317. Tatsumi, Y., 1989. Migration of fluid phases and genesis of basalt magmas in subduction zones. J. Geophys. Res. 94, 4697e4707. Taylor, W.R., GReen, D.H., 1988. Measurement of reduced peridotite-C-O-H solidus and implications for redox melting of the mantle. Nature 332, 349e352. Tenner, T., Hirschmann, M.M., Humayun, M., 2012. The effect of H2O on partial melting of garnet peridotite at 3.5 GPa. Geochem. Geophys. Geosyst. 13. https://doi.org/10.1029/2011GC003942. Thibault, Y., Holloway, J.R., 1992. Carbon dioxide interaction with an olivine leucite melt; solubility and trace element partitioning. In: Anonymous (Ed.), AGU 1992 Spring Meeting. American Geophysical Union, Washington, DC, United States, p. 351.

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Till, C.B., Grove, T.L., Withers, A.C., 2012. The beginnings of hydrous mantle wedge melting. Contrib. Mineral. Petrol. 163, 669e688. Toplis, M.J., 2004. The thermodynamics of iron and magnesium partitioning between olivine and liquid: Criteria for assessing and predicting equilibrium in natural and experimental systems. Contrib. Mineral. Petrol. 149, 22e39. Trønnes, R., 2002. Stability range and decomposition of potassic richterite and phlogopite end members at 5e15 GPa. Mineral. Petrol. 74, 129e148. Trønnes, R.G., Frost, D.J., 2002. Peridotite melting and mineralemelt partitioning of major and minor elements at 22e24.5 GPa. Earth Planet. Sci. Lett. 197, 117e131. Tuttle, O.F., Bowen, N.L., 1958. Origin of granite in light of experimental studies in the system NaAlSi3O8KAlSi3O8-SiO2-H2O. Geol. Soc. Am. Mem. 74, 1e153. Ulmer, P., Trommsdorff, V., 1998. Phase relations of hydrous mantle subducting to 300 km. In: Fei, Y.-W., Bertka, C., Mysen, B.O. (Eds.), Mantle Petrology: Field Observations and High-Pressure Experimentation. Geochemical Society. Vielzeuf, D., Holloway, J.R., 1998. Experimental determination of the fluid-absent melting relations in the pelitic system. Contrib. Mineral. Petrol. 98, 257e276. Wallace, M.E., Green, D.H., 1988. An experimental determination of primary carbonatite magma composition. Nature 335, 343e346. Walter, M.J., 1998. Melting of garnet peridotite and the origin of komatiite and depleted lithosphere. J. Petrol. 39, 29e60. Wendlandt, R.F., Mysen, B.O., 1980. Melting phase relations of natural peridotiteþCO2 as a function of degree of partial melting at 15 and 30 kbar. Am. Miner. 65, 37e44. Wyllie, P.J., 1977. Peridotite-CO2-H2O, and carbonatitic liquids in the upper asthenosphere. Nature 266, 45e47. Yasuda, A., Fujii, T., Kurita, K., 1994. Melting phase relations of an anhydrous mid-ocean ridge basalt from 3 to 20 GPa: Implications for the behavior of subducted oceanic crust in the mantle. J. Geophys. Res. 99, 9401e9414. Yaxley, G.M., Brey, G.P., 2004. Phase relations of carbonate-bearing eclogite assemblages from 2.5 to 5.5 GPa; implications for petrogenesis of carbonatites. Contrib. Mineral. Petrol. 146 (5), 606e619. Yoder, H.S., Kushiro, I., 1969. Melting of a hydrous phase: phlogopite. Am. J. Sci. 267A, 558e582. Yoder, H.S., Tilley, C.E., 1962. Origin of basaltic magma: an experimental study of natural and synthetic rock systems. J. Petrol. 3, 342e532. Zhang, C., Duan, Z., 2009. A model for C-O-H fluid in the Earth’s mantle. Geochem. Cosmochim. Acta 73, 2089e2102. Zhang, Y.-G., Frantz, J.D., 2000. Enstatite-forsterite-water equilibria at elevated temperatures and pressures. Am. Mineral. 85, 918e925. Zhang, J., Herzberg, C.T., 1994. Melting experiments on anhydrous peridotite KLB-1 from 5.0 to 22.5 GPa. J. Geophys. Res. 99, 17729. https://doi.org/10.1029/94JB01406.

CHAPTER

Element distribution during melting and crystallization

3

3.1 Introduction Element distribution between a mineral assemblage and a magmatic liquid is an important aspects of mass transport by magma. The extent to which this takes place depends on the solubility and solution behavior of the element(s) of interest in as well as element partitioning between coexisting minerals and melt.1 The partition coefficients, in turn, are controlled by temperature, pressure, chemical composition, and activity-composition relations in coexisting melt and minerals. In a melting process, the bulk partition coefficient between an entire mineral assemblage and the melt also depends on the stoichiometry of the melting reaction. Melting may be in the form of batch melting or fractional melting. Redox equilibria of major, minor, and trace elements can also affect the element distribution between minerals and melts. These features are the subject of this chapter. First, the basic principles will be addressed. This will be followed by summaries of major, minor, and trace element partition coefficients as a function of composition, temperature, pressure, and redox conditions involving major mineral groups in the Earth.

3.2 Principles For a simple exchange reaction of the form: ia þ jb 5ib þ ja ;

(3.1)

where i and j are components and a and b are different phases, the exchange equilibrium coefficient is: !
b g b i Xi gj Xj !a ; K ¼
a • (3.2) Xi gi Xj g j

1

In this chapter, “melt” and “magmatic liquid” often are synonymous unless otherwise specified.

Mass Transport in Magmatic Systems. https://doi.org/10.1016/B978-0-12-821201-1.00001-8 Copyright © 2023 Elsevier Inc. All rights reserved.

113

114

Chapter 3 Element distribution during melting

where gi etc. are activity coefficients and Xi etc. are mol fractions so that the activity of component, i, in a phase (a or b in this case) is related to the mol fraction and activity coefficient as; ai ¼ Xi $gi : (3.3) !b gi gj !a , accommodates, therefore, any compositional The activity coefficient ratio in Eq. (3.2), gi gj effect of the dissolved components, i and j, in both phases, a and b. For major element components, the activity coefficients usually vary as a function of their concentration, so that an activity-composition diagram takes the form illustrated in Fig. 3.1. However, for trace elements, the activity coefficients in Eq. (3.2) can be constant. When constant, their solution behavior is according to Henry’s Law so that for coexisting phases a and b, for components, i and j, the activity coefficient ratio is constant. !b gi gj !a ; ¼ constant. (3.4) gi gj

,k =1 i

=k •X

le

i

:a

ab

w

ari

La

l, k

=v

ao ul t’s Ac

tua

R

activity, ai

This behavior differs from solution behavior according to Raoult’s Law. In this latter case, the activity of i and j in the two phases equals 1 so that the activity coefficient ratio in Eq. (3.4) also equals 1.

X, : a i=k• i ’s Law nt ta s n o k=c

Henry

mol fraction, Xi

FIGURE 3.1 Principles to illustrate relationships between mol fraction and activity of component, i, in solid solutions. Also shown are the relationships under conditions of Henry’s Law and Raoult’s Law.

3.3 Trace element substitution in melts and minerals

115

The distribution of component, i, between two phases, a and b, within the Henry’s Law domain is ¼ Dab i

Xia Xib

:

(3.5)

Within the concentration range of Henry’s Law, the value of Diab , is constant. An example of this kind of behavior is shown for olivine-melt partitioning as a function of Sm concentration in Fig. 3.2. From an experimental perspective, whether or not a partition coefficient is according to Henry’s Law is determined, therefore, by relationships such as illustrated in Fig. 3.2. Here, it can be seen how the partition coefficient for a trace element of geochemical interest, Sm, is independent of trace element concentration over a range of low concentration until the partition coefficient begins to change with a further increase in trace element concentration. In summary, the low concentration range without concentration dependence is that where the element of interest dissolves in the coexisting melt and crystals dissolves according to Henry’s Law.

3.3 Trace element substitution in melts and minerals Deviations from Henry’s Law behavior observed in relationships between partition coefficients and bulk element concentration (Fig. 3.2) could reflect changes in solution behavior of an element in either crystals, in melts, or both. A factor of major importance for the solution behavior is Young’s modulus, E ¼ stress/strain. Young’s modulus typically is much greater for crystals than for melts (Beattie, 1993; Blundy and Wood, 1994). It reasonable, therefore, that deviations from Henry’s Law occurs at lower element concentrations in minerals than in melts.

2.8 2.6

olivine-melt DSm •102

2.4 2.2 2.0 1.8 1.6 1.4 1.2 0.1

1 Sm in olivine, ppm

10

FIGURE 3.2 Relationship between mineral-melt partition coefficient and concentration in mineral phase using olivine-melt partition coefficient of Sm between olivine and melt at 2.5 GPa and 1075 C as an example. Modified after Mysen (1979).

116

Chapter 3 Element distribution during melting

3.3.1 Trace element substitution in minerals Onuma et al. (1968) were among the first to recognize that ionic radius and formal electrical charge of trace elements played major roles in determining the energetics of trace element substitution in minerals. They found that there were simple parabolic relationships between mineral/melt partition coefficients and ionic radius. These principles were demonstrated for clinopyroxene and orthopyroxene by Onuma et al. (1968). This treatment was expanded to include most major rock-forming minerals by Jensen (1973) and Matsui et al. (1977). As seen in Fig. 3.3. the more crystallographic sites might be available for substitution, the more complex (more maxima and minima) are these socalled Onuma diagrams. There is also a tendency for the parabola to become narrower the greater the radius difference and charge difference between that of the trace element of interest and the crystallographic site into which it may substitute. In addition to the specific parabola that exists for each group of elements with fixed electrical charge, there also exists a linear relationship such as (Onuma et al., 1968) ln Dimineralmelt ¼ Aðri  ro Þ2 þ B:

(3.6)

In Eq. (3.6), Dimineralmelt , is the mineral/melt partition coefficient for element, i, ri is its ionic radius, and ro is what Onuma et al. (1968) referred to as the most favorable ionic radius of a given site. In Eq. (3.6), A is a constant that reflects elastic constants of the crystal, and B is a constant that is governed by charge-balance in the crystal structure.

10

10 A

Partition coefficient, Dimineral-melt

Ca

1

Na

Ba

K

Li La

0.1

Ce Mn

Gd

Nd Sm

Tb Rb

Yb

0.01

0.001

0.4

0.6

0.8 1.0 1.2 Ionic radius, Å

1.4

1.6

Partition coefficient, Dimineral-melt

Mg

Al

B

Sc

Sr

Co Cr

1

In Tb Gd Yb Eu Sm Ca Lu Mn

Ce La

K

Na Sr Rb Ba Ca

Li

0.1

0.01 0.4

0.6

0.8

1.0 1.2 1.4 Ionic radius, Å

1.6

1.8

FIGURE 3.3 Relationship between mineral-melt partition coefficients and ionic radius. (A) Example using plagioclase phenocryst-matrix pairs. (B) Example using hornblende-matrix pair. Notice the several maxima in the hornblende-matrix pair, which likely reflects substitutions in different sites in the hornblende structure. Modified after Matsui et al. (1977).

3.3 Trace element substitution in melts and minerals

Lu

Partition coefficient, Dimineral-melt

0.1

117

Yb

Tb

Eu Sm

0.01

Ce

0.001

0

0.02

0.04

0.06

0.08

0.10 2

0.12

2

Ionic radius difference, (rREE-rMg) , Å

FIGURE 3.4 Orthopyroxene (bronzite)-melt partition coefficients for various rare earth elements as a function of the radius difference between the rare earth element and Mg. Modified after Onuma et al. (1968).

As can be seen in Fig. 3.4, a simple logelinear relationship exists between partition coefficients and the radius difference of elements with specified formal electrical charge. The values of A and B will, therefore, be functions of the type of mineral as well as the trace element of interest. The ideas outlined in the early papers summarized earlier, were quantified in more recent treatments from which quantitative modeling has been developed (Blundy and Wood, 1994; Wood and Blundy, 2001, 2003; Van Westrenen et al., 1999, 2000). It was found, for example, that there exists a simple linear relationship between the bulk modulus and the expression, Z/r3 (Z: formal electrical charge, r: average cation-oxygen distance; see Fig. 3.5). Furthermore, these data line up well with the cation-oxygen polyhedral relationship for silicate tetrahedra by Hazen and Finger (1979). An equilibrium coefficient, Ki, is related to the free energy change(s) associated with melting of component, i, and the exchange energy between component in a melt and a crystal: ! mineralmelt DGmineral fusion  DGexchange Ki ¼ exp : (3.7) RT In Eq. (3.7) and subsequent equations, R is the gas constant and T is temperature (Kelvin). The mineral-melt exchange energy was considered approximately equal to the strain energy around a monovalent cation in the melt (see Brice, 1975). From this, Blundy and Wood (1994) derived an

118

Chapter 3 Element distribution during melting

Bulk modulus, K, GPa

300

200

100

0

0

0.05

0.10

0.15 zcd-3 (Å-3)

0.20

0.25

FIGURE 3.5 Relationship between bulk modulus, K, and the product of mean ionic charge and mean cation-oxygen distance, zcd, as in Eq. (3.8). Data points are from plagioclase, diopside and augite for 1þ, 2þ, and 3þ cations. Modified after Blundy and Wood (1994).

expression for the relationship between the partition coefficient, ionic radii, Young’s modulus, E, and Avogadros’ number, NA:     
4pENA r0 =2 r02  ri2 þ 1=3 r03  ri3 0 Di ¼ Di $exp : (3.8) RT The example from Blundy and Wood (1994) in Fig. 3.6 shows the success of this equation. Critical variables are the D0i and r0. These are the ideal partitioning values and ionic radii. Their values depend on the element under consideration and the crystal structure in which an element is dissolved. In the example in Fig. 3.6, the behavior is referenced to Ca2þ with its Do-value at 2.0 and the ˚ (Bundy and Wood, 1994). r0 at 1.02 A Variable mineral-melt partition coefficients as a function of mineral composition can have substantial effects on trace element evolution of igneous rock suites. An example is the effect of plagioclase solid solutions on mineral-melt partition coefficients such as for Sr in plagioclase in the example in Blundy and Wood (2003): ln DSrplagiolasemelt ¼ ð26.8  26.7XAn Þ=RT:

(3.9)

In the example using this relationship to describe the evolution of igneous rock complexes, using plagioclase evolution during fractionation of basalts from Yemen, the plagioclase composition effects2 2

Plagioclase-melt partition coefficients more often than not are correlated with the An content of the plagioclase. Details of this feature will be discussed in Section 3.3.2.1.

3.3 Trace element substitution in melts and minerals

119

1

Partition coefficient, Dimineral-melt

Ho Yb

Gd

Lu

Sm Eu Nd

0.1

0.01 0.95

La

Ce

1.00

1.05 1.10 Cation radius, Å

1.15

1.20

FIGURE 3.6 Relationship between REE partition coefficients of pyroxene-melt (ortho- and clinopyroxene) pairs (see Blundy and Wood, 1994, for source experimental data) and cation radius. Modified after Blundy and Wood (1994).

Melt composition relative to start, CL/C0

show how much variation in Sr concentration in the lava is affected by the variation in plagioclase-melt partition coefficients as the plagioclase composition evolved during fractional crystallization (Fig. 3.7).

2.0

1.5 9)

. qn

(3.

e

1.0

0.5

0.0 0.0

0.2

0.4 0.6 Melt fraction, F

0.8

1.0

FIGURE 3.7 Evolution of the Sr content of lava from the Aden Main Cone relative to initial Sr content (Sro) as a function of degree of crystallization and changing Sr partition coefficient as a function of their An content. Modified after Blundy and Wood (2003).

120

Chapter 3 Element distribution during melting

Of course, this example (Fig. 3.7) does not take into consideration the effects of magma composition on mineral-melt partition coefficients. Principles governing the influence of melt composition and melt structure will be addressed next.

3.3.2 Trace element substitution in melts Effects of melt composition (and structure) on element partitioning between minerals and melts have been evaluated in terms of individual oxide components of the melt solvent (e.g., Hart and Davis, 1978; Watson, 1976; Schmidt et al., 2006), in terms of melt structural features (Mysen and Virgo, 1980; Nielsen, 1985; Walter and Thibault, 1995; Jaeger and Drake, 2000; Mysen, 2007a, b), and by thermodynamic treatment (O’Neill and Eggins, 2002; Toplis, 2005; Evans et al., 2008). Two-liquid partition coefficients, where two immiscible liquids coexist at fixed temperature, pressure, and redox conditions, offer a glimpse at how melt composition can affect mineral-melt partition coefficients (Watson, 1976; Ryerson, 1978). By studying the partitioning of a range of trace elements between coexisting, immiscible melts in the K2OdAl2O3dFeOdSiO2 system (Roedder, 1951; see also Fig. 3.8), Watson (1976) found that essentially all elements tended to be favored by the basic melt. In Fig. 3.8, showing the immiscible melts in the K2OdAl2O3dFeOdSiO2 system, the basic melt is that nearest the FeO corner. Notably, among alkali metals and alkaline earths, for example, the more electronegative3 the cation, the larger is the partition coefficient, basic melt/acidic melt (Fig. 3.9A). In comparison, the partition coefficients for rare earth elements are essentially the same for all the elements (Fig. 3.9B). Watson (1976) concluded, therefore, that there is a positive correlation between the extent to which an element exhibits preference for the basic melt and the Z/r (and Z/r2) of the cation (Fig. 3.9C).

20 wt% K2O•Al2O3

40 wt%

80

2

SiO

SiO

wt% 2

SiO2

30

40 FeO, wt%

50

FIGURE 3.8 Coexisting melts in the system K2OdFeOdAl2O3dSiO2 at 1180 C and ambient pressure showing the composition of coexisting melts used for two-liquid partition coefficients by Watson (1976). Modified after Roedder (1951); Watson (1976).

Electronegativity is defined as the ratio, Z/r2, where Z is formal electrical charge and r is ionic radius.

3

Concentration in felsic melt, wt%

A

Ba

0.6 0.5

1:

Cs

0.4

+

0.2

+ Mg

+ +

0.1

+ 7 8 2 3 4 5 6 Concentration in mafic melt, wt%

9

B 0.3

Sm

1:1

Concentration in felsic melt, wt%

Ca

0.3

1

La

0.2 Lu

0.1

1

Z/r, Å-1

Sr

1

20 18 16 14 12 10 8 6 4

2 3 4 5 6 7 8 9 10 11 Concentration in mafic melt, wt% P

C

Zr Sr

2 Cs

1

Mg Ba

Ta Ti Cr Sm Mn Ca La

Lu

2 3 4 5 6 7 8 Partition coefficient, Dmafic-felsic

9

10

FIGURE 3.9 Trace element distribution between coexisting immiscible melts as shown in Fig. 3.8 at ambient pressure. (A) Distribution of alkali metals and alkaline earths. Notice the systematic evolution as a function of the electronic nature of the cation. (B) Distribution of rare earth elements. (C) Distribution coefficient, basic/felsic melt, as a function of the Z/r (cation charge divided by radius). Modified after Watson (1976).

122

Chapter 3 Element distribution during melting

50 30

Dolivine-melt Ni

20 15 10 1250˚C

7 5 3 2 0.20

1350˚C 1450˚C

0.25

0.30

0.35

Si/O

FIGURE 3.10 olivinemelt , as a function of Si/O ratio in melt at temperatures Olivine-melt partition coefficient for Ni, DNi indicated.

Modified after Hart and Davis (1978).

Analogous melt composition effects were reported by Hart and Davis (1978) in their study of olivine-melt partition coefficients for Ni as a function of the Si/O ratio of the melt (Fig. 3.10). With increasing Si/O ratio, which corresponds to increasingly felsic melt, the Dolivinemelt is a linear and Ni positive function of Si/O of the melt at constant temperature. Interestingly, Evans et al. (2008) and Schmidt et al. (2006) found a log-log relationship of olivine-melt partition coefficients and SiO2 concentration in the melt for a large number of elements including rare earth elements (REE) and high field strength elements (HFSE). The data shown in Figs. 3.9 and 3.10 most likely reflect the fact that most trace and minor elements are network-modifiers4 (see Chapter 5 for a more detailed discussion of the behavior networkmodifiers in melt structures). The proportion of nonbridging oxygens in a silicate melt does, therefore, increase the greater the abundance ratio, metal/silicon. Relationships between mineral-melt partition coefficients and proportions (activity) of nonbridging oxygen have been expressed in terms of relationships to nonbridging oxygen per tetrahedrally coordinated cations, NBO/T (e.g., Mysen and Virgo, 1980; Jaeger and Drake, 2000). When developing relationships with intensive variables together with those expressing partition coefficients as a function of melt composition variable(s), it is important to keep in mind that the Gibbs Phase Rule: P þ F ¼ C þ1,

4

(3.10)

A network-modifier is linked to oxygen in an oxygen polyhedron with more than four oxygens. In other words, networkmodifiers are not tetrahedrally coordinated to oxygen in the structure.

3.3 Trace element substitution in melts and minerals

123

where P is the number of phases, C is the number of components, and F is the degree of freedom, makes it challenging to find systems wherein identification of individual compositional and structural variables of a melt in equilibrium with a crystal can be isolated without changing additional parameters such as temperature and pressure. Fortunately, in some simple systems such as NaAlSi3O8dCaAl2Si2O8dMg2SiO4 and NaAlSiO4dCaMgSi2O6dSiO2, the NBO/T can be changed significantly along ambient-pressure isotherms (see Schairer and Yoder, 1960, 1966 for liquidus phase diagrams). Trace element partition coefficients in such systems will be described next.

3.3.2.1 Melt structural effects, NBO/T Typically, there is a correlation between mineral-melt partition coefficients and NBO/T 5 of the melt (Fig. 3.11). By comparing clinopyroxene-melt partition coefficients for rhyolite and basalt melt, for example, the Mg partition coefficient might differ by more than 200% (Toplis and Corgne, 2002). The NBO/T of typical rhyolite melt averages near 0.1, whereas the average for basalt melt is near 0.8 (Mysen and Richet, 2005). There is, however, no simple unifying relationship with which to link all partition coefficients to NBO/T. The relationships can be linear (Jaeger and Drake, 2000), exponential (Toplis and Corgne, 2002), or parabolic (Kushiro and Mysen, 2002) depending on the mineral phase(s) and composition. For an exchange equilibrium such as A i þ Bj ¼ Aj þ Bi ;

(3.11)

AB , is; the exchange equilibrium coefficient, Kij  B  A AB Kij ¼ Xi =Xj = Xi =Xj : 2þ

2þ

2þ

(3.12) 2þ

2þ

For systems that involve divalent cations, Mg , Ca , Mn , Co , and Ni , Mysen (2007a) found that the extent to which the exchange equilibrium coefficients vary with the NBO/T of the melt is a simple function of the ionic radius of the divalent cations (Fig. 3.12). This change increases as the ionic radius of the cation decreases.

3.3.2.2 Melt structural effects, site preference The different forms of the relationships between partition coefficients and NBO/T of the melt reflect the fact that there are other melt structural parameters, in addition to NBO/T, affecting crystal-melt element partitioning. One such parameter is preference for specific network-modifying cations to form bonding with specific nonbridging oxygen positions in the melt. In a sense, this concept resembles intracrystalline distribution of cations and anions in crystalline materials. This site-preference in melts was first proposed by Kohn and Schofield (1994) and subsequently documented with Magic Angle Spinning Nuclear Magnetic Resonance (MAS NMR) data of silicate glasses temperature-quenched from their melt by Lee and Stebbins (2003). In general, when there are two or more network-modifying cations in a silicate melt, the most electronegative among these tends to associate with nonbridging oxygens in the most depolymerized silicate species in the melt. Two

5

NBO/T: Nonbridging oxygen (NBO) per tetrahedrally coordinated cation (T). For the most part, T-cations are Si4þ and Al3þ (see also Chapter 5).

124

2.0

A

5

olivne/melt

KD (Ca-Mn)

Fe liq/silicate melt

10

DGa

cpx/melt

C 0.10

1.5

15

DMg

B

1.0 0.5

0.08 0.06

0.0 0.04 -0.5

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

NBO/T

0.0

W

0.5

1.0 NBO/T

1.5

2.0

0.5

1.0

1.5

2.0

2.5

NBO/T

FIGURE 3.11 clinopyroxenemelt as a function on the NBO/ Element distribution between silicate melt and minerals as a function of the NBO/T of the melt. (A) DMg

T of the melt (Modified from Toplis and Corgne, 2002). (B) Partitioning of W and Ga between molten iron and silicate melt. (C) Exchange olivinemelt , as a function of NBO/T of the melt. equilibrium coefficient between olivine and melt of Ca and Mn, KCaMn

(A) Modified after Toplis and Corgne (2002). (B) Modified after Mysen and Dubinsky (2004).

Chapter 3 Element distribution during melting

20

olivine-melt

olivine-melt

Ni

K i-Mg

olivine-melt (ref)] -K i-Mg olivine-melt (ref) K i-Mg

100

100•[K i-Mg

125

(ref)

3.3 Trace element substitution in melts and minerals

50 Co

0 Mn

-50 Ca

-100 0.0

0.5

1.0

1.5

2.0

2.5

NBO/T of melt FIGURE 3.12 olivinemelt , for i ¼ Ca, Mn, Co, and Ni Changes in exchange equilibrium coefficient between olivine and melt, KiMg

relative to Mg as a function of the evolution of NBO/T of the melt at constant temperature and pressure. The changes are calculated relative to a value at the largest NBO/T in the experiments (marked with arrow. Modified after Mysen (2007a).

examples of how such preferences affect mineral-melt partition coefficients are shown in Fig. 3.13 for Co-Mg and Fe2þ-Mg exchange equilibrium coefficients for olivine-melt pairs;  melt  olivine olivinemelt KFe ¼ XFe2þ =XMg ; (3.13) = XFe2þ =XMg 2þ Mg and melt  olivine  olivinemelt KCoMg ¼ XCo =XMg : = XCo =XMg

(3.14)

2þ

For both Fe -Mg and Co-Mg, the exchange partition coefficient increases with increasing Na/ (Na þ Ca) of the melt at constant temperature and NBO/T (Mysen, 2007a; see also Fig. 3.13). The change in Na/(Na þ Ca) affects the availability of sites to be occupied by Mg, Fe, and Co, which leads to the relationship in Fig. 3.13. A particularly interesting exchange equilibrium is the Fe2þ-Mg between olivine and melt because the exchange equilibrium coefficient for this equilibrium often has been used to deduce petrogenetic olivinemelt originally determined to history of basaltic melts. Here, the assumption has been that the KFe 2þ Mg be near 0.3 by Roeder and Emslie (1970) remains the same for different magma compositions. If so, olivinemelt ¼ 0:3 value would effectively define the Mg/(Mg þ Fe) of magma formed by partial the KFe 2þ Mg melting of a peridotite upper mantle with Mg/(Mg þ Fe)-values in the 0.88e0.92 range. Ulmer (1989)

126

Chapter 3 Element distribution during melting

0.75

0.28 olivine-melt

0.65

KFe2+-Mg

olivine-melt

0.70 KCo-Mg

B

0.30

A

0.60

0.26 0.24 0.22

0.55

0.20

0.50 0.0

0.2 0.4 0.6 Na/(Na+Ca)

0.0

0.2 0.4 0.6 Na/(Na+Ca)

FIGURE 3.13 olivinemelt and K olivinemelt , as a function of Na/ Changes of olivine-melt exchange equilibrium coefficients, KCoMg 2þ Fe Mg

(Na þ Ca) at constant NBO/T as indicated of the melt.

Modified after Mysen (2007a).

olivinemelt depends on pressure and Kushiro and Walter (1998) observed, in noted, however, that the KFe 2þ Mg olivinemelt varied between 0.2 and 0.4 as a function of NBO/T a study of melting of peridotite, that the KFe 2þ Mg

of the partial melt (Fig. 3.14A). There is, however, considerable scatter in the data in Fig. 3.14A because the NBO/T variations also are significantly dependent on both temperature and pressure. Temperature and pressure both affect mineral-melt partition coefficients and exchange equilibrium coefficients (Ulmer, 1989; Kushiro and Walter, 1998). In other words, the data shown in Fig. 3.14A reflect potentially NBO/T, temperature, and pressure changes. There might also be issues with variations in the redox state of iron in the melt unless the Fe3þ/Fe2þ of the melt is determined. The redox 0.36

A

0.34

0.35

0.32

olivine-melt -Mg

0.40

KFe

olivine-melt

KFe(total)-Mg

0.45

0.30

B

0.30 0.28

0.25

0.26

0.20 0.0 0.5 1.0

1.5 2.0 2.5 3.0 3.5 4.0 NBO/T of melt

0.24 0.0

0.5

1.0 1.5 2.0 NBO/T of melt

2.5

3.0

FIGURE 3.14 Evolution of the K olivinemelt as a function of NBO/T of the melt in natural peridotite systems (A) and in the 2þ Fe Mg

K2dNa2OdCaOdMgOdFeOdAl2O3dSiO2 system (B). Modified after (A) Kushiro and Walter (1998). (B) Kushiro and Mysen (2002).

3.3 Trace element substitution in melts and minerals

127

ratio of iron was not in the two studies by Ulmer (1989) and Kushiro and Walter (1998). Without that olivinemelt should be replaced by K olivinemelt . Then, the exchange equilibrium information, the KFe 2þ FeðtotalÞMg Mg coefficient depends on the redox state of iron in melt, which, in turn depends on oxygen fugacity, melt composition, temperature, and pressure (Mysen, 1975). olivinemelt , Kushiro and Mysen (2002) conducted a series In order to isolate NBO/T effects on the KFe 2þ Mg of experiments at constant temperature, ambient pressure, and oxygen fugacity. The redox state of iron of the melt was determined with Mo¨ssbauer spectroscopy. The result was a better-defined parabola olivinemelt value near 0.25 and a maximum near 0.35 (Fig. 3.14B). with a minimum KFe 2þ Mg An alternative approach to this problem was provided by Toplis (2005). He determined the activity coefficient ratio of Fe2þ and Mg in melt in equilibrium with olivine and found this ratio to be primarily dependent on the SiO2 concentration in the melt, temperature, and pressure. He then regressed all available data from his own work and from the literature (Fig. 3.15) and arrived at an empirical equation for the olivine-melt exchange equilibrium as a function of melt composition (SiO2, mol%), pressure, P (MPa), and temperature, T (K):
 6766 7:34  þ ln½0:036XSiO2  0:22 KFe2 Mg ¼ exp RT R    (3.15) 3000ð1  2XFo 0:035ðP  0:1Þ þ ; þ RT RT

0.50

Calculated KFe2+-Mg

olivine-melt

0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.15

High Pressure 0.1 MPa 0.20

0.25

0.30

0.35

Measured K

0.40

0.45

0.50

olivine-melt Fe2+-Mg

FIGURE 3.15 Comparison of experimentally observed and modeled.K olivinemelt 2þ Fe Mg

Modified after Toplis (2005).

128

Chapter 3 Element distribution during melting

where XSiO2 and XFo (mol fraction of SiO2 in the melt and mol fraction of forsterite component in olivine) are in mol %. From this relationship, Toplis (2005) reported separate effects of SiO2 conolivinemelt ¼ 0.22e0.40), temperature between 1200 and 2000K (K olivinemelt ¼ centration (KFe 2þ Mg Fe2þ Mg olivinemelt ¼ 0.30e0.36) and olivine composition 0.29e0.39), pressure between ambient and 7 GPa (KFe 2þ Mg olivinemelt ¼ 0.44e0.28). An important implication between 10 and 100 mol% forsterite component (KFe 2þ Mg olivinemelt -value to be used to deduce provenance of of these relationships is that there is no unique KFe 2þ Mg

magmatic rocks in equilibrium with olivine during initial melting and subsequent fractional crystallization in the Earth’s interior.

3.3.2.3 Melt structural effects, Al 5 Si exchange

In aluminosilicate melts with nonbridging oxygen (NBO/T > 0), mineral-melt partition coefficients depend on the Al/(Al þ Si) of the melt even at constant melt NBO/T, temperature, pressure, and composition of the mineral (Mysen, 2007b). This behavior is illustrated for forsterite-melt partition coefficients from the system NaAlSiO4dSiO2dMg2SiO4 at ambient pressure (Fig. 3.16A and B). For divalent cations such as Ni2þ and Co2þ, the olivine-melt exchange partition coefficients, forsteritemelt and K forsteritemelt , are linear and negative functions of increasing Al/(Al þ Si). KNiMg CoMg These exchange equilibria are more sensitive to Al/(Al þ Si) the more electropositive the element of interest (Fig. 3.16C). Moreover, the effect is greater in systems where tetrahedrally coordinated Al3þ is charge-balanced with Naþ than when charge-balanced with Ca2þ as in the system CaAl2Si2O8dSiO2dMg2SiO4 (Fig. 3.16C). The general principles governing relationships between partition coefficients and Al/(Al þ Si) of the melt may be understood in by considering the equilibria among the Q-species6 in depolymerized silicate and aluminosilicate melts. In silicate melts with nonbridging oxygen (depolymerized melts), equilibria between structural units with different degree of silicate polymerization can be described with expressions such as (see also Stebbins, 1987; and Chapter 5 for details); 2Qn 5Qnþ1 þ Qn1 :

(3.16) 3þ

In aluminosilicate melts at pressures less than about 5e6 GPa, essentially all the Al substitutes for Si4þ in the Q-species with the largest number of bridging oxygen (most polymerized species, Qnþ1). This substitution drives, therefore, equilibrium (3.16) to the right (Merzbacher et al., 1990; Mysen et al., 2003). With this information in hand, the changes in exchange equilibrium coefficient such as illustrated in Fig. 3.16 most likely reflect changes in activity coefficient ratio in the melt (gM/gMg)melt, where M is the cation of interest, as a function of the Al/(Al þ Si) of the melt. It is the increased Qn1 abundance that results in lowering of (gM/gMg)melt (Mysen and Shang, 2005). This activity coefficient change does, in turn, cause the changes in exchange equilibrium coefficients shown in Fig. 3.16.

The Q-species represent discrete silicate structural units. As discussed in detail in Chapter 6, there are five discrete units defined by their number of bridging oxygen (0, 1, 2, 3, and 4). These are indicated by the superscript used in the notation, Qn. This structural situation exists in most natural magma because with few exceptions, the proportion of alkali metals and alkaline earths exceed that required for charge-balance of tetrahedrally coordinated Al3þ. Most magmatic liquids will, therefore, comprise nonbridging oxygen and, therefore, several coexisting Qn-species. 6

0.85

A

0.80

K Co-Mg

olivine-melt

0.75 0.70 0.65 0.60 0.55

0.0

0.1

0.2

0.3

0.4

Al/(Al+Si) B

2.6 2.4

K Ni-Mg

olivine-melt

2.2 2.0 1.8 1.6 1.4 0.0

0.1

0.2

0.3

0.4

100•[K i-Mg

1.6

C

Ni

(ref)

Co

olivine-melt

1.4

K i-Mg

olivine-melt

olivine-melt (ref)] -K i-Mg olivine-melt (ref) K i-Mg

Al/(Al+Si)

Mn

1.2

1.0 0.2

0.3 Al/(Al+Si)

FIGURE 3.16 Exchange equilibrium coefficients for olivine-melt pairs and various divalent cations as a function of the Al/ olivinemelt as a function of melt Al/(Al þ Si). (B) (Al þ Si) of the melt at constant NBO/T of the melt. (A) KCo Mg olivinemelt olivinemelt with i ¼ Ni, Co, and Mn as a function as a function of melt Al/(Al þ Si). (C) Changes in KiMg KNi Mg of changes of Al/(Al þ Si) of the melt relative to melts of the highest Al/(Al þ Si) in the experiments. Data were obtained with experiments in the system NaAlSiO4dMg2SiO4dSiO2 at ambient pressure and 1450 C. Modified after Mysen (2007b).

130

Chapter 3 Element distribution during melting

The different behavior of the Na- and Ca-systems reflects the fact equilibrium (3.16) is more sensitive to Al/(Al þ Si) the more electropositive the cation(s) involved in the charge-balance of tetrahedrally coordinated Al3þ (e.g., Roy and Navrotsky, 1984; Mysen, 1999). It follows that the olivinemelt diminishes the larger Z/r2 of the charge-balancing cation for influence of Al/(Al þ Si) on KMMg tetrahedrally coordinated Al3þ (Z: formal electrical charge, r: ionic radius). This effect also is greater the more electropositive the M-cation. Translated to natural magmatic liquids, this means that these effects on transition metal-mineral exchange equilibria would be greater for a felsic magma such as rhyolite or dacite than for a more mafic magma such as basalt. This is because in felsic magma, tetrahedrally coordinated Al3þ is chargebalanced with alkali metals, whereas in mafic magma, this charge-balance is accomplished with alkaline earths (see also Chapter 5 for more detailed discussion of these phenomena).

3.4 Element partitioning, intensive, and extensive variables Relationships between element partitioning, temperature, and pressure are seen in the simple equations vlnD=vð1 = TÞ ¼  DH=R;

(3.17)

and vlnD=vP ¼ DV=RT: (3.18) In order to calibrate individual effects of temperature and pressure, it is necessary, however, first to consider how to isolate composition, temperature, and pressure effect. This is a challenging proposition in light of the fact that Gibbs Phase Rule (Eq. 3.11), when applied to multicomponent natural systems, leads to the complication that those variables do not change independently of each other.

3.4.1 Olivine-melt olivinemelt , Olivine-melt partition coefficients, Dolivinemelt , and exchange equilibrium coefficients, Kij i vary systematically with melt composition/structure, temperature, pressure, and redox conditions. Most of the effect of melt structure on Dolivinemelt were discussed earlier as part of the presentation of i principal effects. This was so because most of the experimental studies aimed at characterization of these effects were carried out with olivine and melt.

3.4.1.1 Olivine-melt partitioning and temperature As noted earlier, the Gibbs Phase Rule illustrates why it is challenging to separate temperature and pressure effects. It is noted, though, that a number of such efforts, relying on empirical relationships, have been reported for chemically simple systems. In those experimental studies, the temperature and pressure effects have been isolated with reasonable precision. Major experimental efforts have been devoted to olivine-melt partitioning as a function of temperature (Colson et al., 1988; Kinzler et al., 1990; Beattie, 1993; Putirka et al., 2007; Mallman et al., 2013; Matzen et al., 2013). Both major and trace elements have been employed for this purpose. An example of major element partitioning between olivine and melt as a function of temperature was that reported by Beattie (1993). He relied on the observation that the forsterite-fayalite solid

3.4 Element partitioning, intensive, and extensive variables

131

solution is nearly ideal (Nafziger and Muan, 1967). With that assumption, a thermometer that links olivine and melt composition to temperature of equilibration was developed. This relationship was incorporated in a summary review by Putirka (2008):  13603 þ 4:943•107 P ðGPaÞ•109  105

: (3.19) TðKÞ ¼ ol=melt Melt þ 2ln3C Melt  NF 6:26 þ 2lnDMg þ 2 ln 1:5CNM SiO2 ol=melt

In this equation, C is concentration and DMg is olivine-melt partition coefficient for Mg. The NF variable is the sum of the concentration of the oxides, SiO2, NaO0.5, KO0.5, and TiO2 and NM is the sum of the oxides, MgO, FeO, CaO, MnO, NiO, and CoO in the melt. The comparison between calculated and observed temperature based on Eq. (3.19) (Fig. 3.17) illustrates the precision of this relationship. Putirka (2008) noted, however, that although the Beattie (1993) relationship works very well at ambient pressure and without volatiles in the melts, it does not handle pressure and H2O content very well. Putirka et al. (2007) reported an expression that takes into account the effect of H2O in melts on the olivine-melt partition coefficient for Mg. An early experimental study of how temperature (and composition) affects trace element olivinemelt partition coefficients was reported by Colson et al. (1988). They faced the same problems as others in that Gibbs Phase Rule (Eq. 3.10) restricts the extent to which individual variables can be isolated in multicomponent systems. That restriction notwithstanding, Colson et al. (1988) reported how temperature, melt MgO content, and the forsterite content of the olivine can be integrated (Fig. 3.18). In this example, it is evident that the Dolmelt becomes increasingly sensitive to temperSc ature with decreasing MgO content of the melt. Such a relationship, which likely holds for numerous other transition metal partition coefficient (Watson, 1977; Hart and Davis, 1978), may not necessarily be because of the MgO content (Fig. 3.19) because MgO and SiO2 contents of the melt are correlated.

Calculated tempetrature, ˚C

2000

1800

1600

1400

1200 1000 1000

1200

1400

1600

1800

2000

Experimentally observed tempetrature, ˚C

FIGURE 3.17 Comparison of temperatures observed experimentally with those calculated with Eq. (3.19). Modified after Beattie (1993).

132

Chapter 3 Element distribution during melting

: 10

t%)

(w tion

tra

cen

0.25

on Oc

DSc

olivine-melt

Mg

0.20

n atio

%):

(wt

12

tr

cen

on Oc

Mg

n tratio

): 14

(wt%

en

0.15

0.10

: 16 wt%) ion ( t a r t ): 18 en conc n (wt% MgO ncentratio co MgO

MgO

conc

1100

1200 Temperature, ˚C

1300

FIGURE 3.18 olivinemelt and temperature for different MgO concentrations in melt (wt%). Relationship between DSc

Modified after Colson et al. (1988).

A

1.4

7

B

1.2

olivine-melt

5

1.0

DMn

DNi

olivine-melt

6

0.8

4 0.6

3

0.04

0.05 0.06 1/MgO

0.07

0.02

0.04

0.06 1/MgO

0.08

0.10

FIGURE 3.19 olivinemelt as a function of 1/MgO of Olivine-melt partition coefficients as a function of melt composition. (A) DNi

olivinemelt as a function of 1/MgO of the melt in the 1250e1450 C temperature the melt at 1450 C. (B) DMn range.

Modified after (A) Hart and Davis (1978). (B) Watson (1977).

3.4 Element partitioning, intensive, and extensive variables

133

Notably, Watson (1977) did not see much of a temperature effect on the Mn partitioning, whereas both Hart and Davis (1978) and Colson et al. (1988), for a wide range of transition metal partition coefficients, reported significant temperature effects. Furthermore, from a linear fit to the expression: lnKDolivinemelt ¼ 

DH DS þ ; RT R

(3.19)

where DH and DS are enthalpy and entropy change of an exchange reaction of the type shown in Eq. (3.10), R is the gas constant, T is temperature (K), and KDolivinemelt is the exchange equilibrium coefficient of the type shown in Eq. (3.11), the DS/R increases systematically with increasing cation radius (Fig. 3.20). This relationship indicates, therefore, that the olivine-melt exchange equilibrium coefficients, and olivine-melt partition coefficients, become increasingly sensitive to temperature the larger the cation radius. The partition coefficients of REE also have been calibrated as a thermometer (Mallman et al., 2013). In this case, an expression such as
 melt þ 2612 X melt melt melt 3230  100PðGPaÞ  1402Fo þ 1933XCaO þ X NaO0:5 KO0:5  569XSiO2 T ðK Þ ¼ olivinemelt 1:471  logKScV (3.20) was reported. The results, shown in Fig. 3.21, indicate how well Eq. (3.20) reproduces the experimentally determined temperatures.

3.4.1.2 Olivine-melt partitioning and pressure Eq. (3.18) illustrates how pressure can affect olivine-melt partition coefficients. The volume change associated with the solution of the element of interest in the melt governs the extent of the pressure

1 Mn

ΔS/R

0

Ca

Co

-1 -2 Ni

-3 0.7

0.8

0.9 Ionic radius, Å

1.0

1.1

FIGURE 3.20 The entropy of exchange, DS, as a function of cation radius of various divalent cations for the exchange between olivine and melt. Modified after Colson et al. (1988).

134

Chapter 3 Element distribution during melting

Experimentally observed tempetrature, ˚C

1600

1500

1400 1:

1

1300

1200

1100 1100

1200

1300

1400

1500

1600

Calculated tempetrature, ˚C FIGURE 3.21 Comparison of experimentally observed temperature and temperature calculated with Eq. (3.20). Modified from Mallman et al. (2013).

effect. Therefore, with knowledge of partial molar volume of the oxides of interest together with the compressibility and thermal expansion of the melt, relationship between partition coefficients and pressure can be derived. Whereas partial molar volume of major element components of melts is available (Lange and Carmichael, 1987), much less experimental data exist for minor and trace element components (Knoche et al., 1995). Similarly, volume, compressibility, and thermal expansion data are available for major element component in olivine (forsterite and fayalite; see Fei, 1995; Knittle, 1995), but such data are scarce for minor and trace element components. Most of the experimental data on pressure effects on olivine-melt partitioning behavior, therefore, are from direct measurements of partition coefficients as a function of pressure (Mysen and Kushiro, 1979; Ulmer, 1989; Agee and Walker, 1990; Suzuki and Akaogi, 1995; Taura et al., 1998). The FeeMg exchange equilibrium and Al partitioning between olivine and melt are the two major element environments that have attracted most attention (Ulmer, 1989; Agee and Walker, 1990; Tro¨nnes et al., 1992; Taura et al., 1998). Lesser amount of data exists for other major elements such as Na and Ca, for example (Tro¨nnes et al., 1992). In the experimental study by Ulmer (1989), Fe2þ and Mg2þ partitioning between olivine and picritic melt was reported to pressures as high as 3 GPa. The H2O contents varied between 2 and 3 wt.% in the starting composition, which meant that the H2O contents of the melts in equilibrium with olivine were higher than those value. The H2O contents were not, however, determined.

3.4 Element partitioning, intensive, and extensive variables

135

Ulmer (1989) reported a pressure-dependence of the Fe2þ-Mg exchange coefficient,
olivine
melt 2þ Mg olivinemelt KFe2þ  Mg ¼ Fe • Fe , that was described with the expression: 2þ Mg olivinemelt ¼  0:521  0:002 þ 0:032  0:002ðGPaÞ: KFe 2þ  Mg

(3.21)

The simple linear fit to the experimental data (Fig. 3.22) was judged valid between ambient pressure and 3 GPa (Fig. 3.22) for a melt of picritic composition. It is to be noted, however, that olivinemelt also can vary with temperature and bulk composition as discussed earlier (Figs. 3.21 the KFe 2þ  Mg and 3.10). Furthermore, the simple linear relationship in Eq. (3.21) (Fig. 3.22), probably cannot be extrapolated to higher pressure. Ulmer (1989) noted, for example, that Herzberg (1987), from calculations based on elastic properties of olivine and melt, concluded that the pressure-dependence of olivinemelt likely decreases with increasing pressure. We also note that in another experimental study KFe 2þ Mg by Tro¨nnes et al. (1992) to about 10 GPa, no pressure effect was reported. The partial molar volume difference between FeO and MgO in melts (Lange and Carmichael, 1987) would suggest, however, that the exchange equilibrium coefficient should increase with increasing pressure such as in the results summarized in Fig. 3.22.

0.40

KFe2+-Mg

olivine-melt

0.35

0.30

0.25 0

1

2

3

Pressure, GPa FIGURE 3.22 Evolution with pressure of the olivine-melt exchange equilibrium coefficient.K olivinemelt 2þ Fe Mg

Modified after Ulmer (1989).

Chapter 3 Element distribution during melting

Partition coefficient, log DAl

olivine-melt

136

0

-1

-2

2

4

6

8 10 12 Pressure, GPa

14

16

FIGURE 3.23 olivinemelt , as a function of pressure. Aluminum partition coefficient, DAl

Modified after Taura et al. (1998).

Aluminum partitioning between olivine and melt as a function of pressure has been examined in a few experimental studies (Agee and Walker, 1990; Suzuki and Akaogi, 1995; Taura et al., 1998). Taura et al. (1998) concluded, for example that the Dolivinemelt increases with increasing pressure and Al2 O3 decreasing temperature: lnDolivinemelt ¼ 0:082ðGPaÞ  8290=TðKÞ; Al2 O3

(3.22)

in the 1400e1800 C temperature and 0e6 GPa pressure range (see also Agee and Walker, 1990). Taura et al. (1998) extended the pressures to 14 GPa, and noted that lnDolivinemelt remains a linear Al2 O3 function of pressure (Fig. 3.23). Coincidentally, they also reported the olivine-melt partition coefficients of Li and Na to be positive and linear functions of pressure. Olivine-melt trace element partition coefficients also vary with pressure (Mysen and Kushiro, 1979; Suzuki and Akaogi, 1995; Taura et al., 1998). Taura et al. (1998) reported, for example, that essentially all di-, tri-.and quadrivalent cations show decreased olivine-melt partition coefficient with increasing pressure. The partition coefficients of trivalent cations seemed the most pressure-sensitive (Fig. 3.24). Transition metal partition coefficients, and in particular, that of Ni also has been addressed as function of pressure (Mysen and Kushiro, 1979; Taura et al., 1998; Matzen et al., 2013). The simple partition coefficient, Dolivinemelt decreases with increasing pressure as do Co2þ and Mg2þ partition Ni coefficients (Mysen and Kushiro, 1979; Taura et al., 1998). It is notable, though, that according to Taura et al. (1998), the Ca2þ partition coefficient might show a slight increase as the pressure is increased (Fig. 3.24). The pressure dependence of olivine-melt partition coefficients of both major and trace elements has been rationalized in terms of the link between partition coefficients and ionic radii (the so-called Onuma diagrams; see Onuma et al., 1968). Taura et al. (1998) proposed, for example, that the reason why the Al3þ partition coefficients increase with increasing pressure, whereas the partition coefficients of other trivalent cations decrease, is because of the considerably smaller ionic radius of

A

olivine-melt

0

i=Li

Partition coefficient, log Di

Partition coefficient, log Di

olivine-melt

3.4 Element partitioning, intensive, and extensive variables

i=Na

-1

-2 2

6

8 10 12 14 Pressure, GPa

olivine-melt

C i=Cr i=V

0

i=Sc i=Al

-1 i=Y

-2

2

4

6

8 10 12 14 Pressure, GPa

16

B i=Mg

0

i=Ni

i=Co i=Fe i=Mn

-1 i=Ca

-2 2

16

Partition coefficient, log D i

Partition coefficient, log D i

olivine-melt

1

4

1

137

4

6

0 D

8 10 12 14 Pressure, GPa

16

i=Si

-1 -2

i=Ti

-3

i=Zr

-4 2

4

6

8 10 12 14 Pressure, GPa

16

FIGURE 3.24 Diolivinemelt for monovalent (A), divalent (B), trivalent (C), and quadrovalent (D) cations as a function of pressure. Modified after Taura et al. (1998).

Al3þ compared with the other trivalent cations for which partition coefficients have been determined (Fig. 3.24). Ionic radius arguments also have been proposed for the changes in the pressuredependence of the partition coefficients of divalent cations (Taura et al., 1998).

3.4.1.3 Olivine-melt partitioning and redox conditions Redox conditions can affect olivine-melt partition coefficients of aliovalent major elements such as iron (Mysen, 1975; Kushiro and Mysen, 2002; Matzen et al., 2011) and trace elements such as W, U, Cr, Sc, and V (Colson et al., 2000; Canil and Fedortchouk, 2001; Mallmann and O’Neill, 2013; Fonseca et al., 2011; Shishikina et al., 2018) as these elements can exist in different oxidation states

138

Chapter 3 Element distribution during melting

within the oxygen fugacity (fO2 ) range of the Earth and terrestrial planets. An fO2 range of about eight orders of magnitude was proposed by Papike et al. (2004). Variations in redox ratio of a major element such as iron also can affect the melt structure, which, in turn, would affect olivine-melt partition coefficients that depend on melt structure even though their oxidation state may not be affected (Mysen, 2006). When examining FeeMg exchange equilibria between olivine and melt without considering the redox state of iron, the variations of fO2 will cause changes because the redox ratio is iron in melt is sensitive to fO2 (Fig. 3.25). In the oxygen fugacity range between that defined by the magnetiteolivinemelt changes by several hundred % hematite and iron-wustite buffers oxygen buffers,7 the KFeMg olivinemelt may not vary by more than 15%e20% in such an f -rage (Fig. 3.26). The even though the KFe 2þ O2 Mg olivinemelt also depends on oxygen fugacity reflects the fact that as the Fe3þ/Fe2þ of observation that KFe 2þ Mg

a melt in equilibrium with olivine changes, so does the NBO/T of the melt. Given the premise that olivine-melt partition coefficients in general varies with the NBO/T of the melt (see discussion earlier),

0.30

olivine-melt

KFe(total)-Mg

0.25

0.20

0.15

0.10

FD

FD

A3

0.05 -7

-5

-4 -1 log fO 2 (MPa)

1

FIGURE 3.25 olivinemelt , as a function of oxygen fugacity in the system Olivine-melt exchange equilibrium coefficient, KFeðtotÞMg

CaOdMgOdFeOdFe2O3dAl2O3dSiO2 (FDA3) and CaOdMgOdFeOdFe2O3dSiO2 (FD) at 1300 C and ambient pressure. Modified after Mysen (2006).

The oxygen fugacity defined by these buffers are controlled, respectively, by the reactions 6Fe2O3 ¼ 4Fe3O4 þ O2, and 2FeO ¼ Fe þ O2. The shorthand used for these two oxygen fugacity buffers are MH and IW. Other buffer reactions discussed in this chapter are the quartz-fayalite-magnetite (QFM) and nickel-nickel oxide (NNO) buffers. The relevant buffer reactions are: 3Fe2SiO4 þ O2 ¼ 3SiO2 þ 2Fe3O4 and 2Ni þ O2 ¼ 2NiO. 7

KFe2+-Mg

139

FD

3 FDA

olivine-melt

3.4 Element partitioning, intensive, and extensive variables

log fO2 (MPa)

FIGURE 3.26 Evolution of the exchange equilibrium coefficient, K olivinemelt , as a function of oxygen fugacity relative to that 2þ Fe Mg

of the QFM oxygen buffer in the system CaOdMgOdFeOdFe2O3dAl2O3dSiO2 (FDA3) and CaOdMgOdFeOdFe2O3dSiO2 (FD) at 1300 C and ambient pressure. Modified after Mysen (2006).

so does the partition coefficient and equilibrium exchange coefficients of olivine-melt systems. A few examples of this are shown in Fig. 3.27. Trace element partition coefficients also depend on the redox state of the element itself. For example, the redox state of uranium varies between U4þ and U6þ in the redox range of terrestrial processes. As a result, the Dolivinemelt varies with redox conditions (Fonseca et al., 2011; see also U example with tungsten in Fig. 3.28). Analogous partitioning behavior has been reported for transition metals. Vanadium is an example. Its olivine-melt partition coefficient is significantly fO2 -dependent (Canil and Fedortchouk, 2001; Mallmann and O’Neill, 2013). In the example in Fig. 3.29, the oxygen fugacity, expressed relative to the oxygen fugacity defined by the QFM (quartz-fayalite-magnetite) oxygen buffer, DQFM, is (Mallmann and O’Neill, 2013)

8 melt 60 wt%S in melt

iO

ln DTi

60 wt%SiO in melt

40 wt%) and even greater in the crust (>55 wt%). The SiO2 contents of partial melts from a peridotite source in the upper mantle ranges from 45 to 55 wt% in the absence of volatiles such as H2O. However, this concentration can exceed 60 wt% at shallow upper mantle depth when melting often takes place in the presence of H2O (see also Chapters 2 and 7 for discussion of the role of H2O in silicate melts and melting). In view of the important abundance of SiO2 in the Earth, thermodynamic properties describing its melting behavior will be discussed. Following that description, we will proceed to chemically more complex systems. A number of silica phases (about 20) have been identified (e.g., Sosman, 1965), but their stability relationships are not always well understood. What is clear is that at relatively low pressure (1 GPa), the three main polymorphs are quartz, tridymite, and cristobalite. These three polymorphs exist both in an a- and a b-form (e.g., Haney, 1994). Among these, b-cristobalite is the stable form at the melting temperature (1726 C; Jackson, 1976; Richet et al., 1982). Low values for the enthalpy and entropy of fusion (DHf, DSf) of quartz and cristobalite (Table 4.2) are some features of SiO2 that differ significantly from those of essentially all other silicate minerals for which data are available (Robie and Hemingway, 1995). For example, the DHfusion is less than 10 kJ/mol and DSfusion 6 J/mol K (depending slightly on which polymorph is chosen for the crystalline phase; see Table 4.2). These low enthalpy and entropy values indicate that no or insignificant bond breakage takes place during melting because bond breakage requires hundreds of kJ/mol of energy and several tens of J/mol K entropy of fusion. For example, the DSfusion of other tectosilicates such as albite (NaAlSi3O8) and nepheline (NaAlSiO4) is 5e10 times greater than that of cristobalite (see data compilation by Richet and Bottinga, 1986). Among the possible polymorphs stable at the melting temperature, the data summary in Table 4.2 indicate that the characteristics of molten SiO2 and cristobalite more similar than any other silica polymorphs. The volume change is 0.1 cm3/mol and entropy and enthalpy of fusion of 4.61 J/mol K and 8.91 kJ/mol, respectively (Bourova et al., 2000). From the enthalpy and entropy of the quartz to coesite and stishovite high pressure phase transformations (Akaogi and Navrotsky, 1984; Ono et al., 2017), the thermodynamic properties of fusion of high-pressure polymorphs such as coesite and stishovite at ambient pressure are many times greater than the low-pressure polymorphs, quartz, and cristobalite. Table 4.2 Thermodynamic properties (enthalpy, entropy, and volume change) of b-cristobalite and b-quartz at their melting points (metastable melting for b -quartz) (Richet and Bottinga, 1986; Bourova and Richet, 1998). Property

b-cristobalite

b-quartz

Tf(K) DVfus(cm3/mol) DSfus(J/mol K) DHfus(kJ/mol)

1999 0.1 4.61 8.92

1673 3.8 6.06 9.10

4.2 Energetics of melting

B O

Si

2O Na

K2 O

2

-Si

2

O , Si t al.

O2

) 11

20

- ae 2O ar Naugaw (S

NBO/Si of melt

Entropy of fusion, Sfusion,J/mol K

Heat of fusion, Hfusion, kJ/mol

A

229

iO 2

O-S Na 2

K2 O

-S

iO

2

NBO/Si of melt

FIGURE 4.13 Enthalpy and entropy of melting (panels A and B), DHfusion and DSfusion, of crystalline materials along the binary composition joins as indicated as a function of the extent of melt polymerized, expressed as NBO/Si from data compilation by Richet and Bottinga, 1986) and data from Sugawara et al. (2011).

4.2.2.3 Fusion of metal oxide-SiO2 compounds With the addition of metal oxides to SiO2, be they oxides of alkali metals or alkaline earths, a silica polymorph remains on the liquidus until the metal/SiO2 ratio reaches that of K2O•4SiO2 (Charles, 1967), Na2O•2SiO2 (Williamson and Glasser, 1965), and CaO•SiO2 (Rankin and Wright (1915). In other words, the more electronegative the metal cation, the further toward the metal oxide composition is the movement of the liquidus surface of a silica polymorph away from SiO2 (see also Table 6.1 in Mysen and Richet, 2019, for a summary review of these relationships). The enthalpy and entropy of melting (DH fusion and DS fusion) increases rapidly as metal oxides are added to SiO2 (Fig. 4.13). The increased enthalpy (four to five times greater for Na2Si2O5 and Na2SiO3 than the DH fusion for b-cristobalite, for example; see Fig. 4.13). These variations of thermochemical variables (Figs. 4.13 and 4.14) to a considerable extent are in response to structural changes in the melts resulting from the Metal/Si increases and, therefore, the extent of silicate polymerization decrease (NBO/Si increases).3 The electronic properties of the metal cation also affect these relations. The more electronegative the metal cation, the larger are the DH fusion and DS fusion values. Melting of the three-dimensional structure of b-cristobalite for compositions with increasing M/Si requires breakage of SieO bonds (bond energy near 600 kJ/mol), which results in a rapid increase in enthalpy of fusion (Fig. 4.13A; see also Naylor, 1945; Richet and Bottinga, 1986; Sugawara et al., 2011). The melt system also becomes increasingly disordered as evidenced by the increased entropy of melting, DS fusion (Fig. 4.13B). 3

These structural features are discussed in Chapter 5 [section (5.2.3)] and illustrated in Fig. 5.15.

230

Chapter 4 Energetics of melts and melting in magmatic systems

A

B

FIGURE 4.14 Enthalpy and entropy of melting (panels A and B), DHfusion and DSfusion, of crystalline materials along the binary composition joins as a function of the ionization potential, Z/r,2 of the metal cation from data compilation by Richet and Bottinga, 1986).

The equilibrium among silicate structures, Qn, in depolymerized melts (M/Si > 0), is described with an equilibrium of the type: 2Qn ¼ Qn1 þ Qnþ1 ;

(4.4)

where n defines the number of bridging oxygen in the silicate unit (see also Stebbins, 1987, for further discussion of these notations).4 The equilibrium constant, K, for Eq. (4.4) at fixed temperature above their glass transition is positively correlated with the ionization potential of the metal cation (Chapter 5; Fig. 5.18; see also Mysen, 1999). This change leads to increased disorder in the melt structure, which results in enhanced configurational entropy (Mysen, 1995). This evolution, in turn, results in increased entropy difference between crystals and melts and, therefore, increased DS of fusion, as seen in Fig. 4.14. These thermochemical effects of melting are more profound the more electronegative the cation (Fig. 4.14). For example, moving from K2SiO3, via Na2SiO3 to CaSiO3 compositions, the DH fusion increases from 20 kJ/mol via 52 kJ/mol for Na2SiO3 to 62.2 kJ/mol for DH of melting of CaSiO3 (Adamkovicova et al., 1996; Richet et al., 1984; Richet and Bottinga, 1986). For MgSiO3, where Mg2þ is even more electronegative than Ca2þ in CaSiO3, the enthalpy of melting is 77 kJ/mol (Stebbins et al., 1984; Richet and Bottinga, 1986). Similarly, the entropy change of melting, DS fusion, increases from about 16 J/mol K for K2SiO3 to 42 J/mol K for MgSiO3. It seems, therefore, that the more 4 As discussed in more detail in Chapter 5, the n-value can be an integer between 0 and four and changes at certain M/Si ratios of silicate melts. Three distinct equilibria describe the melt structure in discrete intervals between that of tectosilicate and orthosilicate with n ¼ 3, 2, and 1 (see also Mysen and Richet (2019), Chapter 6, for detailed review of these features.

4.2 Energetics of melting

231

electronegative the metal cation, the greater the structural reorganization upon melting and crystallization. This difference is also consistent with the observation that Eq. (4.4) shifts to the right with increasing electronegativity of the metal cation (Mysen, 1999) and, therefore, results in greater dissimilarity between the melt and crystal strructures at the melting point.

4.2.2.4 Fusion of aluminosilicates Substitution of Al3þ for Si4þ in melts and crystals has profound effects on the energetics of melting. For example, for compositions along the meta-aluminosilicate joins such as SiO2eNaAlO2, as the Al/(Al þ Si) increases, both DH and DS of fusion increase by about a factor of 10 between that of pure SiO2 and melt compositions with Al/(Al þ Si) where albite is on the liquidus (Fig. 4.15; see also Schairer and Bowen, 1955; Stebbins et al., 1983, 1984; Richet and Bottinga, 1984). This evolution likely at least in part is a reflection of the fact that while the structure of Al-substituted SiO2 melt resembles that of the SiO2 endmember (Taylor and Brown, 1979; Neuville and Mysen, 1996), the structure of the crystalline phases on the liquidus along the SiO2eNaAlO2 join (albite, jadeite, and nepheline) differs significantly from that of the melt (in contrast to the aforementioned situation with pure SiO2). As a result, the enthalpy of fusion of the Al-bearing compositions is much greater than that if pure SiO2. However, both DH and DS of fusion for compositions along the SiO2eNaAlO2 join tend to decrease as Al/(Al þ Si) increases beyond the Al/(Al þ Si) ¼ 0.25 value (Fig. 4.15A and B). This evolution, at least partly, is in response to the weakening of SieO bonds as Si4þ is replaced by Al3þ (Smyth and Bish, 1988).

B

2

aA lO -N 2

Si O

2

lO aA -N 2

O

2

Si

O Al

lO2

KAlSi3O8

Al/(Al+Si)

-NaA

a -N O2

2

CaAl2Si2O8

Si

SiO

Entropy of fusion, Sfusion,J/mol K

CaAl2Si2O8

KAlSi3O8

Heat of fusion, Hfusion, kJ/mol

A

Al/(Al+Si)

FIGURE 4.15 Enthalpy and entropy of melting (panels A and B), DHfusion and DSfusion, of crystalline materials along metaaluminosilicate joins, NaAlO2eSiO2, KAlO2eSiO2, and CaAl2O4eSiO2 joins as a function of Al/(Al þ Si) from data compilation by Richet and Bottinga (1986).

232

Chapter 4 Energetics of melts and melting in magmatic systems

The situation with SiO2eNaAlO2 compositions remains with other cations replacing Na þ such as K and Ca2þ (Fig. 4.15). For example, for the K-feldspar composition, KAlSi3O8, the enthalpy of fusion in nearly the same as that of albite. In a comparison of nepheline and anorthite compared on the basis of eight oxygens, the DH fusion is 98 and 136 kJ/mol for these two compounds, respectively. This 35% difference reflects the significantly different structure of anorthite composition melt where two Al3þ cations are charge balanced with Ca2þ as compared with only one Naþ per Al3þ for nepheline composition. This different charge-balance environment has profound effects on the two melt structures. The Na2Al2Si2O8 mixture is a nearly ideal mixture of the SiO2 and NaAlO2 endmembers, whereas for CaAl2Si2O8, three different structural entities coexist and these do not seem to mix ideally (see Chapter 5; section 5.2.4, and Fig. 5.20). This latter structural environment, therefore, leads to a much greater DH fusion than the nearly ideal Na2Al2Si2O8 melt structure. Furthermore, as also seen in Fig. 4.15, the entropy of fusion for other melt compositions along the SiO2eNaAlO2 join is considerably less than for other compositions along the SiO2eCaAl2O4 join (see also Ryerson, 1985, for a discussion of thermodynamic implications of such melt structural features). This difference also results in greater structural disorder in melts along the SiO2eCaAl2O4 compared with SiO2eNaAlO2 (and SiO2eKAlO2) melts (see also Lee and Stebbins, 1999, 2000). The electronic properties of the metal cation, M, that serve to charge-balance tetrahedrally coordinated Al3þ in silicate melts affect the extent to which an (Al,Si)eO bond length deviates from an ideal length. This deviation was denoted D(TO) by Navrotsky et al. (1985). As illustrated in Fig. 4.16, the D(TO)-value increases with increasingly electronegative M-cation. It also seems reasonable to conclude, therefore, that extent of disorder in the melt would increase with increasing D(TO). Such a disorder increase would lead to enhanced DS and DH of melting and crystallization. Although such data are limited, Navrotsky et al. (1985) observed that the enthalpy of vitrification of glass compositionally along meta-aluminosilicate joins such as SiO2eMnþ1/nAlO2 joins is indeed positively, in fact, nearly linearly, correlated with (DTO) when calculated on the basis of two oxygen (as in SiO2; Fig. 4.16). The enthalpy of vitrification is not enthalpy of melting as this requires addition of temperature-dependent heat capacity terms of the glass and melt as well as that of the glass transition and temperature-dependent enthalpy of the crystalline material, but does, nevertheless offer a sense of how energetics of melting can be related to the nature of the metal cation(s) required for chargebalance of tetrahedrally coordinated Al3þ in system. þ

4.2.2.4.1 Fusion of peralkaline aluminosilicates While the existing thermochemical data for melting of aluminosilicate systems offer information on the effect on enthalpy and entropy change during melting of essentially fully polymerized aluminosilicate compositions along SiO2eMnþ1/nAlO2 joins, those data offer limited insight into the energetics of melting of peralkaline aluminosilicates. This latter issue is important because essentially all magmatic rocks (with the exception of a few rhyolitic compositions) are peralkaline aluminosilicates (Fig. 4.17). The heat capacity of peralkaline Al-bearing silicate melts depends on the (Na þ K)/Al and Al/(Al þ Si) (Bouhifd et al., 1998; Falenty and Webb, 2010). Such compositional changes also cause Qn-species equilibria such as Eq. (4.4) to shifts to the right because essentially all the Al3þ substitutes for Si4þ in Q4 structural units (Merzbacher et al., 1991; Mysen et al., 1981, 2003). This shift leads to increased structural disorder and, therefore, increased melt entropy and heat capacity. Moreover, from

4.3 Heat content, heat capacity, and entropy of silicate melts and magma

233

25

20

15

10

5

0 0

0.01

0.02

0.03

0.04

0.05

0.06

FIGURE 4.16 Relationship between the deviation of the T-O bond length, D(TO), and enthalpy of devitrification as a function of electronic properties of the alkali and peralkaline earth metal serving to charge balance Al3þ in the T-O bond. Modified from Navrotsky et al. (1985).

a liquidus phase equilibrium standpoint, this structural change enhances the liquidus volume of nepheline (Mysen and Richet, 2019, Chapter 8). It is tempting to suggest, therefore, that increasing peralkalinity [(Na þ K)/Al] and Al/(Al þ Si) of peralkaline melts would lead to enhanced entropy of fusion (more disordered structure of the melt), but likely decreased enthalpy of fusion because of the decreased (Si,Al)eO bond strength compared with that of SieO bonds. Unfortunately, such experimental data are not yet available. Further discussion of this important circumstances needs to await such experimental data.

4.3 Heat content, heat capacity, and entropy of silicate melts and magma The heat content of silicate melts, including magmatic liquids, is the sum of the heat content of the crystalline material, Hxtal, the heat of fusion, DH fusion, and heat content of the melt to the temperature of interest, Hmelt: H total ¼ Hxtal þ DH fusion þ Hmelt :

(4.5)

234

Chapter 4 Energetics of melts and melting in magmatic systems

SiO2

gm Rang ac eo om f po sit io

10

30

ma

40 50

60 70 80

90

20

80

meta-aluminous

Definition of peraluminous, meta-aluminous and peralkaline aluminosilicate melts in terms of SiO2, Al2O3, and Mn þ On/2 endmembers, where M is alkali metals and alkaline earths. Also shown is the range of most natural magma compositions within the triangle.

ns

FIGURE 4.17

peralkaline

70 60 50 40 30

peraluminous20

90

10 10

Mn+On/2

20 30 40 50 60

70

Mn+AlnO2n

80 90

Al2O3

The illustration in Fig. 4.12 shows why the heat of fusion should be defined at a specific temperature. The slopes of the enthalpy curves for crystals and melts differ so that the difference between the two curves, which is the heat of fusion, also becomes temperature dependent. The heat capacity, Cp, is related the heat content as: Cp ¼ Htot =T:

(4.6)

Temperature-induced structural changes seen in molten silicates (and magmatic liquids) are referred to as configurational changes. The configurational heat capacity, Cpconfig , is an expression of the energy needed to achieve such changes. The extent of these configurational changes is expressed by the configurational entropy, Sconfig, which is related to Cpconfig as: Sconf ¼

Cpconfig

dT: (4.7) T It is generally assumed that the heat capacity difference between glass and melt at the glass transition temperature, Tg is the configurational heat capacity, Cpconfig (see also section 5.1 of Chapter 5 for further discussion of the glass transition). At higher temperatures, the configurational heat capacity of melts often, but not always, does not vary significantly with increasing temperature (see sections (4.2.3)e(4.2.5) below). At temperatures below the glass transition, the contributions to the heat capacity are vibrational and increases with increasing temperature until it approaches the so-called

4.3 Heat content, heat capacity, and entropy of silicate melts and magma

235

Dulong and Petit limit (3R/g atom; see also Fig. 4.18 and Richet and Bottinga, 1995, for example). The configurational heat capacity, therefore, can be expressed approximately as: Cpconfig wCpmelt  3R:

(4.8)

Configurational properties such as entropy and heat capacity can be determined with calorimetric methods such as discussed in the premelting section above, for example. A second method relies on linkage between configurational properties and transport properties such as viscosity (Adam and Gibbs, 1965; Richet, 1984): Sconfig ¼

Be : Tðlog h  Ae Þ

(4.9)

In Eq. (4.9), h is melt viscosity, and Ae and Be are fitting parameters that relate to the configuration transformations (Toplis, 1998) and T is temperature (kelvin). In a comparison of configurational entropy obtained calorimetrically and from viscous behavior, Richet and Bottinga (1985) reported very good agreement (Fig. 4.19). A third method with which to determine configurational properties relies on knowledge of the melt structure as a function of temperature and composition (Mysen, 1995; Stebbins, 2008). In this method, the configurational entropy is divided into topological and mixing entropy, Stop and Smix, so that the configurational entropy is: Sconfig ¼ Stop þ Smix :

(4.10)

For equilibria among Q -species such as summarized in Eq. (4.4) for n ¼ 3, which is the typical situation for most magmatic liquids (Mysen, 1987), it was found that in terms of heat capacity contributions to the configurational heat capacity, the mixing term only provides between 25% and 30% of the total (Stebbins, 2008). n

FIGURE 4.18

40

Heat capacity, Cp (J/g atom K), of various compositions both Al-free and Al-bearing as well as a Na-silicate composition with 25 mol % TiO2 as a function of temperature. Also shown are the ranges of glass and melt as well as the glass transition, which appears as vertical lines for the various composition. The DuLong-Petit limit is shown as a horizontal dashed line.

35

30

25

DuLong-Petit limit

20

15 300

600

Modified from Richet and Bottinga (1995).

melt

glass

900

1200

Temperature, K

1500

1800

236

Chapter 4 Energetics of melts and melting in magmatic systems

FIGURE 4.19

60

Modified from Richet and Bottinga (1985).

Mg3Al2Si3O12

50

Scal, J/mol K

Comparison of entropy values obtained calorimetrically, Scal, and from viscosity [eqn. 4.9], Svis, of various melt compositions as indicated on diagram. The 1:1 relationship is shown. as a dashed line.

40

CaAl2Si2O8 NaAlSi3O8

30 CaMgSi2O6

KAlSi3O8

20 MgSiO3

10 CaSiO 3 0 0

10

20

30

40

50

60

Svis, J/mol K One way to address this deficiency could be determine the configurational heat capacity contribution from each of the Qn-species. This can be done by calibrating the configurational heat capacity contribution from each of the Qn-species with the calorimetrically determined configurational heat capacity in melts along metal oxide-silica joins. From the resultant heat capacity of individual Q  species, Cpconfig Qi , a summation of the type Cpconfig ¼

i X i¼1

  XQi Cpconfig Qi ;

(4.11)

would yield total configurational heat capacity of the melt. A comparison with the resultant configurational heat capacity and measured heat capacity in melt along the Li2OeSiO2, Na2OeSiO2, and K2OeSiO2 join shows how well this procedure works (Fig. 4.20). An alternative, more recent approach to this issue relied on estimating the value of the enthalpy change for Eq. (4.4) such as for disilicate melt, M2Si2O5 (M ¼ alkali metal), as an example (Stebbins, 2008). With n ¼ 3, Eq. (4.4) becomes: 2Q3 ¼ Q2 þ Q4 .

(4.12)

For this reaction, the equilibrium constant, K, is XQ2 • XQ4 K¼  2 : XQ3

(4.13)

Configurational heat capacity, calculated, J/mol K

4.3 Heat content, heat capacity, and entropy of silicate melts and magma

237

FIGURE 4.20 Comparison of configurational heat capacity values obtained from Eq. (4.11) (Mysen, 1995) compared with configurational heat capacity for the same binary metal oxidesilica melt compositions as reported in the summary by Richet and Bottinga (1986).

14

Modified from Mysen (1995).

12

1:1

10

K2O-SiO2 Na2O-SiO2 Li2O-SiO2

8 8 16 10 12 14 Configurational heat capacity, observed, J/mol K

The enthalpy change for Eq. (4.12), then, is:   DS þ RTln K ; DH¼  T

(4.14)

where K is from Eq. (4.13). The DH can then be extracted from the slope of a plot of ln K versus 1/T. From the temperature-dependence of Eq. (4.12), determined in-situ at temperatures above the glass transition, the DH decreases from about 30 kJ/mol for M ¼ K to slightly above 0 for M ¼ Li. For M ¼ Na, the DH is near 20 kJ/mol (Mysen, 1997). As can be seen for M ¼ Na as in Na2Si2O5, for example (Fig. 4.21), the calorimetric value for Cpconfig is 14.4 K J/K gfw (gram formula weight; see Richet, 1984). However, for a value of DH ¼ 20 kJ/mol at the glass transition for Na2Si2O5, a Cp-value of only near 2.5 J/mol gfw is the result. Nearly DH ¼ 50 kJ/mol for equilibrium (4.12) is needed to reach the measured configurational heat capacity (14.4 K J/K gfw) from mixing of the Qn-species alone. This is obviously not the situation. It follows, therefore, that there must a major contribution to Cpconfig from topological heat capacity. Of course, if mol fractions in Eq. (4.13) were replaced by activities of the Q-species, this problem might be reduced. Activity-composition relations in silicate melts will be discussed in section 4.3.

4.3.1 Heat capacity and entropy of magmatic liquids The earliest attempts to determine heat capacity and enthalpy of magmatic liquids were reported as early as about 130 years ago (Roberts-Austen and Ru¨cker, 1891; Barus, 1893). An example of the results of those early studies shows a significant discontinuity in the mean heat capacity of basalt glass

238

Chapter 4 Energetics of melts and melting in magmatic systems

20

Configurational heat capacity, Cpconfig ,J/mol K

Tg (glass transition temperature)

15

50 kJ/mol Cp (across glass transition)

10

40 kJ/mol

30 kJ/mol

5

20 kJ/mol 10 kJ/mol 0

400

800

1200 Temperature, K

1600

2000

FIGURE 4.21 Relationship between configurational heat capacity, Cpconfig , temperature, and enthalpy change for equilibrium (4.12). Also indicated in the heat capacity change across the glass transition, DCp, for Na2Si2O5 composition melt. See also text for discussion. Modified from Stebbins (2008).

in the 800e900 C temperature range (Fig. 4.22). The authors did not address this change, but it seems likely this is a glass-to-supercooled melt transformation because this temperature is several hundred degrees lower than the solidus temperature of basalt at ambient pressure (see also Chapter 1). That concern notwithstanding, in a much more recent comparison of experimental data (Fig. 4.11B; see also Bouhifd et al., 2007) it can be seen how those early data (Roberts-Austen and Ru¨cker, 1891; Barus, 1893) compare with results obtained by modern methods (drop calorimetry was employed to temperatures as high as 1800 K by Bouhifd et al., 2007). From data such as in Fig. 4.11B, the heat capacity, Cp, was derived from the expression5: Cp ¼ a þ bT þ c=T 2 þ d=T 0:5 ;

(4.14)

where the temperature, T, is in kelvin. The Cp-data (Fig. 4.23) are compared with the results of Lindroth and Krawza (1971) as well as results from modeling using the method by Berman and Brown (1985) and Richet (1987) together with results from calculations using the simple expression: X Cp ¼ Xi Cp ðmineralÞ; (4.15) 5

The coefficients for the basalt in this study can be found in the original paper (Bouhifhd et al., 2007).

4.3 Heat content, heat capacity, and entropy of silicate melts and magma

FIGURE 4.22

1.3

Mean heat capacity, J/mol K

239

Mean heat capacity of a basalt composition as a function of temperature. The starting materials probably is a glass although this does not appear clear from the original text (RobertsAusten and Ru¨cker, 1891). The discontinuity near 800 C then likely would reflect the material crossing the glass transition.

1.2

1.1

1.0

Data from Roberts-Austen and Ru¨cker (1891).

0.9

0.8

Configurational heat capacity, Cpconfig ,J/g K

400

600

800 Temperature, ˚C

1000

1200

FIGURE 4.23

1.25 1.20 1.15 1.10

Lin

1.05 1.00 0.95

B

0.90 0.85 400

a erm

na

nd

B

row

Ri

500

ch

t dro

n(

et

19

ha

) 85

8 (19

7)

600

nd

mo

K

raw

de

mo

za

(19

71

Configurational heat capacity of crystalline basalt (solid dots from Bouhifd et al., 2007) compared with data from other sources as indicated on panel.

)

eqn. (4.15)

l

Modified from Bouhifd et al. (2007).

de

l

700

800 900 Temperature, K

1000

1100

1200

where Cp ðmineralÞ is the heat capacity of the minerals constituting the basalt and Xi is the mol fraction of the individual minerals (Bouhifd et al., 2007). Mineral data from Richet and Fiquet (1991) and Gillet et al. (1991) were used for this purpose. As can be seen, the results of the calculations with the Berman and Brown (1985) and Richet (1987) models are within 1% of the experimental values while the results using Eq. (4.15) deviate more and more from the experimental data the higher the temperature. In a comparison of the mean heat capacity of basalt glass and melt from Bouhifd et al. (2007) and heat capacity data for andesite and rhyolite glass and melt from Neuville et al. (1993), it is clear that the mean heat capacity of rhyolite and andesite glass at the glass transition temperature is greater than that of basalt (Fig. 4.24). Those data also indicate that the heat capacity change across the glass transition to supercooled liquid is greater for basalt than andesite and greater for andesite than for rhyolite. In other words, the configurational heat capacity, Cpconfig , of basalt melt exceeds that of andesite melt, which exceeds that of rhyolite melt.

mean heat capacity, Cm ,J/g K

1.30

A

1.20

1.10 1.00 0.90

basalt

Tg

mean heat capacity, Cm ,J/g atom K

0.80 400

600

1000 1200 Temperature, K

1400

1600

1800

28 B 26 24 22 20 Tg

18 16 400

mean heat capacity, Cm ,J/g atom K

800

25

600

800

andesite

1000 1200 Temperature, K

1400

1600

1800

C

24 23 22 21 20 Tg

19

rhyolite

18 17

400

600

800

1000 1200 Temperature, K

1400

1600

1800

FIGURE 4.24 Mean heat capacity of basalt (A), andesite (B), and rhyolite (C) as a function of temperature. The temperature of the glass transition indicated with arrow and marked Tg Modified from Bouhifd et al. (2007) and Neuville et al. (1993).

4.3 Heat content, heat capacity, and entropy of silicate melts and magma

241

It is also notable that there is a positive temperature dependence of Cpconfig for all three types of  . basalt  . andesite magma. The rate of change with temperature is vCpconfig vT > vCpconfig vT > . rhyolite  (Neuville et al., 1993; Bouhifd et al., 2007). The positive temperature depenvCpconfig vT dence likely reflects a combination of structural changes with temperature perhaps driven by the presence of iron (Lange and Navrotsky, 1992; Tangeman and Lange, 1998), TiO2, and Al2O3 (Tangeman and Lange, 1998) in the magmatic liquids. As will also be discussed in more detail in sections 4.3.3 and 4.3.4, the presence of these oxides all results in changes in configurational heat capacityof melts . with temperature. The Fe2O3 and TiO2 have the greatest effects. The reason why the slopes, vCpconfig

vT , decrease the more felsic the magma likely is because the Fe2O3 and TiO2

contents of magmatic liquids decrease the more felsic the magma (http://earthchem.org).

4.3.1.1 Volatiles, heat capacity, and entropy of magmatic liquids Volatiles such as H2O and halogens can have profound effects on melt structure and melt properties (see Chapters 7 and 8). It is not a surprise, therefore, that thermodynamic properties of magmatic liquids also vary significantly whenever such volatiles are dissolved in the melts (Bouhifd et al., 2006, 2013; Whittington et al., 2009; Di Genova et al., 2014; Robert et al., 2014, 2015). Bouhifd et al. (2006) found, for example, that the glass transition temperature decreased and the magnitude of the heat capacity change across the glass transition increased with increasing H2O content of the magma (Fig. 4.25; see also Bouhifd et al., 2006; Di Genova et al., 2014). Moreover, the effect of dissolved H2O

100

A

B

0.0

5.0

90 Heat capacity, Cp, J/g atom K

Heat capacity, Cp, J/g atom K

100

0.5

2.2

80 70 60 50

0.0

90 3.0

1.5

80 70 60 50 granite

phonolite

40

40 400

600

800

Temperature, K

1000

400

600

800

1000

Temperature, K

FIGURE 4.25 Heat capacity, Cp, of hydrous phonolite (A) a granite (B) glass and melt as a function of temperature with different H2O contents as indicated on individual curves as numbers. Modified from Bouhifd et al. (2006).

242

Chapter 4 Energetics of melts and melting in magmatic systems

on the heat capacity change across the glass transition interval is greater for more mafic magmas such as phonolite compared with the more felsic granite composition magma (Fig. 4.25A, B). It is also notable that whereas for dry magma compositions the heat capacity of basalt melt is the greatest (96.6 J/mol K) and the lowest for trachyte and pantellerite magma (91.6 and 90.5 J/mol K, respectively), with increasing H2O concentration in the magma, the heat capacity values for the different magma types approach one another. With more than 10 mol% H2O, the Cp-values of the various magma compositions examined by Di Genova et al. (2014) (basalt, latite, trachyte, and pantellerite) differ somewhat, although no specific compositional effect can be discerned in the data (Fig. 4.26). Presumably, this evolution reflects the fact that the structural features of hydrous magma governing heat capacity become increasingly similar the more H2O-rich the magma. The partial molar heat capacity of H2O may als be extracted from data such as shown in Figs. 4.25 and 4.26 (Bouhifd et al., 2006): Cp ðliquidÞ ¼ XH2O CpH2O þ ð1  XH2O ÞCpliquid ðanhydrousÞ:

(4.16)

From this expression and the measured heat capacities, the heat capacity of hydrous magma ranges between about 25 J/mol K for latite magma to about 55 J/mol K for pantellerite magma (Di Genova et al., 2014). By adding other volatiles such as, for example, fluorine, to basaltic liquids, the effects on heat capacity on an equimolar basis is even greater than the effect of H2O (Fig. 4.27; see also Robert et al., 2015). This might not be surprising in light of the complex solution mechanism of fluorine in silicate melts compared with that of H2O, mechanisms that vary with both fluorine concentration and magma composition (Mysen et al., 2004).

Heat capacity of melt, Cp(melt), J/mol K

ba

sa

lt m

elt

lat

ite

me lt pantellerite melt

trachy te

melt

H2O content of melt, mol % FIGURE 4.26 Heat capacity of various natural melts, as indicated on diagram, as a function of their H2O content. Modified from Di Genova et al. (2014).

4.3 Heat content, heat capacity, and entropy of silicate melts and magma

243

35

Heat capacity of volatile-free basalt glass and melt as a function of temperature compared with the same composition with H2O and F at concentrations indicated on individual curves.

volatile

30

2.02 % F

FIGURE 4.27

-free

40

Modified from Robert et al. (2015).

25

20

15 400

600

800 Temperature, K

1000

1100

It is evident from this discussion of entropy and heat capacity in magmatic liquids that there are major changes with magma composition and type and proportion of volatiles in solution. It is, however, less clear how other compositional variables affect the thermodynamic properties. To reach such an understanding, it is necessary to isolate the effects of those individual components. This can be done only by examination of the behavior in chemically simple systems wherein only one variable can be changed at the time. A summary of some of the most important variations thus identified will be addressed next.

4.3.2 Heat capacity, entropy, and silicate melt polymerization in metal oxideSiO2 systems Before addressing the behavior of entropy and heat capacity in simple binary systems, an important point made by Sugawara et al. (2011) is worth a comment. They noted that because even in metal oxide-SiO2 system where there is no stable liquid immiscibility above the liquidus, metastable immiscibility toward the SiO2-rich portion of the systems exists at lower temperatures (see Fig. 6.1 in Mysen and Richet 2019, for summary of those phase equilibrium data). Sugawara et al. (2011) also commented that when combining available thermochemical data from melts in the Na2OeSiO2 system, which shows such a metastable immiscibility, there is a strong tendency for deviation from a simple linear relationship between heat capacity and SiO2 content of the melts from experiments using differential scanning calorimeter. It was suggested that this deviation occurs because of separation of an SiO2-rich supercooled liquid during heating of the sample in the scanning calorimeter. This observation is worth remembering when discussing thermochemical data not only for Na2OeSiO2 melts, but also for other similar systems (where metastable phase separation takes place) such as Li2OeSiO2 (Kracek, 1930) and BaOeSiO2 (Eskola, 1922). In the K2OeSiO2 system, the metastable

244

Chapter 4 Energetics of melts and melting in magmatic systems

immiscibility gap exists only at temperatures below that of the glass transition (Kracek et al., 1937), so this potential complication in examination of high-temperature thermochemical data probably does not exist. Experimental assessment of effects of melt polymerization, NBO/T or NBO/Si,6 has been carried out in simple systems such as Rb2OeSiO2, K2OeSiO2, Na2OeSiO2, Li2OeSiO2, CaOeSiO2 SrOeSiO2, and BaOeSiO2 (Stebbins et al., 1984; Richet and Bottinga, 1980, 1985; Richet et al., 1984, 1991; Tequi et al., 1992; Knoche et al., 1994; Sugawara et al., 2011; see also Review by Richet and Neuville, 1992). By systematically changing the metal oxide/SiO2 ratio, the effect of NBO/Si on the thermodynamics of the melts and glasses can be extracted. By changing the metal cation, an understanding of possible effects of electronegativity of the metal cation on heat capacity and entropy can be obtained. The configurational entropy melts is always a positive function of temperature because of the relationship: Z T config Cp   config config vT; (4.17) S ðTÞ ¼ S Tg þ T Tg where T (kelvin) is the temperature of interest above the glass transition, Tg is the glass transition   temperature, Sconfig Tg is the configurational entropy at the glass transition temperature, and Cpconfig is the configurational heat capacity of the melt. As a result, whether or not Cpconfig depends on temperature, the configurational entropy is a positive function of temperature, resulting in relationships such as illustrated in Fig. 4.28. The configurational contribution to entropy, which does not vary in the glass (Fig. 4.28B), increases by about 10 J/mol K per 100K in melts (Richet and Bottinga, 1984, 1986). However, the configurational entropy contribution represents only about 10% of the total entropy of many silicate melts. The configurational heat capacity, Cpconfig , for several metal oxide-SiO2 melts is a linear function of composition as illustrated in Fig. 4.29A, for example (Richet and Neuville, 1992). Interestingly, however, the ratio of change of Cpconfig with SiO2 content increases the more electronegative the metal cation. This relationship may be the result of Eq. (4.12) shifting to the right with increasing electronegativity of the metal cation. This shift likely causes this increase because the configurational heat capacity of the individual Qn-species increases the more depolymerized the species (Mysen, 1995). We also note, though, that K2OeSiO2 melts are an exception to this simple behavior because vCpconfig = vT is positive and increases with increasing temperature (Fig. 4.29B). The vCpconfig =vT increases the higher the K2O/SiO2 ratio. To date, a melt structural explanation for this behavior of melts in the K2OeSiO2 system has not been offered.

6

NBO/T: Nonbridging oxygen per tetrahedrally coordinated cations (usually Si and Al). NBO/Si: Nonbridging oxygen per silicon. For metal oxide-SiO2 melts such as described in this section, the NBO/Si parameter will be used.

4.3 Heat content, heat capacity, and entropy of silicate melts and magma

Entropy, S, J/mol K

700

70 A

600

60

melt

500

B

50 crystal

400

40

glass

300

30

200

20

100

10

0

245

0

500

1000 1500 Temperature, K

2000

0 800

1000 1200 1400 Temperature, K

1600

FIGURE 4.28 Entropy and heat capacity of metasilicate crystals, glasses and melts. A. Entropy and configurational entropy of diopside (CaMgSi2O6) as a function of temperature. The glass transition temperature is indicated by arrow. Dashed line shows the entropy of diopside crystals with the double arrow marked DSfusion, showing the entropy of fusion of diopside at its melting temperature. B. Evolution of the configurational entropy of CaMgSi2O6 and Ca2Si2O6 glass and melt as a function of temperature. Modified from Richet and Neuville (1992).

25

25 A

B

CaO

1800 K

20

20

15

15

1200 K

BaO

10

5 40

10

50

60

70 80 mol %

90

100

5 40

50

60

70 80 mol %

90

100

FIGURE 4.29 Configurational heat capacity, Cpconfig , of various metal oxide - SiO2 melts as a function of their SiO2 content. A. For heat capacity of melts as indicated where the Cpconfig is a linear function of composition, B. Cpconfig of K2OeSiO2 melts at two different temperatures as indicated where Cpconfig depends nonlinearly on composition and temperature. Modified from Richet and Neuville (1992).

246

Chapter 4 Energetics of melts and melting in magmatic systems

For the melts where the Cpconfig is a linear function of the metal oxide/SiO2 ratio, partial molar heat   O and capacity of SiO2 and the metal oxide has been derived by solving for Cpconfig Mnþ 2=n Cpconfig ðSiO2 Þ with two linear equations of the type:     nþ O XM nþ O þ Cpconfig ðSiO2 Þ 1  XM nþ O ; Cpconfig ¼ Cpconfig M2=n 2=n

(4.18)

2=n

where the X-values are mol fractions. Obviously, contributions from K2O require more complex expressions. The same can be said for iron oxide, aluminum oxide, and titanium oxide contributions. Those contributions will be discussed next.

4.3.3 Heat capacity and entropy in Al-bearing systems Whether Al3þ substitutes for Si4þ in meta-aluminosilicates, peralkaline or peraluminous aluminosilicate melts and glasses has profoundly different effects of their thermochemical properties (Fig. 4.30). For alkali aluminosilicate melts, the configurational heat capacity reaches a minimum value at the meta-aluminosilicate compositions, whereas for alkaline earth aluminosilicate melts, the configurational heat capacity reaches a maximum (Fig. 4.30A; see also Webb, 2008, 2011). In fact, there is a systematic, and positively correlated, relationship between the Cpconfig at the

25 A

B

18

20

16

14 15 12 10 10

8

5 0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.5

1.0

1.5

2.0

2.5

3.0

FIGURE 4.30 Configurational heat capacity at the glass transition temperature of aluminosilicate melts A. As a function of the proportion of metal oxide, MxO, relative to Al2O3 for Naþ, Ba2þ, and Ca2þ. B. Value of configurational heat capacity at the glass transition temperature as a function of Z/r2 of the metal cation. Modified from Webb (2008, 2011).

4.3 Heat content, heat capacity, and entropy of silicate melts and magma

247

meta-aluminosilicate composition and the Z/r2 (electronegativity) of the metal cation (Fig. 4.30B). It is quite likely that this evolution is a reflection of the fact that the more electronegative the metal cation, the more similar is the energy of the M-O and AleO bonds in the melt. The heat capacity at the glass transition is close the Dulong-and-Petit limit of 3 Rg atom K. Because the Dulong and Petit limit is determined by the number of atoms in the formula unit, the composition dependences of Cpl and Cpconf are the same. For analogous melt compositions, Cpconfig increases in the order Mg > Ca > Na (Richet and Neuville, 1992). Moreover, for the Mg- and Cameta-aluminosilicate melts, the configurational heat capacity is essentially a linear function of Al/ (Al þ Si), whereas the Cpconfig for the SiO2eNaAlO2 melts is distinctly nonlinear with a near constant Cpconfig between SiO2 and Al/(Al þ Si)w0.25, before it increases rapidly with a further increase of Al/ (Al þ Si). These effects likely are because in alkaline earth aluminosilicates, two Al3þ cations are charge-compensated for each metal cation, whereas only one Al3þ is charge-compensated by the monovalent Naþ cation. There is, therefore, less flexibility and probably longer-range order in the alkaline earth aluminosilicate glasses and melts (Taylor and Brown, 1979a), thus leading to the linear relationship between Cpconfig and Al/(Al þ Si) for those compositions. Less experimental data exist for melt compositions away from the meta-aluminosilicate joins. Some data do, however, exist (Webb, 2008, 2011) so that, for example, for both alkali and alkaline earth peralkaline aluminosilicate melts, the configurational entropy decreases systematically with decreasing Al2O3 content (Fig. 4.31). The configurational heat capacity of aluminosilicate melts also has been examined as a function of temperature (Richet and Bottinga, 1984; Tangeman and Lange, 1998). There typically is a small temperature effect on Cpconfig in aluminosilicate melts. Notably, Richet and Bottinga (1984) reported a slight positive effect for melts along the SiO2eNaAlO2 join, whereas Tangeman and Lange (1998), in their experiments with peralkaline melts in the Na2OeAl2O3eSiO2 system, noticed a slight negative effect (Fig. 4.32). The latter effect may be a reflection of a temperature-dependent distribution of Al3þ among coexisting Qn-species in the melt (see Mysen, 1999), whereas the effect in SiO2eNaAlO2 melt probably reflect temperature-dependent Al-distribution among coexisting, 3-dimensionally interconnected structures (Neuville and Mysen, 1996). There is much less data in (Ca, Mg)OeAl2O3eSiO2 systems even though data in such a composition space are needed to describe the thermochemistry of andesitic and basaltic magma (Mysen and Richet, 2019, Chapter 18). It is possible, however, that because of the structure of melts in alkaline earth aluminosilicate systems appears to be less temperature sensitive (Marumo and Okuno, 1984), the thermochemical data probably also are.

4.3.4 Heat capacity and entropy in Fe- and Ti-bearing melt systems Thermochemical properties of Ti- and Fe-bearing silicate melts (and glasses) as a function of temperature often differ from other silicate and aluminosilicate compositions (see, for example, review by Richet and Bottinga (1986), and more recent review by Richet (2009). The behavior might relate to the observation that both Ti4þ and Fe3þ might occupy structural positions in melts somewhat different from other major element components. This difference includes, for example, clustering of the TiO4 and FeO4 tetrahedra in the silicate melt structure (see also Chapter 5 and Mysen and Richet (2019), Chapters 10 and 13 for reviews of those melt structural features).

248

Chapter 4 Energetics of melts and melting in magmatic systems

Configurational entropy, Sconfig, J/mol K

13 12 11 10 9 8 7 6 0.0

Ba Sr Ca Mg Na

0.1

0.2

0.3

0.4

0.5 0.6 n+ M 2/nO

0.7

0.8

0.9

1.0

Mn+2/nO+Al2O3 FIGURE 4.31 Configurational entropy, Sconfig, of various alkali and alkaline earth aluminosilicate melts as a function of proportion of metal oxide to alumina. Modified from Webb (2008, 2011).

Solution of TiO2 in alkali silicate melts and glasses results in unusual configurational entropy and heat capacity features (Richet and Bottinga, 1985; Lange and Navrotsky, 1993 Tangeman and Lange, 1998; Bouhifd et al., 1999, Roskosz et al., 2004). For the Na2O•2SiO2 composition, for example, the configurational heat capacity is independent of temperature, whereas for the same composition with w25 wt% TiO2 added, the Cpconfig decreases about 5%/100K although this rate of decrease slows down somewhat as the temperature increases. Similar relationships have been reported for K2O•2SiO2 (Richet and Bottinga, 1985) as well as more SiO2-rich alkali silicate melts (Tangeman and Lange, 1998; Bouhifd et al., 1999) and alkali aluminosilicate melts (Roskosz et al., 2004) (Fig. 4.33). Absent alumina, the Cp of the liquids decreases with increasing SiO2 content (Fig. 4.33B). The presence of Al2O3 a silicate melt does seem to cause a slight increase in the DCp and, therefore, Cpconfig , at the glass . transition. The vCpconfig vT of the melts also appears to become slightly more negative with increasing

4.3 Heat content, heat capacity, and entropy of silicate melts and magma

32

249

B

A

100

30

90 Cp=11.85 J/gfw K

28

80

26 70 24 60 22

1000

1200

1400 1600 Temperature, K

1800

300

400

500

600 700 Temperature, K

800

900

1000

FIGURE 4.32 Heat capacity, Cp, of various aluminosilicate glass and melts as a function of temperature. A. Heat capacity of meta-aluminosilicate glass and melts as indicated as a function of temperature (from Richet and Bottinga, 1984). B. Heat capacity of Na2O•2SiO2 þ 17.6 wt% Al2O3 added as a function of temperature. The heat capacity change across the glass transition is indicated on figure (data from Tangeman and Lange, 1998). Modified from Richet and Bottinga (1984); Tangeman and Lange (1998).

TiO2 concentration in alkali aluminosilicate melts (Fig. 4.33C; see also Roskosz et al., 2004). Interestingly, the configurational entropy of alkali aluminosilicate melts decreases with increasing TiO2 content (Fig. 4.33C). The behavior of the configurational properties with TiO2 added to alkali silicate melts likely reflects the structural behavior of Ti4þ in such melts. This behavior involves adjustments in TieO bond length as a function of temperature and probably also changes in the distribution of TiO4 clusters and possibly oxygen coordination in the melt (Dingwell, 1992; Mysen and Neuville, 1995; Farges, 1997; Reynard and Webb, 1998; Henderson et al., 2002). In alkali aluminosilicate melts, the possibility also exists that Al-titanate entities might form (Mysen and Neuville, 1995; Gan et al., 1996; Romano et al., 2000). Iron-bearing silicate melts also exhibit a distinctly temperature-dependent configurational heat capacity (Tangeman and Lange, 1998; Chevrel et al., 2013). Compared with Fe-free alkali silicates, the DCp at the glass transition is considerably greater in the presence of Fe (Fig. 4.34). Moreover, compared with TiO2, the effect of Fe2O3 on the vCpconfig =vT of alkali silicate melts is not as distinct (Figs. 4.33 and 4.34). This difference likely reflects both changes in clustering of FeO4 and TiO4 as well as the fact that Ti4þ may also undergo coordination changes with temperature, whereas there is no evidence of temperature-dependent coordination changes in Fe-bearing alkali silicate melts. It is notable, though, that the DCp at the glass transition increases systematically with increasing extent of melt depolymerization (increasing NBO/T), an increase that is more rapid the more polymerized (smaller NBO/T-values) the melt (Fig. 4.35). The Fe3O3, which comprises >99% of the iron oxide in the alkali silicate melts in the studies on configuration properties discussed here, in some ways behaves like Al2O3. This is evident, for

110 A 100 90 80 70 60 50 400 110

600 800 1000 Temperature, K

1200

B

105

12

100

180

00

K

0K

95 12

00

K

90 180

0K

85 80 40

50

60

70

80

90

100

12 C

11

10

9

8

0

2

4

6

8

10

FIGURE 4.33 Heat capacity and entropy of TiO2-containing alkali silicate and alkali aluminosilicate glasses and melts. A. Effect of temperature on the heat capacity, Cp, of Na-aluminosilicate melts Ti-free (0%) and with 10% TiO2 as a function of temperature (Roskosz et al., 2004). B. Effect of temperature and SiO2 content of heat capacity of liquids in the systems SiO2-xK2O-(1-x)TiO2 and SiO2-xNa2O-(1-x)TiO2 (Bouhifd et al., 1999). C. Effect of TiO2 content of entropy of melts at 900K (Bouhifd et al., 1999). Modified after Bouhifd et al. (1999); Roskosz et al. (2004).

4.3 Heat content, heat capacity, and entropy of silicate melts and magma

251

FIGURE 4.34

110

Effect of temperature and iron content on heat capacity of Na silicate melts with and without Fe2O3 (composition indicated on individual curves).

100 90 80

Modified after Tangeman and Lange (1998).

70 60

Configuarationl heat capacity, Cpconfig, J/gfw K

50 300

400

500

600 700 Temperature, K

800

900

1000

FIGURE 4.35 Configurational heat capacity, Cconfig , at the p glass transition of melts long the Na2OeSiO2 join as a function of the NBO/T of the melt.

16

Data from Tangeman and Lange (1998).

14 12 10 0.0

0.5

1.0 1.5 NBO/T of melt

2.0

example, when comparing the Cconfig of Na2OeFe2O3eSiO2 melts with Cconfig of Na2OeAl2O3eSiO2 p p as a function of Na/(Na þ Al) and Na/(Na þ Fe) (Fig. 4.36; see also Falenty and Webb, 2010). In both systems, there is a Cconfig minimum near the composition where Na:Fe3þ and Na:Al3þ are 1:1. This p minimum may reflect the fact that in both systems at the composition of these minima, all Naþ, Al3þ, and Fe3þ are bound in NaAlO2 and NaFeO2 complexes, thus minimizing the structural disorder in the melts. Such a minimization would lead a minimum in configurational entropy and, therefore, configurational heat capacity as shown in Fig. 4.36. The thermochemical behavior illustrated in Figs. 4.34e4.36 probably does not reflect changes in the Fe3þ/Fe2þ of the melt as a function of composition and temperature because for melts of these compositions and in this temperature range, the iron is for all practical purposes is completely oxidized to Fe2O3 (Mysen et al., 1984; Mysen and Virgo, 1989). Furthermore, there is no evidence for Fe3þ undergoing coordination transformation under the conditions studied. It is more likely, therefore, that the principal cause of the temperature dependent Cpconfig is changing FeO4 cluster behavior in the melt as a function of temperature.

Chapter 4 Energetics of melts and melting in magmatic systems

14 13 O3 e2 -F eO iO 2 -F 3-S O 2O Na Al 2

Configuarationl heat capacity,Cpconfig, J/mol K

252

12 11 10

Na 2O Al2 O -FeO3 -S iO2

9

O3 e2 F O- O 2 Fe -Si O- 2O 3 2 Na Al

-FeO Na 2O SiO 2 Al 2O 3

8 7

0.40

0.45

0.50 0.55 0.60 Na2O+FeO Na2O+FeO+Fe2O3+Al2O3

FIGURE 4.36 Effect on the configurational heat capacity, Cpconfig , of the abundance of network-modifying cations as oxide, Na2O and FeO, relative to the sum of the abundance of those oxides plus Fe2O3þAl2O3 for melts in the systems Na2OeFeOeAl2O3eSiO2 (open circles) and Na2OeFeOeAl2O3eFe2O3eAl2O3eSiO2 Na2OeFeOeAl2O3eSiO2 (closed circles). Modified after Falenty and Webb (2010).

4.3.5 Thermodynamics of mixing and solution When applying thermodynamic data from compositionally simple melt systems to natural magmatic liquids as a function of composition, temperature and pressure, it is necessary to take into account thermal affects associated with mixing of simple system components. Closely associated with this problem is the thermodynamics of solution. Such mixing can have profound effects on the evolution of magmatic systems not only because of addition of components, but because thermal effects of mixing often leads to crystallization trends that differ from what may be expected simply by numerical combination of the components (see, for example, Yoder, 1976). Among the few studies examining the thermodynamics of mixing of natural magmatic liquids, the focus has been on how one might relate the activity of SiO2 to rock type (Carmichael et al., 1970; Ghiorso et al., 1983; Linard et al., 2008). Activities of geochemically important trace and minor elements (Hirschmann and Ghiorso, 1994) as well as Fe2þ and Fe3þ also have been reported (Doyle, 1988; Gaillard et al., 2003). More recently, software packages (e.g., MELTS and pMELTS; see Ghiorso and Sack, 1995; Ghiorso and Hirschmann, 2002; Ghiorso et al., 2002) to compute thermodynamic properties, phase relations, and element distribution among minerals and melts have been provided. Results of MELTS-based calculations also have been employed for geothermometry and geobarometry (Gualda and Ghiorso, 2014; Pamukcu et al., 2015).

4.3 Heat content, heat capacity, and entropy of silicate melts and magma

253

4.3.5.1 Activity-composition relationships Characterization of activity-composition relationships is, of course, of particular importance in understanding the behavior of magmatic liquids in the Earth’s interior as such information aids in describing melting and crystallization relationships and element partitioning, for example. In recognition of this, an early study by Carmichael et al. (1970) sought to characterize specific igneous rock types, in particular those formed by partial melting of a peridotite mantle, in terms of activity of SiO2. They proposed that the reaction: 2MgSiO3 ¼ Mg2 SiO4 þ SiO2 ;

(4.19)

for example, would be appropriate to define the activity of SiO2, aSiO2, of the system via the expression: ln amelt SiO2 ¼

DG0 ; RT

(4.20)

where Carmichael et al. (1970) chose SiO2 glass as the standard state (DG0). Carmichael et al. (1970) noted that a change of the aSiO2 from 100.15 to 100.10 could correspond to an increase in SiO2 concentration from 48 to 75 wt% SiO2 because of the nonideal nature of the solid solution of the magmatic liquids. A number of other SiO2 activity buffer assemblages have been considered as potentially useful in specific circumstances (Fig. 4.37). This collection of equilibria includes one with which the oxygen fugacity could be defined: 2Fe3 O4 þ 3SiO2 ¼ 3Fe2 SiO4 þ O2 .

(4.21)

In an expansion of the concept discussed above, Ghiorso et al. (1983) used regular solution modeling to calculate the aSiO2 for a number of magmatic liquids (Fig. 4.37B). It is, perhaps also worth noting that this early treatment provided the groundwork for the much more comprehensive subsequent treatment known as MELTS (Ghiorso and Sack, 1995; Ghirso et al., 2002) with which the melting and crystallization behavior of a wide array of igneous rocks can be calculated. To overcome limitations caused by the compositional complexity of magmatic liquids, it is necessary to break the systems down to simpler environment within which specific compositional, temperature, and pressure variables could be established. How this could be carried out was originally indicated in a survey how of liquidus phase boundaries between minerals defining activities of individual components could be established. An early indication of the feasibility of such an approach was that of Kushiro (1975) who reviewed the compositional space of liquidus boundaries between mineral phases such as olivine and orthopyroxene, the equilibrium between which defines aSiO2, for example. Eq. (4.19) is an example of this approach. Here, it can be seen how the liquidus boundary shifts between the MgO and SiO2 endmembers (forsterite/orthopyroxene in Fig. 4.38A; orthopyroxene/ cristobalite in Fig. 4.38B) as a function of the added third component. For components with a positive slope as a function of increased concentration, the activity coefficient of SiO2 decreases as the component concentration increases, whereas the opposite trend is the case for the oxides leading to negative slope (Fig. 4.38A, B; see also Kushiro, 1975). The treatment summarized in Fig. 4.38 was expanded upon by Ryerson (1985). He employed the shifts of liquidus volumes of SiO2 polymorphs (Fig. 4.39A and B) to compute activity of SiO2 in various binary metal oxide-SiO2 and ternary aluminosilicate systems (Fig. 4.39C and D). It is evident

254

Chapter 4 Energetics of melts and melting in magmatic systems

0.0

Temperature, 104/T (K-1) 6 7

5 0.0

quartz tholeiite

8

tholeiite tite ensta rite forste

andesite

alkali olivine basalt

l ine sp lase ric pe

nephelinite

-2.0 ite

ton llas e it n lar

wo

Activity of SiO2, log aSiO2

-1.0 Activity of SiO2, log aSiO2

0.1 MPa

tholeiite

olivine

koma

tiite

basalt

0.5 GPa

-0.5 leucit e basa nite

1GPa

1.5 GPa

uga

ndit

e

2 GPa

3 GPa

-1.0

-3.0

4 GPa 5 GPa

A 600

B 700

800 900 1000 1100 1200 Temperature, ˚C

1600

1200 Temperature, ˚C

1000

FIGURE 4.37 Relationships between activity of SiO2, aSiO2, and temperature for A. Several basaltic magmatic liquids, and B. For a number of magmatic liquids as a function of temperature and pressure. Modified after Carmichael et al. (1970); Ghiorso et al. (1983).

from the liquidus data in Fig. 4.39A, for example, that at any temperature, the SiO2 liquidus volume expands toward the metal oxide endmember the more electronegative the metal cation. Furthermore, the same trend can be seen for the metal cation employed to charge-balance Al3þ in the aluminate complexes (Fig. 4.39B). For the decomposition of MgSiO3 to Mg2SiO4 and SiO2 polymorph stability field, the activity coefficient of SiO2 of the melt, gSiO2, along the enstatite/forsterite liquidus boundary is summarized in Fig. 4.39C for the effect of various oxides. The effect of aluminate addition (Fig. 4.39B) is shown in Fig. 4.39D. The results of these calculations (Fig. 4.39C, D) indicate that the activity coefficient of SiO2 in the silicate melts increases systematically with increasing electronegativity of the added metal cation from Kþ to P5þ (Fig. 4.39C) or with increasing electronegativity of the cation that forms the charge balance of Al3þ in the aluminate complex (Fig. 4.39D).

4.3 Heat content, heat capacity, and entropy of silicate melts and magma

0.5

A Al2O3 FeO

TiO2

B

CaO Al2O3

mole number

K2O

0.3

0.2

K2O

0.2

forsterite

0 40

protoenstatite

MgSiO3

80 60 70 SiO2 concentration, mol %

0 50

protoenstatite

0.1 0.1

FeO

Na2O

0.3

CaO

0.4 mole number

TiO2

Na2O

255

cristobalite

60 80 70 SiO2 concentration, mol %

90

FIGURE 4.38 Relationship between SiO2 concentration and concentration of various oxides affecting A. The SiO2 concentration of the forsterite/protoenstatite liquidus boundary and B. The protoenstatite/cristobalite liquidus boundary. Modified from Kushiro (1975).

Results of a number of studies, relying on both experimentally determined data (from calorimetry) and various modeling efforts, have been reported for melts along binary Mn2/nþeSiO2 joins for M ¼ Ba, Sr, Fe, Co, Ca, Mg, Na, and K (Wu et al., 1993a, b; Jung et al., 2007; Romero-Serano et al., 2010; Sugawara et al., 2009, 2011). In all cases, the activities of SiO2 and the metal oxide are nonlinear functions of the M/Si ratio as illustrated, for example, for CaOeSiO2, FeOeSiO2 and K2OeSiO2 melts in Fig. 4.40. However, the more electropositive the metal cation, the smaller is the deviation from linear relation between aSiO2 and melt composition. This feature is evident, for example, in the comparison between CaOeSiO2 and K2OeSiO2 melt data in Fig. 4.40B and C. Relationships between the activity coefficient of SiO2, gSiO2, and the ionization potential of the metal cation, Z/r2, for each value of electrical charge, Z, is, in fact, a nearly linear function of Z/r2 (Fig. 4.40D). The activity of SiO2 in any of these melt systems also increases and that of the metal oxide decreases with increasing temperature (Fig. 4.41; see also Sugawara et al., 2011). The activity-composition data (Figs. 4.40 and 4.41) in the past were rationalized in terms of silicate polymerization equilibria (Hess, 1975; Gaskell, 1977; Ottonello, 2001). However, more recent structural information of silicate melt has led to the conclusion that equilibria among Qn-species of the kind indicated in Eq. (4.4) is a more accurate representation of silicate, aluminosilicate melt, and magmatic liquid structure (Virgo et al., 1980; Schramm et al., 1984; Stebbins, 1987; Maekawa et al., 1991; Buckermann et al., 1992; Mysen, 1987, 1997, 1999). It is likely, therefore, that to a considerable extent the activity-composition relations such as illustrated in Figs. 4.39e4.41 could be better represented by mixing Qn-species.

Chapter 4 Energetics of melts and melting in magmatic systems

2000

Temperature, K

1800 1600 1400 1200

A

° ° MgO ° ° ° ° ° °° ° ° ° °° ° ° ° CaO ° ° ° ° ° SrO ° BaO ° ° ° ° ° ° ° ° ° ° ° ° ° Li 2O ° ° ° Na2O ° K° 2O

1000 50

60

70

80

90

B 2000

Temperature, K

256

1800

Ca0.5AlO2

1600

1400

100

NaAlO2

70

80 90 mol % SiO2

0.6 0.4

C

°

MgO

°° CaO

°° ° ° ° BaO

SrO

° °° ° Li 2 O ° ° ° ° ° ° ° ° ° ° °° ° ° Na2O °°° ° °° ° ° ° °° ° ° K O

0.2 0.0

2

-0.2 50

60

70 80 mol % SiO2

90

100

Activity coefficient of SiO2, ln γSiO2

Activity coefficient of SiO2, ln γSiO2

mol % SiO2 0.8

KAlO2

100

D 0.4

0.2

Ca0.5AlO2

NaAlO2

0.0

KAlO2 -0.2

60

70

90 80 mol % SiO2

100

FIGURE 4.39 Relationship between liquidus boundary of SiO2 polymorph (cristobalite or tridymite) and concentration and activity of SiO2. A. Liquidus boundary of SiO2 polymorph and type of alkali metals and alkaline earth in binary metal oxide - SiO2 systems. B. Liquidus boundary of SiO2 polymorph and type of alkali metals and alkaline earth in ternary metal oxide - Al2O3 - SiO2 systems as indicated on individual curves. C. Relations between activity coefficient of SiO2, gSiO2, and type of alkali metals and alkaline earth in binary metal oxide - SiO2 systems derived by using Eqs. (4.19) and (4.20). D. Relations between activity coefficient of SiO2, gSiO2, and type of alkali metals and alkaline earth in ternary metal oxide - Al2O3 - SiO2 systems derived by using Eqs. (4.19) and (4.20). Modified from Ryerson (1985).

4.3 Heat content, heat capacity, and entropy of silicate melts and magma

1.0

A

Distin et al. (1971), 1785˚C Distin et al. (1971), 1880˚C Distin et al. (1971), 1960˚C Schumann and Ensio (1951), 1350˚C

Activity of FeO, aFeO

1.0

0.9

B

0.8 Activity of SiO2, aSiO2

1.2

0.8 0.6 0.4

0.7 0.6 0.5 0.4 0.3 1550˚C CaO-SiO2

0.2 0.1

0.2 0

20 30 mol % SiO2

0.0 40

50

40

C Activity coefficient of SiO2, ln γSiO2

1500˚C 1400˚C 1300˚C 1200˚C 1100˚C

-4.0

-5.0 1500˚C

-6.0

-7.0 40

45

50

55 60 mol % SiO2

65

70

D

Activity of KO0.5, log aKO0.5

-3.0

10

257

1300˚C

1400˚C

0.4 0.3 M2+

0.2 0.1 0.0

M+

-0.1

1100˚C

50

60 70 80 mol % SiO2

90

100

-0.2 0

1

Z/r2, Å-2

2

3

FIGURE 4.40 Relationships between composition and activity of components in simple metal oxide-SiO2 systems A. Relations between activity of FeO, aFeO, and SiO2 concentration in the FeOeSiO2 melt system at various temperatures (calculated isotherms from Ottonello, 2001). B. Activity of SiO2, aSiO2, as a function of SiO2 concentration at 1550 C, C. Relationships between activity of K2O, aKO0.5, and SiO2 content in K2OeSiO2 melts calculated at various temperatures by Wu et al. (1993a,b). D. Activity coefficient of SiO2, gSiO2, for Mþ and M2þ cations as a function of their ionization potential, Z/r2, for various binary metal oxide - SiO2 melts (from Mysen, 1995). Modified from Mysen (1995); Wu et al. (1993a); Ottonello (2001).

258

Chapter 4 Energetics of melts and melting in magmatic systems

Activity of Na2O, log aNa2O

-2

-4

-6

-8

1500˚C 1400˚C 1300˚C 1200˚C 1100˚C

-10

1000˚C 900˚C

-12

40

50

60 70 mol % SiO2

80

90

100

FIGURE 4.41 Activity of Na2O in Na2OeSiO2 melts as a function of their SiO2 content and temperature. Modified from Sugawara et al. (2011).

Viewed in this manner, Mysen (1995) found that the logelog relations of activity coefficients of all the Qn-species present are linearly related and independent of both the nature of the metal cation and the Al/(Al þ Si) ratio of the melt (Fig. 4.42). As these calculations were done by reference to the relevant crystalline species on the liquidus, temperature was necessarily also a variable. However, within the error of the results, no effect of temperature was observed. It seems, therefore, that instead of expressing activity-composition in terms of oxide components, the use of the silicate and aluminosilicate species actually in the melt seems to be a more efficient approach to this problem.

4.3.5.2 Energetics of mixing Thermochemical data of mixing in binary metal oxide silicate melts also have been determined experimentally as well as with molecular dynamics simulations (Hovis et al., 2004; Morishita et al., 2004; Sugawara et al., 2011; Seo and Tsukihashi, 2004; Zhang et al., 2010). For Na2OeSiO2 melts, there is a small excess enthalpy (Fig. 4.43A; see also Hovis et al., 2004). The excess is likely to increase with decreasing temperature and eventually to result in metastable immiscibility near the glass transition (see also Mysen and Richet, 2019, Fig. 6.1; for review of published Na2OeSiO2 liquidus phase relations). Zhang et al. (2010), using first-principles molecular dynamics simulation at 4000 K, observed a tendency to generate excess heat of mixing in MgOeSiO2 melts with between 80 and 90 mol % SiO2 although the compositional extent of this maximum depends somewhat on the methods used for calculation. There is a maximum in the entropy of mixing near 75 mol% SiO2 in melts in the Na2OeSiO2 system (Sugawara et al., 2011; see also Fig. 4.43B), and a corresponding configurational entropy at approximately the same composition. This maximum likely reflects steric incompatibility of Q4 and

2.0 A 1.8 1.6 1.4 1.2 1.0 0.8 0.6 -3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

1.0 B 0.8

0.6

0.4

0.2

0.0 -1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

3 C

2

1

0 -3

-2

-1

0

FIGURE 4.42 Relationship between activity coefficient of Qn-species and their concentration in binary alkali silicate melts as indicated. A. For Q2 species. B. For Q3 species. C. For Q4 species. Modified from Mysen (1995).

260

Chapter 4 Energetics of melts and melting in magmatic systems

-140 A

B

Entropy of mixing, J/mol K

al tu

-150

ac

Enthalpy of solution, kJ/mol

5 -145

g

in

ix

m al

e

-155

id

-160

0 -5

-10

-15

50 Na2O

60

70

80 mol %

90

100 SiO2

-20

0 Na2O

20

40

60 mol %

80

100 SiO2

FIGURE 4.43 Enthalpy of solution in Na2OeSiO2 melts as a function of their composition. B. Entropy of mixing among Na2OeSiO2 melts as a function of composition. Modified from Hovis et al. (2004); Sugawara et al. (2011).

Q3 structural units, which for all practical purposes are the two coexisting silicate structures in the composition region where the entropy of mixing maximum occurs in the melts. These features have also been observed as variations in the partial molar enthalpies of SiO2 in Li2OeSiO2, Na2OeSiO2, and K2OeSiO2 melts, where a change from negative to positive values is observed for SiO2-rich compositions (Morishita et al., 2004). The SiO2 content where this crossover takes place decreases as the metal cation becomes increasingly electronegative. The abundance of Q4 units in metal-oxide silicate melts also is positively correlated with the electronic properties of the metal cation. It seems, therefore, that the critical factor governing excess heat of mixing in binary metal oxide silicate melt and glass systems is the abundance of Q4 structural units relative to structural units with nonbridging oxygen (n < 4 in the Qn-species). Experimental data also address Si 5 Al substitution for a number of alkali and alkaline earth cations in meta-aluminosilicate melts (Fig. 4.44A; see also. Roy and Navrotsky, 1984). From K to Mg, all enthalpy-composition relationships succeed each other in the order of increasing ionization potential of the metal cation although different curves seem to exist for cations with different formal electrical charge (Fig. 4.44B). Of special interest is the fact that there is no sharp boundary between the alkaline and alkaline earth series, as the data for the Li and Ba compositions fall practically on the same curve in Fig. 4.44A. For nearly all systems, there is negative enthalpy of mixing between SiO2 and MxAlO2, which indicates strong affinity between these components. Moreover, as the Al/(Al þ Si) increases the heat

4.3 Heat content, heat capacity, and entropy of silicate melts and magma

K+

Mg

Entalpy of solution, -ΔHs, KJ/mol

Entalpy of solution, -ΔHs, KJ/mol

10

Ca

10

Sr Ba

0 Cs Rb Li

-10

Na K

-20

Na+

5 Si

A 40

60 mol %

80

100 SiO2

O

2

-M

Al O

2

0 Ba2+

Li+

Si

O

2

-M

Al

2

O

4

-5

0 20 MxAlO2 (x=1, 2)

261

B 0.50

Sr2+ Ca2+

0.75

1.00 2

1.25

1.50

-2

Z/r , Å

FIGURE 4.44 Enthalpy of solution of various meta-aluminosilicate glasses as a function of their composition. A. As a function of SiO2 content (mol%). B. as a function of ionization potential of the metal cation, Z/r2. Modified from Roy and Navrotsky (1984).

of solution also increases (becomes more negative; see Roy and Navrotsky, 1984). For the Ca- and Mgmeta-aluminosilicate glasses, the enthalpy of mixing is positive as the pure Al-endmember is approached. It appears that whereas such simple correlations between enthalpy of solution and Al/(Al þ Si) is clear for any group of metal cations with the same formal electrical charge, a separate trend can be seen for each series of differently charged metal cations (Fig. 4.44B). An enthalpy minimum exists near 50 mol % SiO2 (Navrotsky, 1994). The magnitude of this minimum varies significantly with the electronic properties of the M-cation. It falls near 10 kJ/mol for Mg- and below 20 kJ/mol for K-aluminosilicates. The depths of these minima correlate with the relative extent of freezing-point depressions at eutectics (See summary by Mysen and Richet, 2019, Fig. 8.1). These depths also follow the relative stabilization energy trends illustrated in Fig. 4.17. In contrast, the compositions of the eutectics do not match those of the enthalpy minima. The reason is that enthalpy is not the only factor determining phase equilibria. Finally, we note that only Mg-aluminosilicates unmix at very high SiO2 content along the meta-aluminous join (See Mysen and Richet, 2019, Chapter 8, for review of data). Consistent with this observation, the Mg meta-aluminate join is the only one for which the enthalpy-composition relationship of the glasses in Fig. 4.44A shows an initial maximum and then the SiO2 deviates positively from ideal mixing for compositions near SiO2 (Stolyarova et al., 2011).

262

Chapter 4 Energetics of melts and melting in magmatic systems

30 Ca

Enthalpy of mixing, kJ/mol

Mg

Si

20

2

O6

-N

aA

lSi

3

O8

10 O8 l 2Si 2 -CaA Si 2O 6

0 g CaM

-10 -20 -30 0.0

CaMgSi2O6

0.2

0.4

0.6

0.8

Mol fraction, XCaAl2Si2O8/XNaAlSi3O8

1.0 CaAl2Si2O8/ NaAlSi3O8

FIGURE 4.45 Enthalpy of mixing of melts along the joins CaMgSi2O6eNaAlSi3O8 and CaMgSi2O6eCaAl2Si2O8 as indicated on the diagram. Modified from Sugawara et al. (2009).

The energetics of mixing of composition join between Al-free and Al-bearing compositions (peralkaline compositions; see also Fig. 4.17) are complex because Al3þ under these conditions will partition between the coexisting Qn-species (Merzbacher et al., 1991; Mysen et al., 1981, 2003). The extent to which this occurs likely depends on the distribution of metal cations between the various coexisting Qn-species. The enthalpy of mixing of melts along joins such as CaMgSi2O6eNaAlSi3O8, CaMgSi2O6eCaAl2Si2O8, and CaSiO3eCaAl2Si2O8 illustrates this effect (Fig. 4.45; see also Sugawara et al., 2009; Tarina et al., 1994; Navrotsky et al., 1989). Unfortunately, thermodynamic data do not seem to exist for silicate-aluminosilicate mixtures with alkali metals only.

4.4 Thermodynamics of melts and liquidus phase relations The liquidus phase relations in silicate and aluminosilicate systems in the past have been used to deduce structural features of the liquid near the liquidus (Bottinga and Richet, 1978; Bottinga et al., 1981; Burnham, 1981; Ghiorso, 1985; Burnham and Nekvasil, 1986). The results of computations of thermodynamic data for high-temperature solutions such silicate melts have been employed to calculated liquidus phase relations (Blander and Pelton, 1987; Chartrand and Pelton, 1999; Blander, 2000; Decterov et al., 2002; Jung et al., 2005; Richet and Ottonello, 2010) or combinations of the two (Ghiorso and Sack, 1995; Ghiorso et al., 2002; Ghiorso, 2018).

4.4 Thermodynamics of melts and liquidus phase relations

263

2800 2600 Liquid

2200

uid

Mg2SiO4+liquid uid

MgO+liquid

1600

SiO2(tr)+liquid MgO+Mg2SiO4 Mg2SiO4+ MgO

1400 1200

0 MgO

2 liquids

3

MgO

SiO

1800

+liq

2000 Mg

Temperature,˚C

liq (cr)+ SiO 2

2400

20

40

Mg2SiO4+MgSiO3

60 wt %

80

100 SiO2

FIGURE 4.46 Calculated liquidus phase diagram of the system MgOeSiO2 relying on free energy minimization [eqn. 4.22]. Data points are from Bowen and Anderson (1914) and Greig (1927. Calculations are from Bottinga et al. (1981). Modified after Bottinga et al. (1981).

In their consideration of phase relations and melt structure, Bottinga and Richet (1978) assumed a distribution of the liquidus phases in the MgOeSiO2 system (periclase, forsterite, clinoenstatite, SiO2 polymorphs) with their chemical formulae calculated on the basis of eight oxygen. They, then, simply computed a situation where the distribution of these entities should produce a minimum free energy: G¼

n X n¼1

mnL Nn

(4.22)

where mnL is the chemical potential of the n species and Nn is the number of moles of the species. Also included are entropy and enthalpy of melting of the species. It was also required, of course, that at the liquidus, the chemical potential of the individual species in melt and minerals is the same. As can be seen in Fig. 4.46, this model reproduces the liquidus phase relations in the system MgOeSiO2 (Bowen and Andersen, 1914) at ambient pressure quite well. Computations of thermodynamic data for high temperature solutions such as silicates have been employed on several occasions often with reasonably good success. Various methods, as summarized by Blander (2000), have been employed for this. Liquidus phase relations in the Na2OeAl2O3eSiO2 at ambient pressure are an example of this approach (Chartrand and Pelton, 1999; see also Fig. 4.47). Here, the Gibbs free energy of formation of

264

Chapter 4 Energetics of melts and melting in magmatic systems

1800

A SiO2(crist) +liquid

1400

Na6Si2O7

Na2SiO3+ Na2SiO3+ Na6Si2O7

20 Na2O

SiO2(trid)+liquid

liquid

SiO2(qtz)+liquid

30

Na2Si2O5

600

Na6 Si8O 19 +liq

Na2Si2O5+liquid

1000 800

uid

Na6Si2O7+liquid Na2SiO3+liquid

Na2SiO3

1200

liquid

Na4SiO4

Temperature,˚C

1600

40

Na6Si8o19+ Na2Si2O6

Na6Si8O19+SiO2(qtz)

Na6Si8O19

50

60 70 Mol %

80

90

100 SiO2

1800

B

Temperature,˚C

1700 1600 1500

SiO2(crist)+liquid liquid

1400 1300

SiO2(trid)+liquid

1200 1100

NaAlSi3O8+liquid

NaAlSi3O8+SiO2(trid)

1000 0

10 NaAlSi3O8

1600

20

30

40

50 60 wt %

70

80

90 100 SiO2

C

liquid

uid

1400 1300 1200

NaAlSi3O8(ab)+liq

Temperature,˚C

1500

Al2Si2O10(mul)+liquid

1100 0 NaAlSi3O8

NaAlSi3O8(ab)+Al2Si2O10(mul)

5

10 wt %

15

20 Al2O3

FIGURE 4.47 Liquidus phase relations calculated for A. the joins Na2OeSiO2, B. NaAlSi3O8eSiO2, and C. NaAlSi3O8eAl2O3 (Modified after Chartrand and Pelton, 1999). The original source (Chartrand and Pelton, 1999) also contains the citations to the data points shown in the three diagrams.

4.4 Thermodynamics of melts and liquidus phase relations

265

second-nearest energy pairs, Dg, was employed. For example, interaction with Na and Si was expressed as: ðNa  NaÞ þ ðSi  SiÞ ¼ 2ðNa  SiÞ;

DgNaSi ¼ uNaSi  xNaSi T;

(4.23)

so that the Gibbs free energy of solution can be expressed as a summation of the interactions and the configurational entropy. Aspects of the resultant liquidus phase relations are illustrated in Fig. 4.47 for binary joins in the system Na2OeAl2O3eSiO2. As can be seen in Fig. 4.47A, the liquidus surface in the Na2OeSiO2 system is reasonably well reproduced until about 70 mol% SiO2. Above this SiO2 concentration, there are significant differences with the data obtained by experimental determination of the phase relations (see Chartrand and Pelton, 1999; for sources of those experimental data). This difference likely reflects the rapid structural changes in the Na2OeSiO2 melts in this high-SiO2 region (e.g., Maekawa et al., 1991), changes that cannot be handled with precision in the model. Reproduction of the liquidus phase relations along the join SiO2eNaAlSi3O8 (Fig. 4.47B) is considerably better. This probably is a result of the fact that the structural evolution of the melts along this join is quite simple with Al substitution for Si forming a near ideal solution (Navrotsky et al., 1982). Finally, for the liquidus surface along the NaAlSi3O8eAl2O3 join (Fig. 4.47C), there is again significant deviation from the experimental phase equilibrium data (Schairer and Bowen, 1956). This is not surprising in light of the significant structural changes in melts along such a join (Taylor and Brown, 1979; Bessada et al., 1999). In summary, it appears that the method used as illustrated in Fig. 4.47 does a good job in duplicating liquidus phase relations over concentration intervals where there is little structural change in the melt or where the melt approximates an ideal solution. However, when there are significant melt structural variations, the method is less successful. The MELTS thermodynamic model for melt-mineral equilibria (Ghiorso and Sack, 1995) is based on minimization of chemical potentials: G ¼

n X i¼1

Xi m0i þ RT

n X i¼1

Xi ln Xi þ

n X n 1X Wi; j Xi Xj ; 2 i¼1 j¼1

(4.24)

and in the presence of H2O: G ¼

n X i¼1

Xi m0i þ RT

n X i¼1

Xi lnXi þ

n X n 1X Wi;j Xi Xj þ RT½XH2O lnXH2O þ ð1  XH2O Þlnð1  XH2O Þ; 2 i¼1 j¼1

(4.25) where X is mol fraction (of subscript), m is chemical potential R is the gas constant and T is temperature (kelvin). The minimization in the presence of H2O does not consider the multiple structural roles of H2O in silicate melts (see, for example, discussion in Chapter 7). This method has been used to compute proportions of minerals and melts and their compositions as a function of temperature and pressure (pressure effects expanded in pMELTS; see Ghiorso et al., 2002). It can also be used to calculate equation-of-state of melts and their components and fractions of minerals and melts during partial melting as illustrated with the comparison of computed and experimentally calibrated proportions of melt and minerals during partial melting of a peridotite, KLB1 (Fig. 4.48; see also Ghiorso et al., 2002).

266

Chapter 4 Energetics of melts and melting in magmatic systems

ol+opx+cpx+liq

ol+opx+liq

90

ol+liq

ene

yrox

op clin

ne

xe

ro py

ho

wt %

70

ort

olivine 50

30 liquid 10 1300

1400 Temperature, ˚C

1500

FIGURE 4.48 Calculated percent melting in equilibrium with mineral assemblages indicated as a function of temperature. Modified after Ghiorso et al. (2002).

4.5 Concluding remarks Thermodynamic data of melts and minerals are used to describe the behavior silicate melts (magmatic liquids) and their melting and crystallization properties and processes. Enthalpy and free energy of melting is central to characterization of those processes. The behavior of these properties is linked to structural variations of the melts. In addition, for many minerals, there is also a premelting effect that can involve up to more than 20% of the enthalpy of melting itself. Premelting is particularly important in minerals that also contain alkali metals and alkaline earths. Lack of consideration of premelting can lead to erroneous heat and entropy of fusion budgets. Premelting also has been detected in properties such as diffusion and electrical conductivity. Thermodynamic characterization of the melting process is critical for our understanding of formation and transport of melts in the Earth’s interior. The contribution of the melting energy of individual minerals to the overall energy budget can be more than 90% with the remainder being enthalpy and free energy of melt mixing. The latter energy contribution is sensitive to the silicate composition and is greater for alkaline earth aluminosilicate systems than for alkali aluminosilicate systems. As a result, mixing energy is greater for basaltic than for dacitic and rhyolitic magmatic systems. Configurational properties such as configurational entropy and heat capacity also contribute to the melting budget. Their values tend to increase in melt environments where alkaline earths are the dominant network-modifying cations. In other words, configurational properties of basaltic magma are greater than rhyolitic magma, for example. Solution of volatiles such as H2O and halogens will also enhance configurational properties.

References

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The thermodynamic data can be employed to calculate melting and crystallization phase relations. The results of such calculations are more similar to experimentally determined data with systems involving alkali aluminosilicates compared with alkaline earth aluminosilicates. This difference follows from the different mixing behavior in these systems. Alkali aluminosilicate melts often mix nearly ideally, whereas there are often significant deviations from ideal mixing in alkaline earth aluminosilicate melt systems. Again, therefore, results of calculated melting and crystallization phase relations of felsic igneous rocks typically are more accurate than those for mafic rocks such as basalt.

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Pamukcu, A.S., Gualda, G.A.R., Ghiorso, M.S., Miller, C.F., McCracken, R.G., 2015. Phase-equilibrium geobarometers for silicic rocks based on rhyolite-MELTS-Part 3: application to the Peach Spring Tuff (ArizonaCalifornia-Nevada, USA). Contrib. Mineral. Petrol. 169. https://doi.org/10.1007/s00410-015-1122-y. Rankin, G.A., Wright, F.E., 1915. The ternary system CaO-Al2O3-SiO2. Am. J. Sci. 39, 1e79. Reynard, B., Webb, S.L., 1998. High-temperature Raman spectroscopy of Na2TiSi2O7 glass and melt: coordination of Ti4þ and the nature of the configurational changes in the liquid. Eur. J. Mineral 10, 49e58. Richet, P., 1984. Viscosity and configurational entropy of silicate melts. Geochem. Cosmochim. Acta 48, 471e483. Richet, P., 1987. Heat capacity of silicate glasses. Chem. Geol. 62, 111e124. Richet, P., 2009. Residual and configurational entropy: quantitative checks through applications of Adam-Gibbs theory to the viscosity of silicate melts. J. Non-cryst. Solids 355, 628e635. Richet, P., Bottinga, Y., 1980. Heat-capacity of liquid silicates - new measurements on NaAlSi3O8 and K2Si4O9. Geochem. Cosmochim. Acta 44, 1535e1541. Richet, P., Bottinga, Y., 1984. Glass transitions and thermodynamic properties of amorphous SiO2, NaAlSinO2nþ2 and KAlSi3O8. Geochem. Cosmochim. Acta 48, 453e471. Richet, P., Bottinga, Y., 1985. Heat capacity of aluminum-free liquid silicates. Geochem. Cosmochim. Acta 49, 471e486. Richet, P., Bottinga, Y., 1986. Thermochemical properties of silicate glasses and liquids: a review. Rev. Geophys. 24, 1e26. Richet, P., Bottinga, Y., 1995. Rheology and configurational entropy of silicate melts. Struct. Dyn. Proper. Silicate Melts 32, 67e93. Richet, P., Fiquet, G., 1991. High-temperature heat capacity and premelting of minerals in the system MgO-CaOAl2O3-SiO2. J. Geophys. Res. B 96, 445e456. Richet, P., Mysen, B.O., 1999. High-temperature dynamics in cristobalite (SiO2) and carnegieite (NaAlSiO4): a Raman spectroscopy study. Geophys. Res. Lett. 26, 2283e2286. Richet, P., Neuville, D.R., 1992. Thermodynamics of silicate melts; configurational properties. In: Saxena, S.K. (Ed.), Thermodynamic Data; Systematics and Estimation. Springer, New York, NY, United States, pp. 132e161. Richet, P., Ottonello, G., 2010. Thermodynamics of phase equilibria in magma. Elements 6, 315e320. https:// doi.org/10.2113/gselements.6.5.315. Richet, P., Bottinga, Y., Denielou, L., Petitet, J.P., Tequi, C., 1982. Thermodynamic properties of quartz, cristobalite and amorphous SiO2; drop calorimetry measurements between 1000 and 1800 K and a review from 0 to 2000 K. Geochem. Cosmochim. Acta 46, 2639e2659. Richet, P., Bottinga, Y., Te´qui, C., 1984. Heat capacity of sodium silicate liquids. J. Am. Ceram. Soc. 67, C6eC8. Richet, P., Robie, R.A., Rogez, J., Hemingway, B.S., Courtial, P., Tequi, C., 1990. Thermodynamics of open networks - ordering and entropy in naalsio4 glass, liquid, and polymorphs. Phys. Chem. Miner. 17, 385e394. Richet, P., Robie, R.A., Hemingway, B.S., 1991. Thermodynamic properties of wollastonite, pseudowollastonite and CaSiO3 glass and liquid. Eur. J. Mineral 3, 475e484. Richet, P., Robie, R.A., Hemingway, B.S., 1993. Entropy and structure of silicate-glasses and melts. Geochem. Cosmochim. Acta 57, 2751e2766. Richet, P., Ingrin, J., Mysen, B.O., Courtial, P., Gillet, P., 1994. Premelting effects in minerals - an experimentalstudy. Earth Planet Sci. Lett. 121, 589e600. Richet, P., Mysen, B.O., Andrault, D., 1996. Melting and premelting of silicates: Raman spectroscopy and X-ray diffraction of Li2SiO3 and Na2SiO3. Phys. Chem. Miner. 23, 157e172. Richet, P., Mysen, B.O., Ingrin, J., 1998. High-temperature X-ray diffraction and Raman spectroscopy of diopside and pseudowollastonite. Phys. Chem. Miner. 25, 401e414.

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Taylor, M., Brown, G.E., 1979. Structure of mineral glasses. II. The SiO2-NaAlSiO4 join. Geochem. Cosmochim. Acta 43, 1467e1475. Taylor, M., Brown, G.E., 1979a. Structure of mineral glasses. I. The feldspar glasses NaAlSi3O8, KAlSi3O8, CaAl2Si2O8. Geochem. Cosmochim. Acta 43, 61e77. Te´qui, C., Grinspan, P., Richet, P., 1992. Thermodynamic properties of alkali silicates: heat capacity of Li2SiO3 and lithium-bearing melts. J. Am. Ceram. Soc. 75, 2601e2604. Thie´blot, L., Te´qui, C., Richet, P., 1999. High-temperature heat capacity of grossular (Ca3Al2Si3O12), enstatite (MgSiO3), and titanite (CaTiSiO5). Am. Mineral. 84, 848e855. Thompson, J.G., Withers, R.L., Whittaker, A.K., Trail, R.M., Fitzgerald, J.D., 1993. A reinvestigation of lowcarnegieite by XRD, NMR and TEM. J. Solid State Chem. 104, 59e73. Toplis, M.J., 1998. Energy barriers associated with viscous flow and the prediction of glass transition temperatures of molten silicates. Am. Mineral. 83, 480e490. Ubbelohde, A.R., 1978. The molten state of matter: melting and crystal structure. John Wiley & Sons. Vanduijn, J., Degraaff, R.A.G., Ijdo, D.J.W., 1995. Structure determination of CaMgGeO4. Mater. Res. Bull. 30, 1489e1493. Victor, A.C., Douglas, T.B., 1963. Thermodynamic properties of magnesium oxide and beryllium oxide from 298 to 1200K. J. Res. Natl. Bur. Standards Sect. A 67, 325e329. Virgo, D., Mysen, B.O., Kushiro, I., 1980. Anionic constitution of 1-atmosphere silicate melts: implications of the structure of igneous melts. Science 208, 1371e1373. Webb, S.L., 2008. Configurational heat capacity of Na2OeCaOeAl2O3eSiO2 melts. Chem. Geol. 256, 92e101. Webb, S.L., 2011. Configurational heat capacity and viscosity of (Mg, Ca, Sr, Ba)O-Al2O3-SiO2 melts. Eur. J. Mineral 23, 487e497. White, W.P., 1909. Melting point methods at high temperature. Am. J. Sci. s4e28, 474e489. Whittington, A.G., Bouhifd, M.A., Richet, P., 2009. The viscosity of hydrous NaAlSi3O8 and granitic melts: configurational entropy models. Am. Mineral. 94, 1e16. Williamson, J., Glasser, F.P., 1965. Phase relations in the system Na2Si2O5-SiO2. Science 148, 1589e1591. Wu, P., Eriksson, G., Pelton, A.D., 1993a. O2ptimization of the thermodynamic properties and phase-diagrams of the Na2O-SiO2 and K2O-SiO2 systems. J. Am. Ceram. Soc. 76, 2059e2064. Wu, P., Eriksson, G., Pelton, A.D., Blander, M., 1993b. Prediction of the thermodynamic properties and phase diagrams of silicate systemsdevaluation of the FeO-MgO-SiO2 system. ISIJ Int. 33, 26e35. Yamanaka, T., Mori, H., 1981. The structures and polytypes of a-CaSiO3 (pseudowollastonite). Acta Crystallogr. B37, 290e300. Yoder, H.S., 1976. Generation of Basaltic Magma. National Academy of Science, Washington, D. C, p. 276. Zhang, L., Van Orman, J.A., Lack, s.D.J., 2010. Molecular dynamics investigation of MgOeCaOeSiO2 liquids: influence of pressure and composition on density and transport properties. Chem. Geol. 256 (275), 50e57. Ziegler, D.C., Navrotsky, A., 1986. Direct measurement of the enthalpy of fusion of diopside. Geochem. Cosmochim. Acta 50, 2461e2466.

CHAPTER

Structure of magmatic liquids

5

5.1 Introduction Characterization of the structure of magmatic liquids is a prerequisite for understanding how their physical and chemical properties vary with temperature, pressure, redox conditions, and bulk chemical composition. To some extent, the structural concepts resemble those in crystal structures, whereas in some other ways, they differ. The main difference is, perhaps the absence of long-range structural order in silicate melt and glass. The structural differences and similarities between silicate melts and their glasses are also important. These relations are the topic of this chapter. The roles of volatiles in magmatic systems will be discussed in the next chapters (Chapters 7e8).

5.2 Glass versus melt and glass transition Many structural features of amorphous materials described in this chapter qualitatively may characterize both molten and glassy silicates. These two amorphous states also differ, however, in many important respects. This is because glass is a kinetic and, therefore, a nonequilibrium state, whereas a melt is an equilibrium state. Magmatic liquids in nature are in their equilibrium states and are, therefore, commonly also described as melts. We will discuss, therefore, the similarities and differences between a glass and its melts before addressing more general structural aspects of magmatic liquids. The glass transition temperature (Tg) is where the tangents to the glass and liquid curves of a given property intersect (Fig. 5.1). The Tg is the temperature below which the structural configurations are frozen in. The glass transition temperature is, however, dependent on the cooling rate of a melt and the acquisition rate of the method used to determine the glass transition. It is higher for higher cooling rates or shorter experimental time scales. The example shown in Fig. 5.2 is the glass transition temperatures for CaAl2Si2O8 from viscometry, ultrasonic, and Brillouin scattering experiments. The glass transition temperatures differ because the experimental time frames of those properties are on the order of 102, 10
6, and 10
10 s, respectively. The glass transition is a second-order thermodynamic transformation, and appears, for example, as a discontinuity in the entropy function as a function of temperature (Fig. 5.3). At temperatures lower con than the glass transition temperature, the configurational heat capacity, Cconf p , is 0. The Cp increases across the glass transition temperature range. The magnitude of this heat capacity change varies as a function of bulk melt composition and also as a function of type and concentration dissolved volatiles Mass Transport in Magmatic Systems. https://doi.org/10.1016/B978-0-12-821201-1.00003-1 Copyright © 2023 Elsevier Inc. All rights reserved.

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Chapter 5 Structure of magmatic liquids

FIGURE 5.1 Definition of glass transition and glass transition temperature using thermal expansion, Dl/l, as an example. Note that there is a narrow temperature range across which transformation from glass to liquid occurs. The glass transition temperature is defined as the intersection of he thermal expansion of glass and liquid. Redrawn after Mysen and Richet (2019).

FIGURE 5.2 Glass transition temperature for CaAl2Si2O8 glass as a function of probe frequency as indicated (see also text). Note that CaAl2Si2O8 liquid behaves as a glass when examined with Brillouin scattering. Redrawn and modified after Mysen and Richet (2019).

(Bouhifd et al., 2004). The configurational heat capacity of supercooled melts and higher-temperature melts often is independent of temperature. It can, however, vary, whenever there are temperaturedependent structural changes of the melt and supercooled melt.

5.2 Glass versus melt and glass transition

277

FIGURE 5.3 Glass transition defined by configurational entropy (here, NaSi2O5 glass and liquid is used as an example). At temperatures below the of the glass transition, the configurational entropy does not vary with temperature, whereas above the glass transition, he configurational entropy increases with increasing temperature as the number of configurations that can be attained in the liquid state also increases with increasing temperature. Whereas the configurational entropy of silicate glasses at their glass transition temperature is approximately independent of glass composition, in liquid and relaxed state, the temperature-dependence is indeed dependent on the liquid composition. This means that the two curves will meet at different temperature, which corresponds to different glass transition temperature. Redrawn after Richet and Neuville (1992).

The physical behavior of glass in response to imposed variables reflects how the glass was manufactured. For example, by subjecting a glass to a set of pressure and temperature below the glass transition the results are different from the behavior of a glass formed by temperature-quenching of melt from temperatures above the glass transition. In this chapter, glass and melt are not distinguished unless pointed out specifically by referring to a glass or a melt. Exceptions to this statement include, for example, equation-of-state, which differs for a melt and its glass (Ohtani et al., 2005). Moreover, equation-of-state of glass obtained with molecular or noble gases as pressure medium in high-pressure experiments using a diamond anvil cell differs from that absent gas pressure medium in such experiments. Examination of a glass formed by temperature-quenching of its melt offers information on melt structure at the glass transition, but not of melt at higher temperatures. Temperature-dependent structural features cannot, therefore, be discerned in a study of such glass structure. That disclaimer notwithstanding, glass structure can serve as a proxy for a number of structural features of melts and supercooled liquids. Therefore, some structural information may be obtained by examination of glass formed with different quenching rates.

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Chapter 5 Structure of magmatic liquids

5.3 Silicate melt and glass structure In this section, we will address principal compositional variables that control the silicate structure both of compositional simple melts as well as compositionally more complex natural magmatic liquids. Silicate melts with volatiles in solution will be discussed separately in Chapters 7 and 8. Magmatic liquid structure comprises a network of oxygen tetrahedra that are linked together via corner-shared oxygen. Some of the tetrahedra share oxygen with polyhedra that have more than four oxygen ligands. There are, therefore, two distinctly different kinds of oxygen in the silicate network of silicate melts such as magmatic liquids. These are bridging (BO) and nonbridging oxygen (NBO) (Fig. 5.4). Bridging oxygen are those shared by neighboring tetrahedra, whereas nonbridging oxygen links the corner or corners of a tetrahedron to oxygen polyhedra with more than four oxygen ligands (Fig. 5.4). The central cation in the oxygen tetrahedra is defined as a network-forming cation (marked as “T” in Fig. 5.4). In magmatic liquids, Si4þ and Al3þ are the dominant T-cations. Additionally, there are minor amounts of tetrahedrally coordinated cations such as Fe3þ, Ti4þ, and P5þ. However, as discussed in detail later in this Chapter, these latter cations typically form separate tetrahedra and tetrahedral clusters in the structure, whereas Al3þ can substitute for Si4þ in the structure. The central cation in the linking oxygen polyhedra, marked “M” in Fig. 5.4, is a networkmodifying cation. The M-cations in magmatic liquids are alkali metals and alkaline earths. The types and proportions of network-forming and -modifying cations in magmatic liquids are systematic functions of magma type. The dominant network-modifying cations in rhyolitic and granitic magma are alkali metals, whereas in more mafic magma, the dominant network-modifying cations are alkaline earths with their Mg/Ca ratio of these increasing the more mafic the magma.

FIGURE 5.4 Schematic representation of the principal building blocks in the structure if aluminosilicate melt. BO, Bridging oxygen; NBO, Nonbridging oxygen; T, Tetrahedrally coordinated cation (typically Si4þ and Al3þ). Also shown is network-modifying cations, M (alkali metals and alkaline earths).

5.3 Silicate melt and glass structure

279

FIGURE 5.5 Principal geometric variables in tetrahedral network. d: Interatomic distance, q: Intertetrahedral angle, (Si,Al)eOe(Si,Al).

The main structural variables within the tetrahedral network are the intertetrahedral angle, q, and the distance, d, from the nearest-neighbor oxygen to the next-neighbor tetrahedrally coordinated cation (Fig. 5.5). The q- and d-values are correlated. In general, the greater the d-value, the smaller is the qvalue (Brown et al., 1969; Gibbs et al., 1981). However, for a pure SieO network where the SieO bond is essentially incompressible (Hazen, 1988), decreasing intertetrahedral angle, q, results in weakening of the SieO bond without necessarily changing the SieO bond length. X-ray radial distribution (XRDF) analysis is useful to determine T-O, T-T, and OeO bonds lengths (T ¼ tetrahedrally coordinated cation, O ¼ oxygen; Taylor and Brown, 1979; Henderson et al., 2009). In some circumstances, this method has been employed to map bond lengths to distances reaching several coordination spheres (Taylor and Brown, 1979). Along the SiO2e NaAlO2 join, for example, the XRDF of NaAlSi3O8 glasses and crystalline equivalents (albite) ˚ , which is the approximate distance between the exhibits significant similarity to at least 3 A central T-cations to the second nearest neighboring tetrahedron. However, the extent of similarity between glass/melt and its crystalline equivalent to a considerable extent depends on the nature of the cation(s) serving to charge-balance Al3þ in tetrahedral coordination in the silicate structure. There is, for example, longer-distance order in the Ca-aluminosilicate glass systems than in those of Na-aluminosilicate (Lee and Stebbins, 1999).

5.3.1 Degree of silicate polymerization, NBO/T The degree of polymerization of silicate melts, including that of magmatic liquids, can be conveniently described with the NBO/T parameter. The NBO/T describes the extent to which the network of silicate tetrahedra are linked together with bridging and nonbridging oxygen (Fig. 5.4). In the NBO/Texpression, NBO denotes nonbridging oxygen. The T-cation (tetrahedrally coordinated cation) resides near the center of the oxygen tetrahedra. In natural magmatic systems at low pressure, the main Tcations are Si4þ and Al3þ with Fe3þ, P5þ, and Ti4þ as possible minor components (see review by Mysen and Richet, 2019; Chapters 9, 11, 12, and 14). When any of these cations undergo coordination transformation, the NBO/T-value changes. Pressure is the most common means with which to cause coordination transformation of T-cations. While NBO/T can be calculated from bulk composition when Si4þ and Al3þ are tetrahedrally coordinated (see Table 5.1), current high-pressure data are insufficient for NBO/T calculations of melts and magma where there is partial or complete coordination transformation of T-cations.

280

Chapter 5 Structure of magmatic liquids

Table 5.1 NBO/T calculation with known T-cations. Step 1 Step 2

Step 3

Convert composition to atomic proportions T ¼ Si þ Al þ Fe3þ. Assign Mþ and M2þ cation to Al3þ and Fe3þ for charge-balance in tetrahedral coordination. The order of charge-balance is: Kþ>Naþ>Ca2þ>Fe2þ>Mg2þ (see Navrotsky et al., 1982 for relative stability data) The NBO ¼ (2O-4T) and NBO/T ¼ (2O-4T)/T from formal charge of T-cations (4) and (2).

The NBO/T distribution of magmatic liquids at or near-ambient pressure for each major igneous rock group is nearly Gaussian (Fig. 5.6). The melt representing each rock type also has a distinct maximum in its distribution function. There is, however, some overlap in NBO/T-values between magma types. The NBO/T-values of these maxima decrease systematically as the melts become more SiO2-rich (average NBO/T is 0.83  0.21, 0.41  0.16, and 0.09  0.08, for tholeiite, andesite, and rhyolite melts, respectively. See also Table 5.2 for average composition of these magma types). The NBO/T of natural magmatic liquids also correlates broadly with compositional variables such as Al/ (Al þ Si) and Mg/(Mg þ Fe) (see also Mysen and Richet, 2019, Chapter 18).

5.3.1.1 Melt properties and degree of melt polymerization (NBO/T)

Semiquantitative predictions of properties sometimes can be made with the aid of the NBO/T-value of the melt (Figs. 5.7e5.9). Such predictions are semiquantitative because other compositional

FIGURE 5.6 Distribution of nonbridging oxygens per tetrahedrally coordinated cations, NBO/T, of melts of major igneous rocks. Average compositions of these magmatic rocks can be found in Table 5.2. Each rock group has a distinct maximum in its distribution function. These maxima decrease systematically as the melts become more felsic. The average NBO/T-value of each of the groups follows the same trend (0.83  0.21, 0.41  0.16, 0.20  0.18, and 0.09  0.08, for tholeiite, andesite, and rhyolite melts, respectively). Modified and redrawn after Mysen and Richet (2005).

5.3 Silicate melt and glass structure

281

Table 5.2 Average chemical composition of rock types discussed in the text. Tholeiite

Phonolite

Andesite

Rhyolite

No. of analyses

532

560

1997

764

SiO2 TiO2 Al2O3 FeO(T) MnO MgO CaO Na2O K2O P2O5 Na/(Na þ Ca) Al/(Al þ Si) NBO/T

50.29  2.37 2.06  0.82 14.79  1.82 10.94  1.59 0.18  0.03 7.15  2.5 10.09  1.38 2.41  0.55 0.53  0.38 0.26  0.12 0.3 0.26 0.69

55.56  3.72 0.87  0.63 19.31  5.40 4.02  1.73 0.24  1.05 2.47  1.86 1.18  2.28 8.21  1.57 5.23  1.01 0.21  0.20 0.63 0.29 0.21

57.51  4.08 0.93  1.55 15.93  1.45 7.08  1.85 0.14  0.05 3.90  1.82 7.17  1.85 3.42  0.77 1.51  0.86 0.23  0.13 0.46 0.26 0.35

72.18  3.52 0.39  0.29 13.23  1.50 2.90  1.79 0.10  0.19 0.48  0.51 1.53  1.24 4.03  1.09 3.79  1.42 0.09  0.09 0.81 0.18 0.08

variables not included in the NBO/T-variable affect many properties. These additional properties are proportions and types of T-cations, types, and proportions of network-modifying cations, bond distance, and bond length. One could, of course, obtain necessary magma viscosity data by measuring in the laboratory the viscosity of all possible types of magmatic liquids under all possible conditions. This is, however, an unrealistic approach to this problem because it would require thousands of laboratory labor hours to complete the necessary experiments. Viscosity models have, therefore, been proposed based on more limited experimental data combined with compositional and structural parameters, including NBO/T. Semiquantitative relationships between NBO/T and melt viscosity from chemically simple systems may be extended to natural magmatic liquids under pressure and temperature conditions where the proportion of tetrahedrally coordinated cations can be calculated (Mysen, 1987; see also Table 5.1). However, quantitative viscosity modeling by using the NBO/T alone is not possible because other compositional variables also affect melt viscosity. An early and fairly successful approach to model (and predict) silicate melt viscosity was the model by Bottinga and Weill (1972). They assumed that the viscosity of a silicate melt could be expressed as an additive function of the mol fractions of most oxide components, Xi. For Al3þ, they assumed complexing with alkali metals such as MAlO2. The proposed expression was ln h ¼

i X i¼1

xi Di ;

(5.1)

where Di is a regression coefficient that relates viscosity contributions from component, i, to the overall viscosity. The value of Di was obtained by fitting viscosity melt data from a variety of simple systems.

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Chapter 5 Structure of magmatic liquids

FIGURE 5.7 Calculated activation energy of viscous flow of melts from major rock-groups as a function of calculated NBO/ T (see Table 5.1) at ambient pressure. Also shown is the distribution of activation energy. Inserts show activation energy as a function of bulk melt Al/(Al þ Si) with NBO/T ¼ 0.20  0.05 and of binary Na2OeSiO2 melts. Data from Bockris et al. (1955) and redrawn after Mysen and Richet (2005).

A central question following Eq. (5.1) is whether melt viscosity is an additive function of melt composition. In other words, are the Di-coefficients independent of melt composition? In light of more recent work on melt viscosity (see, for example, Richet and Bottinga, 1984; Toplis, 1998), constant Divalues are not likely to be a quantitatively realistic assumption. This is so in particular because of multiple structural roles of alkali metals and alkaline earths and the fact that AleO bond strength varies as a function of how tetrahedrally coordinated Al3þ is charge-balanced. For example, the

5.3 Silicate melt and glass structure

283

FIGURE 5.8 Molar volume of melts from major rock-groups as a function of calculated NBO/T (see Table 5.1) at ambient pressure. Also shown is the distribution of molar volumes. Insert shows molar volume as a function of SiO2/ metal oxide ratio for metal oxides indicated. Data from Tomlinson et al. (1958) and redrawn after Mysen and Richet (2005).

viscosity of SiO2eNaAlO2 melt differs significantly from SiO2eCaAl2O4 melt (Riebling, 1964, 1966; Toplis and Dingwell, 2004). Other viscosity models have, therefore, been proposed. One empirical model, which does not incorporate structural information either, is that of Giordano and Dingwell (2003, 2004) log h ¼ c1 þ ½c1 c2 = ðc3 þ SMÞ

(5.2)

where c1, c2, and c3 are numerical parameters. The SM is the molar oxide sum, Na2O þ K2O þ CaO þ MgO þ MnO þ FeOtotal/2. The fact that SM does not contain contributions from either of the major components, SiO2 and Al2O3, is cause of concern because the concentration of these two oxides are major controlling factors for melt viscosity. Most likely, the influence of Si4þ and Al3þ is hidden in the complex nature of the c1-3 parameters. Moreover, the use of oxide components results in problems similar to that of Eq. (5.1) in that an additive nature is assumed. The limitations of the Giordano and Dingwell (2003, 2004) model notwithstanding, it does reproduce magma viscosity better than other viscosity models. Viscosity of natural magma in the

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Chapter 5 Structure of magmatic liquids

FIGURE 5.9 Olivine/melt partitioning as a function of NBO/T of the melt. (A) Mn partition coefficient, Mnolivine/Mnmelt. (B) Fe2þ/Mg exchange partition coefficient as a function of NBO/T of the melt. Redrawn from Mysen (2007a).

1200e1600 C temperature range was calculated with this model to obtain a high-temperature activation energy of viscous flow, Eh (Fig. 5.7). Activation energy also is of interest because it can be related to bond strengthdas originally proposed by Bockris et al. (1955). In the 1200e1600 C temperature range, the calculated melt viscosities are assumed to be Arrhenian   (5.3) log h ¼ log ho þ exp Eh = RT : Eq. (5.3) was employed to obtain the activation energies of high-temperature viscous flow, Eh, for tholeiite, andesite, and rhyolite melts. This activation energy decreases as an exponential function of NBO/T with a rapid decrease in the NBO/T-range between about 0 and about 0.3 and a much slower decrease as the NBO/T increases further (Fig. 5.7).

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285

There is considerable scatter in the activation energy versus NBO/T data (Fig. 5.7). This scatter may be in part because the viscosity also depends on the Al/(Al þ Si)-ratio (Riebling, 1964, 1966; Toplis et al., 1997). The remaining scatter is probably because the high-temperature activation energy of viscous flow also is somewhat dependent on the type of network-modifying cations, M (Bockris et al., 1955, 1956). There are several different network-modifying cations in natural magmatic liquids (for the most part Ca, Mg and to a lesser extent Fe2þ). For melts of individual igneous rock groups, there is a near-Gaussian distribution in activation energy of viscous flow (Fig. 5.7). The maxima in the distribution of individual melt groups range over about 50 kJ/mol where, broadly speaking, as the melts become more felsic, there is an increase in both the maximum values and in the average activation energies (average values: 135  3, 142  5, 146  5, and 167  7 kJ/mol, for tholeiite, andesite, phonolite, and rhyolite melts at ambient pressure, respectively). These distributions do, of course, follow the distribution of NBO/T-values (Fig. 5.6) as NBO/T of a melt is a dominant variable governing melt viscosity. The equation-of-state of natural magma (density, compressibility, and thermal expansion) is an important factor governing magma ascent through planetary interiors. Models with which to describe molar volumes, thermal expansion, and compressibility of oxide components in the melts have been derived for natural magma compositions (e.g., Bottinga and Weill, 1970; Bottinga et al., 1982, 1983; Lange and Carmichael, 1987; Kress and Carmichael, 1991). For melts containing all the major components of natural magmatic liquids at near-ambient pressure, Lange and Carmichael (1987) suggested that the molar volume, V, of magmatic liquids simply is the sum of the partial molar volume of individual components V¼

i X i¼1

Xi V i :

(5.4)

where Xi is mol fraction and V i is partial molar volume of oxide, i. Whereas the Lange and Carmichael (1987) data were calibrated by using chemically complex melts resembling natural compositions as starting compositions, Bottinga et al. (1982, 1983) used data from simple binary and ternary melt systems to derive molar volume and thermal expansion of natural silicate melts. In this latter model, at constant temperature the molar volume is, P 0 1 xj Kj i X j B C V¼ (5.5) Xi V i þ XA @ V  þ XA P A x j i¼1 j

where V is a constant, j are components, Al2O3, Na2O, K2O, MgO, CaO, and FeO, XA is the mol fraction of Al2O3, and Kj are constants associated with components, j. This treatment does, therefore, take into account effects of bulk composition and, in particular, the role of Al2O3. The isolation of Al2O3 is important because the AleO bond energy varies with local charge distribution (Riebling, 1964, 1966; Toplis et al., 1997). From the Bottinga et al. (1982, 1983) formulations in Eq. (5.5), the molar volume distributions of tholeiite, andesite, phonolite, and rhyolite melts are distinctly different with the volume maxima of each distribution increasing the more felsic the melts (Fig. 5.8). Notably, the volume trends of melts in simple SiO2-MO melts are qualitatively similar, although they differ quantitatively. The slope of the

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Chapter 5 Structure of magmatic liquids

volume versus NBO/Si in binary SiO2-MO melts decreases as the ionization potential of the M-cation decreases (see insert in Fig. 5.8). The average molar volume for each group of melt follows the same trend of increasing molar volume with increasing SiO2 content and, therefore, in general decreasing NBO/T (24.2  0.8, 26.9  0.8, 27.9  1.1, and 27.9  0.5 cm3/mol for tholeiite, andesite, phonolite, and rhyolite melts, respectively; see also Table 5.2 for average composition of these magma types). The volumes of natural magmatic liquids show a spread of about 1 cm3/mol for any NBO/T-value. This trend suggests that there are also other structural factors playing a role. One is that the molar volume of aluminate components depends on the proportion of Al3þ and on the nature of the chargebalance of Al3þ in tetrahedral coordination (Seifert et al., 1982). The Al/(Al þ Si) ratio alone does not, however, explain the spread because the relationship between molar volume and NBO/T retains a spread in volume between 0.5 and 1.0 cm3/mol even for melts with fixed Al/(Al þ Si). One structural refinement relates to how Al3þ may occupy specific structural entities in the melts such as distribution among structural entites in the melt, for example. Another refinement is the type of chargecompensation of Al3þ. These factors require more structural data from alkaline earth aluminosilicate melts than currently available before realistic testing can be carried out. Information on partitioning of elements and isotopes between melts, minerals and fluids is needed for characterization of igneous processes. However, partition coefficients for a given element can vary widely as a function of melt composition (e.g., Watson, 1977; Jurewicz and Watson, 1988; Jaeger and Drake, 2000; Toplis and Corgne, 2002; Mysen, 2007a,b; 2008). It is necessary, therefore, to establish how melt composition governs the structural variables that affect mineral/melt partition coefficients. Melt/mineral partition coefficients typically decrease with increasing NBO/T of the melt (Mysen and Virgo, 1980; Thibault and Walter, 1995; Jana and Walker, 1997; Jaeger and Drake, 2000). There is not, however, a unifying relationship between partition coefficients and the NBO/T because sometimes the relationships are linear (Mysen and Virgo, 1980; Jaeger and Drake, 2000), but more often than not the mineral/melt partition coefficients are nonlinear functions of NBO/T of the melt (Watson, 1977; Jurewicz and Watson, 1988; Colson et al., 1988; Libourel, 1999; Kushiro and Mysen, 2002; Mysen, 2007a,b; see also Fig. 5.9A). Moreover, the functional form, even for relatively similar cations (in terms of charge and ionic radius) such as Fe2þ and Mg, differs (Mysen, 2007a). These latter variations likely reflect different and nondeal solution behavior of Fe2þ and Mg in the melts because the (Fe2þ, Mg) solid solution in olivine is nearly ideal (Olsen and Bunch, 1970). The spread in activity coefficient melt ratio, gmelt Fe2þ/gMg (Toplis, 2004; see also Fig. 5.10) probably also can be explained in this manner. Interestingly, the activity coefficient ratio also increases with increasing SiO2 of the silicate melt (Toplis, 2004) and, therefore the NBO/T of the melts. It is likely that correlations between partition coefficients and NBO/T of the melt are because most cations in silicate melt are network modifiers. The exact nature of the relationship depends on the element and element pair of interest.1 The exceptions to this rule are Si4þ, Al3þ, Fe3þ, Ti4þ, and P5þ because these cations commonly occupy tetrahedral coordination in melts. Recently, some experimental information suggests that light element stable isotope fractionation involving silicate melts also depend on melt composition and, therefore, melt structure (Wang et al., 2015; Dalou et al., 2015; Mysen, 2018). However such data have not as yet been extended to natural magmatic systems, so this information will not be discussed further here. 1

These relationships were discussed in detail in Chapter 3 in sections on relationships between mineral-melt element partitioning and melt composition and melt structure.

5.3 Silicate melt and glass structure

287

FIGURE 5.10 Activity coefficient ratio, of Fe2þ and Mg in melt as a function of SiO2 concentration in melt. Redrawn from Toplis (2005).

5.3.2 SieOeAl bonding and charge-balance of tetrahedrally coordinated Al3D The substitution of Al3þ for Si4þ in tetrahedral coordination in a glass and melt (and crystalline materials, for that matter, see Angel et al., 1991; Prewitt et al., 1976; Phillips and Ribbe, 1973) is not simply an exchange of Al3þ for Si4þ, but requires charge-compensation to obtain a local electric charge of 4 for tetrahedrally coordinated Al3þ. This charge-balance can be accomplished with the aid of a metal cation such as an alkali metal or an alkaline earth Si4 þ 5Al3þ þ 1=nMnþ :

(5.6)

The strength of the AleO bond depends on the extent to which it is perturbed by the chargebalancing cation. The perturbation, D(TO)aver, of the TeO bond (T ¼ Si þ Al) resulting from the nature of Al3þ charge-balancing cation, can be expressed as a deviation from ideal SieO and AleO bond lengths (Navrotsky et al., 1985); DðTOÞaver ¼ X$DðAlOÞ þ ð1
XÞ$DðSiOÞ.

(5.7)

In Eq. (5.7) D(AlO) and D(SiO) represent the difference of SieO and AleO bond lengths from ˚ , respectively (Navrotsky et al., 1985). ideal values, 1.712 and 1.581 A The perturbation of the TeO bond lengths resulting from different forms of charge-balance of tetrahedral Al3þ affects the stability of mixed aluminosilicates. For example, the stabilization enthalpy, DHstab, relative to the enthalpies of solution of SiO2 and aluminosilicate, DHsoln, has been formulated as follows (Navrotsky et al., 1985): h i   (5.8) DHstab ¼ DHsoln MX=n AlX Si1
x O2
DHsoln ðSiO2 Þ =X: As seen in Fig. 5.11, the perturbation of the TeO bond length is negatively correlated with the stabilization enthalpy. In other words, the more perturbed (and, therefore, weakened) the TeO bond by various charge-balancing cations, the less stable is the aluminosilicate complex. This conclusion is similar to that which was reached from thermodynamic data (Navrotsky et al., 1982). The TO perturbation, DTOaver, can be correlated with melt properties, including those of magma, that depend on AleO bond strength. Melt viscosity is an example of such a property (Fig. 5.12). The

288

Chapter 5 Structure of magmatic liquids

AleO bond perturbation in natural magmatic liquids can, for example, be related to magma type. Given that the alkaline earth/alkali metal ratio increases the more mafic the magma, it follows that the AleO bond perturbation also increases the more mafic the magma. This, in turn, implies that the bond strength of the AleO bonds diminishes the more mafic the magma so that any magma property that can be linked to AleO bond strength would also evolve systematically with composition of the magma. Transport properties such as viscosity and diffusion fall in this category.2

FIGURE 5.11 Enthalpy of stabilization, DHstab, from Eq. (5.8) for meta-aluminosilicate melts as a function of perturbation of TeO bond length, DTOstab. Here, the T-cation is Si þ Al. Numbers in parentheses indicate the Al/(Al þ Si) ratio of the melt. Redrawn from Navrotsky et al. (1985).

2

Transport properties will be described and discussed in Chapter 9.

5.3 Silicate melt and glass structure

289

FIGURE 5.12 Activation energy of viscous flow expresses as a function of perturbation of the TeO bonding in melts.

Alkali metals and alkaline earths can serve both as network modifiers and to charge-balance tetrahedrally coordinated Al3þ (Fig. 5.13). Distribution of network-modifying and charge-balancing cations between different structural positions depends on both electronic properties of the cation and the bulk chemical composition of magmatic liquids (Fig. 5.13). In general, the ionization potential of both network-modifying and charge-balancing decreases the more felsic a magmatic liquid. There is also a tendency of the most electropositive cations (e.g., alkali metals) to serve to charge-balance tetrahedrally coordinated Al3þ compared with more electronegative cations such as alkaline earths. This tendency is related to the relative stability of the aluminate complexes in silicate melts. The more electropositive the charge-balancing cation, the more negative is the heat of solution of the aluminate complex in the melt (Navrotsky et al., 1982). There is structural evidence to suggest differences between a cation in charge-balancing role and as network-modifier. From molecular orbital calculations it has been proposed that the Na-NBO (NBO: nonbridging oxygen) bond is shorter than Na-BO (BO: bridging oxygen) bond. The CaeNBO distances are shorter than Ca-BO distances, for example (Cormack and Du, 2001; Ispas et al., 2002; Cormier et al., 2003). The NaeO bond distance might be as much as 10% shorter for Na-NBO than of the Na-BO. This difference can be detected in the 23Na MAS NMR spectra of melts and glasses because different bond lengths affect the shielding of the Na nucleus. The Na nucleus becomes more deshielded with increasing Na/Si, which would lead to increased Na-NBO distance with increasing Na/ Si (Xue and Stebbins, 1993; Lee and Stebbins, 2003; Cormier and Neuville, 2004). Given the premise that both Al/(Al þ Si) and alkaline earth/alkali metal ratios vary significantly in magmatic liquids (Table 5.2), differences between mafic and felsic magma to a considerable extent may be characterized in the same terms. From the several thousand analyses of natural melts, Kþ, Naþ, and Ca2þ for all practical purposes are the cations that charge-balance tetrahedrally coordinated cations in melts of natural composition (Fig. 5.13). For andesitic and less felsic (lower SiO2 contents) melts, the main charge-balancing cations are Ca2þ and Mg2þ. The proportion of Ca2þþMg2þ relative

290

Chapter 5 Structure of magmatic liquids

FIGURE 5.13 Abundance, calculated as percent relative to total, of cations serving to charge-balance tetrahedrallycoordinated Al3þ and also serving as network-modifier in melts as indicated. Rock data used in the calculation from http://Earthchem.org. Presentation redrawn from Mysen and Richet (2005).

5.3 Silicate melt and glass structure

291

to (NaþþKþ) decreases as the magma composition becomes more felsic so that alkali charge-balanced Al3þ dominates over Ca2þ in rhyolite melt (Fig. 5.13). In the most felsic magmatic liquids about 80% or less of total alkalis serve to charge-balance tetrahedrally coordinated Al3þ, while between 20% and 80% of total Ca2þ serve as network modifiers. In less felsic melts such as andesite and tholeiite, alkali metals are never network modifiers because Na þ K serve exclusively to charge-balance Al3þ in tetrahedral coordination. A fraction of Ca2þ is also a network-modifier in such melts, whereas Mg2þ and Fe2þ are always network modifiers.

5.3.2.1 (Al,Si) mixing and melt and magma properties The ionization potential of the charge-balancing cation(s) also has an influence on the extent of Al 5 Si ordering in aluminosilicate melt structures (Seifert et al., 1982; Lee and Stebbins, 1999, 2006), which, in turn, affects thermodynamic properties of aluminosilicate melts (Lee and Stebbins, 1999). This happens, for example, because even though Naþ and Ca2þ have similar ionic radii (Whittaker and Muntus, 1970), these two cations can charge-balance two and one tetrahedrally coordinated Al3þ, respectively. Melt properties, including Al 5 Si ordering of Na-charge-balanced aluminosilicate melt structure, are different from Ca-charge-balanced aluminosilicate melt structure. The relationships between Al/Si-ratio and properties of natural magmatic liquids also change between felsic and mafic magmatic liquids because of the greater ordering of Al3þ and Si4þ in basaltic melt compositions compared with rhyolite melt compositions driven by the electronic nature of the charge-balancing cation(s). The variable Al 5 Si ordering impacts on thermodynamic properties of aluminosilicate melts (Lee and Stebbins, 2000). These thermodynamic properties include configurational entropy and enthalpy. Configurational entropy of alkaline earth aluminosilicate melts is greater than that of alkali aluminosilicate melts (Richet and Neuville, 1992). Activity-composition relations along SiO2-aluminate joins are near ideal with alkali charge-balanced Al3þ,whereas there are significant deviations from ideal mixing along SiO2daluminate join with alkaline earths for charge-balance of Al3þ in tetrahedra coordination (Roy and Navrotsky, 1984).3 Electronic properties of the charge-balancing cation affect physical properties of aluminosilicate melts. This feature is well illustrated in volume and compressibility data of aluminosilicate melts (Roy and Navrotsky, 1984; see also Fig. 5.14). Magmatic liquids with alkaline earths for charge-balance of Al3þ are less compressible than those where alkali metals are the dominant charge-balancing cations. From such relationships, it follows that alkali basalt magma, for example, is more compressible than tholeiitic magma. Andesite and rhyolite magmatic liquids are more compressible than basaltic liquids. Melt viscosity and its temperature and pressure dependence also are sensitive to the electronic properties of the charge-balancing cation or cations (Kushiro, 1978, 1981; Urbain et al., 1982). Translated to natural magmatic liquids where the type and proportions of the charge-balancing cations varies significantly (Fig. 5.13), effects of Al/Si-ratio on properties of different magmatic liquids also will be affected differently. For example, the different compressibility of felsic melts such a rhyolite magma compared with the compressibility of mafic melts such as basalt magma, in addition to their different SiO2 contents, results in different extent to which (Al,Si)eO bonds are affected by Al/(Al þ Si) of the magmatic liquid (see Chapter 9 for more 3

The reader is referred to Chapter 4 for more detailed discussion of these features.

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Chapter 5 Structure of magmatic liquids

FIGURE 5.14 Molar volume of melts along meta-aluminosilicate melts as indicated as a function of their Al/(Al þ Si). Notice how the molar volume evolution in melts with mono- and divalent cations for Al3þ charge-balance as a function of Al/(Al þ Si) differ. Redrawn from Roy and Navrotsky (1984).

details). This difference, in turn, also results in the pressure-dependence of magma viscosity is greater for felsic than mafic melts (Kushiro et al., 1976).

5.3.3 Silicate speciation (Qn-species) A comparison of vibrational and NMR spectra of melt, glass and their crystalline equivalents of simple binary and ternary compounds leads to the suggestion that there exist considerable structural similarities between glass, melts, and their crystalline equivalents as originally noticed by Etchepare (1972) in a Raman spectroscopic study of CaMgSi2O6 crystalline and glassy materials. Brawer and While (1975) expanded such studies to include a broad range of amorphous and crystalline materials with varying metal oxide/SiO2 ratios. From the Raman spectra of metal oxide silicate glass, Brawer and White (1975) found structural units resembling SiO2, Si2O5, and SiO3 units with apparent maximum abundance for compositions corresponding to the crystalline equivalents. Virgo et al. (1980) suggested that disproportionation reactions such as; Si2O5 5 SiO3 þ SiO2, describe their equilibrium relations.

(5.9)

5.3 Silicate melt and glass structure

293

In a vibrational spectroscopic study of glass (formed by temperature-quenching of their melts) compositionally ranging from pure SiO2 to compositions near orthosilicate, not only do SiO2, SiO3and Si2O5-like structures exist, but there are additional types of units such as Si2O7, and SiO4 groups (Mysen et al., 1982). The stoichiometric notations (SiO2, Si2O5, SiO3, Si2O7, and SiO4) were replaced by the so-called Qn concept starting with Schramm et al. (1984) in their study of 29Si NMR spectra of Li2OeSiO2 glasses. In this notation, the superscript, n, denotes the number of bridging oxygen in the structural unit. In this notation, therefore, SiO2 unit is equivalent to Q4, Si2O5 to 2Q3, SiO3 to Q2, Si2O7 to 2Q1, and SiO4 to Q . An equation equivalent to (5.9), then can be written using Qn-species notation (Stebbins, 1987); 2Qn 5 Qn


1

þ Q n þ 1.

(5.10)

In Eq. (5.10), the n-values are integers between 0 and 4 (Stebbins, 1987; Zhang et al., 1996). The n-values and Qn-abundance depend on the bulk polymerization of the magmatic liquid. Silicate glass and melt structure comprising a small number of well-defined anionic silicate units not only is supported by an extensive 29Si MAS NMR literature, but is also consistent with Raman spectra of the materials. In fact, a striking feature of alkali and alkaline earth glass Raman spectra is that, regardless of the metal/silicon ratio, the frequencies assigned to antisymmetric SieO stretch vibrations in the various Qn-species are nearly independent of glass composition (Mysen et al., 1982). This feature can be interpreted to indicate that there is no structural variation of the individual silicate unit. Only their proportions change as a function of changing bulk composition of melt. Silicon-29 NMR spectra of glass have been used to determine the abundance ratios of structural units (see Fig. 5.15). In pure SiO2 glass, only Q4 species exists (with the possible exception of some bond defects). Addition of metal oxide to SiO2 results in decreasing Q4 abundance and an increase of Q3 and Q2 abundance. The Q3 abundance reaches a maximum near the disilicate stoichiometry (Si2O5). The Q2 abundance reaches a maximum at melt stoichiometry near that of metasilicate (SiO3). Similar Qn-species abundance behavior exists in natural magmatic liquids (Fig. 5.16). The information in Figs. 5.15 and 5.16 can be interpreted to indicate that the abundance of Qnspecies also varies with the electron properties of the network-modifying metal cation both in the simple silicate glasses and melts as well as chemically more complex natural magmatic liquids. This is because for a melt with fixed M/Si-ratio, and, therefore, NBO/T, the abundance of Q3 species decreases with increasing ionization potential of M-cations, whereas the abundance of Q2 and Q4 increase (see also Fig. 5.15). These relationships suggest that Eq. (5.10) shifts to the right, at least for n ¼ 3, with increasing ionization potential of the metal cation (Mysen, 1997; Lin et al., 2010). The data scatter for natural magmatic liquids in Fig. 5.16 may be the result of effects of different metal cations such as illustrated in Fig. 5.15.

5.3.3.1 Silicate (Qn)-species and temperature The information discussed in previous sections comprised data recorded on glasses that had been temperature-quenched from melt equilibrated at temperatures above that of their glass transition. The structure of such glasses is, therefore, that of supercooled melt frozen within the glass transition range. However, both melt structure and melt properties above the glass transition temperature vary with temperature (Bockris et al., 1955; Seifert et al., 1981; Stebbins et al., 1985; Dingwell and Webb, 1990; McMillan et al., 1992; Mysen and Frantz, 1993). Therefore, structure and property data of glasses cannot be extrapolated quantitatively to conditions of a hightemperature melt.

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Chapter 5 Structure of magmatic liquids

FIGURE 5.15 Qn-species abundance in binary alkali silicate melts as a function of bulk melt NBO/Si and ionization potential, Z/r2, of the alkali metal. Notice how, for given bulk melt NBO/Si, Qn-species abundance evolves as systematic functions of the ionization potential of the alkali metal. This evolution reflects increasing equilibrium constant for Eq. (5.10) with increasing ionization potential. Redrawn from Maekawa et al. (1991).

5.3 Silicate melt and glass structure

295

FIGURE 5.16 Calculated Qn-species evolution for natural magma compositions at ambient pressure as a function of their NBO/T. Data base: http://Earthchem.org.

The structural relaxation in metal oxide-silica glasses occurring as the temperature is increased across glass transition is manifested by a distinct change in the slope of the Qn abundance versus temperature relationship (Fig. 5.17). Below the glass transition, Tg, the Qn-species abundance does not vary with temperature, whereas above Tg, the species abundance varies systematically with temperature while the overall NBO/T of the melt remains constant. From in situ, high-temperature studies of several metal oxide silicate melt systems at temperatures above that of the glass transition (McMillan et al., 1992; Mysen and Frantz, 1993), Eq. (5.11) with n ¼ 3 shifts to the right with increasing temperature. This shift can be expressed in terms of the effect of temperature on the constant, K, for that equilibrium; XQ2 $XQ4 K¼  2 XQ 3

(5.11)

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Chapter 5 Structure of magmatic liquids

FIGURE 5.17 Evolution of Q 2, Q 3, and Q4 as a function of temperature above and below the glass transition. Note how below the glass transition, the Qn-species abundance does not change with temperature, whereas above Tg it does. Redrawn from Mysen (1999).

where it is assumed that the mol fraction of the individual Qn-species, XQn, is equal to activity. For a glass below its glass transition temperature, the equilibrium constant in Eq. (5.11) does not vary with temperature (Fig. 5.18). Above the glass transition, ln K is a linear function of reciprocal temperature. This ln K also is a positive function of the ionization potential of the metal cation (Mysen and Frantz, 1993). The enthalpy (DH) of reaction (5.10) can be estimated from the slope of the ln K versus 1/T relationship in Fig. 5.18; ln K ¼
DH=RT þ DS=R:

(5.12)

The DH is positively correlated with the ionization potential of the network-modifying metal cation (see insert of Fig. 5.18). The DH-behavior is because increasingly electronegative metal cation form bonding with nonbridging oxygen in increasingly depolymerized Qn-species (Jones

5.3 Silicate melt and glass structure

297

FIGURE 5.18 Equilibrium constant, K, as a function of inverse absolute temperature for Na2Si2O5 composition melt below and above the glass transition. Insert shows the enthalpy change, DH, for reaction (5.10) as a function of ionization potential of different metal cations for disilicate melts, M2Si2O5. Redrawn from Mysen (1999).

et al., 2001; Lee and Stebbins, 2003) and Q2 is less polymerized than Q.3 The result is a shift Eq. (5.11) to the right, which leads to increased values of the equilibrium constant, K, in Eq. (5.12). Qualitatively, these relationships can also be extended to the temperature-dependent Qn-species in magmatic liquids. In light of the fact that the abundance ratio, alkaline earth/alkali metal, increases as a magma becomes increasingly mafic, the DH of the speciation reaction also increases the more mafic the magma.

5.3.3.2 Silicate (Qn)-species, cation coordination, and pressure Numerous magmatic processes take place at depth in the Earth. It is necessary, therefore, to characterize pressure effects on structure and relationships between structure and property of magma at pressures greater than ambient. Pressure can affect the structure silicate melts by (1) decreased intertetrahedral angles and associated lengthening of (Si,Al)eO bridging bonds (Brown et al., 1969; Xue et al., 1991; Gaudio et al., 2008; Sanchez-Valle and Bass, 2010), (2) changes in the disproportionation reaction (5.11) (Dickinson

298

Chapter 5 Structure of magmatic liquids

et al., 1990; Xue et al., 1991), and (3) coordination changes of network-forming and networkmodifying cations (Diefenbacher et al., 1998; Lee et al., 2005; Wilding et al., 2008; Adjaoud et al., 2008; Lee, 2011). Aluminosilicate compositions make up about 95% of the chemical composition of natural magmatic liquids. Aluminosilicate melts differ from Al-free silicate melts in that bond length and bond angle changes generally take place at lower pressures (Seifert et al., 1983; Sykes et al., 1993; Poe et al., 2001; Sakamaki et al., 2012). This difference is likely because the strength of IVAleO bond is only 20%e30% of that of IVSieO bonds. Aluminum coordination changes typically occur and lower pressure than coordination changes of Si4þ (Ohtani et al., 1985; Yarger et al., 1995; Bryce et al., 1999; Lee and Stebbins, 2006; Allwardt et al., 2007; Ni and de Koker, 2011; Karki et al., 2011; Drewitt et al., 2011). At pressures up to several GPa, the aluminosilicate melt structure responds to applied pressure by (Si,Al)eOe(Si,Al) and Oe(Si,Al)eO angle compression (Fig. 5.19). The (Si,Al)eOe(Si,Al) angle compression is governed by both Al/(Al þ Si) and the ionization potential of the cations that chargecompensate tetrahedral Al3þ. For example, the intertetrahedral angle is more sensitive to pressure in SiO2eNaAlO2 than in SiO2eCaAl2O4 melts (Mysen et al., 1983; see also Fig. 5.19). Furthermore, whereas the decrease of intertetrahedral angle is positively correlated with Al/(Al þ Si) in SiO2e NaAlO2 melts, the intertetrahedral angle in SiO2eCaAl2O4 melts becomes less compressible with increasing Al/(Al þ Si) (Mysen et al., 1983). This different pressure response is because of the different electronic environment of Al3þ linked to different charge-compensating metal cation. In the SiO2eNaAlO2 system, substitution of Al3þ for Si4þ results in increasing Al/(Al þ Si) in the 3dimensionally interconnected rings. Because of bond weakening as the bulk Al/(Al þ Si) increases, these bonds become more flexible and the (Si,Al)eO-(Si,Al) angles more compressible. In SiO2eCaAl2O4 melts, on the other hand, the Al/(Al þ Si) in the coexisting three-dimensionally interconnected structural units does not vary with the bulk Al/(Al þ Si). Only their proportions do (Fig. 5.20). Therefore, the changes in average intertetrahedral angles merely reflect variations of the proportions and compressibility of these units. Among these structural units, the more open Aldeficient or Al-free unit (Si-unit in Fig. 5.20) likely is the most compressible. As the abundance of these latter structural entities decreases with increasing Al/(Al þ Si), melt compressibility of the melt also decreases. Angle compression and bond length expansion become less important with increasing metal/Siratio and, therefore, increasing NBO/T of a melt. This is because the fully polymerized Q4 species are more compressible than less polymerized Qn-species and the proportion of Q4 species decreases as a melt becomes more depolymerized (NBO/T increases). It follows that the more felsic a magmatic liquid, the more compressible it is. Therefore, any magma property that is linked to (Si,Al)eOe(Si,Al) angle compression becomes more important the more silica-rich a magma. Pressure effect on magma viscosity is an example of this structural effect. As the (Si,Al)eOe(Si,Al) angle is compressed, the (Si,Al)eO bond strength diminishes and the activation energy of viscous flow decreases. As seen from Eq. (5.3), melt viscosity is proportional to activation energy of viscous flow. Therefore, viscosity decreases more rapidly with increasing pressure the more felsic the magma as also has been observed experimentally (Kushiro et al., 1976). An additional consideration is that the Q4/SQ0e4 abundance ratio even for magma of fixed NBO/T, is linked to the abundance ratio of metal cations, M2þ/Mþ. With divalent cation such as Ca2þ, and even more so Mg2þ, the Q3 abundance is lower than is the case for monovalent network-modifying cations, Mþ (Mysen, 1987). When this happens, the Q4 þ Q2

5.3 Silicate melt and glass structure

299

FIGURE 5.19 Intertetrahedral angle change, (Si, Al)eOe(Si, Al), as a function of pressure for melts along the joins SiO2eCaAl2O4 and SiO2eNaAlO4 at Al/(Al þ Si) as indicated in diagram. Notice how much more compressible this angle is for alkali aluminosilicate melts. Data from Mysen et al. (1983).

abundance increases to ensure fixed NBO/T-value. Therefore, tholeiite magmas are more compressible than alkali basalt, for example. Again, this implies that any magma property that depends on magma compressibility is more sensitive to pressure for tholeiitic than for alkali basaltic magma. Melt structural changes with pressure can also take place because of volume change of reaction (5.10). The DV of this reaction is governed by the partial molar volumes of the Qn-species, which, in turn, are linked to the proportion bridging (BO) and nonbridging (NBO) oxygens (Bottinga and Richet, 1995). The DV also depends on the compressibility of the metal-oxygen polyhedra, and on the compressibility of the individual Qn structural units. The partial molar volume of bridging oxygen is greater than that of nonbridging oxygen (Bottinga and Richet, 1995), a suggestion that is consistent with the larger Si-BO bond distance than Si-NBO bond distance (Lee and Stebbins, 2003). The Q4-species with its four bridging oxygen bonds, therefore, likely has the largest partial molar volume. The Q2 species with two nonbridging and two bridging oxygens likely will have a smaller partial molar volume than Q3 species with only one nonbridging and two bridging oxygen. The DV of reaction (5.10), therefore, most likely is negative. The volume effect probably is further enhanced because of the greater compressibility of Q4 structures compared with Q3 and Q2. Reaction (5.10) will, therefore, shift to the right with increasing pressure. These

300

Chapter 5 Structure of magmatic liquids

FIGURE 5.20 Species evolution with Al/(Al þ Si) for melts along the join SiO2eCaAl2O4. Here the Si-unit is approximately SiO2 stoichiometry, Si0.5Al0.5-unit approximately CaAl2Si2O8, and Al-unit, AlO2. The Al/(Al þ Si) of these units does not change with changes in bulk melt Al/(Al þ Si). Only their abundance changes as shown in the Figure. Redrawn from Seifert et al. (1982).

volume considerations above are consistent with observed changes of the species abundance that define Eq. (5.10) with pressure (Mysen, 1990; Xue et al., 1991; Dickinson et al., 1990). The Q2 and Q4 abundance does indeed increase with pressure, whereas that of Q3 decreases. As pressure is increased to 8e10 GPa or more, there is a gradual increase in oxygen-coordination surrounding the metal cations in aluminosilicate melts (Yarger et al., 1995; Bryce et al., 1999; Lee and Stebbins, 2006; Lee et al., 2012; Allwardt et al., 2005, 2007; Kelsey et al., 2009; Ni and de Koker, 2011; Drewitt et al., 2011; see also Fig. 5.21). Increasing coordination number results in increased bond lengths. The MeO bond length is considerably more sensitive to pressure than are AleO and SieO bond lengths (Drewitt et al., 2011, 2015; Ni and De Koker, 2011). This, in turn, leads to greater changes in coordination numbers of network-modifying than network-forming cations as the pressure is increased (Fig. 5.22). In may be suggested, in fact, that there likely is a positive correlation between bond strength and sensitivity of cations of coordination transformation with increasing pressure. Applied to natural magmatic systems, those latter relations imply that the more mafic a magma and, therefore, the greater the proportion of network-modifying metal cations, the grater is the rate of increased average oxygen-coordination with increasing pressure. Moreover, with increasing ionization potential of the charge-balancing cation for Al3þ, the Al3þ coordination becomes increasingly sensitive to pressure (Fig. 5.23). These differences are greater in alkaline earth than in alkali aluminosilicate melts (Ni and de Koker, 2011; Drewitt et al., 2015). The results from the Drewitt et al. (2015) experiments are also interesting in that they subjected both melt and its glass to high pressure. For melts, there is the difference in coordination number response between the different cations. However, for the glass there is no difference (see Fig. 4 in

5.3 Silicate melt and glass structure

301

FIGURE 5.21 Abundance evolution of Qn-species in temperature-quenched melts as a function of pressure for composition Na2Si2O5. Redrawn from the data of Xue et al. (1991).

FIGURE 5.22 Average coordination numbers for cations indicated as a function of pressure at temperatures near 3000K. Redrawn from Drewitt et al. (2011).

Drewitt et al., 2015). One must be careful, therefore, when using the pressure-induced behavior of glass as a proxy for pressure-induced structural behavior of its melt.

302

Chapter 5 Structure of magmatic liquids

The pressure-dependent coordination of Al3þ has attracted more attention than the coordination behavior of Si4þ and network-modifying cations. In numerical simulations, four-, five-, and sixfold coordinated Al3þ is found in high-pressure alkali aluminosilicate melts. The proportions of IVAl decreases, that of VAl initially increases, but passes through a maximum at a few GPa pressure. In contrast, VIAl increases gradually with increasing pressure (Bryce et al., 1999; Ni and de Koker, 2011). In a MAS 27Al NMR study, evidence for partial coordination transformation of Al3þ in a (NaAlSi3O8)50(Na2Si4O9)50 sample at  6 GPa (Lee et al., 2006), both five- and sixfold coordinated Al3þ reported. It is also clear that the proportion of both five- and sixfold coordinated Al3þ is positively correlated with pressure, but that the pressure at which higher oxygen-coordination numbers can be detected is considerably less than that where minerals with Al3þ in sixfold coordination become stable (Lee et al., 2006, 2012). Moreover, the pressure at which any coordination change begins to take place, and finishes, is sensitive to Al/(Al þ Si). These pressures also decrease as a melt becomes increasingly depolymerized (Lee et al., 2012). Finally, the extent of coordination changes with pressure also depends on the electronic properties of the charge-balancing cation (Fig. 5.23). For peralkaline4 melt compositions in the system K2OeCaOeMgOeAl2O3eSiO2, Allwardt et al. (2007) found that average Al3þ coordination increases the greater the ionization potential of the charge-balancing metal cations. It warrants notice, though, that the melts in that latter experimental study also are peralkaline with different degree polymerization at ambient pressure (NBO/T differences). As discussed above, the response of Al3þ coordination to pressure also depends on peralkalinity (Lee et al., 2003, 2006). Finally, the treatment in Fig. 5.23 does not consider the tendency of the more electronegative (higher Z/r2-value) metal cations to associate with NBOs, whereas the more electropositive cation serves to charge-compensate Al3þ when in tetrahedral coordination (see, for example, Neuville et al., 2008; for more discussion of these effects). Although little direct structural information exists for natural melts at high pressure and temperature (the results of Drewitt et al., 2011; 2013, 2015; and Sanloup et al., 2013 appear to comprise most of such data), the experimental information obtained by examination of chemically simpler systems, in particular aluminosilicate melts, provides a basis on which general structural trends of natural magmatic liquids may be extracted. The overall extent of melt polymerization of magmatic melts decreases as these become more felsic. The pressure at which coordination changes of networkforming cations (Si4þ and Al3þ) takes place increases with decreasing NBO/T. It follows that the more felsic a magmatic liquid, the greater is the pressure at which Al3þ and Si4þ coordination transformation begins. In other words, coordination changes in basalt melt would occur at shallower depth than andesite and rhyolite melt. Furthermore, when comparing tholeiite and alkali basalt melt, the latter has the greater proportion of alkaline earths. It follows that Si4þ and Al3þ coordination in tholeiite melt occurs at shallow depth in the Earth than in alkali basalt melt. Given that such coordination transformation leads to an increase in the NBO/T of a magma, any melt property that depends on its NBO/T will also be more sensitive to pressure for magma compositions that tend to favor coordination transformations. This includes all transport properties (see Chapter 9 for detailed discussion) and mineral/melt major and trace element partitioning (see Chapter 3 for detailed discussion). Moreover, as magma compressibility decreases as the magma becomes less polymerized (increasing

4

See Fig. 5.24 for definition or peralkaline, meta-aluminous and peraluminous aluminosilicate compositions.

5.3 Silicate melt and glass structure

303

FIGURE 5.23 Average Al3þ coordination number as a function of pressure and ionization potential, Z/r2, of the metal cations for CaOeK2OeAl2O3eSiO2 (Z/r2 ¼ 1.02, NBO/T ¼ 0.35), CaOeMgOeK2OeAl2O3eSiO2 (Z/r2 ¼ 2.22, NBO/ T ¼ 0.5), and CaOeMgOeAl2O3eSiO2 (Z/r2 ¼ 2.93, NBO/T ¼ 0.7) melts. The glasses were formed by tempeature-quenching from temperatures above their liquidii and quenching rates exceeding 100 C/s. Redrawn from thee data from Allwardt et al. (2007).

NBO/T), the pressure at which magma compressibility decreases is less for basaltic melts than for more felsic magmas such as andesite and rhyolite, for example (see Chapter 10 for detailed. discussion).

5.3.3.3 Silicate (Qn)-species and cation ordering

The proportion of Qn-species both in simple synthetic silicate melts and chemically complex magmatic liquids is governed by the overall ratio of network-modifying to network-forming cations (Figs. 5.15 and 5.16). The Qn-species abundance also can vary as a function of the type of metal cation in the alkali silicate glass (Fig. 5.15) so that Eq. (5.10) shifts to the right, at least with n ¼ 3, with increasing ionization potential of the metal cation (Mysen, 1997; Lin et al., 2010). This shift is also seen in the DH-value extracted from the temperature-dependent equilibrium constant Eq. (5.11), which becomes increasingly negative as the ionization potential of the metal cation decreases (insert in Fig. 5.18). The relationship between ionization potential of M-cations and Qn abundance in metal oxide silicate melts (Fig. 5.15) leads to the suggestion that the nonbridging oxygens in the various Qn-species are not energetically equivalent. This feature, originally proposed by Kohn and Schofield (1994), has been substantiated via 29Si MAS NMR and 17O triple quantum NMR spectroscopy (Jones et al., 2001; Lee and Stebbins, 2003; Lee et al., 2003). Other properties, such as mineral/melt partitioning, for

304

Chapter 5 Structure of magmatic liquids

example, also indicate some ordering of nonbridging oxygen in silicate glasses and melts (Kohn et al., 1994; Mysen, 2007b). This feature also may help explain why melt/mineral element partitioning depends on the proportion and type of major element metal cations in the melt (Mysen, 2007b). As an example, for the Ca, Mg exchange between olivine and melt, the most electronegative cation, Mg2þ, is associated with Q0 and Q2 silicate species only, whereas the less electronegative cation, Ca2þ, is associated with more polymerized silicate species such as Q3 and Q2 (Mysen, 2007b). It is clear, therefore, that the more electronegative the metal cation, the stronger is its tendency to bond with nonbridging oxygen in the least polymerized Qn-species available. This is also seen in the effect of cation size on OeSieO angles in SiO3 chains in glasses. Here, the chain becomes increasingly buckled the smaller the cation (Yasui et al., 1983). Similar structural effects have been observed in crystalline metasilicate structures (Liebau and Pallas, 1981).

5.3.4 Al3D substitution for Si4D in magmatic systems In magmatic liquids, the dominant substitution for Si4þ is with Al3þ. As noted in Section 5.3.2 above, such substitution, whether in melts, glasses or crystalline materials, requires charge-compensation in order to reach an effective 4þ electrical charge. In depolymerized silicate melts, which includes most natural magmatic liquids, charge-balance of Al3þ takes place when the proportion of charge-balancing cation(s) (alkali metals and alkaline earths) is equal to, or in excess of, that of the proportion of Al3þ. It is convenient, therefore, to subdivide aluminosilicate melt composition into three groups (Fig. 5.24). With excess alkali metal or alkaline earth over that required to provide a formal charge of 4þ for Al in tetrahedral coordination, the system is termed “peralkaline.” When the proportion is

FIGURE 5.24 Definition of peralkaline, peraluminous, and meta-aluminous compositions in the Mnþ On/2eAl2O3eSiO2 where M is alkali metals and alkaline earths. Data range for most igneous rocks from http://Earthchem.org.

5.3 Silicate melt and glass structure

305

exactly equal to that required to provide a formal charge of 4þ for Al3þ in tetrahedral coordination, the system is termed “meta-aluminous.” When the proportion of Al3þ exceeds that of available cations for charge-balance, the system is “per-aluminous.” Among natural magmatic liquids, essentially all are peralkaline. The exception is peraluminous granitic magma. A number of properties and structural features of melts and glasses tend to reach maximum or minimum values at or near the SiO2dMn þ AlnO2n (meta-aluminosilicate) compositions (Roebling, 1964, 1966; Toplis and Dingwell, 2004; Webb, 2007, 2011; see also Fig. 5.25, which illustrates this effect with configurational heat capacity). It has been proposed that in order to account for this effect, the abundance of fivefold coordinated Al3þ (VAl) increases as the composition shifts into the peraluminous region (Neuville et al., 2007). The proportion fivefold coordinated Al3þ has been reported as positively correlated with the ionization potential of the charge-balancing cation. With the fivefold coordination of Al3þ, the proportion of nonbridging oxygen also increases as a magma becomes more peraluminous. An implication of this information is that the more mafic a magma with the greater M2þ/Mþ abundance ratio (see average bulk composition of magma in Table 5.2), the greater is the proportion of fivefold coordinated Al3þ. Another proposed structural mechanism for Al3þ in peraluminous melts is to form Al triclusters (Thompson and Stebbins, 2011). The Al3þ in triclusters remains in fourfold coordination. In this structural environment, the proportion of nonbridging oxygens would decrease as the melt becomes more peraluminous.

FIGURE 5.25 Variations in configurational heat capacity of sodium aluminosilicate melts as a function of peralkalinity, Na2O/ (Na2O þ Al2O3). Redrawn from Webb (2008, 2011).

306

Chapter 5 Structure of magmatic liquids

The increasing configurational heat capacity also increases as melts become peralkaline (Richet, 1984). Nearly all magmatic liquids are peralkaline. The greater the metal oxide/aluminosilicate ratio (greater NBO/T), the greater is the configurational heat capacity. As discussed in more detail in Chapter 9, the greater the configurational heat capacity, the greater is the deviation from Arrhenian behavior of magma transport properties. Translated to magmatic liquids, this trend in general leads to the conclusion that the more mafic a magma, the greater is the deviation from Arrhenian transport properties. In most magmatic liquids, therefore, multiple Qn-species coexist in which Al,Si substitution leads to further structural complexity. In such melts, Merzbacher et al. (1990) concluded that Al3þ resides dominantly in Q4 units. Their observation is similar to other results from 29Si and 27Al MAS NMR as well as results from molecular dynamics simulations of peralkaline, low-Si and melts in the Na2OdAl2O3dSiO2 system (Engelhardt et al., 1985; Cormier et al., 2003; Allwardt et al., 2003; Mysen et al., 2003). These features are why Al3þ occupies predominantly the Q4 structural location (Fig. 5.26A). The Al,Si substitution leads to increasing Q4 abundance and, at the same time, decreasing Q3 and Q2 abundance with increasing Al/(Al þ Si) (Fig. 5.26). The bulk melt NBO/T does not change in this process. In peralkaline alkaline earth aluminosilicate glasses and melts, some of the Al3þ also is in five- and sixfold coordination, where the proportion of the Al-species are functions of both Ca/Mg and Al/ (Al þ Si) even at ambient pressure (Neuville et al., 2008). The proportion of higher-coordinated Alspecies in these melts generally decreases with increasing Ca/(Ca þ Mg) ratio. The proportion of higher-coordinated Al-species also increases as a melt becomes less aluminous. Finally, in mixed Ca,Mg aluminosilicate melts, there is ordering of Ca2þ and Mg2þ among the oxygen anions to which

A

Al/(Al+Si)Q

n

0.3

0.2

0.1

0.0 0.0

60

Q4

0.2 Al/(Al+Si)

Q

3

Q

2

0.4

Concentration, mol %

0.4

Q4

B

50 40 30

Q2

20

Q3

10 0.0

0.2 Al/(Al+Si)

0.4

FIGURE 5.26 Al3þ-distribution in peralkaline Na aluminosilicate melts. A. Al/(Al þ Si) in coexisting Q 2, Q 3, and Q4 structural units. Notice how the Al abundance increases rapidly in Q4 units, whereas there is little Al3þ in Q3 and Q2 units. B. Q 2, Q 3, and Q4 abundance evolution in Na2Si3O7eNa2(NaAl)3O7 melts as a function of bulk melt, Al/ (Al þ Si) at ambieznt pressure. Redrawn from Mysen et al. (2003).

5.3 Silicate melt and glass structure

307

they bond so that the local nonbridging oxygen environment is enriched in Mg2þ over the average Ca/ Mg abundance ratio, whereas Ca2þ preferentially serves to charge-balance tetrahedral Al3þ (Kelsey et al., 2008). The comments above notwithstanding, the structural role of Al3þ in alkaline earth aluminosilicates melts is less well known than alkali aluminosilicate melts at least in part because liquid immiscibility limits in ternary aluminosilicate melts restricts the compositional range that can be examined (see Osborn and Muan, 1960b,c for liquidus phase diagrams). Further, rapid nucleation of supercooled liquids on the time scale of spectroscopic measurements of melts (Roskosz et al., 2005) tends to restrict the temperature range over which the structure of peralkaline melts can be studied. Given that in most magma composition, essentially all tetrahedrally coordination Al3þ is charge balanced by Ca2þ (Fig. 5.13), application of existing aluminosilicate melt structural data to natural magmatic liquids is somewhat limited in particular for mafic melts such as basaltic magma.

5.3.4.1 Qn-species, Al-distribution, and properties of magmatic liquids There are several examples of how variations in silicate species abundance resulting from variations in alkali/alkaline earth or Al/Si abundance ratios can govern cation exchange equilibria between melts and minerals. For example, Fe2þ-Mg olivine/melt exchange equilibrium coefficients in the 8component system K2OeNa2OeCaOeMgOeMnOeFeOeAl2O3eSiO2 evolve as a parabolic function of NBO/T of the melt (Kushiro and Mysen, 2002; see Fig. 5.9B). This parabolic trained reflects the evolution of Q,4 Q3, and Q2 species abundance in the melt as a function of bulk melt NBO/T Kushiro and Mysen, 2002). The maximum in Fig. 5.9B corresponds to the maximum Q3 abundance. Multiple network-modifying cations exist in magmatic liquids. These cations exhibit a preference for specific types on nonbridging oxygen. Among these, the cation with the largest ionization potential (Z/r2), which is Mg2þin most natural magma, would show a preference for nonbridging oxygen in the most depolymerized silicate structures (Lee et al., 2003). Such preferences among NBO in silicate melts can also be observed in evolution of crystal/liquid partitioning as a function of available NBO sites such as relationship to Na/(Na þ Ca) of a melt, for example (Fig. 5.27). The evolution in this latter figure is a direct reflection of how cation preferences affect activity-composition relationships in melts as long as the activity coefficient ratio of the pair of elements does not vary with chemical composition. For an exchange equilibrium of the form imelt þ Mgmin ¼ imin þ Mgmelt,

(5.13)

we have an equilibrium coefficient  min=melt KDði
MgÞ ¼

Xi XMg

min   Xi melt $ ; XMg

(5.14)

where X is mol fraction, i is an element different from Mg, and min denotes mineral. There is a positive correlation between the exchange equilibrium coefficient and the Na/(Na þ Ca) of the melt (Fig. 5.27A). This relations exists because increasing Na/(Na þ Ca) results in increasing availability of the most depolymerized Qn-species because Na þ forms bonding with nonbridging oxygen in the most polymerized of available Qn-species (Mysen, 2007b). The magnitude of this effect increases the greater the ionization potential of the i-cation. The exchange equilibrium coefficient is a systematic function of NBO/T of the melt because NBO/T-evolution governs the evolution of the Qn-species with this effect also linked to the ionization potential of the i-cation (Mysen, 2006; see also Fig. 5.27B).

308

Chapter 5 Structure of magmatic liquids

FIGURE 5.27 Olivine/melt exchange equilibrium coefficients, i¼Mg (Eq. 5.14) as a function of compositional variables. (A) Changes in i ¼ Ca, Mn, Fe2þ, Co, and Ni exchange coefficients as a function of Na/(Na þ Ca) for melts with constant NBO/T relative to value with no Na in system. (B) Changes in i ¼ Ca, Mn, Co, and Ni exchange coefficients as a function of NBO/T of melt calculated relative to values at NBO/T ¼ 2.5. Redrawn after Mysen (2007a).

In natural magmatic liquids, the Na/(Na þ Ca) ratio can be correlated with magma type. The more felsic it is, the higher is Na/(Na þ Ca) (see also Table 5.2). Furthermore, comparing the structure of alkali basalt and tholeiite melt, for example, the Q3 abundance in alkali basalt likely is higher and those of Q2 and Q4 species lower compared with tholeiite magma because of their different alkali metal/ alkaline earth abundance data (see Table 5.2). An implication of this structural difference is that exchange equilibrium coefficients such as illustrated in simple systems in Fig. 5.27 for transition metals likely would be smaller in alkali basalt in equilibrium with olivine, for example, than in tholeiite melt in equilibrium with olivine. It is likely that similar differences might exist for pyroxene/magma partitioning, but quantitative data of this nature are not as yet available. There are at least one additional compositional (and, therefore, structural) variable, Al/(Al þ Si), that affects activity coefficients of network-modifying cations in silicate melts (Mysen, 2007b). Changes in Al/(Al þ Si) results in structural changes that affect availability of structural positions for exchange of Al3þ for Si4þ. This happens because Al3þ exhibits preference for specific Qn-species. This preference and change in Qn distribution, in turn, can govern the activity coefficient of nonbridging oxygen. Such changes in activity coefficients govern exchange equilibria among networkmodifying cation such as, for example, Co and Mg and Ni and Mg (Fig. 5.28). In both cases the exchange equilibrium coefficient decreases with increasing Al/(Al þ Si) even though the degree of polymerization of the aluminosilicate network is not changed. Magma viscosity is another property that responds on the Al-distribution between Qn-species (Dingwell, 1986; Toplis and Dingwell, 1997). As an example of this principle, in the depolymerized simple system composition, Na2Si2O5eNa2(NaAl)2O5, which has an NBO/T-value similar tholeiitic

5.3 Silicate melt and glass structure

0.85

A

309

B

2.6

0.80 2.4

0.75 Ni-Mg

2.0

KD

KD

Co-Mg

2.2

0.70 0.65

1.8

0.60 1.6

0.55 1.4

0.0

0.1

0.2

Al/(Al+Si)

0.3

0.4

0.0

0.1

0.2

0.3

0.4

Al/(Al+Si)

FIGURE 5.28 (A) Co-Mg exchange coefficient between olivine and melt, Eq. (5.14), for i ¼ Co, as a function of Al/(Al þ Si) at constant temperature and NBO/T of the melt and ambient pressure. (B) NieMg exchange equilibrium coefficient for olivine and melts. Redrawn from Mysen (2007a).

magma, there is a minimum viscosity at intermediate Al/(Al þ Si) (Fig. 5.29). This feature is a reflection of two competing melt structural effects. One is the fact that the distribution of Qn-species Al/(Al þ Si) tends to favor Q4-species, which would lead to increasing melt viscosity. The other is the fact that for Qn-species, increasing Al/(Al þ Si) leads to decreasing melt viscosity because of the weakened (Si,Al)eO bonds with increasing Al/(Al þ Si). Very likely, the nature of the chargebalancing metal cation also would affect these trends (as seen in meta-aluminosilicate compositions (see Toplis and Dingwell, 1997), but detailed information, and, therefore, quantitative application to natural magma, is not yet available.

5.3.5 Other tetrahedrally coordinated cations (P5D and Ti4D) Phosphorus is a tetrahedrally coordinated cation in most Al-free silicate glasses or melts, even in the system SiO2eP2O5 where the double-bonded P ¼ O bonding in the phosphate tetrahedra in melts accommodates the charge distribution (Shibata et al., 1981). In depolymerized melts, phosphorus forms phosphate complexes with different degree of polymerization, NBO/P. The value of NBO/P depends on P-content (Nelson and Tallant, 1984, 1986; Dupree, 1991; Kirkpatrick and Brow, 1995). The structural behavior of phosphorus in aluminosilicate melts differs from that in Al-free (or Al-poor) melts. The 31P NMR spectra of aluminosilicate glasses are quite broad and resemble those of 29Si in this respect. It has been suggested that Al-phosphate complexes are distributed within the aluminosilicate melt structure as various isolated PO4 complexes bonded to metal cations (Kirkpatrick and Brow, 1995; Cody et al., 2001).

Chapter 5 Structure of magmatic liquids

Activation energy, EK, kJ/mol

310

500

400 NBO/T=0.0 300

NBO/T=1.0

200 0.0

0.1

0.2

0.3

0.4

0.5

Al/(Al+Si) FIGURE 5.29 Activation energy of viscous flow for melts along the joins, NaAlO2eSiO2 (NBO/T ¼ 0) and Na2Si2O5 e Na2(NaAl)2O5 (NBO/T ¼ 1.0) at constant temperature and ambient pressure. Redrawn from Dingwell (1986) and Toplis et al. (1997).

The structural information on Ti4þ in silicate melts suggests that this cation may be in several different coordination states depending on the composition and structure of the melt solvent and perhaps also the Ti concentration (Alberto et al., 1995; Farges, 1997, 1999; Cormier et al., 2001; Henderson et al., 2002; Alderman, 2014). Its complex structural behavior is such that systematic relationships between oxygen-coordination and intensive and extensive variables have not as yet been developed. It is clear, for example, that fourfold coordination of Ti4þ is only one of several alternatives (Alberto et al., 1994). Properties of Ti-bearing silicate melts also indicate multiple possible structural roles of Ti4þ in melts. The larger volar volume of Ti4þ in alkali silicate melts than in alkaline earth silicate melts is an example of this (Dingwell, 1992). The temperaturedependent configurational heat capacity of Ti-bearing silicate melts is another example. Temperature-dependent coordination changes of Ti4þ in aluminosilicate melts has been reported (Mysen and Neuville, 1995).

5.4 Iron in magmatic liquids All magmatic liquids contain iron. The iron concentration in general increases the more mafic the melt (see also Table 5.2 for summary chemical data). In order to characterize the structure and properties of magmatic liquids, it is necessary, therefore, to describe the structure and property behavior of iron-bearing silicate melts and how those variables affect magma properties such as mineral/melt partitioning behavior, activity/composition relations, magma viscosity, and equation-of-state just to mention a few examples.

5.4 Iron in magmatic liquids

311

5.4.1 Redox relations of Fe3D and Fe2D The redox ratio of iron, Fe3þ/SFe, in melts and minerals is important because it can be used as a probe of the redox conditions during magma formation and evolution (Mo et al., 1982; Kress and Carmichael, 1988; Carmichael and Ghiorso, 1990; Cottrell and Kelley, 2011) and, therefore, aid in the establishment of the oxygen budget of the Earth. The Fe3þ/SFe also can also be a factor affecting the melt structure because of the often different structural roles of Fe3þ and Fe2þ (Mysen and Virgo, 1985; Carmichael and Ghiorso, 1990; Jackson et al., 2005; Borisov et al., 2015). The oxygen fugacity at magma formation can vary by nearly 10 orders of magnitude depending on magma type (Fig. 5.30). In natural magmatic liquids, the Fe3þ/SFe ratio ranges from essentially 0 to near 1 (Fig. 5.31). As can be seen in the latter figure, there is, in fact, a broad positive correlation between Fe3þ/SFe and SiO2 content of the magma. There is also a distribution of values within a given rock type, which may suggest that the conditions that established the Fe3þ/SFe-values differ for different rock types. Again, the more felsic the magma, the more oxidized the Fe3þ/SFe maximum (Fig. 5.31). This general observation has led to suggestions that there may be systematic relations between magma type and oxygen fugacity (Carmichael and Ghiorso, 1990).Notably, however, from experimentally determined relationships between Fe3þ/SFe and melt polymerization, NBO/T, the Fe3þ/SFe actually decreases as the NBO/T decreases (Fig. 5.32). The relationship between redox state of iron and magma type is unlikely, therefore, to be governed by magma polymerization. More likely, this means that the oxygen fugacity during formation of felsic magma tend to be higher than for mafic magma such as basalt. The more oxidized magma types tends to be formed in H2O-rich environments such as subduction zones, for example. Possible relationships between redox ratio of iron and H2O content of magma is, therefore, of interest. The redox ratio of iron in magmatic liquids as a function of H2O content has been

FIGURE 5.30 Oxygen fugacity range of terrestrial magma as calculated by Carmichael and Ghiorso (1990). Also included in the figure are the univariant oxygen fugacity lines for the oxygen buffer reactions; 4Fe3O4 þ O2 ¼ 6Fe2O3, 2Ni þ O2 ¼ 2NiO, and 2Fe þ O2 ¼ 2FeO.

312

Chapter 5 Structure of magmatic liquids

FIGURE 5.31 Distribution of Fe3þ/SFe among selected igneous rock groups. Input data from the collection of igneous rock analyses; http://Earthchem.org.

FIGURE 5.32 Redox ratio of iron, Fe3þ/SFe, in binary metal oxide silicate melts as indicated on the figure with 5 wt% total iron added (as Fe2O3) as a function of NBO/T of the melt. Here T ¼ Si4þþ Fe3þ. Redrawn from Virgo et al. (1981).

5.4 Iron in magmatic liquids

313

FIGURE 5.33 Redox ratio of iron, Fe3þ/SFe, with H2O concentration in rhyolite melt. The melts were equilibrated at 200 MPa and 1430  50 C at the fO2 of the NNO (Ni þ 0.5O2¼NiO) oxygen buffer. Redrawn from Baker and Rutherford (1995).

the subject of several experimental studies. Notably, no effect was reported for basalt and other depolymerized melts (Moore et al., 1995; Wilke et al., 2005; Botcharnikov et al., 2005). For more silicic composition, however, increasing H2O concentration tends to result in increasing Fe3þ/SFe (Baker and Rutherford, 1996; Wilke et al., 2002; Schuessler et al., 2008; Lesne et al., 2011; see also Fig. 5.33). In this respect, the effect on the redox ratio of iron resembles that of an increased alkali content in similar melts (Giuli et al., 2012), which also results in increasing Fe3þ/SFe. Increasing Fe3þ/SFe with increasing water concentration (and water activity) is consistent with increasing proportion of H2O resulting in depolymerization, which is known to correlate positively with increasing Fe3þ/SFe (Botcharnikov et al., 2005; Maia and Russsel, 2006; Borisov et al., 2013; Cochain et al., 2012).

5.4.1.1 Modeling redox ratio of iron in magmatic liquids A number of purely empirical models with which to relate redox ratio of iron to oxide composition of magma, temperature, and oxygen fugacity has been proposed (Kennedy, 1948; Fudali, 1965; Lauer, 1977; Sack et al., 1980 Kilinc et al., 1983; Kress and Carmichael, 1988; Nikolaev et al., 1996; Ottonello et al., 2001; Jayasuriya et al., 2004; Borisov et al., 2015). In most of these treatments, it was assumed that the iron redox relationship to temperature and oxygen fugacity was independent of melt composition Furthermore, at constant T and fO2 , the redox ratio often has been assumed to be an additive function of oxide concentration with the models taking simple forms of the type;

314

Chapter 5 Structure of magmatic liquids

lnðxFe2 O3 = xFeo Þ ¼ a ln fO2 þ b=T þ c þ

X

di x i ;

(5.15)

where xi designates an oxide mol fraction, a, b and c are constants, and the di are specific parameters for SiO2, Al2O3, “FeO”, MgO, CaO, Na2O and K2O. In most cases, multiple regression, using oxide compositions, were employed (Sack et al., 1980; Kress and Carmichael, 1991; Jayasuriya et al., 2004). There are, however, problems with some of assumptions made in these models. The assumptions are, for example, inconsistent with the nonlinear dependence of redox ratio on total iron content because these models do not take iron content into account. The Fe3þ/SFe increases with increasing total iron content of silicate melts (Densem and Turner, 1938; Mysen et al., 1984; Borisov et al., 2015). Moreover, it is implied that components other than SiO2 and Al2O3 do not affect the redox ratio appreciably or, perhaps, that such effects are hidden in the coefficients. Network-formers -and modifiers should influence the redox state in differing ways as has been documented in simple binary metal oxide silicate systems (e.g., Virgo et al., 1981). Models also have been proposed that utilize Margules parameters to account for the deviations from ideality (Jayasuriya et al., 2004; Borisov, 2010); "  3þ  n X Fe O1:5
DG W 3þ
j
WFe23þ
j
ln
Xj Fe ¼ 0:25 ln f O2 2þ RT RT Fe O j (5.16) #  W 3þ
W 2þ  Fe Fe þ XFe2þ O
XFe3þ O1:5 RT To distinguish the effects of network-forming and modifying cations, Mysen (1987) modified Eq. (5.15) as follows       ln xFe3þ =xFe2þ ¼ a ln fO2 þ b=T þ c þ d Al=ðAl þ SiÞ þ e Fe3þ =ðFe3þ þ Si þ Sfi xi ; (5.17) where xi designates the NBO/T-value pertaining to the network-modifying cation, i. Although a better fit to the input data base of Kilinc et al. (1983) was obtained in this way, this model has not been extensively used in the literature. Probable reasons are the need for structural information and the iterative nature of the calculation due to the fact that the redox ratio of iron is function of both FeO and Fe2O3 contents. In simple treatments of the redox relations of iron, it is assumed that the activity coefficient ratio of Fe3þ/Fe2þ equals 0.25. It follows from the relationships between redox ratio and iron content that this assumption is not correct (Larson and Chipman, 1953; Mysen, 2006). Moreover, given that the redox ratio varies with Al/(Al þ Si) and the nature of the metal cations in the system as well as the degree of polymerization, NBO/T (Mysen et al., 1984, 1985a,b), clearly assumptions of ideal mixing of iron components in silicate melts and natural magma cannot be correct. One may, of course, also try to cope with thermodynamic nonideality via the choice of components such that the stoichiometry coefficient remains close to 0.25. Kress and Carmichael (1988) used FeO and FeO1.464 for this purpose. The equation lnðxFeo1:464 = xFeo Þ ¼ 0:232 ln fO2
ðDH þ SWi xi Þ=RT þ DS=R;

(5.18)

was then fitted to a data set complemented by new measurements made at very low oxygen fugacities.

5.4 Iron in magmatic liquids

315

Pressure effects on the redox ratio, Fe3þ/SFe, were incorporated by Kress and Carmichael (1991) as part of a study of the compressibility of Fe-bearing melts. An assessment of pressure effects is necessary because the partial molar volumes of FeO and FeO1.5 differ (Mo et al., 1982; Lange, 1994). Kress and Carmichael (1991) reanalyzed some of their previous experimental data and reverted to Eq. (5.15) to which they added pressure-dependent terms; lnðxFe2 O3 =xFeO Þ ¼ a ln fO2 þ b=T þ c þ Sdi xi (5.19) þ e½1
T0 =T
lnT=T0  þ f P=T þ gðT
T0 ÞP=T þ hP2 =T; where e, f, g and h are fit parameters and T0 (1673K) a reference temperature. These various models have been tested by Nikolaev et al. (1996). In spite of their differences, the models were found to give similar results, with typical deviations of 0.03e0.05 from the measured redox ratios. Less reliable predictions were observed for felsic melts of the andesite-rhyolite series. As tested by Partzsch et al. (2004) with new measurements, the latest models of Kress and Carmichael (1991) and Nikolaev et al. (1996) generally reproduce the observed Fe3þ/SFe ratios to within 0.05. Deviations of up to 0.1 are nonetheless observed, particularly for felsic compositions or in redox ratios governed by strongly oxidizing conditions.

5.4.2 Structural role of iron in magmatic systems In order to characterize the relations discussed in the previous section, an understanding of the structural role of Fe3þ and Fe2þ in melts is needed. The speciation of ferrous and ferric iron in peralkaline silica-rich melts and glasses has been reported for both rhyolite and more mafic basalt compositions (Me´trich et al., 2006).

5.4.2.1 Fe3þ in magmatic liquids Bond length is often used to infer oxygen-coordination number. The IVFe3þ-O the bond length in ˚ , whereas the VIFe3þ-O distance varies from near 2.0 A ˚ to as much as crystalline materials is w1.90 A ˚ . The coordination number(s) of Fe3þ in silicate melts does, however, seem to vary between four 2.1 A and six depending on compositional variations. For example, the IVFe3þ-O bond lengths depend somewhat on the ionization potential of the alkali and alkaline earth cations in the melt (Menil, 1985; Johnson et al., 1999; Burkhard, 2000). It also depends total iron content. These bond length variations may be due to variations in Fe3þ coordination (Holland et al., 1999; Weigel et al., 2008). For example, this distance in glasses and melts along the (Na2O)0.3•(SiO2)0.7-(Na2O)0.3•(Fe2O3)0.7 join decreases with increasing Fe3D content (Fig. 5.34). Linear extrapolation of those data to lower Fe3þ concen˚ at low iron concentrations (1e2 mol %). This Fe3þ trations suggest distances near or above 2 A abundance decrease results in bond distances similar to those of Fe3þ coordination polyhedra with more than four oxygens ligands. Weigel et al. (2008), on the other hand, reported Fe3þ-O bond lengths that are best interpreted as mixed four- and fivefold coordination, which is similar to the coordination behavior proposed by Lukanin et al. (2002). An effect of Fe3þ concentration on the Fe3þ coordination also has been suggested (Mysen et al., 1984). Variable Fe3þ-O bond distance, d, can also be inferred from changes in the isomer shift of Fe3þ from 57Fe resonant absorption Mo¨ssbauer spectroscopy of glasses and melts, ISFe3þ (Menil, 1985; Jackson et al., 1993; Johnson et al., 1999): dFe3þ
O ¼ 1.58 þ 1.30ISFe3þ.

(5.20)

316

Chapter 5 Structure of magmatic liquids

FIGURE 5.34 SieO and FeeO bond distances along the join (Na2O)0.3•(SiO2)0.7 e (Na2O)0.3•(Fe2O3)0.7 as a function of iron content added as shown on the figure. Redrawn from Holland et al. (1999).

The isomer shift of Fe3þ in glasses (formed by temperature-quenching of melt) is affected by total iron content, Al/(Al þ Si), and the proportion of alkali metals relative to alkaline earths. Corre˚ , for the lowest iron oxide content (2.2 mol % as sponding dFe3þ-O-values range from about 1.99 A ˚ Fe2O3) in Na2Si2O5 glass, to 1.89 A for the Na2Si2O5 glass sample with the highest iron oxide content (13.4 mol %). For glasses and melts along the nominal SiO2eNaFeO2 join, the average bond distance ˚ . These variations in bond distance again would be consistent with ranges between 1.99 and 1.86 A variable oxygen-coordination numbers for Fe3þ.

5.4.2.2 Fe2þ in magmatic liquids The coordination numbers of ferrous iron in silicate glasses and melts have been the focus of a number studies. For example, X-ray and neutron-based methods have provided Fe2þ-O distances (Waseda and Toguri, 1978; Calas and Petiau, 1983; Waychunas et al., 1988; Holland et al., 1999; Rossano et al., 2000; Farges et al., 2004; Jackson et al., 2005; Weigel et al., 2008; Giuli et al., 2012). In peralkaline, iron-bearing alkali silicate glasses, the Fe2þ-O distance and M-O distances decrease slightly with increasing iron oxide content (Holland et al., 1999; see also Fig. 5.34). The Fe2þ-O bond-length decrease was correlated with a decrease of the Fe2þ coordination numbers from about 5 to about 4. The latter numbers are in close agreement with those reported more recently by Weigel et al. (2008), which were obtained by an analysis of neutron diffraction data. However, from EXAFS and molecular dynamics simulation of iron-rich alkaline ˚. earth silicate glass (CaFeSi2O6), Rossano et al. (2000) reported Fe2þ-O distances between 1.99 and 2.00 A Such distance would correspond to Fe2þ coordination numbers near or slightly below 6 (Brese and O’Keefe, 1994). Rossano et al. (2000) suggested an average coordination number of 4.3 through a combination of 70% IVFe2þ and 30% VFe2þ. Jackson et al. (2005), from EXAFS data obtained from ˚ with a corresponding peralkaline silicate glasses, reported Fe2þ-O bond lengths between 1.94 and 2.07 A evolution of Fe2þ coordination numbers from 4 to 5.7 depending on the type and proportion of alkali and alkaline earths present. Notably, Waseda and coworkers (Waseda and Toguri, 1978; Waseda et al., 1980) in

5.4 Iron in magmatic liquids

317

˚ , as their early, in-situ-high-temperature X-ray work interpreted Fe2þ-O bond lengths of 2.05e2.10 A 2þ 2þ indicating sixfold coordination of Fe . In more recent work on Fe -O bond length and coordination ˚ bond length is consistent with sixfold numbers is also consistent with the conclusion that 2.05e2.10 A 2þ coordination of Fe (Brese and O’Keefe, 1994). Optical spectroscopy is another method suited for examination of the structural role of transition metals in silicate melts (Wong and Angell, 1976; Fox et al., 1982; Calas and Petiau, 1983; Keppler, 1992; Bingham et al., 2002, 2007). In spectra of Fe2þ-bearing glasses of NaAlSi3O8 þ 3wt% FeO and (NaAlSi3O8)0.5(CaMgSi2O6)0.5 þ 2 wt% FeO composition (Keppler, 1992), a broad peak maximum near 9000 cm
1 was assigned to Fe2þ in sixfold coordination. Similar assignments of Fe2þ from optical spectra of other Fe2þ-rich glasses have been made by Bell and Mao (1974) and Nolet et al. (1979). The hyperfine parameters (isomer shift and quadrupole splitting) of Fe2þ from 57Fe Mo¨ssbauer resonant absorption spectroscopy also have been used to distinguish between the possible 4, 5, and 6 oxygen-coordination numbers for Fe2þ. In reduced Fe-bearing Ca-silicate glasses, fitting of the Fe2þ hyperfine parameter distribution (Alberto et al., 1994; Mysen, 2006) yields maximum ISFe2þ-values between 1.1 and 1.2 mm/s, which is consistent with Fe2þ in sixfold coordination. However, the nature of the alkali metals and alkaline earths also affect the hyperfine parameters of Fe2þ (Mysen, 2007a).

5.4.3 Magma properties and redox ratio of iron Variations of Fe3þ/SFe of silicate melts affect their degree of polymerization, NBO/T. This results in changes in any property that depends on NBO/T of the magma, including melt viscosity (Dingwell and Virgo, 1988) and mineral/melt partition coefficients (Mysen, 2007a). Given that transport properties are related, this means that not only melt viscosity, but also diffusion and conductivity in natural magmatic liquids are affected by the redox ratio of iron. Melt viscosity is correlated with NBO/T (see, for example, Fig. 5.7). As Fe3þ/SFe decreases, one might expect a viscosity decrease of iron-bearing melts, including magmatic liquids. This is exactly what happens. Variations in NBO/T of iron-bearing melts governed by changes in redox ratio of iron which in its simplest form can be written as: Fe3þ þ 2O2
¼ Fe2þ þ O2. 2


(5.21)

In Eq. (5.21) the O represents nonbridging oxygen. As written, this means that reduction of Fe3þ to Fe2þ would involve an increase in NBO/T. The result would be a relationship between Fe3þ/SFe and the melt viscosity (Fig. 5.35). The redox ratio of iron can be correlated with mineral/melt transition metal partition coefficients, be it compositionally simple melt compositions or natural magmatic liquids, because the partition coefficients depend on NBO/T of the melt and this NBO/T varies with redox ratio of iron. The redox ratio of iron, in turn, is covered by oxygen fugacity, fO2. Therefore, mineral/melt partition coefficients will depend on fO2 as illustrated in Fig. 5.36. Given that the more felsic a magma, the higher is its Fe3þ/ SFe, the implication is that at least some of the differences in mineral/melt transition metal partition coefficients may be linked to how the redox ratio of iron depends on the bulk composition of a magma. All the compositional variables discussed in this section are those encountered in chemically complex natural magmatic liquids and all do, therefore, affect activity-composition relations of any solute added to such a melt system. Only some cations have been examined experimentally (Kushiro and Walter, 1998; Kushiro and Mysen, 2002; Toplis, 2004; Mysen and Shang, 2005; Mysen, 2007a,b), but very likely the

318

Chapter 5 Structure of magmatic liquids

FIGURE 5.35 Ambient-pressure and isothermal viscosity of NaFeSi2O6 melts as a function of Fe3þ/SFe of the melt. Redrawn from Dingwell and Virgo (1988).

FIGURE 5.36 Ca partition coefficient between olivine and melt in the systems shown at ambient pressure as a function of oxygen fugacity. Redrawn from Mysen (2006).

behavior of all cations will be affected. Moreover, physical properties of magma, including equation-ofstate, viscosity, and diffusivity are also dependent on the redox ratio of iron.

5.5 Concluding remarks Characterization of the structure of magmatic liquids is central to understanding the behavior of their chemical and physical properties. That understanding, in turn, governs description of magma transport.

References

319

The structural building block of all silicate melts is the aluminosilicate tetrahedron with oxygen in the corners and Si4þ and Al3þ in the center. The tetrahedra are linked in the corners either to other tetrahedra or to oxygen in polyhedra with a larger number of oxygen ligands. The former oxygen is termed a bridging oxygen, whereas the latter is a nonbridging oxygen. The proportion of nonbridging oxygens, NBO, relative to the proportion of tetrahedrally coordinated cations, T, forms the parameter, NBO/T. The average NBO/T-range of most natural magma is between near 0 for rhyolitic magma to near 1 for basaltic magma. Transport properties and equation-of-state of natural magma can be correlated with their NBO/T. Most mineral/melt element partition coefficients also are correlated positively with their NBO/T of the magmatic liquid. Five discrete forms of aluminosilicate species can be found in silicate melts. These are described as Qn-species, where n denotes the number of bridging oxygen. The n-values are 0, 1, 2, 3, and 4. The dominant species in felsic magma such as rhyolitic and dacite, are Q4 and Q3 with minor proportions of Q,2 whereas in mafic magma such as tholeiitic liquid, the dominant species are Q3 and Q2 with minor proportions of Q0 and Q4. The nonbridging oxygens in the Qn-species are not energetically equivalent. As a result, oxygen bonding with network-modifying cations show preference for specific nonbridging oxygens. This also means that magma properties that depend on element distribution among the nonbridging oxygens depend on the proportion of alkali metals and alkaline earth. Examples are relationships between mineral/melt element partitioning and alkali metal/alkaline earth abundance ratios. Another variable is Al/(Al þ Si), which affects magma viscosity in nonrandom fashion. Mineral/melt partition coefficient can also be affected by Al/(Al þ Si) even at constant NBO/T, temperature and pressure.

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Prewitt, C.T., Sueno, S., Papike, J.J., 1976. The crystal structures of high albite and monalbite at high temperatures. Am. Mineral. 61, 1213e1255. Richet, P., 1984. Viscosity and configurational entropy of silicate melts. Geochim. Cosmochim. Acta 48, 471e483. Richet, P., Bottinga, Y., 1984. Anorthite, andesine, wollastonite, diopside, cordierite and pyrope: thermodynamics of melting, glass transitions, and properties of the amorphous phases. Earth Planet Sci. Lett. 67, 415e432. Richet, P., Neuville, D., 1992. Thermodynamics of silicate melts: configurational properties. Thermodynamic Data, pp. 132e161. Riebling, E.F., 1964. Structure of magnesium aluminosilicate liquids at 1700 C. Can. J. Chem. 42, 2811e2821. Riebling, E.F., 1966. Structure of sodium aluminosilicate melts containing at least 50 mole % SiO2 at 1500 C. J. Chem. Phys. 44, 2857e2865. Roskosz, M., Toplis, M.J., Besson, P., Richet, P., 2005. Nucleation mechanisms: a crystal-chemical investigation of highly supercooled aluminosilicate liquids. J. Non-Cryst. Solids 351, 1266e1282. Rossano, S., Ramos, A.Y., Delaye, J.M., 2000. Environment of ferrous iron in CaFeSi2O✖ glass: contributions of EXAFS and molecular dynamics. J. Non-Cryst. Solids 273, 48e52. Roy, B.N., Navrotsky, A., 1984. Thermochemistry of charge-coupled substitutions in silicate glasses: the systems Mn+ 1/nAlO2-SiO2 (M ¼ Li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba, Pb). J. Am. Ceram. Soc. 67, 606e610. Sack, R.O., Carmichael, I.S.E., Rivers, M., Ghiorso, M.S., 1980. Ferric-ferrous equilibria in natural silicate liquids at 1 bar. Contrib. Mineral. Petrol. 75, 369e377. Sakamaki, T., Wang, Y.B., Park, C., Yu, T., Shen, G.Y., 2012. Structure of jadeite melt at high pressures up to 4.9 GPa. J. Appl. Phys. 111. https://doi.org/10.1063/1.4726246. Sanchez-Valle, C., Bass, J.D., 2010. Elasticity and pressure-induced structural changes in vitreous MgSiO3enstatite to lower mantle pressures. Earth Planet. Sci. Lett. 295, 523e530. Sanloup, C., Drewitt, J.W.E., Konopkova, Z., Dallady-Simpson, P., Morton, D.M., Rai, N., van Westrenen, W., Morgenroth, W., 2013. Structural change in molten basalt at deep mantle conditions. Nature 503, 104e107. https://doi.org/10.1038/nature12668. Schramm, C.M., DeJong, B.H.W.S., Parziale, V.F., 1984. 29Si magic angle spinning NMR study of local silicon environments in-amorphous and crystalline lithium silicates. J. Am. Chem. Soc. 106, 4396e4402. Schuessler, J.A., Botcharnikov, R.E., Behrens, H., Misiti, V., Freda, C., 2008. Oxidation state of iron in hydrous phono-tephritic melts. Am. Mineral. 93, 1493e1504. Seifert, F.A., Mysen, B.O., Virgo, D., 1981. Structural similarity between glasses and melts relevant to petrological processes. Geochim. Cosmochim. Acta 45, 1879e1884. Seifert, F.A., Mysen, B.O., Virgo, D., 1982. Three-dimensional network structure in the systems SiO2-NaAlO2, SiO2-CaAl2O4 and SiO2-MgAl2O4. Am. Mineral. 67, 696e711. Seifert, F.A., Mysen, B.O., Virgo, D., 1983. Raman study of densified vitreous silica. Phys. Chem. Glasses 24, 141e145. Shibata, N., Horigudhi, M., Edahiro, T., 1981. Raman spectra of binary high-silica glasses and fibers containing GeO2, P2O5 and B2O3. J. Non-Cryst. Solids 45, 115e126. Stebbins, J.F., 1987. Identification of multiple structural species in silicate glasses by 29Si NMR. Nature 330, 465e467. Stebbins, J.F., Murdoch, J.B., Schneider, E., Carmichael, I.S.E., Pines, E., 1985. A high-temperature high-resolution NMR study of 23Na, 27Al and 29Si in molten silicates. Nature 314, 250e252. Sykes, D., Sato, R., Luth, R.W., McMillan, P., Poe, B., 1993. Water solubility mechanisms in KAlSi3O8 melts at high-pressure. Geochim. Cosmochim. Acta 57, 3575e3584. https://doi.org/10.1016/0016-7037(93)90140-r. Taylor, M., Brown, G.E., 1979. Structure of mineral glasses. II. The SiO2-NaAlSiO4 join. Geochim. Cosmochim. Acta 43, 1467e1475.

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Toplis, M.J., Dingwell, D.B., Hess, K.-U., Lenci, T., 1997. Viscosity, fragility, and configuration entropy of melts along the join SiO2-NaAlO2. Am. Mineral. 82, 979e990. Thibault, Y., Walter, M.J., 1995. The influence of pressure and temperature on the metal-silicate partition coefficients of nickel and cobalt in a model C1 chondrite and implications for metal segregation in a deep magma ocean. Geochim. Cosmochim. Acta 59, 991e1002. Tomlinson, J.W., Heynes, M.S.R., Bockris, J.O.M., 1958. The structure of liquid silicates. Part 2. Molar volume and expansivities. Trans. Faraday Soc. 54, 1822e1834. Toplis, M.J., 1998. Energy barriers associated with iscous flow and the prediction of glass transition temperatures of molten silicates. Am. Mineral. 83, 480e490. Toplis, M.J., 2004. The thermodynamics of iron and magnesium partitioning between olivine and liquid: criteria for assessing and predicting equilibrium in natural and experimental systems. Contrib. Mineral. Petrol. 149, 22e39. Toplis, M.J., Corgne, A., 2002. An experimental study of element partitioning between magnetite, clinopyroxene and iron-bearing silicate liquids with particular emphasis on vanadium. Contrib. Mineral. Petrol. 144, 22e37. Toplis, M.J., Dingwell, D.B., 2004. Shear viscosities of CaO-Al2O3-SiO2 and MgO-Al2O3-SiO2 liquids: implications for the structural role of aluminium and the degree of polymerisation of synthetic and natural aluminosilicate melts. Geochim. Cosmochim. Acta 68, 5169e5188. Urbain, G., Bottinga, Y., Richet, P., 1982. Viscosity of liquid silica, silicates and aluminosilicates. Geochim. Cosmochim. Acta 46, 1061e1072. Virgo, D., Mysen, B.O., Kushiro, I., 1980. Anionic constitution of 1-atmosphere silicate melts: implications of the structure of igneous melts. Science 208, 1371e1373. Virgo, D., Mysen, B.O., Seifert, F.A., 1981. Relationship between the oxidation state of iron and structure of silicate melts. Carnegie Instn. 80, 308e311. Washington, Year Book. Wang, Y., Cody, G., Cody, S.X., Foustoukos, D., Mysen, B.O., 2015. Very large intramolecular D-H partitioning in hydrated silicate melts synthesized at upper mantle pressures and temperatures. Am. Mineral. 100, 1182e1189. Waseda, Y., Toguri, J.M., 1978. The structure of the molten FeO-SiO2 system. In: Transactions of the American Institute of Mining, Metallurgy and Petroleum Engineering, 9B, pp. 595e601. Waseda, Y., Shiraishi, Y., Toguri, J.M., 1980. The structure of the molten FeO-Fe2O3-SiO2 system by X-ray diffraction. Trans. Jpn. Inst. Met. 21, 51e62. Watson, E.B., 1977. Partitioning of manganese between forsterite and silicate liquid. Geochim. Cosmochim. Acta 41, 1363e1374. Waychunas, G.A., Brown, G.E., Ponader, C.W., Jackson, W.E., 1988. Evidence from x-ray absorption for network-forming Fe2+ in molten alkali silicates. Nature 332, 251e253. Webb, S.L., 2008. Configurational heat capacity of Na2OeCaOeAl2O3eSiO2 melts. Chem. Geol. 256, 92e101. https://doi.org/10.1016/j.chemgeo.2008.04.003. Webb, S.L., 2011. Configurational heat capacity and viscosity of (Mg, Ca, Sr, Ba)O-Al2O3-SiO2 melts. Eur. J. Mineral. 23 (4), 487e497. https://doi.org/10.1127/0935-1221/2011/0023-2135. Weigel, C., Cormier, L., Calas, G., Galoisy, L., Bowron, D.T., 2008. Nature and distribution of iron sites in a sodium silicate glass investigated by neutron diffraction and EPSR simulation. J. Non-Cryst. Solids 353 (24e25), 2479e2494. https://doi.org/10.1016/j.jnoncrysol.2007.03.017. Whittaker, E.J.W., Muntus, R., 1970. Ionic radii for use in geochemistry. Geochim. Cosmochim. Acta 34, 945e957. Wilke, M., Behrens, H., Burkhard, D.J.M., Rossano, S., 2002. The oxidation state of iron in silicic melt at 500 MPa water pressure. Chem. Geol. 189, 55e67. Wilke, M., Partzsch, G.M., Bernhardt, R., Lattard, D., 2005. Determination of the iron oxidation state in basaltic glasses using XANES at the K-edge. Chem. Geol. 220, 143e161.

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Wong, J., Angell, C.A., 1976. Glass Structure by Spectroscopy. Marcel Dekker Inc., New York. Xue, X., Stebbins, J.F., 1993. 23 Na NMR chemical shifts and local Na coordination environments in silicate crystals, melts and glasses. Phys. Chem. Miner. 20, 297e307. Xue, X., Stebbins, J.F., Kanzaki, M., McMillan, P.F., Poe, B., 1991. Pressure-induced silicon coordination and tetrahedral structural changes in alkali oxide-silica melts up to 12 GPa; NMR, Raman, and infrared spectroscopy. Am. Mineral. 76 (1e2), 8e26. Yarger, J.L., Smith, K.H., Nieman, R.A., Diefenbacher, J., Wolf, G.H., Poe, B.T., McMillan, P.F., 1995. Al coordination changes in high-pressure aluminosilicate liquids. Science 270, 1964e1966. Yasui, I., Hasegawa, H., Imaoka, M., 1983. X-ray diffraction study of the structure of silicate glasses. Part 1. Alkali metasilicate glasses. Phys. Chem. Glasses 24, 65. Zhang, P., Dunlap, C., Florian, P., Grandinetti, P.J., Farnan, I., Stebbins, J.F., 1996. Silicon site distributions in an alkali silicate glass derived by two-dimensional Si-29 nuclear magnetic resonance. J. Non-Cryst. Solids 204, 294e300.

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CHAPTER

Structure and properties of fluids

6

6.1 Introduction Among the two main mass and transport media in the Earth (fluids and magmatic liquids), fluids are the most pervasive. This is so because, in contrast to magma, fluids can exist at temperatures ranging from ambient to those of magmatic processes (see Thompson, 2010; for recent summary). As a consequence, fluids can play a role in processes with and without magmatic liquids and are, therefore, central to both metamorphic and magmatic processes. Fluids encounter less resistance to movement through the Earth than does magma because fluids are much less viscous and less dense than magmatic liquids (Audetat and Keppler, 2004; Hack and Thompson, 2011; Ni et al., 2017). As a result, mass transport by fluids can be more efficient than by magmatic liquids. Fluids include supercritical fluids, which exhibit complete miscibility from fluid to melt. A number of H2O-bearing silicate systems can exhibit complete miscibility in the pressure-temperature regime of the upper portions of the Earth’s mantle (Shen and Keppler, 1997; Kessel et al., 2005; Mibe et al., 2007). The properties of fluids governing their role in geologic processes depend on the fluid composition as well as temperature and pressure. Their compositions, in turn, is a result of their mode of formation. Fluids can form by devolatilization during metamorphism (e.g., Yardley and Bodnar, 2014; Evans and Tomkins, 2020) or being included in magmatic liquids and exsolved during their cooling and crystallization (Aubaud et al., 2005; Audetat and Edmons, 2020). Other variables such as oxygen fugacity can also be important for elements that can exist in multiple oxidation states when dissolved in fluids. These elements include, for example, iron, chromium, and many high-field strength elements (HFSE) (Scholten et al., 2019; Klein-BenDavid et al., 2011; Watenphul et al., 2014; Peiffert et al., 1996; Li and Audetat, 2015). Compositionally, most fluids can be described within system CeOeHeNeS. In addition, halogens can under some circumstances play important roles. The ultimate source of magmatic volatiles typically is sediments cycled into the Earth in subduction zones. These sediments contain nitrogen (w400e500 ppm), carbon (as CO2 or CH4; total carbon content: 0.3e8 wt%), sulfur in the range 0.05e1 wt%, and H2O (up to about 10 wt%). These volatiles initially are contained in clay minerals that gradually release H2O during increasing temperature and pressure (Schmidt and Poli, 1998; Bekaert et al., 2021). Under some circumstances, redox conditions can also impact on the transport capability of fluids in the Earth. Sulfur, N, and C exist in multiple oxidation states in the redox range of natural processes. Their properties, therefore, can be greatly affected by changing fluid speciation controlled by variable Mass Transport in Magmatic Systems. https://doi.org/10.1016/B978-0-12-821201-1.00010-9 Copyright © 2023 Elsevier Inc. All rights reserved.

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redox conditions. For example, the solubility as CO2
3 or SO4-based complexes in aqueous solutions differs significantly from those of the reduced CH-3 and S2
complexes (Mao et al., 2011; Ayers et al., 2012; Tiraboschi et al., 2017; Dietrich et al., 2018; Schmidt et al., 2018). The volatile components are recycled in the Earth, beginning with descent in subduction zones, and returning to the surface via igneous processes above subduction zones and midocean ridges. Changes in redox conditions during these processes can affect the recycling process. For nitrogen recycling, for example, its oxidation state during initial descent in subduction zones is critical because N2 can be released at relatively shallow depth (100 km), whereas reduced nitrogen, such as NH3 can be þ recycled into the Earth’s mantle because NH
2 and NH4 complexes can form bonding with silicate minerals and melts (Duit et al., 1986; Galloway, 2003; Bebout et al., 2013; Li et al., 2015). In minerals, þ reduced nitrogen as NHþ 4 can be exchanged for K (Watenphul et al., 2009, 2010). Carbon can exist as either CO2 or CH4. There is evidence, for example, for formation of reduced carbon, as CH4, in the portions of descending slabs in subduction zones (Tao et al., 2018). At depths of melting, methane is dissolved in magmatic liquids by substitution of CH
3 -groups for oxygen in silicate tetrahedra (Mysen and Yamashita, 2010; Mysen et al., 2011). Bulk composition, redox conditions, temperature, and pressure do, therefore, affect how fluids impact on igneous and metamorphic processes in the Earth and, in turn, their transport capacities. Characterization of those processes requires information on solubility and solution mechanisms and also experimental data on partitioning of volatiles and their solutes between melts, minerals, and fluids. Such data can be obtained by experimental studies as well as numerical simulation. The objective of the present chapter is to review and discuss the main aspects of these variables. Among the volatile components in fluids in the Earth, H2O is by far the most important as it is a very effective solvent of major, minor, and trace elements at high temperature and pressure (Manning, 1994; Zhang and Frantz, 2000; Newton and Manning, 2007, 2008), affect physical and chemical properties in crustal and mantle rocks (Kohlstedt et al., 2006) and their partial melting products (see Chapters 1 and 2). In magmatic systems with multicomponent fluids, H2O typically dominates (Audetat and Edmonds, 2020). In this role, H2O may also control the exsolution process of volatiles to form a separate fluid phase. Water release is also of central importance in most metamorphic processes as those involve dehydration of a wide range of OH-containing minerals. Minerals containing other volatile components tend to be stable throughout the pressure-temperature range of most metamorphic processes. The behavior of H2O-rich fluids is, therefore, a central theme of this chapter.

6.2 Fluid/melt partitioning of volatile components The dominant fluid species in metamorphic and magmatic systems are H2O, CO2, SO2, and SO3. To a lesser degree, reduced species of sulfur and nitrogen, together with halogens, and noble gases can be involved. Among the latter, noble gases will not be addressed here at least in part because of their low abundance and because the experimental basis for understanding their behavior is somewhat limited, and in part because noble gases are not efficient transport media for rock-forming chemical components. However, interested readers might consult Chapter 8 where there are also references to the literature relevant to the solubility behavior of noble gases in silicate melts, including magmatic liquids.

6.2 Fluid/melt partitioning of volatile components

333

Initially, the fluids in and released from metamorphic rocks are derived from the fluid content of the sedimentary precursors. These sediments and their fluids evolve in accretionary prisms and during subduction following initial sedimentation in ocean basins. The main components are H2O, C, and S species often together with halides (Fyfe et al., 1978; Yardley and Bodnar, 2014). Among these, both C and S species may exist in several oxidation states depending on redox conditions. Minor proportions of nitrogen may be derived from the decomposition of organic materials (Bebout et al., 2013). In its oxidized form, nitrogen is dissolved as molecular N2. In this form, nitrogen has minor effects on the geochemical budget, and gets recycled back to the atmosphere at comparatively shallow depth in subduction zones (Galloway, 2003). In addition, the nitrogen abundance in the Earth is so small (several ppm; see Johnson and Goldblatt, 2015) that its impact on behavior of fluids in the Earth is not great except in very specific circumstances (Busigny et al., 2011; Bebout et al., 2013). Fluid composition and fluid speciation in magmatic liquids and as a separate fluid phase during igneous evolution are governed by fluid/melt/mineral partition coefficients during initial melting, by fluid separation during ascent and, finally, during cooling and magmatic crystallization (see, for example, a review by Baker and Alletti, 2012; Audetat and Edmonds, 2020). During magma ascent and exsolution of fluids, the fluid species most soluble in the magmatic liquids will be enriched in the magma, whereas the coexisting fluid will be enriched in the less soluble fluid species. In a typical magmatic system with H2O and CO2 as the main fluid species, at pressures greater than that corresponding to slightly less than 5 km, the fluid becomes enriched in CO2 while the magma is H2O enriched during exsolution processes (Eggler and Kadik, 1979; Papale et al., 2006). At lower pressure than that corresponding to about 5 km depth,1 circumstances exist where the fluid becomes enriched in H2O over that of CO2 (Eggler and Kadik, 1979). For magmatic liquids formed by fluid-induced melting in the peridotite prism overlying subducting slabs, halogens, and in particular Cl, play an important role (Bernini et al., 2013; Kawamoto et al., 2014). Oxidized sulfur can also be important in this tectonic setting (Scaillet et al., 1998; Binder and Keppler, 2011).

6.2.1 Fluid/melt partitioning of H2O In the presence in H2O only, silicate-H2O phase relations are such that H2O contents in coexisting melt increases and that in coexisting fluid decreases (silicate species abundance increases) with increasing temperature until the critical endpoint is reached. An example of this effect can be seen in the melting phase relations of the system NaAlSi3O8eH2O (Fig. 6.1; see Shen and Keppler, 1997). As can be seen in Fig. 6.1, the extent of coexisting melt and fluid increases with increasing temperature until, at 765 C sand 1.45 GPs, the critical endpoint is reached. Expressed in terms of a fluid/melt partition coefficient for H2O, for the case shown in Fig. 6.1, its value decreases from about 4.9 at the lowest temperature investigated (650 C) to 1 at the critical endpoint at 765 C (Fig. 6.1B). Also shown in Fig. 6.1B are fluid/melt partitioning data of H and D from in situ diamond cell experiments from Mysen (2013). Here, the temperature-dependence of the fluid/melt deuterium partition coefficients differs slightly from that of hydrogen. This should not be a surprise given that the mass of deuterium is twice that of hydrogen. It is also known, for example, that this mass difference results in fractionation between H and D in aluminosilicate melts and melt/fluid systems (Mysen, 2013; Wang et al., 2015; Dalou et al., 2015a). The fluid/melt H2O partition coefficients in Mysen (2013) are more sensitive to temperature than those from Shen and Keppler (1997; Fig. 6.1B). This should not be a surprise because these two studies

334

Chapter 6 Structure and properties of fluids

780

DHfluid/melt 2O

My

720 700

melt+fluid

se

n(

20

3

13

)

My

se

n(

20

)

Temperature, C

4

fluid

melt

B 7 199 ler ( epp dK n an She

740

5

A

760

13

)

680

H

2 D

660 1

640 0 20 NaAlSi3O8

40

60 wt%

80

100 H2O

400

500 600 700 Temperature, ˚C

800

FIGURE 6.1 H2O distribution in the Na2OeAl2O3eSiO2eH2O system. (A) Immiscibility gap in temperature-composition space for the system NaAlSi3O8eH2O. Note that in these data are polybaric because pressure increases with . The Shen and increasing temperature. (B) Partition coefficient for H2O between melt and fluid, Dfluid/melt H2O Keppler (1997) data are from the NaAlSi3O8eH2O system, whereas the Mysen (2013) data are from the system Na2OeAl2O3eSiO2eH2O/D2O. Modified after (A) Shen and Keppler (1997); (B) Mysen (2013). Note that both data sets are polybaric.

differ in the composition of the melt and the pressure evolution over the temperature range examined in the diamond cell. Whereas Shen and Keppler (1997) examined the behavior in NaAlSi3O8eH2O, Mysen (2013) worked with a peralkaline composition in the Na2OeAl2O3eSiO2eH2O system. The temperature/pressure coordinates of the phase boundaries of a plot such as in Fig. 6.1A depend, therefore, on both pressure and bulk composition. In compositionally very different systems such as, for example, the system MgOeSiOeH2O, Mibe et al. (2002) and Stalder et al. (2001) both reported the critical point to be at pressures over 10 GPa. For basaltdH2O, the critical point is near 5 GPa (Kessel et al., 2005). This large difference from the NaAlSi3O8eH2O data in Fig. 6.1A likely reflects very significantly different solubility and solvent behavior of silicate components in H2O in the different silicate systems. The fluid/melt partition coefficient of H2O becomes a more complex function of fluid composition in the case of multicomponent fluids (Botcharnikov et al., 2015; Webster et al., 2009, 2017). Webster et al. (2009) reported that the H2O content of fluid increases with increased salinity (NaCl and KCl). However, the data as reported make it difficult to extract detailed relationships.

6.2.2 Fluid/melt partitioning of CO2 Despite the fact that CO2 is the second-most important volatile species in the Earth (Jambon, 1994), surprisingly little has been done experimentally to determine the fluid/melt partition coefficient of CO2 (or, for that matter, CH4). However, from the phase relations in the NaAlSi3O8eH2OeCO2 system to 2.5 GPa (Eggler and Kadik, 1979), fluid/melt partition coefficients as a function of temperature and

6.2 Fluid/melt partitioning of volatile components

335

FIGURE 6.2 derived from the liquidus phase Melting phase relations in the system NaAlSi3O8eH2OeCO2. A. Dfluid/melt CO2 relations in the NaAlSi3O8eH2OeCO2 system. B. Distribution in H2OeCO2 space of coexisting fluids and melt as a function of pressure for temperatures indicated in the NaAlSi3O8eH2OeCO2 system. Modified after Eggler and Kadik (1979).

pressure can be inferred. As seen in Fig. 6.2A, this fluid/melt partition coefficient is relatively insensitive to pressure at more than w1 GPa pressure. However, at lower pressures (corresponding to crustal conditions), the fluid/melt partition coefficient increases rapidly reflecting the rapidly changing liquidus surface in this system at these lower pressures (Fig. 6.2B). The fluid/melt partitioning behavior of CO2 is complicated because under oxidizing conditions,
carbon can exist as molecular CO2, as CO2
3 , and as HCO3 groups (Mysen, 2015a, 2018). Under reducing conditions, where carbon may exist as CH4 in the fluid, reduced carbon in silicate melts exists both as molecular CH4 and as CH3 groups replacing oxygen in the silicate tetrahedra (Mysen et al., 2009, 2011). Even though in silicate-COH systems both HCO3/CO3 and CH3/CH4 abundance ratios vary in melts and coexisting fluids, the exchange equilibria for oxidizing conditions (Fig. 6.3A): 2

CO2
3 ðmeltÞ þ HCO3
ðfluidÞ ¼ CO3 ðfluidÞ þ HCO3 ðmeltÞ;

and reducing conditions (Fig. 6.3B):

(6.1)

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Chapter 6 Structure and properties of fluids

FIGURE 6.3 Exchange equilibrium coefficients for oxidized carbon (CO2) [Eq. (6.1)] and reduced carbon [Eq. (6.2)] as a function of temperature, 1/T(Kelvin). A. ln [(XCO3/XHCO3)fluid/ln (XCO3/XhCO3)melt] versus 1/T. B. ln [(XCH4/ XCH3)fluid/ln (XCH4/XCH3)melt] versus 1/T. Modified after Mysen (2015a, b).

CH4 ðmeltÞ þ CH3 ðfluidÞ ¼ CH4 ðfluidÞ þ CH3 ðmeltÞ;

(6.2)

are such that with increasing temperature under oxidizing conditions, the CO3/HCO3 abundance ratio in melts increases faster than in coexisting fluid. The enthalpy change, DH, for Eq. (6.1) is
44  9 kJ/mol with the assumption of ideal mixing (Mysen, 2015a). Under reducing conditions, the CH4/CH3 abundance ratio in fluid increases faster than in coexisting melt with a DH for Eq. (6.2) of 34  3 kJ/mol (Mysen, 2015b). The experimental data in Fig. 6.3, which were obtained in situ at high temperature and pressure in an externally heated diamond anvil cell with a Na2OeAl2O3eSiO2eCO2eH2O composition, appear to be the only such data currently available. However, given that we know that the CO2
3 /CO2 abundance ratio in CO2-saturated silicate melts is a sensitive function of variables such as degree of silicate polymerization, Al/(Al þ Si), and nature and abundance of alkaline earths and alkali metals (Holloway et al., 1976; Fine and Stolper, 1985; Brooker et al., 2001), it is likely that those variables also affect exchange equilibria such as illustrated in Fig. 6.3. Variations in such equilibria will also affect the bulk melt fluid/melt carbon partition coefficient. However, experimental data of this nature do not yet appear to exist.

6.2.3 Fluid/melt partitioning of chlorine Among the halogens, data exist for F, Cl, Br, and I (Bureau et al., 2000; Kravchuk and Keppler, 1994; Webster et al., 2009; Baker and Alletti, 2012; Beyer et al., 2012; Hsu et al., 2019), Among the halogens, chlorine has attracted the most attention among experimentalists. This attention probably is driven by the fact that Cl-complexes are often considered responsible for enrichments of economically important metals in fluids and melts (Frank et al., 2011; Zajacz et al., 2013; Simmons et al., 2016).

6.2 Fluid/melt partitioning of volatile components

337

FIGURE 6.4 Chlorine distribution between saline fluid and melt using a phonolitic composition, A. Fluid-melt equilibria with immiscibility gap as a function of NaCl concentration (mol fraction) and pressure. B. Evolution of Cl concentration in coexisting melt and fluid at various pressures as indicated. The abrupt changes at pressures 150 MPa reflects the existence of immiscibility in this pressure range. Modified after Signorelli and Carroll (2000).

At pressures less than about 200 MPa, the system H2OeNaCl is subcritical at and below magmatic temperatures (Fig. 6.4; see also Signorelli and Carroll, 2000). The Cl distribution between fluid and melt changes dramatically as pressure is increased from the subcritical to the supercritical region (Fig. 6.4B). At the pressures of the subcritical region, the Cl concentration in melt changes little as a function of the Cl in the fluid phase, whereas at higher pressures these two concentrations are correlated. It is notable, though, that for any Cl solubility in the fluid, that in the melt decreases with increasing pressure. This effect results from the fact that the molar volume difference of NaCl in aqueous fluid and H2O-rich melt is negative (Shinohara et al., 1989; Signorelli and Carroll, 2002). It is to be kept on mind, however, that under anhydrous conditions, the Cl solubility is a positive function of pressure (Webster et al., 1999; Dalou and Mysen, 2015). Notably, Dalou and Mysen (2015) found that the pressure effect on Cl solubility decreases as melts become aluminous. When changing from anhydrous to hydrous conditions they observed, however, that the Cl solubility in aluminosilicate melts decreased with increasing H2O content. In this case, the decrease was related to the fact that increasing H2O content of the melt results in silicate depolymerization (see also Chapter 7). This solubility behavior implies that the partition coefficient, Dfluid/melt ,2 likely would increase with increasing Al/(Al þ Si) and H2O content of the melt. Cl Botcharnikov et al. (2015), on the other hand, concluded that the effect of H2O concentration on Cl solubility of melt depends on total pressure. At pressures less than 0.2 GPa, they found that the Cl solubility in a melt increased with increasing H2O content, whereas at higher pressure, they noticed decreased solubility. Of course, Dalou and Mysen. (2015) did experiments at 1.5 GPa, whereas Botcharnikov et al. (2015) conducted their experiments at lower pressures, between 50 and 200 MPa. Therefore, the data from Botcharnikov et al. (2015) and Dalou and Mysen (2015) are, in fact, in accord. This possible pressure effect may be because the molar volume of H2O in fluid is quite 2

Dfluid Cl ¼ concentration of Cl in fluid divided by concentration of Cl in melt.

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Chapter 6 Structure and properties of fluids

pressure-dependent at such low total pressures (Burnham et al., 1969a) so the DVfluid-melt may change as the pressure is increased.3 From experiments with natural magma compositions, the fluid/melt partition coefficient for chlorine in the presence of H2O decreases with increasing pressure (Kilinc and Burnham, 1972; Shinohara et al., 1989; Signorelli and Carroll, 2000; see Fig. 6.5). Moreover, the fluid/melt partition coefficient is a strong function of Cl concentration as well as other components such as sulfur (Webster et al., 2009; Beermann et al., 2015; see also Fig. 6.6). Whether the significant deviation from linearity in Fig. 6.6A is because of deviations from ideal solution in the fluid or melt, or both, cannot be ascertained. It is clear, however, that nonideal mixing plays an important role in solution of Cl in fluids and melts under hydrous conditions (Schmidt and Bodnar, 2000). It is of interest, though, that when fluid/melt expressing the D Cl as a function of total Cl content in the melt, for example, possible pressure effects are at best barely discernible (Botcharnikov et al., 2015; see also Fig. 6.6B). Temperature also affects the fluid/melt partition coefficient for Cl (Webster, 1992; Hsu et al., 2019). However, whereas Webster (1992), studying the behavior in haplogranite compositions, suggested a temperature effect of on the order of a factor of 10 in the 800e1000 C temperature range, Hsu et al. (2019), relying both on their own experimental data as well as data existing in the literature, and examining the chlorine partitioning behavior same temperature interval, concluded that the temperature-variations in fluid/melt partition coefficients were between a factor of 2 and 3 (Fig. 6.7). There is no obvious reason for this difference. The Dfluid/melt is sensitive to compositional variations, be they in fluid (Signorelli and Carroll, 2000; Cl Chevuvhelov et al., 2008; Beermann et al., 2015; Botcharnikov et al., 2015; Hsu et al., 2019) or the melt (Webster et al., 2009; Botcharnikov et al., 2015; Dalou et al., 2015a; Iveson et al., 2017). Among

FIGURE 6.5 Evolution of the fluid/melt partition coefficients of Cl in two different compositions (phonolite and rhyolite)eH2OeNaCl systems as a function of pressure. Data sources can be found in Signorelli and Carroll (2000). Modified after Signorelli and Carroll (2000). 3

These volume effects are discussed in detail in the section on properties of H2O below [Section 6.2.2].

6.2 Fluid/melt partitioning of volatile components

339

FIGURE 6.6 Chlorine distribution between fluid and melt in basalt and andesite systems. A. Evolution of Cl concentration in coexisting fluid and melt in a basalt system as a function of added sulfur (as indicated on figure). B, Chlorine fluid=melt , in an andesite system as a function of Cl concentration in melt and pressure as partition coefficient, DCL indicated on figure. Modified from Beermann et al. (2015) (A) and Botcharnikov et al. (2015) (B). Additional data sources used can be found in original citations.

FIGURE 6.7 fluid=melt

, as a function of Cl concentration in melt in a Evolution of chlorine partition coefficient, DCL garaniteeH2OeCl system at 200 MPa and different temperatures as indicated. Modified from Webster (1992).

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Chapter 6 Structure and properties of fluids

FIGURE 6.8 fluid=melt

at 200 MPa total Chlorine solubility and fluid/melt partitioning as a function of bulk composition. (A) DCl pressure as a function of SiO2 content of melt for melt compositions ranging from basalt to rhyolite. Original data of this diagram cited in caption to this figure in original text. (B) Anionic fraction of Cl, expressed as Cl/ (Cl þ O) as a function of extent of polymerization of melt, NBO/T. Melt compositions are pantellerite, phonolite, trachytes and rhyolites. Modified after (A) Botcharnikov et al. (2015); (B) Signorelli and Carroll (2002). See caption of original source for detailed citation to individual data.

the most significant melt compositional variable is the SiO2 content (Fig. 6.8) The more silica-rich, the greater the fluid/melt partition coefficient (Botcharnikov et al., 2015). This relationship would likely be even more pronounced if the NBO/T 4 parameter of the melt was used in replacement of the SiO2 (Signorelli and Carroll, 2002; Metrich and Rutherford, 1992; see Fig. 6.8B). The SiO2 of magmatic liquids typically is negatively correlated with the melt NBO/T so that the lower the SiO2 concentration, generally the greater is the NBO/T of the melt (Mysen and Richet, 2019). However, the SiO2 content of a melt is not the only contributor to NBO/T. Moreover, NBO/T does not incorporate all relevant melt structural variables. Additional variables include the types and proportions of alkali metals and alkaline earths, compositional variables that are known to affect the solubility and solution mechanisms of Cl in silicate melts, for example. Among existing data relevant to effects of fluid composition, Iveson et al. (2017) concluded that the Dfluid/melt is positively correlated with the Al2O3/(CaO þ Na2O þ K2O) of a hydrous dacite melt Cl (Fig. 6.9A). When examining a related variable (Na2O þ K2O)/Al2O3 of phonolite melt (Signorelli and Carroll, 2002), the correlation with Cl solubility in melt in positive (Fig. 6.9B). Of course, this means that the Al/(Na þ K) relationship is negative. So, even if the chlorine concentration in the fluid did not change, the data from Signorelli and Carroll (2002) would also imply that Dfluid/melt increases Cl with increasing Al/(Na þ K). In other words, the data of Signorelli and Carroll (2002) and those of Iveson et al. (2017) do not disagree, at least qualitatively. 4

NBO/T: Nonbridging oxygen per tetrahedrally coordinated cations. See Chapter 5 for further discussion of this melt structural parameter.

6.2 Fluid/melt partitioning of volatile components

341

FIGURE 6.9 fluid=melt

as a Chlorine distribution between melts and fluids as a function of Al/metal rations of melt. (A) DCl function of Al2O3/(CaO þ Na2O þ K2O) of melt, by mol. (B) Chlorine solubility in pantellerite and rhyolite melts in equilibrium with saline aqueous solutions as a function of (Na þ K)/Al ratio of the melt at 100 MPa pressure. Modified after (A) Iveson et al. (2017). (B) Signorelli and Carroll (2000).

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Chapter 6 Structure and properties of fluids

Additional volatile species in fluids also can play important roles in defining the Dfluid/melt Cl (Kravchuk and Keppler, 1994; Beermann et al., 2015; Hsu et al., 2019). For example, increasing Cl concentration such as from NaCl, results in increasing fluid/melt partition coefficient for Cl (Fig. 6.10A). In contrast, increasing CO2 concentration in an H2OeCO2eNaCl environment with the mol fraction of NaCl nearly constant results in decreasing Dfluid/melt (Hsu et al., 2019; See also Cl Fig. 6.10B). It is striking, however, that Chevychelov et al. (2008) did not see any effect of added fluorine on the fluid/melt partition coefficient of Cl. Sulfur is another interesting element. Beermann et al. (2015) observed that there is a positive correlation between the Dfluid/melt and the sulfur content of the fluid even under relatively oxidizing Cl conditions (FMQþ2.8)5 where one might expect sulfur to exist in its oxidized state in the fluid (Fig. 6.11). Beermann et al. (2015) did notice, however, that when decreasing to oxygen fugacity to near that of the QFM oxygen buffer,6 there is essentially no variation in the Dfluid/melt with increasing Cl sulfur content of the fluid (Fig. 6.11). At the fO2 of the QFM buffer, most of the sulfur in fluids is expected to be in its reduced form (see, for example, Beermann et al., 2015).

FIGURE 6.10 fluid=melt

Fluid/melt partition coefficient of chlorine, DCl

fluid=melt

as a function of fluid composition. (A) DCl

as a

fluid=melt DCl

function of mol fraction of NaCl in fluid at two different temperatures as indicated. (B) as a function of mol fraction of CO2 in H2OeCO2 fluid with NaCl added. Effects of pressure and mol fraction of NaCl, XNaCl, are indicated on individual curves.

5 The notation, FMQþ2.8, means that the oxygen fugacity is 2.8 orders of magnitude higher than that defined by the FMQ (fayalite-magnetite-quartz) oxygen buffer. 6 Oxygen fugacity is often referred to standard oxide buffers. The most common ones are: hematite-magnetite (HM): 2Fe3O4 þ 0.5O2 ¼ 3Fe2O3, nickel-nickel oxide I(NNO): Ni þ O2 ¼ NiO, quartz-fayalite-magmetite (QFM): 3Fe2SiO4 þ O2 ¼ 3SiO2 þ 2Fe3O4, wustite-magnetite (MW): 3FeO þ 0.5O2 ¼ Fe3O4, and iron-wustite (W): Feþ0. 5O2 ¼ FeO. Another buffer not so frequently employed is the Re-ReO2 buffer: Re þ O2 ¼ ReO2. This latter reaction buffers the oxygen fugacity slightly below that of the MH buffer (less than one order of magnitude).

6.2 Fluid/melt partitioning of volatile components

343

FIGURE 6.11 fluid=melt

and sulfur content of fluid with Cl contents as indicated on individual lines at Relationship between DCl 200 MPa total pressure and oxygen fugacity at QFM þ 2.8. In other words, sulfur is oxidized. Modified after Beermann et al. (2015).

FIGURE 6.12 Halogen distribution between silicate melts and aqueous fluids. (A) Relationship between fluorine concentration in coexisting aqueous fluid and H2O-rich melt for various granitic melt compositions. Original data sources given in caption to the original diagram. (B) Relationship between Cl and F concentrations in silica-rich rocks of various extents of Al/metal ratio. (A and B) Modified after Dolejs and Zajacs (2018). Original data sources given in Dolejs and Baker (2004).

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Chapter 6 Structure and properties of fluids

6.2.4 Fluid/melt partitioning of fluorine Fluid/melt partition coefficients for fluorine typically is less than 1 for all compositions relevant to terrestrial magmatic processes (Dolejs and Zajacz, 2018; see Fig. 6.12A). In his regard, fluorine differs from all other halogens for which the fluid/melt partition coefficients exceed 1. There are, nevertheless, systematic variations in the fluid/melt partition coefficients for F depending on the magma composition. For felsic magma-fluid systems, for example, the F/Cl abundance ratio increases from near 1 for peralkaline compositions to greater values for meta-aluminous and weakly metaluminous compositions, and also increases even more as the magma becomes more peraluminous (Fig. 6.12B). This solubility difference is a reflection of the different solubility behavior of Cl and F in magmatic liquids. The solubility of fluorine typically can exceed 10 wt% and is several percent even at high temperature and ambient pressure (see Chapter 8), whereas for the heavier halogens (Cl, Br, I, Xe), the solubility at ambient pressure is from a fraction of as percent for Cl to ppb level for Xe (Kirsten, 1968; Miyazaki et al., 2004). Even when comparing the behavior of Cl and F, their solubility behavior in magma (and fluid) differs significantly. For example, while Cl solubility decreases as magmatic liquids becomes more aluminous, the opposite trend was observed for F (Fig. 6.13; see also Dalou et al., 2015b). The solubility also increases with increasing H2O content in contrast to Cl, where the solubility in melts decreases with increasing H2O (Dalou and Mysen 2015; see also Fig. 6.13B). This means that whereas Dfluid/melt increases with increasing Al/(Al þ Si) of the magmatic liquid, the opposite trend would be Cl expected for Dfluid/melt . F The different solubility behavior of Cl and F reflects different solution mechanism. Whereas Cl dissolves to form various complexes with Al, alkali metals and alkaline earths, and with no sign of SieCl bonding, for F, the exact opposite is correct. The SieF bonding dominates the solution

FIGURE 6.13 Fluorine solubility in Na2OeAl2O3eSiO2 melts at 1.5 GPa. (A) Fluorine solubility in melt as a function of the Al/ (Al þ Si) of the melt at 1.5 GPa pressure. (B) Fluorine solubility in melt as a function of the H2O content of the melt at 1.5 GPa pressure. Modified from (A) Dalou et al. (2015b); (B) Dalou and Mysen (2015).

6.2 Fluid/melt partitioning of volatile components

345

FIGURE 6.14 Evolution of fluorine contents of coexisting aqueous fluid and volatile-saturated basalt as a function of F contents at 200 MPa total pressure with oxygen fugacity controlled at that of the NNO oxygen buffer. Modified after Chevychelov et al. (2008).

mechanism, but metal-Al-fluorides become more important as Al/(Al þ Si) increases (Dalou et al., 2015b). Relatively few experiments have been carried out to determine fluid/melt partitioning of F (Xiong et al., 1998; Kravchuk et al., 2004; Chevychelov et al., 2008; Webster et al., 2009). Among these, systematic data were reported only by Chevychelov et al. (2008) who found that there is a near linear correlation between F in melt and fluid (Fig. 6.14). Interestingly, this relationship does not seem dependent on whether Cl also is present. As noted above, Chevychelov et al. (2008) also concluded that the chlorine partition coefficient was not dependent on the F concentration. One might speculate that this behavior is a reflection of the different solution mechanisms of Cl and F in the melts, and perhaps the fluids. It seems reasonable to speculate that Dfluid/melt will also depend on compositional variables such as F H2O, Al/(Al þ Si) and (Na þ K)/Al because the F solubility in melts depends on these variables. However, there does not appear to be experimental data with which such variables have been examined.

6.2.5 Fluid/melt partitioning of bromine and iodine Considerably less is known about the geochemical behavior of Br and I than about F and in particular Cl. There are, nevertheless, some experimental data comparing these four halogens. As can be seen in Fig. 6.15, there is an essentially linear relationship between the bromium in fluids and melts and iodine in fluids and melts (Bureau et al., 2000; see Fig. 6.15A and B) with the Dfluid/melt < Dfluid/melt Br I (Fig. 6.15C). The relationships between Br and I in fluids and melts seem linear and pass through the origin (Fig. 6.15A and B). From the experimental data of Bureau et al. (2000), it appears, therefore, that both Br and I in fluids and melts follow Henry’s Law. There is also a log-linear relationship between the fluid/melt partition coefficients and ionic radius of the halogens (Fig. 6.15C):

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Chapter 6 Structure and properties of fluids

FIGURE 6.15 Halogen solubility and fluid/melt partitioning at 200 MPa and 900 C. (A) Evolution of Br contents of coexisting aqueous fluid and hydrous NaAlSi3O8 composition melt. (B) Evolution of I concentration of coexisting aqueous fluid and hydrous NaAlSi3O8 composition melt. (C) Fluid/melt partition coefficients as a function of the ionic radius of the halogen. Modified after Bureau et al. (2000).

6.2 Fluid/melt partitioning of volatile components

fluid=melt

lnDi


 A . i ¼
11.7 þ 7.2r


347

(6.3)

It is noted again that there is relatively little information on fluid/melt partitioning of Br and I, but it is likely that these partition coefficients also depend on bulk chemical composition of the magma. Therefore, the general applicability of the relationships in Fig. 6.15 and Eq. (6.3) is not well known. The limited data available should be kept in mind when applying this information to natural magmatic processes.

6.2.6 Fluid/melt partitioning of sulfur Sulfur is the third-most important volatile component in the Earth (Jambon, 1994). At times, its abundance resembles that of CO2 and H2O (Baker and Alletti, 2012). Sulfur-rich hydrothermal fluids can serve as transport media of metals to form economically viable ore deposits such as deposits of many transition metals (Pokrovski et al., 2008; Jego et al., 2016). Oxidized sulfur is also a critically important component in degassing processes of magmatic liquids during their ascent and cooling (Oppenheimer, 2003) The partitioning behavior of sulfur between fluids and melts has, therefore, been the subject of significant experimental activity. An important variable governing the fluid/melt partition coefficient of sulfur (Dfluid/melt ) is the S oxygen fugacity. Translated to a relationship between fluid/melt sulfur partition coefficient and its dependence on temperature, pressure and oxygen fugacity, Gennaro et al. (2020) proposed the expression: fluid=melt

logK S

¼ a=T þ bP þ cDNNO þ d.

(6.4)

In this equation, T is temperature ( C), P is pressure (MPa) and DNNO is the oxygen fugacity difference from that of the NNO buffer (log units). In the summary of Gennaro et al. (2020), which includes a number of published data sets (see Gennaro et al., 2020, for citations), it is clear that the Dfluid/melt decreases very rapidly in the vicinity of the oxygen fugacity of the NNO oxygen buffer S (Fig. 6.16). Under oxidizing conditions, the relationship between sulfur concentration in coexisting aqueous fluid and melt is linear and passes through the origin (Fig. 6.17). Oxidized sulfur in this environment follows, therefore, Henry’s Law in both phases. The slope of the relationship and, therefore, the Henry’s Law constant, does, however, depend on the bulk composition of the system (Fig. 6.17). The sulfur partition coefficients also are dependent on the presence of other volatile species in the fluid and in addition to composition of the melt (Binder et al., 2018; Webster et al., 2011; Zajacs et al., 2012; Zajacs, 2015; Beermann et al., 2015). In fluid, chlorine is particularly important (Beermann et al., 2015; see also Fig. 6.18). At oxidizing oxygen fugacity conditions such as QFM þ 2.8 in Fig. 6.18 where essentially all sulfur is as S6þ, the Dfluid/melt increases rapidly with increasing chlorine S (NaCl) concentration, whereas under reducing conditions, such as near the QFM oxygen buffer, this effect is quite small or perhaps nonexistent (Fig. 6.18). Interestingly, regardless of redox conditions, for a given fixed NaCl concentration, the linear relationship between melt and fluid concentration of sulfur indicates Henry’s Law behavior (Binder et al., 2018; see also Fig. 6.19). Notably, under 7

The notation DNNO as well as analogous notations such as, for example, DQFM and DIW, is an expression of the difference in oxygen fugacity, in logarithmic units, from the oxygen buffer indicated.

7

348

Chapter 6 Structure and properties of fluids

FIGURE 6.16 fluid=melt

and oxygen fugacity relative to that of the NNO buffer, DNNO for a variety of Relationship between Ds igneous rocks superimposed on which are the calculated curves for this relationship from Eq. (6.4) (Gennaro et al., 2020) at temperatures and pressures indicated on individual curves. Modified after Gennaro et al. (2020). The original sources to the data in this figure can be found in the caption to source figure of this diagram.

FIGURE 6.17 Evolution of sulfur content coexisting aqueous fluid and hydrous melt as a function of their sulfur content for different compositions as indicated on diagrams equilibrated at 500 MPa and 1240 C with the oxygen fugacity controlled 1.4 log units above that of the NNO buffer. In other words, the sulfur is oxidized. Modified after Zajacs (2015).

6.3 Structure and properties of H2O in fluids

349

100 80

DSfluid/melt

40

0.2 wt% S

30 20

1.8 wt% S

10

0.5-1.0 wt% S

0 0

5 10 15 20 25 Chlorine concentration in fluid, mol%

30

FIGURE 6.18 fluid=melt

and chlorine concentration in fluid for a basaltic melt composition and with Relationship between Ds DQFM þ 2.8 oxygen fugacity, 1050 C and 100 MPa temperature and pressure, respectively. Also shown with stars are data points at more reducing oxygen fugacity (DQFM ¼ 0.5). Modified after Beermann et al. (2015).

conditions such as, for example, those defined by the NNO oxygen buffer, the fluid/melt partition coefficient decreases as the NaCl concentration in the system increases, whereas under more oxidizing conditions (e.g., as those defined the ReeReO2 oxygen buffer; see Pownceby and O’Neill, 1994), the NaCl concentration in the fluid has no influence on the fluid/melt partition coefficient for sulfur (Binder et al., 2018; see also Fig. 6.19). Under oxidizing conditions (ReeReO2 buffer), the sulfur partition coefficient also depends systematically on H2O content (Webster and Botcharnikov, 2011), SiO2 content (Scaillet et al., 1998), the proportion of the sum of alkali metals and alkaline earths versus Si þ Al þ Fe3þ (Webster and Botcharnikov, 2011) and the NBO/T of the melt (Zajacs, 2015). It is also notable, that increasing peralkalinity, whether from excess alkali metals or excess alkaline earths, also leads to increased Dfluid/melt . S Perhaps not surprisingly in light of the strong association of sulfur and Fe2þ in silicate melts (Fincham and Richardson, 1954; Abraham et al., 1960; Park and Park, 2012), the fluid/melt partition coefficient decreases rapidly with increasing FeO concentration in the melt.

6.3 Structure and properties of H2O in fluids Ever since the late 18th century, it has been recognized that H2O likely is the most important fluid during most rock-forming processes. Spallanzani (1792e97) suggested, for example, that the steam emanating from volcanoes and vents likely was H2O. Subsequently, it became evident that among the many fluids encountered in most geological systems, H2O has the greatest abundance (Jambon, 1994).

350

Chapter 6 Structure and properties of fluids

FIGURE 6.19 Sulfur distribution between aqueous fluid and hydrous granitic melt with NaCl and sulfur added at oxygen fugacity  NNO. 200 MPa and 750e850 C. (A) Sulfur contents of coexisting fluid and melt at the different fluid=melt as a NaCl concentrations (mol fraction) indicated and at the NNO oxygen fugacity. (B) Evolution of Ds function of sulfur content of melt with different NaCl concentrations as indicated at the oxygen fugacity controlled 1.4 log units above that of the NNO. Notice how the oxygen fugacity seems to affect the effect of fluid=melt . NaCl content on Ds Modified from Binder et al. (2018).

Among the many potential fluid species in the CeOeHeNeS þ halogen system, under most conditions, H2O has the most influence on both the physics and chemistry of rock-forming processes (Kushiro, 1972; Mysen and Boettcher, 1975a, b; Whittington et al., 2000; Bouhifd et al., 2006; Kohlstedt et al., 2006; Grove et al., 2012). Ultimately, these effects reflect the structure of H2O-bearing magma and the various properties and processes involving melts, fluids, and rock-forming minerals. In

6.3 Structure and properties of H2O in fluids

351

this discussion, we will, therefore, emphasize the role of H2O among fluid species. Other species such as CO2, CH4, N2, SO3, and S2
(Schmidt and Watenphul, 2010; Mao et al., 2010; Lazar et al., 2014; Li and Keppler, 2014; Mysen et al., 2014; Lamadrid et al., 2017; Etschmann et al., 2019), will be discussed as components added to H2O, but will not be central to the present discussion.

6.3.1 Structure of liquid and supercritical H2O The structure of liquid and supercritical H2O has been examined via various theoretical models as well as by direct experiment (Walrafen et al., 1988; Brodholt and Wood, 1993; Gorbaty and Kalinichev, 1995; Hoffmann and Conradi, 1997; Boero et al., 2000; Kawamoto et al., 2004; Weck et al., 2009). Experimental data will be described first followed by a discussion of results from numerical simulations.

6.3.1.1 Experimentally determined structure Some of the experiment studies of the structure of H2O have been conducted along the pressuretemperature path of the liquid/vapor curve to pressures and temperatures exceeding those of the critical point of H2O (Hoffmann and Conradi, 1997; Katayama et al., 2010; Sahle et al., 2013), whereas other experiments have been along temperature-pressure paths defined by experiments in the fixed volume hydrothermal diamond anvil cell as originally described by Bassett et al. (1994), and occasionally under isothermal conditions to various pressures (Mysen et al., 2013). With the hydrothermal diamond anvil cell, chemical and physical measurements of the samples can be carried out while the sample is at the temperature and pressure of interest. In the first two types of experiments, increasing temperature leads to increasing pressure. In the third type, pressure was adjusted at each experimental temperature in order to maintain isobaric conditions. In the experiments along the pressure-temperature path of the melt-vapor curve of H2O (Fig. 6.20), results from NMR, Raman, infrared, and X-ray spectra have been interpreted to indicate coexisting monomers and dimers in the structure of H2O even as the pressure conditions within the supercritical region (Gorbaty and Kalinichev, 1995; Hoffmann and Conradi, 1997; Katayama et al., 2010). In the proton NMR spectra (Hoffmann and Conradi, 1997), recorded from ambient conditions to 40 MPa and 600 C, it was noted that the chemical shift of 1H was quite sensitive to both temperature and pressure (Fig. 6.21A and B). A discontinuity on the curves in Fig. 6.21A and B was observed when the melt-vapor curve was crossed. Under all circumstances, the chemical shift decreased with both increasing temperature and pressure. This implies deshielding of the proton nucleus, which, in turn, reflects gradual destruction of hydrogen bonding responsible for the existence of dimers or more polymerized structures in the aqueous fluid (Schneider et al., 1958). It was noted, however, that hydrogen bonding persisted to the highest temperatures (600 C) and pressures (40 MPa) of these experiments. Those temperature/ pressure conditions were well inside the supercritical region of H2O. Hoffmann and Conradi (1997) calibrated the chemical shift in the 1H NMR spectra as a function of H2O density to reach an expression for the proportion of hydrogen bonding. Those authors noted that there appeared to be a limit of
6.6 ppm in the chemical shift, which was set to the conditions of no hydrogen bonding (Fig. 6.21C) The relationship between H2O density and proportion of hydrogen bonding was calibrated as;

352

Chapter 6 Structure and properties of fluids

FIGURE 6.20 Pressure-temperature diagram of the melting and evaporation phase relations of H2O. Modified by Wagner and Pruss (2002).

X ¼ 0.2439s þ 1.61;

(6.5)

where X is the proportion of hydrogen bonding and s is the change in chemical shift. The structure of H2O also has been examined with laser Raman, neutron, and X-ray Raman methods (Walrafen et al., 1986; Frantz et al., 1993; Soper and Ricci, 2000; Mysen, 2010; Sahle et al., 2013). The partial radial distribution functions from X-ray and neutron diffraction (Sahle et al., 2013; Soper and Ricci, 2000) are consistent with increasing importance of hydrogen bonding with increasing pressure. Increasing temperature leads to lesser importance of hydrogen bonding. From the laser Raman spectra of H2O, increasing temperature and pressure approaching 1000 C and nearly 2 GPa, respectively, shows a characteristic change on the low-frequency side of the Raman envelope centered near 3600 cm
1 (Frantz et al., 1993; Foustoukos and Mysen, 2012). This Raman intensity envelope comprises bands assigned to OH stretching with the low-frequency side containing a signal from hydrogen-bonded OH-groups [whether in molecular H2O or in OH-groups bonded to a silicate network (Frantz et al., 1993; Walrafen et al., 1986, 1988, 1999; Mysen, 2010; Foustoukos and Mysen, 2012; see also Fig. 6.22)]. At a few tens of MPa pressure, the proportion of hydrogen bonding increases with increasing pressure (Fig. 6.23), in agreement with the proton NMR data of Hoffmann and Conradi (1997). Walrafen et al. (1986, 1999) noted that the proportion of hydrogen bonds and, therefore, dimers or more polymerized species in the H2O structure, increases with increasing pressure until reaching the critical point of H2O, which located is at 22.1 MPa and 374 C. At this point, the Raman data have been interpreted to suggest 17.4% hydrogen bonding. Notably, this structural evolution also implies that the dimerization reaction, 2H2O ¼ (H2O)2, involves a negative volume change.

6.3 Structure and properties of H2O in fluids

353

FIGURE 6.21 Relationship between 1H chemical shift from NMR spectra and various properties of H2O. Also shown is the extent of hydrogen bonding in H2O from a calibration of the 1H NMR chemical shifts. A. 1H NMR chemical shift as a function of temperature with pressure indicated on individual curves. B. 1H NMR chemical shift as a function of pressure with temperatures shown on individual curves. C. 1H NMR chemical shift as a function of H2O density with temperatures shown on individual curves. Modified after Hoffmann and Conradi (1997).

354

Chapter 6 Structure and properties of fluids

FIGURE 6.22 Examples of Raman shifts of the 3600 cm
1 envelope recorded as a function of temperature as indicated and 200 MPa total pressure. Modified after Frantz et al. (1993).

FIGURE 6.23 Evolution of Raman band intensity ratios in the 3600 cm
1 envelope. Ihyd is the intensity of the low-frequency portion of the envelope, whereas IO..H is that of the high-frequency portion. (A) Logarithm the intensity ratio as a function of pressure. (B) Logarithm the intensity ratio as a function of temperature. Modified after Walrafen et al. (1999).

6.3 Structure and properties of H2O in fluids

355

For Raman spectra along the melt/vapor curve (see Fig. 6.20), the proportion of hydrogen bonding and, therefore, polymerized species such as H2O dimers in the structure, can be expressed as (Walrafen et al., 1999): lnðX dimer =X monomer Þ ¼ a þ b=T;

(6.6)

where Xdimer and Xmonomer are the proportions of dimers and monomers and T is temperature (Kelvin). This relationship yields a straight line where the slope of this line results in an enthalpy change of 20.1 kJ/mol (Fig. 6.23B) for the formation of hydrogen bonding in pure H2O at temperatures and pressures less than those of the critical point. An X-ray Raman scattering study along a pressure-temperature path near the melt-vapor curve was reported by Sahle et al. (2013). They also employed modeling relying on molecular dynamics and density functional theory simulations as an aid in the interpretation of the X-ray scattering spectra. Sahle et al. (2013) also found a positive relationship between the density of H2O and the proportion hydrogen bonds relative to the number of oxygeneoxygen linkages (Fig. 6.24).

FIGURE 6.24 Proportion of hydrogen bonds relative to total number of oxygen. (i.e., H2O molecules) in the 22e200 C temperature range as a function of H2O density where density reflects imposed pressure in the 0.1e1.6 MPa range for the 22e200 C temperature range. Modified after Sahle et al. (2013).

356

Chapter 6 Structure and properties of fluids

It seems, therefore, that at least in the comparative low pressure-temperature regime of the meltvapor curve for pure H2O (Fig. 6.20), hydrogen bonding and, therefore, polymerization of at least some H2O molecules (17%e20%) exist even into the supercritical region. Experiments have, however, been reported to much higher pressure and somewhat higher temperatures (Kawamoto et al., 2004; Katayama et al., 2010; Mysen, 2010; Foustoukos and Mysen, 2012). In the Raman spectra of the w3600 cm
1 envelope assigned to OH-stretch vibrations, Kawamoto et al. (2004) observed a rapid change in the rate of decrease of the frequency of the intensity maximum of this envelope as pressure exceeded 1.3 GPa at 300 C (Fig. 6.25). This frequency decrease was interpreted as a pressure and density-dependent change in proportion of the structural entities in the H2O. In light of the other data discussed above, one of these entities might be polymerized H2O, whereas the other is not. Diminishing intensity of the low-frequency limb of the 3600 cm
1 Raman intensity envelope with increasing temperature has been reported by Mysen (2010) and Foustkoukos and Mysen (2012) to pressures near 1 GPa. In these and other high-temperature Raman spectra (Walrafen et al., 1986, 1988, 1999), this low-frequency portion of the spectrum (see also the fitted Raman spectra in Fig. 6.25) has been interpreted as due to OH vibrations influenced by hydrogen bonding, which enhanced the Raman intensities. From the results of the fitted Raman spectra (Fig. 6.25), it is seen that the slope of the relationship between Raman intensity ratios and 1/T for H2O falls in two temperature ranges (Fig. 6.26). This, in turn, implies two different DH-values for formation of hydrogen bonds. At temperatures less than about 200 C, the enthalpy of the H-bond formation is 21.6  0.8 kJ/mol, which happens to be nearly the same as the enthalpy of D-bond formation in D2O at low temperature (23.3  1.6 kJ/mol at temperatures less than about 100 C; see Walrafen et al., 1996) and only slightly higher than for D2O at higher temperature (14.4  0.8 kJ/mol at T  700 C; see Foustkoukos and Mysen, 2012). In comparison, the enthalpy for hydrogen bond formation at less than 700 C is 43.3  0.8 kJ/mol. In other words, the deuterium-bond is much weaker than the hydrogen bond at high

FIGURE 6.25 Frequency sift of the maximum intensity point of the 3600 cm
1 envelope of Raman spectra of H2O. (A) As a function of pressure. (B) As a function of H2O density. Modified after Kawamoto et al. (2004).

6.3 Structure and properties of H2O in fluids

357

FIGURE 6.26 Evolution of Raman band intensity ratios in the 3600 cm
1 envelope where Ihyd is the intensity of the lowfrequency portion of the envelope, whereas IO..H is that of the high-frequency portion reflecting the proportion of hydrogen bonded to nonhydrogen bonded H2O as a function of temperature from the sources indicated on the individual curves. Modified after Foustoukos and Mysen (2012).

temperature and the difference between the energy of H- and D-bonding at low and high temperatures is much greater for hydrogen bonding. The data in Fig. 6.26 also indicate that the proportion of H-bonding in H2O decreases rapidly with increasing temperature. At the highest temperature of the Frantz et al. (1993) experiments (525 C), for example, the proportion of H-bonding was reported to be down to 2%e3%, whereas for the much higher-pressure experiments by Foustoukos and Mysen (2012), at 525 C, the proportion of hydrogen bonding is about 40%. This significant difference again goes to show, therefore, how sensitive hydrogen bonding in H2O is to pressure. Notably, Katayama et al. (2010), using X-ray diffraction, recorded spectra along the melting curve of H2O to 17 GPa and 850 K, and interpreted their spectra to reflect the presence of two structural entities coexisting in the entire pressure range examined. The position of the first diffraction peak was interpreted to indicate changes on the coordination number of the H2O molecule until about 4 GPa was reached. At 4 GPa pressure, the coordination number was interpreted to be 9 (Fig. 6.27). At higher pressure, no further coordination changes were recorded. Katayama et al. (2010) noted that this coordination number (8e9) is typical

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Chapter 6 Structure and properties of fluids

FIGURE 6.27 Oxygen coordination number (from H2O molecules) in H2O as a function of pressure at 850 K. Modified after Sahle et al. (2013).

for simple liquids such as noble gases. At pressures higher than 4 GPa, the X-ray data were interpreted to show only a decreased nearest-neighbor distance without further coordination changes. The X-ray diffraction data of H2O to 600 C and 4.5 GPa (Weck et al., 2009) have been interpreted to indicate structural behavior as a function of pressure resembling that reported by Katayama et al. (2010) (Figs. 6.27 and 6.28). In both experimental studies, the coordination number of oxygen increased rapidly to pressures of several GPa before the changes in coordination number became quite insensitive to pressure with a further pressure increase. However, in the Katayama et al. (2010) study, this change in oxygen coordination was reported to be near 4 GPa, whereas Weck et al. (2009) reported the change of rate in oxygen coordination number with pressure was between 2 and 3 GPa. Interestingly, Weck et al. (2009) examined both H2O and D2O and found an almost fixed coordination number difference with the oxygen coordination in D2O being about 0.5 units higher than that of H2O (Fig. 6.28). This different response to pressure likely reflects the greater mass and radius of deuterium compared with hydrogen. At least one study of H2O structure, using oxygen pre-edge spectra, indicate, however, that the transformation between the two structures involve an enthalpy change of only 7.5  1.6 kJ/mol (Pylkka¨nen et al., 2011). This value is only15%-20% of the DH-value for H-bond breakdown reported from studies using other methods. Pylkka¨nen et al. (2011) concluded, therefore, that there was no evidence in their neutron diffraction spectra for H-bond breakdown with temperature. It is unclear,

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359

FIGURE 6.28 Oxygen coordination number (from H2O and D2O molecules as indicated) in H2O and D2O as a function of pressure at 500 K. Modified after Weck et al. (2009).

however, how this can be given the overwhelming amount of data to the contrary from the large number of other experimental studies discussed earlier (Walrafen et al., 1986, 1999; Frantz et al., 1993; Hoffmann and Conradi, 1997; Katayama et al., 2010; Sahle et al., 2013).

6.3.1.2 Numerical modeling of structure Numerical modeling of the structure of liquid and supercritical H2O in part has focused on structural features via computed pair correlation functions (Brodholt and Wood, 1990; Boero et al., 2000; Weck et al., 2009) and in part via comparison of vibrational spectra obtained by experiment and computation (Duan et al., 1995). For the most part, however, computations have focused on properties such as diffusion and viscosity (Brodholt and Wood, 1990, 1993; Boero et al., 2000; Zhang and Duan, 2005; Duan et al., 2009; Sakuma et al., 2013; see also discussion later in the chapter) rather than simulation of the structure of H2O fluid. Duan et al. (1995) were able, for example, to calculate the topology of the 3600 cm
1 intensity envelope in the Raman spectrum of H2O as a function of H2O density and compared the simulated spectra with experimental spectra (Lindner et al., 1970; Frantz et al., 1993). The frequency of the peak maximum from the calculation and experiments agreed within experimental error (Fig. 6.29). This agreement implies the computations also were able to predict polymerization of H2O molecules and, therefore, the existence of hydrogen bonding holding these molecules together. Pair distribution functions with which to describe the structure of H2O often have been simulated with numerical modeling (Brodholt and Wood, 1990, 1993; Boero et al., 2000; Chen et al., 2010; Ikeda

360

Chapter 6 Structure and properties of fluids

FIGURE 6.29 Comparison of observed (Frantz et al., 1993) and calculated (Duan et al., 1995) shift of the intensity maximum of the 3600 cm
1 envelope in the Raman spectra of H2O as a function of their density, and, therefore, pressure. Modified from Duan et al. (1995).

et al., 2010). In these models, simulation of the OeO, HeH, and OeH pair distribution functions, g(i-j), served as a principal tool with which to obtain the structure of H2O.8 Among the radial distribution functions, Brodholt and Wood (1993) noted that g(OeO) from H2O at 27 C (Fig. 6.30) is consistent with tetrahedral ordering because the OeOeO bond angle is nearly identical that of the ideal structure. Also seen in Fig. 6.30, the OeH distribution function, g(OeH), calculated from 27 C to higher temperatures, gives the length of the hydrogen bond to be 0.183 nm at 27 C. Notably, with increasing temperature the intensity of the first peak in the g(OeH) distribution function decreases, but is still present thus indicating that at least some hydrogen bonding remains at least to 398 C at a density of H2O of 0.5 g/cm3 (Fig. 6.30B). The temperature evolution of these intensities is, however, significantly dependent on the density of H2O. At the density of 1.5 g/cm3, for example, the first peak in the g(OeH) radial distribution is still present thus indicating that there remains some hydrogen bonding under these conditions (Brodholt and Wood, 1993). In general, the results from the numerical computations by Brodholt and Wood (1993) indicate that for all practical purposes, hydrogen bonding has disappeared by 500e550 C. Density is a factor, but the results of the computations are such that it is not easy to quantify. The 500e550 C maximum temperature for hydrogen bonding from the Brodholt and Wood (1993) simulations differs slightly from the experimental results using NMR, Raman spectroscopy and X-ray diffraction, where hydrogen bonding

8 In simple terms, a pair distribution function, G(r), whether obtained by experimental measurement or numerical modeling, describes the number of atoms of interest [here H and O distances from H, and O to become g(OeO), g(OeH) and g((HeH)] compared with the distances in an ideal gas structure.

6.3 Structure and properties of H2O in fluids

361

FIGURE 6.30 Radial distribution functions for OeO and OeH distances simulated with radial distribution calculations at the two temperatures indicated with H2O density of 0.5 g/cm.3 Modified from Brodholt and Wood (1993).

seemed to exist to temperatures above about 600 C (Hoffmann and Conradi, 1997; Katayama et al., 2010; Foustoukos and Mysen, 2012). There appears to be some disagreement regarding the how pressure affects hydrogen bonding. Whereas Brodholt and Wood (1993) suggested that there was little pressure effect, Frantz et al. (1993), Hoffmann and Conradi (1997) and Katayama et al. (2010) concluded that major pressure effects caused changes in the extent of hydrogen bonding in H2O. This is particularly evident in the evolution of the pressure-dependent H2O molecule coordination number from the in situ X-ray diffraction data by Katayama et al. (2010; see also Fig. 6.27) and in situ, high-pressuretemperature structural data by Frantz et al. (1993), Gorbaty and Kalinichev (1995), Kawamoto et al. (2004), and Foustoukos and Mysen (2012). The pressure-temperature diagram from in situ X-ray diffraction shows a particularly nice description of the transformation from hydrogenbonded, tetrahedrally coordinated H2O structure to simple liquids, conceptually resembling the structure of noble gas in liquid form, at higher temperature and pressure (Ikeda et al., 2010; see also Fig. 6.31). Interestingly, Walrafen et al. (1988), concluded that increased frequency of the 3600 cm
1 Raman envelope also reflected a pressure-induced breakdown of hydrogen bonding. Notably, however, the results of the first-principles molecular dynamics studies (Boero et al., 2000; Kalinichev, 2001) indicated very significant density effects (and, therefore, pressure effects) on the role of hydrogen bonding because both the symmetric and antisymmetric stretching modes (near 3600 cm
1) are significantly dependent on H2O density whether determined experimentally or by molecular dynamics simulations. Both frequencies decrease with increasing density of H2O and, therefore, pressure, which would indicate enhanced importance of hydrogen bonding in H2O with increasing density and, therefore, pressure (Fig. 6.32).

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Chapter 6 Structure and properties of fluids

FIGURE 6.31 Schematic pressure-temperature diagram for H2O indicating the regions of various H2O structural features as a function of temperature and pressure as indicated on the Figure. Modified after Ikeda et al. (2010).

FIGURE 6.32 Shift of the intensity of the maximum intensity point of the 3600 cm
1 Raman intensity envelope as a function of H2O density from numerical simulations. Modified from Kalinichev (2001).

6.3 Structure and properties of H2O in fluids

363

6.3.2 Properties of liquid and supercritical H2O Properties of liquid and supercritical H2O will simply be referred to as properties of H2O unless characterization of a specific state of H2O is necessary. These properties include measured and calculated thermodynamic properties, transport properties, equation of state, and dielectric properties.

6.3.2.1 Thermodynamic properties and equations of state of H2O Overall, thermodynamic properties of H2O have been obtained both by experimental determinations and through numerical simulations of various kinds (Brodholt and Wood, 1990, 1993; Johnson and Norton, 1991; Withers et al., 2000; Kalinichev, 2001; Zhang and Duan, 2005; Dolejs, 2013).

6.3.2.1.1 Experimental data The primary property determined experimentally often is volume or density. From an experimental perspective, determination of volume properties provides the link to other thermodynamic properties because of thermodynamic relationships such as: ðvG=vPÞT ¼ V;

(6.7)

where G is Gibbs free energy, P is pressure and V is volume. Entropy is linked to volume as: ðvS=vPÞ ¼ ðvV=vTÞP ;

(6.8)

H ¼ G þ TS.

(6.9)

lnðf =f o Þ ¼ ðG
Go Þ=RT;

(6.10)

and enthalpy as: Finally, fugacity is: where f and G are the fugacity and Gibbs free energy at the standard state. The earliest experiments were those of Keyes (1933) to temperatures of 550 C. Kennedy (1950) noted, however, that much of those early data carried substantial errors. He, therefore, redesigned the necessary instrumentation and determined the PeVeT data to 1000 C and 250 MPa (Fig. 6.33). In the temperature and pressure range from ambient to 460 C at 30 MPa, Kennedy (1950) relied on the experimental results of Keyes et al. (1936). More recent data relying on the Kennedy (1950) result actually, therefore, use the 1936 data by Keyes et al. (1936). Kennedy (1950) noted, however, that even though there was agreement between his data and those of Keyes et al. (1936) over most of the temperature-pressure range, near the critical point for H2O, where properties change rapidly as a function of temperature and pressure, there was some disagreement. More recent experimental data, such as, for example, those of Burnham et al. (1969a), relied on experimental methods resembling those of Kennedy (1950). The Burnham et al. (1969a) specific volume data, converted to molar volume in the example in Fig. 6.34, was noted to be in close agreement with the 1935 experimental data of Bridgman (1935) at low pressure and the International Steam Tables (Bain, 1964) at higher pressure. As seen in Figs, 6.33 and 6.34, it is also evident that at low pressure, the molar volume changes rapidly as a function of temperature near the critical point of H2O, but is a nearly linear function of temperature at higher temperature. The rapid volume change near the critical point likely reflects rapid changes in the H2O structure as the H2O polymers break down (see Section 6.2.1), while at higher temperatures, the structure of H2O resembles a simple o

o

364

Chapter 6 Structure and properties of fluids

FIGURE 6.33 Examples of experimentally determined temperature-dependent molar volume of H2O at two different pressures (30 and 250 MPa) to illustrated how pressure affects the thermal expansion of H2O. Modified after Kennedy (1950).

molecular structure resembling, perhaps, the structure of noble gases (Frantz et al., 1993; Weck et al., 2009), the compressibility of which is a simple, near linear, function of pressure. At higher pressure, such as, for example, the 800 MPa data in Fig. 6.34, likely the structure still comprises H2O polymers, the proportion of which gradually disappears with increasing temperature (Foustoukos and Mysen, 2012). As a result, the molar volume changes gradually with a slight positive (vV/vT) as the proportion of polymers (and, therefore, hydrogen bonding) diminishes. In addition, there exist compilations of some experimentally determined thermodynamic properties of H2O to very high temperatures and pressures (Kennedy, 1950; Pistorius and Sharp, 1960; Burnham et al., 1969a, b; Harvey et al., 2000; Wagner and Pruss, 2002; Wagner and Kretzschmar, 2008). Among these, compilations of thermodynamic properties of H2O by Burnham et al. (1969b) and Wagner and Pruss (2002), are those most commonly used. These compilations differ somewhat in what data are summarized. Burnham et al. (1969b) list data on specific volume, Gibbs free energy, entropy, enthalpy, fugacity, and fugacity coefficients. The fundamental basis for these compilations is the specific volume

6.3 Structure and properties of H2O in fluids

365

FIGURE 6.34 Examples of experimentally determined temperature-dependent molar volume of H2O at two different pressures (100 and 800 MPa) to illustrated how pressure affects the thermal expansion of H2O (Burnham et al., 1969a).

data from Burnham et al. (1969a) together with the Steam Tables (Bain, 1964). Wagner and Pruss (2002) relied on the IAPWS-959 formulations for the most part although they also used a range of more recent data. The result of this was tabulation of density, enthalpy, entropy, isochoric and isothermal heat capacity, and speed of sound. Both data sets were reported from 0 to 1000 C and pressures from ambient to 1 GPa. In other words, the temperature and pressure ranges of the Burnham et al. (1969b) and Wagner and Pruss (2002) were essentially the same. For thermodynamic data to higher pressure, Pistorius and Sharp (1960) tabulated information on entropy and Gibbs free energy to 25 GPa and the same temperature range (0e1000 C). The entropy and Gibbs free energy were calculated from on specific volume data existing at that time (Kennedy et al., 1958; Holser and Kennedy, 1958) by employing the formulations:

9

IAPWS-95 is an abbreviation for the International Association for the Properties of Water and Steam, published in 1995.

366

Chapter 6 Structure and properties of fluids

FIGURE 6.35 Effect of pressure on thermodynamic properties of H2O. (A) Relationship between pressure and Gibbs free energy. (B) Relationship between pressure and entropy. Modified from Wagner and Pruss (2002).

o

ZP 

S¼S
Po

vV vT

 p

vP

(6.11)

and ZP G ¼ Go þ

VvP

(6.12)

Po

In Eqs. (6.11) and (6.12), S is entropy, G is Gibbs free energy, V is volume, and P is pressure. Subscript, o, refers to standard state. Pistorius and Sharp (1960) relied on fitting polynomials to existing entropy and Gibbs free energy data and reported results to 1000 C and 25 GPa (Fig. 6.35). They noted the difficulty associated with estimates of errors in the results of the calculations but suggested 2%e4% error in the Gibbs free energy and 6% error in the entropy data. Equation of state (EOS) of H2O to high pressure was reported by Abramson and Brown (2004). They determined the EOS of H2O by measuring the speed of sound in a diamond cell to w6 GPa (Fig. 6.36). The speed of sound data were then converted to density of H2O to 6 GPa total pressure by

6.3 Structure and properties of H2O in fluids

367

FIGURE 6.36 Sound velocity of H2O as a function of pressure at the temperatures indicated on individual curves. Modified from Abramson and Brown (2004).

FIGURE 6.37 Density of H2O as a function of pressure at the temperatures indicated derived from sound velocity data. Modified after Sanchez-Valle et al. (2013).

368

Chapter 6 Structure and properties of fluids

FIGURE 6.38 Refractive index (A) and polarizability (B) of H2O as a function of H2O density at the temperatures indicated on the diagrams. Modified from Sanchez-Valle et al. (2013).

calibrating the relationships relying primarily on the density and speed of sound data compilation by Wagner and Pruss (2002). More recently, Sanchez-Valle et al. (2013) also employed acoustic velocity measured in H2O contained in a diamond anvil cell to 7 GPa and 400 C. From these measurements, they derived refractive index, polarizability and density of H2O (Figs. 6.37 and 6.38). In addition, compressibility and thermal expansion were derived together with the isobaric heat capacity of H2O (Fig. 6.39). In the

6.3 Structure and properties of H2O in fluids

369

FIGURE 6.39 Thermodynamic properties of H2O as a function of pressure and temperature. (A) Heat capacity of H2O, and (B) Isothermal compressibility of H2O as a function of pressure at 200 and 400 C. Modified from Sanchez-Valle et al. (2013).

370

Chapter 6 Structure and properties of fluids

latter data, it is striking how the heat capacity and compressibility drops rapidly through the first 1e1.5 GPa, followed by a much gentler slope of the relationships at higher pressures. Sanchez-Valle et al. (2013) concluded that linearity of refractive index with density and essential insensitivity to temperature together with the high-pressure behavior of heat capacity and compressibility would be consistent with little structural change of H2O in the temperature and pressure range of the highestpressure portion of their experiments. This conclusion is in accord with the pressure-dependent structural data of H2O discussed earlier, which indicate a simple molecular structure of H2O at these pressures (Weck et al., 2009; Katayama et al., 2010; see also Figs. 6.27 and 6.28). Another method with which to determine the PeVeT properties of fluid is to grow them as fluid inclusions in synthetic minerals such as quartz and corundum. Quartz has been used at comparatively low pressure and temperature (Bodnar and Sterner, 1987), but given the significant solubility of quartz in H2O at high pressure and temperature, this host for fluid inclusions becomes unsuitable. In order to improve on this situation, Brodholt and Wood (1994) grew fluid inclusions in corundum crystals to 1600 C and 2.5 GPa because corundum is less soluble in H2O than quartz (Becker et al., 1983; Manning, 1994). Compared with other data published at the time, the Brodholt and Wood (1994) results are the closest to the calculated results published by Kerrick and Jacobs (1981) and Brodholt and Wood (1993). Even those data are, however, 2%e4% lower than the results of Brodholt and Wood (1994). Interestingly, the experimental data from Burnham et al. (1969a), where pressure and temperatures (0.95 GPa, 1000 C) overlap, are in complete agreement with measurements by Brodholt and Wood (1994) using the synthetically grown inclusion in corundum. At this pressure (0.95 GPa), there is also agreement with the Kerrick and Jacobs (1981) results (Fig. 6.40) obtained via a computation with the Redlich-Kwong equation. Another approach that may be used for the measurement of density of synthetic fluid inclusion is 1 H MAS NMR, which has been used to measure the frequency shift in resonances in the NMR spectra from H2O inclusions in synthetic corundum (Withers et al., 2000). In this case, the shift is a systematic function of the fluid density. Calibration was accomplished by using published experimental data and fitting those to a simple linear equation: r ¼ ad þ b;

(6.13)

where r is density and d is chemical shift. When comparing the results with published density data (Holloway, 1977; Delaney and Helgeson, 1978; Haar et al., 1984; Saxena and Fei, 1987; Saul and Wagner, 1989; Bolonoshko and Saxena, 1991; Brodholt and Wood, 1993; Pitzer and Sterner, 1994), Withers et al. (2000), using this NMR-based method, noted that their results were most similar to Brodholt and Wood (1993). However, the latter data also entered into the calibration of the 1H NMR chemical shifts, so the close agreement should not be surprising. The closest agreement among the other data were those of Pitzer and Sterner (1994) and Saul and Wagner (1989) (Fig. 6.41). The other data tended to underestimate H2O density compared with the Withers et al. (2000) measurements. The exception where the results of Holloway (1977), which significantly overestimated the H2O density (Fig. 6.41A).

6.3.2.1.2 Numerical modeling Properties of H2O and other fluids (see later in the chapter) have been the subject of considerable, and often quite successful, numerical modeling (Kerrick and Jacobs, 1981; Brodholt and Wood, 1990, 1993; Johnson and Norton, 1991; Belonoshko and Saxena, 1991; Zhang and Duan, 2005). Results of

6.3 Structure and properties of H2O in fluids

371

FIGURE 6.40 Effect of temperature on experimentally-determined molar volume of H2O compared with volume information from various calculations as indicated on the diagram. Modified from Brodholt and Wood (1994).

molecular dynamics calculations not infrequently closely resemble the results of experiments (see, for example, Brodholt and Wood, 1990; Burnham et al., 1969a). For example, under conditions where molecular dynamics calculations were carried out with a water density of 1 g/cm3, the experimental density data by Burnham et al. (1969a) gave density values  2.6% of the 1.0 g/cm3 value of Brodholt and Wood (1990) in the temperature and pressure range of ambient to 444 C and 47e900 MPa. Knowledge of PeVeT properties of H2O to pressures considerably greater than the pressure limit in Brodholt and Wood (1990) is necessary for characterization of the role of H2O in deeper portions of the Earth’s mantle. With this need in mind, Brodholt and Wood (1993) extended the molecular dynamics calculated results to much higher temperatures and pressure (w2200 C and 35 GPa). These calculations relied on more recent information than the earlier calculations by Pistorius and Sharp (1960) discussed above. Presumably, this also means that the errors in the data were smaller. However, it should be kept in mind that when considering results from very high temperature and pressure conditions, the maximum temperature and pressure to which comparison between experimental and modeling results can be made, typically do not exceed 1000 C and 1 GPa. At higher pressures, comparison may be made with experimental data on transformation of ice structure, but these are experiments at low temperature (see, for example, the data on IceVII to IceVIII by Hemley et al., 1987), and even under these conditions, there are significant differences between the experimental data

372

Chapter 6 Structure and properties of fluids

FIGURE 6.41 Comparison between experimentally determined H2O density (Withers et al., 2000) and results from various models. (A) Comparison with results from Redlich-Kwong-based calibration (Holloway, 1977). (B) Comparison with results from Saul and Wagner (1989) calculations, and (C) Comparison with results from calculations from Pitzer and Sterner (1994). Modified from Withers et al. (2000).

6.3 Structure and properties of H2O in fluids

373

FIGURE 6.42 Comparison of results of partial molar volume of H2O from the calculations by Brodholt and Wood (1993), H2O , with results from other calculations as indicated on diagram, V H2O , expressed as the difference VBW other 93 between the two volumes in cm3/mol. Modified from Brodholt and Wood (1993).

and the results of molecular dynamics calculations (Brodholt and Wood, 1993). These issues must be remembered when comparing results of calculations with experimentally determined values. For example, a comparison with other calculated volume data show differences by as much as 4% with the difference showing a tendency to increase with increasing pressure (Fig. 6.42). Another high-temperature/high-pressure PeVeT simulation of H2O was reported by Belonoshko and Saxena (1991). A few examples of the temperature/pressure dependence of the molar volume of H2O from their computations are shown in Fig. 6.43. A comparison of the calculated results with shock wave experimental data indicates volume differences by as much as approximately 5%. Notably, the

374

Chapter 6 Structure and properties of fluids

FIGURE 6.43 Calculated molar volume ofmH2O as (A) a function of temperature at various pressures, and (B) As a function of pressure. Modified from Belonoshko and Saxena (1991).

FIGURE 6.44 Dehydration data the brucite (Mg(OH)2) breakdown to periclase (MgO) and water (H2O). Solid dots are results from numerical simulation by Belonoshko and Saxena (1991), whereas open symbols are results from various experimental studies. Modified from Belonoshko and Saxena (1991). See Belonoshko and Saxena (1991) for sources of the experimental data.

6.3 Structure and properties of H2O in fluids

375

thermal expansivity decreases rapidly with increasing pressure so that at 100 GPa, it is essentially zero (Fig. 6.43A). From those data, Gibbs free energy can be calculated based on Eq. (6.7). From those results, Belonoshko and Saxena (1991) calculated the dehydration curve for brucite [Mg(OH)2] and compared their results with experimental data (Fig. 6.44). At pressures below about 1 GPa, the difference between calculated and experimental dehydration curve is about 20e25 C whereas at high pressures, this difference decreases. A number of other numerical simulations have been reported. However, they suffer from the problem that the results cannot be benchmarked against well-established experimental data. So, in the end, results of simulations are compared with other simulations. From such comparisons, it is not feasible to establish whether one or more models might be better than others.

6.3.3 H2OeNaCl There exists considerable evidence for participation of saline fluids in high-grade metamorphic processes. For example, fluid inclusions from granulite facies terranes contain significant amounts of halides (Touret, 1995; Touret and Huizenga, 2011). Saline fluids also can participate in magmatic processes. For example, there is evidence for saline fluids in the mantle wedge overlying the subducting slab in subduction zones (Kawamoto et al., 2013) where partial melting takes place (Benard et al., 2018). In these environments, chlorine seems to be the dominant halogen although other halogens may participate at times (Manning and Aranovich, 2014). As a first step toward characterization of saline fluids in metamorphic and magmatic terranes, characterization of structure and properties of the simple model system H2OeNaCl is needed.

6.3.3.1 Structure of H2OeNaCl fluid The structure of H2OeNaCl fluids to high temperature and pressure has been examined both by experimental means (Botti et al., 2004; Coppa et al., 2006; Zhang et al., 2011; Sahle et al., 2017) and by numerical modeling (Brodholt, 1998; Coppa et al., 2006). For example, radial distribution functions derived from neutron diffraction data using mixed H2O, D2O fluids, lead to the conclusion that the ˚ from the Cl
anion. Notably, the protons of the H2O molecules nearest H2O molecule is about 2 A
˚ from point toward the Cl (Botti et al., 2004). The oxygen in the H2O molecules was located about 3A
the Cl anion. Botti et al. (2004) concluded that the H2O molecules were randomly distributed around the Cl
anion and that the average solvation number for H2O from CleH and CleO distances is 5.8 (Heuft and Meijer, 2003; see also Fig. 6.45). A somewhat similar study by Sahle et al. (2017) using Xray Raman spectroscopy coupled with numerical simulation of the radial distribution functions, expressed the results in terms of the fraction of H2O molecules in hydration shells as a function of temperature (Fig. 6.46). It is clear that at room temperature nearly all H2O is in hydration shells, but this fraction (w0.9) decreases with increasing temperature (w0.7 at 400 C, for example; see Fig. 6.46). The larger fraction of the H2O is in hydration shells surrounding Cl
compared with the number of H2O molecules surrounding Naþ (Fig. 6.46). Numerical simulations also have been employed to estimate the oxygen coordination numbers. Of course, this coordination number is, in effect, the number of H2O molecules in the H2O hydration shell around Naþ and Cl
in the H2OeNaCl fluids. At ambient temperature and pressure, in the numerical simulations by Brodholt (1998), he found that the oxygen coordination number around Cl
is about

376

Chapter 6 Structure and properties of fluids

FIGURE 6.45 Results of calculations using density functional theory of the H2O solvation shell around Hþ and O
in H2O molecules and an H2OeHCl solution A. Examples of distribution functions of the CleH and CleO bonds. B. Relative abundance of oxygen coordination number of CleO bonds. Modified after Heuft and Meijer (2003).

6.3 Structure and properties of H2O in fluids

377

FIGURE 6.46 Fraction of solvated H2O in solvation spheres around Naþ and Cl
from molecular dynamics simulation of local structure of H2OeNaCl solutions. Modified after Sahle et al. (2017).

7.5, whereas this number is near 5 for Naþ. Seemingly, these coordination numbers did not seem significantly dependent on the NaCl concentration in fluid. These calculated results also agree well with the experimental data of Heuft and Meijer (2003) (Fig. 6.45). Increasing temperature results in a decrease in number of H2O molecules around both Cl
and Naþ while pressure in the range between ambient and 0.5 GPa at 1000 C results in decreased hydration numbers (Brodholt, 1998) thus suggesting the hydration number is not significantly dependent on pressure. In fact, the observation that the position of the first peak in the distribution functions is dependent only on temperature, but not pressure (Fig. 6.47) is consistent with this conclusion.

6.3.3.2 Properties of H2O-Chloride fluid Among the properties perhaps most often considered when discussing properties of aqueous fluids is the dielectric constant. This probably is because this constant can be related to solubility and volume behavior under most conditions (Pitzer, 1983; Walther and Schott, 1988; Frantz et al., 1993). As noted above, from the volume behavior, a number of other thermodynamic properties can be derived [see Eqs. (6.7e6.10)].

378

Chapter 6 Structure and properties of fluids

FIGURE 6.47 Results of molecular dynamics simulation of the first peak in radial distribution functions for H2OeNaCl solutions as a function of temperature and pressure as indicated on diagram. Modified after Brodholt (1998).

An example of the effect of dissolved chloride in the system H2OeSiO2eKCl shows how the solubility of SiO2 is linked directly to the dielectric constant and how this constant varies with chloride concentration (Walther and Schott, 1988):   X  X  mw ðSiO2 Þ w 1 1 A
X B
X cþ a þ cþ a (6.14) ¼

ln þ mðSiO2 Þ RT εw ε εRT εRT where mw(SiO2) is the molality of SiO2 in pure H2O, m(SiO2) is the molality in the H2O-chloride mixture, εw and ε are the dielectric constants in pure H2O and the mixture, w is the Born parameter (Born, 1920), A and B are linearly dependent on to ionic strength of the solution, and a and c are Brønsted’s interaction parameters. An example of how the SiO2 solubility increases with increasing dielectric constant is shown in Fig. 6.48. Given the positive correlation between dielectric constant and solution density, the data in Fig. 6.48 also illustrates how the SiO2 solubility (in this case) increases with increasing fluid density.

6.3 Structure and properties of H2O in fluids

379

FIGURE 6.48 Solubility of quartz in H2OeKCl solution expressed as a function of the inverse of the dielectric constant, 1/ε, at 300 MPa and 600 C. Modified after Walther and Schott (1988).

Another, related variable that can be related to solution density is the limited equivalent conductance (Frantz and Marshall, 1984). For most ionic salts, there are linear relations. For the H2OeNaCl system, for example, the relationship is: L ¼ 1876
1160rH2 O;

(6.15)

where L is the limited equivalent conductance (see, for example, Marshall and Frantz, 1987, for definition of the terms used in measuring conductance of solutions), and rH2 O is the density of H2O. Interestingly, the limited equivalent conductance increases with increasing ionic radius of the halide in solution (Frantz and Marshall, 1984). It also increases with decreasing density of a solution (Frantz et al., 1993; see Fig. 6.49A). Notably, whereas in the temperature range from ambient to about 350 C the limited equivalent conductance is nonlinear function of solution density, at higher temperature, the relationship is essentially linear (Fig. 6.49A). Frantz et al. (1993) also noticed that solution density increases with dielectric constant (Fig. 6.49B). The correlation in this case was, however, not clearly linear in any temperature range. It was noted, though, that as the temperature increased, and fluid density decreased, the relationship became more linear. It was suggested that this evolution related to

Chapter 6 Structure and properties of fluids

Limiting equivalent conductance. cm2/ohm

380

2000

A

1000

0 0.0

0.2

0.4 0.6 0.8 Density, g/cm3

1.0

1.2

70

B Dielectric constant, ε

60 50 40 30 20 10 0 0.0

0.2

0.4 0.6 0.8 Density, g/cm3

1.0

1.2

4•10-2

C

Viscosity, Pa s

3•10-2

2•10-2

1•10-2

0 0.0

0.2

0.4 0.6 0.8 Density, g/cm3

1.0

1.2

FIGURE 6.49 Various physical properties of H2O and H2OeNaCl properties in the 100e505 C temperature range as compiled by Frantz et al. (1993). (A) Density of H2O as a function of limiting equivalent conductance. (B) Density as a function of dielectric constant, and (C) Density as a function of viscosity. Modified after data compilation by Frantz et al. (1993). See Frantz et al. (1993) for detailed sources of the data.

6.3 Structure and properties of H2O in fluids

381

the fact that although dielectric constant is an expression of the ability of a solution to orient itself in an external electrical field, this effect is counteracted by hydrogen bonding. As discussed above, the extent of hydrogen bonding decreases with increasing temperature (see also Walrafen, 1988, 1999; Foustoukos and Mysen, 2012). As a result, the relationships in Fig. 6.49 become more linear. Finally, the fluid viscosity also changes from distinctly nonlinear at low temperature to essentially linear at temperatures above about 500 C. Again, this evolution likely reflects the disappearance of hydrogen bonding in the H2O as the temperature exceeds 500 C. Thermodynamic properties of H2OeNaCl solutions also are distinct functions of the NaCl concentration (Franz, 1982; Anderko and Pitzer, 1993; Pitzer and Jiang, 1996; Brodholt, 1998). Among the publications cited here, only the study by Franz (1982) was purely experimental. He used the breakdown of brucite, Mg(OH)2, to periclase (MgO) þ water to define the fugacity of H2O in mixed H2OeNaCl solutions from a linear fit to the expression for the fugacity of H2O in the mixed H2Oe NaCl solution: ln fHo2 O ¼

DH DV DS
ðP
1Þ þ RT RT R

(6.16)

FIGURE 6.50 The temperature-dependence of the brucite ¼ periclase þ H2O dehydration reaction as a function of H2O fugacity in the system MgOeH2OeNaCl at 200 MPa where the H2O/NaCl ratio was employed to control the fugacity of H2O. Modified after Franz (1982).

382

Chapter 6 Structure and properties of fluids

FIGURE 6.51 Relationship between activity of h2O, aH2O, and mol fraction of NaCl, XNaCl, at 200 MPa derived from the phase relations summarized in Fig. 6.50 and compared with results of calculations by Pitzer and Jiang (1996). Data compilation by Pitzer and Jiang, 1996.

where f is fugacity, P is pressure, R is the gas constant, T is temperature (Kelvin), DH is enthalpy change, and DV and DS volume and entropy change, respectively, for the breakdown reaction: MgðOHÞ2 ¼ MgO þ H2 O.

(6.17)

From the linear fit in Fig. 6.50 (Franz, 1982), the activity in the H2OeNaCl solution is: aH2 O ¼ fHm2 O =fHo2 O

(6.18)

which results in an evolution of the activity of H2O along the H2OeNaCl join that barely deviates from 1 (Fig. 6.51) over the entire compositional range between pure H2O and about 45% NaCl in solution. Interestingly, these experimental data are essentially the same as the activity-composition relations from the calculated EOS by Anderko and Pitzer (1993) as discussed by Pitzer and Jiang (1996). The near-ideality of the H2OeNaCl mixtures indicated by the data in Fig. 6.51 appears to contrast with the data compilation by Bischoff and Pizer (1989) of the phase relations in this system. Here, it

6.3 Structure and properties of H2O in fluids

383

FIGURE 6.52 Results of data compilations for the system H2OeNaCl by Bischoff and Pitzer (1989). (A) Immiscibility gap in pressure-XNaCl (mol fraction of NaCl) of the system H2OeNaCl at different temperatures as indicated. (B) Evolution of the critical point, c.p., as a function of temperature and pressure. Modified after Bischoff and Pitzer (1989). See original figures in Bischoff and Puzter (1989) for the data sources used by them to derive the figures illustrated in modified form in the diagrams here.

was noted that there exists a wide field of immiscibility between H2O-rich and NaCl-rich fluids (Fig. 6.52A). The critical point (c.p.) appears to be close to the H2O-end of the binary and shifts to more H2O-rich compositions with increasing temperature. The immiscibility persists to at least 60 MPa and 500 C (Fig. 6.52B). In order to have immiscibility at 500 C and below and near ideality at 590 C and above, the solution behavior must be changing drastically over this narrow temperature interval of 90 C.

6.3.4 H2OeCeOeH In the CeOeH system, the two species to be considered here are CO2 and CH4 as these are the two main species relevant to rock-forming processes in the Earth. Carbon dioxide is the species under the aforementioned redox conditions defined by the MW10 buffer and more oxidizing, whereas under more reducing conditions, CH4 dominates.

6.3.4.1 H2OeCO2 Structure and properties, mostly thermodynamic properties, have been determined by both experiment and numerical simulation of H2OeCO2 solutions (Brodholt and Wood, 1993; Frost and Wood, 1997; 10

MW stands for magnetite-wu¨stite with the oxygen fugacity controlled by the reaction, 3FeOþ2O2¼Fe3O4

384

Chapter 6 Structure and properties of fluids

FIGURE 6.53 Temperature-composition (CO2/H2O abundance) of phase relations in the H2OeCO2 system at A. 1 GPa, and B. At 4 GPa illustrating, in particular, how the H2O-rich fluid dissolves more CO2 and the CO2-rich fluid more H2O with increasing pressure. Modified after Abramson et al. (2017).

Frantz, 1998; Aranovich and Newton, 1999; Duan and Zhang, 2006; Liu et al., 2011; Schmidt, 2014; Mysen, 2015a; Abramson et al., 2017). Phase relations were determined by conventional methods, whereas structural information was obtained by spectroscopic means carried out while the fluids were at the temperature and pressure of interest. The phase relations on the join H2OeCO2 exhibits a wide immiscibility gap, the maximum temperature of which increases with increasing pressure (Abramson et al., 2017; see Fig. 6.53). The width of the miscibility gap, does, however, shrink rapidly with increasing pressure. The structure of
the fluids outside the miscibility gap comprises molecular CO2, CO2
3 , together with HCO3 groups at least to pressures below about 1.6 GPa (Frantz, 1998; Schmidt, 2014; Mysen, 2015a). At higher pressure, Martinez et al. (2004) concluded that the bicarbonate, HCO
3 , was not stable in the fluid. At the 200 MPa of the experiments by Frantz (1998), molecular CO2 becomes increasingly important
with increasing temperature as do the CO2
3 groups. The abundance of HCO3 groups decreases continuously with increasing temperature (Fig. 6.54). This abundance evolution differs from results of calculations using SUPCRT92 (Johnson et al., 1992; Frantz, 1998). In these calculations, the abun
dance of CO2
3 groups decreases with increasing temperature, whereas the HCO3 abundance passes  through a maximum between 300 and 400 C. Clearly care must be exercised when using SUPCRT92 for these purposes. Experiments at higher pressure, using a hydrothermal diamond anvil cell, were also aimed at determination of species abundance as a function if temperature and pressure (Schmidt, 2014; Mysen, 2015a). For example, in the experiments by Schmidt (2014), The CO2
3 and CO2 abundance decreases

6.3 Structure and properties of H2O in fluids

385

FIGURE 6.54 Experimentally-determined speciation in K2CO3eH2O and KHCO3eH2O fluids as a function of temperature at 200 MPa. Modified from Frantz (1998).

with increasing pressure while that of the HCO-3 shows an increase (Fig. 6.55). Furthermore, these pressure effects diminish with decreasing temperature. This means that the equilibrium 2
2HCO
3 ¼ CO3 þ CO2 þ H2 O;

(6.19)

shifts to the left with increasing pressure. This conclusion is in accord with the results of Mysen
(2015a), who observed a linear relation between the ln (CO2
3 /HCO3 ) in both fluids and coexisting CO2-saturated silicate melts with a DH of the equilibrium at 20  9 kJ/mol (Fig. 6.56), which is within the DH-range observed for this equilibrium in the coexisting melt. Of course, in the Mysen (2015a) experiments, pressure also increases as the temperature increases, which according to Schmidt (2014) also drives Eq. (6.19) to the left. Property measurements of H2OeCO2 fluids have focused mostly on thermodynamic properties, and among those, mostly on activity-composition relations. These measurements have employed volume measurements as a means to derive activity and activity coefficients of the fluid species (Frost and Wood, 1997; Deering et al., 2016) as activity coefficient, g, of component, i, can be linked to partial molar volume of component, i, and the volume of pure i so that: 1 lngi ¼ RT

ZP ðV i
Vi ÞdP: 1

(6.20)

386

Chapter 6 Structure and properties of fluids

FIGURE 6.55

Activities of CO2
3 , HCO3 , NaCO3 , and CO2 (panels AeD) as a function of pressure and temperatures as indicated on individual curves.

Modified after Schmidt (2014).

Activity coefficients also have been obtained by using the relationship between mol fraction and activity of H2O dissolved in silicate melts (Burnham, 1979; Eggler and Kadik, 1979):  melt 2 (6.21) amelt H2O ¼ k XH2O : for mol fraction of H2O in melt less than 0.5 (Burnham, 1979). A more complex function was used for more water-rich systems. Given that the activity of H2O in melt and fluid is the same, the activity of

6.3 Structure and properties of H2O in fluids

387

FIGURE 6.56 2
Evolution of HCO
3 /CO3 abundance ratio of H2OeCO2 fluid as a function of temperature.

Modified after Mysen (2015a).

FIGURE 6.57 Activity-composition relations in the H2OeCO2 fluids at 800 C and 1.4 GPa. Data points are from experimental results by Aranovich and Newton (1999), whereas curves are from calculations by Duan and Zhang (2006). Modified after Duan and Zhang (2006).

388

Chapter 6 Structure and properties of fluids

H2O in the fluid could be derived. A final, and perhaps intuitively simpler, method is to determine decarbonation and dehydration reactions such as, for example (Aranovich and Newton, 1999): CaCO3 þ SiO2 ¼ CaSiO3 þ CO2 ;

(6.22)

MgCO3 þ MgSiO3 ¼ Mg2 SiO4 þ CO2 ;

(6.23)

Mg3 Si4 O10 ðOHÞ2 ¼ 3MgSiO3 þ SiO2 þ H2 O.

(6.24)

and

Regardless of method employed, the activity-composition relations were quite similar with only a slight excess volume (Fig. 6.57). This comparison includes the results from the molecular dynamics simulations by Duan and Zhang (2006). There is close agreement between the results from experiments and from simulation although the differences tend to be slightly greater as the pressure is increased (Frost and Wood, 1997; Aranovich and Newton, 1999).

6.3.4.2 H2OeCH4 Experimental data on structure and properties of methane in fluids under conditions relevant to hightemperature/-pressure petrological processes is quite limited perhaps because of the experimental

FIGURE 6.58 Evolution of CH3/CH4 abundance ratio of reduced CeOeH fluid as a function of temperature. Modified after Mysen (2015b).

6.3 Structure and properties of H2O in fluids

389

FIGURE 6.59 Results of numerical simulation molar volumes of H2OeCH4 fluids as a function of H2O/CH4 ratio at 400 C and pressures indicated on curves. Lines are results from Zhang et al. (2007), whereas data points from experiments by Shmonov et al. (1993). Modified from Zhang et al. (2007).

challenges associated with controlling the CH4/H2O ratio. There is one experimental study using the externally heated diamond anvil cell for the H2OeCH4 system to 1.7 GPa and 900 C (Mysen, 2015b). Here, it was demonstrated that at the oxygen fugacity conditions of the MoeMoO2 buffer (about an order of magnitude more oxidizing than that of the FeeFeO buffer), molecular CH4 coexisted with CH3 groups in melts and coexisting fluid. These CH3 groups substituted for oxygen in the silicate tetrahedra of silicate dissolved in the fluid (Mysen et al., 2011). An equilibrium reaction of the type: Qn þ 2CH4 ¼ 2CH3
þ H2 O þ Qnþ1 ;

(6.25)

where the superscript, n, denotes the number of bridging oxygen in the silicate species in the Qnotation.11 Eq. (6.25) shifts to the right with increasing temperature with a DH ¼ 16  5 kJ/mol for the fluid (Fig. 6.58). The DH-value of Eq. (6.25) for the fluid is about 1/3 of that in coexisting melt (Mysen, 2015b).

11

The concept of Qn-species to describe the structure of silicates was described in detail in Chapter 5.

390

Chapter 6 Structure and properties of fluids

FIGURE 6.60 Speciation in SeOeH fluid as a function of oxygen fugacity expressed relative to that of the NNO buffer. Modified after Scaillet et al. (1998).

Among property measurements of H2OeCH4 fluids, those of Shmonov et al. (1993) seems the most relevant showing a distinctly nonlinear volume evolution as a function of H2OeCH4 fluid composition (Fig. 6.59). The results of the numerical simulation of H2OeCH4 volumes by Zhang et al. (2007) are in very good agreement with the experimental data of Shmonov et al. (1993).

6.3.5 H2OeSeOeH Sulfur species are the third-most important fluid species in igneous processes (Symonds et al., 1994). Sulfur in igneous rocks occurs both in its reduced form, S2
and oxidized forms, SO2 and SO3. As can be seen from the abundance relationships in fluid of the SeOeH system as a function of oxygen fugacity, reduced sulfur species dominate in oxygen fugacity conditions more reducing than slightly above that of the nickel-nickel oxide (NNO) buffer, whereas oxidized sulfur dominates under more oxidizing conditions (Fig. 6.60; see also Scaillet et al., 1998). This means that in light of the fO2 distribution of igneous rocks (see, for example, Carmichael and Ghiorso, 1990), igneous rocks more mafic than andesite will have essentially all sulfur in melts and exsolving gases in sulfide form (H2S), whereas more silica-rich igneous rocks such as dacite and rhyolite with their fO2 often more oxidizing

6.3 Structure and properties of H2O in fluids

391

FIGURE 6.61 Equilibrium data for sulfur redox reactions in sulfur-bearing aqueous fluids. A. Equilibrium constant, K, for reaction, 2H2S þ 3O2 ¼ 2SO2 þ 2H2O in the 50e200 MPa pressure range. Notice that this equilibrium constant does not seem dependent on total pressure B. Equilibrium constant, K, for reaction, SO2 þ 0.5O2 ¼ SO3 in the 50e200 MPa pressure range as indicated on individual curves. C. Enthalpy change for the reaction, SO2 þ 0.5O2 ¼ SO3, in S-bearing aqueous fluids as a function of fluid density. Modified from Binder and Keppler (2011).

392

Chapter 6 Structure and properties of fluids

FIGURE 6.62 Log fO2 versus temperature relations of the two oxidation reactions for sulfur indicated on individual curves. Also shown are the curves for the NNO (NieNO) and RRO (Re-ReO2) oxygen fugacity buffer curves (dashed lines) as well as a few data points for dacite eruptions as indicated. Modified from Binder and Keppler (2011). The sources of the eruptions are provided in the figure caption of the original diagram of Binder and Keppler (2011).

than NNO þ 212 essentially all their sulfur and sulfur in exsolved gases will be in oxidized form, SO2 and SO3, or their hydrated form, sulfuric acid (Scaillet et al., 1998). As sulfate, whether as salt or sulfuric acid in aqueous solution, at temperatures in the several hundred degrees centigrade range, sulfate exists at isolated ions and sulfate clusters (Reimer et al., 2015). The cluster size increases with increasing temperature (which also is coupled to decreased fluid density and dielectric constant). More broadly, an experimental study by Binder and Keppler (2011) aimed to determine the thermodynamics of sulfur redox reactions such as: 2H2 S þ 3O2 ¼ 2SO2 þ 2H2 O.

(6.26)

from the temperature-dependence of the equilibrium constant for this reaction (Fig. 6.61), the DH is 1442  63 kJ/mol (Binder and Keppler, 2011). There is no pressure effect of this reaction, which implies that the DV must be near 0. In contrast, the reaction describing oxidation from SO2 to SO3: SO2 þ 0.5O2 ¼ SO3 ;

12

This notation implies oxygen fugacity two log units more oxidizing than that of the NNO oxygen buffer.

(6.27)

6.4 Solubility behavior in fluid: H2OeSiO2

393

is both temperature and pressure dependent (Fig. 6.61B) with the DH decreasing (becomes more negative) from
160  50 kJ/mol to
308‘9 kJ/mol between 150 and 250 MPa, for example (Binder and Keppler, 2011). Binder and Keppler (2011) correlated this evolution of the reaction enthalpy with the fluid density. Increased density leads to increasingly negative DH (Fig. 6.61C). In an application of these experimental data to description of fluid phase in various silica-rich volcanic eruptions, Binder and Keppler (2011) concluded that, for the most part, the volcanic gases exsolved from these eruptions is dominated by SO2 (Fig. 6.62). They also noted, however, that even at the oxygen fugacity of the Re-ReO2 oxygen buffer (about 2.5 orders of magnitude greater fO2 than the fO2 of the NNO buffer), about 10% of the sulfur is in the form of SO3, which means that in a hydrous fluid system, sulfuric acid would have played a significant role in the gas exsolution process.

6.4 Solubility behavior in fluid: H2OeSiO2 6.4.1 Solubility of SiO2 in H2O

In view of the fact that most rocks contain more than about 50 wt% SiO2, an understanding of the interaction between H2O fluid and dissolved SiO2 to high temperatures and pressures is fundamental to our understanding of the role of H2O in rock-forming processes. Solubility and solution mechanism(s) of SiO2 in H2O are among the properties needed for this purpose. Experiments at pressures and temperatures below the second critical end point (see Fig. 6.63) have, therefore, been carried out since

FIGURE 6.63 Pressure-temperature phase relations of the system SiO2eH2O. Modified after Kennedy et al. (1962).

394

Chapter 6 Structure and properties of fluids

the 1940s (Kennedy, 1944, 1950; Morey and Hesselgesser, 1951; Morey et al., 1962; Anderson and Burnham, 1965). Among these data, the first detailed study probably was that of Kennedy (1950). Here, solubility of SiO2 was determined in the three-phase and two-phase regions seen in Fig. 6.63. Notably, in the low-pressure range of the SiO2 solubility, there is an inflection near the critical point of H2O (Fig. 6.64). In fact, below about 70 MPa, the temperature-dependence of the SiO2 solubility in H2O is negative. As the pressure is increased, the extent of this inflection diminishes so that above about 100 MPa, the inflection point is barely discernible in the solubility curves in Fig. 6.64. It is also notable that the pressure at which the inflection occurs shifts to high temperature the higher the pressure (see arrow in Fig. 6.64). The experimental data in Fig. 6.64 (Kennedy, 1950) extend only to 175 MPa, which corresponds to about 5 km depth in the crust. However, H2O plays important roles in rock-forming processes to much greater depth. This reality, therefore, has resulted in research expanding to greater and greater pressure as technology permitted. For example, Weill and Fyfe (1964) extended to solubility data to pressure of 400 MPa in the 400e550 C temperature range (Fig. 6.65A), which corresponds perhaps to about twice the depth in the crust than that reached by the Kennedy (1950) data. In fact, those solubility experiments were extended to about 1000 MPa by Anderson and Burnham (1965), which corresponds to a depth near 20 km in the Earth (Fig. 6.65B).

FIGURE 6.64 Solubility of SiO2 in aqueous fluid as a function of pressure for pressures indicated on individual curves.

6.4 Solubility behavior in fluid: H2OeSiO2

395

FIGURE 6.65 Solubility of SiO2 in aqueous fluids as a function of temperature and pressure. (A) Solubility to 400 MPa at temperatures shown on individual curves. Also shown are two data points from Morey and Hesselgesser (1951) (B) Solubility to 900 MPa at temperatures shown on individual curves. Modified after (A) Weill and Fyfe (1964); (B) Anderson and Burnham (1965).

It is clear from those and subsequent data that the rate of SiO2 solubility with pressure increases significantly with increasing temperature. This effect is evident in the data reported by Anderson and Burnham (1965), which extended to 1000 MPa in the 500e900 C temperature range (Fig. 6.65B). These latter authors also proposed that the speciation reaction of the dissolved SiO2 is of the form: SiO2 ðxtalÞ þ nH2 O ¼ SiO2 $nH2 OðsolnÞ.

(6.28)

The formation of the hydrated complex, SiO2$nH2O was preferred over species of the kind, Si(OH)4, because Anderson and Burnham (1965) noted that the conductivity of H2OeSiO2, measured at 600 C and 150 MPa (Franck, 1961), is not appreciably greater than that of pure H2O. The enthalpy and volume change of Eq. (6.28) can be extracted from the temperature and pressure dependence of the SiO2 solubility because the equilibrium constant from Eq. (6.28) is: DH DS þ RT R

(6.29)

  TDV ¼ DH T

(6.30)

ln K ¼
and



vXSiO2 vP



As can be seen from the relationship between solubility and temperature (Fig. 6.66), the relationship is nearly linear until the second critical endpoint of the H2OeSiO2 system is approached. Near the critical point, the SiO2 solubility versus temperature curves show inflection as the rate of solubility with temperature increases more rapidly. From the linearity of the solubility curves at lower

396

Chapter 6 Structure and properties of fluids

FIGURE 6.66 Log solubility of SiO2 in aqueous fluid as a function of temperature (1/T, Kelvin) with isobars as indicated. Modified after Anderson and Burnham (1965).

temperature, the enthalpy change of Eq. (6.28) can be derived and from Eq. (6.29), and the volume change from Eq. (6.30) (Fig. 6.67A and B). The enthalpy change increases with increasing pressure (Fig. 6.67A), whereas the volume change decreases (Fig. 6.67B). In fact, above about 300 MPa, the volume change is essentially a linear function of pressure, which implies that the compressibility is nearly constant, while at lower pressure, the compressibility changes rapidly with increasing pressure. From the volume change, by combining with the molar volume of H2O, assuming dissolved SiO2 does not affect this value, and the molar volume of quartz, the partial molar volume of dissolved SiO2 can be obtained (Fig. 6.67C). It is noted, though, that the value of n in Eq. (6.28) affects the resulting partial molar volume of dissolved SiO2 (Fig. 6.67C). In fact, given the scatter in the data even for constant n-value, it is possible that the proportion of H2O in the dissolved silica complexes may vary as a function of temperature and pressure. More recently, Newton and Manning (2000) modeled SiO2 solubility in H2O and concluded that the n-value in SiO2$nH2O(soln) is closer to 5. However, as discussed in more detail below, the dissolved species are considerably more complex involving not only solvated H2O, but also OH-groups within the silica structure and, furthermore, different SieO polymers. It must be remembered that the partial molar volume of dissolved silica will be quite different if SiO2 dissolves in H2O to form different complexes. From more recent experimental structural studies of SiO2 dissolved in H2O at high temperature and pressure, different complexes have indeed been proposed (Zotov and Keppler, 2002; Mysen, 2010; Sverjensky et al., 2014; see also further discussion of solution mechanisms of SiO2 in H2O in Section 6.3.2 below).

6.4 Solubility behavior in fluid: H2OeSiO2

397

FIGURE 6.67 Thermodynamic data for the SiO2 solubility reaction, SiO2(xtal) þ nH2O ¼ SiO2$nH2O(aq). A. Effects of pressure on the enthalpy change of the reaction shown for two different temperatures. B. Effects of pressure on the volume change of the reaction shown for two different temperatures. C. Partial molar volume of SiO2$nH2O(aq) as a function of pressure for n ¼ 1, 2, and 3, as shown on the figure. Modified after Anderson and Burnham (1965).

398

Chapter 6 Structure and properties of fluids

More recent experimental data on SiO2 solubility in H2O have been reported primarily by the experiments of Craig Manning and coworkers (see, for example, Manning, 1994; Newton and Manning, 2000, 2008; Hunt and Manning, 2012). Interestingly, the method used in these studies (weight loss of oxide coexisting with fluid) in principle is the same as that which begun with Kennedy (1950). It is not surprising, therefore, that where these data overlap in temperature/pressure space, the SiO2 solubilities obtained by Kennedy (1950) and Manning and several coworkers differ by less than 3% for the most part. In more recent experimental studies, the SiO2 concentration has been expressed by molality (mol/ kg) so that the solubility of SiO2 determined by weight loss after and experiment becomes:
 before after
weightquartz weightquartz (6.31) mSiO2 ¼ molecular weightH2 O$weightH2 O Concentration expressed as molality lends itself to simpler thermodynamic treatment. As seen in Fig. 6.68, the rate of SiO2 solubility increase with pressure the higher the temperature, an observation similar to that of earlier experimental studies (Weill and Fyfe, 1964; Anderson and Burnham, 1965). Notably, the experimental results by Anderson and Burnham (1965), where their temperatures and pressures overlap with Manning (1994), for all practical purposes are the same. Moreover, when the solubility is expressed as a function of the log rH2O (density of pure H2O), the relationships become linear. In addition, there seems to be very close agreement with solubility results reported elsewhere (Anderson and Burnham, 1965; Hemley et al., 1980; Walther and Orville, 1983) (Fig. 6.68B). The solubility of SiO2 not only has been linked to fluid density and temperature (Manning, 1994), it can also be correlated with the dielectrical constant of a solution. This has been demonstrated for SiO2 dissolved in a number of different solutions, including H2OeAreSiO2 (Walther and Schott, 1988). From regression analysis of their and those of experimental data of others, Manning (1994) arrived at an empirical expression that may be used to calculate the solubility in SiO2 in H2O to perhaps 2 GPa total pressure: 5764:2 1:7513$106 2:2869$108 þ
logmSiO2 ¼ 4:262
T T2 T3   5 1006:9 3:5689$10 þ þ 2:8454
$logrH2O T T2

(6.32)

The data used for this regression, in addition to the solubility data by Manning (1994), were the SiO2 solubilities in H2O from Hemley et al. (1980), Fournier and Potter (1982), and Walther and Orville (1983). Given that the relationship between log mSiO2 and log rH2O in Fig. 6.68B is linear, it has been suggested that the data may be extrapolated to higher pressure (Manning, 1994). This extrapolation was carried out in order to compute the phase diagram for the H2OeSiO2 system to as much as 5 GPa (Fig. 6.69). The source of the phase boundaries in that phase diagram are those indicated in the caption of the original diagram. The phase boundaries shown as thin lines were computed with Eq. (6.32). Manning (1994) noted that these data can be employed to model SiO2 metasomatism in source regions of magma in the mantle above descending slabs in deeper portions of subduction zones.

6.4 Solubility behavior in fluid: H2OeSiO2

399

FIGURE 6.68 Solubility of SiO2 in aqueous fluid. (A) As a function of pressure at the temperatures indicated on figure. (B) As a function of density of H2O at temperatures indicated on figure. Modified after Manning (1994). Data sources in addition to the results from Manning (1994) are given in the figure captions of the original text.

400

Chapter 6 Structure and properties of fluids

FIGURE 6.69 Calculated [Eq. (6.32)] SiO2 solubility isobars and isotherms (dashed lines) in aqueous fluids as a function of H2O density. Modified after Manning (1994). Sources of the data defining the phase boundaries in this diagram are given in the caption of the original source.

Sverjensky et al. (2014) developed a model with which to compute silica solubility in H2O to about 6 GPa. This model was based on the Helgeson, Kirkham, and Flowers model (Helgeson et al., 1981) for thermodynamic behavior of aqueous electrolytes to 600 C and 0.5 GPa. For this purpose, Sverjensky et al. (2014) extrapolated the dielectric constant of H2O to higher pressure (6 GPa) by linear extrapolation of the logarithm of the dielectrical constant against the logarithm of the density of H2O. The SiO2 solubility thus obtained was in very good agreement with experimental data at pressures at or less than 100 MPa, but showed some deviation from experimental data at pressures above 1 GPa and temperatures above about 600e700 C.

6.4.2 Solubility mechanism of SiO2 in H2O Various solution mechanisms of SiO2 in aqueous fluids have been proposed. Many of these have been derived from the SiO2 solubility data. Most of these models employ OH-bearing monomers and dimers and perhaps even trimers as the structural entities of dissolved silica (Wendlandt and Glemser, 1964; Newton and Manning, 2003; Zotov and Keppler, 2002; Mysen, 2010; Mysen et al., 2013). Interestingly, Wendlandt and Glemser (1964) used the density of SiO2-saturated fluid as an indicator of the extent to which the dissolved silicate is polymerized:

6.4 Solubility behavior in fluid: H2OeSiO2

401

Density less than 0.05g=cm3 : SiO2 ðxtalÞ þ 2H2 OðfluidÞ ¼ SiðOHÞ4 ðfluidÞ;

(6.33a)

Density less than 0.45g=cm3 : 2SiO2 ðxtalÞ þ 3H2 OðfluidÞ ¼ Si2 OðOHÞ6 ðfluidÞ;

(6.33b)

Density greater 0.56g=cm3 : SiO2 ðxtalÞ þ H2 OðfluidÞ ¼ SiOðOHÞ2 ðfluidÞ.

(6.33c)

and

In other words, the greater the density of the fluid, the greater is the degree of silicate polymerization of the dissolved silica species. More recently, Manning and coworkers (Newton and Manning, 2002, 2008; Hunt and Manning, 2012) modeled the SiO2 solubility mechanisms in terms of degree of polymerization of SiO2 species as a function of total SiO2 content of aqueous fluids. Presumably, aqueous fluid density increases with increasing SiO2 concentration in the fluid. For example, at the temperature and pressure conditions of the second critical endpoint of the H2OeSiO2 system (1080 C and 1 GPa; see Kennedy et al., 1962) speciation such as illustrated in Fig. 6.70 was proposed (Newton and Manning, 2008). In this treatment, a simple polymerization reaction resembling Eq. (6.33b) was used. Structure modeling also has been carried out with molecular dynamics simulation from which, in addition to structure, partial molar volume of SiO2 in solution was calculated (Spiekermann et al., 2016). From computations at 2400 and 3000 K with fluid density at 1.88 g/cm3 and SiO2/H2O ratio

FIGURE 6.70 Calculated silica speciation as a function of SiO2 mol fraction in SiO2eH2O at 1 GPa and 1080 C. Modified after Newton and Manning (2008).

402

Chapter 6 Structure and properties of fluids

equal to 1, those two temperatures corresponds to 4.3 and 4.6 GPa pressures, respectively. In this study, Spiekermann et al. (2016) employed the simple reaction: 2SiOH ¼ SiOSi þ H2 O; 1

2

3

(6.34)

4

The result was a distribution of Q , Q , Q , and Q (Fig. 6.71). In a sense these results agree with those of Newton and Manning (2008) at conditions near the second critical endpoint in that the latter authors concluded that the structure consisted of monomers, dimers and more polymerized species (Fig. 6.70) and for that matter the structure proposed by Wendlandt and Glemser (1964) as summarized in Eqs. (6.33aec). A different solubility mechanism was proposed by Gerya et al. (2005) based on monomer-forming reactions: SiO2 ðxtalÞ þ 2H2 OðfluidÞ ¼ SiO2 $2H2 OðfluidÞ;

(6.35)

and the polymer-forming reaction: SiO2 $ 2H2 OðfluidÞ þ ðSiO2 Þn
1$ðH2 OÞnðfluidÞ ¼ ðSiO2 Þn$ðH2 OÞnþ1ðfluidÞ þ H2 OðfluidÞ. (6.36) The SiO2 solubility obtained with this model agrees within a few % with experimental solubility data such as shown, for example, in Fig. 6.68. The solution mechanism assumes the existence of monomers, dimers, and trimers in the fluid. In contrast with other experimental data, the model of Gerya et al. (2005) leads to the conclusion than the dissolved silica in aqueous solution is significantly polymerized at all temperatures above 400 C. Direct measurements of speciation in H2OeSiO2 fluids while the sample was at the desired temperature and pressure initially was reported by Zotov and Keppler (2002) and subsequently

FIGURE 6.71 Calculated fraction of individual Qn-species defined by their n-values in SiO2eH2O fluid at the two temperatures indicated. Modified after Spiekermann et al. (2016).

6.4 Solubility behavior in fluid: H2OeSiO2

403

expanded upon by Mysen (2010) and Mysen et al. (2013). In all cases, Raman spectroscopy was employed as the structural tool probing the sample in externally heated hydrothermal diamond anvil cells while the sample was at the desired temperatures and pressures. At pressures and temperatures below 0.6 GPa and 500 C, the Raman spectra were interpreted to comprise only a single signal, near 770 cm
1, assigned to SieO vibrations in monomers [Si(OH)4]. At higher pressures and temperatures, Zotov and Keppler (2002) also reported evidence for dimers and proposed that the reaction: 2H4 SiO4 ¼ H6 Si2 O7 þ H2 O;

(6.37)

describes the dimerization. The equilibrium constant for Eq. (6.37), takes the form (Zotov and Keppler, 2002): lnKðP; TÞ ¼ lnKðPo ; TÞ


DVeqn:ð6:37Þ 1 ðP
Po Þ
RT RT

ZP VH2O dP;

(6.38)

Po

where P is pressure, Po is pressure at the standard state, DV Eq. (6.38) is the volume change of reaction (Eq. 6.37), T is temperature (Kelvin), R is the gas constant and VH2O is the molar volume of H2O. The temperature-dependence of the equilibrium constant (Fig. 6.72) results in enthalpy and entropy changes for the polymerization Eq. (6.37) of 12.6  1.3 kJ/mol and 40.7  1.3 J/mol K, respectively (Zotov and Keppler, 2002). These thermodynamic data were based on the assumption that Raman intensity ratios are equivalent to concentration ratios. With that assumption, for the intensity ratios of the same Raman vibrations, the temperature dependence reported by Zotov and Keppler (2002) and Mysen (2010) were the same (the area ratio A610/A770 in Fig. 6.73). However, when employing the intensity ratios of the SieO stretch vibrations from Q0 and Q1 as a function of temperature (A875/A770 in Fig. 6.73), the resulting DH of Eq. (6.37) is much smaller. Notably, with the Q0 and Q1 concentrations computed from the intensities of the 770 and 870 cm
1 Raman bands (assigned to SieO stretching in Q0 and Q1), this results agrees well with the evolution of the Q0 and Q1 abundance evolution in the calculation of Sverjensky et al. (2014) (Fig. 6.74), whereas if computed from the 770 and 600 cm
1 bands (SieO stretching in Q0 and SieOeSi bending in Q1 species), the abundance of Q1 is underestimated relative to the results of the calculations by Sverjensky et al. (2014). Solubility and structural data such as reported in Mysen (2010) was extended to 5.4 GPa and 900 C by Mysen et al. (2013). In this case, Q0, Q1, and Q2 species of the silica were observed in aqueous fluid In fact, the abundance of the variously polymerized Qn-species is positively correlated with the concentration of SiO2 in the aqueous fluid. For the mol fraction of Q0, Q1, and Q2 species, for example, the following relationship holds: XQ1 þ XQ2 ¼ 1:3 þ 0:1$ðmSiO2 Þ1:5 XQ0

(6.39)

where the X-values are mol fractions and mSiO2 is molality. As seen in Fig. 6.75, the abundance of the polymerized species, Q1 and Q2, increases with increasing temperature at constant pressure and increasing pressure at constant temperature. It is clear, therefore, the concentration of SiO2 is a critical factor in determining the polymerized of dissolved SiO2, a feature qualitatively similar to the relationship between SiO2 content and structure of silicate melts (Mysen et al., 1982). In fact, when

404

Chapter 6 Structure and properties of fluids

FIGURE 6.72 Temperature dependence of the equilibrium constant, K, for the polymerization reaction in SiO2eH2O fluid, 2H4SiO4 ¼ H6Si2O7 þ H2O, at 500 MPa from in-situ Raman spectra of the aqueous fluid. Modified after Zotov and Keppler (2002).

expressed as a function of mSiO2, the SiO2 concentration alone defines the evolution of the Qn-species abundance regardless of pressure (Fig. 6.75B). It is, furthermore, clear from the relationship between Qn-speciation, temperature, and pressure that the enthalpy change becomes increasingly negative with increasing pressure (Fig. 6.76A) and the volume change slightly more negative with increasing pressure (Fig. 6.76B) for the polymerization reaction: 2Q1 ¼ Q0 þ Q2 ;

(6.40)

from the temperature and pressure relations fitted to the expression: ln K ¼
DH=RT þ DS=R
ðDV=RTÞ$ðP
0.1Þ;

6.41)

where K is the equilibrium constant, DH the enthalpy change, DS the entropy change, DV volume change, P is pressure (MPa), T is temperature (Kelvin) and R is the gas constant. In other words, the silicate speciation reaction (Eq. 6.40) shifts to the right with increasing pressure, a feature also observed in silicate melts at high pressure (Xue et al., 1991).

6.4 Solubility behavior in fluid: H2OeSiO2

405

FIGURE 6.73 Temperature dependence of the equilibrium constant, K, for the polymerization reaction in SiO2eH2O fluid, 2H4SiO4 ¼ H6Si2O7 þ H2O, at variable pressure (governed by temperature; see text) from in-situ Raman spectra of the aqueous fluid by using the Raman bands assigned to SieO
(O
; Nonbridging oxygen) stretch vibrations in Q0 (770 cm
1band with integrated area, A770 and Q1 (875 cm
1 band with integrated area, A875)). Also shown are the data from Zotov and Keppler (2002) who used the area ratio of SieO
stretch vibration forQ0 abundance and the SieOeSi bending vibration for Q1 at 610 cm
1). The same area ratio from Mysen (2010) is also shown. Modified after Mysen (2010).

406

Chapter 6 Structure and properties of fluids

FIGURE 6.74 Calculated solubility of SiO2 in aqueous fluid in the SiO2eH2O system as a function of temperature at pressures indicated on individual solubility isobars. Also shown is experimentally measured solubility from Mysen (2010). A. Solubility calculated for the solubility reaction, Quartz þ 2H2O ¼ Si(OH)4(aq) where Si(OH)4(aq) is a monomer. B. Solubility calculated for the solubility reaction, 2Quartz þ 3H2O ¼ Si2O(OH)6(aq), where Si2O(OH)6(aq) is a dimer. Modified after Sverjensky et al. (2014).

6.4.3 Properties of H2OeSiO2 fluid The properties silicate-bearing aqueous fluids are critical for our understanding of transport of mass in the Earth’s interior, and perhaps in particular in the source region of melting in subduction zone (Tatsumi, 1989; Peacock, 1993; Tatsumi and Eggins, 1995). These properties include wetting angle (see Chapter 11), viscosity (Chapter 9), density (Chapter 10), and fluid composition (Mibe et al., 1998; Audetat and Keppler, 2004; Kawamoto, 2004, 2006; Hack and Thompson, 2011; Guo et al., 2016). Whereas there are significant experimentally determined transport data of saline, aqueous aluminosilicate fluids (Audetat and Keppler, 2004; Kawamoto, 2006; Hack and Thompson, 2011), less data exist for the simpler system H2OeSiO2. Some experimental data and molecular dynamics results exist for Si diffusion at high temperature and pressure (Watson and Wark, 1997; Yokoyama and Sakuma, 2018), but few if any experiments appear to have been carried out for other transport properties such as viscosity and electrical conductivity, for example. Fortunately, one set of transport data, once available, may be linked to others because there exist functional relationships between different transport properties with expressions such as, for example, the StokeseEinstein (1905) and Eyring (1935a, b) equations. These expressions have been shown applicable to amorphous silicate systems: Stokes
EinsteinðEinstein; 1905Þ: h ¼

kT 6prD

(6.42)

6.4 Solubility behavior in fluid: H2OeSiO2

407

FIGURE 6.75 Experimentally determined, from in-situ Raman spectroscopy, Qn-speciation in SiO2eH2O fluid. Qnspeciation is expressed as a ratio of polymerized species with n ¼ 1 and two of the sum of the two relative to monomers, Q0. A. As a function of temperature at the two pressures indicated on individual curves. B. As function of SiO2 concentration, mSiO2, at 1.8 and 5.2 GPa and with n ¼ 1 and n ¼ 2. Modified after Mysen et al. (2013).

408

Chapter 6 Structure and properties of fluids

FIGURE 6.76 Evolution of equilibrium constant, K, for the speciation reaction, 2Q1 ¼ Q0 þ Q2. A. As a function of temperature, 1/T at two different pressures as indicated. The DH for the reaction at 1.8 and 5.2 GPa also is shown. B. As a function of pressure sat 800 and 900 C as shown on curves. Also shown is the volume change of the reaction derived from the pressure dependence. Modified after Mysen et al. (2013).

where h is viscosity, k is Boltzman’s constant, D is diffusion coefficient, and T is temperature (Kelvin): Eyring equationðEyring; 1935a; bÞ: h ¼

kT aD;

(6.43)

where the additional variable, a, is the jump distance. Experiments with fluid compositions in the system H2OeSiO2 at 1 GPa resulted in a straight line relationship between ln D (diffusivity) and 1/T (temperature), from which a line relation of the form: DðSiO2 Þ ¼ 2.81$10
5 expð
6271=TÞ;

(6.44)

resulted (Watson and Wark, 1997; see also Fig. 6.77). Notably, the straight line fit is quite good over the 500e900 C temperature range even though the SiO2 concentration in the aqueous fluid from the data of Manning (1994) should increase by about a factor of 15 in this temperature range! However, the silica speciation in this concentration range likely is the same (from extrapolation of the Mysen et al., 2013 data to 1 GPa), so perhaps the linear relationship should not be so surprising. This is also

6.4 Solubility behavior in fluid: H2OeSiO2

409

FIGURE 6.77 Diffusion coefficient for SiO2 in SiO2eH2O solution as a function of temperature at 1 GPa pressure. Modified after Watson and Wark (1997).

consistent with the results of the molecular dynamics calculations of Si diffusivity by Yokoyama and Sakuma (2018) who concluded that the D(SiO2) decreases with degree of polymerization of the Sibearing complexes in fluid but should not change as long as the degree of polymerization of the silicate species remain the same. Whether or not the StokeseEinstein relation [Eq. (6.42)] can be applied to SiO2eH2O fluids was assessed by Watson and Wark (1997). They found that the results were not reliable. The Eyring equation on the other hand [Eq. (6.43)] has been found reliable for silicate melts (Shimizu and Kushiro, 1984). Given the structural similarities between SiO2-saturated aqueous fluid and H2O-saturated silicate melts, it may be suggested that it could also be applied to silicate-bearing aqueous solutions to calculate viscosity at high temperature and pressure from the diffusivity of SiO2. However, results of such calculations do not seem to have been published. There also is a simple relationship between electrical conductivity and diffusion. The Nernste Einstein equation is of the form:

410

Chapter 6 Structure and properties of fluids

FIGURE 6.78 Solubility of SiO2 in H2OeNaCl fluids as a function of mol fraction of NaCl. A. Molality, mSiO2, at 700 C and various pressures shown as a function of mol fraction of NaCl. B. Log molality of SiO2 at 1 GPa as a function of mol fraction of NaCl along isotherms shown in the figure. Modified after Newton and Manning (2000). These figures also contain other published data. The relevant references are given in the original text.

l¼

F 2 ZD ; kT

(6.45)

where l is conductivity and Z is electrical charge. However, this relation has not yet been applied to SiO2eH2O fluid systems.

6.4.4 H2OeSiO2eNaCl Experimental information on solubility and other properties of fluids in the system H2OeSiO2 offers significant information on metamorphic and igneous processes for the simple reason that SiO2 is the dominant rock-forming oxide, and H2O often is the dominant fluid component. However, in crustal and upper mantle environments, fluids often can be saline where the dominant salt typically is NaCl (Keppler, 1996; Manning and Aranovich, 2014). There has been, therefore, considerable effort aimed at determining SiO2 solubility in H2OeNaCl fluids at high temperature and pressure (Anderson and Burnham, 1967; Xie and Walther, 1993; Newton and Manning, 2000, 2006; Shmulovich et al., 2001; Cruz and Manning, 2015; Scheuermann et al., 2018). Results of models with which to calculate the SiO2 solubility in H2OeNaCl fluids also have been reported (Fournier, 1983; Walther and Schott, 1988; Newton and Manning, 2000, 2016; Akinfiev and Diamond, 2009; Shi et al., 2019).

6.4 Solubility behavior in fluid: H2OeSiO2

411

A peculiar feature of the SiO2 solubility in H2OeNaCl fluids is that while it decreases systematically with increasing NaCl concentration at pressures above about 0.5 GPa, at lower pressure, there is an initial solubility increase with mol fraction of NaCl (XNaCl) equal to or less than about 0.1 before a further XNaCl increase results in decreasing SiO2 solubility (Xie and Walther, 1993; Newton and Manning, 2000; see also Fig. 6.78A). Expressed as log mSiO2, the SiO2 solubility is, however, a linear function of XNaCl and, furthermore, the slope on this relationship (Fig. 6.78B) is essentially the same in the temperature range examined experimentally (500e900 C). Whether or not these relationships hold at higher temperatures and XNaCl (XNaCl > 0.6) is not known. It seems reasonable to suggest, however, that the relationship does not hold because the nature of the hydrous silica species might begin to change as the activity of H2O decreases with increasing NaCl concentration. While there is general agreement as to how the SiO2 solubility in H2OeNaCl fluids changes with temperature, pressure, and NaCl concentration, a wide range of possible solubility models has been proposed. These were summarized by Akinfiev and Diamond (2009). One group of models has been referred to as electrostatic models where the solubility was linked to dielectric constants (Franck, 1973; Walther and Schott, 1988), whereas the other used fluid density as a principal variable affecting solubility (Newton and Manning, 2000, 2016; Cruz and Manning, 2015; Shi et al., 2019). Of course, as discussed elsewhere in this Chapter (Fig. 6.49), there is a link between the dielectric constant and fluid density, so that in principle, the two groups of models might not be all that different. Among those many models, the one recently published by Shi et al. (2019) seems to reproduce the SiO2 solubility in H2OeNaCl fluids over the widest range of temperature, pressure and NaCl concentration. Those authors considered a simple dissolution reaction: SiO2 ðxtalÞ þ nH2 O ¼ SiO2 $nH2 OðfluidÞ;

(6.46)

with the equilibrium constant for Eq. (6.46): aSiO2 ; aSiO2 ðxtalÞanH2 O

(6.47)

aSiO2 ¼ mSiO2 gSiO2

(6.48)

aH2O ¼ dH2O lH2O

(6.49)

K¼ where

and In Eqs. (6.47)e(6.49), a is activity, g is activity coefficient, and dH2O is the concentration of H2O. These equations can be combined to yield (Shi et al., 2019)13: logmSiO2 ¼ logK þ nlogrsoln $F þ loglH2O =gSio2

(6.50)

As can be seen in the examples in Fig. 6.79A, this model describes the experimental data for SiO2eH2O systems quite accurately at least to the temperature (650 K) and pressure (200 MPa) where comparisons with experimental data were made. In fact, the accuracy probably is better than the experimental accuracy. Notably, this model does quite well without resorting to complex solutes as proposed in other models (see, for example, Newton and Manning, 2016). However, in the more 13

The reader is referred to Shi et al. (2019) for detailed description of this model.

412

Chapter 6 Structure and properties of fluids

FIGURE 6.79 Calculated SiO2 solubility in H2OeNaCl fluids. (A) As a function of temperature as the quartz saturation pressure (solid line) compared with various published data (open circles; see Shi et al., 2019 for citations to original sources of these data). (B) As a function of mol fraction of NaCl at 900 C and 1 GPa. Data points are from Shmulovich et al. (2001). The data sources of the dashed lines are Fournier et al. (1982) and Akinfiev and Diamond (2009).

6.5 Solubility behavior in fluid: H2OeSiO2eMgO

413

complex system, SiO2eH2OeNaCl, the model appears to overestimate the SiO2 solubility compared with the experimental data of Fournier (1983) and Newton and Manning (2016), for example, whereas it underestimates the solubility compared to the data from Akinfiev and Diamond (2009; Fig. 6.79B). Even though characterization of SiO2-bearing aqueous solutions is a critical first step toward understanding the behavior of aqueous solutions in natural processes, considering only SiO2 is an obvious oversimplification. The next step toward characterization of naturally occurring aqueous fluid can be reached be examination of the effect of other major element components such as MgO and Al2O3. Fluids in this compositional environment will be considered next.

6.5 Solubility behavior in fluid: H2OeSiO2eMgO The system SiO2eMgO often is employed as a model system for peridotite in the Earth’s mantle because it comprises major mantle minerals such as olivine and orthopyroxene. By adding H2O to this system, one might consider this as a model system for the behavior of aqueous solutions in the Earth’s mantle (Nakamura and Kushiro, 1974; Yamamoto and Akimoto, 1977; Konzett and Ulmer, 1999; Zhang and Frantz, 2000; Newton and Manning, 2002; Mibe et al., 2002; Stalder et al., 2001).

6.5.1 Solubility of MgOeSiO2 in H2O The importance of the solubility of SiO2 and MgO components in H2O at high pressure and temperature was recognized early on by Nakamura and Kushiro (1974) who examined MgOeSiO2 solubility in H2O at 1.5 GPa and several temperatures (1280e1340 C). Only one example, at 1280 C, is shown as there was little temperature effect on the phase relations in this temperature range (Fig. 6.80). As can be seen in Fig. 6.80, at the 1.5 GPa of these experiments, there is a continuous solubility from the melt near the SiO2 corner to fluid near the H2O corner. Moreover, in particular in the environment near the H2O corner, the fluid is essentially pure SiO2 þ H2O at 1.5 GPa and 1280e1340 C. In other words, at least at this pressure, aqueous fluids in equilibrium with Mg-rich crystalline phases such as Mg2SiO4 (forsterite) and MgSiO3 (enstatite) are essentially pure SiO2. This finding is in accord with more recent data in the same system at similar temperature and pressure conditions (Zhang and Frantz, 2000; Stalder et al., 2001; Mibe et al., 2002; Newton and Manning, 2002). In fact, the Mg/Si ratio remains near 0 at pressures at or below about 2 GPa before this ratio begins to increase as pressure is increased beyond 2 GPa (see, for example, Mibe et al., 2002; Zhang and Frantz, 2000). This compositional evolution of aqueous fluid in equilibrium with Mg2SiO4 and MgSiO3 crystalline phases is illustrated in the MgSiO4eSiO2eH2O triangle in Fig. 6.81 illustrating the evolution of the Mg/Si ratio of the fluid as a function of increasing pressure from 1 to 10 GPa. Interestingly, though, at and above the 10 GPa pressure Melekhova et al. (2007) observed that the total silicate content of the fluid increased rapidly with increasing temperature, whereas at 13.5 GPa, such temperature effects on solubility were not observed (Fig. 6.82A). It is also notable that at 13.5 GPa, the MgO/SiO2 abundance ratio in the fluid decreased rapidly with increasing temperature (Fig. 6.82B). It is not totally clear, however, how this latter observation can be made consistent with the results from Stalder et al. (2001) who suggested that there was complete miscibility between fluid and melt in the MgOeSiO2eH2O system at pressures near 12 GPa (Fig. 6.83). Stalder et al. (2004) argued that the pressure of the critical endpoint in the MgOeSiO2eH2O likely is the same or at least similar to that which may be expected in a hydrous peridotite in the upper mantle. That conclusion differed, however, significantly from that of Mibe et al. (2007) who suggested that the second critical endpoint for peridotite-H2O is near 4 GPa. This matter remains unresolved, but it seems

414

Chapter 6 Structure and properties of fluids

FIGURE 6.80 Phase relations in the system Mg2SiO4eSiO2eH2O at 1280 C and 1.5 GPa showing the extent of hydrous melts and silicate-saturated fluids. Modified after Nakamura and Kushiro (1974).

reasonable to suggest that the actual critical endpoint in peridotite-H2O is somewhere between the 4 and 12 GPa pressures proposed in the two contrasting studies (Stalder et al., 2004; Mibe et al., 2007). In this context, we note that the pressure at which such complete miscibility exists, is quite sensitive to bulk silicate composition. For example, in a basalt - H2O system, the fluid becomes supercritical in the 4e5 GPa range (Kessel et al., 2005). In hydrous granite and feldspar systems, the pressure at which this occurs is near 1 GPa (Bureau and Keppler, 1999). It remains unclear why this significant compositional dependence exists, which probably is because it is not established why there is immiscibility between hydrous melts and aqueous fluids at lower pressures than that of the critical endpoint. Clearly, however, the solubility and solution mechanisms in aqueous fluids and hydrous silicate melts are important to further our understanding of this phenomenon.

6.5 Solubility behavior in fluid: H2OeSiO2eMgO

415

FIGURE 6.81 Evolution of fluid composition in the system Mg2SiO4eSiO2eH2O as a function of pressure. The 1 GPa-data are from Zhang and Frantz (2000). Modified after Mibe et al. (2002).

6.5.2 Solubility mechanism of MgOeSiO2 in H2O Given the premise that at least at pressures below about 2 GPa, the aqueous fluid in equilibrium with magnesium silicate minerals is essentially pure SiO2, the solution mechanism of solids in the MgOeSiO2eH2O system also must resemble that of SiO2 in the system SiO2eH2O at pressures below about 2 GPa. However, at any pressure and temperature, the solubility in the MgOeSiO2eH2O system is significantly less than in the SiO2eH2O system (Zhang and Frantz, 2000; Newton and Manning, 2002; Mysen et al., 2013). Whether in H2O-satrated silicate melts or silica-saturated aqueous fluid, there is a positive correlation between the degree of silica polymerization and the silicate content of the solution and melt (Buckermann et al., 1992; Newton and Manning, 2002, 2003; Mysen, 2010; Sverjensky et al., 2014). From the solubility behavior, it would be reasonable to conclude that at given temperature and pressure, the degree of silicate polymerization in aqueous fluid in the MgOeSiO2eH2O system is less than in the SiO2eH2O system. This is precisely what was observed

416

Chapter 6 Structure and properties of fluids

FIGURE 6.82 Compositional evolution of fluids in the MgOeSiO2eH2O system in equilibrium with dense hydrous magnesium silicate phases. (A) Total silicate content of fluid as a function of temperature at 11 and 13.5 GPa as indicated on diagram. (B) Evolution of MgO/SiO2 ratio of fluid as a function of temperature at 11 and 13.5 GPa as indicated on diagram. Modified after Melekhova et al. (2007).

6.5 Solubility behavior in fluid: H2OeSiO2eMgO

417

FIGURE 6.83 Composition of coexisting silicate-saturated aqueous fluid and H2O-saturated melt in the system MgOeSiO2eH2O at different pressures and temperatures of the solidus of those pressures. Modified from Stalder et al. (2001).

experimentally in a diamond cell study using Raman spectroscopy as the structural tool (Mysen et al., 2013). The fluid in equilibrium with enstatite in the MgOeSiO2eH2O system examined by Mysen et al. (2013) at any pressure and temperature is less polymerized than the fluid in the SiO2eH2O system at the same temperature and pressure. A comparison of the Qn-species evolution in SiO2eH2O and MgOeSiO2eH2O illustrates this difference (Fig. 6.84). Not only is the abundance of polymerized Qnspecies at given temperature and pressure greater in the SiO2e H2O fluids, the extent to which polymerization has progressed also in greater in the SiO2eH2O fluids compared with MgOeSiO2eH2O fluids. This would be expected in light of the greater silica solubility in fluids in the SiO2eH2O system. The equilibrium among the Qn-species in the MgOeSiO2eH2O fluid is, therefore, simpler than in the SiO2eH2O [Eq. (6.37)]: 2Q0 ¼ Q1 .

(6.51)

From the linear fits to temperature and pressure (Fig. 6.85). A striking difference between the results in Fig. 6.85 (MgOeSiO2eH2O) and those of SiO2eH2O (Fig. 6.76) is that whereas the DH and

418

Chapter 6 Structure and properties of fluids

FIGURE 6.84 Experimentally determined, from in-situ Raman spectroscopy, Qn-speciation in SiO2eH2O and MgOeSiO2eH2O fluid as a function of temperature at the pressures indicated on individual curves. See also Caption to Fig. 6.75 for more detail. Modified after Mysen et al. (2013).

DV for the polymerization reaction in SiO2eH2O [Eq. (6.31)] depend on pressure and temperature, there are no such effects for the simpler equilibrium in MgOeSiO2eH2O fluids [Eq. (6.51)]. Here, DH and DV appears nearly independent of temperature and pressure. The negative DV (near
2 cm3/mol) implies that the molar volume of Q0 species with its isolated SiO4
4 tetrahedra is smaller than the molar volumes of more polymerized silicate species such as Q1, which contain bridging oxygens. This different volume behavior is understandable because isolated SiO4
4 tetrahedra can be packed more densely than the polymerized Qn-species, which contain SieOeSi bridges.

6.5.3 MgOeSiO2 solubility in saline solutions The solubility of Mg2SiO4 (forsterite) and MgSiO3(enstatite) in H2OeNaCl fluid has been determined at 1 GPa (Macris et al., 2020). Enstatite dissolves incongruently to forsterite plus fluid, whereas

6.5 Solubility behavior in fluid: H2OeSiO2eMgO

419

FIGURE 6.85 Evolution of the equilibrium constant for the reaction, 2Q0 ¼ Q1 for dissolved silicate in fluids the system MgOeSiO2eH2O. (A) As a function of temperature with DH-values for the reaction on each line. (B) As a function pressure at temperatures indicated on each line with DV for the reaction indicated on each line. Modified after Mysen et al. (2013).

forsterite dissolved congruently under all conditions. The forsterite solubility increases with increasing NaCl concentration (Fig. 6.86A), which differs somewhat from dissolution of enstatite, which shows decreasing Si and increasing Mg concentration with increasing NaCl in the fluid (Fig. 6.86B). This latter solubility behavior in principle is similar to that of enstatite dissolution in pure H2O (Ryabchikov et al., 1982; Zhang and Frantz, 2000; Newton and Manning, 2002). It is also interesting that in some ways this solubility behavior resembles the melting behavior of enstatite in the presence of H2O, under which conditions of enstatite-H2O melts incongruently to forsterite þ melt to at least 3 GPa pressure (Kushiro et al., 1969). The decreasing SiO2 concentration in fluid with increasing NaCl, in principle would be analogous to the solubility behavior of SiO2 in H2OeNaCl fluids, which also shows decreasing solubility with increasing NaCl concentration at total pressures of 1 GPa (Newton and Manning, 2000; see also Fig. 6.78). It seems, therefore, that two competing effects are at play. The solubility of the MgO component increases with increasing NaCl concentration, whereas the SiO2 component exhibits the 1

5 km depth is the typical depth of crustal magma chamber that comprise mostly dacite and more felsic compositions (Ryan, 1987).

420

Chapter 6 Structure and properties of fluids

FIGURE 6.86 Solubility of silicate components in fluids in the system MgOeSiO2H2OeNaCl. (A) Mg2SiO4 solubility as a function of mol fraction of NaCl at 1 GPa and at temperatures indicated. (B) Mg and Si solubility in equilibrium with forsterite as a function of mol fraction of NaCl in fluid at 1 GPa at temperatures indicated on individual lines. (C) Mg/Si ratio of fluid in equilibrium with forsterite at 1 GPa and 800 and 900 C as a function of NaCl concentration of the fluid. Modified after Macris et al. (2020).

6.5 Solubility behavior in fluid: H2OeSiO2eMgO

421

opposite effect. Notably, the Mg solubility in fluids in the MgSiO3eH2OeNaCl system increases with increasing XNaCl although the solubility is lower than in the Mg2SiO4eH2OeNaCl system (Fig. 6.87). Again, this difference likely is because the SiO2 solution behavior is to decrease solubility. Given the lower Mg/Si of enstatite compared with forsterite, the lower bulk silicate solubility would be expected. The increasing Mg/Si with increasing NaCl concentration (Fig. 6.86C) follows as a direct result of the decreasing SiO2 concentration in H2OeNaCl fluid with increasing XNaCl. It appears, therefore, as if the solubility behavior of Mg2SiO4 and MgSiO3 simply is a combination of two factors. One is driven by the MgO component, which becomes increasingly soluble with increasing XNaCl probably forming some sort of Mg-chloride complex in the fluid. In fact, Macris et al. (2020) from the solubility behavior in this system, proposed that a mixed OH, Cl species (MgClOH) existed in the fluid. The other effect is the solubility behavior of SiO2, which, at the pressure and temperature of the data in Figs. 6.86 and 6.87, decreases with increasing XNaCl. This effect reflects the decreased activity of H2O with increasing XNaCl in H2OeNaCl solution (Aranovich and Newton, 1996).

6.5.4 Properties of MgOeSiO2eH2O fluid Aside from the thermodynamics extracted from solubility data with the aim to model solution behavior, there is not much additional data on properties of MgOeSiO2eH2O fluids. However, at least in the pressure range where the fluid is essentially pure SiO2eH2O, fluid properties such as those discussed under SiO2eH2O should be essentially the same after taking into account that the SiO2 solubility in the MgOeSiO2eH2O fluid is less. A possible exception to this statement might be where the fluid is a mixture of H2O and halogens where Mg-chloride and/or Mg-fluoride complexes might also form in the fluid (Macris et al., 2020). However, to the knowledge of the author, no such experimental data have yet been reported. However, halogens, and in particular fluorine, can be dissolved in concentrations greater than 1 wt% in mantle minerals such as forsterite (Bernini et al., 2013). From this behavior it is tempting to suggest that MgeF complexes may also form in aqueous fluids in

FIGURE 6.87 Mg solubility in fluids in the system MgOeSiO2eH2OeNaCl as a function of mol fraction of NaCl in equilibrium with forsterite and with enstatite at 800 and 900 C and 1 GPa pressure as indicated on diagram. Modified after Macris et al. (2020).

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Chapter 6 Structure and properties of fluids

which case solubility and solution behavior of Mg and Si in fluid might be affected. However, until such experimental data are obtained, this suggestion remains speculation.

6.6 Solubility behavior in fluid: H2OeAl2O3(eNaCleKOHeSiO2) Al2O3 is the second-most abundant oxide in most igneous and metamorphic rocks. It is important, therefore, to examine how Al2O3 might dissolve in aqueous fluids. The endmember situation is H2OeAl2O3. It is generally assumed that among the rock-forming major oxides, Al2O3 is the least soluble in pure H2O. Natural evidence indicates, however, that there are situations where Al2O3 has been rather mobile. Such observations lead to the suggestion that the Al2O3 in metasomatic fluids, at least at times, may have been significantly soluble (e.g., Kerrick, 1990; McLelland et al., 2002). The principal question then is what are the added fluid components that results in enhanced Al2O3 solubility?

6.6.1 Al2O3eH2O with and without halogens In order to develop an experimental data base with which better to be able characterize rocks showing significant Al2O3 mobility, Al2O3 solubility not only in pure H2O, but also in the presence of added components such as chlorides and NaOH and KOH has been examined (Anderson and Burnham, 1967; Becker et al., 1983; Azaroual et al., 1996; Newton and Manning, 2006; Tropper and Manning, 2004; Brooks and Steele-MacInnis, 2019). Addition of more oxide components such as SiO2 and alkali metals may also affect the Al2O3 solubility. Those features will be discussed in the following section. The pressure-temperature stability field of corundum in the Al2O3 system is limited on the low temperature side by diaspore and H2O (Kennedy, 1959; see also Fig. 6.88). Experiments aimed at characterization of corundum solubility in pure H2O have, therefore, been carried out at temperatures above that of the diaspore breakdown. Early solubility experiments in the system Al2O3eH2O to 2 GPa and 700 C, indicated that the Al2O3 solubility is indeed very low, in the ppm range, but that the solubility is a linear function of pressure (Becker et al., 1983; see also Fig. 6.89) with the pressure dependence expressed with the simple linear regression equation; Al2 O3 ðaqÞ ¼
12.37 þ 0.724 PðGPaÞ.

(6.52)

In a later experimental study (Walther, 1997), it was found that the log molality (log mAl2O3), is a linear function of the inverse of the dielectric constant, ε (Fig. 6.90); logmAl2O3 Al2O3 ¼
4.24 þ 2.5$10
3 TðKÞ
10.5ð1=eÞ.

(6.53)

Such linear relationships have also been discussed for other oxide components with the suggestion that such linear relationships are common for relations between dielectric constant and solubility of most major element oxide components (Walther and Schott, 1988). It was, furthermore, suggested that in the simple Al2O3eH2O system, the principal Al-bearing species were Al(OH)-4 and Al(OH)3 with the reaction; + þ AlðOHÞ
4 þ H ¼ AlðOHÞ3 þ H2 O;

(6.54)

6.6 Solubility behavior in fluid: H2OeAl2O3(eNaCleKOHeSiO2)

423

Pressure, PH2O=Ptot, GPa

4

3 Gibbsite (Al2O3•3H2O)

2 Diaspore + H2O (Al2O3•H2O)

1 Corundum + H2O (Al2O3)

0 100

200

300 400 Temperature, ˚C

500

600

FIGURE 6.88 Pressure-temperature phase relations in the system Al2O3eH2O. Modified after Kennedy (1959).

describing the equilibrium (Pokrovski and Helgeson, 1995). An example of the temperaturedependence of this reaction (Fig. 6.91; see also Walther, 1997) illustrates how the equilibrium constant, K, decreases with increasing temperature before reaching a minimum value between 250 and 300 C. At temperatures higher than that, the equilibrium constant increases. Very likely this evolution may suggest more than one equilibrium reaction describing the speciation in the Al2O3eH2O fluids. This is further evident with the data in Fig. 6.91B, where the equilibrium constant for a second equilibrium is shown as a function of temperature; AlðOHÞ+3 þ Hþ ¼ AlðOHÞþ 4 þ H2 O;

(6.55)

By adding KOH or NaCl to the Al2O3eH2O system, the Al2O3 solubility increases by several orders of magnitude (Pascal and Anderson, 1989; Walther, 1997, 2001; Wohlers and Manning, 2009; Newton and Manning, 2006). The solubility is, for example, a linear and positive function of the KOH concentration at given temperature and pressure (Azaroual et al., 1996; see also Fig. 6.92A) and a positive function of NaCl although this latter relationship is not linear (Newton and Manning, 2006; see also Fig. 6.92B). In the Al2O3eH2OeKOH system (Pascal and Anderson, 1989; Azaroual et al., 1996), the principal additional species responsible for the enhanced Al2O3 solubility has been proposed to be KAl(OH)4 (or

424

Chapter 6 Structure and properties of fluids

FIGURE 6.89 Solubility of Al2O3 in aqueous fluid in equilibrium with corundum in the Al2O3eH2O system as a function of pressure at 670e700 C. Modified after Becker et al. (1983).

Na equivalent). By adding chloride to the system, the principal additional species in the fluid could be NaAl(OH)4 and Al(OH)2Cl (Newton and Manning, 2006). The relationships to KOH concentration (Fig. 6.92A) has been proposed to be (Newton and Manning, 2006; Wohlers and Manning, 2009), For KOH: logmAl ¼ 1; 004logmK
0.165;

(6.56)

where, therefore, there is an essentially 1:1 increase in Al2O3 and KOH concentration. The effect of NaOH and KOH on the Al2O3 solubility for all practical purposes is the same (Anderson and Burnham, 1967; Wohlers and Manning, 2009). This 1:1 relation would suggest a K-bearing Al-species such as KAl(OH)4 in the fluid, for example. The nonlinear fit to NaCl concentration (Fig. 6.92B) has been described with the empirical expression (Newton and Manning, 2006): mAl2O3 ¼ 0.001373
0.02227X NaCl þ 0.03477ðX NaCl Þ1=2 .

(6.57)

Anderson and Burnham (1967) found that the effects of KCl and NaCl on the Al2O3 solubility are essentially the same. The observation that Al-bearing complexes that do not include alkali metals leads to the suggestion that Cl-bearing complexes enhances the Al2O3 solubility. An Al(OH)2Cl complex could serve this purpose, for example (Newton and Manning, 2006).

6.6 Solubility behavior in fluid: H2OeAl2O3(eNaCleKOHeSiO2)

425

FIGURE 6.90 Solubility of Al2O3 in aqueous fluid in equilibrium with corundum in the Al2O3eH2O system as a function of the inverse of the dielectric constant, 1/ε, at 600 C and 200 MPa. Modified after Walther (1997).

FIGURE 6.91 Equilibrium constant, log K, as a function of temperature for various Al2O3 solubility reactions in H2O in the 50e200 MPa pressure range from data sources indicated on diagrams. (A) log K for the reaction shown in Eq. (6.54) and on the diagram. (B) log K for reaction shown in Eq. (6.55) and also shown on diagram. Modified after Walther (1997).

426

Chapter 6 Structure and properties of fluids

FIGURE 6.92 Solubility of Al in aqueous fluid in equilibrium with corundum in the Al2O3eH2OeKOH and Al2O3eH2OeNaCl. (A) Al solubility, mAl, as a function of KOH concentration in the Al2O3eH2OeKOH system at 50e200 MPa pressure and 400 C. (B) As a function of NaCl concentration in the system Al2O3eH2OeNaCl at 800 C and 1 GPa. Modified after (A) Azaroual et al. (1996); (B) Newton and Manning (2006).

6.6.2 H2OeAl2O3-alkali aluminosilicate with and without halogens In order to approach conditions found in nature, SiO2 and alkali metals need to be added to the system describing Al2O3 solubility in aqueous solutions (Currie, 1968; Anderson and Burnham 1983; Manning, 2007; Wohlers et al., 2011; Schmidt et al., 2014). The first step in this procedure is to assess the effect of added SiO2 alone. The solubility in aqueous fluid in the Al2O3eSiO2eH2O at 1 GPa and 700 C is 5.8 mmolal (Manning, 2007), which is between 3.3 and 4.8 times greater than the Al2O3 solubility in the Al2O3eH2O system without SiO2 (Tropper and Manning, 2004; Becker et al., 1983). This difference indicates that there is some interaction between dissolved Al and Si in the fluid. It should be noted, though, that the whereas the Si content of the fluid was 0.3  0.1 molal, that of Al was 0.008  0.007 molal. In other words, for all practical purposes, the fluid was essentially all silicate. Possible Si and Al species in aqueous fluid coexisting with kyanite (AlSiO5) and kyanite þ quartz were addressed by Manning (2007). As seen in Fig. 6.93, the monomer and dimer species of silica dominate with total Si solubility between 1.5 and 3.5 orders of magnitude greater than total Al solubility depending the Al concentration (Fig. 6.93). Among the Al species, HAlSiO4 abundance dominates over that of HAlO2 and AlO
2 by one and two orders of magnitude, respectively. By adding NaCl to corundum þ quartz, the Al2O3 solubility in the fluid is increased further (Newton and Manning, 2008; see also Fig. 6.94). As can be seen from the results of the least squares fit to the experimental data, the molality, mAl2O3, is a complex and positive function of both the SiO2 and NaCl concentrations:

6.6 Solubility behavior in fluid: H2OeAl2O3(eNaCleKOHeSiO2)

427

FIGURE 6.93 Concentration of silicate and aluminate species in the system Al2O3eAl2SiO5eH2O at 700 C and 1 GPa calculated as a function of Al concentration in fluid. Modified after Manning (2007).

  2 mSiO2 XNacl  0:3: mAl2O3 ¼ m0Al2O3 þ 0:0025
0:048XNaCl þ 9:733XNaCl
 1=2 þ 0:0012
0:21XNACl þ 0:0757XNaCl m2SiO2

(6.58)

where m0Al2O3 is the Al2O3 molality in NaCl-free systems. A somewhat different expression was given for more NaCl-rich solutions that the expression for XNaCl  0.3 in Eq. (6.58). A number of experimental studies have been carried out by adding Na in the form of albite (NaAlSi3O8) to Al2O3eH2O solutions (Currie, 1968; Anderson and Burnham, 1983; Woodland and Walther, 1987; Schmidt et al., 2014). The total aluminosilicate solubility in the NaAlSi3O8eH2O system is on the order of a wt%, which is several orders of magnitude greater than the corundum solubility in pure H2O (see discussion earlier). Interestingly, at pressures less than about 0.7 GPa in the 500e700 C range, the total solubility of albite is actually less than that of SiO2 in the SiO2eH2O system, but exceeds the SiO2 solubility values at greater pressures (Fig. 6.95). In all experimental studies involving aqueous fluid and albite composition, the data indicate that albite dissolves incongruently. Currie (1968) was perhaps the first to report this effect. However, some questions about the method used was raised subsequently (Anderson and Burnham, 1983). Higher

428

Chapter 6 Structure and properties of fluids

FIGURE 6.94 Phase relations in the Al2O3eSiO2eH2OeNaCl system expressed in terms of Al2O3 and SiO2 solubility at 1 GPa and 800 C. The lines denoted 0.03, 0.1 etc., are NaCl isopleths calculated from the expression, where X is mol fraction and m is molality. Modified after Newton and Manning (2008).

solubility in aqueous fluid than that reported by Currie (1968) was reported by Anderson and Burnham (1983), for example. It was suggested that the method used by Currie (1968) might have been responsible for this discrepancy. That comment notwithstanding, it is clear from the Currie (1968) data that the Na and Al concentrations do not evolve along a single 1:1 line (Fig. 6.95), thus supporting even at that time the notion that NaAlSi3O8 does dissolve incongruently in H2O at high temperature and pressure. The extent of this deviation is perhaps even more clear in the relationship between Al and Na concentration (Fig. 6.96). The solution always exhibits excess Na over the 1:1 ratio expected for the NaAlSi3O8 stoichiometry. Although not determined experimentally, it is tempting to suggest that the

6.6 Solubility behavior in fluid: H2OeAl2O3(eNaCleKOHeSiO2)

429

FIGURE 6.95 Solubility in aqueous solution of individual components from the system NaAlSi3O8eH2O as a function of pressure and temperature. (A) Concentration of Si in fluid as a function of pressure at temperatures indicated. (B) Concentration of Al in fluid as a function of pressure at temperatures indicated. (C) Concentration of Na in fluid as a function of pressure at temperatures indicated. Modified after Currie (1968).

430

Chapter 6 Structure and properties of fluids

FIGURE 6.96 Relationship between Na and Al solubility at different temperatures (as shown) in the system NaAlSi3O8eH2O from the data of Davis (1972). Modified from Anderson and Burnham (1983).

excess Na might be associated with some of the Si4þ in solution. We also note that the deviation from Na:Al ¼ 1:1 diminishes with increasing temperature (Fig. 6.96). An interesting situation is encountered in the NaAlSi3O8 system when the pressure-temperature conditions for the reaction: albite ¼ jadeite þ quartz; 500e600 C

(6.59)

is reached. This takes place near 1.5 GPa in the range studied by Wohlers et al. (2011). The solubility of both jadeite (NaAlSi2O6) and quartz (SiO2) is less than that of albite (NaAlSi3O8). Therefore, as the phase transformation in Eq. (6.59) is reached, a further pressure increase results in decreasing bulk solubility as well as decreased solubility of the individual components (Fig. 6.97). It is also striking that while the Na/Al ratio decreases below the ideal value of 2 with increasing pressure at pressures below that of the phase transformation of Eq. (6.59), at higher pressure this ratio increases rapidly (Fig. 6.98). It is not clear why this happens because very likely there are no structural changes in dissolved components because there are no structural changes in NaAlSi2O6 melt in this pressure/ temperature regime (Lee et al., 2012). However, Al undergoes a coordination change from four in albite to six in crystalline jadeite. It is possible that there are differences in albite/fluid and jadeite/fluid partition coefficients that could be responsible for this change in the Na/Al ratio of the fluid.

6.6 Solubility behavior in fluid: H2OeAl2O3(eNaCleKOHeSiO2)

431

FIGURE 6.97 Solubility of individual components in the system paragonite þ quartz þ H2O at pressures below and above the phase transformation in Eq. (6.59) (marked as a vertical line in the diagrams) as a function of pressure at 600 C. Open symbols are conditions without paragonite in the phase assemblage. (A) Al solubility. (B) Na solubility, (C) Si solubility, and (D) Total solubility. Modified after Wohlers et al. (2011).

432

Chapter 6 Structure and properties of fluids

FIGURE 6.98 Na/Al ratio in aqueous fluid in the system paragonite þ quartz þ H2O as a function of pressure at 500 and 600 C. Modified after Wohlers et al. (2011).

Dissolution of albite in H2OeNaCl fluids have been reported in the 0.1e0.9 GPa pressure and 400e800 C temperature, ranges, respectively (Shmulovich et al., 2001; Tagirov et al., 2002). In addition, effects of HF on albite solubility was reported by Tagirov et al. (2002). By adding NaCl to the H2O fluid, Shmulovich et al. (2001) reported a continuous decrease in albite solubility (Fig. 6.99). They also noted that while albite dissolves incongruently at 0.5 GPa, the experimental evidence at 0.9 GPa was that the dissolution was near congruent. In this regard, there may be a small difference between the solution behavior in pure H2O and in H2OeNaCl (Anderson and Burnham, 1983; Shmulovich et al., 2001). It is noted, however, that although Anderson and Burnham (1983) reported data only to 700 C, they did notice that the solution approached congruent with increasing temperature (Fig. 6.96). It is possible, therefore, that were it possible to compare results at the same temperature and pressure, the two data sets were in accord. There are, however, some disagreement between the experimental albiteeH2OeNaCl experimental results of Shmulovich et al. (2001) and those of Tagirov et al. (2002). The latter authors agreed that at low mol fraction of NaCl, the albite solubility decreased with increasing NaCl content (molality less than 0.01). However, with more NaCl in solution, the solubility of albite increased in the Tagirov

6.7 Minor and trace elements in aqueous fluid

433

FIGURE 6.99 Solubility of NaAlSi3O8 in the system NaAlSi3O8eH2OeNaCl as a function of NaCl concentrations at 0.9 GPa and temperatures shown on individual curves. Modified after Shmulovich et al. (2001).

et al. (2002) study (Fig. 6.100A). Tagirov et al. (2002) proposed that low NaCl concentration, Al3þ, is dissolved in the form of AlðOHÞ
4 . So, when the activity of H2O decreases with increasing NaCl abundance, the concentration of this Al-species decreases. However, at some point, the activity of NaCl is sufficient to stabilize and NaAl(OH)3Cl0 species in the fluid. At this point, as the activity of NaCl increases, this Cl-bearing Al-species dominates and increases with increasing NaCl abundance ion the fluid. In a mixed halide environment, NaAlSi3O8eH2OeNaCl(0.5m)-NaF, the concentration of the various Al-species increases continuously with increasing fluorine molality, mF (Fig. 6.100B). As can be seen in Fig. 6.100B, there is a much larger number of F-bearing species from the NaAlSi3O8 solubility behavior than is the case in the F-free NaAlSi3O8eH2OeNaCl system (Fig. 6.100A). Moreover, according to the discussion by Tagirov et al. (2002), the abundance of each and every one of these species increases with increasing F concentration. This difference reflects the different interactions between the NaAlSi3O8 component Cl and F in the aqueous fluid.

6.7 Minor and trace elements in aqueous fluid Aqueous fluids not only carry major elements in solution, minor and trace elements also can be found in significant concentrations. This effect can be particularly important in subduction zone settings where magma often carry unique signatures of trace element enrichments caused by transport in aqueous fluids from a dehydrating subducting slab to the overlying mantle wedge where partial melting takes place (Mysen and Boettcher, 1975b; Wyllie, 1982; Ayers and Watson, 1993; Elliott et al., 1997; Brenan et al., 1998; Baier et al., 2008; Till et al., 2011; D’Souza and Canil, 2018). Solubility experiments have focused on elements such as Ca, Sr, Cr, REE, Ti, Zr, U, Th, Au, Ag, Cu, An, Cu in aqueous solutions (Pokrovski et al., 2005; Liebscher et al., 2013; Watenphul et al., 2014; Antignano and Manning, 2008; Bali et al., 2011; Wilke et al., 2012; Mysen, 2015c). Those components tend to form complexes in the fluid, perhaps mostly with sulfur (Guo et al., 2018; Bali et al., 2012) and

434

Chapter 6 Structure and properties of fluids

FIGURE 6.100 Aluminum speciation in saline fluids in the system albite-aragonite-quartzeH2OeNaCl and albitearagonite-quartzeH2OeNaCleNaF. (A) Al-speciation as a function of Al and Na concentration in the system albite-aragonite-quartzeH2OeNaCl at 400 C and 50 MPa in slightly acidic solution (pH ¼ 7.1e4.8). (B) Alspeciation as a function of Al and F concentration in the system albite-aragonite-quartzeH2OeNaCl(0.5m)NaF at 450 C and 50 MPa at pH ¼ 5.6. Modified after Tagirov et al. (2002).

chlorine (Zajacs et al., 2008). Oxyanion complexes bonded to alkali metals and alkaline earths also can have profound effects on their solubility in aqueous fluids (Mysen, 2018, 2019).

6.7.1 Ti solubility The solubility of Ti is critical for characterization of rutile stability in magmatic systems, in particular in subduction zone setting. In those settings, rutile governs the abundance of a number of geochemically important trace elements (Ayers et al., 1993; Brenan et al., 1994; Stalder et al., 1998; Keppler, 2017). An understanding of rutile solubility provides, therefore, an aid in characterizing petrogenetic processes in subduction zones. The solubility of Ti in pure H2O is quite low, perhaps around 10 ppm or so. The solubility, expressed as log Ti, is a linear function of 1/T (Kelvin) and pressure. The solubility increases with increasing temperature and pressure (Antignano and Manning, 2008; Mysen, 2012; see also Fig. 6.101) From those data, the DH and DV for the reaction: rutile ¼ TiO2 ðaqueousÞ;

(6.60)

were found to be 104 kJ/mol and
3.4 cm /mol, respectively. A similar solubility was reported by Mysen (2012). He concluded that the DH of reaction (Eq. 6.60) was on the order of 50e60 kJ/mol, but he did not correct for the pressure effect in his experiments. From the Raman spectra of the H2OeTiO2 fluid, Mysen (2012) concluded that Ti occupied sixfold coordination in the fluids in the simple 3

6.7 Minor and trace elements in aqueous fluid

435

FIGURE 6.101 Titanium solubility in in aqueous fluid in the system TiO2eH2O (A) as a function of temperature at 1 GPa pressure, and (B) as a function of pressure at 800 C. Modified after Antignano and Manning (2008).

H2OeTiO2 system. Pressure played a role when using the hydrothermal cell for this purpose as done by Mysen (2012) where pressure increased in the fixed volume sample chambers used in those experiments as the temperature was increased (see also Bassett et al., 1994). This means that the

436

Chapter 6 Structure and properties of fluids

50e60 kJ/mol value is a minimum value. We also note that Audetat and Keppler (2005), also employing a hydrothermal diamond anvil cell, found 10e25 ppm solubility in the 1e2.25 GPa pressure range. However, they reported DH of Eq. (6.60) to be 74.7 kJ/mol and the volume change to be
6.1 cm3/mol. Addition of SiO2 to the H2OeTiO2 system does not affect the Ti solubility appreciably (Antignano and Manning, 2008). However, by adding a Na compound, be it NaAlSi3O8 (Hayden and Manning. 2011) or Na aluminosilicate or just Na-silicate (Mysen, 2012), the Ti solubility is greatly enhanced. By adding NaAlSi3O8 to the system, the Ti solubility increased to 0.3e0.4 wt% (Hayden and Manning, 2011) and from 0.4 to about 0.6 wt% by adding NaCl (Tanis et al., 2016). We note that the Ti solubility in H2OeNaCl is about the same as the solubility when adding NaAlSi3O8. In TiO2eNaFeH2O fluids, the Ti solubility increases by between 50% and 100% compared with the Ti solubility in TiO2eNaCleH2O fluids (Tanis et al., 2016). From the in situ Raman spectra of the fluids containing Na-silicate compounds, Mysen (2012) proposed a solubility reaction such as: 4Q1Si ðNaÞ þ 4H2 O þ TiO2 ¼ 4QoSi ðHNaÞ þ Q0Ti ðNaÞ;

(6.61)

where, therefore, the solution of Ti is in the form of a Q -like species with Ti in fourfold coordination. This structural role differs, therefore, from Ti in solution in pure H2O where it occupies sixfold coordination with oxygen. From the temperature-dependence of this equilibrium (Fig. 6.102), it is evident that the DH is lower by up to about 50% in the (Na þ Al)-bearing systems compared with the DH from the simpler Na-silicate þ TiOeH2O system (Fig. 6.102). 0

4þ

6.7.2 Zr solubility The solubility of Zr in the ZrO2eH2O system also is quite low, at the ppm level at temperatures and pressures corresponding to the deep crust and upper mantle (Wilke et al., 2012; Mysen, 2015c). The ZrO2 dissolves congruently with on the order of 20e60 ppm Zr in solution in the 600e900 C and 300e900 MPa, temperature and pressure ranges, respectively (Mysen, 2015c; see also Fig. 6.103). However, zircon (Zr2SiO4) dissolves incongruently to an SiO2-rich fluid with crystalline ZrO2 (baddeleyite) in the solid residue. The Zr solubility is quite sensitive to added components in the fluid. In particular, the presence of Naþ can result in the solubility increasing by approximately an order of magnitude (Fig. 6.103). However, addition of SiO2 to ZrO2eH2O has only minor (a few ppm) effects on the Zr4þ solubility (Wilke et al., 2012; Mysen, 2015c). However, Wilke et al. (2012) observed that by adding Al2O3 to this solution, the Zr solubility decreases. Adding SiO2 to the Na-bearing system has at best minor effects on the solubility. It seems, therefore, that Zr complexes do not include Si and Al to a significant extent, but does incorporate alkali metals. We also note that for Na-bearing aqueous fluids in equilibrium with zircon, the solubility increases systematically with increasing temperature, whereas a pressure increase results in a Zr solubility decrease (Fig. 6.104; see also Wilke et al., 2012). These trends exist whether or not Na-bearing compounds are added to the solution. The decreased solubility with increasing pressure implies that the molar volume of Zr in the fluid is greater than the coexisting ZrO2 and Zr2SiO4. It follows, therefore, the Zr speciation in the fluid likely differs significantly from the crystalline materials with which the fluid equilibrated.

6.7 Minor and trace elements in aqueous fluid

437

FIGURE 6.102 Equilibrium constant, log K, for Eq. (6.61) as a function of temperature (1/T) and pressure for the systems Na2$4SiO2(NS4)eH2OeTiO2 and Na2O$4SiO2þ10 mol% Al2O3(NA10)eH2OeTiO2 as indicated on the individual lines in the diagram. Note that the pressure evolution for the two systems as a function of temperature differs. Modified after Mysen (2012).

The solution mechanism of Zr in aqueous solutions is very much dependent on the additives in the solution. For the simple system, ZrO2eH2O, the equilibrium simply is: ZrO2 ðxtalÞ ¼ ZrO2 ðfluidÞ;

(6.62a)

K 6.62a ¼ mZrO2 ðfluidÞ;

(6.62b)

with the equilibrium constant: where m is molality. From linear relationship between ln K6.62a and 1/T(Kelvin), we have a DH ¼ 43  16 kJ/mol (Mysen, 2015c). Interestingly, this DH-value is similar to that of Ti in

438

Chapter 6 Structure and properties of fluids

FIGURE 6.103 Zirconium solubility in aqueous solutions as a function of temperature and pressure for the various systems indicated on individual dashed lines. Modified after Mysen (2015c).

TiO2eH2O [Eq. 6.60]. For more complex solution mechanisms derived by addition of Na compounds and SiO2, we have solution equilibria such as (Mysen, 2015c): ZrO2 ðxtalÞ þ ð4 NaOHÞ ¼ Na4 ZiO4 ðfluidÞ þ H2 O;

(6.63)

2ZrO2 ðxtalÞ þ NaOH þ 2SiO2 ¼ NaZr2 Si2 O8 ðOHÞðfluidÞ þ H2 O;

(6.64)

and

6.7 Minor and trace elements in aqueous fluid

439

FIGURE 6.104 Zr solubility in aqueous fluids with Na-silicate components added. (A) Zr solubility in the system Zr2SiO4þ10 wt% Na2Si3O7(NS3)eH2O expressed as Zr isopleths (ppm) in pressure temperature space. (B) Zr solubility in the system Zr2SiO4þ16 wt% Na2Si2O5(NS2)eH2O as a function of pressure at temperatures indicated on individual curves. Modified after Wilke et al. (2012).

440

Chapter 6 Structure and properties of fluids

with DH ¼ 232  29 kJ/mol. In both these latter cases, the formation of zirconate and silicozirconate complexes lead to the much greater solubility in the aqueous solutions compared with the simple system ZrO2eH2O. This solubility behavior resembles aspects of the titanate solution mechanism in Eqs. (6.61), (6.63) and (6.64). In fact, one might suggest that formation of such oxycomplexes not only leads to enhanced Zr and Ti solubility, but may also cause greater solubility of other nominally insoluble cations such as, for example, HFSE. In summary, the key to enhanced solubility of HFSE in aqueous solutions is the stabilization of oxycomplexes associated with alkali metals or, perhaps alkaline earths. The exact form in which the metal cation is added to the solution may not be the most important variable. It is, of course, likely, that the exact nature of the cation will affect the solubility and the more electropositive it is, the greater is the solubility of the oxycomplex. One might speculate, for example, that fluid in equilibrium with felsic magma will be alkali metal rich and, therefore, form oxycomplexes with greater solubility in aqueous solutions than fluids in equilibrium with mafic igneous rocks where alkaline earths are more likely to stability the oxycomplex. Of course, in addition to the different alkali metal/alkaline earth ratios in felsic and mafic systems, the felsic systems tend to form under more oxidizing conditions than mafic igneous rocks (Mysen, 2003; Carmichael and Ghiorso, 1990), which leads to more oxidized HFSE in the melt and exsolved aqueous fluids. That in turn, leads to more HFSE-rich fluids in equilibrium with felsic magma compared with mafic magma such as fluids in equilibrium with basalt magma, for example.

6.7.3 Salinity of aqueous solutions and trace element solubility A number of elements that may be essentially insoluble in pure H2O exhibits significant solubility in saline aqueous solutions such as H2OeNaCl and H2OeNaF. These elements include actinides such as U and Th, and transition metals, including Sn, W, Mo, Cr, Pb, Zn, Ag, and Fe (Bailey and Ragnarsdottir, 1994; Bali et al., 2011, 2012; Duc-Tin et al., 2007; Watenphul et al., 2014; Zajacs et al., 2008). Salinity also has major effect on solubility of alkali metals, alkaline earths, and rare earth elements (Kawamoto et al., 2014; Rustioni et al., 2021). Rustioni et al. (2021) suggested that the influence of salinity on alkali metal and alkaline earth solubility is greater than the effect of salinity on the solubility of transition metals. In fact, in an experimental study in the 4e6 GPa pressure range, it was found that element content in fluid, expressed in terms of fluid/crystal partition coefficients, increases with increasing Cl content (Rustioni et al., 2021; see also Figs. 6.105 and 6.106). Among the alkali metals, their solubility increases significantly as the alkali metals becomes more electropositive in both aqueous and saline, aqueous fluid. Moreover, between 5 and 6 GPa, the effect of Cl seems to reverse for certain elements such as SiO2, Al2O3, FeO and MgO. Rustioni et al. (2021) suggested that this effect may reflect a transition to a supercritical state of the fluid under which conditions the silicate anions appear to compete for the Cl anion thus reducing the effect of Cl on the solubility of the various elements. There also exists a number of additional experimental data on trace element solubility in aqueous solutions with and without added components. Some of the most important among those data sets will be summarized below. We will first address effects of salinity followed by some examples of effects of sulfur.

6.7 Minor and trace elements in aqueous fluid

441

FIGURE 6.105 Partition coefficient of elements as indicated between omphacite in an eclogite phase assemblage and aqueous fluid at 4 GPa and 800 C with and without Cl as indicated. Modified after Rustioni et al. (2021).

FIGURE 6.106 (A) Na2O solubility in saline solutions in equilibrium with an eclogite mineral assemblage at 4 GPa and 700e800 C as function of chloride concentration (added as NaCl). (B) CaO solubility in saline solutions in equilibrium with an eclogite mineral assemblage at 4 GPa and 700e800 C as function of chloride concentration (added as NaCl). Modified after Rustioni et al. (2021).

442

Chapter 6 Structure and properties of fluids

6.7.3.1 U and Th solubility The solubility at high temperature and pressure of uranium and its sister element, Th, varies not only with fluid composition. Their solubility in aqueous solutions also depends on oxygen fugacity because these elements can exist in several oxidation states. In some of these oxidation states, U and Th may form oxyanions that also can affect their solubility (Bailey and Ragnarsdottir, 1994; Peiffert et al., 1996; Bali et al., 2011). Under reducing conditions such as, for example, those defined by the FeeFeO buffer, uranium is essentially insoluble in pure H2O. Under these fO2-conditions, uranium in aqueous solution exists completely as UO2 (Peiffert et al., 1996). However, the solubility increases rapidly with increasing oxygen fugacity and also with increasing salinity of the aqueous fluid (Bali et al., 2011; see also Fig. 6.107A) so that under conditions corresponding to intermediate depth in subduction zones, uranium solubility in aqueous fluids is near 1000 ppm. In this evolution, an increasing fraction of

FIGURE 6.107 (A) Solubility of U, and Th in aqueous solutions in equilibrium with UO2 and ThSiO4, respectively, as a function of oxygen fugacity at 800 C and 2.61 MPa. (B) Solubility of U in NaCl-bearing aqueous solution in equilibrium with UO2 as a function of NaCl concentration at 800 C and 2.61 GPa. Modified after Bali et al. (2011).

6.7 Minor and trace elements in aqueous fluid

443

uranium exists as U6þ (Peiffert et al., 1996). In addition, the U solubility also increases with increasing Cl concentration in the fluid (Fig. 6.107B). Interestingly, the chlorine effect seems independent of the oxidation state of uranium (Bali et al., 2011). An empirical relation describing these relationships is (Bali et al., 2011); logUðsolubilityÞ ¼ 2.681 þ 0.1433log f O2 þ 0.594Cl.

(6.65)

However, Peiffert et al. (1996) observed that the effect of oxygen fugacity decreased as the Cl concentration in saline solutions increased. Reasons for this apparently different conclusion are not clear. Furthermore, Peiffert et al. (1996) observed that equivalent concentrations of fluorine in the saline solutions increased the uranium solubility by as much as a factor of 20 compared with fluorinefree H2O. Relationships similar to those for Cl in Fig. 6.108, were reported for fluorine. Those relationships lead to the suggestion that oxidized U and Th may form complexes with oxygen and that this oxycomplex is charge-balanced with a cation such as Naþ or Kþ, or both. This possible solution mechanism is supported by the observation that under oxidizing conditions, the uranium solubility is a positive and linear function of the (Na þ K)/Al of the fluid (Peiffert et al., 1996). Most likely, these are U6þ-based complexes form UO2þ 2 entities. In some ways, this principle is the same as that which describe the increased solubility of Ti4þ and Zr4þ and other HFSE in aqueous solution described in the previous sections.

6.7.3.2 Cr3þ solubility The solubility of Cr3þ in aqueous solutions generally has been considered very low (Watenphul et al., 2014) even though evidence from pegmatitic rocks indicates the Cr3þ may indeed by reasonably

FIGURE 6.108 Solubility of U in saline aqueous solutions in equilibrium with granite melt at 770 C and 200 MPa. (A) Solubility as a function of oxygen fugacity, log fO2 for chlorine concentrations as indicated on the individual lines in the diagram. (B) Solubility as a function of oxygen fugacity, log fO2 for fluorine concentrations as indicated on the individual lines in the diagram. Modified after Peiffert et al. (1996).

444

Chapter 6 Structure and properties of fluids

soluble in fluids because of significant metasomatic alteration involving chromium in metamorphic rocks (Marshall et al., 2003). This observation has led to solubility experiments with saline solutions (Klein-BenDavid et al., 2011; Watenphul et al., 2014). Klein-BenDavid et al. (2011) extended their experiments to 6 GPa in light of the fact that inclusions in diamonds can be quite Cr-rich. In comparison, the experiments by Watenphul et al. (2014) were in the pressure range of the deep crust (0.6 GPa). In the Watenphul et al. (2014) experiments, chlorine was added as HCl with Cl
in the molality range between 0.046 mol/kg to 0.828 mol/kg. The Cr3þ solubility in saline solutions increases systematically with increasing pressure, decreasing temperature (Fig. 6.109A), and increasing Cl
concentration (Fig. 6.109B). Notably, the pressure data in Fig. 6.109A do not distinguish between different chlorine concentration (Watenphul et al., 2014) although in general, increasing pressure is associated with increasing Cl concentration in the fluid (Fig. 6.109B). From molecular dynamics simulations and Raman spectroscopy, these trends are consistent with formation of Cr-bearing complexes of the type Cr(H2O)2Cl4 where each Cr3þ is surrounded by 3 or 4 Cl anions and 1 or 2 H2O molecules (Watenphul et al., 2014).

6.7.3.3 Molybdenum solubility The solubility of molybdenum in aqueous and saline solutions is on the order of 100 to 10,000 ppm (Ulrich and Mavrogenes, 2008; Bali et al., 2012; Hurtig and Williams-Jones, 2014). The solubility also is a strong function of both oxygen fugacity and salinity of the solution (Bali et al., 2012). For example, the Mo solubility increases by on the order of 2 orders of magnitude when the fO2 increases by about 4 orders of magnitude. Oxidized Mo solubility increases by about 1 order of magnitude when NaCl

FIGURE 6.109 (A) Solubility of chromium, mCr, in the system Cr2O3eH2OeHCl as a function of pressure at various temperatures. (B) Solubility of chromium, mCr, in the system Cr2O3eH2OeHCl as a function chloride concentration, mCl, at pressures indicated and 600 C. Modified after Watenphul et al. (2014).

6.7 Minor and trace elements in aqueous fluid

445

content of the solution increases from 0 to about 15 wt% (Fig. 6.110). These relationships can be summarized in the following empirical relationship; logmMo ¼ 0.44log f O2 þ 0.42logmNaCl
1.8$1000=T þ 4.8.

(6.66)

The solubility of fully oxidized Mo (MoO3), on the other hand, is independent of oxygen fugacity, but is a significantly positive function of chloride concentration in the fluid (Ulrich and Mavrogenes, 2008; Hurtig and Williams-Jones, 2014 see also Fig. 6.110C). Ulrich and Mavrogenes (2008) proposed the following solution mechanism of molybdenum under these oxidizing conditions: MoO2 þ KCl þ 2H2 O ¼ KHMoO4 þ HCl þ 2H2 .

(6.67)

þ

We note that it is the K from the KCl that stabilizes the molybdate complex, KHMoO4. Moreover, expression (Eq. 6.67) leads to the suggestion that the redox state and, therefore, Mo solubility, is a function of H2 fugacity, which in an aqueous environment could equally well be expressed as oxygen fugacity. In order to work around this issue, Ulrich and Mavrogens (2008) suggested that the EXAFS data reported by Yokoi et al. (1993) might comprise the solution to this problem. The latter authors suggested complexes of the type, MoO2Clþ, MoO2Cl2, and MoO2Cl
3 with increasing chlorine concentration. We note that in this case, molybdenum remains in its 6þ state throughout. Then, there is no need to include hydrogen fugacity as in Eq. (6.67). These two solution mechanisms are, however, in stark contrast. In one, the Kþ from KCl stabilizes the molybdate without participation by Cl. In the other, Mo is stabilized entirely by Cl complexing without involvement of the alkali metal. A somewhat similar set of species stabilized under oxidizing conditions can be seen in the phase diagram in Fig. 6.111 (Hurtig and Williams-Jones, 2014). This diagram also illustrates how the speciation of Mo changes as a function of fO2 and fHCl.

6.7.3.4 Tungsten solubility Tungsten is another element that can exist in multiple oxidation states in the fO2-range of terrestrial processes. One would expect, therefore, a relationship between tungsten solubility and fO2, which is exactly what has been found (Fig. 6.112; see also Bali et al., 2012). Notably there is no effect of HCl on the W solubility in saline aqueous solutions. The empirical relationship to fO2 is, therefore, simpler than that for Mo in Eq. (6.67): logmW ¼ 0.07log f O2
4.72$1000=T þ 4.43.

(6.68)

We also note that the W-solubility relationship with fO2 is less pronounced than is the case for Mo (Figs. 6.110 and 6.112; see also Wood and Vlassopoulos, 1989; Bali et al., 2012). As to the salinity, Wood and Vlassopoulos (1989) concluded that when chlorine was added as NaCl, there was a significant effect on WO3 solubility. Moreover, the tungsten solubility increased even more significantly upon addition of NaOH to the aqueous solution (Fig. 6.113). It seem reasonable to conclude, therefore, that it is the Naþ cation and not Cl
that governs the solubility even when NaCl is added to aqueous solutions. With this in mind, the solution mechanism may be described as (Wood and Vlassopoulos, 1989): WO3ðsolidÞ þ H2 O þ NaCl ¼ NaHWO4 þ HCl;

(6.69)

WO3 ðsolidÞ þ NaOH ¼ NaHWO4 .

(6.70)

and

446

Chapter 6 Structure and properties of fluids

FIGURE 6.110 Molybdenum solubility in saline solutions. (A) Solubility of MoO2 as a function of oxygen fugacity in 5 wt% NaCl saline solution at 2.61 GPa. (B) Mo solubility as a function of NaCl concentration at 2.61 GPa and the oxygen fugacity of the NNO buffer. (C) Solubility of Mo in KCl-bearing aqueous solutions at 700 C as a function of KCl concentration. Modified from Bali et al. (2012); Ulrich and Mavrogenes (2008).

6.7 Minor and trace elements in aqueous fluid

447

FIGURE 6.111 Stability relations of Mo-bearing phases as a function of oxygen and HCl fugacity at 400 C and 20 MPa. Modified after Hurtig and Williams-Jones (2014).

FIGURE 6.112 Solubility of Mo and W oxide in saline aqueous solutions at 2.61 GPa with 5 wt% NaCl added to the solution. Modified after Bali et al. (2012).

448

Chapter 6 Structure and properties of fluids

FIGURE 6.113 (A) Solubility of WO3 in H2OeNaOH solutions at 500 C and 100 MPa as a function of NaOH concentration. (B) Solubility of WO3 in H2OeNaOH solutions at 500 C and 100 MPa as a function of NaCl concentration. Modified after Wood and Vlassoupolos (1989).

It is the formation of the Na-tungstate complexes that govern the increased tungsten solubility with increasing NaCl and NaOH. It is quite likely that similar relationships could be found when employing other electropositive cations in Eqs. (6.69) and (6.70).

6.7.3.5 Tin solubility The interest in tin solubility behavior in fluids (and melts) is driven by the economic interest in cassitierite (SnO2), which is found associated with granite intrusion and association hydrothermal veins (see, for example Wilson and Eugster, 1990, for summary of this literature). Tin may, however, also exist as Sn2þ, so that the abundance ratio, Sn2þ/Sn4þ is a function of redox conditions. In addition, halogen compounds, and in particular chloride-bearing compounds, affect the solubility (Kovalenko et al., 1986; Wilson and Eugster, 1990; Taylor and Wall, 1993; Duc-Tin et al., 2007; Schmidt, 2018). The Sn solubility in saline solutions is significantly dependent on NaCl, HCl, and HF concentration (Duc-Tin et al., 2007; see also Fig. 6.114). From the solubility behavior of tin, Duc-Tin et al. (2007) proposed the following speciation reactions involving chlorine and fluorine. For chlorine: SnO2 þ HCl þ H2 ¼ SnðOHÞCl þ H2 O;

(6.71)

SnO2 þ 2HCl þ H2 ¼ SnCl2 þ 2H2 O

(6.72)

SnO2 þ NaCl ¼ SnðOHÞCl þ NaOH.

(6.73)

SnO2 þ 2HF þ H2 ¼ SnF2 þ 2H2 O.

(6.74)

For fluorine:

It is evident from the solubility data in Fig. 6.114 that the effects of HCl, HF, and NaCl on the tin solubility are about the same. However, the individual species depend on chlorine concentration (Taylor and Wall, 1993), an example of which is shown in Fig. 6.115. It may not be surprising that the

6.7 Minor and trace elements in aqueous fluid

449

FIGURE 6.114 Solubility of Sn in saline (Cl, F) aqueous solutions in equilibrium with cassetierite (SnO2) at 700 C and 140 MPa. (A) Solubility of inferred Sn species, SnOHCl as a function of NaCl concentration. (B) Proportion of Sn species, SnOHCl to H2O as a function of mol fraction of HCl. (C) Ratio of mol fractions, XSnF2/XH2O, as a function of mol fraction of HF. Modified after Duc-Tin et al. (2007).

450

Chapter 6 Structure and properties of fluids

FIGURE 6.115 Distribution of H2O-bearing Sn-species in the system SnO2eH2OeHCl at 700 C and 200 MPa as a function of HCl concentration, mHCl. Modified after Taylor and Wall (1993).

abundance of the simple chloride, species, SnCl2, increases and the mixed OH, Cl species, Sn(OH)Cl, decreases with increasing HCl molality (Fig. 6.115). More recently, a study of the structure of the Sn-species at high temperature and pressure was reported wherein the experiments were conducted in situ, using Raman spectroscopy in a hydrothermal diamond anvil cell (Schmidt, 2018). Here, it was concluded that the dominant Sn4þ species were [SnCl4(H2O)2]0, [SnCl3(H2O)3]þ, and [SnCl5(H2O)]-. Their abundance is somewhat dependent on temperature at fixed HCl concentration (Fig. 6.116). The tin solubility also increases with increasing HCl concentration in the fluid. The rate of increase depends, however, on fO2, which implies that different Cl complexes formed with different oxidation state on Sn are involved (Fig. 6.116). Under more reducing conditions, Schmidt (2018) concluded that the dominant species in solution was SnCl
3. We do note, however, that in the presence of alkali metals, alkali-bearing Sn complexes also get stabilized (Taylor and Wall, 1993). This is probably yet another example of formation of oxycomplexes of HFSE formed by association of metal cations. It has been concluded from the studies summarized above that the most important variable controlling the tin solubility in hydrothermal solutions is the Cl concentration. Other variables such as fO2, pH, temperature, and pressure seem less important (Schmidt, 2018). We should note, however, that other reports indicate that both pH and redox conditions contribute to tin solubility in important ways (Wilson and Eugster, 1990; Taylor and Wall, 1993).

6.7.4 Sulfur in aqueous solutions and trace element solubility Sulfur in aqueous solution can exist in multiple oxidation states, which, in turn, will affect its influence on the solubility of trace elements in S-bearing solutions. The sulfur species are H2S, SO2, SO3, and

6.7 Minor and trace elements in aqueous fluid

451

FIGURE 6.116 Solubility on SnO2 in H2OeHCl solutions as a function of HCl concentration, mHCl, at various oxygen buffers and temperatures as indicated. Modified after Schmidt (2018).

HSO3 (Binder and Keppler, 2011; Eldridge et al., 2018). The principal equilibria among the species can be written as; 2H2 S þ 3O2 ¼ 2SO2 þ 2H2 O;

(6.75)

where the effect of oxygen fugacity on the proportion of oxidized (SO2) and reduced (H2S) sulfur species changes from essentially pure H2S to essentially pure SO2 over about an order of magnitude in fO2 (Binder and Keppler, 2011; see also Fig. 6.117). The equilibrium constant for Eq. (6.75) is essentially independent of pressure. From its temperature dependence, the DH and DS are, respectively
160  49.8 kJ/mol and
43.1  47.7 J/mol K (Binder and Keppler, 2011). The second reaction is that where SO2 is oxidized to SO3: 2SO2 þ O2 þ 2SO3 .

(6.76)

For this reaction, the temperature dependence of the equilibrium constant depends on pressure. As a result, both the enthalpy change and entropy change become increasingly negative as pressure increases (Binder and Keppler, 2011). In addition, Eldridge et al. (2018) noted that bisulfite, HSO
3 can play a significant role.

452

Chapter 6 Structure and properties of fluids

FIGURE 6.117 Oxidation state of sulfur in HeOeS fluids as a function of oxygen fugacity at 150 MPa and 800 C. Modified after Binder and Keppler (2011).

In addition, another sulfur species, S
3 , originally proposed by Pokrovski and Dubrovinski (2011) was proposed to be an important intermediate species stabilizing transition metals (Tossell, 2012; Mei et al., 2013; Pokrovski et al., 2015). In the numerical simulations by Tossell (2012), he noted that for the simple reaction: S2
6 ¼ 2S3 ;

(6.77)

there is a negative free energy change at high temperature (
110 kJ/mol at 450 C, for example) while at ambient temperature the DG of the reaction is positive (25 kJ/mol). Sulfur speciation plays a significant role in stabilizing, in particular, transition metals in S-bearing aqueous fluids (Stefansson and Seward, 2003; Pokrovski et al., 2008; Nagaseki and Hayashi, 2008; Etschmann et al., 2010; Trigub et al., 2017; Liu et al., 2020). Some of the most important principles governing the solubility behavior of transition metals in sulfur-bearing solution will be summarized below.

6.7.4.1 Au solubility The solubility and solution mechanism(s) of gold in sulfur-bearing aqueous solutions have focused on reducing conditions (Gibert et al., 1998; Pokrovski et al., 2008; Zezin et al., 2011; Trigub et al., 2017). However, there is evidence from porphyry-copper deposits that these were formed under significantly oxidizing conditions (See Guo et al., 2018, for a summary of this literature). However, experiments aimed at characterizing the solubility of Au in oxidized sulfur solutions is comparatively scarce. A few experimental data on Au solubility in S-rich oxidizing (H2SO4) and saline solutions have been reported (Guo et al., 2018). In these experiments, the effect of H2SO4 was nowhere near as great at that of NaCl. There was, nevertheless, some increase in Au solubility as the H2SO4 content of the

6.7 Minor and trace elements in aqueous fluid

453

fluid increased (Fig. 6.118A). Interestingly, the effect of oxygen fugacity in the range from slightly above that of the QFM oxygen buffer to about five orders of magnitude above, is small whether or not saline solutions were employed (Fig. 6.118B). From the Raman spectra of the solutions, it was established that under all these circumstances sulfur existed solely as H2SO4 and SO2 (Guo et al., 2018). The experimental data base describing Au solubility in solutions contained reduced sulfur species is considerably more extensive than that describing solution behavior under oxidizing conditions (Gibert et al., 1998; Zezin et al., 2011; Trigub et al., 2017). Under these conditions, solution mechanisms described by an expression such as; xAuðsÞ þ yH2 S þ zHS
¼ Aux Hð2xþz
xÞ Sz
yþz þ x=2H2 ðgasÞ;

(6.78)

FIGURE 6.118 A. Gold solubility in H2OeHCl (3.5 wt%) -NaCl (20 wt%)-H2SO4 solution as a function of H2SO4 concentration at 800 C and 200 MPa. B. Gold solubility in H2OeHCl (3.5 wt%) -NaCl (20 wt%)-H2SO4 solution (0 and 16.4 wt% H2SO4) as a function of oxygen fugacity at 800 C and 200 MPa as a function of H2SO4 concentration at 800 C and 200 MPa. Modified after Guo et al. (2018).

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Chapter 6 Structure and properties of fluids

have been proposed (Gibert et al., 1998). In general, the solubility of Au in the presence of essentially all reduced sulfur, is positively correlated with concentration of H2S (Fig. 6.119; see also Triub et al., 2017). The Au solubility also increases rapidly with increasing pH (Fig. 6.119B). The Au solution mechanism can then be described with an expression of the type; þ AuðsÞ þ 2H2 SðaqÞ ¼ AuðHSÞ
2 þ H þ 0.5H2 ;

(6.79)

Eq. (6.79) illustrates, therefore, how pH and redox conditions play a role in the solubility of Au in reduced sulfur solutions. For example, Pokrovski et al. (2008) concluded that AuHS complexes dominated with pH < 5, whereas at higher pH conditions, the dominant Au species was Au(HS)
2 (Fig. 6.119C). Notably, sulfur species of this kind were also inferred from Au L3-edge X-ray absorption (Trigub et al., 2017). Interestingly, the fluid/melt partition coefficient for Au, as well as other transition metals such as Ag, Cu, and Zn, decrease rapidly with decreasing pressure under fixed pH conditions. The mechanisms proposed so far do not consider the S-3 ion proposed by Pokrovski and Dubrovinsky (2011) originally inferred from the Raman spectra of sulfur-bearing aqueous solutions to pressures above 0.5 GPa at comparatively low temperature (250 C) (Pokrovski and Dubrovinski, 2011; Pokrovski and Dubessy, 2015). It has been proposed from experimental results that an Au complex resembling Au(HS)S
3 , existed as one of the Au complexes (Pokrovski et al., 2015; see also Fig. 6.120). It was also proposed that the increased Au solubility exists in a narrow pH-range between about 3 and 6 and a log fO2-range between
21 and
23 at 450 C and pH ¼ 5. This fO2-range is near that of the MH oxygen buffer at the 450 C of the experiments (Fig. 6.120). As can be seen in the data summary in Fig. 6.120, the Au solubility can be as much as nearly two orders of magnitude higher than Au complexes with conventional sulfide anions. Pokrovski et al. (2015) proposed that this solution mechanism would be a much more efficient dissolution, and therefore, transport mechanism of Au in epithermal magmatic porphyry deposits.

6.7.4.2 Ag solubility The silver solubility and speciation in S-bearing aqueous solutions depends on pH and temperature. The principal reactions are pH-dependent (Stefansson and Seward, 2003; Tagirov et al., 2006) perhaps in a manner similar to that of Au. The total silver solubility is temperature dependent at the 50 MPa pressure where the experiments were conducted. However, Pokrovski et al. (2008) observed a decreased Ag solubility with increasing pressure. Notably, there is a narrow pH-interval with the greatest Ag solubility although both the pH-width and the total Ag solubility increases systematically with increasing temperature (Stefansson and Seward, 2003; Tagirov et al., 2006; see also Fig. 6.121). Under acid conditions, the solubility reaction is (Stefansson and Seward, 2003): 0.5Ag2 SðxtalÞ þ 0.5H2 SðaqÞ ¼ AgHSðaqÞ.

(6.80)

Under near neutral conditions, the expression describing the equilibrium is: 0.5Ag2 SðxtalÞ þ 0.5H2 SðaqÞ þ HS
¼ AgðHSÞ
2;

(6.81)

and under alkaline conditions, the dominant equilibrium is: 0.5Ag2 SðxtalÞ þ 2HS
¼ Ag2 SðHSÞ2
2 .

(6.82)

6.7 Minor and trace elements in aqueous fluid

455

FIGURE 6.119 Solubility of gold in sulfur-bearing systems. (A) Solubility of Au in HeOeS solutions as a function of pH at 450 C and 100 MPa with molality of H2S, mH2S ¼ 1, and hydrogen fugacity, fH2 ¼ 0.1 MPa. (B) Solubility of Au in HeOeS solutions as a function of H2S concentration, mH2S, at 450 C and 100 MPa and pH ¼ 3  0.2. (B) Speciation of Au-sulfide complexes in HeOeS solutions as a function of pH and total Au content of solution. Modified after (A) Trigub et al. (2017); (B) Pokrovski et al. (2008).

456

Chapter 6 Structure and properties of fluids

FIGURE 6.120 Gold concentrations and speciation in HeOeS fluids in equilibrium with gold. (A) As a function of oxygen fugacity at 450 C, 75 MPa, pH ¼ 5 and with 10 wt% NaCl. (B) As a function of pH at 400 C, 50 MPa, 1 wt% S, 10 wt% NaCl, and (C) as a function of pressure at 500 C, 2 wt% S, pH ¼ 4e6, H2S/SO2 ¼ 1:1, and 3 wt% NaCl. Modified after Pokrovski et al. (2015).

6.7 Minor and trace elements in aqueous fluid

457

FIGURE 6.121 Solubility of silver species in HeOeS solutions as a function of Ag concentration with total sulfur content, mS ¼ 0.1 molal at different temperatures as indicated on individual diagrams. Modified after Stefansson and Seward (2003).

With increasing temperature, the abundance curve in Fig. 6.121 becomes increasingly asymmetric toward the higher pH values where Eq. (6.82) dominates. However, Eq. (6.80) exhibits the broadest pH range over which it plays a role.

6.7.4.3 Cu solubility As is often the case with transition metals, the solubility and fluid/melt partition coefficients of copper in aqueous solutions increases significantly through formation of sulfide-bearing complexes (Crerar and Barnes, 1976; Mountain and Seward, 2003; Nagaseki and Hayashi, 2008; Pokrovski et al., 2008; Etschmann et al., 2010; Frank et al., 2011). In its most general form, the solution mechanism of Cu2S in sulfide-bearing aqueous solutions can be expressed as (Mountain and Seward, 2003); 2xCu2 SðxtalÞ þ ðy
2xÞHS
¼ Cux Sy Hx¼z
27 þ ðy
z
2xÞHþ z

(6.83)

458

Chapter 6 Structure and properties of fluids

FIGURE 6.122 Logarithm of the equilibrium constant for Eq. (6.84) as a function of temperature (1/T). Modified from Mountain and Seward (2003). Also included are data from Mountain and Seward (1999) and Crerar and Barnes (1976).

This general reaction can be broken down into simpler expression, similar to the Ag solubility expressions above, depending on pH as well as temperature and pressure. The expression for the effect of pH near neutral is (Mountain and Seward, 2003): 0.5Cu2 SðxtalÞ þ 1; 5HS
þ 0.5Hþ ¼ CuðHSÞ
2.

(6.84)

The logarithm of the equilibrium constant for Eq. (6.84) is a somewhat nonlinear function of 1/T (Fig. 6.122). This curvature suggests in its simplest form that the enthalpy change for Eq. (6.84) is temperature dependent. Another, perhaps related, possibility, which has not been explored, is that more than one equilibrium joins the solubility environment with increasing temperature. The positive correlation between the equilibrium constant and 1/T in Fig. 6.122 implies that the Cu2S(xtal) solubility in sulfide-bearing aqueous solutions increases with increasing temperature. This is precisely what is seen in Fig. 6.122 (see also Etchmann et al., 2010). The decrease above about 400 C is because the measurements were in the vapor region, whereas at lower temperature, the solubility measurements were in the liquid region.

6.7.4.4 Zn solubility The solubility behavior of Zn in S-bearing aqueous solutions in many ways resembles that of Ag and Cu discussed above. The Zn solubility depends, therefore, on temperature, pressure, and pH. The basic solubility reaction was proposed by Bourcier and Barnes (1987) and is of the kind;

6.7 Minor and trace elements in aqueous fluid

ZnSðxtalÞ þ mH2 SðaqÞ þ nHS
¼ ZnðH2 SÞm
1ðHSÞn
2þn .

459

(6.85)




In this environment, the zinc solubility is a positive function of HS concentration in the aqueous fluid (Fig. 6.123). Individual equilibria, the predominance of which depends on pH, were proposed by Tagirov and Seward (2010); ZnSðxtalÞ þ H2 SðaqÞ ¼ ZnðHSÞ2 ðaqÞ

(6.86)

ZnðHSÞ
3;

(6.87)




ZnSðxtalÞHS þ H2 SðaqÞ ¼

and so forth. These principles are also in accord with the result of numerical simulation (Mei et al., 2016). The proportion of the individual species varies with both temperature and pH as illustrated with the examples in Fig. 6.123 (Tagirov and Seward, 2010). In these results, increasing temperature results in decreased abundance of the Zn(HS)
4 complex while the abundance of other Zn sulfide species is relatively insensitive to temperature. Compared with other published speciation data, Tagirov and Seward (2010) noted that the formation constants for the Zn(HS) 2 and Zn(HS)
3 were somewhat lower than published by others (Hayashi et al., 1990; Daskalakis and Helz, 1993). It was also noted that the total ZnS solubility in the Tagirov and Seward (2010) study was considerably lower than those of Hayashi et al. (1990) and Daskalakis and Helz (1993). Tagirov and Seward (2010) proposed that these differences resulted from problems with analytical methods in the earlier experimental studies The total Zn solubility is also sensitive to pH, with a solubility maximum near that of neutral pH, but slightly alkaline as the temperature is increased. The zinc solubility decreases rapidly with both increasing and decreasing pH (Fig. 6.124). This behavior is at least qualitatively similar to that of Ag and Cu.

FIGURE 6.123 Solubility of ZnS in NaHSeH2S solutions as a function of HS
concentration in solution, mHS-. (A) At 100 C and pH ¼ 6.1, and (B) At 350 C and pH ¼ 8.9. Modified after Bourcier and Barnes (1987).

460

Chapter 6 Structure and properties of fluids

FIGURE 6.124 Solubility of sphalerite, ZnS, in H2S solution as function of pH and total sulfur concentration, ms ¼ 0.1 at 15 MPa and various temperatures as indicated on the individual curves in the diagram. Modified from Tagirov and Seward (2010).

6.7.4.5 Mo solubility Experimental data on the solubility of Mo in sulfide-bearing aqueous solutions are surprisingly rare (Zhang et al., 2012). Zhang et al. (2012) noted, however, that the Mo solubility in S- and Cl-bearing solutions can be expressed as a function of temperature, sulfur and oxygen fugacity and the concentration of NaCl in solution in the 600e800 C temperature range at 200 MPa: log mMo ¼ 0.458$log f O2 þ 0.463$log f s2 þ 0.731 þ logm NaCl
1.57$1000=T þ 6.37.

(6.88)

As seen in Fig. 6.125, the Mo solubility increases with increasing temperature and increasing fO2, while increasing fS2 has the opposite effect on Mo solubility. The speciation of the Mo complex in solution depends on the activity of sulfide. For example, from in situ X-ray absorption spectroscopy (XAS), Zhang et al. (2012) concluded that the principal species 2
was a mixture of molybdate (MoO2
4 ) and thiomolybdate (MoO4-xSx , where x ¼ 1, 2, 3, 4). Again, the more oxidizing the conditions, the more soluble is Mo (Fig. 6.126). The x-value in the

6.7 Minor and trace elements in aqueous fluid

461

FIGURE 6.125 Solubility of MoS2 in NaCl-bearing, sulfur-containing aqueous fluid. (A) As a function of temperature at the magnetite (Fe3O4)-pyrrhotite (FeS) buffer. Notice that both fS2 and fO2 of this buffer changes with temperature, and, therefore also affect the data in this diagram. (B) MoS2 solubility as a function of oxygen fugacity at 700e800 C. C. MoS2 solubility as a function of sulfur fugacity at 700e800 C. Modified after Zhang et al. (2012).

462

Chapter 6 Structure and properties of fluids

FIGURE 6.126 Number of ligands surrounding S and O as a function of NaHS concentration in aqueous S-bearing solutions  at 80 MPa. (A) S- and O-ligands in partially S-replaced MoO2
4 species at 30 C. (B) S- and O-ligands in  C. species at 286 partially S-replaced MoO2
4 Modified after Liu et al. (2020).

thiomolybdate is a positive function of the concentration of HS-in the aqueous solution and where the exchange with sulfide is more rapid the lower the temperature. The fO2-dependent Mo solubility is, therefore, another example of enhanced solubility of oxycomplexes of HFSE in aqueous complexes. It also appears that for the group of elements forming

References

463

oxycomplexes in aqueous solution, one or more of the oxygens in this structure can be replaced by sulfur. As noted here, this is observed for Mo, and has also been observed for rhenates (Xiong and Wood, 2002). Sulfur substitution has also been observed in SiO4 tetrahedra under very reducing conditions (Hayashi and Tatsumisago, 2020).

6.8 Concluding remarks Fluids in system CeOeHeNeS play important roles throughout the silicate Earth although not much is known about fluid behavior at pressures exceeding the Earth’s transition zone. Other volatiles with more specialized properties include halogens, and in particular F and Cl, and noble gases. Noble gases have no great solvent capacity, while halogens can alter element solubility in aqueous fluids greatly. All the CeOeHeNeS components can exist in different oxidation states within the redox range of the silicate Earth. Oxidized species in fluids are H2O, CO2, N2, SO2 and SO3. Anionic complexes such
2
as OH
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Wang, Y., Cody, G., Cody, S.X., Foustoukos, D., Mysen, B.O., 2015. Very large intramolecular D-H partitioning in hydrated silicate melts synthesized at upper mantle pressures and temperatures. Am. Mineral. 100, 1182e1189. Watenphul, A., Schmidt, C., Jahn, S., 2014. Cr(III) solubility in aqueous fluids at high pressures and temperatures. Geochem. Cosmochim. Acta 126, 212e227. https://doi.org/10.1016/j.gca.2013.10.054. Watenpuhl, A., Wunder, B., Heinrich, W., 2009. High-pressure ammonium-bearing silicates: implications for nitrogen and hydrogen storage in the Earth’s mantle. Am. Mineral. 94, 283e292. https://doi.org/10.2138/ am.2009.2995. Watenphul, A., Wunder, B., Wirth, R., Heinrich, W., 2010. Ammonium-bearing clinopyroxene: a potential nitrogen reservoir in the Earth’s mantle. Chem. Geol. 270, 240e248. https://doi.org/10.1016/ j.chemgeo.2009.12.003. Watson, E.B., Wark, D.A., 1997. Diffusion of dissolved SiO2 in H2O at 1 GPa, with implications for mass transport in the crust and upper mantle. Contrib. Mineral. Petrol 130, 66e80. Webster, J.D., 1992. Water solubility and chlorine partitioning in Cl-rich granitic systems: effects of melt composition at 2 kbar and 800 C. Geochem. Cosmochim. Acta 56, 679e687. https://doi.org/10.1016/00167037(92)90089-2. Webster, J.D., Botcharnikov, R.E., 2011. Distribution of sulfur between melt and fluid in S-O-H-C-Cl-bearing magmatic systems at shallow crustal pressures and temperatures. Rev. Mineral. Geochem. 73, 247e283. https://doi.org/10.2138/rmg.2011.73.9. Webster, J.D., Kinzler, R.J., Mathez, E.A., 1999. Chloride and water solubility in basalt and andesite melts and implications for magma degassing. Geochem. Cosmochim. Acta 63, 729e738. Webster, J.D., Tappen, C.M., Mandeville, C.W., 2009. Partitioning behavior of chlorine and fluorine in the system apatite-melt-fluid; II, Felsic silicate systems at 200 MPa. Geochem. Cosmochim. Acta 73, 559e581. https:// doi.org/10.1016/j.gca.2008.10.034. Webster, J.D., Goldoff, B.A., Flesch, R.N., Nadeau, P.A., Silbert, Z.W., 2017. Hydroxyl, Cl, and F partitioning between high-silica rhyolitic meltseapatiteefluid(s) at 50e200 MPa and 700e1000 C. Am. Mineral. 102, 61e74. Weck, G., Eggert, J., Loubeyre, N., Deshiens, N., Bourasseau, J.-B., Maillet, J.-B., Mezouar, M., Hanfland, M., 2009. Phase diagrams and isotopic effects of normal and deuterated water studied via x-ray diffraction up to 4.5 GPa and 500 K. Phys. Rev. B 80. https://doi.org/10.1103/PhysRevB.80.180202. Weill, D.F., Fyfe, W.S., 1964. The solubility of quartz in H2O in the range 1000e4000 bars and 400e550 C. Geochem. Cosmochim. Acta 28, 1243e1255. https://doi.org/10.1016/0016-7037(64)90126-7. Wendlandt, H.G., Glemser, O., 1964. The reaction of oxides with water at high pressures and temperatures. Ang. Chim. 3, 47e54. Whittington, A., Richet, P., Holtz, F., 2000. Water and the viscosity of depolymerized silicate melts. Geochem. Cosmochim. Acta 64, 3725e3736. Wilke, M., Schmidt, C., Dubrail, J., Appel, K., Borchert, M., Kvashnina, K., Manning, C.E., 2012. Zircon solubility and zircon complexation in H2OþNa2OþSiO2Al2O3 fluids at high pressure and temperature. Earth Planet. Sci. Lett. 349e350, 15e25. Wilson, G.A., Eugster, H.P., 1990. Cassiterite solubility and tin speciation in supercritical chloride solutions. In: Spenser, R.J., Chouo, I.-M. (Eds.), Fluid-Mineral Interactions: A Tribute to H. P. Eugster. The Geochemical Society, pp. 179e195. Withers, A.C., Kohn, S.C., Brooker, R.A., Wood, B.J., 2000. A new method for determining the P-V-T properties of high-density H2O using NMR: results at 1.4e4.0 GPa and 700e1100 C. Geochem. Cosmochim. Acta 64, 1051e1057. Wohlers, A., Manning, C.E., 2009. Solubility of corundum in aqueous KOH solutions at 700 degrees C and 1 GPa. Chem. Geol. 262, 310e317. https://doi.org/10.1016/j.chemgeo.2009.01.025.

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CHAPTER

Water in magma

7

7.1 Introduction Water-rich magmatic processes are particularly important in and near convergent plate boundaries where H2O content of several wt% has been reported from melt inclusions in phenocrysts (Sisson and Layne, 1993). In other tectonic settings, the H2O content of mantle-derived magma typically is less than 1 wt% (Sobolev and Chaussidon, 1996). H2O profoundly affects melting temperatures and melting phase relations of upper mantle rocks. H2O causes solidus temperature reductions of hundreds of degrees and results in large changes of melt compositions on the solidus (Kushiro, 1978; Mysen and Boettcher, 1975; Kushiro, 1972, 1990; Till and Grove, 2012; Mitchell and Grove, 2015). Dissolved water also results in major changes in melt density, compressibility, viscosity and other transport properties and, therefore, magma aggregation and ascent mechanisms and rate (Watson, 1994; Behrens and Nowak, 1997; Schulz et al., 1996; Rich et al., 2000; Giordano et al., 2004; Bouhifd et al., 2015). In this chapter, we will discuss the solubility behavior and solution mechanisms of H2O in silicate melts such as natural magmatic liquids. As described in detail in Chapter 6, H2O also is a profound solvent of oxide components that make up the chemical composition of fluids in magmatic systems and may, therefore, change the chemical composition of source regions of hydrous magma (Manning, 2004; Mysen, 2014). In fact, silicate melts and water-rich fluids can become completely miscible under upper mantle temperature and pressure conditions (Shen and Keppler, 1997; Mibe et al., 2007). These features are, for the most part, discussed in Chapter 6.

7.2 Speciation and abundance Volatiles in the Earth’s interior chemically are in system HeOeCeNeS. Within this system, the speciation of the volatiles depends on fluid composition and redox conditions. Oxidized species are H2O, CO2, SO2, and N2, whereas the reduced fluid species in the Earth are dominated by CH4, NH3, H2S, and H2. Under all conditions, H2O is the dominant component with an abundance averaging around 400 ppm and representing around 60% of the Earth’s total volatile budget. In magmatic liquids, H2O in midocean ridge basalt and ocean island basalt typically is considerably less than 1 wt% (Sobolev and Chaussidon, 1996; Grove et al., 2012). In contrast, magma in subduction zone settings can contain more than 6 wt% H2O (Parman et al., 2011). In terms of abundance, the second and third most components are S and C in the 80e100 ppm abundance range and comprising about 20% each of Mass Transport in Magmatic Systems. https://doi.org/10.1016/B978-0-12-821201-1.00002-X Copyright © 2023 Elsevier Inc. All rights reserved.

483

484

Chapter 7 Water in magma

80

Percent

60

40

H 2O 20

C as 0

CO2

Sulfur

FIGURE 7.1 Relative abundance of the main volatiles in the Earth. Modified and redrawn after Jambon (1994).

the budget of volatiles (Jambon, 1994; see also Fig. 7.1). Nitrogen, is often used as a tracer of the behavior of volatiles. Its average abundance is, however quite low and seems to average near 10 ppm (Marty, 2012; Johnson and Goldblatt, 2015). This number is, however, somewhat uncertain because the nitrogen abundance in the Earth’s core is poorly constrained.

7.3 Principles of solubility Whether simple model system melt or chemically complex natural magma and regardless of the specific volatile component, the principles that govern solubility of volatiles in silicate melts are the same. These principles are illustrated in the schematic representation in Fig. 7.2. There is a pressure-temperature range within which volatile-saturated silicate melts and silicatesaturated volatiles coexist (“melt þ fluid” field in Fig. 7.2A). The boundary with silicate melt on the one side and silicate melt þ fluid on the other describes the solubility of the volatile component in the silicate melts. These principles are illustrated with the peridotite þ H2O and rhyolite þ H2O example in Fig. 7.2B. The immiscibility fields of rhyolite melt þ H2O and peridote þ H2O in Fig. 7.2B extend to about 1 and 4 GPa, respectively. The right side of the immiscibility field shows the boundary with fluid only. This boundary describes the solubility of silicate components in the fluid (see Chapter 6 for detailed discussion of fluids). The left side of the maximum describes the H2O solubility in the melt. At temperatures above the solvus (above the critical point, c.p., in Fig. 7.2), there is complete miscibility between silicate melt and aqueous fluid. The extent of the immiscibility field and the slope of the phase boundaries at temperatures below c.p. depend on pressure and temperature, itself (Holtz et al., 1995). The extent of the immiscibility shrinks with increasing pressure (Fig. 7.2A). The left and right slopes may be positive or negative functions of temperature. This slope depends on pressure and bulk chemical composition. It will also vary with the type of volatile component under consideration. The temperature/pressure coordinates of the critical point, c.p., are sensitive to bulk chemical composition, the composition of the volatile component, and pressure. For silicate þ H2O systems, the coordinates of the critical point ranges from about 1 GPa near 1200 C for granitic compositions to

7.4 H2O solubility

5

SUPERCRITICAL FLUID

P(1) P(2)>P(1)

aqueous fluid

silicate melt + fluid crystals +melt

2 1

silicate crystals +aqueous fluid Silicate

3

Volatile component

B

SUPERCRITICAL FLUID peridotite composition (~1200˚C)

UID FL

P(2)

Pressure, GPa

silicate melt

4

ME LT

A

485

rhyolite composition (~700˚C)

0 Silicate

H2 O

FIGURE 7.2 (A) Principles of phase relations and solubility in silicate systems coexisting with a single volatile component. (B) Solvus of peridotite-H2O and rhyolite-H2O in pressure-composition space. Redrawn after Bureau and Keppler (1999) and Mibe et al. (2007).

nearly 4 GPa near 1200 C for peridotite-H2O (Bureau and Keppler, 1999; Mibe et al., 2007). The coordinates of the solvus of basalt þ H2O molten systems falls in between the two extremes (peridotite and rhyolite) illustrated in Fig. 7.2B (Kessel et al., 2005). It is likely that this evolution of the solvus primarily reflects the silicate solubility in aqueous fluid because the silicate solubility in fluids typically is more sensitive to silicate composition than the H2O solubility in silicate melts. At given temperature and pressure, the silicate solubility in aqueous fluid decreases as the alkaline earth/alkali metal abundance ratio increases (Mysen et al., 2013). This ratio typically decreases in the order rhyolite > andesite/dacite > basalt > peridotite. Changes in redox conditions could also affect solvii. For example, a reduction of oxygen fugacity from that near the nickel-nickel oxide (NNO) to the iron-wu¨stite (IW) buffer would result in reducing the H2O concentration in the fluid to about 80% with the remainder being H2. Such a change in speciation of the fluid, in turn, would probably lead to an expansion of the immiscibility gap in Fig. 7.2 because the solubility of H2 in silicate melts is much less than H2O (Luth and Boettcher, 1986). Analogous situations are likely to be found in silicate-COH, silicate-NOH, and silicate-SOH systems because in all three cases, the volatile speciation is quite sensitive to redox conditions. The solubility and solution mechanisms of those latter volatiles in magmatic liquids at high temperature and pressure is discussed in Chapter 8.

7.4 H2O solubility Water in magmatic liquids has been of interest for more than 300 years. The first report on water solubility in magma was by Spallanzani (1792e1797) who attempted to determine water contents in basalt magma. His attempts were unsuccessful. Following that very early attempt, the first modern H2O solubility data were obtained by Goranson (1931) who conducted experiments on H2O solubility in molten granite. During the last 60þ years, students of water solubility in silicate melts often returned to experiments in compositionally simple

486

Chapter 7 Water in magma

r hy

and

20

esit e

10

rol i

te

SiO2

30

80

sa

lt

70 60

ba

M n+ O

50

mol %

< 1 GPa > 1 GPa

50

O3 Al 2

n/ 2

40

90

FIGURE 7.3 Distribution of bulk compositions in the system MnþNn/2eAl2O3eSiO2 (M ¼ alkali metals and alkaline earths) for which solubility of H2O in melts has been determined.

systems beginning with SiO2eH2O (Tomlinson, 1956; Kurkjian and Russel, 1958; Moulson and Roberts, 1961) before embarking on examination of chemically more complex melt systems, including natural magmatic liquids (Uys and King, 1963; Hamilton et al., 1964; Coutures and Peraudeau, 1981; Behrens et al., 2001; Mysen and Wheeler, 2000; Holtz et al., 1997; Behrens et al., 2001). A summary of compositions that have been studied experimentally shows that most experimental data of H2O solubility in magma have been conducted at pressures below 1 GPa (Fig. 7.3).

7.4.1 H2O solubility in simple system melts Experimental examination of H2O solubility in chemically simple systems is more common than studies of H2O solubility in chemically more complex magmatic liquids. This situation probably reflects the fact that it is technically simpler to develop solubility models from experiments with only one variable at the time, as can be done in simple system studies. Such information may then be extrapolated to magmatic liquid compositions. We will, therefore, first focus on H2O solubility in simple systems.

7.4.1.1 H2O solubility in SiO2 melt SiO2 is the compositionally simplest silicate melt in which H2O solubility has been studied. The information obtained from those studies forms the basis for subsequent experimental work in binary, ternary, and chemically more complex melts, including natural magmatic liquids. The early experimental examinations of the SiO2eH2O system were conducted at low H2O pressure and total pressure near ambient (Tomlinson, 1956, Kurkjian and Russell, 1958; Shackleford and Masaryk, 1976). Under those conditions, the H2O solubility is linearly proportional to the square

7.4 H2O solubility

487

FIGURE 7.4 Solubility of H2O in SiO2 glass and melt. (A) Solubility as a function of the square root of H2O pressure and pressures below ambient. and (B) Solubility as a function of the square root of H2O pressure at pressures above ambient. Redrawn after (A) Moulson and Roberts (1961) and (B) Holtz et al. (1997).

root of the H2O pressure, OPH2O (Fig. 7.4A). Such a relationship is what would be expected if all dissolved H2O simply breaks oxygen bridges and form SieOH bonding (Wasserburg, 1957): SiO2 þ H2O 5 2SiO(OH)2.

(7.1)

With increasing pressure, the linear relationship between OPH2O and water solubility in SiO2 melt disappears (Fig. 7.4B). The solubility in SiO2 melt increases with increasing pressure, but the relationship no longer is a linear function of OPH2O (Kennedy et al., 1962; Holtz et al., 1997). The rate of water solubility increase with pressure is also pressure-dependent. These changes may indicate that the DVof H2O solution in the melt is negative, but decreasingly so with increasing pressure. This inference is consistent with experimental data indicating that the partial molar volume of H2O in silicate melts decreases with increasing pressure, but that of coexisting silicate-saturated fluid decreasing even more so (Mysen, 2002a, 2002b; Sakamaki et al., 2009; Agee, 2008; Malfait et al., 2014).

7.4.1.2 H2O solubility in metal Oxide-SiO2 melt Addition of metal oxides to SiO2 melt adds complexity to the solubility behavior of H2O in the melts (Fig. 7.5). There is both increasing and decreasing H2O solubility depending on the metal oxide/SiO2 ratio (Kurkjian and Russell, 1958; Uys and King, 1963; Coutures and Peraudeau, 1981). The solubility initially decreases with increasing metal/Si-ratio before reaching a minimum

488

Chapter 7 Water in magma

FIGURE 7.5 Solubility of H2O in metal oxidedSiO2 melts as a function of composition. (A) Along binary metal oxide-SiO2 joins for compositions indicated and (B) as a function of Na2O/(Na2O þ CaO) ratio (molar) in the system Na2OeCaOeSiO2. Redrawn after (A) Kurkjian and Russell (1958) and (B) Coutoures and Peraudeau (1981).

value at intermediate SiO2 concentrations. As the SiO2 concentration is decreased further, the H2O solubility increases (Fig. 7.5A). This behavior remains at high pressure and temperature (Mysen and Cody, 2004). In mixed metal oxide silicate melts, the H2O solubility is positively correlated with the abundance of the most electropositive cation at both low and high pressure (e.g., increasing Na/Ca ratio; see Fig. 7.5B; see also Mysen and Cody, 2004). This is, of course, the situation in natural magmatic liquids where both alkali metals and alkaline earths can be found. For example, in comparing rhyolite and basalt melt, the former is dominated by alkali metals serving as network modifier, whereas in the latter, alkaline earths dominate (see Chapter 5). This means that the H2O solubility in rhyolite melt is greater than in basalt melt in part because of the different metal cation abundance in these different magma compositions. The solubility behavior illustrated in Fig. 7.5 also implies that H2O solubility is greater in alkali basalt than in tholeiite melt. Many of the features of H2O solubility in metal oxide melts at near ambient pressure remain under high-pressure conditions. For example, decreasing water solubility with increasing metal oxide/SiO2 ratio was reported in the ranges 0.8e2 GPa and 1000e1300 C for Na2OeSiO2 melts (Fig. 7.6A; see also Mysen and Cody, 2004). In other words, as a melt becomes more polymerized, the H2O solubility increases. In terms of natural magmatic liquids, this implies that the more felsic a magma, the greater the H2O solubility. This effect is in addition to the alkali metal versus alkaline earths discussed above. The solubility of H2O also varies with temperature, but is less sensitive to temperature than to pressure (Fig. 7.6B and C), as would also be expected from the principles illustrated in Fig. 7.2A.

FIGURE 7.6 H2O solubility in silicate melts as a function of temperature, pressure, and melt composition. (A) Solubility in Na2OeSiO2 melts at 0.8 GPa total pressure as a function of Na/Si ratio at two different temperatures as indicated. In these melts, the Na/Si ratio is equivalent to NBO/Si so that data show how H2O solubility decreases as a melt becomes depolymerized. (B) H2O solubility as a function of total pressure for two compositions as shown. Notice how the H2O is more sensitive to pressure, the more polymerized the melts (Na2O$4SiO2 with NBO/Si ¼ 0.5 and Na2O$2SiO2 with NBO/Si ¼ 1.0). (C) H2O solubility of H2O in Na2O$4SiO2 melt as a function of temperature at the two different pressures indicated. Notice how that temperature dependence becomes less negative with increasing total pressure. Redrawn after (AeC) Mysen and Cody (2004).

490

Chapter 7 Water in magma

3.0 meta-aluminous

H2O solubility in melt, mol %

3.5

2.5

2.0

1.5

peraluminous

peralkaline

1.0

-0.2

-0.1

0.0

0.1

Al/(Na+K)

FIGURE 7.7 Solubility of H2O in K2OeNa2OeAl2O3eSiO2 melt as a function of Al/(Na þ K). Notice that for peralkaline melt, the solubility decreases with alumina content and the melts become decreasingly peralkaline (Al2O3 increases), whereas for peraluminous melts, an increase of alumina content results in increasing H2O solubility. Redrawn after Dingwell et al. (1997).

The temperature effect on H2O solubility can change from negative to positive as the temperature or pressure is changed (Fig. 7.6C). The pressure at which this change occurs depends on the melt composition (Holtz et al., 1995). Increasing pressure shifts the silicate-rich limb in Fig. 7.2A toward more water-rich values. In other words, the H2O solubility increases with pressure (Fig. 7.6B). Interestingly, though, this pressure increase also depends on melt composition. The more polymerized the silicate, the more sensitive is its H2O saturation level to pressure (Fig. 7.6B). Furthermore, the slope of the silicate-rich limb of the solvus in Fig. 7.2A changes from negative toward positive with increasing pressure, which is what is also seen by comparing, for example, the solubility in Na2O$4SiO2 quenched melt with temperature at 0.8 GPa, where the solubility decreases with increasing temperature, and at 1.65 GPa where it does not (Fig. 7.6C).

7.4.1.3 H2O solubility in aluminosilicate melt Aluminosilicate systems are effective models of natural magmatic liquids (see also Chapter 5, Fig. 5.25). The solubility of H2O in aluminosilicate melts may, therefore, be employed as a proxy for the solubility of H2O in natural magmatic liquids. In general, the rules that govern temperature and pressure-dependent solubility in Al-free silicate melts also apply, at least qualitatively, to the solubility of H2O in aluminosilicate melts (Behrens, 1995;

7.4 H2O solubility

491

FIGURE 7.8 (A) Solubility of H2O in melts along the join SiO2eNaAlSi3O8 as a function of NaAlSi3O8 content at 1200 C and 200 MPa. (B) Solubility in melt along the KAlSi3O8eNaAlSi3O8 and LiAlSi3O8eNaAlSi3O8 and joins to illustrate the effect of changing charge-balancing cation. Mol % calculated with no. of oxygen equal to 8. Redrawn from (A) Holtz et al. (1997)) and (B) Romano et al. (1996).

Behrens et al., 2001). However, aspects of water solubility in aluminosilicate melts also are influenced by complex reactions involving Al3þ and the dual structural roles of metals as both charge-balancing and network-modifying cations.1 The proportion of the latter may change with H2O content of a melt. For example, as illustrated in Fig. 7.7 there is negative correlation between water solubility and Al2O3 content in peralkaline and a positive correlation with Al2O3 in peraluminous melts (Mysen, 2002; Dingwell et al., 1997; see also Chapter 5, Fig. 5.24). There is, therefore, a minimum solubility near the meta-aluminosilicate compositions (Fig. 7.7). For melts along this meta-aluminous join, water solubility increases with increasing Al2O3 (McMillan and Holloway, 1987; Holtz et al., 1997; see also Fig. 7.8A). In addition, the ionization potential of the metal cation or cations serving to charge-balance Al3þ in aluminosilicate melts also affects H2O solubility (Behrens et al., 2001; Romano et al., 1996; Mysen, 2002; see Fig. 7.8B). The more electronegative the charge-balancing cation, the lower is the H2O solubility in such melts. The water solubility in ternary aluminosilicate melts and chemically more complex natural magmatic liquids on both the peraluminous and peralkaline side of alkali metaaluminosilicate joins is greater than at the meta-aluminosilicate stoichiometry (Mysen, 2002; Dingwell et al., 1997). Excess Al3þ (Al/(K þ Na) > 0) has a much greater effect on H2O solubility than excess alkalis [(K þ Na)eAl>0]. From limited data in Ca-aluminosilicate melts (excess Ca2þ over that needed to charge-balance tetrahedrally coordinated cations such as Al3þ (0.5Ca2þ ¼ Al3þ), similar 1 The concept of charge-balance of Al3þ in aluminosilicate melts was discussed in detail in Chapter 5. Briefly, alkali metals and alkaline earths can serve as charge-balancing cations and also as network-modifying cations. Their respective roles in natural magma were summarized in Fig. 5.13.

492

Chapter 7 Water in magma

FIGURE 7.9 Solubility of H2O in tetrasilicate melts, Na2O$4SiO2 and CaO$4SiO2, as a function of Al2O3 added to illustrate both the effect of increasing Al2O3 content of the melt and the ionization potential, Z/r2, of the networkmodifying and charge-balancing cation. Redrawn after Mysen and Cody (2004).

solubility behavior has been reported (Fig. 7.9). However, in these latter melt compositions, the water solubility is less than for peralkaline alkali aluminosilicate melts (Mysen and Cody, 2004). This solubility difference diminishes as the melts become more aluminous. Water solubility and solution mechanisms for compositions along meta-aluminosilicate joins, SiO2eMnþ1/nAlO2, have attracted considerable attraction because of the relevance of such melts to our understanding of the role of H2O in natural magmatic liquids. This is particularly so for felsic melts such as those of rhyolitic and dacitic composition, which have a very high modal abundance of feldspar components (Goranson, 1938; Burnham, 1975; Silver and Stolper, 1989; Holtz et al., 1997; Kirschen and Pichavant, 2001; Behrens et al., 2001; Benne and Behrens, 2003). The water solubility of melts on SiO2eMnþ1/nAlO2 joins varies with compositional variables such as Al/(Al þ Si) (Holtz et al., 1997) and with the type of alkali metal or alkaline earth that serves to charge-balance in tetrahedral coordination (Romano et al., 1996; Holtz et al., 1997, Fig. 7.8). The typical systematic relation between property and ionization potential of metal cation does not, however, apply here as the Li-aluminosilicate shows much higher H2O solubility than either Na- or K-aluminosilicate melt. One might surmise that this is related to the significantly smaller ionic radius ˚ ) compared with Naþ (1.08A ˚ ) and Kþ (1.38A ˚ ), which may affect the electronic of Li4þ (0.78A 3þ environment surrounding the Al to the extent that H2O solubility is affected. Of course, lithium is not important in natural magmatic liquids, but may serve as a proxy for Mg2þ. If so, this may result in enhanced H2O solubility in Mg-rich magma.

7.4 H2O solubility

493

In mixed aluminosilicate melts, the H2O solubility is a nonlinear function of the metal oxide abundance ratios (Romano et al., 1996). This nonlinearity likely is because with two or more cations potentially available for charge-balance of Al3þ, there will be a nonrandom distribution of these cations among structural locations in the melt. This, in turn affects the H2O solubility.

7.4.2 Miscibility between hydrous melts and aqueous fluids Because H2O solubility in melts increases with increasing pressure and, at high pressure, with increasing temperature, there is a pressure-temperature coordinate at and above which there is complete miscibility between aqueous fluid and silicate melts. Such behavior was observed first in the SiO2eH2O system where the melting curve terminated in a second critical endpoint near 970 MPa and 1080 C (Kennedy et al., 1962). The mutual solubility of silicate in fluid and H2O in coexisting melt increases with increasing temperature and pressure and eventually reaches the critical endpoint (Fig. 7.2). The solvus thus obtained and the temperature/pressure coordinates of the critical endpoint depend on silicate composition. The pressure is lower the higher the metal oxide/SiO2 ratio and for fixed metal oxide/ SiO2 ratio the less electronegative the cation (illustrated with Naþ vs. Ca2þ in Fig. 7.10; see also Shen and Keppler, 1997; Bureau and Keppler, 1999; Sowerby and Keppler, 2000). Along the SiO2eNaAlO2 join, for example, the temperature of the critical point decreases isobarically with increasing Al/ (Al þ Si) (Shen and Keppler, 1997; Sowerby and Keppler, 1999). There remain, however, some uncertainty as to the quantitative details of this relationship. In chemically more complex systems, the topology of the solvus depends on other composition variables. For example, an increasing abundance of components that cause silicate depolymerization tends to reduce temperatures and pressures of the critical point (Sowerby and Keppler, 2002; Mysen, 2013). By adding Al2O3 to a hydrous Na silicate system, the melt limb of the solvus shifts to considerably more polymerized compositions (Bureau and Keppler, 1999). Moreover, it appears that both the solvus and pressure/temperature coordinates of the critical point are sensitive to the abundance ratios of alkaline earths versus alkalis (Fig. 7.10). It follows that in alkali-rich and silica-rich systems such as rhyolite and granite, the critical point tends to be in the 1e2 GPa range at temperatures less than 1000 C, whereas in alkaline earth-rich and silica-poor systems such as peridotite the critical point appears to occur at pressures in excess of 4 GPa and 1000 C (Bureau and Keppler, 1999; Stalder et al., 2001; Mibe et al., 2007; see also Fig. 7.2B). The critical point for basalt melt þ H2O is near 5  0.5 GPa and 1025  25 C (Kessel et al., 2005). It is not clear whether it is the ionization potential of the metal or the silica content that drive the immiscibility. However, increasing peralkalinity is known to decrease the temperature-pressure coordinates (Sowerby and Keppler, 2002). Addition of fluorine and boron oxide have the same effect.

7.4.3 Water solubility and mixed volatiles Characterization of silicate systems with mixed volatiles is important because not only will water solubility be affected, but the phase relations and degassing environment also will (Mysen and Boettcher, 1975; Eggler and Kadik, 1979; Wallace et al., 2003). The solidus temperatures are also affected as are the compositions of exsolved gases. Magma properties will also reflect the nature and proportion of mixed volatiles.

494

Chapter 7 Water in magma

FIGURE 7.10 Pressure-temperature trajectories of the critical point, c.p., for haplogranite and Ca-granite compositions. Insert shows schematic of the immiscibility field and the effect of ionization potential on the critical point illustrating expansion as the cation(s) become more electronegative. Redrawn from Bureau and Keppler (1999).

Experimental data from an environment where H2O is part of a fluid mixture with two or more components are relatively limited. Among those for which experimental data do exist, the most common mixture is H2O þ CO2 (Mysen, 1976; Holtz et al., 1993; Tamic et al., 2001; Behrens et al., 2009; Shishkina et al., 2010). Some solubility data also have been reported for silicate þ H2O þ H2 (Bezmen et al., 2011) and silicate þ H2O þ F systems (Holtz et al., 1993). In silicate melt þ H2O þ CO2 systems, the H2O solubility in melt is a positive function of the H2O/ (H2O þ CO2) abundance ratio (Fig. 7.11). The effect shown in Fig. 7.11 reflects both the mixing behavior of H2O þ CO2 fluid as well as possible effects of dissolved CO2 on the melt structure. The influence of H2 in H2O þ H2 mixtures on water solubility are different from that of CO2 in CO2þH2O mixtures (Schmidt et al., 1999; Bezmen et al., 2011). Bezmen et al. (2011) observed a maximum in total water solubility with 10 mol% H2 in the fluid (Fig. 7.12). Moreover, there appears to be a significant effect of silicate composition because the solubility of H2O þ H2 fluid increases as the melt became less silicate-rich (Bezmen et al., 2011). The solubility maximum near

7.4 H2O solubility

495

FIGURE 7.11 Solubility of H2O in rhyolite and basalt melt in equilibrium with H2O þ CO fluid at 200 MPa and 1100 C as a function of the molar proportion of those fluid species, (H2O/(H2O þ CO2))fluid. Redrawn from Tamic et al. (2001).

FIGURE 7.12 Solubility of H2O in simple binary and ternary melts as indicated on Figure as a function of mol fraction of H2 in H2þH2O fluid at 950 C and 200 MPa. Redrawn from Bezemen et al. (2011).

496

Chapter 7 Water in magma

H2/(H2þH2O) ¼ 0.1 makes it clear that the melt þ H2O þ H2 mixture cannot be treated as an ideal solution, a feature also noted by Luth and Boettcher (1986) in their study of freezing point depression caused by H2 at high pressure for various silicate compounds. Fluorine, which also affects silicate melt structure in many ways like H2O (see Chapter 8), results in increased H2O solubility (Sorapure and Hamilton, 1984; Holtz et al., 1993). It is not clear, however, whether this effect results from changes in melt structure by dissolved fluorine, thus causing increased water solubility, or from changes in the fluid speciation in the presence of fluorine. Most probably, it is the latter because the main effect on silicate structure by dissolved fluorine is depolymerization (Mysen et al., 2004) and, as noted above (Fig. 7.6), increasing NBO/T results in decreasing H2O solubility in silicate melts and increasing fluorine content, causing increasing NBO/T of the melt, results in H2O solubility increase.

7.4.4 Water solubility in natural magmatic liquids Water solubility in simple model composition and chemically complex natural melts (magmatic liquids) increases systematically with increasing pressure until the second critical endpoint is reached (see Paillat et al., 1992, for discussion of this concept). Silicate-rich fluids can no longer be distinguished from hydrous melts beyond the critical endpoint such as reported for melting of hydrous sediments in subduction zones, for example (Schmidt et al., 2004). Below these pressures and temperatures, water solubility in magmatic liquids (as in simple melts) increases systematically with increasing pressure (Zhang, 1999; Lesne et al., 2011; see Fig. 7.13). As for simple system melts, the H2O solubility in magmatic liquids is negatively temperature dependent at low pressure but gradually shifting to a positive one at higher pressure (Holtz et al., 1995; Shishkina et al., 2014). The water solubility in magma depends on all the compositional variables reported in simple systems. The solubility at given temperature and pressure does indeed increase with SiO2 content (Shishikina et al., 2014; see also 7.14). Furthermore, the electronic properties of the networkmodifying cations can have significant effects. For example, an increase of the ionization potential (Z/r2, where Z is formal electrical charge and r is ionic radius) of alkali metals results in increased water solubility in granitic melt compositions (Dingwell et al., 1997; see Fig. 7.15). When alkali metals are exchanged with alkaline earths, the water solubility, at least in a phonolite melt composition (essentially that of an alkali-rich and aluminous granite) actually decreases (Schmidt and Behrens, 2008). Finally, as noted by Dingwell et al. (1997), in felsic melt the water solubility increases with increasing peralkalinity and increasing peraluminosity from a minimum value near the metaaluminosilicate melt (Fig. 7.16). This trend is similar to that observed in simple ternary aluminosilicate melts (Mysen and Acton, 1999).

7.4.5 H2O solubility models for natural magma Several models have been proposed for calculation of H2O solubility in magmatic liquids (Spera, 1974; Burnham, 1975; Dixon and Stolper, 1995; Moore et al., 1998; Duan, 2014; Lesne et al., 2011). With the exceptions of the models developed by Stolper and coworkers and by Burnham (1975), the models are largely empirical and based on limited solubility data (see Zhang, 1999, for a review). Their broader applicability cannot be tested rigorously so that we will restrict ourselves to detailed

7.4 H2O solubility

497

FIGURE 7.13 Solubility of H2O in basalt and rhyolite melt as at function of pressure. Redrawn from compilation of data by Zhang (1999).

FIGURE 7.14 Solubility of H2O in natural magmatic liquids as a function of their SiO2 content at 500 MPa and 1200e1250 C. Notice how the solubility in these chemically complex systems follow the same pattern with increasing solubility as the melt becomes more polymerized as in simple binary and ternary melts. Redrawn from Shishikina et al. (2014).

498

Chapter 7 Water in magma

FIGURE 7.15 Solubility of H2O in granite composition melt with excess alkali metals added and identified with their ionization potential. Notice how the solubility increases systematically with increasing ionization potential, Z/r2. Redrawn from Dingwell et al. (1997).

examination of the models proposed by Burnham (1975) and Silver and Stolper (1985, 1989) and Dixon and Stolper (1995) with just brief comments on other H2O solubility models. The Burnham (1975) H2O solubility model relies on magma compositions being converted to what was referred to NaAlSi3O8 equivalent mole weights. Burnham (1975) then used the solubility equation; ! melt vXHmelt VHo O  V H2 O 2O  ; (7.2) ¼  2 vP RT vln amelt =vX melt H2 O

H2 O T

to calculate the solubility of H2O. In Eq. (7.2), XHmelt is mol fraction of H2O in melt, amelt H2 O is H2O 2O activity, VHo 2 O is molar volume of pure H2O, and V H2 O is the partial molar volume of H2O dissolved in the magma. An example from Burnham (1975) shows very good correspondence between solubility in magma with compositions ranging from basalt to pegmatite (Fig. 7.17). Interestingly, if, as often assumed, the partial molar volume of H2O in silicate melt is independent of melt composition, it follows from Eq. (7.2) that the activity of H2O in magma also is independent of magma compositions. The advantage of the Stolper and coworker model (Silver and Stolper, 1985, 1989; Dixon and Stolper, 1995) is its potential to characterize rigorously water solubility thanks to its structural foundation. It takes advantage of the fact that water dissolves partly as molecular H2O and partly as OH-groups that form bonding with metal cations and partly Si and Al in the aluminosilicate structure, melt

7.4 H2O solubility

499

FIGURE 7.16 Solubility of H2O in haplogranite melt as a function of its peralkalinity, (Na þ K)/Al. Notice how these solubility trends resemble those in simple ternary melts shown in Fig. 7.7. Redrawn from Dingwell et al. (1997).

H2O(melt) 5 O(melt) þ 2OH (melt),

(7.3)

where O(melt) denotes oxygen in the melt. This model does not distinguish between bridging and nonbridging oxygens. By fitting data of the proportion of molecular H2O and OH-groups in silicate quenched melts (glasses) from infrared spectra, and combining those results with an evaluation of the equilibrium between water as molecular H2O in melts and H2O in coexisting fluid, Dixon and Stolper (1995) reproduced the water solubility in a range of chemically simple as well as more complex natural basalt melts (Fig. 7.18). Even though the Stolper and coworkers solution model has the potential to characterize the solubility of water in natural magmatic liquids, much additional experimental data are

500

Chapter 7 Water in magma

FIGURE 7.17 H2O solubility in Columbia River basalt melt, Mt. Hood andesite, and Harding pegmatite melt as a function of pressure at 1100 C. Solid line shows the solubility in NaAlSi3O8 composition melt. Redrawn from Burnham (1975).

needed before it can be used with confidence for all melt compositions. It, thus, carries more promise than more recent empirical models (Moore et al., 1998; Liu et al., 2004; Lesne et al., 2011) or thermodynamically-based models where numerous fitting parameters are needed absent comprehensive thermodynamic data (Burnham, 1975; Duan, 2014). The OH/H2O ratio, which is an independent variable requiring determination, depends, however, on several factors including temperature above the glass transition. Details of the variations in OH/H2O are not as well-known as would be desired. We do know, however, that this ratio is a function of temperature (above the glass transition temperature) and bulk composition of magma (Dingwell and Webb, 1990; Nowak and Behrens, 1995, 2001; Shen and Keppler, 1995; Cody et al., 2020; Sowerby and Keppler, 1999). In addition, the Stolper and coworkers model relies on the assumption that the partial molar volume of H2O in silicate melts is the same. Many experimental studies have concluded that this is the case. (Silver et al., 1990; Ochs and Lange, 1997, 1999; Richet and Polian, 1998; Richet et al., 2000; Bouhifd et al., 2015). Moreover, if the partial molar volume were the same and melts and glasses and were independent of melt composition, the melt-H2O mixture would have to be nonideal. However, if that were the case, the conclusion by Burnham (1975) the magma-H2O can be treated as ideal solution clearly cannot be valid. Existing experimental data on H2O solubility in silicate melts are insufficient to ascertain which of those assumptions are invalid.

7.4 H2O solubility

501

FIGURE 7.18 Calculated H2O solubility from the model by Stolper and coworkers (see details in text) by comparing the results of Dixon et al. (1995) (solid dots) with the calculated data (solid line). Redrawn from Dixon et al. (1995).

Among the empirical models, Moore et al. (1998) used experimental data to calibrate an expression of the form;   a X P melt bi X þ d; (7.4) ln XH2 O ¼ þ þ c ln fHfluid 2O T T i fluid where XHmelt is the mol fraction of H2O in the melt, fHfluid is the fugacity of H2O in the fluid, P and T 2O 2O are pressure, and temperature (kelvin), and a, b, c, and d are empirical fitting parameters. Another empirical model is that of Liu et al. (2004), who arrived at a very simple relationship with which to calculate the equilibrium constant, K, for equilibrium (7.1): ln K ¼ ð2:88  0:37Þ  ð3567  296Þ=T. Lesne et al. (2011) derived an empirical model for H2O solubility in basalt melt:   melt;0 melt;0 ¼ X $f $exp  V ðP  1Þ ; XHmelt H2 O H2 O H2 O 2O

(7.5)

(7.6)

where P is pressure in bar.

7.4.6 Water solution mechanisms in magma The large effects of dissolved H2O on chemical and physical properties of silicate melts implies that H2O significantly affects silicate melt structure. From this information, it is, furthermore, clear that

502

Chapter 7 Water in magma

H2O solution mechanisms and their effect on magma properties and processes depend on both melt composition and pressure (Kushiro et al., 1968, 1976; Presnall and Gasparik, 1990; Xue and Kanzaki, 2004; Cody et al., 2005: Mitchell and Grove, 2015). As originally proposed by Wasserburg (1957) for solution of H2O in SiO2eH2O melt [see also Eq. 7.1], the structural response commonly proposed for solution of water in silicate melts of all kinds is formation of OH-groups formed by of cleavage of bridging oxygen bonds. Similar early suggestions were made by Hamilton et al. (1964) from their experiments on water solubility in natural magmatic liquids. However, the solution mechanisms are considerably more complex than that.

7.4.6.1 Dissolved water and melt polymerization The degree of silicate polymerization of hydrous melts has been determined in the few situations by 29 Si MAS NMR of quenched melts (Cody et al., 2005; Xue and Kanzaki, 2004). However, most experiments have focused on the speciation of dissolved H2O from which the response of the silicate structure was inferred by using, in principle, Eq. (7.1) or more complex versions of this expression. Nearly all published data on water speciation in silicate melts and glasses are from Fourier Transform Infrared Spectroscopy (FTIR). This technique utilizes the overtone band near 5200 cm1 for molecular H2O abundance (H2O) and a what has been proposed to be a combination band near 4500 cm1 as a measure of OH group abundance as. Scholze (1960) originally assumed this band assignment from infrared spectra of SiO2eH2O glasses. One of the problems with the latter band assignment is that if OH-groups form bonding with cations other than Si4þ and Al3þ in tetrahedral coordination, their presence will not be detected in the FTIR spectra near 4500 cm1 because the combination band of M-OH and H2O likely will result in a band frequency somewhere in the 20002500 cm1 range. This can be difficult to detect. Proton MAS NMR spectra will, however, in principle record such OH-groups (Eckert et al., 1988; Cody et al., 2020). Another complicating factor in the interpretation of infrared spectra of hydrous glasses is the influence of hydrogen bonding. Hydrogen bonding can play a significant role in hydrous glasses, but such bonding gradually diminishes with increasing temperature and generally is not detectable in melts abovew650 C (Mysen, 2012). Finally, hydrogen bonding affects IR band intensities and also, therefore, affects molar absorption coefficients (Valyashko et al., 1981). Hydrogen bonding also result in a shift of the OH stretch vibrations to lower frequency values in the vibrational spectra. It follows from this that OH/H2O abundance from proton NMR of glasses formed by temperature-quenching of melts would differ from that obtained by FTIR. In the following discussion, which relies heavily on FTIR data, when referring to OH-groups it is, therefore, implied that these are OH-groups that form bonding to tetrahedral Si4þ and Al3þ unless otherwise stated explicitly. Finally, the quenching rate to form a hydrous glass from a high-temperature hydrous melt can be a factor because the quenching rate causes changes in fictive temperature (Silver et al., 1990; Behrens and Nowak, 2003). The result is different OH/H2O ratio depending quenching rate. In fact, different fictive temperatures obtained by using different quenching rates sometimes have been used to deduce temperature-dependent structural changes in silicate melts (see, for example, Stebbins, 1988). It follows that the fictive temperatures for different composition quenched melts (glasses) with different OH/H2O evolution could simply be the result from the water speciation frozen in at different temperatures. The extent to which dissolved water affects depolymerization and aluminosilicate speciation of silicate melt structure is centrally important to characterize the formation, evolution, and crystallization

7.4 H2O solubility

503

of water-bearing magma because essentially all magma properties directly or indirectly depend on the silicate polymerization, NBO/T. The NBO/T of silicate melts varies with both melt composition and total water content. In most silicate melts, Hþ forms bonding with the nonbridging oxygen to form SieOH bonds, perhaps analogous to SieONa groups, AleOH and alkali and alkaline earth-OH bonds (Kummerlen et al., 1992; Zotov and Keppler, 1998; Zavelski and Salova, 2002; Cody et al., 2005, 2020). Water is, however, a less efficient depolymerization agent than alkali oxides because a portion of the dissolved water exists in molecular form (Zotov and Keppler, 1998; Mysen, 2007) a form that does not affect the silicate polymerization. That and the distinctly nonlinear evolution NBO/Si of a melt with increasing water content (Fig. 7.19) is consistent with several types of water species in hydrous silicate melts. In aluminosilicate melts, serving as proxies for natural magma, the NBO/T is more sensitive to H2O content than Al-free metal oxide silicate melts (Fig. 7.20). This implies, for example, that H2O dissolved in high-alumina basalt melt has a greater effect on their polymerization than H2O in tholeiite melt. The positive correlation between NBO/T from dissolved H2O and Al/(Al þ Si) of the melt would suggest that there is more than a single solution mechanism of H2O in aluminosilicate melts and natural magmatic liquids. In its simplest form, a solution mechanism of water in silicate melts may be described as (Stolper, 1982); H2O (molecular) þ O (melt) 5 2OH (melt),

(7.7)

with the equilibrium constant; K7:7 ¼ ðaOH ðmeltÞÞ2 =aH2 OðmolecularÞÞ$aO ðmeltÞ;

(7.8)

where aOH(melt) etc. is activity of the species in the subscript. In most treatments of this equilibrium, the activities are replaced with mol fractions. Justification of such an assumption can be found in relatively small values of heat mixing of silicate glass-H2O solutions (Clemens and Navrotsky, 1987;

FIGURE 7.19 Evolution of melt polymerization, NBO/T, of haploandesite as a function of concentration of dissolved H2O. Redrawn from Mysen (2014).

504

Chapter 7 Water in magma

FIGURE 7.20 Evolution of melt polymerization, NBO/T, of melts in the system Na2OeAl2O3eSiO2 as a function of H2O content and Al/(Al þ Si) of the melt. Note that the Al/(Al þ Si) value is near that found in most major igneous rocks. Redrawn after Mysen (2007).

Richet et al., 2004) and agreement between calculated and experimentally observed liquidus phase relations in calculations where aluminosilicate-H2O melts were assumed to behave as ideal solutions (Zheng and Nekvasil, 1996). A key variable in Eq. (7.7) is the oxygen activity. It varies with melt composition. For aluminosilicate melts, for example, a more complex expression describes the solubility behavior (Mysen, 2007): 2MAlSix O2xþ1 þ 3H2 O52ðAl::OHÞ þ Qn2 ðMÞ þ ð2x  1ÞQn .

(7.9)

In Eq. (7.9), the Al..OH implies that the Al..OH complex comprises 3 OH groups per Al3þ. According to this solution mechanism, an equivalent portion of M-cations serving as charge-balancers in the anhydrous melt becomes network-modifying in the hydrous melts. This structural feature drives the melt depolymerization. This structural feature likely is an explanation for the increasing rate of depolymerization of aluminosilicate melt by dissolved H2O the greater the Al/(Al þ Si) of the melt illustrated in Fig. 7.19. The third variable affecting H2O solution mechanism(s) in natural magma is the nature and proportion of alkali metals and alkaline earths and the proportion of such metals relative to SiO2 and (SiO2 þ Al2O3) concentration. One aspect of this mechanism is how SieOeSi bridges can be broken   Qn Mmþ þ H2 O5Qn1 ðOHÞ þ 2=mMmþ . (7.10)

7.4 H2O solubility

505

In Eq. (7.10), Qn(Mmþ) represents Q-species the nonbridging oxygen of which form bonding with a metal cation, M, with a positive charge, mþ. This M-cation is, therefore, a network-modifying cation. Given that even in binary metal oxide melts, there is a curved increase in Q-species abundance with increasing H2O content (Zotov and Keppler, 1998) mechanism (7.10) very likely contributes the solution behavior of H2O in silicate melts. Reaction (7.10) is an expression of silicate depolymerization where, therefore, NBO/Si increases. However, as the anhydrous NBO/Si of a melt increases, the extent to which the H2O causes depolymerization of the silicate decreases (Cody et al., 2005). This diminishing effect of dissolved water on melt polymerization via the evolving solution mechanisms above results in the decreasing effect of dissolved H2O on structure and, therefore, properties, of magmatic liquids as these become increasingly mafic. In other words, dissolved H2O in basalt melt has less of an effect on its NBO/T than on the NBO/T of a rhyolitic melt, for example. These relations also imply that any magma property that depends on melt polymerization, will become less dependent on water content the more mafic the melt. Such properties include transport properties (Chapter 9), thermodynamics of mixing (Chapter 4), and element partitioning between minerals and melts (Chapter 3). The NBO/Si evolution in Fig. 7.19 not only reflects nonlinear changes of SieOH/H2O abundance ratio as the anhydrous magma becomes more depolymerized, in addition to formation of (Si,Al)eOH-groups (depolymerization), isolated M-OH-groups also can form in water-bearing metal oxide silicate melts and their glasses (Xue and Kanzaki, 2004, 2008; Cody et al., 2005). Formation of isolated M-OH-groups transforms some of the M-cations from a network-modifying role to form these isolated M-OH complexes and, therefore, results in polymerization of the silicate melt structure. Their abundance increases as the metal oxide/silica ratio of a melt increases (Cody et al., 2005; Xue and Kanzaki, 2008). In aluminosilicate melts such as natural magmatic liquids, the concentration of M-OH bonds increases while AleOH bonding becomes less important with increasing NBO/T (Fig. 7.21). The extent of such interactions between melt structure and dissolved H2O is linked to bulk silicate compositions, water concentration, temperature, and pressure. The extent of SieOH bonding does not seem to be affected (Xue and Kanzaki, 2008). At comparatively low pressure, the Al3þ in AleOH bonds is in fourfold coordination (Xue and Kanzaki, 2008). However, with increasing pressure, an increasing proportion of sixfold coordinated Al3þ has been reported (Malfait et al., 2012). The NBO/Si of hydrous melts with increasing dissolved water as a function of the NBO/Si of the anhydrous equivalent evolves at a rate between that which would be expected if all Hþ acted as network-modifier and that where none of the Hþ serve as network-modifier. The actual values of NBO/ Si of hydrous melt mean that some of the OH-group formation is through isolated NaeOH complexes. A general expression of such a solution mechanism is (Cody et al., 2005; Xue and Kanzaki, 2004; Le Losq et al., 2015); (MO)n þ H2O ¼ [M(OH)2]m.

(7.11)

This equilibrium shifts to the right with decreasing Mnþ-cation radius (Xue and Kanzaki, 2004). Isolated [M(OH)2]m groups in melts also become increasingly important as the M-cation becomes more electronegative and as the abundance ratio, [M(OH)2]/SiO2, increases.

506

Chapter 7 Water in magma

FIGURE 7.21 Evolution of species with OH bonded to M-cation (in this case Ca) and Al for H2O-saturated melts along the join CaMgSi2O6eCaAl2Si2O8 as a function of CaAl2Si2O8 content. Redrawn after Xue and Kanzaki (2008).

As noted briefly above, formation of isolated M-OH-groups transforms some of the network-modifying M-cations from a network-modifying role to become part of these isolated M-OH-groups. A reaction with which to form such groups via interaction with the silicate structure can be written as;   (7.12) 2Q3 M mþ þ H2 O5½MðOHÞ2 m þ 2Q4 . Here, Q3(Mmþ) denotes a Q3-species with a metal cation, Mmþ, forming bonds with its nonbridging oxygen. In other words, formation of isolated [M(OH)2]m complexes results in polymerization of the silicate network (Cody et al., 2005; Xue and Kanzaki, 2004; Xue, 2009). This reaction mechanism becomes increasingly important as the extent of silicate depolymerization of the anhydrous silicate component, NBO/Si (anhydr), increases. In other words, the more mafic a magma, the more important is reaction (7.12) thus further diminishing the effect of dissolved H2O on the melt structure and melt properties.

7.4 H2O solubility

507

7.4.6.2 Water speciation, water concentration, temperature, and pressure The concentration of water dissolved as OH-groups, XOH(melt), and as molecular H2O, XH2O(molecular), in melts evolves as a function of total water concentration (Fig. 7.2). The reader is reminded, though, that the OH-groups shown in this figure are only those that form bonding with tetrahedrally coordinated cations such as Si4þ and Al3þ. It does not, therefore, consider OH-groups that form bonding with network-modifying cations such as alkali metals or alkaline earths. This latter mechanism also is operative in molten silicates (Xue and Kanzaki, 2004; Cody et al., 2005), but the extent to which this occurs and what factors control their abundance have not been established with precision. However, from a 1H MAS NMR spectra of quenched hydrous NaAlSi3O8 melt composition with up to w10 wt% H2O, the proportion of dissolved water as OH-groups increases rapidly throughout this water concentration range, whereas the proportion of molecular H2O reaches a maximum concentration at intermediate total water concentrations (Cody et al., 2020; see Fig. 7.23). The trend shown in Fig. 7.23 differs significantly, therefore, from that obtained by FTIR measurements of the same hydrous silicate glasses where, in fact, the proportion of OH-groups reaches a concentration maximum and that of molecular H2O increases continuously with increasing total water concentration of the sample in a way similar to the speciation evolution in Fig. 7.22. The difference between these data sets is striking. Most likely, the NMR data include all forms of OH-groups, and not only those linked to Si4þ and Al3þ, which may be the structural environment that gives rise to the 4500 cm1 band in the

FIGURE 7.22 Abundance evolution of OH-groups and molecular H2O in melts as a function of total H2O content. All data are from FTIR spectra. Diamonds are data from quenched NaAlSi3O8 and circles from quenched Na2Si4O9 melts. Open symbols represent molecular H2O and closed symbols OH-groups. As discussed in the text, the OHgroups at most are those forming bonding with tetrahedrally coordinated Si4þ and Al3þ only. Redrawn from Silver and Stolper (1989) and Zotov and Keppler (1998).

508

Chapter 7 Water in magma

FIGURE 7.23 Abundance evolution of OH-groups and molecular H2O in melts as a function of total H2O content in NaAlSi3O8 composition melt. As indicated on the Figure, the dashed lines are FTIR data (from Fig. 7.22; original data source: Silver and Stolper, 1989), whereas the solid lines with individual data points indicated are from 1H MAS NMR spectroscopy. Redrawn after Cody et al. (2020).

FTIR spectra. Clearly, this situation is considerably uncertain and requires further study. That concern notwithstanding, here we will discuss the FTIR data as if these reflect OH-groups only in linkage to the tetrahedrally coordinated cations, Si4þ and Al3þ. The trends of (Si,Al)eOH/H2O abundance ratio depend on silicate composition and, therefore, on melt structure. Expressed in terms of NBO/T of anhydrous and hydrous melt, it is clear that the effect of dissolved H2O on NBO/T of the melt decreases the more depolymerized the anhydrous melt (Fig. 7.24). In natural magma, this NBO/T effect means that the more mafic the magma, the smaller is the effect of dissolved water on its extent of polymerization. As discussed further below, this also means that the effect of dissolved H2O on magma properties become less the more mafic the magma. A comparison of OH/H2O abundance evolution determined by FTIR in two different silicate melts reveal significant differences between different melt compositions. This can be seen, for example, in comparing experimental data from Silver and Stolper (1989) and Zotov and Keppler. (1998)

7.4 H2O solubility

509

FIGURE 7.24 Evolution of the difference in hydrous and anhydrous melt melts as a function of their anhydrous NBO/Si. Also shown are the NBO/Si-values corresponding to the maxima in NBO/Si distribution of andesite/dacite and basalt melt as reported by Mysen and Richet (2005) and reproduced in simplified form in Chapter 5. Data from Cody et al. (2005).

(Fig. 7.22). In comparing such data, it must be kept in mind, however, that these are from quenched melts with different glass transition temperatures, which is the temperature where the water speciation is frozen in. At least two different suggestions have been offered to explain composition effects recorded in the OH/H2O ratio glasses formed by temperature-quenching of melts from temperatures above their melting points. Quench effect may be possible because there is a Gibbs free energy change of 25  5 kJ/mol for reaction (7.2) in rhyolite melt, which means that the OH/H2O-ratio decreases as a hydrous melt cools and eventually transforms to a hydrous glass. This would imply that one explanation for the data in Fig. 7.22 simply is that it is a record different glass transition temperatures for different melt compositions. The other explanation is that there is, in fact, a compositional effect on the temperature evolution of the OH/H2O abundance ratio. This latter explanation would also be consistent with recent 1H MAS NMR and FTIR data for quenched melts (glass) of Li2O$4SiO2 (LS4), Na2O$4SiO2 (NS4), and K2O$4SiO2 by Le Losq et al. (2015). They found that (OH/H2O)KS4 > (OH/ H2O)NS4 > (OH/H2O)LS4 even though the glass transition temperature, Tg, follows the pattern, Tg(LS4) > Tg(NS4) > Tg(KS4). We also need to evaluate how molecular H2O may be dissolved in a silicate melt. In general, it seems that three-dimensional cavities in the structure such as those that contain noble gases and other molecular species (e.g., Zhang et al., 2010), would be the most likely structural location for H2O molecules. In that case, the availability and accessibility of such locations govern the proportion of H2O dissolved in molecular form. The cavity abundance and access likely would increase as a melt becomes more polymerized, for example. This concept implies that there likely would be a maximum concentration of molecular H2O that could be dissolved in a given melt. This is exactly the effect

510

Chapter 7 Water in magma

observed from the proton MAS NMR spectra (Fig. 7.23). Translated to magmatic liquids, this concept implies that molecular H2O is more important the more felsic the magma. Given the complications arising by quenching a melt to a glass, a better understanding of the interaction between dissolved water and silicate melt structure is gained through measurements of water speciation in-situ while a hydrous melt is in equilibrium with aqueous fluid at pressures above ambient and high temperatures above those of the glass transition. Experiments of this nature also eliminate concerns that arise from hydrogen bonding because hydrogen bonding that involves molecular H2O and/or structurally bound OH-groups diminishes with temperature with a DH ¼ 10  2 kJ/mol (Mysen, 2010). Hydrogen bonding cannot be detected in vibrational spectra of hydrous melts or glass above about 600 C (Mysen, 2010). Water speciation in melts at temperatures above ambient has been investigated via hightemperature and high-pressure infrared (IR) absorption and Raman spectroscopy (Nowak and Behrens, 1995; Sowerby and Keppler, 1999; Behrens and Yamashita, 2008; Mysen, 2010; Chertkova and Yamashita, 2015). There is some discussion, however, as to possible pressure and temperature dependence of the molar absorption coefficients needed to quantify the IR results (e.g., Withers et al., 1999; Withers and Behrens, 1999; Mandeville et al., 2002; Behrens and Yamashita, 2008). That complication notwithstanding, it is clear from a comparison of OH/H2O recorded while the sample is at high temperature and pressure differs from that of the quenched melt (glass) recorded at ambient temperature and pressure with a significantly higher OH/H2O ratio (Fig. 7.25).

FIGURE 7.25 Abundance evolution of molecular H2O and OH groups bonded to Si4þ in Na2O$4SiO2 melt recorded with FTIR while the sample was at 900 C and after quenching to ambient conditions. Redrawn from Chertkova and Yamashita (2015).

7.4 H2O solubility

511

The equilibrium constant for reaction (7.2) as a function of temperature above the glass transition temperature typically follows a linear relationship of the form: ln K7:2 ¼ a=T þ b;

(7.13)

at temperatures above those of the glass transition. The temperature dependence depends on silicate composition and yields a DH for reaction (7.2) between w 25 and w42 kJ/mol (see the data from Ihinger et al., 1999; Nowak and Behrens, 2001; Botcharnikov et al., 2007; Behrens and Yamashita, 2008). There is a tendency toward increased DH-values with increasing silica content. One might surmise, therefore, that among hydrous silicate melts, DH for SiO2eH2O melt would be the largest. However, high-temperature, experimental data for melts the system SiO2eH2O do not appear to exist. Whether, or the extent to which, pressure affects the water speciation equilibrium (7.2) has been addressed only in a handful of experimental studies. Sowerby and Keppler (1999) concluded that with different total water contents and pressures from ambient to 1 GPa, the DH of this reaction was not sensitive to pressure, as did Zhang et al. (2000) for pressures 0.5 GPa. However, Hui et al. (2008) observed that DH did indeed decrease with increasing pressure to 3.8 GPa and that the rate of DHincrease also increased with increasing pressure. In other words, the water speciation reaction, Eq. (7.2), shifts toward increasing OH/H2O with increasing pressure. Such a shift would mean that increasing pressure results in increasing effects of dissolved H2O on the structure (and properties) of magmatic liquids. This means dissolved water becomes a more effective silicate depolymerizing agent in magmas the greater the depth. Moreover, from the results in Fig. 7.24, this effect decreases the more mafic the magma. There appears not to be experimental data on water speciation in silicate melts at pressures higher than the 3.8 GPa-data reported by Hui et al. (2008). First principles molecular dynamics simulations of hydrous SiO2 and MgSiO3 melts at 2000K have, however, been carried out to pressures near 90 GPa (Anderson et al., 2008; Mookherjee et al., 2008; Karki et al., 2010). From the results of those calculations, the proportion of both isolated H2O molecules and of OH-groups decreases with increasing pressure. However, the proportion of molecular H2O decreases much more rapidly than that of OH-groups, which leads to increased OH/H2O with increasing pressure (Karki et al., 2010), which is in agreement with the experimental results of Hui et al. (2008). Additional, H-species that are more polymerized than isolated OHgroups and single H2O molecules also are formed at these high pressures (Mookherjee et al., 2008; see also Fig. 7.26). In this process, the OeH bond distance increases as does fraction of protons bonded to oxygen. It follows that at these higher pressures the oxygen coordination number around H also increases from a value slightly above 1 at ambient pressure to more than 2 at pressures above 80 GPa. The lengthening OeH bond distance probably means that hydrogen bonding is less important in hydrous magma in the depth of the Earth than is the case for magmas at shallow depth.

7.4.7 H2O in magmatic liquids Water solubility in magmatic liquids qualitatively behaves as does the water solubility in ternary aluminosilicate melts. The H2O solubility increases systematically and nonlinearly with increasing pressure, for example (Zhang, 1999; Lesne et al., 2011; see Figs. 7.6 and 7.13). The temperature dependence changes from negative to positive with increasing pressure (Holtz et al., 1995). Just as for simple system melt, there is a negative temperature dependence of H2O solubility at low pressure before gradually shifting to a positive one at higher pressure (Holtz et al., 1995; Shishkina et al., 2014).

512

Chapter 7 Water in magma

FIGURE 7.26 Pressure-dependence of the speciation of H2O calculated by Karki et al. (2010). Shown in this figure are the species with 1, 2, and 3 oxygens forming bonding with hydrogen as a function of pressure. The increased coordination number is, thus, an expression of increasing polymerization of the H2O molecule with increasing pressure. Redrawn with information from Karki et al. (2010).

The H2O solubility also varies slightly with magma composition, which is again qualitatively similar to the variations observed for simpler binary and ternary melts (Figs. 7.6e7.9, 7.14). It is clear that water solubility at given temperature and pressure does indeed increase with SiO2 content (Shishikina et al., 2014; see also Fig. 7.14). The electronic properties of the modifying cations also can have significant effects (Fig. 7.9). There is a very clear positive correlation between water solubility and the ionization potential of the added alkali metal (Fig. 7.14). An increase of the Na/(Na þ K) ratio of granitic magma composition, for example, results in increased water solubility (Fig. 7.15; see also Dingwell et al., 1997). However, when alkali metals are exchanged with alkaline earths, the water solubility, at least in a phonolitic melt composition (essentially that of an alkali-rich and aluminous granite) actually decreases (Schmidt and Behrens, 2008). It is important to remember, however, that in aluminosilicate melts, including magmatic liquids, portions of the metal cations serve to chargebalance Al3þ in tetrahedral coordination and portions are network-modifiers (see Chapter 5). How the distribution of metal cations between these two structural roles may affect the solubility and solubility mechanisms of H2O in melts is not known, but likely will impact on the solubility of H2O in the magma and, therefore, magma properties. Finally, as noted by Dingwell et al. (1997), in felsic melt, the water solubility increases with increasing peralkalinity and increasing peraluminosity from a minimum value near the meta-aluminosilicate melt (Fig. 7.16), which is a trend similar to that in simple binary and ternary aluminosilicate melts (Mysen and Acton, 1999). It is possible to estimate the evolution of silicate polymerization of magma as a function of magma bulk composition by taking into account the various observed simple system-based compositional effect. When doing this, the NBO/T-evolution with total H2O content can be estimated from the data

7.4 H2O solubility

513

such as those in Fig. 7.19. The data for haploandesite is that from Mysen (2007) from which an exponential fit that links H2O content and magma NBO/T is; NBO=T ¼ 1:10  0:57e0:068XH2 O .

(7.14)

7.4.8 Properties and processes of hydrous magmatic liquids The decreasing slab H2O content with subduction depth probably means that for magma formed by partial melting in subduction zones (whether in the mantle wedge or the slab itself), the deeper the magma source the less H2O will be available for the magmatic liquids. If H2O saturation of the magma defines the degree of melting, the implication is that the deeper the melting, the smaller is the degree of melting (Fig. 7.27). The H2O released from the slab into the melting mantle wedge above the slab affects both magma properties, magma composition, and melting and crystallization temperatures. For example, partial melt formed in the presence of H2O is significantly more silicate and alkali metal rich than partial melts formed in the absence of H2O at the same pressure (Fig. 7.28; see also Mysen and Boettcher,

FIGURE 7.27 Evolution of H2O content of fluid released from slab material of basalt composition based on the stability relations of the relevant hydrous minerals in this material as indicated by arrow in the Figure. Notably, the exact depth where dehydration may take place is sensitive to the composition of the subducting material. The H2O content is expressed relative to the fluid content at the initial descent. Phase equilibrium data used to compute species evolution are from Poli and Schmidt (1998).

Chapter 7 Water in magma

4

B

H2O

50 ree le-f lati

For

20

Increa s H2O c ing onc.

0.75 Olivine

Vo

30

Hydro us

10

Mg SiO

3

Anhydrous

40

ste rite +Li qui En sta d tite +Li qui d

Plagioclase

Na AlS

A

iO

514

0.75 Quartz

Mg2SiO4 10

20

30

40

50 SiO2

FIGURE 7.28 Melt composition in equilibrium with mantle phases noting the effect of H2O. (A) Melt compositional evolution expressed in terms of endmembers, olivine, quartz and plagioclase showing liquid evolution with increasing H2O content. (B) Shift of the forsterite/enstatite liquidus boundary toward the SiO2 corner of thee Mg2SiO4dNaAlSiO4dSiO2 system as a function of H2O content. Note, in particular how the liquids are olivine normative under anhydrous conditions and quartz normative under hydrous conditions. Redrawn from (A) Mitchell and Grove (2015) and (B) Kushiro (1965a,b, 1969).

1975; Kushiro, 1987; Mitchell and Grove, 2015). In addition, at temperature and pressure conditions of partial melting in island arcs, water-rich fluid will dissolve considerably quantities of silicate components (Manning, 2004; see also Chapter 6), which ultimately will be incorporated into the partial melts, and therefore, result in additional changes of partial melts formed by partial melting above subducting slabs. Water dissolved in magmatic liquids affects their physical and chemical properties. These include transport properties (viscosity, diffusion, conductivity) and equation-of-state, in addition to melting and crystallization phase relations (Kushiro, 1972, 1987; Whittington et al., 2000; Richet et al., 1996, 2000; Nowak, 1997; Mitchell and Grove, 2015).

7.4.8.1 Melting and crystallization Melting temperatures and phase relations in the melting interval are profoundly dependent on the activity of H2O in the system. Details of melting phase relations were discussed in Chapters 1 and 2. Here, we will only address the central features of how H2O in solution in silicate melts influences this behavior. Temperatures of melting and crystallization and solubility of water in silicate melts are linked via the Van ’t Hoff equation. Solved for the activity coefficient of dissolved H2O, the activity of H2O, gH2O, is     DH To  TH2 O melt (7.15) $ ln gH2 O ¼  ln XHmelt 2O R To $TH2 O

7.4 H2O solubility

515

melt Here, gmelt H2 O is the activity coefficient of water in melt solution and XH2 O the mol fraction of H2O in the melt, DH the enthalpy of fusion of the silicate phase, To, is the melting temperature of the pure phase and TH2O the melting temperature in the silicate-H2O mixture. The bulk composition of magma in subduction zone environment differs significantly from magma formed near midocean ridges and ocean islands. The latter magma composition is tholeiitic, whereas magma in subduction zones typically are more silicate-rich and often is dominated by andesitic to dacitic compositions. This effect is illustrated in Fig. 7.28A (Mitchell and Grove, 2015) where the magma composition (shown in shaded region) shifts toward the SiO2-rich corner in silicate systems in the presence of H2O. Such an effect of H2O originally was observed by Kushiro (1969, 1972). It is illustrated in more detail with the shrinkage of the quartz liquidus volume in the system Mg2SiOrdNaAlSiO4dSiO2 in Fig. 7.28B. Such shifts reflect decreasing activity coefficient of SiO2 in the magma. That, in turn, is because of the break-up of three-dimensionally interconnected structure of the silicate melt by dissolved H2O. Aluminosilicate liquidus phase relations also change when H2O is added. For example, with increasing water pressure in the NaAlSi3O8eKAlSi3O8eSiO2 system, the liquidus volume of quartz expands relative to Na- and K-feldspar (Fig. 7.29; see also Bowen, 1948; Tuttle and Bowen, 1958; Luth et al., 1964). Further, as the water pressure is increased, the trajectory of the temperature minimum is toward the NaAlSi3O8 corner of the system as indicated by an arrow in Fig. 7.29. Qualitatively, one might infer from these relations that not only does the activity coefficient of SiO2 decrease more than those of the other components needed to form feldspar, but that there is also an effect of dissolved H2O on the activity of Na2O and K2O in the melt.

FIGURE 7.29 Liquidus surface in the system NaAlSi3O8dKalSi3O8dSiO2 at ambient pressure and at 1 GPa H2O pressure showing the boundary between quartz and feldspars. Arrow indicates the direction of shift of the quartz/ feldspar boundary with increasing H2O pressure. Redrawn from Tuttle and Bowen (1958) and Luth et al. (1964).

516

Chapter 7 Water in magma

7.4.8.2 H2O and element partitioning Changes in structure of magmatic liquids by dissolved H2O also affect crystal-melt trace element partitioning. These features are discussed in detail in Chapter 3. Here, we will only discuss some principles resulting from H2O dissolved in magma. The NBO/T of the melt is a principal variable governing partition coefficients (Jaeger and Drake, 2000; Walter, 2001; Kushiro and Mysen, 2002a) and NBO/T is affected by dissolved H2O (Figs. 7.19, 7.20, 7.24 and 7.30). It is, therefore, possible to estimate effects of H2O on mineral/melt partition coefficients provided that the relationship of dissolved H2O to the NBO/T of the magma can be estimated. Given that there is no unique expression that quantitatively describes the relationship between partition coefficients and melt polymerization (Mysen, 2007), here we will simply use an example for changing of the Mg partitioning between olivine and melt by adding H2O to the melt from Mysen (2014):

FIGURE 7.30 Estimated evolution of the NBO/T with H2O content of basalt and rhyolite melt based on the experimentally determined evolution for haploandesite (Fig. 7.19 and reproduced in this diagram) and the relationship between NBO/Si evolution with H2O content and the NBO/Si of anhydrous melt (see Fig. 7.24).

7.4 H2O solubility

ol XMg

Dolmelt  change Mg

¼ 100

!anhydrous 

melt XMg ol XMg

ol XMg

517

!hydrous

melt XMg !anhydrous

.

(7.16)

melt XMg

Analogous relations hold for other transition metals. A consequence of relationships such as illustrated in Fig. 7.31 is that when using partition coefficients from anhydrous systems to deduce petrogenesis in particular to island arc melting and crystallization environments where several weight percent H2O is dissolved in the magma, data from anhydrous systems cannot be applied to characterize the processes. The magnitude of the H2O effect will, of course, depend on the magnitude of the relationship between partition coefficients and NBO/T of the magma (see Chapter 3 for discussion of relationships between crystal/melt partition coefficients and NBO/T of the melt). The extent of the H2O effect will also depend on the bulk composition of the magma as its bulk composition also affects the evolution of NBO/T as a function of H2O content as discussed above. In general, the influence of H2O is greater the more silica-rich the magma so the rhyolite melts show greater effects of dissolved H2O than andesite melt and andesite melt greater effects than basalt melt on their NBO/T (Fig. 7.30) and, therefore, the mineral/melt partition coefficients (Fig. 7.31).

7.4.8.3 Water, melt structure, and hydrogen isotope fractionation Hydrogen isotope fractionation is a tool to model materials transport in geological processes (Hauri, 2002; Shaw et al., 2008; Mysen, 2013; Dalou et al., 2015). In order to do so, it is necessary to establish

FIGURE 7.31 Estimated evolution with H2O content of the melt of olivine-melt partition coefficients for Mg in basalt and rhyolite systems. As discussed in the text, the present calculation is based on the relationships between NBO/T and H2O content of different magma types as shown in Fig. 7.30 and on the known relationship between olivine-melt partition coefficients and NBO/T of the melts in anhydrous systems from Mysen (2007).

518

Chapter 7 Water in magma

how the structure of hydrous silicate melts and silicate-saturated aqiueous fluids may affect the D/H fractionation between melts, fluids, and crystalline materials. The influence of temperature on H/D fractionation between aluminosilicate melts and aqueous fluids in the 0.1e1 GPa pressure range and temperatures to 800 C yields DH-values on the order of 5 kJ/mol (Mysen, 2013), reflecting, therefore, energetically different bonding environments for hydrogen and deuterium in silicate-saturated fluid and water-saturated silicate melt. Interestingly, however, this energy difference appears to diminish with increasing pressure because of the shrinkage of the immiscibility volume with increasing pressure. Diminishing immiscibility volume would suggest greater structural similarity of coexisting melt and fluid. Relying on H and D MAS NMR, Wang et al. (2015) found that there is significant hydrogen isotope fractionation between coexisting structural units in the melt. This feature is important for controlling the effect of dissolved H2O in melts and fluid/melt H/D fractionation in hydrous magmatic systems (Dalou et al., 2015). From experiments carried out in-situ with hydrothermal diamond anvil cells in conjunction with vibrational spectroscopy, Dalou et al. (2015) found the temperature dependence of the fraction factor, afluid-melt 1000 $ ln afluidmelt ¼ 263  26=T 2  126  48;

(7.17)

where T is temperature in kelvin and a ¼ (D/H) /(D/H) (see also Fig. 7.32). By combining these latter data with published information on D/H ratios in melt inclusions from island arc magma (Shaw, 2008), Dalou et al. (2015) found, for example, that at typical island arc magmatic temperatures, the 1000$lnafluid-melt is in the range 102e218, and the fluid from the slab would be in the range 202e70&. More generally, by combining the temperature-dependent D/H fractionation between fluid and melt with typical D/H ratios of the mantle wedge in subduction zone and incorporating typical thermal gradients, the experimental D/H fraction data result in dD profiles such as those illustrated in Fig. 7.33. Notably, the dD increases (becomes less negative) from the mantle wedgee plate interface. Although some of this effect likely stems from the D/H fractionation within silicate species in silicate-saturated fluid, the 1H MAS NMR data of Wang et al. (2015), would indicate the D/ H fractionation among silicate species in the melts plays an important role. In other words, the structure of hydrous magma affects the D/H fractionation between hydrous magma and silicatesaturated aqueous fluids. Parenthetically, this feature likely also would lead to melt structural effects on D/H fractionation between hydrous magma and crystalline materials. fluid-melt

fluid

melt

7.4.8.4 Transport properties of hydrous magma Transport properties of hydrous magmatic liquids can differ by orders of magnitude from those of their anhydrous equivalent (Chekhmir et al., 1988; Richet et al., 1996; Hess and Dingwell, 1997). Melt viscosity, for example, decreases by several orders of magnitude with only a few percent dissolved H2O. There is, however, a greater effect on the viscosity of felsic magmas such as rhyolite as compared with the effect of H2O on the viscosity of basaltic magma (Dingwell et al., 1997; Giordano and Dingwell, 2003; see also Figs. 7.34 and 7.35). However, this difference decreases with increasing H2O concentration in a melt. This difference also diminishes as the H2O content in a magma increases (Fig. 7.35). In order to develop a better understanding of viscosity and the role of H2O in governing magma viscosity, the link between viscosity and configurational properties of silicate melts is useful

7.4 H2O solubility

519

FIGURE 7.32 Melt-aqueous fluid H/D fractionation factor as a function of temperature determined in-situ at high temperature and pressure. Redrawn from Dalou et al. (2015).

(Adam and Gibbs, 1965; Richet, 1984). Melt viscosity, h, can be expressed in terms of configurational entropy as;   h ¼ Ae exp Be = TSconf (7.18) where Ae and Be are constants, T is temperature, and Sconf is configurational entropy. The configurational entropy is linked to configurational heat capacity: S

conf

 h i ðT    conf Tg = Tg þ ðTÞ ¼ Cp Cpconf = T dT; Tg

(7.19)

520

Chapter 7 Water in magma

FIGURE 7.33 Estimated dD in melt above subducting plate as a function of distance from plate/wedge interface and assuming the dD of the unaltered mantle source to be 80&. Isotherms from Grove et al. (2012) and D/H fractionation data from Mysen (2013).

FIGURE 7.34 Viscosity of hydrous and anhydrous basalt and rhyolite melt as a function of temperature. H2O contents are given in parentheses. Redrawn after Giordano and Dingwell (2003).

where Tg is glass transition temperature, T is the temperature under consideration (T > Tg) and Cconf p (Tg) is the configurational heat capacity at the glass transition. The configurational heat capacity and, therefore, configurational entropy and viscosity of hydrous magmatic melts varies as a systematic function of H2O content (Richet et al., 1996; Bouhifd et al.,

7.4 H2O solubility

521

FIGURE 7.35 Viscosity of andesite magma as a function of H2O content at different temperatures. Redrawn from Richet et al. (1996).

2007). For example, the change in configurational heat capacity, DCconf p , across the glass transition increases from 2 J/mol K for anhydrous phonolite melt to about 7 J/mol K with 5 wt% H2O dissolved in the melt (Fig. 7.36). This DCconf is greater the higher the H2O content of a melt. This effect of p dissolved H2O, in turn, causes the viscous behavior of hydrous magma to become increasingly fragile in the terminology of Angell (1985). Increasing fragility implies increasing deviation of viscosity from Arrhenian behavior. Similar to most magma properties affected by dissolved H2O, the melt configurational properties and transport properties decay exponentially with increasing H2O content. Linking back to the solubility and solution mechanisms in magmatic liquids as a function of their degree of polymerization, NBO/T, it follows that the effect of dissolved H2O on magma viscosity depends on the composition of the magmatic liquid. The more felsic the magma, the greater is the effect of dissolved H2O on its NBO/T-values. This means that the more felsic the magma, the greater the effect of dissolved H2O on magma viscosity. By using the information in Fig. 7.24 together with Fig. 5.6 in Chapter 5, the effect of H2O on rhyolite melt is about 2e3 times greater than that of H2O on basalt melt, for example. The equation-of-state of hydrous magmatic liquids also differs significantly from their anhydrous equivalent given that the NBO/T of hydrous melts is greater than anhydrous ones and NBO/T increases with increasing H2O content. In order to address these effects, let us first focus on the partial molar volume of H2O. The partial molar volume of H2O in magmatic liquids typically has been determined by assuming that the volume of H2O in quenched silicate melts (hydrous glasses) can be used as a proxy for H2O in magma at high temperature and pressure. The H2O partial molar volume in such glasses has been reported to be independent of silicate composition, temperature, and pressure (Richet and Polian, 1998; Richet et al., 2000; Ochs and Lange, 1999). An early exception to this conclusion was that of Burnham and Davis (1971) who measured the partial molar volume directly at high

522

Chapter 7 Water in magma

FIGURE 7.36 Change in configurational heat capacity of phonolite melt across the glass transition as a function of H2O content of the melt. Redrawn from Bouhifd et al. (2007).

temperature and pressure and reported that both temperature and pressure affect the partial molar volume of H2O in aluminosilicate melts. It is emphasized here that the data indicating no compositional effects were obtained on quenched melts (glass), whereas the data indicating that there is a compositional effect on the partial molar volume of H2O were obtained on molten, hydrous aluminosilicate melts. Whether or not volume data obtained on glasses can be extrapolated to high-temperature melt also is open to serious concern in part because the thermal expansion coefficients of silicate glasses and melts differ (Bouhifd et al., 2001) and partly because there is extensive hydrogen bonding in hydrous glasses quenched from high temperature, which likely would affect the partial molar volume of H2O. There is no evidence of hydrogen bonding in hydrous melts at temperatures above their liquidus (Mysen, 2010). Direct measurement of partial molar volume of H2O in melts is a challenge because such measurements require conducting the measurements at magmatic temperatures. However, the partial molar volume also can be extracted from H2O solubility data from the expression; ! fH02 O RT melt ln melt . VH 2 O ¼ (7.20) P1 XH 2 O is partial molar volume of H2O in a melt, R is the gas constant, P is pressure, T In Eq. (7.20), VHmelt 2O is temperature (kelvin), f0H2O is the fugacity of pure H2O and Xmelt H2O is the mol fraction of H2O in a melt. Partial molar volume of H2O is linked to density of hydrous melt as;

7.4 H2O solubility P rTmelt ¼

i

523

Xi $Mwti T Vmelt

(7.21)

T is the molar volume of the melt, X is the mol faction where rTmelt is melt density at temperature, T, Vmelt i of component, i, and Mwti its molecular weight. For Na- and K-aluminosilicate melts, the relationship in Eq. (7.20) gives partial molar volume of H2O between 9.5 and 10.5 cm3/mol (Mysen, 2002) at pressures corresponding to deep continental crust. For alkaline earth aluminosilicate melts, the H2O solubility is slightly lower than for alkali

aluminosilicate melts, which results in VHmelt in alkaline earth aluminosilicate melts about 10% higher 2o than in alkali aluminosilicate melts (Mysen, 2002). This, in turn, implies that the effect of dissolved H2O on the volume and the density of basaltic magma is less than the effect of H2O on more felsic magma such as andesite, dacite, and rhyolite and that the density difference between anhydrous and hydrous magma increases with increasing H2O content and decreases with increasing total pressure (Fig. 7.37). From the H2O solubility data there is, however, a significant pressure effect with rapidly decreasing partial molar volume of H2O between ambient pressure to about 500 MPa. It follows that the density

FIGURE 7.37 Calculated density difference between hydrous (wt% H2O indicated) and anhydrous andesite magma as a function pressure/depth. Partial molar volume data for H2O fromMysen, 2002 and for oxide components from Lange (1997).

524

Chapter 7 Water in magma

difference between hydrous and anhydrous magma decreases with increasing pressure. There is less of a pressure effect at higher pressure (Fig. 7.37). The density of magmatic liquids in Fig. 7.37 can be employed, for example, to describe the density evolution of crustal magma chambers in the 3e10 km depth as the H2O of the magma is exsolved (Rutherford et al., 1985; Foden, 1987; Mandeville et al., 1996). Typical recent examples of such magma chambers are the one in Mt. Pinatubo (Philippines) with its most recent eruption in 1990, Mount St. Helens (USA) in 1980 and Mount Unzen (Japan) in 1991. The effect of dissolved H2O on magma chamber density for magma composition such as the dacite at Mount Pinatubo is shown in Fig. 7.38. In this figure, the density was calculated from the partial molar volumes of oxide components from Lange (1997) and the partial molar volume data of dissolved H2O from Mysen and Acton (1999). The decreasing density difference with increasing pressure results from decreasing VHmelt with 2o increasing pressure.

FIGURE 7.38 Evolution of the partial molar volume in haploandesitic melt and silicate-saturated aqueous fluid as a function of pressure. Data from Mysen, 2002.

7.5 Concluding remarks

525

FIGURE 7.39 Energy release from H2O exsolved from magmatic liquids. (A) Energy release from tholeiite and andesite/ dacite magma as a function of depth of release of H2O. The difference between these two magma compositions is because of differences in partial molar volume of H2O. (B) Energy release from historic andesite/dacite eruptions based on estimated depth of H2O release, volume of magma chamber, and degree of crystallinity at the time of eruption. Data used for the calculations and can be found in Mysen, 2002, 2007.

The energy released by exsolution of the H2O during an eruption from shallow crustal magma chambers may also be estimated with the aid of the volume data. In such an estimate, the partial molar volume of silicate-saturated aqueous fluid also needs to be assessed. Mysen and Acton (1999) reported the relationship between pressure and partial molar volume of aqueous fluid in equilibrium with aluminosilicate melt (Fig. 7.39). The resultant energy release (Fig. 7.39A) shows a small compositional effect. This is because of a effect of silicate melt composition on H2O solubility and, therefore, partial molar volume of dissolved H2O (Mysen and Acton, 1999). This information, in turn, can be employed to compute the energy release caused by exsolution of H2O in a number of recent eruption (Fig. 7.39B). The H2O concentration in those magma chambers prior to eruption was estimated from estimated depth of the magma chamber and degree of crystallinity.

7.5 Concluding remarks Characterization of the behavior of H2O in hydrous magma is critical to our understanding transport processes and how these properties depend sensitively on how chemical composition, temperature, and pressure govern the physicochemical properties of these materials. These properties comprise viscosity, diffusion, thermodynamics of mixing, element partitioning between phases, phase relations etc.

526

Chapter 7 Water in magma

Structural information on magmatic liquids and the links between their structure and properties often cannot be obtained directly by studying chemically complex natural systems because the resolving power of spectroscopic methods employed for such purposes diminishes rapidly with increasing chemical complexity. However, structural data from simpler binary and ternary systems can be expanded to chemically more complex systems. A successful use of this approach requires, however, detailed characterization of silicate speciation in fluids and melts as a function of Al/Si-ratio, the type of charge-balance for tetrahedrally coordinated cations, and the type and proportion of network-modifying metals (alkali metals and alkaline earths). Available data permit application to felsic magmatic systems.

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Mysen, B.O., 2002b. Solubility of alkaline earth and alkali aluminosilicate components in aqueous fluids in the Earth’s upper mantle. Geochim. Cosmochim. Acta 66, 2421e2438. Mysen, B.O., 2007. Olivine/melt transition metal partitioning, melt composition, and melt structure e influence of Si4þ,Al3þ substitution in the tetrahedral network. Geochem. Cosmochim. Acta 71, 5500e5513. Mysen, B.O., 2010. Structure of H2O-saturated peralkaline aluminosilicate melt and coexisting aluminosilicatesaturated aqueous fluid determined in-situ to 800 C and w800 MPa. Geochem. Cosmochim. Acta 74, 4123e4139. Mysen, B.O., 2012. Silicate-COH melt and fluid structure, their physicochemical properties, and partitioning of nominally refractory oxides between melts and fluids. Lithos 148, 228e247. Mysen, B.O., 2013. Effects of fluid and melt density and structure on high pressure and temperature experimental studies of hydrogen isotope partitioning between coexisting melt and aqueous fluid. Am. Mineral. 98, 1754e1764. Mysen, B.O., 2014. Water-melt interaction in hydrous magmatic systems at high temperature and pressure. Prog. Earth Planet. Sci. 1, 4. https://doi.org/10.1186/2197-4284-1-4. Mysen, B.O., Boettcher, A.L., 1975. Melting of a hydrous mantle: II Geochemistry of crystals and liquids formed by anatexis of mantle peridotite at high pressures and high temperatures as a function of water, carbon dioxide and hydrogen activities. J. Petrol. 16, 549e593. Mysen, B.O., Cody, G.D., Smith, A., 2004. Solubility mechanisms of fluorine in peralkaline and metaaluminous silicate glasses and in melts to magmatic temperatures. Geochem. Cosmochim. Acta 68, 2745e2769. Mysen B, O., Mibe, K., Chou, I.-M., Bassett, W.A., 2013. Structure and equilibria among silicate species in aqueous fluids in the upper mantle: experimental SiO2-H2O and MgO-SiO2-H2O data recorded in-situ to 900 C and 5.4 GPa. J. Geophys. Res. 118, 6076e6085. Mysen, B.O., Acton, M., 1999. Water in H2O-saturated magma-fluid systems: solubility behavior in K2O-Al2O3SiO2-H2O to 2.0 GPa and 1300 C. Geochem. Cosmochim. Acta 63, 3799e3818. Mysen, B.O., Wheeler, K., 2000. Solubility behavior of water in haploandesitic melts at high pressure and high temperature. Am. Mineral. 85, 1128e1142. Mysen, B.O., Cody, G.D., 2004. Solubility and solution mechanisms of H2O in silicate melts and glasses at high pressure and temperature. Geochem. Cosmochim. Acta 68, 5113e5127. Mysen, B.O., Richet, P., 2005. Silicate Glasses and Melts: Properties and Structure. Elsevier, Amsterdam, 548 pp. Nowak, M., Behrens, H., 1995. The speciation of water in haplogranitic glasses and melts determined by in-situ near-infrared spectroscopy. Geochem. Cosmochim. Acta 59, 3445e3450. Nowak, M., Behrens, H., 1997. An experimental investigation on diffusion of water in haplogranitic melts. Contrib. Mineral. Petrol. 126, 365e376. Nowak, M., Behrens, H., 2001. Water in rhyolitic magmas: getting a grip on a slippery problem. Earth Planet Sci. Lett. 184, 515e522. Ochs, F.A., Lange, R.A., 1997. The partial molar volume, thermal expansivity, and compressibility of H2O in NaAlSi3O8 liquid: new measurements and an internally consistent model. Contrib. Mineral. Petrol. 129, 155e165. Ochs, F.A., Lange, R.A., 1999. The density of hydrous magmatic liquids. Science 283, 1314e1317. Paillat, O., Elphick, E.C., Brown, W.L., 1992. The solubility behavior of H2O in NaAlSi3O8 melts: a reexamination of Ab-H2O phase relationships and critical behavior at high pressure. Contrib. Mineral. Petrol. 112, 490e500. Parman, S.W., Grove, T.L., Kelley, K.A., Plank, T., 2011. Along-arc variations in the pre-eruptive H2O contents of Mariana arc magmas inferred from fractionation paths. J. Petrol. 52, 257e278. Poli, S., Schmidt, M.W., 1998. The high-pressure stability of zoisite and phase relationships of zoisite-bearing assemblages. Contrib. Mineral. Petrol. 130, 162e175.

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Presnall, D.C., Gasparik, T., 1990. Melting of enstatite (MgSiO3) from 10 to 17.5 GPa, and the forsterite (Mg2SiO4) e majorite (MgSiO3) eutectic at 17.5 GPa: implications for the origin of the mantle. J. Geophys. Res. 95, 15771e15778. Richet, P., 1984. Viscosity and configurational entropy of silicate melts. Geochem. Cosmochim. Acta 48, 471e483. Richet, P., Polian, A., 1998. Water as a dense icelike component in silicate glasses. Science 281, 396e398. Richet, P., Whittington, A., Holtz, F., Behrens, H., Ohlhorst, S., Wilke, M., 2000. Water and the density of silicate glasses. Contrib. Mineral. Petrol. 138, 337e347. Richet, P., Lejeune, A.-M., Holtz, F., Roux, J., 1996. Water and the viscosity of andesite melts. Chem. Geol. 128, 185e197. Richet, P., Hovis, G., Whittington, A., Roux, J., 2004. Energetics of water dissolution in trachyte glasses and liquids. Geochem. Cosmochim. Acta 68, 5151e5158. Romano, C., Dingwell, D.B., Behrens, H., Dolfi, D., 1996. Compositional dependence of H2O solubility along the joins NaAlSi3O8-KAlSi3O8, NaAlSi3O8-LiAlSi3O8, and KAlSi3O8-LiAlSi3O8. Am. Mineral. 81, 452e461. Rutherford, M.J., Sigurdsson, H., Carey, S., Davis, A., 1985. The May 18, (1980, eruption of Mount St. Helens; 1, Melt composition and experimental phase equilibria. J. Geophys. Res. 90, 2929e2947. Sakamaki, T., Ohtani, E., Urakawa, S., Suzuki, A., Katayama, Y., 2009. Measurement of hydrous peridotite magma density at high pressure using the X-ray absorption method. Earth Planet Sci. Lett. 287, 293e297. Schmidt, B.C., Behrens, H., 2008. Water solubility in phonolite melts: influence of melt composition and temperature. Chem. Geol. 256, 259e268. Schmidt, B.C., Holtz, F., Pichavant, M., 1999. Water solubility in haplogranitic melts coexisting with H2O-H2 fluids. Contrib. Mineral. Petrol. 136, 213e224. Schmidt W, M., Vielzeuf, D., Auzanneau, E., 2004. Earth Planet. Sci. Lett. 228, 65e84. ¨ ber die quantitative IR-Spektrosskopische Wasser-Bestimmung in Sillicaten. Fortschr. Scholze, H., 1960. U Mineral. 38, 122e123. Schulze, F., Behrens, H., Holtz, F., Roux, J., Johannes, W., 1996. The influence of H2O on the viscosity of a haplogranitic melt. Am. Mineral. 81, 1155e1165. Shackleford, J.F., Masaryk, J.S., 1976. The thermodynamics of water and hydrogen solubility in fused silica. J. Non-cryst. Solids 21, 55e64. Shaw, A.M., Hauri, E.H., Fischer, T.P., Hilton, D.R., Kelley, K.A., 2008. Hydrogen isotopes in Marina arc melt inclusions: implications for subduction dehydration and the deep-Earth water cycle. Earth Planet Sci. Lett. 275, 138e145. Shen, A., Keppler, H., 1995. Infrared spectroscopy of hydrous silicate melts to 1000 degrees C and 10 kbar: direct observation of H2O speciation in a diamond-anvil cell. Am. Mineral. 80, 1335e1338. Shen, A.H., Keppler, H., 1997. Direct observation of complete miscibility the albite-H2O system. Nature 385, 710e712. Shishkina, T.A., Botcharnikov, R.E., Holtz, F., Almeev, R.R., Portnyagin, M.V., 2010. Solubility of H2O- and CO2-bearing fluids in tholeiitic basalts at pressures up to 500 MPa. Chem. Geol. 277, 115e125. Shishikina, T.A., Botcharnikov, R.E., Holtz, F., Almeev, R.R., Jazwa, A.M., Jakubiak, A.A., 2014. Compositional and pressure effects on the solubility of H2O and CO2 in mafic melts. Chem. Geol. 388, 112e129. Silver, L., Stolper, E., 1989. Water in albitic glasses. J. Petrol. 30, 667e710. Silver, L., Stolper, E., 1985. A thermodynamic model for hydrous silicate melts. J. Geol. 93, 161e178. Silver, L., Ihinger, P.D., Stolper, E., 1990. The influence of bulk composition on the speciation of water in silicate glasses. Contrib. Mineral. Petrol. 104, 142e162. Sisson, T.W., Layne, G.D., 1993. H2O in basalt and basaltic andesite glass inclusions from four subduction-related volcanoes. Earth Planet. Sci. Lett. 117, 619e637.

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Sobolev, A.V., Chaussidon, M., 1996. H2O concentrations in primary melts from supra-subduction zones and mid-ocean ridges: implications for H2O storage and recycling in the mantle. Earth Planet Sci. Lett. 137, 45e55. Sorapure, R., Henderson, C.M.B., 1984. The solubility of water in melts of albite composition with varying additions of fluorine. Progr. Exper. Petrol. Nat. Env. Res. Council Publ. Ser. D. 25, 28e30. Sowerby, J.R., Keppler, H., 1999. Water speciation in rhyolitic melt determined by in-situ infrared spectroscopy. Am. Mineral. 84, 1843e1849. Sowerby, J.R., Keppler, H., 2000. Supercritical behavior in pegmatites: direct observation in the hydrothermal anvil cell (abstr.). EOS, Trans. AGU 81, S37. Sowerby, J.R., Keppler, H., 2002. The effect of fluorine, boron and excess sodium on the critical curve in the albite-H2O system. Contrib. Mineral. Petrol. 143 (1), 32e37. Spallanzani, L., 1792e1797. Viaggi alle Due Sicilie e in alcune parti dell’ Appennino, transl. as Travels in the Two Sicilies and Some Parts of the Appenines, J. Robinson, London, 1798). Stamperia di B. Comini, Pavia. Spera, F.J., 1974. A thermodynamic basis for predicting water solubilities in silicate melts and implications for the low velocity zone. Contrib. Mineral. Petrol. 45, 175e187. Stalder, R., Ulmer, P., Thompson, A.B., Guenther, D., 2001. High pressure fluids in the system MgO-SiO2 eH2O under upper mantle conditions. Contrib. Mineral. Petrol. 140, 607e618. Stebbins, J.F., 1988. Effects of temperature and composition on silicate glass structure and dynamics: Si-29 NMR results. J. Non-cryst. Solids 106, 359e369. Stolper, E., 1982. The speciation of water in silicate melts. Geochem. Cosmochim. Acta 46, 2609e2620. Tamic, N., Behrens, H., Holtz, F., 2001. The solubility of H2O and CO2 in rhyolitic melts in equilibrium with a mixed CO2-H2O fluid phase. Chem. Geol. 174, 333e347. Till, C.B., Grove, T.L., Withers, A.C., 2012. The beginnings of hydrous mantle wedge melting. Contrib. Mineral. Petrol. 163, 669e688. Tomlinson, J.W., 1956. A note on the solubility of water in molten sodium silicate. J. Soc. Glass Techn. 4, 25Te31T. Tuttle, O.F., Bowen, N.L., 1958. Origin of granite in light of experimental studies in the system NaAlSi3O8KAlSi3O8-SiO2-H2O. Geol. Soc. Am. Mem. 74, 1e153. Uys, J.M., King, T.B., 1963. The effect of basicity on the solubility of water in silicate melts. Trans. Am. Inst. Metall. Eng. 227, 492e500. Valyashko, V.M., Buback, M., Franck, E.U., 1981. Infrared absorption of concentrated aqueous NaCl04 solutions to high pressures and temperatures. Zeitschrifft Naturforschung A 36, 1169e1177. Wallace, P.J., Dufek, J., Anderson, A.T., Zhang, Y., 2003. Cooling rates of Plinian-fall and pyroclastic-flow deposits in the Bishop Tuff: inferences from water speciation in quartz-hosted glass inclusions. Bull. Volcanol. 65, 105e123. Walter, M.J., 2001. Core Formation in a Reduced Magma Ocean: New Constraints from W, P, Ni, and Co, Paper Presented at Transport of Materials in the Dynamic Earth, Misasa, Japan, pp. 152e153. Wang, Y., Cody, S.X., Foustoukos, D., Mysen, B.O., Cody, G.D., 2015. Very large differences in intramolecular DH partitioning in hydrated silicate melts synthesized at upper mantle pressures and temperatures. Am. Mineral. 100, 1182e1189. Wasserburg, G.J., 1957. The effects of H2O in silicate systems. J. Geol. 65, 15e23. Watson, E.B., 1994. Diffusion in volatile-bearing magmas. In: Carroll, M.R., Holloway, J.R. (Eds.), Volatiles in Magmas. Mineralogical Society of America, Washington, DC, United States, pp. 371e411. Whittigton, A., Richet, P., Holtz, F., 2000. Water and the viscosity of depolymerized aluminosilicate melts. Geochem. Cosmochim. Acta 64, 3725e3736. Withers, A.C., Behrens, H., 1999. Temperature-induced changes in the NIR spectra of hydrous albitic and rhyolitic glasses between 300 and 1000 K. Phys. Chem. Miner. 27, 119e132.

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CHAPTER

Volatiles in magmatic liquids

8

8.1 Introduction Volatiles in magmatic liquids predominantly are within system CeOeHeNeS. In addition, halogens and noble gases can be important contributors to the budget of volatiles. Water (H2O), because of its importance compared with other volatiles, was discussed separately in Chapter 7. The solution mechanisms of volatiles in silicate melts such as magmatic liquids, fall in two categories. One is referred to as reactive solution where there is chemical and structural interaction between the volatile solute and silicate solvent. Solution of reactive volatiles leads to both the volatile component and the silicate melt structure to be affected. This, in turn, results in changes in chemical and physical magma properties. The other form of solution can be termed nonreactive. Here, the solution does not involve chemical and structural interaction between silicate melt and dissolved components. Only negligible influence on melt structure and properties may be the result of dissolving nonreactive volatiles. Some of the reactive and nonreactive volatiles may exist in multiple oxidation states within the redox range of terrestrial planets. For the interior of the Earth, this redox range is from near that of the magnetite-hematite oxygen buffer (Carmichael and Ghiorso, 1990; Brounce et al., 2014) to near that of the iron-wu¨stite (IW) oxygen buffer (Frost and McCammon, 2008; Aulbach and Stagno, 2016). The solubility, speciation, and influence on melt structure and properties can be dependent on the redox state of volatiles. In the CeOeHeNeS system, the nature of some of the species depends on the redox conditions. Under oxidation conditions, the reactive species are OH, CH3, HCO3, CO3, and SO4 groups formed by interaction of H2O, CO2, and SO3 with the melt. Nonreactive species are molecular CO2, H2O, and SO2, together with N2, H2 and noble gases. Under reducing conditions, the reactive species are dominated by OH, CO3, CH4, NH3, and S2
. Hydrogen (H2) can become an important species when conditions are as reducing as those defined by the IW1 oxygen buffer and below. We note that H2O is a dominant volatile species under all redox conditions relevant to magmatic processes in the Earth and the terrestrial planets as discussed in more detail Chapter 7.

In this chapter redox conditions often are referred by reference of oxide/metal equilibria for which the fO2/temperature conditions have been well calibrated. The buffer as designed by the abbreviations IW (iron-wu¨stite), MW (magnetitewu¨stite), QFM (quartz-forsterite-magnetite), NNO (nickel-nickel oxide), and MH (magnetite-hematite). The actual fO2-temperature-pressure relations of these buffers can be found in a summary by Huebner (1971). 1

Mass Transport in Magmatic Systems. https://doi.org/10.1016/B978-0-12-821201-1.00007-9 Copyright © 2023 Elsevier Inc. All rights reserved.

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Chapter 8 Volatiles in magmatic liquids

In addition, halogens, F, Cl, Br, and I, also are reactive volatile components. The speciation of halogens does not seem to depend on redox conditions in redox range of terrestrial planets.

8.2 Oxidized carbon species Carbon species are the second-most important volatile components in the Earth (Jambon, 1994; see also Fig. 7.1). In magmatic systems, CO2 is the dominant volatile in alkali basalt and silicaundersaturated magma such as nephelinite, carbonatite and kimberlite (Huang et al., 1980; Kogarko, 1997; Brooker and Kjaersgaard, 2011), whereas CO2 plays a subordinate role in most subduction zone settings. Notably, though, the CO2/H2O abundance ratio in the latter settings increases with distance from the trench (Poli and Schmidt, 2002; Kawamoto et al., 2013).

8.2.1 Solubility of CO2 in magma Solubility of CO2 in magmatic liquids is central to characterizing the effect of oxidized carbon on magma properties and processes. For example, exsolution of CO2 has been suggested as the driving force of kimberlite eruption (Wyllie, 1980). Dissolved CO2 also has a major influence of melting and crystallization relations of magma in the upper mantle (Eggler, 1975; Foley et al., 2009). 2
In the CeO system, oxidized fluids exists as CO2
3 and CO2. In the CeOeH system, CO3 and
HCO3 species can exist together with CO2. The abundance of these species depends on the pH, fluid composition, temperature, and pressure (French, 1966; Zhang and Duan, 2009). In silicate melt solution, these relations can be complicated further because of interaction between the CeOeH and the silicate structural components (Mysen, 1976; Nowak et al., 2003; Guillot and Sator, 2011). Carbon dioxide solubility in magmatic liquids varies as systematic functions of composition (melt structure), temperature, and pressure (Mysen, 1976; Holloway et al., 1976; Fine and Stolper, 1985; Brooker et al., 2001; Duncan and Dasgupta, 2014). The CO2 solubility increases with increasing pressure (Fig. 8.1A). In general, there is a negative correlation between CO2 solubility and temperature (Eggler and Kadik, 1979; Eggler and Rosenhauer, 1978; Guillot and Sator, 2011; Iacono-Marziani et al., 2012; Morizet et al., 2013), but the effect is small. The solubility is negatively correlated with the degree of polymerization of magmatic liquids. The silicate bulk chemical composition plays an important role in determining the CO2 solubility. Several individual compositional variables are important. First, the CO2 solubility is positively correlated with the overall degree of melt polymerization, NBO/T (Holloway et al., 1976; Brooker et al., 2001; Iacono-Marziani et al., 2012; see Fig. 8.1B). The more depolymerized a magma (greater NBO/T-value), the greater is the solubility of CO2. Given the relationship between magma composition its NBO/T (see Chapter 5), the more mafic a magma, the greater the CO2 solubility. The relationship with NBO/T alone does, however, carry significant data scatter (Fig. 8.1B) because other composition variables also affect CO2 solubility. Interactions between dissolved CO2 and the type and proportions of network-modifying alkalis and alkaline earths may account for some of this scatter as reported, for example, in the positive correlation between CO2 solubility and peralkalinity of a melt (Pearce, 1964; Vetere et al., 2014): CO2 ðwt%Þ ¼ 0:246 þ 0:014exp6:995•NBO=T þ

3:15ðNa þ KÞ . Scations

(8.1)

8.2 Oxidized carbon species

537

FIGURE 8.1 Solubility of CO2 in magmatic liquids. (A) Solubility as a function of pressure for basalt melt and rhyolite melt. Basalt melt composition (wt%). Rhyolite melt composition redrawn from Duncan and Dasgupta (2014) with composition (wt%); 68.81, TiO2: 0.50, Al2O3: 15.72, FeO(total): 0.99, MnO: 0.50, MgO: 0.19, CaO: 1.47, Na2O: 4.19, K2O: 8.33, P2O5: 0.29. (B) CO2 solubility in magmatic liquids as a function of their NBO/T.4 Redrawn from (A) Stanley et al. (2011) and (B)Brooker et al. (2001).

Furthermore, the CO2 solubility in aluminosilicate melts such as magmatic liquids is positively correlated with the Al/(Al þ Si) (Mysen, 1976; Fine and Stolper, 1985). Finally, and quite importantly, the type of alkali metal or alkaline earth also is important with an apparent negative correlation between solubility and the electronegativity of the metal cation (Holloway et al., 1976; Vetere et al., 2014; see Fig. 8.2). These compositional relationships lead to the conclusion that the CO2 solubility in basalt melt exceeds that in more felsic magma (Fig. 8.1A). Further, the solubility in alkali basalt likely is less than in tholeiite melt because the latter magma comprises a larger proportion of highly electronegative cations such as Ca2þ and Mg2þ. In mixed CO2eH2O fluid environments, the CO2 solubility varies with the CO2/H2O ratio (Mysen, 1976; Botcharnikov et al., 2006; Behrens et al., 2009; Shishikina et al., 2010; Iacono-Marziani et al., 2012; see also Fig. 8.3). In certain circumstances, the CO2 solubility reaches a maximum value with CO2/(CO2 þ H2O) between 0.8 and 0.95 (Mysen, 1976; Vetere et al., 2014) probably reflecting the effect of dissolved H2O on melt silicate polymerization combined with the CO2 activity in the system. The solubility likely is more sensitive to the CO2/(CO2þH2O) ratio the more felsic the melt because, as discussed in Chapter 7, H2O has a greater effect on silicate melt polymerization the more felsic the melt.

NBO/T: Nonbridging oxygen per tetrahedrally coordinated cation. This is a measure of the extent of aluminosilkcate polymerization. See also Chapter 5 for further discussion of this structural concept. 4

538

Chapter 8 Volatiles in magmatic liquids

FIGURE 8.2 CO2 solubility in melts along the join Ca2SiO4dMg2SiO4 equilibrated at 3 GPa and 1500 C. Redrawn from Holloway et al. (1976).

FIGURE 8.3 CO2 solubility in phonotephrite melt þ CO2 þ H2O as a function of mol fraction of CO2 in the fluid at 1250 C and 500 MPa. Redrawn from Vetere et al. (2014).

8.2 Oxidized carbon species

539

8.2.2 Solubility mechanisms of CO2 in magma A fraction of the CO2 dissolved in a silicate melt interacts chemically with the silicate structure to form CO2
3 complexes (Pearce, 1964; Mysen, 1976; Fine and Stolper, 1985; Guillot and Sator, 2011; Konschak and Keppler, 2014; Morizet et al., 2015). The proportion dissolved as CO2
3 increases the more mafic the magma. Experimental data suggest that the CO2
3 groups exist as isolated complexes (Morizet et al., 2015). A simple equilibrium between molecular CO2 and carbonate, CO2
3 , is (Eggler and Rosenhauer, 1978; Fine and Stolper, 1985; Nowak et al., 2003; Stanley et al., 2011): CO2 þ O2
5CO2
3 ;

(8.2)

with K ¼ XCO3 =fCO2 •XO2
;

(8.3)

Here, it is assumed that mol fractions, X, can be used in place of activities. The O in these equations is the proportion of oxygen anions in the melt structure. The fO2 is the fugacity of CO2. Formation of CO2
3 -complexes may be accomplished through a reaction whereby the proportion of bridging and nonbridging oxygen in the silicate network are changed. The process involves the release of network-modifying cation(s) and one of the nonbridging oxygen to form CO2
3 complexes. Another nonbridging cation is converted to a bridging oxygen. In other words, the silicate structure becomes polymerized via a solution mechanism that combines Eq. (8.2) with a silicate polymerization reaction: 2


2Qn
1 52Qn þ O2
;

(8.4)

2Qn
1 þ CO2 52Qn þ CO2
3 .

(8.5)

to yield

Given, for example, that CO2 solubility in melts increases with increasing pressure, Eq. (8.2) would suggest that at CO2-saturation, increasing pressure will result in increasing silicate polymerization. This exactly what has been observed (Morizet et al., 2015; see also Fig. 8.4). From the temperature and pressure dependences of equilibrium constant for equilibrium (8.2) (Fig. 8.4; see also Morizet et al., 2013), the standard enthalpy and volume changes for reaction (8.2) are near
14  14 kJ/mol and 23  2 cm3/mol, respectively (Pan et al., 1991; Holloway and Blank, 1994; Thibault and Holloway, 1994). We should note here that the very large uncertainty in the average enthalpy change is due to the widely discrepant nature of one data set (Pan et al., 1991). Without those data, the average enthalpy change is
20  8 kJ/mol. In other words, from the data summarized in Fig. 8.5, equilibrium (8.2) shifts to the left with increasing temperature, thus favoring 2
molecular CO2 over CO2
3 groups, and to the right with increasing pressure, thus favoring the CO3 groups over molecular CO2. This conclusion is also consistent with the results of molecular simulations of Guillot and Sator (2011) to 10 GPa total pressure. The data also accord semiquantitatively with the experimental results from Nowak et al. (2003) who found DH ¼
12  2 kJ/mol for a NaAlSi3O8 melt and
29  2 kJ/mol for a melt of dacitic composition. The latter melt composition is more depolymerized (higher NBO/T) than NaAlSi3O8 composition, which may explain the more

540

Chapter 8 Volatiles in magmatic liquids

FIGURE 8.4 Degree of polymerization, NBO/Si, as a function of pressure of CO2-saturated glass and melts in the system CaOeMgOeAl2O3eSiO2 as a function of pressure. Redrawn from Morizet et al. (2015).

FIGURE 8.5 (A) Temperature- and (B) pressure-dependence of equilibrium constant for equilibrium between molecular CO2 and CO2
3 groups, Eq. (8.2), as shown in Eq. (8.3). Figures are redrawn from Stanley et al. (2011).

8.2 Oxidized carbon species

541

FIGURE 8.6 Equilibrium constant, Eq. (8.3), for equilibrium between molecular CO2 and CO2
3 groups in phonolite and dacite melt together with NaAlSi2O6 and NaAlSi3O8 as a function of temperature with DH-values for Eq. (8.2) derived from the temperature-dependence. Also shown is the NBO/T of the melt (increasing values also emphasized by arrow). The phonolite and dacite melt data are redrawn from Konschak and Keppler (2014) and the NaAlSi2O6 and NaAlSi3O8 melt redrawn from Morizet et al. (2001) and Nowak et al. (2003).

significant shift toward CO2
3 for dacite composition melt. There is, in fact, a systematic correlation between the NBO/T of magma and the DH of reaction (8.2) (Morizet et al., 2001; Nowak et al., 2003; see Fig. 8.6). The more mafic the magma, the more sensitive to temperature is Eq. (8.2). The equilibrium constant of Eq. (8.2) and its temperature-dependence varies with the type of metal cation or cations that become associated with CO2
3 -complexes. A relationship between ionization potential of the metal cation(s) and extent of deformation of the carbonate group, well known in crystalline carbonate structures (White, 1974), also has been inferred for CO2
3 complexes in CO2bearing silicate melts (Sharma et al., 1988). It is possible, therefore, that the extent of steric hindrance of the CO2
3 triangular geometry controls the relationship between CO2 solubility and the type of metal cation(s) (Holloway et al., 1976). This proposal implies, for example, that at fixed pressure, temperature, and NBO/Si of a melt, the CO2 solubility depends on cation properties in the order Kþ > Naþ > Ca2þ > Mg2þ. The temperature-dependence and, therefore, the DH of Eq. (8.2) also varies with melt composition (Morizet et al., 2014; Nowak et al., 2003; Konchak and Keppler, 2014; see Fig. 8.6). The DH is positively correlated with the NBO/T of the melt as seen by comparing phonolite (NBO/T ¼ 0.14), dacite (NBO/T ¼ 0.09), and NaAlSi3O8 (NBO/T ¼ 0) composition melts in Fig. 8.6, for example. Finally, the increased slope of the ln K versus 1/T in NaAlSi2O6 compared with NaAlSi2O8

542

Chapter 8 Volatiles in magmatic liquids

melt (Fig. 8.6), suggests that the Al/(Al þ Si) ratio also affects the energetics of the equilibrium. This latter feature is consistent with speciation data for CO2 dissolved in melts along the SiO2eNaAlO2 (Fine and Stolper, 1985). In melts containing both CO2 and H2O, bicarbonate complexes are possible. Under these circumstances, simple reactions such as þ CO2 þ H2 O5HCO
3 þH .

(8.6)

þ CO2 þ H2 O5CO2
3 þ 2H ;

(8.7)

and

can be combined together with the Q -species equilibrium (Eq. 8.5). A complete equilibrium between the carbonate species, molecular CO2, and the Qn-species in the melts then becomes (Mysen, 2015), n

nþ1 n 2CO2
H2HCO
3 þ H2 O þ 2Q 3 þ 2Q ;

(8.8)

which shows that in silicateeCO2eH2O melt, solution of CO2 in the melt to yield carbonate and bicarbonate species results in melt polymerization albeit at a slower rate than without H2O (and HCO
3 ) (DNBO/T ¼ 0.25 per mol CO2 with H2O and DNBO/T ¼ 0.67 per mol CO2 without it). The NBO/T-decrease is slower because H2O acts to counter the polymerization resulting from carbonate 2
formation in the melts. Finally, the ratio HCO
3 /CO3 decreases with increasing temperature (Mysen, 2015). In other words, Eq. (8.8) shifts to the left and the silicate structure becomes more depolymerized with increasing temperature. In aluminosilicate melts, which are better models for natural magmatic liquids than binary metal oxide-silica melts, the CO2 solubility and the CO2
3 /CO2 ratio also increase by increasing Al/(Al þ Si) of the melt (Mysen, 1976; Fine and Stolper, 1985). This mechanism involves transforming some of the metal cations used for Al3þ-charge-balance to associate with carbonate complexes in the melt instead h 5

nþ M1=n AlO2

 x

h i  nþ • ðSiO2 Þy þ CO2 53 M1=n AlO2

x
4

•ðSiO2 Þy

i4


þ 4xAl3þ þ 2M1=n CO3 (8.9)

In Eq. (8.9), the [(Mnþ1/nAlO2)x
4 • (SiO2)y]4
complex is more polymerized than [(Mnþ1/ nAlO2)x$(SiO2)y], which means than when CO2 is dissolved in fully polymerized aluminosilicate melts and forms CO2
3 complexes, the silicate melt actually becomes depolymerized. A consequence
of these relations is, for example that when CO2
3 or HCO3 -complexes are formed in rhyolitic magma, its silicate network actually becomes depolymerized.

8.2.3 Oxidized carbon (CO2) in magmatic processes In light of the influence of dissolved CO2 on degree of polymerization of magma, NBO/T, any property and process that depends on melt polymerization also depends on the solubility and solubility mechanism(s) of CO2 in magmatic liquids.

8.2.3.1 Melting phase relations The pressure/temperature trajectory of the CO2-saturated peridotite solidus in the Earth’s upper mantle differs from the peridotite solidus trajectory in the absence of volatiles (Fig. 8.7). Below about 2 GPa, the CO2-saturated peridotite shows a small temperature depression of a few tens of degrees (Eggler, 1975). Initial melt composition in this pressure regime is alkali basaltic. Above w2 GPa, the

8.2 Oxidized carbon species

543

FIGURE 8.7 Comparison of pressure-temperature trajectories of volatile-free and CO2-saturated peridotite solidus. Redrawn from Eggler (1975, 1978).

solidus temperature depression increases rapidly to hundreds of degrees and at small degrees of melting the melt is carbonatitic (Eggler, 1978; Dalton and Presnall, 1998). Increasing degree of melting under these latter conditions results in gradual change from carbonatite to carbonate-rich silicate melt (Foley et al., 2009). These trends are direct consequences of the solution mechanisms of CO2 in the magmatic liquids. As CO2
3 groups are formed, the melt actually either becomes more polymerized or, in equilibrium with given mantle mineral assemblages, the activity coefficients of silicate components increase. This, in turn results in melts in equilibrium with upper mantle mineral assemblages becoming increasingly silica deficient (Eggler, 1974). Melting of an upper mantle with both CO2 and H2O depends significantly on whether all of the volatiles are contained in a crystalline phase such as amphibole, phlogopite, or carbonate, or whether there is excess volatiles over that which can be contained in crystalline phases (Eggler, 1978). As can be seen in the phase relations reproduced in Fig. 8.8A, with excess fluid, the composition of partial melt at 2e3 GPa total pressure varies continuously from basanite or nephelinite in an H2O-free environment and then changes gradually ending up as andesitic melt in a CO2-free environment (see also Mysen and Boettcher, 1975, and the topological analysis of this situation by Eggler, 1978). However, with only a small amount of fluid such that all H2O is contained in amphibole (less than about 0.4 wt% fluid for a typical peridotite upper mantle), this amphibole is present in the solid assemblage over a 0e0.8 range of CO2/(CO2þH2O) and the melt is of melilitic composition (Mysen and Boettcher, 1975; Eggler, 1978; Foley et al., 2009). Eggler (1978) termed this condition the Zone of Invariant Melting (ZIVC). Analogous analyses may be carried out with other hydrated phases such as, for example, phlogopite. In such cases, however, the pressures and melt compositions of the zone of invariant melting would be different.

8.2.3.2 Magma properties and CO2-induced melt polymerization A detailed understanding of relationships between many magma properties and their silicate structure is not well established. It is clear, however, that their NBO/T-values almost always play a central role.

544

Chapter 8 Volatiles in magmatic liquids

FIGURE 8.8 Phase relations in peridotiteeCO2eH2O. A. With excess CO2 and H2O over that which can be contained in crystalline phases, and B. With amount of H2O all contained in amphibole. ZIVC denotes “zone of invariant melting.” Redrawn from Eggler (1978).

Solution of oxidized carbon species in the CeOeH system in magmatic liquids can be described with Eq. (8.8). Whether the solution results in silicate melt polymerization or depolymerization depends on the direction of this reaction as a function of temperature, pressure, and silicate melt composition. Magma viscosity is an example of an NBO/T-dependent property. Magma viscosity is also a critical parameter governing magma aggregation at and ascent from depths of original melting (Cashman, 2004). To illustrate how the carbonate speciation may affect the melt viscosity via the effect of speciation on NBO/T, let us take melt viscosity data from a simple system such as Na2OeSiO2 (Bockris et al., 1955), which can be related to melt structure with the simple expression: hðPa sÞ ¼ 4:4 þ 0:75•ðNBO=TÞ
4:1 .

(8.10)

The change in melt polymerization, DNBO/T, with changing speciation abundance ration, XCO3/XHCO3 is (Mysen, 2015): ðDNBO=TÞoxidizing ¼ 0:135 þ 0:59•eð
0:55•ðXCO3 =XHCO3 ÞÞ
0:27•eð
2:3•ðXCO3 =XHCO3 ÞÞ .

(8.11)

From Eqs. (8.10) and (8.11), the melt viscosity may change by up to several hundred percent as a function of carbonate speciation although the exact value of this change will depend on magma composition because of the nonlinear nature of the relationship between magma viscosity and magma chemical composition (Fig. 8.9). Another property significantly dependent on magma polymerization is element partition coefficients between melt and minerals or fluid (Thibault and Walter, 1995; Kushiro and Mysen, 2002).

8.2 Oxidized carbon species

545

FIGURE 8.9 Calculated decrease of melt viscosity in silicate melt þ CO2þH2O as a function of abundance ratio, XCO3/XHCO3. The abundance ratio, XCO3/XHCO3, is transformed to change in NBO/T of melt according to Eq. (8.8). Redrawn after Mysen (2015).

These issues were discussed in detail in Chapter 3. Here, we will only illustrate how partition coefficients can be linked to speciation of carbon dioxide dissolved in the magmatic liquid. For this purpose, let us use the Fe2þ0Mg exchange equilibrium between olivine and melt as the example. This exchange equilibrium coefficient often is often used as an indicator of petrogenetic history of magmatic rocks in the Earth’s interior with the assumption that an exchange equilibrium coefficient,  olivine .  melt  olivine=melt XFe2þ XMg , is constant and equal to 0.3. More recently it KDðFe2þ
MgÞ ¼ XFe2þ XMg olivine=melt

has been shown, however, that melt composition can affect the KDðFe2þ
MgÞ by as much as about 50% olivine=melt

(Kushiro and Walter, 1998; Kushiro and Mysen, 2002; Toplis, 2004). In fact, the KDðFe2þ
MgÞ versus

NBO/T of melts in magmatic systems is parabolic (Fig. 8.10). By using this relationship in combination with the relationship between melt NBO/T and carbon speciation ratio (Fig. 8.9), effects of dissolved CO2 on changes in this equilibrium exchange coefficient can be extracted. For example, for a highly polymerized melt (NBO/T ¼ 0.25 is used in Fig. 8.11), increasing XCO3/XHCO3 abundance ratio results olivine=melt

in a negative change of KDðFe2þ
MgÞ . In contrast, in a highly depolymerized melt (NBO/T ¼ 2.25 is

546

Chapter 8 Volatiles in magmatic liquids

FIGURE 8.10 Equilibrium constant, K

olivine=melt D ðFe2þ
MgÞ

 olivine .  melt  , as a function of degree of ¼ XFe2þ XMg XFe2þ XMg

polymerization of melt at ambient pressure at 1350-1380 C and oxygen fugacity, log fO2, held constant at
6.5 (MPa). Redrawn from Kushiro and Mysen (2002).

olivine=melt

used in Fig. 8.11) the change of KDðFe2þ
MgÞ -values with increasing XCO3/XHCO3 ratio is positive. In terms of magmatic liquids, these differences imply that there are different effects on partition coefficients of CO2 dissolved in felsic magmas compared with what happens with mafic magmas. Several examples of such variations are shown in Chapter 3.

8.2.3.3 Degassing of magma H2O and CO2 typically are the main gas species in magma under upper mantle and crustal redox conditions (Birner et al., 2018). Magma formed by partial melting in most mantle environments tends to have CO2/H2O > 1 (Delaney et al., 1978). An important exception is subduction zone environments (Kelley and Cottrell, 2009), at least to depths near 100 km or so, where the melting environment is dominated by H2O so that CO2/H2O < 1. However, this abundance ratio tends to increase with depth in subduction zone environments (Poli and Schmidt, 2002). This evolution leads to transformation of magma on the peridotite-H2O-CO2 solidus to change from andesitic and quartz tholeiitic to alkali basaltic with increasing distance from the initial subduction. The concentration of volatiles in magmatic liquids may be obtained by volatile content of glass inclusions in phenocrysts or may be inferred from mineral assemblages combined with experimentally determined phase relations. In the former case, there is always a question whether there was degassing from the melt prior to its entrapment. In the latter case, this is not a hindrance for the determination of abundance of CO2 and H2O. It needs to be kept in mind, however, that because of the large differences in CO2 and H2O solubility in magmatic liquids, these often are saturated in CO2 and some CO2 may be lost by degassing at greater depth than that indicated by H2O solubility, for example. When this happens, a portion of the H2O will also be exsolved, but the proportion of CO2 and H2O in gas and melt phase will differ with the

8.2 Oxidized carbon species

FIGURE 8.11 Changes (in %) of equilibrium constant, K

olivine=melt D ðFe2þ
MgÞ

547

 olivine .  melt  , as a function of ¼ XFe2þ XMg XFe2þ XMg

abundance ratio, XCO3/XHCO3, calculated relative to the value in the absence of CO2 in the melt. Two different NBO/T-values as indicated on graph were employed as starting point. For this calculation, the abundance ratio, XCO3/XHCO3, was transformed to change in NBO/T of melt according to Eq. (8.8). Redrawn from Mysen (2015).

548

Chapter 8 Volatiles in magmatic liquids

FIGURE 8.12 Schematic representation of melting curve for crystals þ H2O þ CO2 melting congruently.

CO2/H2O abundance ratio in the gas phase exceeding that in the melt phase. This effect is illustrated schematically in Fig. 8.12 for a simple case where a crystalline assemblage melts congruently to melt þ CO2þH2O. Take composition a, where congruent melting produces melt þ CO2þH2O gas. At the temperature marked with x, for example, the CO2 and H2O concentration in melt and gas is given by x0 and x00 . In other words, the gas phase is enriched in CO2 (x00 ), whereas the melt is enriched in H2O (marked as x0 ). At lower pressure, the temperature interval between the solidus and liquidus is narrower. However, the CO2 enrichment in the gas phase is greater and the H2O content in the melt is greater (Eggler and Kadik, 1979). The difference between the CO2/H2O ratio of fluids and melts not only varies with temperature, but also is dependent on melt composition because, in particular the CO2 solubility is quite sensitive to melt composition. Therefore, the CO2/H2O abundance difference between basalt and rhyolite melt and their exsolving CO2þH2O gas will be greater for rhyolite.

8.3 Reduced carbon (CH4, CO, and carbide) The abundance evolution of reduced and oxidized carbon species in a CeOeH gas phase as a function of oxygen fugacity at low pressure is shown in Fig. 8.13. Not shown is a narrow fO2-range where CO is stable. Because this very narrow fO2-range, CO is not considered a major volatile component in terrestrial magmatism. There is also a minor amount of nitrogen in the Earth’s interior. Nitrogen can exist as N2 under oxidizing conditions and NH3 under reducing conditions. Sulfur can exist as SO2 under oxidizing conditions and H2S under reducing conditions. These are not shown in Fig. 8.13. Further discussion of speciation in C-O-H-N-S gas and fluid phases is found in Chapter 6. Aside from CO2, which is the most important C-bearing volatile component in magma formation, CH4 can under more unusual circumstances also become important because there are samples from the mantle suggesting oxygen fugacity in the vicinity of the iron-wustite oxygen buffer (Smith et al., 2016; Sobolev et al., 2019). Under such conditions, CH4 is the stable C-bearing species together with NH3 and H2S. Moreover, at the core-forming stage of the Earth the oxygen fugacity appears to be have been two to three orders of magnitude below that of the IW buffer (Rubie et al., 2011). Under such redox

8.3 Reduced carbon (CH4, CO, and carbide)

549

FIGURE 8.13 Abundance of gas species (mol fraction) in the system COH for fluid in equilibrium with graphite. Redrawn from Holloway and Blank (1994).

conditions the main volatile species likely were H2S, CH4, H2O, and H2 (Holland, 1984; Kasting et al., 1993; Holloway and Blank, 1994). In H-free environments, the reduced species in CeO fluids is CO or a polymerized (CO)x species under redox conditions down to those defined by the IW buffer (Pawley et al., 1992; Armstrong et al., 2015). A number of recent experimental and modeling studies have proposed additional reduced carbon species as possibilities including, for example, hydrocarbons heavier than CH4 in the CeH subsystem at >20 GPa and >1500 K (Lobanov et al., 2013). However, the latter experiments suffered from composition gradients within the samples contained in a diamond anvil cell at high pressure and temperature so this interpretation is subject to uncertainty. Modeling of reduced species in the CeOeH system also has led to proposed complex organic functional groups such as acetate at high temperature and pressure (Sverjensky et al., 2014). In the latter modeling study, it was assumed that a hard-sphere model for H2O could be used up to mantle pressures even though high-pressure/high
temperature first-principles calculations have indicated a complex structural environment involving molecular H2O, OH-groups, and polymerized H2O (Karki et al., 2010), which would be inconsistent with a hard-sphere model. Those modeling effort should not, therefore, be considered a realistic representation of solution mechanisms of organic complexes in silicate melts at high temperature and pressure.

550

Chapter 8 Volatiles in magmatic liquids

It has been proposed from vibrational spectra of quenched melts that reduced carbon dissolve in iron-bearing silicate melts at high pressure exists as iron carbonyl, Fe(CO)5 (Wetzel et al., 2013; Kadik et al., 2014). However, in other experimental studies it was concluded that the latter vibrational spectroscopic assignment is more consistent with molecular CO and not with carbonyl (Yoshioka et al., 2015). In summary, a number of reduced carbon species have been proposed for reducing conditions in the Earth’s mantle. However, a number of the proposals is controversial. Those controversial suggestions will not be considered further here.

8.3.1 Carbon monoxide (CO) It has been proposed that carbon monoxide solubility in basalt melt is a linear function of CO2 fugacity in the 50e150 MPa pressure range at 1200 C (Pawley et al., 1992; see also Fig. 8.14A). To some extent, this conclusion was supported by the experimental data of Thibault and Holloway (1994). The latter authors also found that the solubility was a linear function of the CO2 fugacity, but that at the highest temperatures and pressures, there was divergence from this simple relationship (Fig. 8.14B). Compared with the solubility of CO2 under more oxidizing conditions, Thibault and Hollway (1994) reported that CO solubility as more sensitive to temperature than CO2 solubility. It has been proposed that CO dissolves in melts in molecular form (Pawley et al., 1992). That suggestion is in agreement with the results from Yoshioka et al. (2015). However, it differs from conclusions inferred from the high-pressure experiments on CO solubility in CaMgSi2O6 and NaAlSi3O8 melts (Eggler et al., 1979) and from limited infrared spectroscopic information from CObearing glasses by Pawley et al. (1992). In both reports, it was suggested that CO2
3 groups were present in the temperature-quenched melts after equilibration at temperatures above their liquidus and a few GPa pressure.

FIGURE 8.14 CO solubility in basalt melt in equilibrium with CO2, CO, and graphite at 1200 C and 50e150 MPa expressed as CO2. (A) Solubility as a function of CO2 fugacity, fCO2. (B) Solubility, expressed as CO2, in leucitite magma as a function of pressure and temperature. Redrawn from (A) Pawley et al. (1992) and (B) Thibault and Holloway (1994).

8.3 Reduced carbon (CH4, CO, and carbide)

551

Experimental studies of carbon speciation in melts (Eggler et al., 1979; Thibault and Holloway, 1994) point to formation as CO2
3 bearing entities from CO as one of the forms of dissolved carbon. How this solution mechanism operates is not clear, because transformation of CO to CO2
3 requires oxidation of carbon (Pawley et al., 1992). One might propose a reaction such as; 2COðfluidÞ þ O2
ðmeltÞ5CO2
3 ðmeltÞ þ C;

(8.12)

2


where O (melt) represents the interaction with the silicate melt structure. However, whether or not reactions of this type may occur has not been documented. The solution behavior of CO in magmatic liquids remains, therefore, a subject open to discussion.

8.3.2 Carbide (C) Metal carbides have been reported in both mantle phases and in meteorites (Kaminski and Wirth, 2017; Anders and Zinner, 1993). Carbide complexing in natural magma has not been reported. Carbide complexing in experimentally formed silicate melts has been reported, but apparently only in SiO2þCeO systems (Renlund et al., 1991; Yurkov and Poliak, 1996). In those studies, various spectroscopic methods were used to determine the nature of the SieC bonding and how the substitution of C for O in silicate tetrahedra affects properties of oxycarbide melts. There appear to be no data on carbon solubility in oxycarbide melts. Reduction of carbon to form SieC bonds can be accomplished via interaction with the silicate network. In principle, this interaction can be written as: C þ 2Qn ¼ SiC þ Qn
2 .

(8.13)

This equilibrium is, therefore, a very efficient mechanism for depolymerization of the silicate melt as the NBO/T decreases by two per mol of carbon. The C/(C þ O) ratio of a melt can be accommodated by an increased number of SieC bonds in the tetrahedral structure as observed in 29MAS NMR spectra of such samples (Renlund et al., 1991). The activation energy of viscous flow of partially substituted oxycarbide SiO2 melt is somewhat less than that of SiO2 melt, but the viscosity is greater than that of SiO2 melt. This difference reflects the stronger SieC bond compared with SieO bonds. Their importance increases with increasing C concentration as seen, for example, in the proportions of such units derived from 29Si MAS NMR spectra. One would expect, therefore, that not only viscosity, but also other transport properties of oxycarbide melts show analogous effects. Moreover, other physical properties such as thermal expansion, hardness, and elastic modules also are higher in the oxycarbide glasses and melts compared with vitreous SiO2 (Renlund et al., 1991). Interestingly, similar features are seen in oxynitride glasses and melts.

8.3.3 Methane (CH4) Methane (CH4) is the dominant reduced C-bearing species in the CeOeH system in equilibrium with graphite under oxygen fugacity conditions between that of the IW buffer to about three orders more reducing that IW. When the activity of oxygen is lowered further, reduced carbon species other than hydrocarbons (CH4) may be stable in melts at high temperature and pressure (Armstrong et al., 2015) although the nature of this or these C-species is uncertain (see also Yoshioka et al., 2015).

552

Chapter 8 Volatiles in magmatic liquids

The solubility of C-bearing species in the CeOeH system in silicate melts decreases gradually as the oxygen fugacity decreases (hydrogen fugacity increases) (Hirschmann and Withers, 2008; Mysen et al., 2011). The solubility of methane, expressed as CO2, commonly is less than 50% of the CO2 solubility (Fig. 8.15), although this redox-dependent solubility difference varies somewhat with melt bulk composition (Mysen et al., 2011; Armstrong et al., 2015). Data for natural compositions (magmatic liquids) seem limited to basalt melt (Ardia et al., 2013; Armstrong et al., 2015). These data do not reveal meaningful bulk compositional effects. However, in the simple system Na2OeSiO2, CH4 solubility increases with increasing NBO/T of the melt. The rate of increase is, however, less than the rate of increase of CO2 solubility with increasing melt NBO/T (Mysen et al., 2011; see also Fig. 8.16). The methane solubility increases with hydrogen content of magmatic liquids (Ardia et al., 2013). This increase might reflect the fact that solution of hydrogen in silicate melts results in formation of OH-groups and, therefore, silicate depolymerization (increasing NBO/T). There is, therefore, a strong silicate compositional dependence of CH4 solubility (see Fig. 8.16). This control is analogous to that seen for oxidized carbon (CO2), the solubility of which also increases with decreasing degree of silicate polymerization. The solution mechanisms of reduced CeOeH species in silicate melts have been addressed by vibrational spectroscopic methods as well as 13C MAS NMR (Kadik et al., 2004, 2011, 2014; Mysen et al., 2011; Mysen and Yamashita, 2010; Stanley et al., 2014; Armstrong et al., 2015). Carbon-13 MAS NMR and Raman spectroscopic data recorded from both quenched melts and from Raman spectra of CH4-bearing melts while these were at high temperature and pressure are consistent with coexisting molecular CH4 and CH3 groups (Mysen and Yamashita, 2010; Kadik et al., 2011; Mysen et al., 2011). A schematic representation of the equilibrium between methyl groups and molecular methane dissolved in hydrous melts is (Mysen et al., 2011): 2Qn þ CH4 5Qn
1 ðCH3 Þ þ Qn
1 ðOHÞ.

(8.14)

FIGURE 8.15 Solubility of carbon in basalt melt, expressed as CO2, under oxidizing and reducing conditions. Redrawn from Pawley et al. (1992).

8.3 Reduced carbon (CH4, CO, and carbide)

553

FIGURE 8.16 Solubility of carbon in haplobasaltic melt, expressed as C under oxidizing and reducing conditions as a function of degree of silicate polymerization, NBO/Si, at 1450 C and 1.5 GPa. Redrawn from Mysen et al. (2011).

In Eq. (8.14), the notations, Qn
1(CH3) and Qn
1(OH), indicate Q-species where at least one of the oxygen atoms in the silicate tetrahedra is replaced by a CH3 and an OH-group, respectively. These latter species are less polymerized than the reactant Qn. The presence of SieCH3 bonds in this fashion is supported by carbon-13 MAS NMR data, which also rule out bonding of the metoxy type, SieOeCH3 (Mysen et al., 2011). Eq. (8.14) shifts to the right with both increasing temperature and increasingly depolymerized silicate melt. This means that in the more depolymerized a melt, the higher is its solubility limit and the greater is the proportion of CH3-groups.

554

Chapter 8 Volatiles in magmatic liquids

8.3.4 Magma properties and CH4-induced melt depolymerization The solubility mechanism of CH4 illustrated in Eq. (8.14) implies that with methane dissolved in a magmatic liquid, the silicate structure becomes depolymerized. Therefore, any magma property that depends on silicate polymerization will vary with the amount of CH4 in solution. It will also be redoxdependent because oxidized carbon (CO2) causes melt polymerization. The amount of experimental data with which to examine effects on melt properties of dissolved CH4 is, however, somewhat limited. An experiment focused on liquidus temperature depression was reported for the system CaMgSi2O6eCH4 where a w100 C temperature depression was observed in the 1.5e2.0 GPa pressure range (Eggler and Baker, 1982). The different pressure-temperature-trajectories of peridotite-CO2 and peridotite-CH4 melting curves give rise to the possibility of redox melting in the upper mantle (Taylor and Green, 1987; Song et al., 2009). Redox melting can occur in a rising mantle diapir if the materials in the diapir encounters different redox conditions during ascent. Methane also affects silicate liquidus phase relations (Eggler, 1975; see also Fig. 8.17). It is clear that the olivine (forsterite) liquidus volume expands in the presence of CH4 compared with

FIGURE 8.17 Effect of CH4 on liquidus phase relations. (A) Phase relations in the system Mg2SiO4eCaMgSi2O6eSiO2eCO2 at 1.5 and 3.0 GPa (solid lines) compared with the liquidus relations volatile-free and with excess H2O (dashed lines). (B) Phase relations at 2.8 GPa in a portion of the system CaOeMgOeAl2O3eSiO2, coexisting in equilibrium with CH4þH2 fluid and graphite and volatile-free conditions abbreviations: Di, diopside; En, enstatite; ga, garnet; Ol, olivine; sp, spinel. Redrawn from data of (A) Eggler (1974), and Kushiro (1969), (B) Eggler and Baker (1982).

8.4 Sulfur solubility

555

volatile-free phase relations and even more so compared with CO2. This olivine liquidus expansion implies that the activity of silica is decreased. Such a decrease, in turn, is what one would expect when methane dissolves to make CH3-groups attached to Si4þ in silicate tetrahedra such as illustrated in Eq. (8.14). Given the solution mechanism discussed earlier, in analogy with the behavior of dissolved H2O, one might expect that dissolved methane will results in decreased magma viscosity, enhanced diffusion, and lowered compressibility, for example. At any depth the in the Earth, such effects will be greater for mafic magma and felsic magma because of the relationship between methane solubility, methane speciation in melt, and melt polymerization. Such experimental data are not, however, available as yet.

8.4 Sulfur solubility Sulfur in magmatic liquids may occupy several oxidation states. Different effects on the magma would be expected depending on oxidation state. Oxidized sulfur, as SO2 or SO3, is comparatively rare, but has been documented during eruptions of relatively silica-rich magmatic systems in subduction zone settings such as the dacite eruption at Mount Pinatubo in 1991, for example (Wallace and Gerlach, 1994). In magmatic liquids, the oxidation state of sulfur varies between S2
and S6þ. The reduced form is common in basaltic liquids, whereas oxidized sulfur is more common in felsic magmas such as andesite, dacite, and rhyolite typically found in subduction zone settings (Carroll and Webster, 1994a,b; O’Neill and Mavrogenes, 2002; Jugo et al., 2010). In basaltic magma such as midocean ridge basalts, the sulfur contents do not deviate much from about 1000 ppm. However, with differentiation and increasing Fe content, in particular, there can be increasing S abundance (Wallace and Carmichael, 1992). The sulfur abundance in midocean basalt is significantly higher than in basalt and andesite magma in subduction environments where total sulfur contents seem to be only several hundred ppm (Carroll and Rutherford, 1987). It has been suggested that these lower sulfur concentrations are the result of sulfur oxidation, degassing, and crystallization of sulfate minerals (Nilsson and Peach, 1993). The oxidation state of sulfur is, therefore, one of the important factors that governs its solubility in melts (Carroll and Webster, 1994a,b; Jugo et al., 2010). Ultimately, the oxidation state will affect properties magmatic liquids (e.g., Richardson and Fincham, 1954; Nagashima and Katsura, 1973; Sosinsky and Sommerville, 1986; Carroll and Webster, 1994a,b; O’Neill and Mavrogenes, 2002; Backnaes et al., 2008, 2011; Park and Park, 2012). The principle redox equilibria governing the oxidation state of sulfur in magmatic liquids are: Oxidation to S4þ : S þ O2 þ O2
ðmeltÞ5SO2
3 ðmeltÞ

(8.15)

Oxidation to S6þ : SO2 þ 1=2O2 þ O2
ðmeltÞ5SO2
4 ðmeltÞ;

(8.16)

(8.17) and reduction to S2
: S2 þ 2O2
ðmeltÞ52S2
ðmeltÞ þ O2 . The equilibrium constants for these reactions as a function of oxygen fugacity, fO2, illustrate how decreasing fO2 leads increased solubility of reduced sulfur and decreased solubility oxidized sulfur (Nagashima and Katsura, 1973; see also Fig. 8.18). Similarly, at constant oxygen fugacity, the sulfur solubility increases with increasing sulfur fugacity as Eqs. (8.15)e(8.17) shift to the right (Backnaes and Deubner, 2011; O’Neill and Mavrogenes, 2002; see also Fig. 8.19).

556

Chapter 8 Volatiles in magmatic liquids

FIGURE 8.18 Sulfur solubility in silicate melts as indicated as a function of oxygen fugacity, fO2, and melt polymerization, NBO/Si, also emphasized with arrows. Redrawn from Nagashima and Katsura (1973).

FIGURE 8.19 Redox ratio of sulfur in haplobasaltic melt as a function of fO2 relative to fO2 of the quartz-magnetite-fayalite (QFM) oxygen buffer. Redrawn from Jugo et al. (2010).

8.4 Sulfur solubility

557

A transition from reduced to oxidized sulfur can be described by combining the fO2-dependent S6þ/S2
-relationships via the redox reaction; S2
þ 2O2 5SO2
4 ; so that oxygen fugacity is linked to the equilibrium     log fO2 ¼ 0:5• log XSO4 =XS2
þ log K8:18

(8.18)

(8.19)

The slope of sulfur redox ratio against fO2 is about 2, which is consistent with the presence of only S2
and SO4 (Jugo et al., 2010; see also Fig. 8.18). The equilibrium constants for equilibria (8.15) and (8.16) are linear functions of oxygen fugacity, fO2, from values above the NNO oxygen fugacity buffer, Ni þ 0.5O2 ¼ NiO (NNO), to two orders of magnitude below it. Therefore, from oxygen fugacities near that of the NNO oxygen buffer and above, from sulfur redox ratio against fO2, sulfur is dissolved solely in oxidized form, SO4, whereas at intermediate oxygen fugacity, below that of the NNO buffer, S2
and SO2
4 coexist. The exact oxygen fugacity interval across which this latter situation exists depends on the silicate composition, whether in simple metal oxide silicate systems (Nagashima and Katsura, 1973; Carroll and Webster, 1994a,b) or more complex systems such as slags or natural magmatic liquids (Klimm et al., 2012; Lesne et al., 2015). The situation in natural magmatic systems is qualitatively such that the proportion of oxidized sulfur, S6þ/SS, becomes a systematic function of oxygen fugacity (Fig. 8.20).

FIGURE 8.20 Redox ratio of sulfur in magmatic liquids and simple system melts with varying NBO/T-values at different oxygen fugacity relative to that of the QFM oxygen buffer. Abbreviations: Ab, NaAlSi3O8; Trond, trondhjemite. Redrawn from data of Jugo et al. (2010), Botcharnikov et al. (2011), and Klimm et al. (2012).

558

Chapter 8 Volatiles in magmatic liquids

8.4.1 Oxidized sulfur (SO2 and SO3) Among the two oxidized states of sulfur, S6þ is the most common in natural magma. However, evidence for S4þ in silicate glasses and melts also has been reported (Me´trich et al., 2002; Bingham et al., 2010; Wilke et al., 2011). It has been suggested, however, that the observed S4þ oxidation state may be the result of interaction between the sample and the X-ray beam used for the XANES spectroscopy employed to determine the oxidation state of sulfur (Me´trich et al., 2010; Wilke et al., 2011). The equilibrium constant for reaction (8.15) is;   K ¼ XSO4 ðmeltÞ= fSO2 •ðfO2 Þ0:5 •XO2
ðmeltÞ ;

(8.20)

where XSO4 is the mol fraction of component SO4, O is oxygen in the melt and may be viewed as an expression of melt structure, and fO2 and fS2 the fugacities of oxygen and sulfur, respectively. Ideally, the activity of SO4 component should be used. However, here, activity of SO4 has been replaced by mol fraction, XSO4 (Holmquist, 1966; see also Backnaes and Deubner, 2011, for a more recent review of this situation). The solubility of oxidized sulfur then becomes;   log XSO4 ¼ 0:5 log fO2 þ log fSO2 þ log K8:20 þ aO2
. (8.21) The solubility of oxidized sulfur is, therefore, a positive function of both oxygen and sulfur fugacity. 2


8.4.1.1 Composition, temperature and pressure effects on oxidized sulfur solubility A relatively small number of experimental studies has been conducted to determine the SO2/SO3 solubility in silicate melts and magmatic liquids. From the experimental data that do exist, in chemically simple binary and ternary melt systems, the sulfur solubility and the slope of the solubility curve are linked to NBO/T(T ¼ Si) of the sulfur-saturated melts. In addition, there also appear to be systematic relationships between electronic properties of the metal cation and sulfate solubility. The solubility of oxidized sulfur increases with decreasing electronegativity of the metal cation(s) (Fig. 8.21). Such a positive correlation has also been reported for natural magmatic liquids so that the solubility decreases as the metal cation becomes more electronegative (Lesne et al., 2015). Interestingly, such correlations with solubility also has been seen for CO2 (see Section 8.1.1 above). There may be a general positive correlation between sulfate concentration and water content in a mixed silicate-S-O-H system although the data appear widely scattered (Lesne et al., 2015). This data scatter notwithstanding, this correlation may simply reflect the fact that dissolved water causes silicate depolymerization, and increased silicate depolymerization drives increasing sulfate solubility (Massotta and Keppler, 2015). Sulfur solubility in magmatic liquids tends to increase with increasing temperature. There is, however, a significant effect of the oxygen fugacity on this temperature-dependence so that under more oxidizing conditions, the solubility in hydrous andesite melt, for example, increases more rapidly with temperature than under more reducing conditions (Carroll and Rutherford, 1987; Luhr, 1990; see also Fig, 8.22).

8.4.1.2 Solubility mechanisms of SO2 and SO3 in magma Based on the solubility data for oxidized sulfur together with a few experimental studies in which the oxidized sulfur speciation was determined (Caroll and Webster, 1994; Backnaes et al., 2008), the solution mechanism of SO3 in magmatic liquids can be written as; 2Qn þ SO3 52Qnþ1 þ SO2
4 ;

(8.22)

8.4 Sulfur solubility

559

FIGURE 8.21 Solubility of sulfur as a function of melt NBO/T and ionization potential of network-modifying cation. Redrawn with data from Ooura and Hanada (1998) (solid symbols) and Nagashima and Katsura (1973) (open symbols).

which is conceptually similar to the solution of CO2 to form CO2
3 (Eq. 8.5). In other words, in simple CeO and SeO volatile system, the principal solution mechanisms of oxidized carbon and oxidized sulfur are similar and in both situations silicate polymerization increases. Experimental data with which to describe the solution mechanisms in hydrous S-bearing systems are not available. It is, however, tempting to speculate that the mechanism in silicate melt þ SeOeH might be conceptually similar to silicate melt þ CeOeH. This seems a reasonable assumption because the solubility of SO2 and CO2 in magma is about the same and the interaction with the silicate melt structure also seems to be similar. In such a case, one may speculate that in analogy with Eq. (8.7) the solution mechanism of oxidized sulfur in the SeOeH system might be written as; SO4 þ H2 O þ Qnþ1 HHSO4 þ Qn .

(8.23)

We must keep in mind, however, that in the sulfur system, SO4 tetrahedra are formed in the melt, whereas C systems, CO3 triangles are formed. This difference likely will result in solubility differences between oxidized carbon and oxidized sulfur.

560

Chapter 8 Volatiles in magmatic liquids

FIGURE 8.22 Temperature-dependence of sulfur solubility in basalt melt under very oxidizing (MMO buffer) and more reducing (NNO) conditions. Redrawn from Carroll and Rutherford (1987).

8.4.1.3 Oxidized sulfur, temperature, and pressure The solubility of oxidized sulfur in magmatic liquids varies both with temperature and pressure. The temperature effect diminishes as the oxygen fugacity decreases (Carroll and Rutherford, 1987; see also Fig. 8.22). In a review of sulfur solubility in magma, Carroll and Webster (1994a,b) also noted that sulfur solubility increases with pressure, as did Mysen and Popp (1980). The pressure effect appears sensitive to both temperature and redox conditions. Surprisingly, perhaps, the pressure effect on SO2 solubility in silicate melts is considerably less than the pressure effect on CO2 solubility (Fig. 8.23). This difference likely reflects different geometries of the CO3 and SO4 complexes in melts.

8.4.1.4 Magma properties and SO2/SO3-induced melt polymerization Crystallization phase relations in the presence of SO2- or SO3-saturated melt would show polymerized silicate minerals expanding their stability field compared with their stability fields in the absence of sulfur. It is clear that under redox conditions where SO3 is the stable sulfur species (typically a few orders of magnitude above the fO2 defined by the NNO buffer; see Luhr, 1990; Baker and Rutherford, 1996) anhydrite (CaSO4) is an early crystallizing phase. In fact, it has been suggested that in order to account for the sulfur release from volcanic eruptions such as El Chicho´n (Mexico) and Mt. Pinatubo (Philippines), the source of the excess sulfur was the early crystallizing anhydrite (Luhr, 1990). The crystal fractionation leading to evolution from basalt to trachyandesite during the 1982 eruption of El Chicho´n may well have been advanced by the crystallization of anhydrite and the associated increase in silicate polymerization of the magma. An alternative is mixing of a sulfide-saturated basalt with highly oxidized dacite magma (Kress, 1997). An increase in this sulfate abundance leads to an increase in the abundance ratio, Qn/Qnþ1, which, in turn, implies depolymerization of the silicate melt.

8.4 Sulfur solubility

561

FIGURE 8.23 Comparison of CO2 and SO2 in CaMgSi2O6 melt on a molar basis (O ¼ 8) as a function of pressure. Redrawn from Mysen (1977).

Degassing of an oxidized hydrous magma with sulfur dissolved as sulfate leads to magma polymerization, which would decrease the sulfur solubility. The degassing process and attendant sulfur exsolution would likely result in crystallization of sulfate minerals such as anhydrite. As noted in Chapter 9, transport properties of magma are closely related to the melt polymerization. One such transport property is diffusion. Although comparative studies of SO2/SO3 saturated magma have not been carried out, some data on sulfur diffusion exists (Watson, 1994; Baker and Rutherford, 1996; Behrens and Stelling, 2011). From this information it is clear, for example, that the diffusivity of oxidized sulfur is lower than reduced sulfur (Behrens and Stelling, 2011; see also Fig. 8.24). As will discussed further below, such a difference likely reflects the different structural roles of sulfur in magmatic liquids depending on the sulfur oxidation state. Dissolved H2O also affects the sulfur diffusion (Baker and Rutherford, 1996). The increased sulfur diffusivity with increasing H2O content likely reflects increased depolymerization of magma caused by dissolved H2O (Fig. 8.24B).

8.4.2 Reduced sulfur (S2L) At oxygen fugacity conditions less oxidizing than about two orders of magnitude below that defined by the NNO oxygen buffer, S2
is the stable form of sulfur in silicate melts (Jugo et al., 2010; Bingham et al., 2010; Backnaes and Deubner, 2011). Natural basaltic and ultramafic magmas typically are formed under fO2 conditions sufficiently reducing to stabilize sulfides in solution because the oxygen fugacity associated with their formation is sufficiently low (Carmichael and Ghiorso, 1990; Wallace and Carmichael, 1992). In addition to oxygen fugacity conditions, the most important factor affecting sulfur solubility in such magmatic systems is melt FeO content (Fig. 8.25), with the highest sulfur solubilities observed in the most FeO-rich melt compositions (w2500 ppm).

562

Chapter 8 Volatiles in magmatic liquids

FIGURE 8.24 Temperature-dependence of sulfur diffusion coefficient in rhyolite melt (A) dry under oxidizing and reducing conditions. (B) of rhyolite melt under dry and hydrous conditions as indicated. Redrawn from Behrens and Stelling (2011).

FIGURE 8.25 Sulfur solubility in basaltic magma as a function of wt% FeO in magma. Open circles are data from (Mathez, 1976). Redrawn from compilation of data by Carroll and Webster (1994a,b).

The oxygen fugacity range of the transition interval between oxidized and reduced sulfur to some extent can be linked to magma polymerization, including H2O dissolved in the magma. The more polymerized a magmatic liquid at given oxygen fugacity, the higher is the fraction of oxidized sulfur. In other words, at given oxygen fugacity, sulfur in felsic magmas tend to be more oxidized than sulfur in more mafic magma compositions such as basalt.

8.4 Sulfur solubility

563

The redox equilibrium can be expressed as2; Qn ðMÞ þ SO3 5M2 S þ Qnþ1 ðM = 2Þ þ 2O2 .

(8.24)

The Q (M/2) implies that the Q -species require only half the number of metal cations for bonding to its smaller number of bridging oxygen compared with the less polymerizing Qn(M)-species. The M2S indicates metal sulfide complex in the melt and glass. The solubility of reduced sulfur in magmatic liquids varies with the fugacity of sulfur and oxygen (Richardson and Fincham, 1954; Sosinsky and Sommerville, 1986; O’Neill and Mavrogenes, 2002; Jugo et al., 2005, 2010; Wilke et al., 2011). It also depends on magma bulk composition and the presence of other volatiles, in particular H2O, in solution (Botcharnikov et al., 2011; Beermann et al., 2015). Even in a chemically simple melt or glass system such as Na2OeSiO2, the sulfur solubility and the slope of the solubility curve are linked to NBO/T (T ¼ Si) of the melts. There also appear to be systematic relationships between electronic properties of the metal cation and sulfur solubility (Fig. 8.21). Such a positive correlation has also been reported for natural magmatic liquids (Lesne et al., 2015). The correlation of the FeO content and sulfide solubility has been expressed as sulfide capacity, Cs, which was originally defined as (Richardson and Fincham, 1954);   Cs ¼ wti fO2 = fS2 ; (8.25) nþ1

nþ1

where wti is the weight fraction of the oxide or oxides of interest. The sulfur capacity is very sensitive to FeO content and less so to other network-modifying cations (Taniguchi et al., 2009; Park and Park, 2012; see also Fig. 8.26). Dissolved H2O has the same effect. The need to generalize sulfur solubility in silicate melts led O’Neill and Mavrogenes (2002) to propose that sulfur capacity can be related to silicate composition via the expression. X ln Cs ¼ A0 M XM AM . (8.26) O’Neill and Mavrogenes (2002) calibrated Eq. (8.26) with 150 experimental data points using natural magma compositions. Those calibrations were then used to back-calculate the sulfur capacity of these 150 melts. This model yields accurate results (Fig. 8.27). One must caution, though, that only chemically complex natural compositions were employed in this calibration. This carries the possibility of offsetting effects. Thus, application of a calibrated Eq. (8.24) to compositions outside the composition range for which the calibration was carried out should be conducted with caution.

8.4.2.1 Hydrous sulfide-bearing melts Speciation in the SeOeH fluid system has been reported from calculations by Lesne et al. (2015). In SeOeH fluids, the dominant S-bearing species are SO2 S2, and H2S. The SO2 species dominates at and above the redox conditions of the NNO buffer, whereas at lower fO2, H2S and S2 dominate (Fig. 8.28). Water and sulfur commonly exist together in magmatic systems much as magma þ H2O þ CO2 systems also are common (see above). Water in magmatic liquids does, however, tend to promote transformation of oxidized sulfate to reduce sulfide (Carroll and Rutherford, 1985). Sulfur solubility in In Eq. (8.24), the Qn(M) and Qnþ1(M/2) notations indicate silicate Qn-species with a nonbridging oxygen (NBO) bonded to a network-modifying metal cation. The superscript denotes the number of bridging oxygen (BO) so that NBO ¼ 4-BO ¼ 4-n. 2

564

Chapter 8 Volatiles in magmatic liquids

FIGURE 8.26 Sulfur capacity, Cs, different metal oxides, CaO and FeO, in CaOeSiO2 and FeOeSiO2 melts. Redrawn from Abraham et al. (1960).

FIGURE 8.27 Comparison of measured and calculated sulfur capacity of 150 natural magma compositions. Redrawn from O’Neill and Mavrogenes (2002).

8.4 Sulfur solubility

H2S

-1

H2 O

H2

-2

S2

-3

log xi

565

-4 -5 SO

-6

2

Ptot = 208 MPa T= 1200°C fH2O=19 MPa

-7 -8

-5

-4

-3

-2

-1

0

1

2

3

log fO2, ΔNNO FIGURE 8.28 Calculated gas species type and abundance in the SeOeH system under conditions indicated on figure. Redrawn from Lesne et al. (2015).

hydrous melts increases compared with the solubility in anhydrous melts whether under reducing or oxidizing conditions. This happens via solution mechanisms of H2O in silicate melts (increasing NBO/T of magma) such as described under silicate melt þ H2O þ CO2 above. Under reducing conditions, Lesne et al. (2015) determined the solution mechanism of reduced sulfur in hydrous melts by vibrational spectroscopic methods, but did not find any clear relationship between reduced sulfur solubility and H2O solubility. This conclusion differs from that of Stelling et al. (2011) who detected HS
complexes in addition of S2
and proposed a solution equilibrium such as; S2
þ H2 O ¼ SH
þ OH
.

(8.27)

In light of the fact, discussed in Chapter 7, that H2O dissolved in silicate melts, be they simple system melts or natural magma, results in silicate melt depolymerization and sulfide solubility is positively correlated with magma NBO/T, it would seem reasonably that as a melt becomes more depolymerized, the reduced sulfur solubility also increases.

8.4.2.2 Oxysulfide Under certain very reducing conditions and lacking hydrogen such as observed in sulfide assemblages in meteorites and perhaps also in core/mantle interfaces such as that of the planet Mercury (Boujibar et al., 2015), the sulfur solubility increases as the oxygen fugacity decreases to several orders of magnitude below that of the IW buffer (Boujibar et al., 2015). Recent work on oxysulfides, in which some of the oxygens in the silicate tetrahedra are replaced with sulfide, has focused on Li-bearing systems because of the use of such materials in Li-ion battery technology. From 29Si MAS NMR examination of Li2SeLiS2eSiO2 glasses, sulfur substitution of the oxygen in silicate tetrahedral takes place in a manner that structurally resembles oxycarbide (see above) and oxynitrides (see below) substitutions. There appears to be systematic relationship among species and proportion of sulfur-bearing and sulfur-free structural units (Tatsumisago et al., 2000; see also Fig. 8.29). It seems reasonable that the relationships observed by Boujibar et al. (2015) also reflect substitution of oxygen with sulfur in the silicate tetrahedra.

566

Chapter 8 Volatiles in magmatic liquids

FIGURE 8.29 Silicate and sulfide (oxysulfide) species in melts in the system Li2SeLi2OeSiO2. Redrawn from Hayashi and Tatsumisago (2020).

8.4.2.3 Magma properties, sulfide-speciation and silicate melt polymerization The link between sulfide- and Qn-speciation illustrated in Eq. (8.22) leads to the conclusion that as the S6þ/S2
ratio decreases and Eq. (8.22) shifts to the right, the melt becomes more polymerized (its NBO/T decreases). An alternative way to view this is that under conditions of constant fO2 and fS2, the sulfur solubility increases the more depolymerized the melt. This implies also that more mafic a melt, the greater is the sulfur solubility. This also implies that during fractional crystallization which commonly shifts magma to become more felsic, the sulfur solubility in the magma decreases and precipitation of sulfide minerals becomes increasingly likely. The relationship between magma NBO/T and sulfide solubility also leads to suggestions that all the magma properties that depend on the NBO/T of the silicate can be linked directly to the redox equilibria involving sulfur species. As also discussed above for carbon solubility behavior, if the oxygen fugacity decreases, the S6þ/S2
decreases, which leads to an NBO/T-decrease as illustrated with the expression derived from Eq. (8.23);   Qnþ1 =Qn ¼ K8:22 • S6þ = S2
•ð1 = fO2 Þ; (8.28) where an NBO/T-decrease, D(NBO/T) is linked to the Qnþ1/Qn-ratio as; DðNBO = TÞ ¼ Qnþ1 =Qn .

(8.29)

8.5 Nitrogen solubility and solution mechanisms

567

Given that most mineral/melt partition coefficients, Dxtal/melt, decrease with increasing NBO/T of the melt (see Chapter 3), the change in crystal/melt partition coefficient, DDxtal/melt, in sulfur-bearing magmatic systems is: DDxtal=melt aS6þ =S2
. (8.30) Because the sulfur solubility increases as a magma becomes more mafic, the effect of sulfur redox ratio on crystal/melt partition coefficients is greater for a basalt melt compared to a rhyolite melt, for example. Another consequence of the relationships between sulfur solubility, sulfur redox ratio and magma NBO/T is that any change in magma polymerization, NBO/T, will affect the sulfur solubility and therefore, whether or not sulfide minerals may crystallize, This is important because although sulfide concentrations in magma are on the order of thousands of ppm (Carroll and Webster, 1994a,b), in particular transition metal trace element sulfide/silicate melt partition coefficients are so large (Mungall and Brenan, 2014) that even a fraction of a percent sulfide crystallization can cause the transition metal abundance in a magmatic liquids to change significantly. A change of NBO/T of a magma could be accomplished by degassing of H2O at or near the surface of the Earth, for example. Transport properties such as diffusion and viscosity are sensitive to melt polymerization with the values of both properties decreasing with increasing NBO/T of a magmatic liquid (see Chapter 9). The magnitude of such effects depends on the composition of the silicate melt because both the sulfur solubility and the sulfur redox ratio depend on bulk composition of magma. Sulfur diffusion has been examined extensively (Baker and Rurtherford, 1996; Freda et al., 2005; de Lemastre et al., 2005; Frischat et al., 2011; Behrens and Stelling, 2011; Backnaes et al., 2011). Sulfur diffusivity depends on its oxidation state (Fig. 8.24). Moreover, the activation energies of diffusion of sulfur under both oxidizing and reducing conditions range between 115 kJ/mol for S2
in hydrous andesite melt (Watson et al., 1994) to 458 kJ/mol in nominally anhydrous NaAlSi3O8 melt (Winther et al., 1998). Such activation energies are in the range of SieO and AleO bond energies, which leads to the suggestion of bond disruption and formation in the silicate network during sulfur diffusion. That would also be consistent with sulfate and sulfide solution mechanisms in silicate melts, which makes it is clear that the solution mechanisms of both SO4 and S2
groups are linked to the silicate network. This conclusion is further supported by the observation that in the sulfur diffusivity increases as H2O is dissolved in magma (Watson et al., 1993). Presumably, this H2O causes disruption of the silicate network, which causes increased diffusivity and decreased activation energy of diffusion.

8.5 Nitrogen solubility and solution mechanisms Nitrogen ranks number five in solar abundance. Its terrestrial abundance resembles that of carbonaceous chondrites (Dauphas, 2017). On the Earth, nitrogen recycling takes place in subduction zones. There is, however, a difference between the proportion of nitrogen being subducted and the amount returned to the Earth’s surface (Roskosz et al., 2013). More nitrogen seems subducted than the amount of nitrogen returned to the surface. An understanding of the solubility and solution behavior of nitrogen in the Earth is important because such information aids us in evaluating relationships between nitrogen reservoirs in the condensed Earth and the atmosphere where N2 is its major component.

568

Chapter 8 Volatiles in magmatic liquids

In the condensed Earth (silicate crust and mantle together with metallic core), the redox conditions are such that nitrogen may exist in more than one oxidation state (Mysen et al., 2008). The oxidized state commonly is considered to be molecular N2, but more oxidized nitrogen can be formed (Roskosz et al., 2006). The reduces states are in the form of various NeH bonded functional group or as NH3, NH2, and NH4. Absent hydrogen, nitride complexing is likely. Nitrogen in these forms exhibits considerably different solubility and solution behavior from oxidized nitrogen in magmatic liquids. Such differences can have major impact on modeling nitrogen distribution in the Earth (Mysen, 2019).

8.5.1 Oxidized nitrogen Nitrogen is often used as a monitor of materials exchange between the solid Earth and its oceans and atmosphere. Adequate characterization of the nitrogen exchange relies on knowledge of bulk nitrogen contents, nitrogen distribution among various reservoirs, and on nitrogen transport mechanisms within and between the reservoirs. It is commonly assumed that nitrogen behavior under these circumstances can be described in terms of the behavior of N2. Even under oxidizing conditions, nitrogen exists as N2, which is nonreactive, and nitrosyl groups, which are (Roskosz et al., 2006). The N2 solubility commonly follows Henry’s Law with a Henry’s Law constant near 5$10
9 mol g
1 bar
1 (Javoy and Pineau, 1991; Libourel et al., 2003; Roskosz et al., 2006). Some variations in the Henry’s Law constant may be ascribed to compositional dependence of the N2 solubility similar to the behavior of noble gases in silicate melts. These variables include extent of silicate polymerization, aluminum substitution of silicon, and the electronic properties and proportions of network-modifying cations (alkali metals and alkaline earths). The N2 solubility increases as the abundance of three-dimensionally interconnected cavities in the silicate structure increases, which is similar to the solubility behavior of noble gases (Carroll and Draper, 1994; Zhang et al., 2010). Increased cavity abundance results from increased silicate polymerization and, therefore, increased SiO2 þ Al2O3 concentration in a melt. The more polymerized a melt, the greater the concentration of three-dimensional cavities and, therefore, the greater the N2 solubility. Moreover, the cavity size likely varies with the types of alkali and alkaline earth cation or cations in the structure (LeLosq et al., 2015) where larger cations favor larger cavities. Larger cavities would enhance the solubility of gas molecules and atoms (Zhang et al., 2010). The increase in N2 solubility in a silicate melt as the radius of the network-modifier cation increases is also consistent with this model (Roskosz et al., 2006). The N2 solubility in silicate melts falls on the line defining solubility of noble gases as a function of their atomic radius (Carroll and Draper, 1994; see also Fig. 8.30) thus suggesting similar solution behavior of noble gases and molecular N2. The positive correlation between the extent of polymerization of silicate melts and nitrogen and noble gas solubility (Miyazaki et al., 1995; Roskosz et al., 2006) also is consistent with this simple solubility model. Nitrosyl groups appear in depolymerized silicate melts under oxidizing conditions (Roskosz et al., 2006). The abundance ratio of nitrosyl groups to molecular nitrogen increases with decreasing pressure and with decreasing ionic radius of the network-modifying cation (Roskosz et al., 2006). The proportion of nitrosyl group also increases the more depolymerized a silicate melt. In view of the observation that deviations from Henry’s Law solution behavior seems linked to the existence of nitrosyl groups in the melts (Roskosz et al., 2006), translated to natural magmatic liquids, the implication of this is that even under oxidation conditions, the extent to which the solution behavior of nitrogen deviates from Henry’s Law becomes more important the more mafic the magma.

8.5 Nitrogen solubility and solution mechanisms

569

FIGURE 8.30 Solubility of noble gases and N2 in basalt melt as a function of atomic diameter of noble gases and molecular diameter of N2. Redrawn from data from Carroll and Draper (1994), and Roskosz et al. (2006).

The equilibrium that describes formation of nitrosyl groups in H-free silicate melts can be expressed as: 12Qn ðMÞ þ 3O2 þ 2N2 52Qn
1 ðNÞ þ 6Qn
1 ðMÞ. (8.31 ) In this reaction, Q (M) and Qn
1(M) denote Q-species with M-cations as network-modifiers and forming bonding, therefore, with nonbridging oxygen. The Qn(M) is more polymerized than Qn
1(M). The Qn
1(N)-species is a structural entity where nitrogen as N3þ effectively serves as a networkmodifying cation in replacement of a metal cation. Such a structure obviously requires that three nonbridging oxygens be linked to the N3þ. In other words, formation of nitrosyl groups in a silicate melt results in silicate depolymerization. The transformation from N2 to N2O (nitrosyl) groups in melts results in depolymerization of the melt (Eq. 8.3). Thus, in principle, magma properties that depend on their NBO/T would aso vary as a function of N2/N2O abundance ratio. The deviations from Henry’s Law behavior caused by the existence of nitrosyl groups in melts will also lead to changes in mineral/melt nitrogen partition coefficients. However, it appears that as of now, these matters have not been addressed experimentally. n

8.5.2 Reduced nitrogen The nitrogen solubility in silicate melts expressed as a function of hydrogen fugacity fall into three distinct groups defined by different hydrogen fugacity (Fig. 8.31; see also Mysen et al., 2008). This solubility behavior reflects different nitrogen-bearing species in the melts under increasingly reducing conditions. This speciation changes from N2 molecules under the most oxidizing conditions, to amide groups coexisting with molecular N2 under intermediate redox conditions and, finally, to ammine groups coexisting with molecular NH3 under the most reducing conditions (Mysen et al., 2008). Those spectroscopic data of the quenched melts are similar to those reported by Kadik et al. (2013) from quenched melts in the system, Na2OeAl2O3eFeOeSiO2eNeOeH. Li et al. (2015) also reported NH3 molecules in silicate glasses quenched from melts, but suggested that NH4 groups may also exist in silicate melts under reducing conditions.

570

Chapter 8 Volatiles in magmatic liquids

FIGURE 8.31 Nitrogen solubility in Na2OeSiO2 melts as a function of hydrogen fugacity, fH2. Redrawn from Mysen et al. (2008).

The solution mechanism of reduced nitrogen in silicate melts can be written as an equilibrium between ammonia, NH3, and ammine groups, NH
2 (Mysen et al., 2008): 2Qn þ NH3 5Qn
1 ðNH2 Þ þ Qn
1 ðOHÞ.

(8.32)

In the reduced NeOeH system, the ammine group, NH2, substitutes for oxygen, which means that solution of reduced nitrogen in melt results in depolymerization of the silicate structure. This equilibrium is analogous to that between reduced carbon species, CH4 and CH3 described above where the CH3 groups substitute for oxygen in the silicate tetrahedra (Mysen et al., 2011). This nitrogen solution mechanism also implies that when a glass or melt is depolymerized (i.e., Qn
1/Qn, increases), the NH2/NH3 ratio should decrease to satisfy the equilibrium constant of reaction (8.32) (Mysen et al., 2008):    2   K ¼ XQn
1 ðOHÞ = XQn • XQn
1 ðNH2 Þ = XNH3 . (8.33) This is precisely what happens (Figs. 8.32 and 8.33). An intermediate redox state of nitrogen, most likely NHþ 2 groups, was reported from the Raman spectra by Mysen et al. (2008) and subsequently by Kadik et al. (2013). Molecular nitrogen, N2, also is present in such melts. In this case, the equilibrium between molecular species and NHþ 2 functional groups in silicate melts can be expressed as: n
1 4Qn þ 2N2 þ 4H2 þ O2 54NHþ . 2 þ 4Q

(8.34)

8.5 Nitrogen solubility and solution mechanisms

571

FIGURE 8.32
Schematic representation of structural relations of ammide (NHþ 2 ) and ammine (NH2 ) groups in silicate melts.

FIGURE 8.33 Abundance ratio, NH
2 /NH3 in silicate melts as a function of NBO/Si of the melts relative to a value for melts at NBO/Si ¼ 0.4. Redrawn from data from Mysen and Fogel (2010).

572

Chapter 8 Volatiles in magmatic liquids

þ This is a redox reaction whereby molecular N2 is reduced to NHþ 2 and the NH2 group effectively serves as a network-modifier and likely bonds to a nonbridging oxygen in the silicate structure. In summary, the solution mechanisms of nitrogen in silicate-N-O-H magmatic liquids can have different effects on the structure depending on the redox state of nitrogen and, therefore, the redox conditions. First, under sufficiently oxidizing conditions where only N2 molecules are stable, there is no effect on silicate structure of dissolved nitrogen. At intermediate redox conditions, molecular NH3 and H2 coexist with amide groups, NHþ 2 , which leads to silicate depolymerization (Eq. 8.34). With further reduction of nitrogen, ammine groups replace oxygen in the silicate tetrahedral network so that the glass and melt structure becomes depolymerized (Fig. 8.32). In hydrogen-free silicate melt-N-O systems under conditions more reducing than that of the IW oxygen buffer, nitrogen can form nitride complexes, either with network-modifying cations such as alkali metals or alkaline earths or with nitrogen replacing oxygen in silicate structures, or both. Oxynitride formation can be expressed as a redox-driven reaction that involves changes in silicate melt polymerization:

Qn ðMÞ þ N2 5Qn
2 N ðMÞ:

(8.35)

In this expression, the Q N(M) is an oxynitride complex. Its silicate structure is more depolymerized than Qn(M) so this nitrogen solution mechanism is a depolymerization mechanism. That behavior contrasts with nitride formed by bonding with metal to create metal nitride complexes. In such a case, metal cations are extracted from their network-modifying role, thus resulting in silicate polymerization: n
2

1=2xN2 þ yQn
1 5My Nx þ yQn ;

(8.36)

where Q and Q are silicate species and MyNx is a metal nitride complex. Whether or which of these nitride solution mechanisms operate in reduced, N-bearing silicate melts is not known. These possible solution mechanisms are analogous to those of highly reduced carbon and sulfur in the absence of hydrogen. n
1

n

8.5.3 Nitrogen in the Earth’s interior During the earliest stages of formation of the Earth, the redox conditions likely were approximately one to three orders of magnitude below the conditions described with IW buffer (O’Neill, 1991; Gessman and Rubie, 2000; Wade and Wood, 2005). Under such conditions, NH3, CH4, H2O, and H2 are the dominant species in the CeOeHeN system (Mysen et al., 2008; Kadik et al., 2015). Nitride complexing would occur in the absence of hydrogen. Crystalline nitrides have been reported from reduced chondrites and diamond inclusions from deep-seated kimberlites (Rubin, 2010; Sobolev et al., 2019). The oxygen fugacity conditions during early Earth core formation were several orders of magnitude lower than those commonly considered for the interior of the modern Earth, which are between those of the QFM and IW oxygen buffer (Carmichael and Ghiorso, 1990; Wade and Wood, 2005; McCammon, 2005). Therefore, the solubility behavior of nitrogen in magmatic liquids in the interior of the modern Earth probably can be described with equilibria such as Eq. (8.32) (Mysen et al., 2008). As noted earlier, the nitrogen solubility in magmatic liquids under these conditions is greater than the solubility when nitrogen exists as molecular N2.

8.6 Hydrogen solubility and solution mechanisms

573

For more reducing conditions such those of the mantle of a young Earth, more reduced nitrogen, in
the form of ammine groups, NH
2 , likely existed in equilibrium with NH3. Here, the NH2 groups replaces one or more of the oxygens in silicate tetrahedra. The equilibrium between N-bearing and other silicate species in magma under such conditions was described with Eq. (8.30). In Eq. (8.30), an SieOeSi bridge is cleaved and the oxygen formerly forming a bridge is replaced by a networkterminating OH
group and an NH
2 group (see also Fig. 8.32). The nitrogen budget of the Earth is governed by the redox state of nitrogen because its solubility is dependent on the nitrogen oxidation state (Fig. 8.31). Subduction zones are major venues for nitrogen flux into and out of the Earth (Busigny et al., 2011) with oxygen fugacity during nitrogen release a major factor (Li and Keppler, 2014). Under oxidizing conditions such as those defined by the QFM buffer and above, which is common in the upper 100 km of subduction zones (Carmichael and Ghiorso, 1990), N2 is a principal nitrogen species. Nitrogen dissolved as N2 in subduction zone magma under such redox conditions likely is recycled and returned to the oceans and the atmosphere because of the low solubility of molecular N2 in magma. Under more reducing conditions such as those of the lithosphere (near the MW oxygen buffer), and greater depth in subduction zones nitrogen exists in reduced form with NeH bonding. In this form, nitrogen is more soluble in magma than as molecular N2 and may remain in the mantle during melting (Bebout et al., 2013). Because the Earth’s interior is undersaturated with respect to nitrogen (e.g., Yoshioka et al., 2018), this nitrogen is not returned to the Earth’s surface even during melting or fluid release because of the compatible nature of reduced nitrogen in silicate minerals at high temperature and pressure (Busigny et al., 2011).
The different solubility behavior of oxidized (N2) and reduced (NH3, NHþ 2 , NH2 ) nitrogen in mantle magma and minerals in the Earth’s interior would lead to an increase in mantle nitrogen through Earth history and a decrease in nitrogen abundance in its oceans and atmosphere. An important conclusion from this is that the behavior of nitrogen in the Earth’s interior cannot simply be discussed in terms of its N2 form.

8.6 Hydrogen solubility and solution mechanisms Hydrogen is an important species in CeOeHeNeS systems under redox conditions near that of the IW oxygen buffer and below (Ni and Keppler, 2013;Boettcher et al., 1973). Such redox conditions appear relatively rare in the modern Earth although examples of fO2 conditions near the IW buffer have been reported from inclusions in deep diamonds (Sobolev et al., 2019). However, H2 likely was a major volatile component during the core-forming stage of the Earth where the oxygen fugacity was less than that of the IW buffer (O’Neill, 1991; Gessman and Rubie, 2000; Wade and Wood, 2005). With H2 as a major fluid species, significant effects on silicate equilibria in the early Earth might be possible (Shinosaki et al., 2014). Hydrogen can dissolve in silicate melts and glasses either in its physical form, where presumably solution is in the form of H2 molecules, through chemical reaction with silicate components, or a combination of both, is also possible (Doremus, 1966; Shackelford et al., 1972; Luth et al., 1987; Schmidt et al., 1998; Mysen and Fogel, 2010; Kadik et al., 2015). The H2 solubility in silicate melts and magma appears nearly independent of the degree of polymerization of silicate melts with perhaps only a small decrease in solubility with increasing NBO/Si of

574

Chapter 8 Volatiles in magmatic liquids

FIGURE 8.34 Hydrogen solubility in silicate melts as a function of NBO/Si of melt. Redrawn from Mysen and Fogel (2010).

the melt (Fig. 8.34). In this respect, hydrogen differs from that of noble gases and N2, the solubility of which decreases significantly as a melt becomes increasingly depolymerized (as discussed in the previous section). However, it should be remembered that the analyses were conducted on quenched melt (glass). There may be a quenching problem because of the small size of the hydrogen molecule so that the data in Fig. 8.34 may, in fact, represent a quenched state different from that at the temperature and pressure conditions under which the melts were originally formed. This possibly complication notwithstanding, from phase equilibrium measurements in silicateeH2OeH2 systems and vibration spectroscopy (Luth and Boettcher, 1986; Luth et al., 1987; Schmidt et al., 1998), hydrogen in silicate melts likely exits both in molecular form and as OH-groups formed by interaction with the silicate melt itself: 3Qn þ 4H2 ¼ 2Qn
2 ðHÞ þ SiH4

(8.37)

Here, two oxygen/silicate tetrahedron is transformed from bridging to nonbridging to form SieOH bonds. This is expressed as a Qn
2(H) species in Eq. (8.35). This solution mechanism is a very efficient silicate depolymerization reaction. It must be remembered, however, that this equilibrium depends strongly on the fugacity of H2, fH2.

8.6.1 Hydrogen in the Earth’s mantle Comparatively little is known about the behavior of hydrogen in silicate systems, which likely is because from an experimental perspective, sample containers such as those made of noble metal are

8.7 Halogen solubility and solution mechanisms

575

open to hydrogen loss under conditions of melting and crystallization of silicate systems. We may, nevertheless, speculate on some effects relevant to melting and crystallization of the Earth’s silicate materials in equilibrium with terrestrial core material. For example, the solidus temperature depression caused by H2 might resemble that of H2O because OH-groups are formed in a hydrogen saturated magma in the deep Earth. The composition of partial melts formed in this manner might also resemble those formed by partial melting of a hydrous mantle. At pressures corresponding to the uppermost mantle, such a melt would be silica-enriched such that it may resemble the composition of magma formed in the continental lithosphere in the presence of H2O (Kushiro, 2001; Tatsumi and Hanyu, 2003). What may happen at greater depth is open to speculation because even the role of H2O under deep mantle pressure and temperature conditions is not well known. However, if we may use the interaction between H2 and crystalline lower mantle (Shinosaki et al., 2014) as a guide for interaction between silicate magma and H2, Eq. (8.35) would be relevant. This means that highly depolymerized magma would be in equilibrium with lower mantle mineral assemblages under the redox conditions of a young Earth. This situation might enhance the fluidity of the early magma ocean, for example.

8.7 Halogen solubility and solution mechanisms Property, solubility, and structure information of halogen-bearing melts and magma is dominated by fluorine and chlorine. Data from Br- and I-bearing silicate melts are much less common. Fluorine is of particular interest as it may have significant effects on the behavior of magmatic liquids formed by partial melting and crystallization. And also, degassing of fluorine-bearing gases during volcanic eruption can have devastating effects on the immediate environment (Aiuppa, 2009; Bellomo et al., 2007). Chlorine on the other hand, has been more of focus in studies on economically important metals in magma and hydrothermal fluids because chloride complexes may enhance the solubility of many economically important metals in magma and hydrothermal fluids (Hsu et al., 2019; Iveson et al., 2019). Experimental data on the behavior of Br and I in magmatic systems is quite rare. Little is known about their solubility and solution mechanisms in magma.

8.7.1 Fluorine solubility Direct determination of fluorine solubility in silicate melts at high temperature and pressure is difficult because of the reactive nature of fluorine. However, fluorine solubility in silicate melts can be inferred from liquidus phase relations. For example, the fluorine content of alkaline earth silicate melts in equilibrium with fluorine-rich immiscible melts in the 1450e1565 C range decreases with increasing ionization potential of the alkaline earth cation (Ershova, 1957). Those and other liquidus phase equilibrium data indicate that the fluorine solubility also increases with decreasing SiO2 and with increasing Al2O3 contents (see Manning, 1981; for data from Al-bearing systems). A positive correlation of fluorine content with Al/(Al þ Si) also has been reported from 1.5 GPa/1400 C experiments in water-free Na2OeAl2O4eSiO2 and K2OeAl2O4eSiO2 systems (Dalou et al., 2015; see Fig. 8.35). There is a simple linear relationship between solubility and Al/(Al þ Si). The relationships in K- and Na-aluminosilicate systems are nearly undistinguishable from one another (Fig. 8.35A). The correlation of solubility with Al/(Al þ Si) remains when H2O is added to the system (Fig. 8.35B). In addition, the fluorine solubility in alkali aluminosilicate melts also is positively correlated with total H2O content of the melts and the effect of H2O increases the more aluminous the melt (Fig. 8.35B).

576

Chapter 8 Volatiles in magmatic liquids

FIGURE 8.35 Fluorine solubility in silicate melts. (A) Solubility in haplorhyolite melt at 1400 C and 1.5 GPa as a function of the Al/(Al þ Si) of the melt. (B) Solubility as a function of H2O and Al2O3 content in haplorhyolite melt at 1400 C and 1.5 GPa. Redrawn from (A) Dalou et al. (2015), and (B) Dalou and Mysen (2015).

8.7.2 Fluorine solution mechanisms The solution mechanisms of fluorine in magmatic liquids have been the subject of experimental study because of the strong effects of dissolved F on magma properties (Van Groos and Wyllie, 1967; Foley et al., 1986; Filiberto and Treiman, 2009). The solution mechanisms may be divided into three different types. In the simples of silicate melts such as fluorinated SiO2 melt, F solution involves exchanging a bridging oxygen with F
(Youngman and Sen, 2004; Fan et al., 2015). This mechanism is in many ways equivalent to breaking SieOeSi bridges with water in SiO2eH2O solution whereupon two OH-groups are formed by dissolving one H2O molecule, which interacts with bridging oxygen (Wasserburgh, 1957). In both situations (F or OH-exchange), the silicate structure is depolymerized. For fluorine, we may write a simple reaction; 2Qn þ F
¼ 2Qn
1 F .

(8.38)

In this equation, QF denotes a Q-species where one of the oxygens in the Q structure has been replaced with F. In principle, more than one oxygen could be replaced with fluorine in this way. This possibility has been found viable through MD calculations (Hayakawa and Hench, 2000). Some vibrational spectroscopic data can also be interpreted to be consistent with multiple F for O exchanges (Rabinovich, 1983; Yamamoto et al., 1983; Duncan et al., 1986). The fluorine solution mechanism in Eq. (8.36) is, therefore, a silicate depolymerization reaction much like the way H2O is dissolved in SiO2 melt. n
1

n
1

8.7 Halogen solubility and solution mechanisms

577

A second mechanism involves formation of complexes with alkali metals, alkaline earths, and even rare earth fluorides (Kizcenski and Stebbins, 2002, 2006; Kizcenski, Du, Stebbins, 2004; Mysen et al., 2004). From 19F MAS NMR spectra of such materials, there is clear evidence for simple metal fluoride complexes that involve specific cations (e.g., NaeF and CaeF) as well as mixed fluoride complexes (Kizcenski and Stebbins, 2006). This solution mechanism results in polymerization of the silicate melt structure. Again, the similarity with H2O is striking (Xue and Kanzaki, 2004; Cody et al., 2005, 2020; see also Chapter 7). A fraction of SieF bonding also has been detected inn these simple systems (Kizcenski and Stebbins, 2006; Ko and Park, 2013). An exchange reaction has been determined (Kizcenski and Stebbins, 2006); Si
O
Si þ M
F ¼ Si
F þ Si
O
M.

(8.39)

29

Fluorine-19 MAS NMR data, combined with Si MAS NMR and high-temperature Raman spectroscopic data, have been used to illustrate the interaction between F and chemically more complex silicate networks (Toplis and Reynard, 2000; Mysen et al., 2004) With monovalent metal cations, Mþ, in peralkaline silicate melts, one can write several solution reactions to illustrate how these F-bearing entities can be formed: 2Qn ðMÞ þ MF52Qnþ1 þ M3 OF.

(8.40)

Formation of mixed F- and O-bearing species, M3OF, causes silicate polymerization. However, given that equilibria such as (8.39) and (8.40) both operate in F-bearing metal oxide silicate melts, the stability of the various fluoride complexes governs the extent to which the degree of polymerization silicate structure will occur. Moreover, as such equilibra also are temperature-dependent (Fig. 8.36), variations in temperature will result is changes in polymerization of silicate melts. Aluminosilicate melts most closely mimic natural magmatic liquids. The third fluorine solution mechanism, which involves AleF bonding, applies to such melts. The importance of AleF bonding has been clearly demonstrated (Schaller et al., 1992; Zeng and Stebbins, 2000; Liu and Nekvasil, 2001; Mysen et al., 2004; Baasner et al., 2014). However, the AleF-bearing species cannot simply be AlF3 but must involve both oxygen and metal cations other than Si4þ and Al3þ (Zeng and Stebbins, 2000; Liu and Tossell, 2003; Mysen and et al., 2004). Under certain circumstances, some of the aluminum may undergo transformation from four- to five- and sixfold coordination at least for highly aluminous melts such as CaAl2Si2O8 (Stebbins et al., 2000). For peralkaline F-bearing aluminosilicate melts with Al2O3-abundance on the order of several mol %, there is little or no spectroscopic evidence for AleF type bonding (Mysen et al., 2004; Dalou et al., 2015). However, as the Al/(Al þ Si) of peralkaline aluminosilicate melts increases and approaches that of most natural magma, structures that include AleF bonding begin to appear. The detailed nature of the species containing AleF bonding have been identified via combinations of numerical simulation, 19 F MAS NMR and 29Si MAS NMR (Liu and Nekvasil, 2001; Liu and Tossell, 2003; Schaller et al., 1992; Zeng and Stebbins, 2000; Mysen et al., 2004). Several different Al-bearing complex, depending on Al/(Al þ Si), are consistent with the experimental and theoretical data. Their abundance changes systematically with the bulk Al/(Al þ Si) (Fig. 8.37). These abundance of the different F-bearing complex as a function of Al/(Al þ S) have different effects on overall aluminosilicate polymerization (Fig. 8.37B). In peralkaline aluminosilicate melts, initial Al3þ substitution for Si4þ and interaction between F and Al results in melt polymerization, but as the Al/(Al þ Si) increases, the net effect of fluorine solution on aluminosilicate

578

Chapter 8 Volatiles in magmatic liquids

FIGURE 8.36 Equilibrium constant for Eq. (8.39) as a function of temperature below and above the glass transition temperature as indicated for Al-free and 5 mol % Al2O3 with fluorine (3%) and F-free melts as indicated. Redrawn from data of Mysen et al. (2004).

polymerization is smaller. This evolution reflects the changing abundance of individual Q-species as a function of Al/(Al þ Si) ratio. In F-free melts, this effect is driven predominantly by nearly all Al3þ substituting for Si4þ in Q4 species, which, therefore, shifts the Q-species equilibrium to the right: 2Q3 ¼ Q2 þ Q4 . 2  K ¼ XQ2 •XQ4 = XQ3 .

(8.41) (8.42)

From the temperature-dependence of the equilibrium constant in Eq. (8.42) at temperatures above the glass transition temperature, the enthalpy of equilibrium (8.39) is 9e10 kJ/mol for Al-free and 11.9e14 kJ/mol for Al-bearing melts. There may be a small effect of dissolved F on the DH-values of Al-bearing melts, whereas for Al-free melts the small changes in silicate polymerization via formation of NaeF complexes does not affect the equilibria significantly. By adding H2O to fluorine-bearing magmatic liquids, we can write (modified from Dalou and Mysen, 2015): 2Qn ðFÞ þ Qnþ1 þ H2 O þ 2MAlO2 ¼ 2Qn
2 ðAlÞ þ 2MF þ Qn
1 ðHÞ;

(8.43)

where Qn
1(H) denotes a Q-species with protons, Hþ, forming bonding with nonbridging oxygen in the Qn
1 species. Reaction (8.43) results in depolymerization of the silicate network. The effect of dissolved F þ H2O on the NBO/T-values of the melts is essentially the same as H2O only (Dalou and Mysen, 2015).

8.7 Halogen solubility and solution mechanisms

579

FIGURE 8.37 (A) Abundance of different types of fluorine bonding in Na2OeAl2O3eSiO2 melts equilibrated at ambient conditions and 1400 C with 3 mol% F as a function of Al/(Al þ Si). Abbreviations: NF: NaeF bonding, NAF: AleF bonding in cryolite or chiolite-like structures, CF, cryolite-like structure with bridges of oxygen in aluminosilicate network; TF, topazdlike structure. (B) Silicate polymerization, NBO/T, of melts in Na2OeAl2O3eSiO2 melts equilibrated at ambient conditions and 1400 C with 3 mol% F as a function of Al/(Al þ Si). Redrawn from (A) Mysen et al. (2004) and (B) Mysen et al. (2004).

8.7.3 Chlorine solubility A major reason for the interest in Cl in melts is that this fluid component can play an important role in the enrichment of economically important metals and also in volcanic degassing processes (Webster, 1997; Aiuppa et al., 2009; Webster et al., 2009; see also Chapter 6). In anhydrous aluminosilicate-chlorine melts, the chlorine solubility is positively correlated with pressure and negatively correlated with Al/(Al þ Si) of the melt (Dalou et al., 2015; see also Fig. 8.38). The chlorine solubility in silicate melts, including magmatic liquids, decreases with increasing Al/ (Al þ Si). This contrasts with fluorine solubility, which increases with Al/(AlþSi). The chlorine solubility in anhydrous silicate melts increases with increasing pressure (Fig. 8.39). In contrast, when solubility is measured in equilibrium fluid, Cl solubility decreases with increasing pressure (e.g., Webster and Holloway, 1988; Shinohara et al., 1989; Me´trich and Rutherford, 1992; Signorelli and Carroll, 2000, 2002). This feature reflects a large partial molar volume difference of chloride complexes in the fluid and the melt (Me´trich and Rutherford, 1992; Webster and De Vivo, 2002). In water-saturated melts, the chlorine solubility is positively correlated with the (Na þ K)/Al ratio (peralkalinity) of the melt as well as its NBO/T-value (Signorelli and Carroll, 2002). It should be

580

Chapter 8 Volatiles in magmatic liquids

FIGURE 8.38 Chlorine solubility in haplorhyolite melt at 1400 C and 1.5 GPa as a function of the Al/(Al þ Si) and ionization potential, Z/r2, the network-modifying cation of the melt. Redrawn from Dalou et al. (2015).

noted, though, that as the compositions in the Signorelli and Carroll (2002) were designed, increasing the (Na þ K)/Al ratio likely resulted in increasing NBO/T of the melt. Thus, it is not clear whether the correlations of chloride solubility with both (Na þ K)/Al and NBO/T are, in fact, interrelated. Finally, the chlorine solubility varies with water content of a melt (Stelling et al., 2008). It is insensitive to H2O content for an initial several percent water content in melt before decreasing rapidly as the water concentration increases further (Fig. 8.40).3 This trend resembles that of CO2 solubility in hydrous melts and reflects an analogous two-solution mechanisms. One is increased NBO/T of melt with increasing dissolved water, which enhances Cl solubility. On the other hand, increasing H2O content in the fluid decreases chloride activity and will, therefore, tend to decrease the Cl solubility in the melt.

3

We note that the behavior in Fig. 8.40 is governed by a single data point at low total H2O content. These feature needs, therefore, to be confirmed.

8.7 Halogen solubility and solution mechanisms

581

9 B

Al-free

Chlorine solubility, mol %

8 7 6 5 10 mol % Al2O3

4 3 2 0.5

1.0

1.5 2.0 2.5 Pressure, GPa

3.0

3.5

FIGURE 8.39 Chlorine solubility in haplorhyolite melt as a function of pressure at Al2O3concentrations indicated on Figure. Redrawn from Dalou et al. (2015).

FIGURE 8.40 Relations between chlorine content ad H2O in basalt melt at 1200 C and 200 MPa. Redrawn from Stelling et al. (2008).

582

Chapter 8 Volatiles in magmatic liquids

8.7.4 Chlorine solution mechanisms Chlorine-35 MAS NMR and chlorine XANES data of silicate and aluminosilicate quenched melts indicate that the solution mechanism is dominated by alkali chloride or alkaline earth chloride complexes (Stebbins and Du, 2002; Sandland et al., 2004; Evans et al., 2008; Baasner et al., 2014; Dalou et al., 2015). For peralkaline melts containing both Na and Ca, Na-chloride complexes dominate over Ca-chloride complexes (Baasner et al., 2014). Baasner et al. (2014) suggested, however, that for peraluminous melts, Ca-chloride complexes might be more abundant. Those authors detected no evidence for mixed (Na,Ca)eCl complexes. In fact, Evans et al. (2008), from their chlorine XANES spectra, concluded that Cl shows distinctive preference for alkaline earths relative to alkali metals in silicate melts. This conclusion is in contrast with that of Sandland et al. (2004) who reported that their 35Cl MAS NMR spectra were best interpreted as mixtures of Na- and Ca-chloride complexes. There was no compelling evidence for AleCl bonding in the glasses, whether in the system CaOeMgOeAl2O3SiO2 or Na2OeCaOeAl2O3eSiO2 (Sandland et al., 2004; Evans et al., 2008; Baasner et al., 2014; Dalou et al., 2015). From the discussion of Baasner et al. (2014) and Dalou et al. (2015), one may, therefore, write a simply polymerization reaction to describe the solution mechanism of chlorine in silicate melts; 2Qn ðMÞ þ MCl ¼ 2Qnþ1 þ M3 OCl.

(8.44)

This expression is analogous to the fluorine solution mechanism in Eq. (8.37) for Al-free silicate melts. Therefore, in this regard, fluorine and chlorine solution mechanisms resemble one another. However, in Al-bearing systems, fluorine forms bonding with Al3þ, which results in silicate depolymerization. No such equivalent reaction exists for chlorine in aluminosilicate melts. It seems, therefore, that Cl solution in silicate melts always leads to silicate melt polymerization, whereas for F more complex mechanisms are involved as discussed above.

8.7.5 Bromine and iodine The solubility and solution mechanisms in silicate melts of the larger halogens, Br and I, have received considerably less attention than Cl and F. However, from the data that do exist (Bureau et al., 2000, 2010; Bureau and Metrich, 2003; Cochain et al., 2015), the same silicate compositional variables seem to govern the solubility of both Cl and Br in hydrous silicate melts. The Br solubility is a positive function of melt NBO/T (Bureau and Metrich, 2003), just like Cl and F solubility. Their solubility is positively correlated with (Na þ K)/Al, for example, with a minimum near the meta-aluminosilicate composition (Bureau and Metrich, 2003). However, the solubility and Br is lower than that of Cl. In fact, for hydrous melts in equilibrium with halogen-bearing aqueous solutions at high temperature and pressure, the solubility is a simple function of the ionic radius of the halogen when expressed as halogen partition coefficient between aqueous fluid and water-saturated NaAlSi3O8 melt (Bureau et al., 2000; see also Fig. 8.41):   A ; (8.45) ln Dfluid=melt ¼
11:7 þ 8:3• ionic radius 

8.7.6 Halogens in magma Properties of fluorine-bearing magmatic liquids are of major interest because of its effect on magma viscosity and other transport properties. For Cl-bearing melts, the focus has been on Cl partitioning

8.7 Halogen solubility and solution mechanisms

583

FIGURE 8.41 Different halogen partition coefficients between coexisting aqueous fluid and fluid-saturated hydrous NaAlSi3O8 melt from 900 C and 200 MPa expressed as a function of ionic radius of the halogen. Redrawn from Bureau et al. (2000).

between aqueous fluids and hydrous silicate melts because of the importance of such information in many geological processes involving mass transport by Cl-bearing fluids (Filiberto and Treiman, 2009; Aiuppa et al., 2009; Alletti et al., 2009; Joachim et al., 2015; see also Chapter 6). Much less information exists for effects of Cl on magma properties. Property data for silicate melts with Br or I have not been reported extensively. It appears reasonable to assume, however, that these components may have effects similar to Cl, but only to a lesser extent because of their lesser solubility in melts. Liquidus phase relations in F-bearing silicate and aluminosilicate systems point to complicated relationships between solubility and silicate composition and suggest that effects on liquidus phase relations are considerably greater by dissolving F than Cl (van Groos and Wyllie, 1967, 1969; Filiberto and Treiman, 2009; Filiberto et al., 2012; Giehl et al., 2014). Addition of HF to haplogranitic melt-H2O at a few hundred MPa total pressure depresses the solidus temperature significantly more than addition of equal concentrations of HCl (Fig. 8.42). In fact, in a comparison of effects on liquidus temperature depressions of a natural basalt by H, F, and Cl, fluorine has the greatest effect, followed by hydrogen (water), and finally chlorine (Filiberto et al., 2008, 2012; Filiberto and Treiman, 2009). Transport properties such as diffusion and viscosity of magmatic liquids are profoundly affected by dissolved fluorine with magma viscosity decreasing rapidly and diffusivity increasing as fluorine is dissolved in the melts (Dingwell and Mysen 1985; Dingwell and Hess, 1998; Alletti et al., 2007; Baasner et al., 2013). Furthermore, in mixed H2OeF systems, the combined effect on the activation the viscosity of peralkaline melts of these two volatiles is greater than that which would be expected simply by mixing linearly the effect of H2O and F (Dingwell and Mysen, 1985). Solution of chlorine in

584

Chapter 8 Volatiles in magmatic liquids

FIGURE 8.42 Effects of Cl and F on the solidus temperature of H2O-saturated NaAlSi3O8 melt. Redrawn from Wyllie and Tuttle (1964).

FIGURE 8.43 Viscosity change of peralkaline Na2OeCaOeAl2O3-SiO2 melt as a function of Cl or F added to melt at 608 C. Redrawn from Baasner et al. (2013).

silicate melts can have a variety of effects on viscosity (Fig. 8.43). For example, for peralkaline compositions, viscosity increases with increasing Cl concentration, whereas the opposite effect is observed for peraluminous melts (Alleletti et al., 2007; Zimova and Webb, 2007; Baasner et al., 2013). Fluorine is particularly important because its solubility in magma at ambient and near ambient pressure is several mol %. This means that F-rich magma remains fluid upon extrusion on the Earth’s surface. This behavior contrasts with that of hydrous magma, which loses its H2O during degassing at

8.8 Noble gas solubility and solution mechanisms

585

near ambient pressure conditions. This H2O loss leads to greatly enhanced magma viscosity and an increase in glass transition temperature as hydrous magma ascends toward the surface. It follows that whereas fluorine-rich magma extrudes quietly, hydrous magma frequently does not. Experimental data on halogen diffusion in silicate melts are somewhat more limited than viscosity data. Some information on F, Cl, and Br diffusion with and without H2O for a natural phonolite composition has been reported (Balcone-Boissard et al., 2009; Baker and Balcone-Boissard, 2009; Bo¨hm and Schmidt, 2013). In anhydrous peralkaline melts, chlorine diffuses about an order of magnitude more slowly than fluorine. Moreover, the activation energy of diffusion of F and Cl differ significantly, which is consistent with the different solution mechanisms of the two halogens, whereas those of H2O and F resemble one another. Dalou et al. (2014) noted that the decrease of mineral/melt partition coefficients of F with increasing H2O content in basaltic magma is consistent with increasing F content in magma as its H2O content increases. In contrast, Cl partition coefficients increase with increasing H2O content. Similarly, the Cl solubility decrease with increasing H2O content results in a decrease of Cl partition coefficients between anhydrous mantle minerals and hydrous basaltic melts (Dalou et al., 2014). This difference of F and Cl partitioning between magma and fluid highlights the potential of F and Cl as tracers of primary H2O content in mantle magmas, especially in subduction zone magmas. Indeed, the variation of a few wt% of H2O produces highly variable Cl/F ratios in magmas (Dalou et al., 2014).

8.8 Noble gas solubility and solution mechanisms The noble gas abundance and isotopic composition have been employed to deduce original abundance of volatiles in the Earth (Craig et al., 1975; Marty and Jambon, 1987) because the behavior of noble gases in magmatic liquids to a first approximation may be treated as if there is no interaction between the dissolved noble gas and the magmatic liquids. In this respect, possibly with the exception of N2, noble gas behavior in magmatic liquids differs from the other volatile components discussed in this chapter. The idea is, however, an oversimplification as it does not take into consideration Coulombic interactions. Moreover, from a physical standpoint, the response of silicate melt structure in which a chemically inert component fills open spaces would differ from that absent this material in solution (Shen et al., 2011). Physical properties such as compressibility, for example, would be affected by such a solution process.

8.8.1 Noble gases in fully polymerized silicate melt structure The dissolution of noble gases in silica glass and melt has been used as a tool with which to probe voids and void size distribution in SiO2 glass and melt structure (Shackelford, 1999; Malavasi et al., 2006; Zhang et al., 2010) the short-range structure of which resembles that of b-cristobalite (Bourova et al., 2000; deLigny et al., 2009). The noble gas content in SiO2 glass and melt increases with increasing temperature and pressure (at least at pressures below several GPa) and decreases with increasing atomic radius of the noble gas (Shackleford et al., 1972; Caroll and Solper, 1991; Guillot and Guissani, 1996). From the temperature-dependence of solubility (Fig. 8.44A), the enthalpy of solution of noble gases in vitreous silica increases with increasing atomic radius from about 30 kJ/mol for Ne solubility to as much as w150 kJ/mol for solution of Xe (Shelby, 1976; Shibata et al., 1998).

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Chapter 8 Volatiles in magmatic liquids

FIGURE 8.44 Solubility of He and Ne in molten SiO2. (A) As a function of temperature, and (B) as a function of pressure.

For pressure up to several hundred MPa, noble gas solubility in melts is a linear or near linear function of pressure (Shackelford et al., 1972; Shelby, 1976; Walter et al., 2000; see also Fig. 8.44B) and, therefore, obeys Henry’s Law: Ki ¼ Xi =fi ;

(8.46)

where fi is fugacity of gas, i, Xi is mol fraction, and Ki is Henry’s Law constant. However, as pressure is increased further, the solubility deviates from linearity and eventually reaches a maximum value at several GPa pressure before further pressure increase results in decreasing solubility (Schmidt and Keppler, 2002; Chamorro-Perez et al., 1996; Bouhifd et al., 2008; Zhang et al., 2010; Niwa et al., 2013). The solution mechanism of noble gases in a fully polymerized structure such as that of fused SiO2 has been described in terms of nonoverlapping interstitial sites or voids in the structure larger than those of the noble gas under consideration (Nakayama and Shackelford, 1990; Caroll and Stolper, 1991; Wulf et al., 1999; Zhang et al., 2010). The decreasing noble gas solubility in silica melt with increasing atomic radius of the noble gas is then understood in terms of the distribution of interstitial sites. With increasing pressure, the concentration of nonoverlapping sites larger than the size of a given noble gas decreases (Zhang et al., 2010; see also Fig. 8.45). This evolution has the effect of decreasing the noble gas solubility. However, at the same time the increasing noble gas fugacity with pressure tends to increase the noble gas solubility (Shelby, 1976; Roeselieb et al., 1992; Walter et al., 2000). This model also is consistent with structural data inferred from Wulf et al. (1999) from X-ray absorption data. The different pressures at which experimentally determined solubility turnovers take place is a reflection of the compressibility of the intertetrahedral angles in three-dimensional network structures. This compressibility varies with Al/(Al þ Si) and with changes in type of cations for charge-balance of tetrahedrally coordinated Al3þ. Substitution of Si4þ with charge-balanced Al3þ in melts along Na meta-aluminosilicate joins results in decreasing noble gas solubility (Walter et al., 2000; Bouhifd et al., 2008; see also Fig. 8.46). The high pressure at which this solubility reaches its maximum before

8.8 Noble gas solubility and solution mechanisms

587

FIGURE 8.45 Solubility of Ar in SiO2melt calculated as a function of pressure (shaded area) and compared with experimental data from Bouhifd et al. (2008) and Chamorro-Perez et al. (1996). Redrawn from calculation results of Zhang et al. (2010).

FIGURE 8.46 Ar solubility in melts along the join SiO2eNaAl2O6 as a function of their Al/(Al þ Si). Redrawn from Walter et al. (2000).

588

Chapter 8 Volatiles in magmatic liquids

decreasing with further pressure increase depends on Al/(Al þ Si) (Bouhifd et al., 2008). This turnover pressure also varies with the type of electrical charge-balance of tetrahedrally coordinated Al3þ (Bouhifd et al., 2008). Very likely, with alkaline earth charge-balanced Al3þ, which become decreasingly compressible with increasing Al/(Al þ Si), the turnover pressure increases with increasing Ak/(Al þ Si) because of the stiffness of AleO bonds in such melts. On the other hand, with alkali-charge-balanced Al3þ which become increasingly compressible with increasing Al/(Al þ Si) (Kushiro 1981), the turnover pressure likely decreases with increasing Al/(Al þ Si). In terms of natural magma, the implication is that the turnover pressure likely is greater for tholeiitic and more ultramafic melts than for alkali basalt melt, for example. The turnover pressure of hydrous magma probably differs from that of anhydrous magma although this effect remains to be demonstrated experimentally.

8.8.2 Noble gases in depolymerized silicate melt structure Natural magmatic liquids, whether highly polymerized rhyolitic or highly depolymerized peridotitic magma or anything in between, some portion of their structure is in the form of Q4 fully polymerized structural units (see Chapter 5). How the presence and concentration of Q4 units in a depolymerized silicate melt will impact on noble gas solubility and solubility mechanisms will be addressed next. With an excess of alkalis or alkaline earth over that required for charge-balance of tetrahedrally coordinated Al3þ, three structural variables govern noble gas solubility. These are (1) the Al/(Al þ Si)ratio, which can affect three-dimensional cavity abundance, dimensions and distributions, and, therefore, contributes to noble gas solubility and its pressure-dependence, (2) the abundance ratio of network-modifying/network-forming cations governs the silicate polymerization and Q-species distribution and, therefore, the availability of three-dimensional cavities. These, in turn, play a role in controlling how neutral atoms and molecules might be dissolved, and finally (3) the proportion of different types of network-modifying cations are important because these govern the abundance of Q4species in a magma. There is a rather broad range of up to more than two orders of magnitude in solubility for each of the noble gases (Fig. 8.47), a range that most likely a reflection of the influence of the above-mentioned compositional and, therefore, structural variables. This is clear, for example, from the distinctively different slopes of the relationship between solubility and atomic radius when separating out rhyolite melt, which is a nearly fully polymerized (NBO/Tw0) and essentially an alkali aluminosilicate melt, and a basalt melt, which is predominantly alkaline earth aluminosilicate melt and is also considerably more depolymerized than rhyolite (typical NBO/T-values between w0.7 and 1.0). The NBO/T-value of the silicate does indeed have a strong influence on noble gas solubility (Shibata et al., 1996, 1998; Paonita, 2005; Iacono-Marziano et al., 2010; see also Fig. 8.48). It also is clear that the effect of melt polymerization becomes more important as the atomic radius of the noble metal decreases. There may also be a slight effect of Al/(Al þ Si) (Paonita, 2005), in particular, for the melts with small NBO/Tvalues (highly polymerized melts such as rhyolite magma, for example). The noble gas solubility in depolymerized melts can be correlated with proportion of bridging and nonbridging oxygen (Shibata et al., 1998; Paonita, 2005). For a simple relationship to proportion of bridging and nonbridging oxygen (BO and NBO, respectively), Paonita (2005) proposed the relationship for the structural control on the Henry’s Law constant, Ki, ln Ki ¼ XiBO ln KiBO þ XiNBO ln KiNBO ;

(8.47)

8.8 Noble gas solubility and solution mechanisms

589

FIGURE 8.47 Noble gas solubility in magmatic liquids ranging from basalt to rhyolite composition as a function of type of noble gas. Redrawn from data in Kirsten (1968), Hayatsu and Waboso (1985), Hiyagon and Ozima (1986), and Lux (1987). BO where XBO i , etc. are mol fractions of bridging and nonbridging oxygen and Ki , etc. are Henry’s Law constants of noble gas, i, for BO and NBO. A more detailed relationship, using Q-species, also has been proposed (Shibata et al., 1998):

Ki ¼

j X j¼0

XQ j KQ j

(8.48)

where XQ j and KQj are mol fraction of and Henry’s Law constant for individual Q-species. The fully polymerized species, Q4, dominates the Ki-value variations (Shibata et al., 1998). The XQj-values in silicate melts and glasses in Eq. (8.48) are governed by chemical composition, temperature, and pressure. It follows, therefore, that the Henry’s Law constant would also be a function of composition, temperature, and pressure in addition to the atomic radius of the noble gas. The noble gas solubility in depolymerized, but Q4-containing, melts is also dependent on pressure (White et al., 1989; Malavasi et al., 2006; Zhang et al., 2010; Guillot and Sator, 2012). This effect is in part because the interstitial vacancy dimensions and distribution in Q4-species change with pressure (Zhang et al., 2010), and in part because increasing pressure results in increased noble gas fugacity. Of course, in depolymerized melts, the Q-distribution is also pressure-dependent (Dickinson et al., 1990; Gaudio et al., 2008), which also contributes to how noble gas solubility in depolymerized melts is affected by pressure.

8.8.3 Noble gases in magmatic systems Characterization of noble gas solubility coupled with data on magma-gas-mineral noble gas partitioning have been used to describe differentiation processes in the Earth (Allegre et al., 1986/87).

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Chapter 8 Volatiles in magmatic liquids

FIGURE 8.48 Solubility of Ne, and Ar, and Kr and Xe vs. degree of silicate polymerization, NBO/Si, melt equilibrated at 1400e1500 C and w100 MPa. Redrawn from Shibata et al. (1998).

Of particular concern when using noble gases for this purpose is the strong melt compositional dependence of solubility as illustrated in the relationship between solubility and NBO/T of magmatic liquids (Figs. 8.46 and 8.48). As a magmatic liquid is fractionated from, for example, basaltic to rhyolitic, the noble gas solubility can increase by more than two orders of magnitude (depending on noble gas considered). Of course, this effect will also depend on the pressure at which degassing occurs because the noble gas solubility in magma reaches a maximum at pressures near 5 GPa (Chamorro-Perez et al., 1996; Bouhifd et al., 2008). Inference on mantle source regions of partial melts also will depend on the compositional effect on noble gas solubility. It will also vary with H2O availability because noble gas solubility decreases with increasing H2O concentration in magma (Fig. 8.48). This, in turn, suggests that the role of noble gas contents of magmatic liquids in inferring source regions and degassing history would be considerably different in the H2O-rich island arc systems compared with midocean basalt and ocean island basalt.

8.9 Concluding remarks Volatiles in magmatic systems can be described in the system of the CeOeHeNeS components. Their solubility in magma depends on magma composition, temperature, pressure, and, for some

References

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species, redox conditions. In particular, S-, N-, and C-bearing species can vary with redox conditions in the redox range of terrestrial processes. Varying speciation also leads to varying solubility. The solution mechanism of volatile components can involve interaction between the volatiles and the silicate melt structure under which circumstances both the speciation of the volatiles and the structure of the silicate melts are affected. Under oxidizing conditions, dissolved CO2 forms carbonate and bicarbonate complexes, which results in increased silicate polymerization. Solution of oxidized sulfur has similar effects. Reducing conditions, on the other hand, results in CH4 and H2S species, the solution of which both results in melt depolymerization. Reduced nitrogen species are of NH3, NH2, and NH4 type. The effects of all these components on the melt structure effects melt properties that vary with melt polymerization. A portion of the above species also dissolves in their molecular form. In this case, the species occupy three-dimensional vacancies in the melt structure. This leads to a positive correlation between their solubility and degree of polymerization of the melt. Solution in this forms stiffens the melt structure, an effect that will result in decreased melt compressibility, for example. Dissolved noble gases will have similar effect on melt properties. Dissolved halogens form halide structures in silicate melts. The nature of these structures affect how melt composition, temperature, and pressure affect halogen solubility, solubility mechanisms, and silicate melt structure and properties.

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Park, J.H., Park, G.-H., 2012. Sulfide capacity of CaO-SiO2-MnO-Al2O3-MgO slags at 1 873 K. ISIJ Int. 52, 764e769. Pawley, A.R., Holloway, J.R., McMillan, P.F., 1992. The effect of oxygen fugacity on the solubility of carbonoxygen fluids in basaltic melt. Earth Planet Sci. Lett. 110, 213e225. Pearce, M.L., 1964. Solubility of carbon dioxide and variation of oxygen ion activity in soda-silicate melts. J. Am. Ceram. Soc. 47, 342e348. Poli, S., Schmidt, M.W., 2002. Petrology of subducted slabs. Annu. Rev. Earth Planet Sci. 30, 207e235. Rabinovich, E.M., 1983. On the structural role of fluorine in silicate glasses. Phys. Chem. Glasses 24, 54e56. Renlund, G.M., Prochazka, S., Doremus, R.H., 1991. Silicon oxycarbide glasses. 2. Structure and properties. J. Mater. Res. 6, 2723e2734. Richardson, F.D., Fincham, C.J.B., 1954. Sulphur in silicate and aluminate slags. J. Iron Steel Inst. 178, 4e15. Roselieb, K., Rammensee, W., Buttner, H., Rosenhauer, M., 1992. Solubility and diffusion of noble gases in vitreous albite. Chem. Geol. 96, 241e266. Roskosz, M., Bouhifd, M.A., Jephcoat, A.P., Marty, B., Mysen, B.O., 2013. Nitrogen solubility in molten metal and silicate at high pressure and temperature. Geochem. Cosmochim. Acta 121, 15e28. Roskosz, M., Mysen, B.O., Cody, G.D., 2006. Dual speciation of nitrogen in silicate melts at high pressure and temperature: an experimental study. Geochem. Cosmochim. Acta 70 (11), 2902e2918. Rubie, D.C., Frost, D.J., Mann, U., Asahara, Y., Tsuno, K., Nimmo, F., Kegler, P., Holzheid, A., Palme, H., 2011. Heterogeneous accretion, composition and core-mantle differentiation of the Earth. Earth Planet Sci. Lett. 301, 31e42. Rubin, A.E., 2010. Mineralogy of meteorite groups. Meteoritics Planet Sci. 32, 231e248. Sandland, T.O., Du, L.S., Stebbins, F., Webster, J.D., 2004. Structure of Cl-containing silicate and aluminosilicate glasses: a Cl-35 MAS-NMR study. Geochem. Cosmochim. Acta 68, 5059e5069. Schaller, T., Dingwell, D.B., Keppler, H., Knoller, W., Merwin, L., Sebald, A., 1992. Fluorine in silicate glasses: a multinuclear magnetic resonance study. Geochem. Cosmochim. Acta 56, 701e708. Schmidt, B.C., Keppler, H., 2002. Experimental evidence for high noble gas solubilities in silicate melts under mantle pressures. Earth Planet Sci. Lett. 195, 277e290. Schmidt, B.C., Holtz, F.M., Beny, J.M., 1998. Incorporation of H2 in vitreous silica, qualitative and quantitative determination from Raman and infrared spectroscopy. J. Non-cryst. Solids 240, 91e103. Shackleford, J.F., 1999. Gas solubility in glasses  principles and structural implications. J. Non-cryst. Solids 253, 231e241. Shackleford, J.F., Studt, P.L., Fulrath, R.M., 1972. Solubility of gases in glass. II. He, Ne, and H2 in fused silica. J. Appl. Phys. 43, 1619e1626. Sharma, S.K., Yoder Jr., H.S., Matson, D.W., 1988. Raman study of some melilites in crystalline and glassy states. Geochem. Cosmochim. Acta 52, 1961e1968. Shelby, J.E., 1976. Pressure dependence of helium and neon solubility in vitreous silica. J. Appl. Phys. 47, 135e139. Shen, G., Mei, Q., Prakapenka, V.B., Lazor, P., Sinogeikin, S., Meng, Y., Park, C., 2011. Effect of helium on structure and compression behavior of SiO2 glass. Proc. Natl. Acad. Sci. U S A 108. Shibata, T., Takahashi, E., Matsuda, J., 1996. Noble gas solubility in binary CaO-SiO2 system. Geophys. Res. Lett. 23, 3139e3142. Shibata, T., Takahashi, E., Matsuda, J., 1998. Solubility of neon, argon, krypton, and xenon in binary and ternary silicate systems: a new view on noble gas solubility. Geochem. Cosmochim. Acta 62, 1241e1253. Shinohara, H., Iiyama, J.T., Matsuo, S., 1989. Partition of chlorine compounds between silicate melt and hydrothermal solutions: I. Partition of NaCl-KCl. Geochem. Cosmochim. Acta 53, 2617e2630.

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Shinozaki, T., Kagi, H., Noguchi, N., Hirai, H., Ohfuji, H., Okada, T., Nakano, S., Yagi, T., 2014. Formation of SiH4 and H2O by dissolution of quartz in H2 fluid under high pressure and temperature. Am. Mineral. 99, 1265e1269. Shishkina, T.A., Botcharnikov, R.E., Holtz, F., Almeev, R.R., Portnyagin, M.V., 2010. Solubility of H2O- and CO2-bearing fluids in tholeiitic basalts at pressures up to 500 MPa. Chem. Geol 277, 115e125. Signorelli, S., Carroll, M.R., 2000. Solubility and fluid-melt partitioning of Cl in hydrous phonolitic melts. Geochem. Cosmochim. Acta 64, 2851e2862. Signorelli, S., Carroll, M.R., 2002. Experimental study of Cl solubility in hydrous alkaline melt: constraints on the theoretical maximum amount of Cl in trachytic and phonolitic melts. Contrib. Mineral. Petrol. 143, 209e218. Smith, E.M., Shirey, S.B., Nestola, F., Bullock, E.S., Wang, J., Richardson, S.H., Wang, W., 2016. Large gem diamonds from metallic liquid in Earth’s deep mantle. Science 354, 1403e1405. Sobolev, N.V., Loginova, A.M., Tomilenko, A.A., Wirth, R., Bul’bal, T., Lik’yanova, L.I., Fedorova, E.N., Reutsky, V.N., Efimova, E.S., 2019. Mineral and fluid inclusions in diamonds from the Urals placers, Russia: evidence for solid molecular N2 and hydrocarbons in fluid inclusions. Geochem. Cosmochim. Acta 266, 197e219. Song, S., Li, S., Niu, Y., Zhang, L., 2009. CH4 inclusions in orogenic harzburgite; evidence for reduced slab fluids and implication for redox melting in mantle wedge. Geochem. Cosmochim. Acta 73, 1737e1754. Sosinsky, D.J., Sommerville, I.D., 1986. The composition and temperature dependence of the sulfide capacity of metallurgical slags. Metall. Trans. B 17B, 331e338. Stanley, B.D., Hirschmann, M.M., Withers, A.C., 2011. CO2 solubility in Martian basalts and Martian atmospheric evolution. Geochem. Cosmochim. Acta 75, 5987e6003. Stanley, B.D., Hirschmann, M.M., Withers, A.C., 2014. Solubility of CeOeH volatiles in graphite-saturated martian basalts. Geochem. Cosmochim. Acta 129, 54e76. Stebbins, J.F., Du, L.-S., 2002. Chloride sites in silicate and aluminosilicate glasses: a preliminary study by 35Cl solid-state NMR. Am. Mineral. 87, 359e363. Stebbins, J.F., Kroeker, S., Lee, S.K., Kiczenski, T.J., 2000. Quantification of five- and six-coordinated aluminum ions in aluminosilicate and fluoride-containing glasses by high-field. high-resolution 27Al NMR. J. Non-cryst. Solids 275, 1e6. Stelling, J., Botcharnikov, R.E., Beermann, O., Nowak, M., 2008. Solubility of H2O- and chlorine-bearing fluids in basaltic melt of Mount Etna at T¼1050-1250 C and P¼200 MPa. Chem. Geol. 256, 102e110. Stelling, J., Behrens, H., Wilke, M., Go¨ttlicher, J., Chalmin-Aljanabi, E., 2011. Interaction between sulphide and H2O in silicate melts. Geochim. Cosmocim. Acta 75, 3542e3558. Sverjensky, D.A., Harrison, B., Azzolini, D., 2014. Water in the deep Earth: the dielectric constant and the solubilities of quartz and corundum to 60 kb and 1200  C. Geoxhim. Cosmochim. Acta 129, 125e145. https:// doi.org/10.1016/j.gca.2013.12.019. Taniguchi, Y., Sano, N., Seetharaman, S., 2009. Sulphide capacities of CaOeAl2O3eSiO2eMgOeMnO slags in the temperature range 1 673e1 773 K. ISIJ Int. 49, 159e163. Tatsumi, Y., Hanyu, T., 2003. Geochemical modeling of dehydration and partial melting of subducting lithosphere: toward a comprehensive understanding of high-Mg andesite formation in the Setouchi volcanic belt, SW Japan. Geochem. Geophys. Geosyst. 4. https://doi.org/10.1029/2003GC000530. Tatsumisago, M., Yamashita, H., Hayashi, A., Morimoto, D., Minami, T., 2000. Preparation and structure of amorphous solid electrolytes based on lithium sulfide. J. Non-cryst. Solids 274, 30e38. Taylor, W.R., Green, D.H., 1987. The petrogenetic role of methane: effect on liquidus phase relations and the solubility mechanisms of reduced C-H volatiles. In: Mysen, B.O. (Ed.), Magmatic Processes: Physicochemical Principles. Geochemical Society, State College PA, pp. 121e138.

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Thibault, Y., Holloway, J.R., 1994. Solubility of CO2 in a Ca-rich leucitite: effects of pressure, temperature, and oxygen fugacity. Contrib. Mineral. Petrol. 116, 216e224. Thibault, Y., Walter, M.J., 1995. The influence of pressure and temperature on the metal-silicate partition coefficients of nickel and cobalt in a model C1 chondrite and implications for metal segregation in a deep magma ocean. Geochem. Cosmochim. Acta 59, 991e1002. Toplis, M.J., 2004. The thermodynamics of iron and magnesium partitioning between olivine and liquid: criteria for assessing and predicting equilibrium in natural and experimental systems. Contrib. Mineral. Petrol. 149, 22e39. Toplis, M.J., Reynard, B., 2000. Temperature and time-dependent changes of structure in phosphorus containing aluminosilicate liquids and glasses: in situ Raman spectroscopy at high temperature. J. Non-Cryst. Solis 263&264, 123e131. Van Groos, K., Wyllie, P.J., 1967. Melting relationships in the system NaAlSi3O8-NaF-H2O to 4 kb pressure. J. Geol. 76, 50e70. Van Groos, A.F.K., Wyllie, P.J., 1969. Melting relationships in the system NaAlSi3O8-NaCl-H2O at one kilobars pressure, with petrological applications. J. Geol. 77, 581e605. Vetere, F., Holtz, F., Behrens, H., Botcharnikov, R.E., Fanara, S., 2014. The effect of alkalis and polymerization on the solubility of H2O and CO2 in alkali-rich silicate melts. Contrib. Mineral. Petrol. 168. Wade, J., Wood, B.J., 2005. Core formation and the oxidation state of the Earth. Earth Planet Sci. Lett. 236, 78e95. Wallace, P., Carmichael, I.S.E., 1992. Sulfur in basaltic magma. Geochem. Cosmochim. Acta 56, 1863e1874. Wallace, P.J., Gerlach, T.M., 1994. Magmatic vapor source for sulfur dioxide released during volcanic eruptions: evidence from Mount Pinatubo. Science 263, 497e499. Walter, H., Roselieb, K., Buttner, H., Rosenhauer, M., 2000. Pressure dependence of the solubility of Ar and Kr in melts of the system SiO2-NaAlSi2O6. Am. Mineral. 85, 1117e1128. Wasserburg, G.J., 1957. The effects of H2O in silicate systems. J. Geol. 65, 15e23. Watson, E.B., 1994. Diffusion in volatile-bearing magmas. In: Carroll, M.R., Holloway, J.R. (Eds.), Volatiles in Magmas, vol. 30. Mineralogical Society of America, Washington, DC, United States, pp. 371e411. Watson, E.B., Wark, D.A., Delano, J.W., 1993. Initial report on sulfur diffusion in magmas. Eos 74, 62e621. Webster, J.D., 1997. Chloride solubility in felsic melts and the role of chloride in magmatic degassing. J. Petrol. 38, 1793e1808. Webster, J.D., De Vivo, B., 2002. Experimental and modeled solubilities of chlorine in aluminosilicate melts, consequences for magma evolution, and implications for exsolution of hydrous chloride melt at Mt. SommaVesuvius. Am. Mineral. 87, 1046e1061. Webster, J.D., Holloway, J.R., 1988. Experimental constraints on the partitioning of Cl between topaz rhyolite melt and H2O and H2OþCO2 fluids: new implications for granitic differentiation and ore deposition. Geochem. Cosmochim. Acta 52, 2091e2105. Webster, J.D., Sintoni, M.F., De Vivo, B., 2009. The partitioning behavior of Cl, S, and H2O in aqueous vaporþ/
saline-liquid saturated phonolitic and trachytic melts at 200 MPa. Chem. Geol. 263, 19e36. Wetzel, D., Rutherford, M.J., Jacobsen, S.D., Hauri, E.H., Saal, A.E., 2013. Degassing of reduced carbon from planetary basalts. Proc. Natl. Acad. Sci. Unit. States Am. https://doi.org/10.1073/pnas.1219266110. White, W.B., 1974. The carbonate minerals. In: Farmer, V.C. (Ed.), Infrared Spectra of Minerals, p. Ch. 12. Mineralogical Society of London, London. White, B.S., Brearley, M., Montana, A.L., 1989. Solubility of argon in silicate liquids at high pressures. Am. Mineral. 74, 513e529. Wilke, M., Klimm, K., Kohn, S.C., 2011. Spectroscopic studies on sulfur speciation in synthetic and natural glasses. Rev. Mineral. Geochem. 73, 41e78.

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Winther, K.T., Watson, E.B., Korenowski, G.M., 1998. Magmatic sulfur compounds and sulfur diffusion in albite melt at 1 GPa and 1300-1500 C. Am. Mineral. 83, 1141e1151. Wulf, R., Calas, G., Ramos, A., Buttner, H., Roselieb, K., Rosenhauer, M., 1999. Structural environment of krypton dissolved in vitreous silica. Am. Mineral. 84, 1461e1463. Wyllie, P.J., 1980. The origin of kimberlites. J. Geophys. Res. 85, 6902e6910. Wyllie, P.J., Tuttle, O.F., 1964. Experimental investigation of silicate systems containing two volatile components. III. The effects of SO3, P2O5, HCl, and Li2O in addition to H2O on the melting temperatures of albite and granite. Am. J. Sci. 262, 930e939. Xue, Y., Kanzaki, M., 2004. Dissolution mechanisms of water in depolymerized silicate melts: constraints from 1H and 29Si NMR spectroscopy and ab initio calculations. Geochim. Cosmochim. Acta 68, 5027e5058. Yamamoto, K., Nakanishi, T., Kasahara, H., Abe, K., 1983. Raman scattering of SiF4 molecules in amorphous fluorinated silicon. J. Non-Cryst. Solids 59&60, 213e216. Yoshioka, T., McCammon, C., Shcheka, S., Keppler, H., 2015. The speciation of carbon monoxide in silicate melts and glasses. Am. Mineral. 100, 1641e1644. Yoshioka, T., Wiedenbeck, M., Shcheka, S., Keppler, H., 2018. Nitrogen solubility in deep mantle and the origin of the Earth’s primordial nitrogen budget. Earth Planet Sci. Lett. 488, 134e143. Youngman, R.E., Sen, S., 2004. The nature of fluorine in amorphous silica. J. Non-cryst. Solids 337, 182e186. Yurkov, A.L., Polyak, B.I., 1996. Contact phenomena and interactions in the system SiC-SiO2-R(x)O(y) in condensed matter .2. Interactions between silicon carbide and silicate glasses at elevated temperatures. J. Mater. Sci. 31, 2729e2733. Zeng, Q., Stebbins, J.F., 2000. Fluoride sites in aluminosilicate glasses: high-resolution 19F NMR results. Am. Mineral. 85, 863e868. Zhang, C., Duan, Z., 2009. A model for C-O-H fluid in the Earth’s mantle. Geochem. Cosmochim. Acta 73, 2089e2102. Zhang, C., Duan, Z., Li, M., 2010. Interstitial voids in silica melts and implication for argon solubility under high pressures. Geochem. Cosmochim. Acta 74, 4140e4149. Zimova, M., Webb, S.L., 2007. The combined effects of chlorine and fluorine on the viscosity of aluminosilicate melts. Geochem. Cosmochim. Acta 71, 1553e1562.

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CHAPTER

Transport properties

9

9.1 Introduction Transport of mass and energy is an important cornerstone of any description of the formation and evolution of the Earth or, for that matter, other planets. Transport properties, which include viscosity, diffusion, and conductivity of magmatic liquids are central to characterization of these processes.1 Mass transport on a large scale is governed by viscosity of participating molten materials such as silicate, sulfide, metal melts, and sometimes fluids, which often is H2O-rich. The transport scales may range from essentially global, such as separation of the Earth’s metallic core from the silicate Earth (Elkins-Tanton, 2012; Rubie et al., 2011), to smaller scale, such as local partial melting, magma aggregation, and ascent (Bercovici and Karato, 2003; Marsh, 2006), and sometimes separation of immiscible melts such as sulfide melt (Zelenski et al., 2018). Electrical properties aid greatly in interpretation of electromagnetic surveys employed to aid in the mapping of distribution of magma and fluid in the Earth’s interior (Watson and Roberts, 2011; Matsuno et al., 2012; Cerpa et al., 2019). Diffusion, which also is important for mass transfer, typically takes place on a smaller scale, from centimeter to perhaps meter scale depending on the composition and structure of the material through which diffusion takes place.2 The aim of this chapter is characterization of the properties needed to describe the many geophysical, geochemical, and petrological processes that depend on transport properties of magmatic liquids on and near the Earth’s surface and in the Earth’s interior.3 To a considerable extent, this characterization relies on laboratory experiments with compositionally simple model melts and to a lesser degree with natural magmatic liquids. Experiments natural magma are, however, both work and finance intensive because the data thus obtained may not be readily applicable to compositions and conditions other than those of a particular experimental protocol. It is desirable, therefore, to model the 1

Transport properties of crystalline materials also are important, in particular on larger time scales and rock volumes than magma. However, in this Chapter, the central focus is magmatic liquids, so the behavior of crystalline materials will not be discussed. 2 Heat (energy) transfer is accomplished via viscous flow as well and thermal conductivity (Hawkesworth et al., 2004). More recent events such as volcanic eruptions are governed by mass and heat transfer, for example (Zhang et al., 2007; Takeushi, 2015). However, for the purpose of this Chapter, which is focused on mass transport, thermal conductivity will not be discussed explicitly. 3 This focus on magmatic liquids does not rule out a role of fluids although there is a lesser focus on their physical properties. That notwithstanding, one Chapter (Chapter 6) does address many chemical and thermodynamic properties of fluids, which are important when characterizing the transport roles of fluids in the Earth. Mass Transport in Magmatic Systems. https://doi.org/10.1016/B978-0-12-821201-1.00008-0 Copyright © 2023 Elsevier Inc. All rights reserved.

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behavior from the perspective of assessment of individual intensive (temperature, pressure, redox conditions) and extensive (chemical composition) perspectives. In this chapter, experimental data obtained by using natural magma compositions will be reviewed. However, to attain a sense of the variability of transport properties that govern natural magmatic processes and to establish what compositional variables require detailed examination before transport models can be developed, examination of compositionally simpler silicate melts will be discussed as well. In these latter experiments, one variable can be changed at the time before applying models thus derived to characterize the transport behavior of the compositionally more complex magmatic liquids.4

9.2 Relationships among transport properties There are functional relationships between viscosity and other transport properties, such as diffusivity and electrical conductivity (see, for example, Tinker et al., 2004; Nemilov, 2011; Mills et al., 2012; Noritake et al., 2012; Pommier et al., 2013; Mills et al., 2013). More generally, the NernsteEinstein equation relates electrical conductivity, si, to diffusivity, Di, of component, i (Nernst, 1888; Einstein, 1905): si ¼ F 2 Zi Di =kT;

(9.1a)

where F is Faraday’s constant, Zi the electric charge of ion i, and k Boltzmann’s constant. A so-called Haven ratio, H, sometimes is included in this expression resulting in the expression: li ¼ F 2 Zi Di =kHT:

(9.1b)

Its value typically ranges between 1 and 4 (Heinemann and Frischat, 1993; Gaillard, 2004; Chakraborty, 1995). The Haven ratio does, however, seem to need adjustments when considering wide ranges of liquid compositions (Heinemann and Frischat, 1993; Gaillard, 2004). The NernsteEinstein relationship has been found to work quite well for network-modifying cations such as, for example, Naþ, in various magmatic and simple-system silicate liquids (see Ni et al., 2015, for a review and Fig. 9.1A, for an example of the efficiency of the relationship). Diffusivity is another property that is related to viscosity. Several expressions have been proposed. The StokeseEinstein equation (Einstein, 1905) is among the more general expressions: h ¼ kT=6pri Di ;

(9.2)

where ri is the radius of the moving particle. However, this expression has not been shown particularly effective for silicate melts and fluids (Watson and Wark, 1997). The Eyring equation, on the other hand (Eyring, 1935a,b), often yields better results (Shimizu and Kushiro, 1984; Reid et al., 2003): h ¼ kT=ai Di ;

(9.3)

4 Magma with crystals and gas bubbles in suspension will behave rheologically differently from bubble- and crystal-free melts (e.g., Scaillet et al., 1997; Caricchi et al., 2007; Mader et al., 2013). It was decided, however, that for the purpose of this presentation, we will focus on bubble- and crystal-free melts and magmas. Readers interested in the behavior of such magmatic systems can find helpful discussions in Bagdassarov et al. (1996), Vetere et al. (2010) and Mader et al. (2013).

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607

FIGURE 9.1 Examples of how precise the NernsteEinstein equation (Eq. (9.1)) and Eyring equation (Eq. (9.3)) can be in linking melt viscosity to diffusivity and cation diffusion to electrical conductivity. (A) Examples of results using the NernsteEinstein equation. (B) Examples of results using the Eyring equation. The results in both diagrams reflect relations determined from a range of simple system and chemically more complex natural magmatic liquids. Both diagrams were modified from Ni et al. (2015). References to the original data sources can be found in the captions to the original diagrams in Ni et al. (2015).

where ai is the jump distance, has been shown more effective, in particular in environments that involve diffusivity in melts of network-forming components such as oxygen (Magaritz and Hofmann, 1978; Watson, 1979; Shimizu and Kushiro, 1984, 1991; Ni et al., 2015). This utility is illustrated in ˚ ) that was Fig. 9.1B where the calculation was carried out by using a jump distance for oxygen (2.8 A 2 ˚ twice the ionic radius of O (1.4 A). Hence, a case may be made that oxygen motion is an integral part of viscous flow. Similar observations have been reported for self-diffusion of Si4þ in SiO2-rich melts (Watson, 1982; Watson and Baker, 1991; Baker, 1990). This latter relationship also makes intuitive sense because Si4þ is an integral part of the silicate network of SiO2-rich melts. It follows naturally from the relationships illustrated in Fig. 9.1 that there is also a simple relationship between electrical conductivity and viscosity of silicate melts and magmas (Pommier et al., 2013).

9.3 Viscosity of magmatic liquids Viscosity of magmatic liquids likely is among the most commonly used property in studies of formation and evolution of the Earth and the planets. Such data also have direct application to adjacent sciences such as glass and materials science, for example. In any study of transport properties of magmatic liquids, it is necessary to consider not only bulk compositional effects (e.g., Bottinga and Weill, 1972; Giordano et al., 2003), temperature, and

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pressure. We also must establish the influence of volatiles such as H2O and CO2 dissolved in the magmatic liquid (e.g., Brearley and Montana, 1989; Ardia et al., 2008; Di Genova et al., 2014). We will, therefore, first examine existing data relevant to how the viscosity of magmatic liquids varies with the aforementioned variables and then address chemically simpler melt systems in order to develop an understanding of how the viscosity of silicate melts is affected by individual compositional variables. This latter type of information also is needed for practical linkages between the various melt transport variables (Hochella and Brown, 1984; Henderson et al., 1985; Susa et al., 2001; Le Losq et al., 2021). Such data are also required to link quantitatively transport properties to thermodynamic variables (Richet, 1984; Mysen, 1998; Neuville and Richet, 1991; Nemilov, 2011).

9.3.1 Magma viscosity, composition, and temperature Before describing viscous behavior of the various different types of magmatic liquids, a short summary of the characteristics of various igneous rock types is useful. A classification scheme relying primarily on the relationship between SiO2 and Na2O þ K2O concentrations was proposed by Le Bas et al. (1986). As the naming of the igneous rocks for which magma viscosity is determined is commonly based on this classification scheme, it is summarized in Fig. 9.2. Among the magma types to be discussed here, we will describe not only the viscous behavior of melts of more common igneous rocks such as basalt, andesite, dacite, and rhyolite, but also viscosity data that have been reported for more alkali-rich types such as trachyte and phonolite (Giordano and Dingwell, 2003; Giordano et al., 2009; Misiti et al., 2011; Di Genova et al., 2013; Stabile et al., 2016). These latter rock types with their alkali-rich magmatic liquids, are important for our understanding of viscous behavior of magma because alkali-rich melt compositions typically have a greater proportion of tetrahedrally coordinated Al3þ charge-compensated with alkali metals. These structural features, in turn, affect many magma properties because the energetics of the AleO bonds in alkali aluminosilicate environments differ significantly from the energetics of AleO bonds with alkaline earths for charge FIGURE 9.2 Igneous rock classification system from Le Bas et al. (1986). Many of the rock names defined here are used in discussions on transport properties in this chapter.

9.3 Viscosity of magmatic liquids

609

balance (Mysen et al., 1981; Navrotsky et al., 1985; see also Chapters 4 and 5). Moreover, the information thus obtained may also aid in the use the transport data to describe igneous processes that seem common in some tectonic provinces (Vetere et al., 2007; Moretti et al., 2018). In general, the viscosity of magmatic liquids increases with increasing SiO2 content such that, for example, the viscosity of the melts at fixed temperatures typically increases from komatiite, via basanite, basalt, andesite, and dacite, to rhyolitic compositions (Fig. 9.3A). Within the temperature range where the materials are in the molten state, the relationship between melt viscosity, log h, and temperature, 1/T (Kelvin) is essentially linear (Fig. 9.3B). Under these conditions, the relationship between melt viscosity and temperature may be approximated with a simple Arrhenius relationship: 
log h ¼ log ho þ Eh = RT ; (9.4) where h is viscosity, Eh, activation energy of viscous flow, R is the gas constant, and T is temperature (Kelvin). 14

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FIGURE 9.3 Viscosity (h)-temperature (1/T) relations for a range of typical igneous rocks as indicated in the diagrams. (A) Relationships covering temperature range from above to below the glass transition temperature illustrating how this relationship becomes increasingly curved as the melt becomes more mafic. (B) Relationship at temperatures above the glass transition to illustrate essentially linear relations, but also showing how the slopes decrease as the magma becomes more mafic. Decreasing slope implies lower activation energy of viscous flow (Eq. (9.4)). Data sources: Dingwell et al. (2004), Hofmeister et al. (2016), Giordano et al. (2006), Neuville et al. (1993), Hobiger et al. (2011), Giordano and Dingwell (2003), Sehlke and Whittington (2016).

610

Chapter 9 Transport properties

The slope of the high-temperature (above the glass transition temperature) viscosity curves in Fig. 9.3B equals Eh/R. In these fits, it is assumed that at the high temperatures where the materials are molten and behaves, therefore, as a relaxed liquid (see also Moynihan et al., 1976; Dingwell and Webb, 1990; Morgan and Spera, 2001), the log h versus 1/T curves are approximately linear (Fig. 9.3B) although upon close inspection it may be seen that there is indeed a slight curvature even in this hightemperature regime. However, from the slopes of the lines in the linear fits such as shown in Fig. 9.3B, we infer that the activation energy of viscous flow at ambient pressure also is a relatively simple function of the silica content of the magma. Average values of activation energies from a number of fits including those in Fig. 9.3B are shown in Table 9.1. From those data, the activation energy of viscous flow increases from about 119 kJ/mol for basanite to 232 kJ/mol for rhyolite melts. There is, therefore, a general increase in activation energy as the magmatic liquid becomes more felsic (more SiO2-rich). A striking exception to that regular evolution is the activation energy of viscous flow of peridotite magma (Dingwell et al., 2004) with its Eh ¼ 189 kJ/mol, which is between that of andesite and dacite melt. This is the case even though its SiO2 content is only 46.85 wt%, whereas those of andesite and dacite in Table 9.1 are on the order of 60e62 wt%, respectively (Hofmeister et al., 2016). The big difference is in the Al/(Al þ Si), which is near 0.1 for peridotite and between 0.27 and 0.31 for dacite and andesite magma, respectively. Evidently, the weakening of (Si,Al)eO bonds with increasing Al/ (Al þ Si) plays an important role in determining the activation energy of viscous flow, an observation that also has been well established from experimental data in compositionally simpler systems (Riebling, 1964, 1966; Toplis et al., 1997; Le Losq et al., 2014). The activation energy data in Table 9.1 are average values from a number of individual data sets (see footnote in Table 9.1, for sources of such data). In fact, within a group of igneous rocks such as, for example, basalt and rhyolite illustrated in Fig. 9.4 (Neuville et al., 1993; Giordano and Dingwell, 2003;

Table 9.1 Average NBO/T versus Eh (kJ/mol) relationship. Rhyolite Dacite Andesite Phonolite Pantellerite Latite Trachyte Shoshonite Basalt Basanite Komatiite Peridotite

NBO/T

(Al/Al D Si)

(K,Na)eAl

Eh

0.006 0.144 0.209 0.226 0.249 0.303 0.317 0.562 0.732 1.119 1.255 2.267

0.205 0.252 0.238 0.279 0.133 0.282 0.234 0.266 0.256 0.243 0.199 0.111

0.724 0.494 0.712 0.857 1 0.642 0.754 0.483 0.443 0.441 0.082 0.23

232.272 210.337 176.863 170.793 198.317 168.810 171.334 165.900 162.620 126.200 119.000 189.900

Original viscosity data from: Alidibirov et al. (1997), Di Genova et al. (2013), Giordano et al. (2009), Hobiger et al. (2011), Hofmeister et al. (2016), Neuville et al. (1993), Stabile et al. (2016), Giordano and Dingwell (2003a, b), Giordano et al. (2006), Goto et al. (1997), Misiti et al. (2011), Romine and Whittington (2015), Sehlke and Whbittington (2016), Le Losq et al. (2015). Liebske et al. (2003).

9.3 Viscosity of magmatic liquids

611

lt me

Viscosity, log η, Pa s

olite rhy e

g ran alt

bas lt me e

g ran

Temperature, 104/T (K-1)

FIGURE 9.4 Viscosity (h) -temperature (1/T) relations for a range rhyolite and basalt composition magma to illustrate the range of viscosity of magmatic liquids within rock groups. Data from Hofmeister et al. (2016), Giordano et al. (2006), Neuville et al. (1993).

Giordano et al., 2006; Hofmeister et al., 2016), there can be rather wide ranges of magma viscosity. At any temperature, basalt melt viscosity can vary by up to at least two orders of magnitude, whereas that of rhyolite can vary by between three and four orders of magnitude (Scarfe and Hamilton, 1980; Hochella and Brown, 1984; Giordano and Dingwell, 2003b; Hobiger et al., 2011; Di Genova et al., 2013; Hofmeister et al., 2016; Sehlke and Whittington, 2016; see also Fig. 9.4). The variations might differ some at different temperatures because not only do the viscosities vary, but the activation energy (which governs the slopes in Fig. 9.4) also does. At temperatures above the glass transition, the structure of the magmatic liquids is relaxed on the viscosity measurement time scale (e.g., Dingwell and Webb, 1990; Askarpour et al., 1993; Webb and Courtial, 1996; Sipp et al., 1997). Under such circumstances, melt viscosity has been linked to

612

Chapter 9 Transport properties

properties such as, for example, configurational properties (e.g., Richet, 1984; Richet and Bottinga, 1986; Toplis, 1998; Toplis et al., 2001), as well as melt structural variables including degree of silicate polymerization and silicate speciation in the melt (Mysen, 1987, 1995; Le Losq et al., 2021). However, at temperatures below the glass transition, where the melts have been transformed to glass, these relationships are less clear because glass is a kinetic state, whereas a melt is in an equilibrium state. As a result of the different states of melts and their glasses, there is commonly a very significant curvature in the log h versus 1/T relations when connecting the low and high-temperature viscosity data (Fig. 9.3). Moreover, qualitatively it appears that the curvature becomes more pronounced the more mafic (less SiO2) the magma. In fact, among common magmatic liquids such as those of the igneous rocks shown in Fig. 9.3, only the most silica-rich magma, such rhyolite, for example, exhibit a near linear relations between low and high-temperature data (Dingwell et al., 1996; Romine and Whittington, 2015). In other words, the viscosity of most magma shows non-Arrhenian behavior (Sehlke and Whittington, 2016). Furthermore, the relationship between magma types that seem so clear when viscosity in the liquid state is considered, are less obvious when comparing the viscosity of their glasses. The extent of this curvature often is described in terms of fragility (Angell et al., 1985). The greater the curvature, the more fragile the silicate melt. A steepness factor, m, also known as fragility index; 2 3 6vðloghÞ7 m ¼ 4  5 ; Tg v Tg T

(9.5)

where Tg is the glass transition temperature and h is viscosity, often is employed to describe this curvature (see, for example, Hess et al., 1996; Whittington et al., 2001). An example of how the fragility index varies with melt composition is shown in Fig. 9.5. Here addition of various alkaline earth oxides to a haplogranitic melt composition leads to an increasing degree of the log h versus 1/T curvature (increased deviation from Arrhenian behavior). Whereas the viscosity of the granite melt itself shows essentially Arrhenian behavior, the addition of increasing amounts of CaO results in marked curvature (Fig. 9.5A). The summary of this behavior resulting from the addition of a number of different oxides (Fig. 9.5B) illustrates how the fragility index increases with increasing oxide concentration even though the melt fragility is relatively insensitive to the type of oxide added. Although it is convenient to describe magmatic liquids with their rock names, those names do not convey the complete chemical compositions and, therefore, do not express the structure of the magmatic liquids. Melt structure governs the properties of magmatic liquids (and those of other silicate liquids). As discussed in Chapter 5, melt structure varies in systematic ways with melt composition. Principal compositional variables are SiO2 and Al2O3 concentrations, the types and abundance of alkali metals and alkaline earths together with their proportions of these relative to SiO2 and Al2O3 as well as the proportion Al/(Al þ Si). A useful summary of these features as pertains to effects on the viscosity of natural magmatic liquids can be seen in the summary of effects of individual oxides added to rhyolitic magmatic liquids (Dingwell et al., 1996; Bartels et al., 2015; see also Fig. 9.6). The data in Fig. 9.6 show some interesting characteristics. First, we note that regardless of the electronic properties of the added oxide, these oxides all affect the viscosity of rhyolitic melts at fixed

9.3 Viscosity of magmatic liquids

613

FIGURE 9.5 Illustration of the effect of adding various alkaline earth oxides to essentially fully polymerized HPG8 haplogranite melt. (A) Viscosity (h)-temperature (1/T) relations to demonstrate how this relationship becomes increasingly nonlinear as the concentration of added oxide (in this case CaO) increases. (B) Relationship between type and concentration of added oxide and the fragility index defined in Eq. (9.5). Modified from Hess et al, (1996).

FIGURE 9.6

14

Effect on melt viscosity (in this case haplogranite melt, HPG8) of added alkali and alkaline earth oxide.

Viscosity, log η, Pa s

12

Modified from Dingwell et al. (1996).

10

MgO CaO SrO BaO Rb2O

8 6

K2O Na2O

4 2

0

5

10 15 Excess oxide, wt%

20

25

614

Chapter 9 Transport properties

temperature. There are also some interesting systematic relationships. Alkali metals have the greatest effects on the magma viscosity, and, interestingly, the effect increases the smaller the alkali cation. The behavior differs somewhat from that caused by alkaline earths which also causes viscosity decreases, but in contrast to the effect of alkali metals, increasing size of the alkaline earth cation results in enhanced effect on the viscosity of the magmatic liquids. It is well known that addition of all those components have systematic effects on melt structure (Kushiro, 1975; Ryerson, 1985; Maekawa et al., 1991; Mysen, 1998) where, commonly, the effects are more pronounced the more electropositive the cation.5 However, such a simple relationship does not seem to apply to the magnitude of the effect on viscosity, at least not for rhyolitic magma. It is probable that this difference is related to how these components affect the charge-compensation of Al3þ in tetrahedral coordination in the magma because the charge-compensation affects the (Si,Al)eO bond strength (see Chapter 5, Section (5.2.4)). This bond strength influences the activation energy of viscous flow and, therefore, the viscosity of the melts. These issues will be discussed next.

9.3.2 Viscosity and structure of magmatic liquids Although an in-depth and detailed understanding of how the viscosity of silicate melts is governed by their structure will be addressed in discussion of viscous behavior of simple-system silicate and aluminosilicate melts below, some general features of the structure of magmatic liquids and how these may relate to magma viscosity is possible from existing data on structure of natural magma (see also Mysen, 1987, and Mysen and Richet, 2019, Chapter 18, for more discussion of the structure of magmatic liquids). This includes, for example, the extent to which silicate melt polymerization can be described in terms of the average number of nonbridging oxygen (NBO) per tetrahedrally coordinated cations (T), NBO/T. A large majority of the tetrahedrally coordinated cations in magmatic liquid structure is Si4þ and Al3þ. There is also a qualitative relationship to the SiO þ Al2O3 concentration as well as the extent to which the aluminosilicate tetrahedra in individual aluminosilicate species in the magmatic liquids are linked together (polymerized). As briefly mentioned earlier, it must be remembered that a discussion of the rheological behavior of amorphous silicate and aluminosilicate systems in terms of their structural features must be restricted to conditions under which the materials are their equilibrium state. In other words, only viscous behavior of melts and supercooled melts (above the glass transition) can be meaningfully discussed. Provided that the structural behavior of the cations in a silicate melt is known, the ratio, NBO/T, can be calculated from chemical composition (as described, for example, in Mysen and Richet, 2005; Table 4.2). This variable, in turn, may then be related to the viscosity of magmatic liquids. A few general observations can be made. A simple relationship between calculated values of the activation energy of magmatic liquids in their liquid state above the temperature of their liquidii (using the model of Giordano and Dingwell, 2003, 2004 and assuming Arrhenian behavior of the liquid) and viscosity show a broad inverse correlation between this activation energy of viscous flow and the NBO/T of the magmatic liquid (Fig. 9.7). It must be kept in mind, though, that the results of calculations such as shown in Fig. 9.7

Electropositivity, and -negativity, is defined as the ratio, Z/r2, where Z is the formal electrical charge and r is the cation radius (in this presentation taken from Shannon and Prewitt, 1969). 5

9.3 Viscosity of magmatic liquids

615

FIGURE 9.7 180

160

150 ph

an

on

de

ol ite 6 (5

140

0)

Activation energy, E η, kJ/mol

64) lite(7 rhyo

170

Distribution of high-temperature (1200e1600 C) activation energy of viscous flow of melts of major igneous rocks as a function of their degree of silicate polymerization, NBO/T. Activation energies were calculated with the model of Giordano and Dingwell (2003, 2004). The number of analyses within each group is the number of analyses used in each rock group. sit

Analyses from http://Earthchem.org.

e(

19

67

)

thole

iite(5

32)

130 0.0

0.5

1.0 1.5 NBO/T of magmatic liquid

2.0

illustrate principles, but quantitative interpretation depends on the accuracy of the viscosity model used to derive the activation energies. The inverse relationship between activation energy of viscous flow and NBO/T of magmatic liquids indicated from the calculated results in Fig. 9.7, remains when employing experimental results from natural magmatic liquids (Fig. 9.8). There is, however, considerable scatter in the experimental data as shown in this diagram so that for any NBO/T-value of a magma, the activation energy values range by nearly 50 kJ/mol or between 25% and 30% (Fig. 9.8A). This data scatter likely reflects the fact that several other compositional/structural variables also affect the activation energy (and actual viscosity). For example, it is well known that the (Si,Al)eO bond energy contributes meaningfully to activation energies of any transport property that involves breakage and reestablishment of such bonds during mass transport (e.g., Bockris and Reddy, 1973; Riebling, 1964, 1966; Bottinga and Weill, 1972; see also Mysen and Richet, 2019, Chapter 18, for review of information). There is, in fact, a better correlation between activation energy and NBO/T when employing data over a narrow Al/(Al þ Si)-range (Fig. 9.8B). Moreover, by isolating the Eh versus NBO/T relations to magmatic liquids where Al3þ is charge balanced exclusively by alkali metals, the Eh versus NBO/T correlation also exhibits less scatter (Fig. 9.8C). One might also expect, therefore, an inverse relationship between activation energy of viscous flow, Eh, and the Al/(Al þ Si). Such relationships were reported for example, by Toplis et al. (1997) for compositionally simpler melts along the join, SiO2eNaAlO2. However, simply relating the activation energy to Al/(Al þ Si) of the magmatic liquids without consideration of their individual NBO/T-values results in a broad scatter without discernible relationships between activation energy and Al/(Al þ Si) (Fig. 9.9). Even when using data from only a narrow range of NBO/T such as, for example the information only for NBO/T  0.05, there is, at best a very subtle decrease in Eh as the melts become more aluminous (Fig. 9.9B).

Chapter 9 Transport properties

Activation energy of viscous flow, kJ/mol

616

A

B

NBO/T of magmatic liquid [Al/(Al+Si)=0.23-0.27]

Activation energy of viscous flow, kJ/mol

Activation energy of viscous flow, kJ/mol

NBO/T of magmatic liquid

C

NBO/T of magmatic liquid (Al3+ charge-balanced w/Na+K)

FIGURE 9.8 Distribution of high-temperature activation energy of viscous flow of magmatic liquids from a range of igneous rocks as a function of their degree of silicate polymerization, NBO/T. (A) Activation energy distribution as a

9.3 Viscosity of magmatic liquids

617

A final compositional effect on Eh to be considered is related to how Al3þ in tetrahedral coordination in the magmatic liquids is charge balanced because of this effect on the (Si,Al)eO bond energy (e.g., Ramberg, 1952; Brown et al., 1969; Majumder and Kulshreshtha, 2004). This can be important because the AleO bond strength with alkali metals for charge-balance is considerably greater than when alkaline earths serve to charge-balance Al3þ. Available data are limited, but there may be a subtle inverse correlation between activation energy of viscous flow and the Al/(Al þ Si) with alkali charge-balanced Al3þ (Fig. 9.9C). Conversely, the relationship between activation energy of viscous flow and NBO/T over a narrow range of Al/(Al þ Si) with alkali metals for charge balance, show a rough inverse correlation as well (Fig. 9.9C).

9.3.3 Viscosity, iron content, and Fe3D/SFe of magmatic liquids The iron content of magmatic liquids ranges from less than 1 to more than 20 wt% (see, for example, http://earthchem.com), the redox ratios of iron ranges between nearly 0 to nearly 1 (Carmichael and Ghiorso, 1990), and the coordination state of Fe2þ and Fe3þ in silicate melts differs depending on chemical composition and Fe3þ/SFe (Virgo and Mysen, 1985; Kress and Carmichael, 1988). This behavior implies that the structure of magmatic liquids depends on their iron content and the redox ratio of iron. Therefore, one might expect that the viscosity of magmatic liquids also does. It may seem surprising, therefore, that the amount of experimental viscosity data on the influence of iron is rather scarce (Cukierman and Uhlmann, 1974; Neuville et al., 1993; Liebske et al., 2003). Among the experimental viscosity data for natural magmatic liquids, only the viscosity data by Cukierman and Uhlman (1974) and Liebske et al. (2003) were reported as a function of the redox ratio of iron in the magmatic liquid. The viscosity of a lunar basalt composition (no. 15555 from the Apollo 15 mission, which contains about 22.5 wt% FeO) with essentially all the iron as Fe2þ shows its viscosity with a distinctly nonArrhenian viscosity behavior (Cukierman and Uhlmann, 1974, Fig. 9.10). It is notable, though, that in the low-temperature region where glass of most other basalt compositions exhibits nonlinear relations, the log h versus 1/T relations of sample no. 15555 appear essentially linear, but does show different slope in the high-temperature region of melt. The high-temperature curvature in the Cukierman and Uhlmann (1974) basalt melt data also differs from the linear relationship between log h and 1/T for magma of more felsic composition at similarly high temperature (Neuville et al., 1993; Richet et al., 1995; Goto et al., 1997; see also Fig. 9.10B). It is also clear (Liebske et al., 2003) that at least the viscosity of andesite melt at fixed temperature exhibits a viscosity increase with increasing Fe3þ/SFe (Fig. 9.11A). In general, increasing Fe3þ/SFe

function of NBO/T of the magmatic liquid calculated from structural data as summarized, for example, in the review of such data by Mysen and Richet (2019). (B) Activation energy distribution as a function of NBO/T of the magmatic liquids within a narrow range of their Al/(Al þ Si) (as indicated on x-axis of diagram). (C) Activation energy distribution as a function of NBO/T of the magmatic liquids for magmatic liquids where tetrahedrally coordinated Al3þ in their melt structure is charge-balanced exclusively with alkali metals (Na and K). Viscosity data sources: Dingwell et al. (2004), Hofmeister et al. (2016), Giordano et al. (2006), Neuville et al. (1993), Hobiger et al. (2011), Giordano and Dingwell (2003), Sehlke and Whittington (2016).

Chapter 9 Transport properties

Activation energy of viscous flow, kJ/mol

618

A

B

Al/(Al+Si) of magmatic liquid (Al3+ charge-balanced w/Na+K)

Activation energy of viscous flow, kJ/mol

Activation energy of viscous flow, kJ/mol

Al/(Al+Si) of magmatic liquid

C

Al/(Al+Si) of magmatic liquid (NBO/T 0.05))

FIGURE 9.9 Distribution of high-temperature activation energy of experimentally-obtained data of viscous flow of magmatic liquids from a range of igneous rocks as a function of their Al/(Al þ Si). (A) Distribution of hightemperature activation energy of viscous flow of magmatic liquids from a range of igneous rocks as a function of their Al/(Al þ Si) for all igneous rocks without additional constraints (see text). (B) Activation energy

9.3 Viscosity of magmatic liquids

619

results in decreasing NBO/T of silicate melts (Mysen et al., 1995). In light of the relationships between the NBO/T of magma and their viscosity discussed earlier (Fig. 9.8), this relationship might, in fact reflect a decreased NBO/T-value as the Fe3þ/SFe of the magma increases. That suggestion would be consistent with the discussion in Chapter 5 (see also Mysen, 2007) showing how NBO/T of melts decreases with increasing Fe3þ/SFe, in particular in the more oxidized compositions. This latter effect also would be in accord with the conclusion (Kress et al., 1988; Virgo and Mysen, 1985) that the coordination state of Fe3þ in silicate melts depends on the redox ratio of iron and that with Fe3þ/SFe less than 0.4e0.5, Fe3þ is in octahedral coordination. In this Fe3þ/SFe-range, decreasing Fe3þ/SFe results in minimal changes of the NBO/T of the silicate melt (Mysen, 2007). At higher Fe3þ/SFe, Fe3þ is in tetrahedral coordination and increasing Fe3þ/SFe results in decreasing NBO/T. This structural behavior would be consistent with the viscous behavior of Fe-bearing andesite in Fig. 9.11. Such a suggestion would also be consistent with the increased activation energy of viscous flow with increasing Fe3þ/SFe of the andesitic magmatic liquids in the Liebske et al. (2003) study (Fig. 9.11B).

9.3.4 Effect of pressure on viscosity of magma A large portion of igneous processes take place at depth in the Earth and, therefore, at pressures above ambient. Magma viscosity, together with their equation-of-state (see Chapter 10), crystallization behavior (see Chapters 1 and 2) and permeability (see Chapter 11), governs these processes. Magma viscosity data obtained at high pressure are, however, less extensive than data at ambient pressure. It is very likely that this limitation reflects the more challenging nature of viscosity experiments conducted at high pressure and temperature. Here, the method most commonly used is the falling sphere method (Bacon, 1936) as first employed by Shaw (1963) in his early high-pressure viscosity experiments of hydrous granite composition melt to 300 MPa total pressure. Among the very first experimental determinations of viscosity of anhydrous magmatic liquids at high pressure were those in which the melt viscosity of a Crater Lake Andesite and a sample of an olivine tholeiite melt from the Kilauea 1921 eruption (Yoder and Tilley, 1962) was determined to 3 GPa pressure (Kushiro et al., 1976) followed by additional experiments on tholeiite magma by Fujii and Kushiro (1977). In those and subsequent experimental studies of basalt melt viscosity, there is either a slight viscosity decrease or a slight increase with increasing pressure (Kushiro et al., 1976; Kushiro, 1986; Sharpe et al., 1983; Rai et al., 2019). It appears that the basaltic magmas with a negative pressure dependence of viscosity appear slightly more polymerized (NBO/T  1; see Fig. 9.12A) compared with those exhibiting a positive pressure dependence of their melt viscosity (NBO/T > 1.5; see also Fig. 9.12B). In fact, Scarfe et al. (1987) in a review of viscosity data existing at that time, concluded that, in general, silicate melts with NBO/T < 1 exhibit negative pressure dependence, whereas those with NBO/T > 1, typically show an increase of their viscosity with increasing pressure

distribution of the magmatic liquids for magmatic liquids as a function of their Al/(Al þ Si) where tetrahedrally coordinated Al3þ in their melt structure is charge-balanced exclusively with alkali metals (Na and K). (C) Activation energy distribution of the magmatic liquids for magmatic liquids as a function of their Al/(Al þ Si) where the NBO/T of the magma is less than 0.05 (granitic and rhyolitic melts). Viscosity data sources: Dingwell et al. (2004), Hofmeister et al. (2016), Giordano et al. (2006), Neuville et al. (1993), Hobiger et al. (2011), Giordano and Dingwell (2003), Sehlke and Whittington (2016).

Chapter 9 Transport properties

Activation energy of viscous flow, kJ/mol

620

Viscosity, log η, Pa s

A

Andesite melt

788˚C

Fe3+/ΣFe of melt

B

Andesite melt

Fe3+/ΣFe of melt

FIGURE 9.11 Viscosity of andesitic liquid as a function of its Fe3þ/SFe. (A) Viscosity at fixed temperature. (B) Activation energy of viscous flow as a function of its Fe3þ/SFe. Modified from Liebske et al. (2003).

3

13

A

B

12 Viscosity, log η, Pa s

Viscosity, log η, Pa s

2

1

0 Lunar basalt melt

-1 5.2

6.0

6.8

11 10

9 8 Andesite melt

7

7.6

6 8.5

9.0

9.5

10.0

10.5

11.0

FIGURE 9.10 Viscosity (h) -temperature (1/T) relations for iron-bearing magma. (A) Lunar basalt magma containing only FeO. (B) Andesitic magma with variable Fe3þ/SFe as indicated on individual curves. Data from Cukierman and Uhlman (1974), Richet et al. (1996), Liebske et al. (2003).

9.3 Viscosity of magmatic liquids

A

621

B

NBO/T=0.90

Viscosity, log η, Pa s

Viscosity, log η, Pa s

NBO/T=0.87

NBO/T=1.1

NBO/T=1.6

Pressure, GPa

Pressure, GPa

FIGURE 9.12 Viscosity of mafic magmatic liquids as a function of pressure. (A) Pressure effect on magma viscosity of basalt melts with NBO/T < 1 (basalt magma). (B) Pressure effect on magma viscosity of basalt melts with NBO/ T > 1 (basalt and peridotite magma). Data from Kushiro (1986), Liebske et al. (2003), Dygert et al. (2017).

at least to pressures of a few GPa. Persikov et al. (2018) noted, however, that there is a viscosity minimum for volatile-free melts of basalt composition near 4e6 GPa above which pressure the basalt melt viscosity increases with a further pressure increase. Such a minimum would also be consistent with the results of numerical simulations by Angell et al. (1982) who, from relations between calculated diffusivity of network-forming cations, inferred that there would be a viscosity minimum in melt viscosity at similar pressures. This viscosity would be consistent not only with the data in Fig. 9.12, but also with the distinctly increasing viscosity of peridotite melt (NBO/T ¼ 2.5) until about 8e10 GPa pressure above which the melt viscosity decreases with additional pressure increase (Liebske et al., 2005; see also Fig. 9.13). The increase is also in accord with results of numerical calculations (Dufils et al., 2018) although in those calculations, the viscosity maximum near 8e10 GPa pressure was not observed. For magma compositions whose melts are more polymerized than those of basalt (e.g., andesite, dacite, and rhyolite), their viscosity decreases with increasing pressure at least in the pressure range corresponding to the Earth’s upper mantle (15 GPa; Kushiro et al., 1976; Liebske et al., 2003a; Tinker et al., 2004; Ardia et al., 2008; Dygert et al., 2017; see also Fig. 9.14). Moreover, the rate of viscosity change with pressure increases the more felsic the melt (and, therefore, smaller NBO/T of the melt). The activation energy of viscous flow, Eh, is also a systematic function of magma type (see summary by Persikov and Bukhtiyarov, 2009 and Fig. 9.15). From the data in Fig. 9.15, there seems, in general, to be a consistent increase in activation energy the more felsic the magma (lower NBO/Tvalues). Interestingly, the rate of change of the activation energy values increases rapidly as magma

622

Chapter 9 Transport properties

FIGURE 9.13

-0.4

Viscosity of peridotite magma as a function of pressure at different temperatures as indicated on individual curves.

-0.6

Modified from Liebske et al. (2005).

Peridotite melt

Viscosity, log η, Pa s

-0.8 -1.0 -1.2

K

00

20

-1.4

K

00

21

-1.6

0K

220

-1.8

0K

230

K

00

24

-2.0

0

2

K

00

25

4

6 8 Pressure, GPa

10

12

14

Comparison of pressure effect on magma viscosity for highly polymerized dacitic magma showing decreasing viscosity with increasing pressure and less polymerized basalt magma showing increasing magma viscosity with increasing pressure. Modified from Tinker et al. (2004), Dygert et al. (2017).

Viscosity, log η, Pa s

FIGURE 9.14

Dacite (NBO/T=-0.24)

Basalt (NBO/T=-1.1)

Pressure, GPa

9.3 Viscosity of magmatic liquids

FIGURE 9.15

400

Semiquantitative summary of evolution of activation energy of viscous flow of a wide range of magmatic liquids expressed in terms of their degree of silicate polymerization, NBO/T.

350

Dunite

Peridotite

Harzburgite

150

Lunar basalt

200

Modified from Persikov and Buktiyarov (2009).

Picrite

250

Thoeiite

300

Granite Andesite

Activation energy, E η, kJ/mol

623

100 50 0

0.5

1.0

1.5 2.0 2.5 NBO/T of melt

3.0

3.5

4.0

compositions change from basalt to rhyolite, whereas for more mafic magma compositions, the change in Eh with melt composition is considerably slower (Fig. 9.15). In more detail, the activation energy of viscous flow of magmatic liquids, even within individual groups of igneous rocks, can vary significantly. For example, in the experimental data of viscous behavior of Bushveld chilled margin rocks (basaltic compositions), show increasing activation energy of viscous flow with increasing pressure (Sharpe et al., 1983; see also Fig. 9.16A showing variable log h vs. 1/T relationships). For the tholeiite and alkali basalt magmas examined by Kushiro (1986), where the viscosity decreases with increasing pressure (Fig. 9.16B), so does the activation energy of viscous flow. The basalts from Kushiro (1986) have NBO/T < 1, whereas those of Sharpe et al. (1983) were less polymerized with NBO/T-values exceeding 1. Further increase in NBO/T such as in the case of the primitive lunar basalts whose viscosity data in Fig. 9.11 show a positive correlation with pressure also show a distinctly increasing activation energy of viscous flow (Rai et al., 2019; see also Fig. 9.16C). Interestingly, the activation energy of viscous flow of the even more depolymerized peridotite magmatic liquids (Liebske et al., 2005) for all practical purposes is independent of pressure (Fig. 9.17) with Eh ¼ 198  23 kJ/mol in the 0e8 GPa pressure range. In the 8e13 GPa range, the activation energy is 195  99 kJ/mol. It is notable, though, that the error of the average Eh is quite large, thus perhaps allowing for a change in activation energy within the 99 kJ/mol error in the average activation energy. One might also expect a change in the pressure-dependent Eh in light of the data from Persikov et al. (2017) (Fig. 9.17B). These apparent conflicts between data sets cannot be resolved within the uncertainties of the experimental data. By decreasing NBO/T beyond those of basalt, magma that displays negative pressure-dependence of the viscosity also shows negative evolution of the activation energy of viscous flow as the pressure increases as illustrated for rhyolite melt, for example (Liebske et al., 2003; Ardia et al., 2008; Dufils et al., 2018; see also Fig. 9.18). As with the viscosity itself, the pressure-dependent values of activation

624

Chapter 9 Transport properties

7 A

Viscosity, lnη Pa s

6 5 4 3 Skaergaaard gabbro melt

2 1 5.0

5.5 6.0 6.5 Temperature, 104/T (K-1)

7.0

B

10

Viscosity, Pa s

K-rich al

kali basa

5.0

lt

Oiv

ine

thole

iite

Alkali olivin

2.0

e basalt

1.0 0

0.5 1.0 Pressure, GPa

1.5

C

Viscosity, logη Pa s

0.0

T=1980

K

-0.4 906

K

T=1

-0.8 Peridotite melt

-1.2

0

1

2 Pressure, GPa

3

4

FIGURE 9.16 Viscosity of mafic and ultramafic melts as a function of pressure. (A) Viscosity of gabbroic magma from Skaergaard intrusion, Greenland. (B) Viscosity of alkali basaltic and tholeiite magma. (C) Viscosity of peridotitic magma. (A) Modified from Sharpe et al. (1983); (B) Modified from Kushiro (1986); (C) Data from Liebske et al. (2005).

M Pa 0.

1

5

8G

Pa

-1.6

-2.0

Activation energy of viscous flow, kJ/mol

0.1

-1.2

G Pa

Viscosity, logη Pa s

-0.8

MP a

8G

Pa

A

5G Pa

9.3 Viscosity of magmatic liquids

625

200 B

175

lite

ber

kim

lt

sa

ba

150

125 3.5

4.0 4.5 5.0 Temperature, 104/T (K-1)

0

5.5

2

4 6 Pressure, GPa

8

FIGURE 9.17 (A) Viscosity (h)-temperature (1/T) relations for peridotitic magma at increasing pressure as indicated on individual curves. (B) Activation energy of viscous flow of kimberlitic and basaltic magma as a function of pressure. (A) Data from Liebske et al. (2005); (B) Data from Persikov et al. (2017).

FIGURE 9.18 Viscosity of rhyolitic magmatic liquid as a function of pressure at temperatures indicated on individual curves.

Viscosity, logη Pa s

7

Data from Ardia et al. (2008).

6

Rhyolite melt

1150˚C

5 1250˚C 1350˚C

4

0.5

1.0 1.5 Pressure, GPa

2.0

2.5

626

Chapter 9 Transport properties

energy of viscous flow also become more pronounced the more felsic (more polymerized) the melt (see, for example, the data for magma in the andesite to rhyolite range by Liebske et al., 2003, 2005; Ardia et al., 2008). The pressure-dependent evolution of Eh reflects the response of the average (Si,Al)eO bond strength to pressure in the various magmatic liquid compositions. As will be discussed in more detail in the section on simple-system melt rheology below, these trends likely reflect the proportion of fully polymerized, Q4 species in the magma (see Chapter 5; Section 5.2.3 for discussion of Qn-species in silicate melts). These species, with the more compressible SieOeSi bonds than less compressible SiO-Si bonds in more depolymerized species, become increasingly abundant the more felsic (more polymerized) the magmatic liquids (Mysen, 1987). As mentioned earlier, the compressibility, in turn, weakens the bridging SieO and AleO bonds, thus leading to decreased activation energy of viscous flow. There are, of course, a number of additional factors affecting this bond strength. These factors also will be discussed further in the section of viscous of simple-system aluminosilicate melts in Section 9.4.2.

9.3.5 Viscosity and volatiles in magmatic liquids The majority of experimental data on transport properties of volatile-bearing magmatic liquids involves the role of H2O and the relevance of H2O in magma to igneous processes near convergent plate boundaries (Kilgour et al., 2016; Soldati et al., 2016). There are only scant data on the viscosity of magmatic liquids in the presence of halogens (Wyllie and Tuttle, 1964; Dingwell et al., 1985; Dingwell et al., 1999; Zimova and Webb, 2007) and even less for CO2-bearing magmatic liquids (Brearley and Montana, 1989; Di Genova et al., 2014).

9.3.5.1 Viscosity of hydrous magmatic liquids Given that pressures above ambient are necessary to dissolve significant amounts of H2O in silicate melts (see Chapter 7, Section (7.3)), most experiments to determine viscosity of hydrous magmatic liquids have been carried out at pressures from several hundred MPa (see, for example, Shaw, 1963; Friedman et al., 1963; Giordano and Dingwell, 2003; Robert et al., 2013) to several GPa (Kushiro, 1978; Ardia et al., 2008; Hui et al., 2009; Persikov et al., 2017). A few exceptions to this statement, such as that of Richet et al. (1996) in a study of hydrous andesite melt and glass, is one which takes advantage of the slow kinetics of exsolution of H2O from silicate melts to conduct viscosity measurements at ambient pressures to temperatures slightly above the glass transition with samples previously synthesized at high pressure and temperature. In the earliest experimental studies on the viscosity of hydrous rhyolite melt and glass, it was clear that melt viscosity decreased rapidly with increasing H2O content (Friedman et al., 1963; Shaw, 1963; see also Fig. 9.19). There is, however, some disagreement between the two early data sets as those of Friedman et al. (1963) tend to show higher viscosity than those of Shaw et al. (1963) at similar H2O contents (Fig. 9.19A, B). This difference may, however, possibly also reflect the higher pressures (100e200 MPa) in the Shaw (1963) experiments compared with those of Friedman et al. (1963; 6e7 MPa). Interestingly, though, Friedman et al. (1963), from the temperature-dependent rhyolite viscosity concluded that increasing H2O contents resulted in decreased activation energy of viscous flow, whereas this did not seem to be the case in the Shaw (1963) experiments. It is, of course, possible, that there is a difference because Shaw (1963) reports temperature-dependence at 4.3 and 6.2 mol %

9.3 Viscosity of magmatic liquids

14

14

A

B

12 Viscosity, logη Pa s

Viscosity, logη Pa s

13

53

12

5˚C

11

635

˚C

10

735

9

Rhyolite melt

8

627

˚C

0

0.2

0.4 0.6 0.8 1.0 H2O content of melt, wt%

10

63

5˚C 735 ˚C

8

785

6

1.2

4

Rhyolite melt

0

1

˚C

2 3 4 5 H2O content of melt, wt%

6

7

FIGURE 9.19 Viscosity of hydrous rhyolite magma as a function of their H2O content. (A) Rhyolite magma viscosity to pressures of 2 MPa. (B) Rhyolite magma viscosity to pressures of 200 MPa. (A) Modified from Friedman et al. (1963); (B) Modified from Shaw (1963).

H2O, whereas Friedman et al. (1963) compared temperature-dependent viscosity data from essentially anhydrous rhyolite and 0.5 wt% H2O. Subsequent experimental data have shown that the main viscosity changes caused by dissolved H2O take place within the first 1 to 2 wt% H2O dissolved in magma and melt (e.g., Richet et al., 1996; Dingwell et al., 1998; Misiti et al., 2006; see also Fig. 9.20). There is also a small, but significant temperature effect on these relations because the rapid low-H2O content viscosity change becomes less distinct the greater temperature (Fig. 9.20). The profound effect of dissolved H2O on the viscosity of magmatic liquids very likely is because solution of H2O in silicate melts results in melt depolymerization (see Chapter 7, Sections (7.3.6) and (7.3.7)). The effect of H2O on melt viscosity is greater the more felsic the magma because as magma becomes more (Si þ Al)-rich, fully polymerized Q4 species in the melt structure is more concentrated (Mysen, 1987). Effects of H2O of silicate melt properties are the most pronounced when dissolved H2O breaks oxygen bridges in fully polymerized Q4 species (see Chapter 7 and also Mysen and Richet, 2019, Chapters 14 and 15 for review of such effects). The aforementioned features also imply, as can be seen in the viscosity data for trachyte melt in Fig. 9.20 (Misiti et al., 2006), that there will be an effect of magma composition on the extent of the influence of dissolved H2O on magma viscosity. For example, even for rhyolitic or granitic melts, whether these are peralkaline or peraluminous, the effect of H2O on the melt viscosity can vary significantly. The temperature of the 1011 Pa s isokom varies by about 150K, for example (Fig. 9.21; see also Dingwell et al., 1998). The more mafic a magma, the smaller the effect of dissolved H2O on magma properties (Mysen, 2014). These properties include viscosity (Richet et al., 1996; Di Genova et al., 2014; see also Fig. 9.22). The effect of H2O on magma viscosity (and essentially any other magma property)

628

Chapter 9 Transport properties

16

Viscosity of hydrous trachyte magma at 1 GPa pressure as a function of its H2O content at different temperatures.

14

Modified from Misiti et al. (2006).

12

Viscosity, logη Pa s

FIGURE 9.20

Trachyte melt 10 8 900 K

6

4

1100 K

2

1300 K 1500 K

0

FIGURE 9.21

Modified from Dingwell et al. (1998).

1

2 3 4 5 H2O content of melt, wt%

6

7

1200 1100 1000 Temperature, K

Viscosity of the 1011 Pa s isokom of hydrous haplogranite (HPG8) magma as a function of H2O content for metaaluminous, peralkaline (increasing Na content as indicated on individual curves) and peraluminous (increasing Al content as indicated on individual curves).

0

900 800

HPGH 8 +2 % +H2O exces s Al HP GH8 +5 % +H2O HPGH exces 8+H2O s Al

700 600

HPGH 8 +10 % +H2O Na

500 0

1

HPGH 8 +5 % +H2O Na

3 4 5 2 H2O content of melt, wt%

6

7

decreases the more mafic the magma (Mysen, 2014) because the number of bridging oxygen bonds in the melt structure to be broken by dissolved H2O diminishes the more mafic the magma (the higher the NBO/T). Of course, the alkali/alkaline earth abundance ratio can also play a role in part because it may affect the distribution of the Qn-species in the magma and in part because this abundance ratio will

9.3 Viscosity of magmatic liquids

629

12 A

hy

dro us

8 6

an

Viscosity, logη Pa s

10

4 Andesite melt

2

Activation energy of viscous flow, kJ/mol

04

6

8 10 12 14 Temperature, 104/T (K-1)

16

B

350

300

250

rhy

200

oli

andes

te

ite

basalt

150

0

1 2 3 H2O content of melt, wt%

4

Fragility nindex, m

C

trach

yte

phono

lite

H2O content of melt, wt%

FIGURE 9.22 Rheology of various hydrous magmatic liquids as a function of temperature and H2O content. (A) Viscosity (h) temperature (1/T) relations for hydrous andesite magma as a function of temperature for H2O contents

630

Chapter 9 Transport properties

affect how Al3þ is charge balanced when occupying tetrahedral coordination in the melt structure. The individual effects on the influence of H2O on magma viscosity of those compositional features cannot be extracted from data on chemically complex magmatic liquids, but will be discussed in Section 9.3.5, which will focus on the viscous behavior of hydrous, but compositionally simpler silicate and aluminosilicate melts. Water dissolved in magmatic liquids also affect the temperature- and pressure-dependence of the magma viscosity (Giordano and Dingwell, 2003; Misiti et al., 2006; Hui et al., 2009). For example, the viscosity of hydrous magma, regardless of their exact bulk composition, is less sensitive to temperature than H2O-free magma (Misiti et al., 2006; Di Genova et al., 2014; See Fig. 9.22). It is also notable that the hydrous magma is often, but not always, less fragile than the anhydrous equivalent (Fig. 9.22A). In fact, there is often a systematic decrease in the fragility index as defined in Eq. (9.5) with increasing H2O in the magma (Whittington et al., 2001; Di Genova et al., 2014). It would seem possible, though, that felsic magmatic liquids such as rhyolite, for example, with its nearly Arrhenian behavior under anhydrous conditions, appear to become more fragile as H2O is dissolved in the magma (Fig. 9.22A). There is, however, more to this than the NBO/T of the magmatic liquid because the rate of decrease of the m index of hydrous phonolite magma, with its considerably higher alkali/alkaline earth abundance ratio, decreases more rapidly than does the m index for hydrous rhyolite magma even though the NBO/T of these two magma types does not differ greatly (Table 9.1). This different vm/vT likely is a reflection of how the H2O dissolved in the magmatic liquid interacts with the Qn-species in the magmatic liquid structure. This different fragility behavior likely also reflects how the tetrahedrally coordinated Al3þ is charge-balanced because the charge-balancing cation and the Al3þ are involved in the solution mechanism of H2O in aluminosilicate melts (Mysen and Virgo, 1986; Cody et al., 2020). Again, these features cannot be discussed in detail with the chemically complex natural magmatic liquids, but will be revisited when discussing the rheological behavior of hydrous simple composition aluminosilicate melts later in this Chapter. The temperature-dependent viscous behavior of hydrous magma, when recorded from temperatures below to above the glass transition, typically exhibits a curvature (e.g., Fig. 9.22A), and often is modeled with the TammanneVogeleFulcher (TVF) equation (Fulcher, 1925); logh ¼ A þ B=ðT  CÞ;

(9.6)

where A, B, and C, are fitting variables, T is temperature and h is viscosity. In the high-temperature region of hydrous melt, however, the relationship between viscosity and temperature is for all practical purposes Arrhenian (Eq. (9.4)). The slope of the log h versus 1/T relationships of hydrous magma does, however, vary both with bulk chemical composition and with the amount of H2O dissolved in the magma (Fig. 9.22). The log h versus 1/T slopes for any magma composition decrease with increasing H2O concentration in the magma (Fig. 9.22A) This decrease, which converts to deccreased activation energy of viscous flow, at least, in part, results from the lowering of the average bond energies of

indicated on individual curves. Note how the curves showing increasing deviation from linearity with increasing H2O content. (B) Activation energy magmatic liquids as a function of their H2O content for increasingly felsic magma as indicated on individual curves. (C) Fragility index (see Eq. (9.5)) of two magma types as a function of their H2O content. Data from Richet et al. (1996), Di Genova et al. (2014a).

9.3 Viscosity of magmatic liquids

631

chemical bonds that need to be broken and reformed as the hydrous melt structure becomes increasingly depolymerized with increasing H2O concentration in the melt.6 The energy budget associated with bond breakage and reformation during viscous flow depends on the bulk composition and H2O content of the magma. As a result, the evolution of the activation energy of viscous flow with increasing H2O is distinctly nonlinear (Fig. 9.22B). The curvature also depends on the bulk chemical composition of the magma as do the actual values of the activation energy because the H2O solution mechanism in aluminosilicate melts varies with changes of bulk composition of magmatic liquids. The effect of dissolved H2O on the activation energy of viscous flow at any H2O content decreases the more mafic the magma (Fig. 9.22B). This conclusion appears to differ for peraluminous granite melts, however (Dingwell et al., 1998). For such magma with 2% and 5% excess Al3þ, the effect of increasing H2O on the slope of the log h versus 1/T (and therefore, activation energy of viscous flow) appears to be the same within experimental uncertainty (Fig. 9.22C). Finally, the pressure-dependent viscosity of hydrous magma differs from that of anhydrous equivalent regardless of the magma type under consideration (e.g., Kushiro et al., 1976; Kushiro, 1978; Persikov et al., 1990; Ardia et al., 2008; Hui et al., 2009; Robert et al., 2013). This effect is evident for all magma compositions, but the more polymerized the anhydrous magma, the greater is the effect of dissolved H2O on the pressure-dependent magma viscosity.

9.3.5.2 Viscosity of magmatic liquids with other volatiles As noted already, experimental data on effects on magma viscosity of volatiles other than H2O dissolved in magmatic liquids is comparatively scarce. A few data have been reported for an effect of CO2 on viscosity a trachybasalt and latite melt from the Phlegrian Fields in Italy (Di Genova et al., 2014). There also exist a few data points on the effect of CO2 on viscous behavior of simple-system silicate melts (Brearley and Montana, 1989; Bourgue and Richet, 2001). Some experimental data on the viscosity of halogen-bearing magma, and in particular F-bearing magma, also have been reported (Zimova and Webb, 2007; Baasner et al., 2013). Given the conclusion that CO2 in silicate melts normally causes melt polymerization (see Chapter 8; Section (8.1.3)), it would not be surprising that the viscosity of CO2-bearing magma tends to be greater than in the absence of CO2 (Fig. 9.23; see also Di Genova et al., 2014). In addition, the activation energy of viscous flow of CO2-bearing magma exceeds that of the CO2-free equivalent. Interestingly, Di Genova et al. (2014) concluded that the effect of CO2 is greater for latite magma than for trachybasalt even though it is likely that the CO2 solubility in trachyte magma exceeds that in latite magma because of the much more polymerized nature of latite magma. Carbon dioxide solubility in silicate melts tends to decrease as a silicate melt becomes more polymerized (see, for example, Morizet et al., 2015). Halogens, and in particular fluorine, can also play important roles in igneous processes (Pichavant et al., 1987; Baker and Villaincourt, 1995; Giordano et al., 2004; Aiuppa, 2009). In existing experimental studies, the influence of fluorine on magma viscosity often is combined with H2O so that it can be difficult to extract the role played by fluorine alone. That complication notwithstanding, it is clear that fluorine dissolved in felsic magmas, for example, greatly enhances the magma fluidity (fluidity¼1/ 6 The depolymerization mechanism of H2O in silicate and aluminosilicate melts depends on both the bulk composition and the H2O content of the magma. These features have been reviewed in Chapter 7 and more extensively by Mysen and Richet (2019) in their Chapters 15 and 18.

632

Chapter 9 Transport properties

FIGURE 9.23

12.5

Viscosity (h)-temperature (1/T) relations for latite melt as a function of its CO2 content.

12.0

Viscosity, logη Pa s

Data from Di Genova et al. (2014b).

11.5 11.0 10.5 10.0

Latite melt

9.5 9.0 1.10

1.15

1.20

1.25

Temperature, 103/T (K-1)

viscosity). Moreover, whether a granite melt is peralkaline, meta-aluminous or peraluminous can have significant effects on how much their viscosity changes upon solution of H2O (Dingwell et al., 1998). Addition of F to hydrous rhyolite melt appears to enhance this further (Fig. 9.24). How much of this 11

A

B Granite melt 1 GPa pressure

3.5

Viscosity, logη Pa s

Melt viscosity, log η (Pa s)

4.0

3.0

2.5

9

7

5

2.0 0.80 0.82 0.84

0.86 0.88 4

0.90 0.92 -1

Temperature, 10 /T (K )

3

0

5 10 15 H2O+F2O-1 concentration,. mol%

20

FIGURE 9.24 (A) Viscosity (h)-temperature (1/T) relations for peralkaline (Na2O þ K2O þ CaO)/Al2O3 ¼ 1.28), metaaluminous (Na2O þ K2O þ CaO)/Al2O3 ¼ 0.98), and peraluminous (Na2O þ K2O þ CaO)/Al2O3 ¼ 0.86), granite composition melt with 1.5 wt% F and 6 wt% H2O at 1 GPa total pressure. (B) Effect of H2O, F2O-1 and mixed H2O þ F2O-1 of viscosity at haplogranite (HPG8) composition melt. Modified from Baker and Villaincourt (1995), Di Giordano et al. (2004).

9.4 Viscosity of model system silicate melts

633

effect is from the 1.5 wt% F and how much from the approximately 6 wt% H2O in the Dingwell et al. (1998) study cannot be extracted from existing data. However, in the experiments with haplograniteeH2OeF melts by Giordano et al. (2004), there does not seem to be a large effect caused by varying either the H2O or the F content within the 3%e6% concentration range of this study. However, from a numerical fit to existing data, they did suggest that viscosity of haplogranite melt with only fluorine is more viscous than in the presence of H2O alone (Fig. 9.24B). That observation notwithstanding, when examining the temperature effects on viscosity, Giordano et al. (2004) concluded that the activation energy of viscous flow of haplogranite melt with H2O and fluorine is smaller than when only H2O is dissolved in the magma. Although there is no clear structural understanding of those various effects on magma viscosity, it does seem clear that by combining H2O and F in solution in the magmatic liquids, the combined effects are greater than if these components were added separately. In light of the complex solution mechanism of fluorine in silicate melts (see Chapter 8; Section (8.6.2)), those melt rheological features most likely would also be significantly dependent on concentration of both H2O and fluorine as well as the bulk composition of the magmatic liquid. The details of this behavior as well as a discussion of existing, very limited rheology data for other halogens, will be addressed in the next sections.

9.4 Viscosity of model system silicate melts The correlations summarized in Section 9.2 in which the rheology of magmatic liquids was summarized, cannot be employed with precision to isolate effects of individual chemical components, structural, or intensive variables. That goal requires additional details developed from studies of viscous behavior in compositionally simpler melt systems. nþ The compositional components of the system M2=n O  Al2 O3  SiO2 ; where M is an alkali metal or an alkaline earth, comprise about 95% of the chemistry of typical igneous rocks (Mysen, 1987). However, to identify the influence of the individual components, this complex system must be  broken    down into components in simple binary

nþ O SiO2 M2=n

ternary

nþ O Al2 O3 SiO2 ; and M2=n

perhaps quaternary systems. In addition, effects of iron and the redox ratio of iron require consideration. This is the manner in which rheology of silicate melts and glasses will be described here. However, in doing so, limitations are imposed by intersection with fields of liquid immiscibility7 and compositions that are unstable at the temperatures at which measurements are to be made. Those limitations restrict the compositional ranges within which properties of silicate and aluminosilicate melts and glasses can be examined experimentally. 7

Liquid immiscibility above liquidus temperatures at ambient pressure exists in SiO2-rich compositions in the systems SrOe SiO2, CaOeSiO2, and MgOeSiO2 (see, for example, Fig. 6.1 in Mysen and Richet, 2019 or Phase Diagrams for Ceramists, https://phaseonline.ceramics.org, for detailed information on the relevant phase relations). The immiscibility fields expand in the order, MgOeSiO2>CaOeSiO2>SrOeSiO2. In Al2O3-bearing systems, the immiscibility volumes shrink with increasing Al2O3 beginning from the M nþ O  SiO2 join (see Fig. 8.4 in Mysen and Richet (2019) or Phase Diagrams 2=n for Ceramists, https://phaseonline.ceramics.org, for detailed information on the relevant phase relations for the Al2O3bearing systems). References to the original sources of this information can be found in those citations. For the readers’ information, the portion of the data relevant to the present discussion in the digital data base, https://phaseonline.ceramics.org, also exists in hard-copy volumes in particular in volume 1, published in 1964 (Levien et al., 1964). Additional information on liquid immiscibility in silicate systems is available in Mazurin et al. (1984).

634

Chapter 9 Transport properties

The aforementioned restrictions notwithstanding, from structural information of relevant melt nþ O= compositions (see Chapters 5, 7, and 8), the main variables to be taken into considerations are M2=n . nþ nþ O ðAl2 O3 þSiO2 Þ ratios, and abundance and abundance ratios of the various M2=n O SiO2 and M2=n components, Al/(Al þ Si), and how tetrahedrally coordinated Al3þ is charge-balanced. In addition, volatiles such as H2O, CO2, and halogens can have significant influence on rheological properties of silicate melts (see Chapters 7 and 8, for discussion of interaction between volatiles and silicate melt structure). Of course, temperature, pressure, and, in specific circumstances, the oxygen fugacity, also need to be taken into consideration. nD OLSiO system 9.4.1 Viscosity of melts and glasses in the M2=n 2

Experimental data summarized in this section include those in simple binary metal oxideesilica joins (Poole, 1948; Bockris and Lo¨we, 1954; Machin and Yee, 1954; Bockris et al., 1955; Rontgen et al., 1956; Knoche et al., 1994; Toplis, 1998) as well as data involving two metal oxides and silica in which the mixing behavior of two metal cations can affect the rheological properties (Poole, 1948; Machin et al., 1952; MacKenzie, 1957; Day, 1976; Neuville and Richet, 1991; Neuville, 2006)8,9,10. The relevant metal oxides are the alkali metals and the alkaline earths. Viscosity data for ferrous iron silicate melts also has been reported in ambient pressure, high-temperature viscosity experiments of melts from the system FeOeSiO2 (Rontgen et al., 1956). However, those data are not included because it is not clear whether or not the oxidation state of iron was adequately controlled in those experiments. nþ O  SiO2 melts decreases as an approximately exponential function of Isothermal viscosity of M2=n their SiO2 concentration (Fig. 9.25; see also Lillie, 1979; Bockris and Lo¨we, 1954; Bockris et al., 1955; Ro¨ntgen et al., 1956; Knoche et al., 1994, for details).11 A striking feature of these data is very rapid drop in viscosity by adding perhaps only a few mol % of a metal oxide. For example, by adding 2.5 mol % K2O to SiO2 supercooled melt at 1600 C, the melt viscosity decreases by about 5.5 orders of magnitude (Bockris et al., 1955). Addition of 5 mol % Na2O to SiO2 in the Na2OeSiO2 melt system causes the viscosity to decrease by about 6.5 orders of magnitude. It is clear, therefore, that in all alkali silicate melts systems, essentially all of the viscosity decrease takes place within the first 10 mol % addition of the M2O component (Bockris et al., 1955). As more metal oxide beyond the initial few percent is added, the rate of viscosity change diminishes rapidly and approaches 0 for some of the 8

An interested reader can access a detailed review of viscosity data until 1987 in Ryan and Blevins (1987). This review also contains detailed information on the various methods employed for experimental determination of viscosity of melts and glasses. 9 This is known as the “mixed alkali effect” (Day, 1976). It affects any melt property that depends on how mixing of metal oxides changes silicate melt structure in ways that affect melt properties. 10 Essentially all the viscosity data for metal oxideesilica melt systems have been reported as a function of bulk chemistry of the system. The principal compositional variable is the M nþ O=SiO2 ratio. However, given the premise that melt viscosity is 2=n more realistically described in terms of melt structure, the presentation and discussion provided in the sections that follow will be primarily in terms of melt polymerization (NBO/T and NBO/Si) and Qn-speciation. To some extent, we will also discuss the topology of the Qn-species as this topology can be affected by the electronic properties of the metal cations (Maekawa et al., 1991; Mysen, 1997) and how steric considerations resulting from cation charge and size can affect the Qn-species (Kohn and Schofield, 1994; Toplis and Corgne, 2002; Mysen and Dubinsky, 2004). 11 Lower-temperature data of glasses can be found in Poole (1948) and Knoche et al. (1994). However, as data from glasses are not equilibrium data, the temperature regions of glass viscosity will not be discussed further in this section.

9.4 Viscosity of model system silicate melts

635

FIGURE 9.25 10

10

10

Viscosity, Pa s

10 10 10 10 10 10 10 10

Relationship between SiO2 concentration and N2OeSiO2 melt viscosity at different temperatures.

9

Data from Knoche et al. (1994).

8 7 6 5 4 3

Na2O-SiO2 melt 2 1

1600˚C

100

1350˚C

90 80 70 SiO2 concentration in melt, mol%

60

alkali silicate melts when MO/SiO2 approaches 1 (corresponding to melt NBO/Si ¼ 2). In contrast, in the alkaline earth melt systems, viscosity effects can be examined only for BaOeSiO2 melts because for oxides of smaller alkaline earths such as SrO, CaO, and MgO, a liquid immiscibility gap between nearly pure SiO2 and from w20 to w40 mol % alkaline earth oxide (Ol’shanskii, 1951) precludes accurate determination of the initial rate of viscosity decrease when alkaline earth oxides are added to SiO2.

9.4.1.1 Viscosity and melt structure Although the use of SiO2 concentration in a melt or magma as a factor with which to describe melt viscosity may be convenient, as we noted in the aforementioned section under viscosity of natural magmatic liquids, correlations between viscosity and SiO2 content do not add to our understanding of what structural factors govern the viscosity of silicate melts and, ultimately, magmatic liquids. Chemical compositional variations can have multiple structural effects that cannot be isolated. However, by addressing relationships between melt viscosity and melt structure directly, those conceptual barriers can be overcome. Attainment of that goal requires an understanding of what melt structural factors govern melt viscosity. As a first step in this direction, let us consider how the viscosity of melts in binary metal nþ oxideesilica systems varies with silicate polymerization.12 In M2=n O  SiO2 melts, we replace NBO/T 12

In chemically complex systems such as natural magmatic liquids, for example, as discussed in detail in Chapter 5, Section (5.2), the expression NBO/T, where T is the sum of tetrahedrally coordination cations (dominant T-cations ion magmatic liquids are Si4þ and Al3þ) and NBO stands for nonbridging oxygens (see Chapter 5, Section (5.2)), is a convenient first-order structural variable with which to measure effects of structure on silicate melt viscosity.

636

Chapter 9 Transport properties

with NBO/Si because Si4þ is the only tetrahedrally coordinated cation in such melts at ambient pressure (see, for example, Virgo et al., 1981, for an early discussion of these relations). The NBO/Si is then related to the SiO2 concentration (mol %) via the following simple expression;   NBO 1  XSiO2 ¼2 ; (9.7) Si XSiO2 where XSiO2 is the mol fraction of SiO2 in the melt. When expressing the melt viscosity as a function of NBO/Si of the melt, the higher the temperature, the more quickly does the viscosity decrease from its value at pure SiO2 (Fig. 9.26). Moreover, by comparing the viscosity data from Na2OeSiO2 and CaOeSiO2 melts, for example, it is obvious that the viscosity of Na2OeSiO2 melts decreases much more rapidly with increasing NBO/Si than does the viscosity of CaOeSiO2 melts. In other words, it appears that on a molar basis alkali metals affect silicate melt viscosity more effectively that the alkaline earths.13 A feature somewhat related to those latter observations is the evolution of melt viscosity of binary nþ M2=n O  SiO2 melts as a function of the ionization potential of the M-cation at fixed temperature and NBO/Si of the melts. In the example of this effect in Fig. 9.27, information was interpolated and extrapolated to a reference condition of 1400 C and NBO/Si ¼ 1 even though in practical terms, as discussed earlier, those conditions might not be attainable for some metal cations. That notwithstanding, for the purpose of isolating the effect of the electronic properties of the metal cation, M, that condition was chosen. As is seen (Fig. 9.27), although there seems to be a small effect of whether the nþ Mnþ cation has n ¼ 1 or 2 (alkaline earths, M2þ, tends to have slightly higher viscosity than M2=n O

SiO2 melts), there is the general tendency that as the M-cation becomes more electronegative (Z/r2 increases, Z ¼ formal electrical charge, r ¼ ionic radius) under isothermal conditions and constant silicate polymerization, the melt viscosity decreases. Moreover, the main effect seems to take place in the Z/r2-range from about 0.5 (corresponding to Kþ) to Z/r2 between 1.5 and near 2 (Sr2þ and Ca2þ). The influence of the electronic properties of the metal cation, Mnþ (n ¼ 1, 2), on the melt rheology reflects the fact that the structure of silicate (and aluminosilicate) melts can be described by a set of coexisting silicate species, denoted Qn-species (Virgo et al., 1980; Stebbins, 1987; Maekawa et al., 1991; Mysen, 1997) where n denotes the number of bridging oxygen in the species and n is an integer with values 0, 1, 2, 3, 4. The proportions of these species varies with the M/Si abundance ratio and with the electronic properties (electronegativity, Z/r2) of the M-cation (Maekawa et al., 1991; Buckermann et al., 1992), and temperature (above the temperature of the glass transition) (Stebbins, 1988; Mysen, 1997). In silicate melts, including natural magmatic liquids, equilibria that describe the relations among silicate species (Qn-species) are of the form: 2Qn ! Qnþ1 þ Qn1 :

(9.8)

13 This different viscosity behavior of alkali metal and alkaline earth silicate melts may be related to different degree of disorder among the Qn-species depending on the electronic properties of the network-modifying cations that form bonding with nonbridging oxygen in these silicate species. It is also to be noted that the concentration of, in particular, the most polymerized Qn-species is sensitive to the electronic properties of the M-cation. Such features will be discussed in Section (9.4) below where relationships between entropy and viscosity of silicate melts will be presented.

9.4 Viscosity of model system silicate melts

637

A

B

11

50

˚C

150

0˚C

1800˚C

1450˚C

FIGURE 9.26 (A) Relationship between Na2OeSiO2 melt viscosity and its NBO/Si values at different temperatures. (B) Relationship between CaOeSiO2 melt viscosity and its NBO/Si values at different temperatures. Data from Bockris et al. (1955).

7

FIGURE 9.27

6

Activation energy of viscous flow of binary metal oxide melts and the ionization potential of the metal cation. Data from Bockris et al. (1955).

Viscosity, Pa s

5

1000˚C NBO/Si=1

4

3

alk

ali

2

me

alkaline earths

tals

1 0.5

1.0

1.5

2.0 Z/r2, Å-2

2.5

3.0

3.5

4.0

638

Chapter 9 Transport properties

For most natural magmatic liquids, the n-value is 3, so that the equilibrium becomes (Mysen, 1987): 2Q3 ! Q4 þ Q2 :

(9.9)

For mafic magmas such as basanite, komatiite, and boninite, for example, an additional equilibrium with n ¼ 2, is needed to describe in Qn-species distribution: 2Q2 ! Q3 þ Q1 :

(9.10)

A key feature of these equilibria is that they shift to the right with increasing temperature at constant Z/r2 of the metal cation and with increasing Z/r2 of the metal cation at constant temperature (Mysen, 1997, 1999). These structural phenomena become critical when discussing the viscosity evolution such as that shown in Fig. 9.27. With a bulk melt NBO/Si ¼ 1, for example, Eq. (9.9) describes the Qn-species distribution. As the Z/r2 is increased and the viscosity decreases with it, this reflects the shift of Eq. (9.9) to the right. In fact, in the CaOeSiO2 melt system (Z/r2 ¼ 2 for Ca2þ) at bulk melt NBO/Si ¼ 1, the proportion of Q3 species is only about 20% of the total, with the remaining split evenly between Q2 and Q4 species (40% each; Mysen, 1987), whereas for Z/r2 ¼ 0.5 (corresponding to Kþ), there is about 95% Q3 species and only a few percent Q2 and Q4 (Stebbins, 1987). In a hypothetical MgOeSiO2 melt system, Q3 species are not stable and the melt would consist of 50% Q2 and 50% Q4 species. It is these Qn-species abundance variations that govern the viscosity evolution in Fig. 9.27. In natural magma, the range in Z/r2-values of cations with the greatest effect includes typical network-modifying cations such as Kþ, Naþ, and Ca2þ, with a lesser effect of Mg2þ. Translated to magma types, this means that comparing a magmas such as phonolite and rhyolite and trachyte and tholeiite, for example, the M2þ/Mþ ratio is greater in rhyolite and tholeiite magma compared with phonolite and trachyte magmatic liquids. Therefore, without consideration of effects of charge-balance of tetrahedrally coordinated Al3þ, which will affect these abundance ratio considerations and will be discussed later in this Chapter, the phonolite and trachyte magmas are likely to more viscous than rhyolite and tholeiite magmas, respectively.

9.4.1.2 Viscosity and temperature

nþ Relationships between temperature and viscosity of M2=n O  SiO2 melt are affected by both the type

of M-cation and the M/Si abundance ratio (Poole, 1948; Shartsis and Spinner, 1952; Bockris et al., 1955; Richet, 1984; Knoche et al., 1994; Toplis et al., 1997). Whereas for SiO2 melt and glass the relationship between log h (viscosity) and 1/T (temperature in Kelvin) is linear and, therefore, strictly follows an Arrhenius function (Eq. (9.4)) with a slope that converts to an activation energy of viscous flow near 515 kJ/mol, addition of any amount of a metal oxide causes a curvature in this relationship (Fig. 9.28). The magnitude of this curvature increases with increasing abundance of the Mnþ cation. This development reflects the increased abundance of Q2 and Q4 structural units at the expense of Q3 units in the melts. That change, in turn, leads to an increase in the entropy of mixing of the silicate melt. Increased entropy of mixing enhances the fragility of silicate melts, which appears as increased curvature in the log h versus 1/T relationships such as seen in Fig. 9.28 (see also Richet, 1984). In addition, the individual Qn-species have different topological entropy contributions, which add further to the overall entropy of the system (Mysen, 1995). Unfortunately, viscosity data as a function of

9.4 Viscosity of model system silicate melts

639

1.0 0.86 8 1.3 1.6 3 4

0. 0.5 35 0

12

0.6

Melt viscosity, log η (Pa s)

7

10

8

6

4 High-T

2

0.4

0.6

0.8

1.0

1.2

1.4

Temperature, 103/T (K-1)

FIGURE 9.28 Viscosity (h)-temperature (1/T) relations for Na2OeSiO2 melts and glasses as a function of the NBO/Si-value of the melt (numbers attached to each curve). Note how the curves deviate more and more from the essentially straight line of SiO2 melt as their NBO/Si-value increases. Data from Knoche et al. (1994).

nþ temperature for glasses and melts of most binary M2=n O  SiO2 systems are lacking, so an effect of the

electronic properties of the Mnþ cation cannot be assessed quantitatively. It is likely, however, that the curvature increases (the melts become more fragile) the greater the Z/r2 of the Mnþ cation.14 Because glass is a nonequilibrium state of materials (see also Chapter 5, Section (5.1) for more discussion of glass versus melt relations and the nature of the glass transition), it is not useful to relate

Mysen (1995) employed published configurational heat capacity data with Qn-species abundance information for Li2OeSiO2, Na2OeSiO2, and K2OeSiO2 melts to derive configurational heat capacity for individual Qn-species and found that the more depolymerized the Qn-species (smaller n-value), the greater is its configurational heat capacity. The implication is that the further equations such as (9.8e9.10) shift to the right, the greater is the effect on the configurational heat capacity, and therefore, configurational entropy, of the melt. This, in turn, means that the further to the right those equations are shifted, the greater is the curvature in diagrams such as in Fig. 9.28. 14

640

Chapter 9 Transport properties

structural features of glass to viscosity changes of a glass as a function of temperature. Instead, only the high-temperature portion of the viscosity versus temperature curves (e.g., Fig. 9.28, marked “high-T”) will be considered. An example, using data for K2OeSiO2 melts (Bockris et al., 1955), of how those curves evolve with temperature and composition shows these the log h versus 1/T relations to be linear in the high-temperature portion (above the glass transition temperature) of the data sets (Fig. 9.29). It is also evident from those data that as the melts become decreasingly polymerized (NBO/Si increases), the slopes become shallower, starting from the viscosity curve for pure SiO2. The slopes as shown with log h10 versus 1/T equal 2.303•Eh/R, where R is the gas constant and Eh is the activation energy of viscous flow, which is shown as a function of NBO/Si-values in the insert in Fig. 9.29. As was the case for the relationship between melt viscosity and NBO/Si of the melt showing a very rapid decrease as the melts become depolymerized (Figs. 9.25 and 9.26), the activation energy of viscous flow decreases rapidly from the 515 kJ/mol value for SiO2 melt to near 300 kJ/mol at an NBO/Si-value of 0.05 and reaches a near constant value slightly below 200 kJ/mol at NBO/Si ¼ 0.4 and above (Fig. 9.29). This activation-energy decrease, which includes the energy of the bonds in the melt needed to be broken and reformed during viscous flow, led Bockris and Reddy (1970, 1973) to suggest that the structure of silicate melts could be described with a small number of stoichiometric silicate species. This structural concept is, of course, similar to that which was later shown from 29Si MAS NMR and Raman spectroscopy, as noted above and discussed in detail in Chapter 5, (Section 5.2.3), that silicate melts could be described in terms of a small number of silicate species defined by their individual number of bridging oxygen per Si (Virgo et al., 1980; Mysen et al., 1982; McMillan, 1984; Stebbins, 1987; Maekawa et al., 1991; Buckermann et al., 1992). The observation that the activation energy of viscous flow is correlated with the NBO/Si of silicate melts is not surprising given the premise that the average bond energy of the bonds in a silicate melt decreases the more depolymerized (higher NBO/Si) the melt. The proportion of MeO bonds increases and that of bridging SieO bonds15 decreases as the NBO/Si of the melt increases. The MeO bond energy is only a small fraction (less than 100 kJ/mol) of those of the bridging SieO bonds (near 600 kJ/mol) (Smyth and Bish, 1988). The Eh versus NBO/Si trend from natural magmatic liquids does show considerable scatter (Figs. 9.7 and 9.8). This scatter likely is because other parameters, in addition to the melt NBO/Si, affect the activation energy of viscous flow. The first among these parameters is possible differences between alkali metals and alkaline earth (i.e., different formal electrical charge). This feature is evident in the activation energy of viscous flow of MOeSiO2 (M ¼ alkaline earth) and M2OeSiO2 (M ¼ alkali metals) melts (Fig. 9.30A). Even though there are distinctly separate activation energy trends for the MOeSiO2 and M2OeSiO2 melts, these trends show less scatter than the bulk (Fig. 9.30A). It would seem, therefore, that there would be separate trends for evolution of activation energy with NBO/Si for each individual alkaline earth and alkali silicate melt data sets (Lillie, 1979; Bockris and Lo¨we, 1954; Bockris et al., 1955; Knoche et al., 1994). Such trends are evident for the alkali silicate melts, K2OeSiO2, Na2OeSiO2, and Li2O (Figs. 9.30B and 9.31). These trends become increasingly well separated as the bulk melt NBO/Si increases. It is likely that this evolution reflects the significantly different abundance of the various depolymerized Qn-species (n  3), as observed in the 29Si MAS

15

A bridging oxygen bond is an SieO bond where the oxygen forms bonding with Si4þ in the center of two neighboring oxygen tetrahedra.

9.4 Viscosity of model system silicate melts

641

12

Activation energy, kJ/mol

Melt viscosity, log η (Pa s)

10

8

6

500 450 400 350 300 250 200 0.2

0.4 0.6 0.8 NBO/Si of melt

1.0

4 5

0.0

/Si=

O NB

0.41 /Si= NBO i=0.57 /S O NB 0.69 /Si= 0 NBO i=1.0 /S NBO

3

0.1

i= O/S

NB

0.24

/Si=

NBO

2

5.00

5.50

6.00

6.50

7.00

7.50

8.00

Temperature, 104/T (K-1) FIGURE 9.29 High-temperature (above glass transition) Viscosity (h)-temperature (1/T) relations for Na2OeSiO2 melts as a function of their NBO/Si-values. The decreasing slope of these curves reflect decreasing activation energy of viscous flow as shown in the insert. Data from Bockris et al. (1955).

NMR spectra of these three melt systems, as a function of increasing NBO/Si (increasing M/Si ratio; see Maekawa et al., 1991; Buckermann et al., 1992). The activation energy of viscous flow of alkaline earth silicate melts (BaOeSiO2, SrOeSiO2, CaOeSiO2, MgOeSiO2) also show differences, but the separation of the individual activation energy trends is smaller than for the alkali silicate melts (Fig. 9.30B and C). This smaller difference is further evidenced in the expression of Eh as a function of the ionization potential of the alkaline earths (Z/r2) in Fig. 9.31. In fact, it could be argued that there is no discernible difference between the activation energy trends with Z/r2 for the alkaline earths, at least for the Sr, Ca, and Mg trends.

642

Chapter 9 Transport properties

A

B

C

FIGURE 9.30 Activation energy of viscous flow of binary metal oxide melts as a function of the NBO/Si of the melts. (A) Relationship separated into melts with alkaline earths (closed symbols) and alkali metals (open symbols). (B) Relationship for individual alkali silicate melts as indicated on individual curves. (C) Relationship for individual alkaline earth silicate melts as indicated on individual curves. Data from Bockris et al. (1955).

9.4 Viscosity of model system silicate melts

643

FIGURE 9.31 Activation energy of viscous flow of metal oxide silicate melts and the ionization potential of the metal cation separated into alkaline earth silicate melts (closed symbols) and alkali silicate melts (open symbols). Data from Bockris et al. (1955).

In summary, it seems, therefore, that although the viscosity and activation energy of viscous flow of binary alkaline earth silicate and alkali silicate melts are correlated with the NBO/Si of the melts, these correlations show considerable scatter. A portion of that scatter results from the different effects of individual alkaline earths and alkali metals on the viscosity parameters primarily because Q4-species abundance varies with the electronic properties of the Mnþ cations. A likely consequence of the viscosity behavior depending on electronic properties and proportions of individual alkali and alkaline earth cations is that whereas for mafic magmatic liquids such as basalt and komatiite with mostly alkaline earths as network-modifying cations, for example, their viscous behavior is not so sensitive to their different Ca/Mg ratios. However, as magma becomes more felsic, the Mþ/M2þ abundance ratio increases. This abundance change also will affect the viscosity trends of such magmatic liquids. Of course, the latter suggestions do not consider the various forms of chargebalance of tetrahedrally coordinated Al3þ. Moreover, effects of mixing such as the so-called “mixed alkali effect” which can play a role, both in Al-free and Al-bearing melts can also affect this conclusion (Day, 1976; Richet, 1984; Neuville, 2006; Le Losq and Neuville, 2013). This effect will be discussed for Al-free melts next.

9.4.1.3 Viscosity and mixed metal oxides Addition of a second cation to a binary metal oxide melt affects transport properties such as viscosity (e.g., Richet, 1984; Neuville and Richet, 1991; Neuville, 2006), diffusivity, and electrical, conductivity (Day, 1976; Ni, 2012). However, the relationship between property and extent of cation mixing is not linear. The deviations, typically negative from straight line connecting the endmembers, are referred to as the “mixed alkali effect” (Fig. 9.32). It is, however, also clear that the extent of these deviations diminishes with increasing temperature (Richet, 1984; Neuville and Richet, 1991; Neuville, 2006) so that at the highest temperature in Fig. 9.32A, at 1600K (1327 C), there is no evidence of a mixed alkali effect. Similar features were reported for mixed Na,K trisilicate melts (Richet, 1984). This feature can

644

14

Chapter 9 Transport properties

13

A

12 Viscosity, Pa s

12

10

Viscosity, Pa s

B

NBO/Si=1.34

8 100

0K 105 0K

6

NBO/Si=2.00 11 1025K

10

4

1050K

9

2 1600K

1075K

0 0.00

0.20

0.60 0.40 Na/(Na+Ca)

0.80

1.00

8 0.00 MgSiO3

0.20

0.40 0.60 Ca/(Ca+Mg)

0.80

1.00 CaSiO3

FIGURE 9.32 Melt viscosity and mixed alkali effects of ternary metal oxide silicate melts. (A) Viscosity from Na-to Ca-silicate melts with fixed NBO/Si-value at 1.34 at different temperatures as indicated. (B) Viscosity from Mg- to Cametasilicate melts (NBO/Si ¼ 2.00) as a function of their Ca/(Ca þ Mg) ratio at different temperatures as indicated on individual curves. Modified from Neuville and Richet (1991), Neuville (2006).

also be seen in the CaOeMgOeSiO2 melt system (Machin et al., 1952; Machin and Yee, 1954; Neuville and Richet, 1991). At temperatures near and slightly above 1000K (supercooled melt region), there is a pronounced minimum (Fig. 9.32A), whereas at the higher temperatures of 1773 K in the viscosity determinations by Machin and Yee (1954) and Machin et al. (1952), there is no mixed alkali effect, and the effect on the viscosity itself is only minor (Fig. 9.33). The extent of deviation from simple linearity at temperatures where the mixing effect is significant also depends on bulk composition of the melt. A comparison of Fig. 9.32A and B would indicate, for example, that at the same temperature, the deviations are greater in a Na,Ca mixed silicate compared with a Ca,Mg mixed silicate. It is not altogether clear, however, whether the different NBO/Si-values of the two systems in Fig. 9.32 (NBO/Si ¼ 1.34 and 2.00 for the Na,Ca and Ca,Mg systems respectively) could play a role. The composition at the viscosity minimum appears also to depend on the viscosity of the endmembers so that in the Na,Ca system where these differ significantly, the minimum viscosity is closer to the high-viscosity endmember (Fig. 9.32A), whereas when the viscosity of the endmember is nearly the same, the minimum appears near the 50:50 mixture of the endmember. It has been suggested that the mixed alkali effects stem from nonrandom mixing of the metal cations among the nonbridging oxygen sites in the melt structure (Neuville, 2006). That suggestion is consistent with 29Si MAS NMR data on glasses with the same metal cation mixtures (Lee and Stebbins, 2003) and with the extent of steric hindrance of cation substitution on energetically nonequivalent oxygen locations in the melts (Kohn and Schofield, 1994; Kushiro and Mysen, 2002; Mysen, 2006). The observation that the mixed alkali effect diminishes with increasing temperature would also be consistent with such a model because it is likely that the cation ordering among nonbridging oxygen locations in the melts diminishes with increasing temperature (Neuville, 2006).

9.4 Viscosity of model system silicate melts

645

FIGURE 9.33 Melt viscosity and mixed alkali effects of ternary CaOeMgOeSiO2 melts as a function of their Ca/(Ca þ Mg) ratio for two different NBO/Si-values as indicated at 1500K.

viscosity, log η, Pa s

NBO/Si=1.33

Data from Machin et al. (1952), Machin and Yee (1954).

CaO-MgO-SiO2 melt 1500 K

NBO/Si=2.44

Activation energy is much less sensitive to mixed alkali effects than viscosity itself. In the Na,Ca system described by Neuville (2006), for example, there is a simple activation energy decrease from 188  8 kJ/mol to 150  3 kJ/mol for the Ca and Na-endmembers, with a nearly straight line connecting the endmembers. This should not, however, be a big surprise given that the NaeO and CaeO bond energies do not differ much compared to SieO bond energies (Smyth and Bish, 1988), which may mean that the activation energy of viscous flow is not affected much by the Na/Ca abundance change. nþ 9.4.1.4 Viscosity of M2=n O  SiO 2 melts and pressure

In light of the fact a large majority of igneous processes take place at pressures above ambient, property data relevant to such high-pressure processes are necessary. One such property is the viscosity of magma. Some experimental data obtained at high pressure exist for viscosity of Na2OeSiO2, (K,Mg)-silicate, and Ca,Mg silicate melts (Kushiro, 1976; Scarfe et al., 1987; Rubie et al., 1993; Reid et al., 2003; Spice et al., 2015). Unfortunately, very little experimental data exist for Mg-silicate melts at high pressure and temperature despite the importance of Mg-rich magma in the Earth’s mantle. This scarcity likely is primarily because the high melting temperatures in Mg-silicate systems precludes controlled high-pressure experiments at temperatures above their liquidus. There are, however, some high-pressure results from molecular dynamics calculations as a function of Mg/Si and Ca/Mg ratios of the melts (Lacks et al., 2007; Zhang et al., 2010). Significant theoretical efforts also have been devoted to computing, via molecular dynamics, transport properties of specific model mantle compositions such as MgSiO3 and Mg2SiO4 melts (Martin et al., 2009; Adjaoud et al., 2011; Spera et al., 2011 Zhao et al., 2014).

646

Chapter 9 Transport properties

It is difficult, however, to ascertain the reliability of those latter computational results because often, but not always, they are not benchmarked against experimental data. One should be cautious, therefore, when applying quantitatively the results of such calculations. It is probably safe, however, to utilize of numerical simulations to extract relative melt viscosity in pressure and composition space. For example, the results of molecular dynamics calculations at 3000K temperature as a function of MgO/SiO2 abundance ratio and pressure (Lacks et al., 2007), offer a systematic view of how NBO/Si of melt may govern the pressure effects on melt viscosity (Fig. 9.34). In fact, the results summarized in Fig. 9.34 may be the only systematic examination of how the viscosity with different melt compositions and melt structure (NBO/Si ¼ 0, 0.1, 1, 2, and 4) respond to high pressure. For example, as can be seen in Fig. 9.34, melt viscosity at 3000 K temperature for the most SiO2-rich and, therefore, most polymerized compositions (NBO/Si ¼ 0 and 0.1) decreases rapidly with increasing pressure and reaches a minimum value at pressures between 10 and 20 GPa. With an additional pressure increase, the viscosity of these two melts increases. The third-most polymerized melt, with NBO/Si ¼ 1, exhibits only a very minor viscosity decrease between ambient and about 10 GPa pressure before further pressure increases also results in increased melt viscosity. The MgOeSiO2 melts less polymerized than NBO/Si ¼ 1 exhibit a pressure-induced

10

Melt viscosity, η, Pa s

1

0.1

0.01 MgO

0.001 0

10

20

30

40

50

Pressure, GPa

FIGURE 9.34 Effect of pressure on the viscosity of MgOeSiO2 melts with different NBO/Si-values as indicated on individual curves. Data from Lacks et al. (2007).

9.4 Viscosity of model system silicate melts

647

viscosity increase (Lacks et al., 2007; Martin et al., 2009; Adjaoud et al., 2011; Spera et al., 2011; see also Fig. 9.34). The viscosity of Na2OeSiO2 melts has been determined experimentally as a function of their NBO/ Si between 0.67 and 2 (Kushiro, 1976; Scarfe et al., 1987; Rubie et al., 1993; see also Fig. 9.35). The two most polymerized of those melts, with NBO/Si ¼ 0.5(not shown) and 0.67, exhibit a distinct viscosity decrease with pressure, whereas the melt with NBO/Si ¼ 1 exhibits an initial viscosity increase to about 1.5 GPa before additional pressure results in decreasing viscosity. The most depolymerized melt, with NBO/Si ¼ 2, shows increasing viscosity with increasing pressure. These experimentally determined viscosity data cannot, however, be compared directly with the molecular dynamics results for MgOeSiO2 melt viscosity (Fig. 9.34) because the latter information extended to much higher pressure (and temperature) than the experimental viscosity data for Na2OeSiO2 melts. Pressure-dependent viscosity of melt of CaMgSi2O6 composition (NBO/Si ¼ 2) also has been reported (Scarfe et al., 1987; Taniguchi, 1992; Reid et al., 2003). Viscosity data to 13.5 GPa show an initial increase with a maximum melt viscosity at pressures between 4 and 8 GPa before a further pressure increase results in decreasing viscosity (Fig. 9.36). Such a maximum was not observed in the calculated viscosity change with pressure, vh/vP, of MgSiO3 melt in Fig. 9.34 (Lacks et al., 2007). Whether this difference between CaMgSi2O6 and MgSiO3 melt viscosity behavior is real or reflect perhaps a problem with the numerical modeling of vh/vP of MgSiO3 melt is difficult to ascertain. There appear, however, to be differences between Ca- and Mg-silicate melt viscous behavior at a high temperature (3000K) in the calculations by Zhang et al. (2010). At ambient pressure, there is no calculated melt viscosity difference between MgSiO3 and CaSiO3, whereas at 20 GPa, the melt viscosity increases systematically with increasing Ca/(Ca þ Mg) from that of MgSiO3 to CaSiO3 (Fig. 9.37) even though the Si and O diffusivity passes through a maximum near 5 GPa and the Eyring equation (Eq. (9.2)) would predict, therefore, a viscosity minimum. The Eyring equation was shown to work quite well when calculating melt viscosity from diffusivity of O or Si (Reid et al., 2003). However, Zhang et al. (2010) did not employ the Eyring equation to compute melt viscosity, but instead employed the Green-Kubo formulation, the physical meaning of which is not clear. Given the conclusion that metasilicate composition melts show increasing melt viscosity with increasing pressure (Figs. 9.35e9.36), the rate of viscosity increase in the lower pressure regimes (less than about 2 GPa) appears to increase from Na2SiO3 melts to MgSiO3 melts. In light of the observation that Q4 species are much more abundant in Na-silicate melts than in Mg-silicate melts (Mysen et al., 1982), one might expect that the abundance of Q4 structural units is an important factor affecting this different viscosity behavior of Na2SiO3 and MgSiO3 melts. There is, in fact a near linear relationship between the rate of increase expressed as percent change per GPa, and the mol fraction of Q4 species in the melts coupled with an increase in highly depolymerized species, including Q0 and Q1 (calculated with the algorithms reported by Mysen, 1987; see Fig. 9.38).16 The compressibility of Qn-species decreases as a systematic function of decreasing number of bridging oxygen, n, in the structure of these 16 The mol fraction of Q4 in these melts was calculated with the algorithms reported by Mysen (1987) for binary M nþ O  SiO2 glasses. The structural data of a glass likely is the structure at their glass transition temperatures, which 2=n are several hundred degrees lower than the temperatures of the melts. However, to as first approximation, the glass data are used absent detailed structural data on these melt compositions at the temperatures above their melting temperature (1392e1650 C, depending on composition; Kushiro, 1969; Kracek et al., 1939). Although, therefore, the quantitative detail might not be accurate, the algorithms provide a sense of how structures in these systems vary as a function of their composition.

648

Chapter 9 Transport properties

100

Na (N 2 O-S BO iO /Si 2 =0 .67

)

Melt viscosity, η, Pa s

2 iO ) -S i=1 2O /S Na BO (N

-SiO2 Na2O Si=1) / O (NB

10

1 2 iO ) -S i=2 2O /S Na BO N (

0

0.5

1.0 1.5 Pressure, GPa

2.0

2.5

FIGURE 9.35 Effect of pressure on the viscosity of binary metal oxide melts with different NBO/Si-values as indicated on individual curves. Modified from Kushiro (1976), Scarfe et al. (1987).

silicate species. Decreasing compressibility implies that the energy of SieO bonds in the structure are less sensitive to pressure. This effect, in turn, leads to the suggestion at as the Mg content of the metasilicate melts increases, their viscosity increases more rapidly.

9.4.1.5 Viscosity and volatiles in M nþ 2=n O  SiO 2 melts

Whereas there is a significant body of experimental and numerical modeling data on the effect of H2O and other volatiles on rheological behavior of aluminosilicate melts, which will be discussed in the nþ O next section (Section 9.4.2), such data are quite scarce for melts in compositionally simpler M2=n SiO2 melts. A few studies have been reported, however, on the effect of fluorine (Dingwell, 1989; Park et al., 2011), but less on rheological effects of H2O (Urbain, 1990). The activation energy of viscous flow of SiO2 melts between w2000 and w2200 C and H2O contents up to 1000 ppm decreases rapidly function of H2O content (Fig. 9.39; see also Urbain, 1990). In fact, only about 100 ppm H2O (w300 ppm by mole) will result in an activation energy drop of about 10%. This means that even with the simplest possible solution model of H2O in SiO2 melt where one H2O molecule forms two SieOH bonds by breaking an SeOeSi bridge (Wasserburg, 1957), this

9.4 Viscosity of model system silicate melts

FIGURE 9.36

1

Effect of pressure on the viscosity of CaMgSi2O6 melts at different temperatures as indicated on individual curves.

0˚C

Melt viscosity, log η (Pa s)

180

Data from Reid et al. (2003).

˚C

1900

0˚C

200

0.1

˚C

2100

˚C

2200

21

00

0.01

0

2

4

6

8 10 Pressure, GPa

˚C

22

00

CaMgSi2O6 melt

Melt viscosity, nomralized to ambient pressure value (=1.0)

649

12

˚C

14

16

1.5

FIGURE 9.37

1.4

Melt viscosity and mixed alkali effects of ternary CaOeMgOeSiO2 melts as a function of their Ca/(Ca þ Mg) ratio at low (0.7 MPa) and high (20 GPa) pressure.

1.3

Modified from Zhang et al. (2010).

a

20

1.2

GP

1.1

0.7 MPa 1.00

0.9

0.00 MgSiO3

0.20

0.40 0.60 Ca/(Ca+Mg)

0.80

1.00 CaSiO3

means that with about 300 ppm of the SieOeSi bridges being broken, this structural change results in nþ O  SiO2 , addithis 10% viscosity drop. Of course, in more complex melt systems such as in M2=n tional solution mechanisms of H2O, including formation of MeOH bonds, will participate in the H2O solution mechanism (Xue and Kanzaki, 2004; Cody et al., 2005). It follows, therefore, that the effect of

650

Chapter 9 Transport properties

FIGURE 9.38 300

Rate of melt viscosity change with pressure as a function of proportion of Q4-species in a magmatic liquids. (1987).

250 Rate of viscosity change, %/GPa

Calculations based on formulations by Mysen

200

150

100

50

0 0.00

0.05

0.10

0.15

0.20

Mol fraction of Q4 species

FIGURE 9.39

Modified from Urbain et al. (1990).

580 Activation energy of viscous flow, kJ/mol

Viscosity of SiO2eH2O melts as a function of H2O content.

560 SiO2-H2O melt 540

520

500 0

200

400 600 800 H2O content of melt, ppm

1000

0.25

9.4 Viscosity of model system silicate melts

651

nþ dissolved H2O in M2=n O  SiO2 melts will not have quite as a dramatic effect on their rheology

behavior as H2O dissolved in SiO2 melt. A few experiments also have been conducted to assess the influence of fluorine on rheology of nþ O  SiO2 melts such as CaMgSi2O6 and Na2OeCaOeSiO2 (Dingwell, 1989; Park et al., 2011). M2=n In both melt systems, increasingly fluorine concentration results in decreasing melt viscosity (Fig. 9.40). It is clear, however, that although significant, the effect of fluorine appears to be nowhere near as strong as that of H2O. This difference, at least in part, likely reflects the fact that solution of nþ O  SiO2 melts results in formation of MnþFn type complexes with lesser proportions fluorine in M2=n of SieF bonding (Mysen et al., 2004; Stebbins et al., 2002; Dalou and Mysen, 2015). Formation of an Mnþ Fn complex tends to cause polymerization of a silicate melt. It is not surprising, therefore, that the effect of fluorine on melt viscosity and activation energy of viscous flow is not as great as that which is expected of H2O. For example, in the F/(F þ O) range in Fig. 9.40, the melt viscosity decreases by about 50%, whereas the activation energy changes very little and remains near 330 kJ/mol (Dingwell, 1989). Similar effects have been reported for fluorine-bearing Na2OeCaOeSiO2 melts (Park et al., 2011). These features will be discussed in much greater details for aluminosilicate melts for which more experimentally determined rheological data of both H2O, F and mixed H2O þ F are available. nD OLAl O LSiO system 9.4.2 Viscosity of melts and glasses in the M2=n 2 3 2

About 95% of the components in magmatic liquids can be described with the endmember components nþ O  Al2 O3  SiO2 , where M nþ is total alkali metals plus alkaline earths (details of this system M2=n FIGURE 9.40

0.0

Viscosity (h) -temperature (1/T) relations for F-bearing CaMgSi2O6 melt as a function of increasing F/(F þ O) abundance ratio.

O) .04

6

F+

6

Modified after Dingwell (1989).

.08 O) =0

+O )=0 .

229

F/(

F+

F/(

F+

O)

-0.1

=0

F/(

-0.2

F/( F

Melt viscosity, log η (Pa s)

=0

CaMgSi2O6 melt

-0.3

5.6

5.8 6.0 6.2 Temperature, 104/T (K-1)

6.4

652

Chapter 9 Transport properties

compositional environment can be found in Mysen and Richet, 2019, Chapter 18). The rheological behavior of melts in this system is closely tied with the structural role of Al3þ, which for the most part occupies tetrahedral coordination (at least at pressures below 6e8 GPa; see, for example, Lee et al., 2012). However, because tetrahedrally coordinated Al3þ requires the presence of alkali metals or alkaline earths for electrical charge balance (Lee and Stebbins, 1999; Seifert et al., 1982), the effect of Al3þ on rheological properties, including the pressure-dependence of viscosity (Kushiro, 1981; Brearley et al., 1986; Suzuki et al., 2002), not only varies with Al/(Al þ Si), but also with the electronic properties of the charge-balancing cation. This is so even in the simplest of environments such as Na2OeAl2O3, CaOeAl2O3, and MgOeAl2O3, for example (Jahn, 2008; Wu et al., 2015a). In the extreme, such as viscous behavior of melts on the SiO2eAl2O3 join where there is no charge-balance of Al3þ, yet another range of rheological behavior governed by presence and abundance of Al2O3, has been observed (Kozakevitch, 1960). In depolymerized, peralkaline aluminosilicate melts, Al3þ exhibits a distinct preference for the most polymerized of available Qn-species (Merzbacher et al., 1990; Mysen et al., 2003), a feature that also may affect the rheological behavior of such melts (Scarfe et al., 1983; Dingwell, 1986; Webb et al., 2007). Of course, for peraluminous melts, yet another set of different structural roles of Al3þ appears likely, which, in turn, impacts of aluminosilicate melts in different ways (Riebling, 1966; Toplis et al., 1997; Falenty and Webb, 2010).

9.4.2.1 Viscous behavior of endmember components Before addressing the rheological behavior of aluminosilicate melts and glasses, it is useful first summarize the viscous behavior of endmember melt compositions such as Al2O3 and the various alkali nþ O. The rheology of molten SiO2 was discussed in the previous Section metals and alkaline earths, M2=n (9.4.1). The viscosity of Al2O3 melt as a function of temperature, in contrast to that of SiO2 melt, is nonArrhenian above its melting temperature (Fig. 9.41A; see also Urbain, 1985; Urbain et al., 1982; Langstaff et al., 2013). There is no evidence for a change in the temperature-dependent viscosity curvature across the melting point of Al2O3 (2071 C; see Aramaki and Roy, 1959; Aksay and Pask, 1975), which would be consistent with the structure of supercooled Al2O3 liquid being in structural continuum with the superliquidus structure. This non-Arrhenian rheological behavior of molten Al2O3 also is consistent with the observed temperature-dependent abundance variations of the structural entities in molten Al2O3 (Florian et al., 1995; Bessada et al., 1999; Winkler et al., 2004; Pfeiderer et al., 2006; Hoang et al., 2007). In contrast, the Arrhenian viscosity behavior of SiO2 melt and supercooled melt is consistent with little or no structural change of molten SiO2 with temperature (see further discussion of SiO2 structure in Chapter 5 and of SiO2 melt viscosity with links to SiO2 structure in Section (9.2.1)).17 The compositional extent of SiO2eAl2O3 melt viscosity is limited by an immiscibility gap that ranges from about 10% to 50% Al2O3 at temperatures near the liquids of Al2O3 (w2071 C). Of course, this immiscibility gap shrinks with increasing temperature, but under all circumstances reflects 17

The structure of SiO2 melt is unique in that both thermodynamic data and results of in situ, high-temperature structural determinations to temperatures across that of melting of the high-pressure polymorph, b-cristoballite, show no evidence of breakage and/or reformation of SieO bonds not already existing in crystalline SiO2 at the melting temperature (Mozzi and Warren, 1969; Richet and Bottinga, 1986; Bourova and Richet, 1998; Richet and Mysen, 1999).

9.4 Viscosity of model system silicate melts

653

-2.5 9.0

Melt viscosity, ln η, Pa s

-3.0

melting temperature (2320 K)

Melt viscosity, ln η, Pa s

Al2O3

-3.5

-4.0

A 3.00

3.50

4.00

4.50 4

5.0 -1

Temperature, 1/T•10 (K )

SiO2-Al2O3

7.0

5.0

3.0

1.0

-1.0

B

4.00

4.40 4.80 5.20 Temperature, 1/T•104 (K-1)

5.60

FIGURE 9.41 (A) Viscosity (h)-temperature (1/T) relations for Al2O3 melt from below to above its melting temperature. (B) Viscosity (h)-temperature (1/T) relations for SiO2eAl2O3 melt. Modified from Urbain (1985), Urbain et al. (1982).

the significantly different structure of molten SiO2 and molten Al2O3. These differences notwithstanding, the viscous behavior of SiO2eAl2O3 melts differs significantly from that of Al2O3 (Urbain et al., 1982). Whereas viscous flow of molten Al2O3 is non-Arrhenian (Fig. 9.41A), for melts with significant proportions of SiO2 added, the melts do show Arrhenian temperature behavior with both the melt viscosity and the activation energy of viscous flow increasing with increasing SiO2 content (Fig. 9.41B). It would appear that these differences reflect the silicate structure being the governing factor in controlling SiO2eAl2O3 viscosity because even for SiO2-rich SiO2eAl2O3 melts, there are multiple AlOn-polyhedra, the proportions of which remain temperature-dependent (Poe et al., 1992; Winkler et al., 2004). It is likely that this control by the SiO2 component is because the SieO bond energy is many times that of AleO bonds without charge balance of the Al3þ in SiO2eAl2O3 melts. nþ O endmembers18 might not be so relevant for our unWhereas melt viscosity data for the M2=n nþ O  Al2 O3 , on derstanding of the viscous behavior of magmatic liquids, viscosity of melts along M2=n

the other hand, can shed light on important aspects of how electrical charge-balance of tetrahedrally coordination Al3þ affects melt viscosity. It appears, however, that experimental viscosity data exist only for melts along the CaOeAl2O3 join (Kozakevich, 1960; Shalomov et al., 1962). Those and related experimental data have been fitted with two different thermodynamically based viscosity model (Decterov et al., 2007; Wu et al., 2015a) an example of which is shown in Fig. 9.42. The models do fit the experimental data well. This is helpful because it substantiates the reliability of estimates the 18

K, Na, Ca, and Mg are the principal network-modifying components in natural magmatic liquids.

654

Chapter 9 Transport properties

FIGURE 9.42

6

Viscosity of CaOeAl2O3 melt as a function of Al2O3/(Al2O3eCaO) ratio at different temperatures as indicated.

4 Melt viscosity, ln η, Pa s

Modified after Wu et al. (2015a).

2

0

150 0˚C 1600 ˚C 1700˚C 1800˚C

-2

-4

-8 0.0

0.2

0.4 0.6 0.8 Al2O3/(Al2O3+CaO) (mole fraction)

1.0

nþ viscosity of melts along other M2=n O  Al2 O3 joins for which experimental data seem lacking but

results of numerical modeling exist (Jahn, 2008; Wu et al., 2015b). The calculated melt viscosity along MgOeAl2O3, Na2OeAl2O3, and K2OeAl2O3 joins all exhibit maxima near the stoichiometry of the aluminate compositions, MgAl2O4, NaAlO2, and KAlO2 (Jahn, 2008; Wu et al., 2015b). This viscosity behavior would be consistent with all or most of the Al3þ occupying tetrahedral coordination with oxygen in the melts with those compositions. At higher Al2O3 concentrations, however, additional Al-bearing species might exist. Such a structural interpretation is, in fact consistent with results of structural simulations of melts along these joins (Poe et al., 1994; Cormier et al., 2003; Licheron et al., 2011).

9.4.2.2 Viscosity of aluminosilicate melts with composition and temperature Possibly contrasting roles of Al3þ in aluminosilicate melts, depending on alkalinity index,19 were originally assumed to exist when it was found that the viscosity of peralkaline aluminosilicate melts increased with increasing Al3þ concentration until reaching compositions. approximately at the meta-

nþ aluminosilicate join followed by a slow viscosity decrease as the SM2=n Al3þ is decreased further

(Kozakevich, 1954; Riebling, 1964, 1966; Taylor and Rindone, 1970; Stein and Spera, 1993; Le Losq and Neuville, 2013). Such melt viscosity data exhibit two characteristics. First, under isothermal conditions, the viscosity maximum is quite pronounced in alkali aluminosilicate systems (Riebling, 1966; Toplis et al., 1997; See Fig. 9.43A). Second, this viscosity maximum is much less evident in CaThe alkalinity index, SM nþ =Al3þ ; describes the extent to which Al3þ is charge-balanced with Mn þ cations in alumino2=n silicate melts [see also Chapter 5, section (5.2.2)]. 19

4

Viscosity, log η, Pa s

A

3

2

1

0

0

0.2

0.4 0.6 Al/(Al+Na)

Viscosity, log η, Pa s

1.0

0.8 B

0.8 Ca

M=

M=Mg

0.5

0.3

0.0 0.3

0.4

0.5 2Al/(2Al+M2+)

C

14

Viscosity, log η, Pa s

0.6

12

10

8

6

4 0.3

0.4

0.5 0.6 Na/(Na+Al)

0.7

FIGURE 9.43 Viscosity of ternary aluminosilicate melts as a function of metal to alumina proportions where thin, vertical line indicates meta-aluminosilicate composition. (A) As a function of Al/(Al þ Si) ratio in Na2OeAl2O3eSiO2 melts at high temperature. (B) As a function of 2Al/(2Al þ M2þ) for M ¼ Ca and Mg in the systems MOeAl2O3eSiO2 at high temperature. (C) As a function of Na/(Al þ Na) ratio in Na2OeAl2O3eSiO2 melts for a range of SiO2 concentrations as indicated at778 C. Modified from Riebling (1964), (1966), Webb et al. (2004).

656

Chapter 9 Transport properties

aluminosilicate melts and essentially absent in Mg-aluminosilicate melts (Fig. 9.43B; see also Riebling, 1964, 1966). Furthermore, the viscosity maximum appears slightly to the peraluminous side of the meta-aluminosilicate join. This maximum does, however, shift toward the meta-aluminosilicate join with decreasing temperature at least in the Na2OeAl2O3eSiO2 melt (Decterov et al., 2007; Webb et al., 2004). For example, at 778 C, Webb et al. (2004) reported that all the Na2OeAl2O3eSiO2 melt viscosity data fell on the same curve regardless of SiO2 concentration (Fig. 9.43C). They also concluded that by converting the bulk composition to NBO/T-values, the maximum corresponds to compositions with NBO/T ¼ 0 with increasing NBO/T with increasing Na/(Na þ Al). It has also been noted that when changing the composition of the haplogranite melt system, HPG8 (albite þ orthoclase þ quartz), by adding alkali metals or alkaline earths, the trend from Fig. 9.43C remains, but the effect of increasing the

nþ M2=n O nþ M2=n O þ Al2 O3

is to reduce the viscosity decrease the more

electronegative the M-cation (decreasing effect in the order K > Na > Ba > Sr > Ca > Mg; Webb et al., 2004; see also Fig. 9.44A). In fact, this viscosity effect remains at temperatures higher than that shown in Fig. 9.44A and at such higher temperatures also retain the cation hierarchy observed by Webb et al. (2004) including the same qualitative relationship between melt viscosity and the ionization potential of the metal (Fig. 9.44B and C). The structural role of Al3þ in aluminosilicate melts compositionally away from the metaaluminosilicate melts seems to have different influence on melt viscosity than in melts along metaaluminosilicate joins (Dingwell, 1986; Scarfe and Cronin, 1986; Toplis et al., 1997; Webb et al., 2007). For example, the viscosity difference between peralkaline aluminosilicate melts as a function of the ionization potential of the metal cation is considerably greater than for both meta- and peraluminosilicate melts (Webb et al., 2007). In an example using melt compositions in the Na2OeCaOeAl2O3eSiO2 system, at any temperature, the viscosity difference between Ca- and Naaluminosilicate melts differs by five to six orders of magnitude. The difference is much greater on the peralkaline side of the meta-aluminosilicate join (Fig. 9.45). This difference would suggest that there is greater variability in the proportion and number of coexisting silicate species in peralkaline than in meta- and per-aluminous melt compositions or at least the effect of the species is greater on the peralkaline side. That suggestion also is consistent with the considerably greater fragility of the peralkaline compared with the peraluminous melts (Fig. 9.45B). Greater fragility appears correlated positively with the entropy of mixing of silicate melts. The entropy of mixing increases with the larger the number of coexisting structural entities in melts (Toplis et al., 1997). Significant differences in the structural behavior of Al3þ in peralkaline aluminosilicate compared with meta-aluminous melts (Toplis et al., 1997) also was observed in a study of melt viscosity along the join Na2Si2O5eNa2(NaAl)2O5 (Dingwell, 1986). Here, the exchange between Si4þ and Al3þ in tetrahedral coordination is accomplished via the (NaAl)4þ charge-compensation. In the Na2Si2O5eNa2(NaAl)2O5 compositional environment, the initial Al/(Al þ Si) increase results in decreasing melt viscosity (Fig. 9.46). However, a minimum is reached at about 25 mol% of the Na2(NaAl)2O5 component followed by a viscosity increase. This trend does not seem particularly dependent on temperature as seen in only small changes in this behavior in the 1050e1350 C temperature interval in Fig. 9.46. This small temperature variation differs, for example, from that typically observed when the “mixed alkali effect” accounts for changes in melt viscosity across various mixed silicate joins such as discussed in Section (9.3.1.3). It seems unlikely, therefore, that the melt viscosity behavior of melts along the Na2Si2O5eNa2(NaAl)2O5 join could be rationalized as a mixed alkali

FIGURE 9.44 Viscosity of aluminosilicate melts as a function of composition. (A) As a function of Mnþ2/n/(Mnþ2/n þ Al) ratio in Mnþ2/n OeAl2O3eSiO2 melts where M equals alkaline earths and alkali metals as indicated on individual curves. (B) Along meta-aluminate-silica joins as a function of aluminate/silica abundance ratio. (C) As a function of electronic properties, Z/r2 of M-cation for meta-aluminosilicate melts at 1550 C and Al/(Al þ Si) ¼ 0.25. Modified from Urbain et al. (1982), Webb et al. (2004), Mysen and Richet (2019).

658

Chapter 9 Transport properties

42

A 14 a/

40

Pe ra l

(C

a+

lin

2A

l)=

12

(N

a/(

6)

10

a+

in

2A

l)=

ou

0.

s

us

0.4

)

lin

)=

38

um

a+

ino

l)=

ka

Al

+A

/(C

4)

lum

Na

Pe a/ ra (N l

e

0.

Pe ra

(N

Pe r a al

(C

ka

fragility index, m

Viscosity, log η, Pa s

(C

e

0.

B

6)

8

36 34

Per a

(Na

lum

/(Na

32

inou

=0.4 s )

+Al)

Pe

30

(Na/( ralkali n Na+ Al)= e 0.6)

28 6

26 700

750

800 850 900 Temperature, ˚C

950

0.0

0.2

0.4

0.6

0.8

1.0

Na/(Na+ Ca)

FIGURE 9.45 Viscosity of Na2OeCaOeAl2O3eSiO2 melts as a function of composition. (A) Temperature-dependent viscosity of peralkaline and peraluminous melts in Na2OeAl2O3eSiO2 and CaOeAl2O3eSiO2 systems as a function of temperature. (B) Fragility index, m (see Eq. (9.5)), in peralkaline and peraluminous Na2OeCaOeAl2O3eSiO2 melts as a function of their Na/(Na þ Ca) ratio. Data from Webb et al. (2007).

effect. Instead, it is more likely that this viscosity evolution reflects the compositionally dependent distribution of Al3þ between coexisting Qn-species in the melt as suggested by Dingwell (1986) and subsequently demonstrated by structural determination of peralkaline Na2OeAl2O3eSiO2 melts (Merzbacher et al., 1990; Mysen et al., 2003). The C-shaped form of the curves in Fig. 9.46 would suggest that at least two different structural mechanisms might compete to control melt viscosity. This seems reasonable because the disproportionation Eq. (9.9) is known to shift significantly to the right as the Al/(Al þ Si) of a peralkaline aluminosilicate melt increases (Mysen et al., 2003). This shift takes place because among the coexisting structural units, Al3þ exhibits a strong preference for Q4 units (Mysen et al., 2003) for structural reasons similar to those observed in crystalline aluminosilicates (Brown et al., 1969)20. The increased concentration of Q4 units thus created would tend increase melt viscosity. On the other hand, the Al/ (Al þ Si) of these Q4 units also increases, which diminishes the (Si,Al)eO bond strength. The evolution of activation energy of viscous flow, Eh, of melts along the Na2Si2O5eNa2(NaAl)2O5 join (Fig. 9.47) differs, for example, from the evolution of Eh with Al/ (Al þ Si) of melts along meta-aluminosilicate joins such as the SiO2eNaAlO2 join in Fig. 9.47 (Toplis et al., 1997). In this latter case, melt structural changes with Al/(Al þ Si) is minimal as there is simply a substitution of the Si4þ with charge balanced (NaAl)4þ. This substitution has negligible effect on the 20 The argument is that because the AleO bond distances exceeds that of SieO (by perhaps 5%), Al3þ would tend to favor structural units with the smallest inter-tetrahedral angle. Among the Qn-species in aluminosilicate melts, the Q4 species has the smallest intertetrahedral angle (Furukawa et al., 1981).

9.4 Viscosity of model system silicate melts

FIGURE 9.46

2.0

Viscosity of Na2Si2O5eNa2(NaAl)2O5 melts as a function of Na2(NaAl)2O5 concentration at temperatures indicated on individual curves.

1050˚C

Viscosity, log η, Pa s

659

1.5

Modified after Dingwell (1986).

1110˚C

1150˚C

1.0

1200˚C 1250˚C 1300˚C

0.5

1350˚C

0 Na2Si2O5

10

20 30 mol % Na2(NaAl)2O5

40 Na2(NaAl)2O5

FIGURE 9.47 Activation energy of viscous flow at high temperature of Na2Si2O5eNa2(NaAl)2O5 and SiO2eNaAlO2 melts as a function of their Al/ (Al þ Si).

Activation energy, kJ/mol

500

Na

400

AlO

2

Modified from Dingwell (1986), Toplis et al. -S iO 2

300

O5 aAl)2

(N Na2 i2O5Na S

200

2

0.00

0.10

0.20 0.30 Al/(Al+Si)

0.40

0.50

(1997).

660

Chapter 9 Transport properties

structure of both glasses and melts along the SiO2eNaAlO2 join (Taylor and Brown, 1979; Neuville and Mysen, 1996) as also seen in the near ideal mixing of SiO2 and NaAlO2 components together with other properties in melts along the SIO2eNaAlO2 join (Navrotsky et al., 1982, 1985; Ryerson, 1985). Therefore, only the weakening of the (Si,Al)eO bridging oxygen bonds with increasing Al/(Al þ Si) affects the viscous behavior. That change is reflected in the decrease in activation energy of viscous flow with increasing Al/(Al þ Si) (Fig. 9.47). Viscosity trends similar to those observed for melts along the SiO2eNaAlO2 joins also have been observed for a range of other metal cations serving to charge-balance Al3þ (Fig. 9.44B). In all of these melt systems, the temperature-dependent viscosity, and, therefore, activation energy of viscous flow, evolve as systematic functions of the electronic properties of the charge-balancing cation. The activation energy of viscous flow increases in the order Na > Ba > Sr > Mg for a given Al/(Al þ Si) as indicated by the increasing slopes of the log h versus 1/T data in Fig. 9.48. Such relationships hold for various Al/(Al þ Si) ratios but decreases, of course, as the Al/(Al þ Si) increases (Fig. 9.48; see also Urbain et al., 1982). It is also notable that the fragility of aluminosilicate melts depends significantly on the electronic properties of the metal cation and, therefore, likely depends on the structure of the metaaluminosilicate melts. For example, whereas melts along SiO2 - alkali meta-aluminosilicate joins are strong with little deviation from Arrhenian temperature behavior, melts along SiO2 - alkaline earth aluminosilicate joins are quite fragile with significant deviation from Arrhenian temperature behavior (Fig. 9.49; see also Toplis et al., 1997; Sipp et al., 2001). This difference, caused by changing chargebalance of tetrahedrally coordinated Al3þ, reflects the significantly different structure of the melts and glass depending on whether the charge-balancing cation is monovalent (alkali metal) or divalent FIGURE 9.48

9.0

Viscosity (h)-temperature (1/T) relations alkaline earth meta-aluminosilicate melts as a function of the electronic properties of the M-cation and Al/(Al þ Si) ratio.

8.0

M=Sr M=Ca

7.0

M=Mg

Melt viscosity, ln η, Pa s

Modified from Urbain et al. (1982).

M=Ba

6.0 5.0 4.0 3.0 M=Ba

2.0

M=Ca M=Mg

M=Sr

1.0 -0.0 -1.0 -2.0

4.0

4.0

5.5

5.0 4

-1

Temperature, 1/T•10 (K )

9.4 Viscosity of model system silicate melts

FIGURE 9.49

16.0

Comparison of viscosity (h)-temperature (1/T) relations of Na- and Ca-charge-balanced aluminosilicate melts compared with relationship for SiO2 melt. Notice how much more extensive deviations from linearity can be observed for the CaAl2Si2O8 composition melt compared with NaAlSi3O8 composition melt.

14.0 Melt viscosity, ln η, Pa s

661

12.0 10.0 8.0

Modified from Sipp et al. (2001).

6.0 4.0 2.0 0.0 3

6 9 12 Temperature, 1/T•104 (K-1)

15

(alkaline earth) (Seifert et al., 1982). In alkali aluminosilicate melts, there is a gradual exchange of Si4þ with Al3þ in similar structural positions with increasing Al/(Al þ Si), whereas in alkaline earth aluminosilicate melts different structural entities with constant Al/(Al þ Si) coexist. The abundance of those latter structural entities changes with changes in the bulk melt Al/(Al þ Si). However, the Al/ (Al þ Si) of these units does not change (Seifert et al., 1982). This latter feature leads to the enhanced fragility of alkaline earth aluminosilicate melts. Alternatively, as proposed by Lee and Stebbins (2000) from their MAS NMR studies of aluminosilicate glasses, the framework disorder in Na- and Ca-metaaluminosilicate melts and glasses differs because Naþ change-balances a single Al3þ, whereas Caw2þ charge-balances two tetrahedrally coordinated Al3þ cations.

9.4.2.3 Viscosity of aluminosilicate melts with pressure Current knowledge of the effect of pressure on rheology aluminosilicate melts has focused on how Al/ (Al þ Si) affects the pressure response of viscosity with the ionization potential of charge-balancing cations of Al3þ and bulk melt NBO/T as the additional variables (Kushiro, 1976, 1978, 1981; Brearley and Montana, 1989; Mori et al., 2000; Suzuki et al., 2002, 2005; Allwardt et al., 2007). The effects of Al/(Al þ Si) and ionization potential (Z/r2) of the charge-balancing cations have been examined to pressures of 2 GPa and less (Kushiro, 1976, 1978, 1981). For melts along the SiO2eNaAlO2 join, the melt viscosity decreases continuously with increasing pressure with perhaps a minor tendency for this pressure effect to increase with increasing Al/(Al þ Si) (Fig. 9.50). For melts along the SiO2eCaAl2O4 join, the melt viscosities are five to six orders smaller than for SiO2eNaAlO2 melts and, importantly, the pressure effect on the viscosity of these melts diminished with increasing Al/ (Al þ Si) so that for CaAl2Si2O8 and more aluminous melts, their viscosity actually increases with increasing pressure (Kushiro, 1981; see also Fig. 9.50). This different viscosity behavior was suggested

662

Chapter 9 Transport properties

FIGURE 9.50

(1981).

Al/(

9

Al+

Al/(

Si)=

Al+

7 Al/(Al+

Si)=0.2

5

5

Al/(Al+Si)=0.33

3

Al/(Al+Si)=0.50

0.67 Al/(Al+Si)=

0.25

Si)=

0.33

CaAl2O4-SiO2

Melt viscosity, ln η, Pa s

Modified from Kushiro (1976), (1978),

11

NaAlO2-SiO2

Pressure effects on melt viscosity in the systems NaAlO2eSiO2 and CaAl2O4eSiO2 melts as a function of their Al/(Al þ Si) abundance ratio as indicated on individual curves.

0 0

0.5

1.0 1.5 2.0 Pressure, GPa

2.5

(Kushiro, 1981) to reflect the effect of pressure on (Si,Al)eOe(Si,Al) angle compression. Such angle compression leads to a weakening of the (Si,Al)eO bonds. The compressibility of SiO2eNaAlO2 melts and, therefore, the compression of their (Si,Al)eOe(Si,Al) bonds, increases with increasing Al/ (Al þ Si), whereas (Si,Al)eOe(Si,Al) bonds in SiO2eCaAl2O4 melt decreases with increasing Al/ (Al þ Si) (see also Chapter 10). This difference is because the (Si,Al)eOe(Si,Al) bridging bonds in SiO2eNaAlO2 melts weaken with increasing Al/(Si þ Al) as a result of the lengthening of these bonds as the Al/(Al þ Si) of the 3-dimensional aluminosilicate structural units increases. For SiO2eCaAl2O4 melts, on the other hand, there is little or no variation in the Al/(Al þ Si) of the bridging oxygen bonds. Instead, the melts consist of coexisting structural entities of SiO2 and Al2Si2O8 type. Here, the Al2Si2O8 entities are quite incompressible whereas the SiO2 entities compress more easily. However, the abundance ratio of SiO2/Al2Si2O8 entities decreases with increasing Al/(Al þ Si) of these melts. Therefore, the SiO2eCaAl2O4 melts become more incompressible and, therefore, the pressure effect on their viscosity becomes less pronounced. Addition of a depolymerized component such as CaMgSi2O6 (NBO/Si ¼ 2) to SiO2eNaAlO2 melts, for example, also diminishes the negative pressure dependence of melt viscosity (Brearley et al., 1986; Suzuki et al., 2005) (Fig. 9.51). In the systems NaAlSi3O8eCaMgSi2O6 and NaAlSi2O6eCaMgSi2O6, the negative pressure effect on melt viscosity decreases with increasing CaMgSi2O6 component. With between 25 and 50 mol % CaMgSi2O6, the viscosity reaches a minimum between 2 and 5 GPa before it increases with further pressure increase (Suzuki et al., 2005). This minimum probably is reached because the compressibility of the aluminosilicate component decreases with increasing pressure and, finally reaches a pressure where the contribution of the depolymerized

Melt viscosity, log η, Pa s

9.4 Viscosity of model system silicate melts

663

4

FIGURE 9.51

3

Pressure effects on melt viscosity of melts along the NaAlSi2O6eCaMgSi2O6 joins as a function of varying NaAlSi2O6/CaMgSi2O6 abundance ratio.

Na

Al

Si

2

O

6

2

Modified from Kushiro (1976), Taniguchi (1992), Reid et al. (2003), Suzuki et al. (2005).

1

(Na •(C AlSi aM 2 O6 ) gS i2 O 75 6) 25

0

(NaAlS i •(CaM 2O6)50 gSi2O 6)

50

Si2O6 CaMg

-1

CaM

gSi2O

6

-2 0

2

4

6 8 Pressure, GPa

10

12

CaMgSi2O6 component to the pressure response takes over. At that point, the melt viscosity begins to increase as the pressure increases further. Most likely, there will be a viscosity maximum at pressures between 6 and 8 GPa above which Al-coordination changes begin take place (Allwardt et al., 2007) and the melt viscosity begins to decrease again (Fig. 9.51). The exact pressure where this coordination change begins, decreases the more electronegative the charge-balancing cation (Allwardt et al., 2007). It follows, therefore, that in aluminosilicate melts, the changeover of the pressure-dependent melt viscosity also will decrease the more electronegative the cation. There is a tendency to this effect for NaAlSi3O8 melt at pressures near 7e8 GPa (Mori et al., 2000). For the less compressible CaAl2Si2O8 melt, on the other hand, such a maximum appears to be reached between 3 and 4 GPa pressure. The pressure at which Al3þ coordination begins to occur also is lower for depolymerized than for fully polymerized aluminosilicate melts (Lee et al., 2012). Translated to natural magmatic liquids, these relationships between pressure and bulk melt composition would imply that the more mafic a magmatic liquid, the lower is the pressure above which its viscosity increases with additional pressure increase. Moreover, comparing, for example, alkali basalt with tholeiite, it would seem likely that the viscosity of alkali basalt would decrease with increasing pressure to greater pressures than that of tholeiite.

9.4.2.4 Viscosity and volatiles in aluminosilicate melts Examination of the behavior of volatiles in aluminosilicate melts primarily is driven by the desire to enhance our understanding of the role of volatiles in governing properties of felsic magmatic system because felsic magmatic systems are environment where volatiles play the most important role both as

664

Chapter 9 Transport properties

regards the composition evolution of the magma and in regard to the eruptive style, for example (Kushiro, 1972; Mysen and Boettcher, 1975; Vetere et al., 2010: Takeuchi, 2011; Moretti et al., 2018; Cassidy et al., 2018). The dominating volatiles in these environments are H2O and halogens (specifically fluorine and chlorine) (Dixon, 1997; Gaetani and Grove, 1998; Manning and Aranovich, 2014). In this section, we will, therefore, focus on the effect on H2O and F, and to a lesser extent, Cl, on the viscosity of aluminosilicate melts.

9.4.2.4.1 H2O and melt viscosity The effect of H2O, whether dissolved in complex natural or simpler synthetic silicate and aluminosilicate melts, is to lower the melt viscosity (Friedman et al., 1963; Shaw et al., 1963; Persikov et al., 1990; Dingwell et al., 1999 Whittington et al., 2000, 2009; Romano et al., 2001; Ardia et al., 2008; Robert et al., 2013; Di Genova et al., 2014). Typically, the melt viscosity decreases more rapidly during the first few thousand ppm H2O in solution before the rate of viscosity decrease slows as the H2O content is increased further (Fig. 9.52). Increasing H2O content generally also leads to decreased temperature-dependence of the melt viscosity (Fig. 9.53; see also Hess and Dingwell, 1996; Giordano et al., 2008; Whittington et al., 2009). An extrapolation of the viscosity data for hydrous NaAlSi3O8 melt based on the configurational entropy model of silicate melt viscosity (Richet, 1984; see also Section 9.3.4) results in the systematic evolution of the temperature-dependent viscosity of hydrous NaAlSi3O8 melt in Fig. 9.53B. This decreasing temperature-dependence with increasing H2O content implies a gradual decrease of the activation energy of viscous flow as a function of increasing H2O content. FIGURE 9.52

Modified from Dingwell et al. (1996).

14 Melt viscosity, log η, Pa s

Viscosity of hydrous haplogranite (HPG8) composition melt as a function of H2O content at different temperatures as indicated on individual curves.

16

12 Haplogranite melt (HPG8)-H2O 10 8 700˚C

6

800˚C 900˚C

4 2 0

0.5

1.0 1.5 2.0 2.5 H2O content in melt, wt%

3.0

9.4 Viscosity of model system silicate melts

665

FIGURE 9.53 Comparison of viscosity (h)-temperature (1/T) relations of hydrous melts along meta-aluminosilicate joins as a function of their H2O content. (A) Data for hydrous CaAl2Si2O8 melts. (B) Data for hydrous NaAlSi3O8 melts. Modified from Taniguchi (1992), Sipp et al. (2001), Giordano et al. (2008), Whittington et al. (2009).

Such a viscosity evolution would be consistent with a simple solution model for H2O in silicate melt of the type: H2 O ¼ 2OH þ O;

(9.11)

originally proposed by Wasserburg (1957) and subsequently refined in a large number of experimental studies (see Chapter 7, for review of those data). With Eq. (9.11), increasing H2O content would lead to a gradual increase of the NBO/T of the melt, which, in turn, qualitatively results in a gradual viscosity decrease such as discussed in Sections (9.3.1.1) and (9.3.1.2). The solubility mechanism of H2O in silicate, aluminosilicate, and magmatic melts is not, however, as simple as indicated by Eq. (9.11). The mechanism involves interaction between OH-groups and Si4þ, Al3þ, and alkali and alkaline earth cations where the effects of these individual mechanisms depend on melt composition and H2O content (Xue and Kanzaki, 2004; Malfait and Xue, 2010; Cody et al., 2005, 2020; Malfait, 2014; Le Losq et al., 2015). Such complex solution mechanisms might be behind the variable activation energy of viscous of for meta-aluminosilicate melts, M nþ Aln Si4n O8 (M ¼ Li, Na, K, Ca, Mg) as a function of their H2O content (e.g., Romano et al., 2001). Here, significant variability depending on both the H2O content and the electronic properties of the chargebalancing cations would suggest a much more complex relationship between H2O contents of aluminosilicate melts and their H2O content given the assumption that the activation energy of viscous flow reflects the sum of bond energies of from bonds that are disrupted and reformed during viscous flow (Fig. 9.54). One might surmise from the relations in Fig. 9.54 that a critical factor in how H2O affects viscous behavior is the electronic properties of the cations that serve to charge-balance Al3þ in tetrahedral coordination, both directly and more indirectly as a result of altering the AleO bond

666

Chapter 9 Transport properties

Activation energy of viscous flow of alkali and alkaline earth meta-aluminosilicate melts as a function of their H2O content for different metal cations as indicated on individual curves. Data from Romano et al. (2001).

Activation energy, kJ/mol

FIGURE 9.54

600

500

400

300

0.0

0.5

1.0 1.5 2.0 2.5 H2O content of melt, wt%

3.0

energies as the charge-balancing cations are varied. In detail, these structural processes involve how these relationships change as some of the charge-balancing cation may form bonding with OH-groups, thus changing the charge-balance of tetrahedrally coordinated Al3þ. Such solution processes also can include Alþ forming AleOH bonds, thus changing the role of charge-balancing cations to become network-modifier (Mysen and Virgo, 1986a, b). Water in aluminosilicate melts also affects the effect of pressure on melt viscosity (Whittington et al., 2009) because H2O in solution causes changes of the NBO/T of melts, which, in turn, affects the pressure-dependence of melt viscosity as discussed in Sections (9.3.1) and (9.3.2). In model aluminosilicate systems, most of the experimental data are from hydrous NaAlSi3O8 and the quartzalbite-orthoclase composition corresponding to the so-called “granite minimum”21 in the NaAlSi3O8eKAlSi3O8eSiO2 system (HPG8) (Kushiro, 1978; Dingwell, 1987; Dingwell et al., 1996, 1998; Romano et al., 2001; Whittington et al., 2004, 2009). Some experiments were conducted at ambient pressure to temperatures slightly above the glass transition from presynthesized hydrous glasses (Dingwell et al., 1996, 1998; Romano et al., 2001), whereas others were conducted at the actual pressure-temperature conditions of interest (Kushiro, 1978; Dingwell, 1987; Whittington et al., 2004, 2009). In an interesting comparison of the influence of alkali metals and H2O on HPG8 (quartz þ orthoclase þ albite mixture to form a haplogranite composition) viscosity at 700 C22 (Fig. 9.55), the alkali metals, on a molar basis, all have approximately the same effect on the melt viscosity (Dingwell et al., 1996). In contrast, H2O lowers the viscosity by an additional nearly two orders of 21 The “granite minimum” is the composition of melts in the system NaAlSi3O8 (Ab)eKAlSi3O6 (Or)eSiO2eH2O existing at the lowest temperature in this system (Tuttle and Bowen, 1958). 22 The glass transition temperature for this composition is less than 700 C.

9.4 Viscosity of model system silicate melts

FIGURE 9.55

16

Effect of excess oxide (alkali oxides and H2O) on haplogranite (HPG8) melt viscosity as a function of increased concentration of excess oxide and type of cation.

14 Melt viscosity, log η, Pa s

667

12

Modified from Dingwell et al. (1996).

10 Cs2O 8 K2O 6

H2O

Na2O

4 2 0.0

0.2 0.1 0.3 Excess oxide, mol fraction, XM2O

0.4

magnitude compared with the effect of the alkali metals. It is not clear why this is the case because H2O dissolved in silicate melts does not cause as extensive melt depolymerization as do the alkali metals (see comparison of data by Maekawa et al., 1991; Mysen and Cody, 2005; see also Chapter 15 in Mysen and Richet, 2019). However, this complexity goes to show that melt viscosity is controlled by factors more complex than simply melt polymerization, NBO/T. Interestingly, the relative change of NaAlSi3O8 melt viscosity by H2O at high pressure appears to be similar to that observed for hydrous melts at ambient pressure immediately above the glass transition temperature (compared the 0.1 MPa and 2.5 GPa curves in Fig. 9.56A). This leads to the suggestion that despite the structural changes of molten NaAlSi3O8 caused by pressure, dissolved H2O has a similar effect on rheological properties. It is not clear why this is the case in light of the observation that the temperature-dependent viscosity for different H2O contents differ significantly (Fig. 9.53B), and despite the fact that the pressure-dependent viscosity of hydrous metaaluminosilicate melts diminishes rapidly as H2O content of the melt increases (Fig. 9.56B; see also Dingwell, 1987; Whittington et al., 2009). These data make it abundantly clear that our understanding of the role of H2O in silicate melts and its effect on melt properties remain unclear and, furthermore, that whereas we have some understanding how the activation energy of viscous flow may relate to melt structure, the effect of melt structure with or without H2O on the absolute values of viscosity remains unresolved.

9.4.2.4.2 Halogens and melt viscosity Halogen concentrations in natural magmatic liquids generally are low except in a few magmatic environments where fluorine and chlorine contents of felsic and alkaline igneous rocks may reach several percent (Beollomo et al., 2007; Zhang et al., 2007; Aiuppa, 2009). In such environments,

668

Chapter 9 Transport properties

3.5

5 B

3.0 Melt viscosity, log η, Pa s

Melt viscosity, log η, Pa s

A

2.5

0.1 M

Pa

2.0

1.5

1.0 0

2.5 G

4

3.0

2.0

Pa

0.5

2.0 1.0 1.5 2.5 H2O content in melt, wt%

3.0

1.0

0

0.5

1.0 1.5 Pressure, GPa

2.0

2.5

FIGURE 9.56 Influence of H2O and pressure on viscosity of NaAlSi3O8 composition melt. (A) Effect of increasing H2O content at different pressures as indicated on individual curves. (B) Effect of increasing pressure for anhydrous and hydrous NaAlSi3O8 melt as indicated on individual curves. Modified from Whittington et al. (2009).

halogens, and in particular fluorine in melt solution, may exert significant effects on the magma properties as halogens in silicate melts causes major melt structural changes (Manning, 1981; Dingwell and Mysen, 1985; Dingwell and Hess, 1998; Dolejs and Baker, 2005; Filiberto and Treiman, 2009; Dalou et al., 2015). The viscosity of aluminosilicate melts is affected by fluorine in ways resembling that of H2O. In fact, at times, fluorine can have greater effect on viscosity than water in particular in the low concentration ranges (Fig. 9.57; see also Dingwell and Mysen, 1985; Dingwell and Hess, 1998; Alletti et al., 2007; Baasner et al., 2013). These differences are likely to result from the structure of fluorinebearing aluminosilicate melts depending on the fluorine concentration (Mysen et al., 2004). In a comparison of pressure effects on the viscosity of H2O- and F-bearing NaAlSi3O8 melts (Fig. 9.58) is notable that whereas the vh/vP of F-bearing melts seems quite similar to that of anhydrous NaAlSi3O8 melt, in the presence of H2O, the melt viscosity seems to approach a minimum value at pressures near 1.5 GPa. In light of the discussion earlier in this Chapter that the vh/vP decreases as a melt becomes depolymerized, it would seem that perhaps dissolved fluorine has a lesser effect on the NaAlSi3O8 melt structure compared with H2O. This idea, in turn, might reflect the experimental observation that fluorine can form NaF complexes as well as Na-aluminoflurosilicate complexes in aluminosilicate melts (Mysen et al., 2004). Such complex solution mechanisms can actually result in melt polymerization, and, therefore, could counter melt depolymerization resulting from the formation of SieF and AleF-containing aluminosilicate melts (see also Dalou et al., 2015). In mixed H2OeF melt systems, the effect of H2O and F together on the viscosity of peralkaline melts is greater than that which would be expected simply by mixing linearly the effect of H2O and F (Fig. 9.59; see also Dingwell and Mysen, 1985). This situation probably reflects interaction between

9.4 Viscosity of model system silicate melts

669

Melt viscosity, log η (Pa s)

FIGURE 9.57 Comparison on a molar basis of the influence of fluorine, H2O and Na2O on the viscosity of NaAlSi3O8 composition melt as a function of the abundance of the excess oxides.

NaAlSi3O8 5

Modified from Dingwell et al.(1987).

3 X=F X=OH

1

0.0

X=Na (NBO)

0.1

0.2

0.3

X/(X+O), (X = F, OH, NBO) FIGURE 9.58

Melt viscosity, log η, Pa s

4

Effect of addition of fluorine and H2O on the pressure dependence of NaAlSi3O8 melt viscosity. Vola

(Kus

Modified from Dingwell (1987).

tile-f

hiro,

ree

1978

)

3 NaAlSi3O3 melt

2

OH/( (Din

OH+

gwe

0.75

F/(F

O)=0

ll, 19

87)

.1

(Din

+O)=

gwe

1.5 Pressure, GPa

ll, 19

0.1

87)

2.25

the two volatiles in the melt solution perhaps resembling the interaction of H2O and F in aqueous solutions (e.g., Bulychev and Tokhadze, 2010). If so, there must be a significant temperature effect on this behavior as the extent of deviation from simple linear combination of fluorine and water diminishes rapidly with increasing temperature (Fig. 9.59).

670

Chapter 9 Transport properties

FIGURE 9.59

Modified from Dingwell and Mysen (1985).

1000˚C

3 Melt viscosity, log η, Pa s

Viscosity of NaAlSi3O8 composition melt at 0.75 GPa pressure in the presence of H2O and fluorine at X/(X þ O) ¼ 0.2 (X ¼ OH, F) as a function of OH/ (OH þ F) abundance ratio at different temperatures as indicated on individual curves.

NaAlSi3O3 melt 0.75 GPa X/(X+O)=0.2

1200˚C

2

1400˚C

1 0.00

0.25

0.5 OH/(OH+F)

0.75

1.00

Solution of chlorine in silicate melts can have a variety of effects on viscosity. For example, for peralkaline compositions, melt viscosity increases with increasing Cl concentration, whereas the opposite effect is observed for peraluminous melts (Alletti et al., 2007; Zimova and Webb, 2007; Baasner et al., 2013; see also Chapter 8, Fig. 8.43). These changes probably reflect changing forms of chloride complexing, perhaps driven by the changing structural role of Al3þ in peraluminous melts where charge-compensation of Al3þ, accomplished with alkali and alkaline earth cations, differs significantly from that in peralkaline aluminosilicates glasses and melts.

9.4.3 Viscosity of iron-bearing silicate melts Iron in magmatic liquids can cause changes of their rheological behavior in part because of the structural roles of Fe2þ and Fe3þ differ (e.g., Alberto et al., 1995; Johnson et al., 1999) and in part because variations of the redox ratio, Fe3þ/SFe, result in changes in extent of polymerization, NBO/T, of silicate melts (Dingwell and Virgo, 1987). As discussed in the aforementioned sections (Sections 9.3.1 and 9.3.2), the NBO/T is one of the important structural variables affecting melt viscosity. Variations in NBO/T of iron-bearing melts governed by changes in redox ratio of iron in its simplest form can be written as: Fe3þ þ 2O2 ¼ Fe2þ þ O2 .

(9.12)

where O2 represents nonbridging oxygen. As written, this means that reduction of Fe3þ to Fe2þ would involve an increase in NBO/T of the melt (Mysen, 2006). The viscosity of iron-bearing silicate melts, therefore, will depend not only on the proportion of iron oxides, but also on the redox ratio of iron (Shirashi et al., 1978; Mysen et al., 1985; Dingwell and Virgo, 1987, 1988; Osugi et al., 2013).

9.4 Viscosity of model system silicate melts

671

However, when iron oxide is completely reduced and existing as FeO only, the melt viscosity increases smoothly from FeO-rich toward SiO2 (Fig. 9.60A), a viscosity behavior that resembles perhaps of composition between CaOeSiO2 and MgOeSiO2 (see Section (9.3.1.1)). Analogies between the effects of FeO, MgO and BaO on viscosity have been observed in a number of experimental studies. For peralkaline melt systems in equilibrium with air where essentially all iron is in its ferric state, on the other hand, the viscosity-temperature relations are nearly Arrhenian such as in the Na2Si4O9eNa2(NaFe)2O9 melt system, for example (Fig. 9.60B). Increasing concentration of the Fecomponent leads to a rapid decrease in viscosity. This effect is much greater in this system than in the equivalent Na2Si4O9eNa2(NaAl)2O9 system (Fig. 9.47). For example, the minimum viscosity and activation energy of viscous flow seen in the analogous Al-system (Figs. 9.46 and 9.47) have not been observed in melts along the Na2Si4O9eNa2(NaFe)2O9 (Fig. 9.60; see also Shiraishi et al., 1978; Dingwell, 1986, 1991). The viscosity of ferrite melts with different alkali and alkaline earth metal cations offers insight into how possible charge-balance of completely oxidized Fe3þ might be stabilized in the melts and how different forms of charge balance of tetrahedrally coordinated Fe3þ can affect melt viscosity. In such systems, Mnþ FenO2n, the viscosity increases with increasing metal oxide content from pure nþ O (Fig. 9.61). Melts in the Na2OeFe2O3 system Fe2O3 toward alkali and alkaline earth oxide, M2=n . nþ exhibit a distinct maximum near the equimolar M2=n O Fe2 O3, and at a slightly higher value for the BaOeFe2O3 system. For other alkaline earths such as Ca2þ and Sr2þ the ferrite melt viscosity increases smoothly across the compositional space (Sumita et al., 1983). These variations are linked the relative affinity of the metal cations for Fe3þ in order to accomplish some form of chargecompensation perhaps resembling that which governs the charge-compensation of tetrahedrally coordinated Al3þ and as discussed in Chapter 5 (see also Navrotsky et al., 1982). One interpretation of the maxima for Naþ and Ba2þ systems in Fig. 9.61 is that most of the Naþ and a high fraction of Ba2þ associate with Fe3þ, but only portion of the Ca2þ and Sr2þ do. It follows, therefore, that the proportion of tetrahedral Fe3þ seems to pass through a clear maximum for Naþ and Ba2þ, but to increase almost continuously for Ca2þ and Sr2þ. Structural interpretation of Mo¨ssbauer spectra of alkali- and alkaline earth-bearing iron silicate melts also accords with this interpretation (Mysen et al., 1984). The viscosity of simple silicate and aluminosilicate melts with all its iron either as Fe2þ or as Fe3þ differs significantly from redox conditions where Fe2þ and Fe3þ coexist. The latter circumstances are the most relevant to natural magmatic liquids, the Fe3þ/SFe of which typically ranges from near 0.1 for Mid-Ocean Ridge Basalts (MORB) to perhaps near 1 for felsic magma in island arc settings (see, for example, a summary of redox data of iron in magmatic liquids by Carmichael and Ghiorso, 1990). For a broader range of alkali metals and alkaline earths, the Fe3þ/SFe increases as the metal cation(s) becomes more electropositive and as the total iron content of a system increases, consistent with other experimental data on redox relations of iron in silicate melts (Virgo et al., 1981; Mysen et al., 1984). This Fe3þ/SFe increase consistently leads to increased viscosity (Fig. 9.62; see also Dingwell, 1991; Dingwell and Virgo, 1987, 1988). The structural interpretation of the hyperfine parameters derived from the 57Fe resonant absorption Mo¨ssbauer spectroscopy of the samples, is that the Fe3þ remained in tetrahedral coordination in the melts for which viscosity data are summarized in Fig. 9.62 (Dingwell and Virgo, 1987, 1988). Consistent with the relative strength of association with Fe3þ, these effects are greater in alkali than in alkaline earth systems (Dingwell, 1991).

Viscosity, log η (Pa s)

-1.0

A

-1.2 SiO2-FeO melts -1.4

-1.6

-1.8 60 SiO2

70

80 mol %

100 FeO

90

Viscosity, log η (Pa s)

2.5

B

2.0

1.5

1.0 Na2Si2O9-Na2(NaFe)2O9 melt

0.5

Activation energy of viscous flow, kJ/mol

5 10 15 20 Fe2O3 content of melt, mol %

175 C 170 165 160 155 150 145

Na2Si2O9-Na2(NaFe)2O9 melt

140 5

10

15

20

Fe2O3 content of melt, mol %

FIGURE 9.60 Effects of iron on viscosity of silicate melts. (A) Viscosity along the FeOeSiO2 melt join as a function of composition. (B) Viscosity of melts along the Na2Si4O9eNa2(NaFe)2O9 join as a function of iron content. (C) Activation energy of viscous flow of melts along the Na2Si4O9eNa2(NaFe)2O9 join as a function of iron content. Modified from Shirashi et al. (1978), Dingwell and Virgo (1987).

9.5 Modeling melt viscosity

FIGURE 9.61

0.04 Viscosity, log η (Pa s)

673

Viscosity of melts along Mnþ2/nO-SiO2 melts for M ¼ Na and Ba, as a function of their composition.

0.03 M=Ba

Modified from Sumita et al. (1983).

M=Na

0.02

0.01

20 Mn+ 2/nO

60

40 mol %

80 Fe2O3

At high temperature, the influence of redox ratio on the viscosity of silicate melts is of the same magnitude as the intrinsic effects of iron, whether ferrous or ferric. For Ca ferrisilicates, the substitution of Fe3þ for Si4þ lowers the viscosity by less than one order of magnitude (Mysen et al., 1985). For Na-bearing systems, interesting comparisons have been made by Dingwell (1989) with aluminosilicates of the same stoichiometry (Figs. 9.44 and 9.63). In agreement with other comparison between properties of ferri- and aluminosilicate melts, the viscosity as a function of SiO2 content manifests itself in the systematically lower viscosities of ferrisilicates compared with the viscous behavior reported aluminosilicates with analogous stoichiometry. It would seem, therefore, that the stability of Fe3þ in silicate melts, governed by charge-balancing cations such as alkali metals and alkaline earths, resembles that experienced with Al3þ. However, the rate of change of melt viscosity with changing SiO2 content is greater in the Fe3þ-bearing melt than in the equivalent Al3þ-bearing melts (Figs. 9.44 and 9.63). This difference at least in part may be because of the greater Feþ-O distance than the AleO and SieO distance (Taylor and Brown, 1979; Henderson et al., 1984; Brese and O’Keefe, 1991) and in part because Fe3þ-bearing complexes might cluster in the structure (Hayashi et al., 1999). Both structural features could affect the melt viscosity of ferrisilicate melts differently that how the structural role of Al3þ may affect the viscosity of aluminosilicate melts.

9.5 Modeling melt viscosity A variety of models with which to calculate melt and magma viscosity has been proposed. These models can be divided into empirical modeling with chemical compositions as principal variable in addition to temperature (Giordano et al., 2003, 2004, 2008; Zhang et al., 2007), models relying on assumed melt species (Bottinga and Weill, 1972; Shaw, 1972; Goto et al., 1997), modeling with melt structural parameters (Mysen, 1995; Giordano and Russell, 2018), and thermodynamically-based

674

Chapter 9 Transport properties

FIGURE 9.62 (A) Viscosity of melts with the stoichiometry Mnþ n/2 FeSi2O6 as a function of the redox ratio of iron for different M-cations as indicated. (B) Comparison of the melt viscosity of sodium alumino- and ferri silicates along the meta-aluminous and meta-ferric joins SiO2-NaRO2 (R ¼ Al, Fe) at 1400 C. The numbers near the data points indicating the redox ratios of the samples. Modified from Dingwell (1991), Dingwell and Virgo (1987, 1988).

FIGURE 9.63 (A) Viscosity of melts along ferrisilicate joins, Mnþ FenO2neSiO2, as a function of Mnþ FenO2n/SiO2 abundance ratio and type of alkali and alkaline earth cations. Modified from Dingwell (1989).

9.5 Modeling melt viscosity

675

models (Adam and Gibbs, 1965; Richet, 1984; Toplis et al., 1997; Davis, 1999; Whittington et al., 2004, 2009; Le Losq et al., 2021). There are many variations to these themes, including hybrid models with which to handle H2O in melt solution, for example (Baker, 1996; Russell and Giordano, 2017). There also are models that expand on the formalism in the TVF expression (Fulcher, 1925). This equation, which is of the form: logh ¼ A þ

B ; T C

(9.13)

where A, B, and C are fitting parameters and T is temperature (Kelvin), is often used for empirical models where various melt compositional variables were fitted into this format (e.g., Hess and Dingwell, 1996; Misiti et al., 2011). Unfortunately, many of these proposed models incorporate an even larger number of fitting parameters than in the original TVF expression (Eq. (9.13)) so the general applicability becomes difficult and whose reliability is difficult to assess. In many, perhaps most cases, it is not clear whether the models to calculate melt and magma viscosity can be extended to compositions and conditions beyond those within which the experimental data on which the models are based. It is not worthwhile, therefore, to devote significant time and space to those. The exception to this statement can be found in the configurational entropy model originally proposed by Adam and Gibbs (1965) and translated to viscous behavior and configurational properties of silicate melts, including magmatic liquids, beginning with Richet et al. (1984) and expanded to include hydrous magmatic liquids by Whittington et al. (2009). The expression describing the viscosity of silicate melts in the configurational entropy model is (Richet et al., 1984): logh ¼ Ae þ

Be ; TSconfig

(9.14)

where h is viscosity (Pa s), T is temperature (Kelvin), Sconfig is configurational entropy and Ae and Be are constants. Among these two constants, Be is related to the free energy barriers that hinder cooperative rearrangements of the liquid. This variable is, therefore, significantly dependent on melt composition and structure. In this model, the three main variables affecting Be are the electronic properties of the alkali metals and alkaline earths and their proportions, the melt polymerization, NBO/T, and the Al/(Al þ Si) (Toplis, 1998). The configurational entropy, Sconfig, is related to the heat capacity change associated with the change from a glass to the liquid at the glass transition temperature, Cconfig , so that the configurational entropy at temperature, p T, is: S

config

ðTÞ ¼ S

config


 Tg þ

ZT Tg

Cpconfig T

; vT:

(9.15)

From this expression and using available thermodynamic data for anhydrous and hydrous granite melt compositions, a very good agreement between observed and calculated melt viscosities was observed relying on thermodynamic data from the literature (Richet, 1984; Whittington et al., 2004; Toplis et al., 1997; see also Fig. 9.64).

676

Chapter 9 Transport properties

Modeling viscosity of dry and hydrous aluminosilicate melts as indicated from the model of Whittington et al. (2009). Modified from Whittington et al. (2009).

Calculated melt viscosity, log ηcalc, Pa s

FIGURE 9.64

14 12 10 1

1:

8 6 4

granite NaAlSi3O8 melt melt Dry Hydrous

2 0 0

2 4 6 8 10 12 14 Observed melt viscosity, log ηobs, Pa s

9.6 Diffusion Diffusion data for magmatic liquids are needed to characterize compositional evolution and gradients in the magma in temperature-pressure-composition space. The first attempt to do so was that of Bowen (1921) who determined diffusion coefficients for melts in the system CaAl2Si2O8eNaAlSi3O8 e CaMgSi2O6. Since then, more recent experimental data for melts in this system with additional composition, temperature, and pressure relationships have been reported (Shimizu and Kushiro, 1984, 1991; Reid et al., 2001; Tinker et al., 2003). Results from molecular dynamics simulations in this and other chemical systems are also abundant. Diffusion in silicate melts is a process that differs from melt viscosity because whereas viscosity is a bulk melt property, diffusivity refers to the behavior of specific components in the melts. As a result of this difference, the diffusivity of major and trace elements in silicate melts tend to be Arrhenian, whereas, as discussed in the previous section, viscosity, more often than not, does not show Arrhenian behavior. In effect, whenever melt viscosity involves bond breakage that change in intensity as a function of temperature in the temperature region above the glass transition, the viscosity in nonArrhenian (e.g., Richet, 1984; Angell, 1985). Those differences between viscosity and diffusion notwithstanding, there also are links between viscosity and diffusivity. For a given magmatic liquid, for example, the activation energy of viscous flow tends to increase with increasing anionic radius and increasing electrical charge. That of diffusion follows the inverse trend (Jambon, 1982; Henderson et al., 1985; Ni et al., 2015).23 This is as would

23

For readers interested in detailed discussion of diffusion mechanisms, two good review papers on the subject are those of Watson (1994) and Chakraborty (1995).

9.6 Diffusion

677

expected from the Eyring equation (Eq. (9.3)), for example. Another link is found in the fact that diffusion and viscosity trends can be explained with the same melt structural features. Self-diffusivity of network-forming components (Si, Al, O) has been linked successfully to melt viscosity via the Eyring expression (Eq. (9.3)) (Shimizu and Kushiro, 1984; Baker, 1990) although there might be limitations as to the precision of such relationships. Baker (1990) observed, for example, that from the chemical diffusivity of Si4þ in felsic magmas in the dacite-rhyolite compositional range, the diffusivity from the melt viscosities tended to be underestimates compared with the actual diffusivity (Fig. 9.65). Although these differences have not been addressed in detail, it would seem that one uncertainty is the choice of jump distance in the Eyring equation and that this distance might depend on the degree of silicate melt polymerization. The jump distance could differ by more than 50% for different SiO2 concentrations as concluded, for example, by Noritake (2021) in a molecular dynamics examination of diffusivities in Na2OeSiO2 melts. This conclusion also is in accord with the experimental results in Fig. 9.65, which indicate greater deviations between observed and calculated diffusivity with increasing SiO2 content. This might lead to the suggestion, therefore, the jump distance during diffusion increases as a magmatic liquid becomes more felsic, a feature needing consideration when using diffusion of network-forming components (Si, Al, O), via the Eyring equation, to estimate melt viscosity.

9.6.1 Diffusion, composition, and temperature Mass transport by diffusion in magmatic liquids broadly can be subdivided into those cations that serve as network-modifiers (alkali metals and alkaline earths among the major element components as well as geochemically important trace elements) and network-formers (predominantly Si, Al, and O). The diffusivity of these two groups of elements can differ by as little as an order of magnitude to many

FIGURE 9.65 Calculating Si diffusion in rhyolite melts with different SiO2 contents from their viscosity using the Eyring equation (Eq. (9.3)).

2

Calculated Si diffusivity, log Dcalc, m /s

-12

-13 Si diffusion

%

t 5w

6

-14

%

t 0w

SiO

SiO

2

Modified from Baker (1990).

2

7

-15

-16 -16

1:1

t%

w 75

SiO

2

-15 -14 -13 2 Observed Si diffusivity, log Dobs, m /s

-12

678

Chapter 9 Transport properties

orders of magnitude depending on the magma composition, temperature, and pressure (Henderson et al., 1985; Baker, 1990; Bryce et al., 1999; Horbach et al., 2001; Noritake, 2021). Noritake (2021) in a molecular dynamics study of diffusion concluded, for example, that networkmodifying elements move through thermal hopping events, whereas network-formers transfer via breakage of (Si,Al)eO bonds in the structure. Of course, even thermal hopping requires bond breakage although in this latter case, the bond energy is much less, on the order of 50e200 kJ/mol, compared with SieO bonds with bond energy in the 500e600 kJ/mol range. This difference is illustrated by the activation energy of Na þ diffusion in Na2OeSiO2 melts, near 90 kJ/mol (Horbach et al., 2001), which is in this same range, whereas the activation energy of Si4þ diffusion in SiO2 melt is on the order of 500 kJ/mol (Mikkelsen, 1984). This latter activation energy is not greatly different from the SieO bond energy (Smyth and Bish, 1988) and within about 10%e20% of the activation energy of viscous flow of SiO2 (Urbain et al., 1982). It has been suggested that oxygen transfer is via oxygen exchange between bridging and nonbridging oxygen in the melt structure (Noritake, 2021). Such an exchange mechanism would be in accord with the interpretation of in situ, high-temperature NMR spectra of K2Si4O9 melt by Farnan and Stebbins (1990). One could, however, argue that an oxygen exchange also would involve breakage and reformation of (Si,Al)eO bonds. It would not be surprising, therefore, that oxygen and silicon diffusivities in silicate melts do not differ by much compared with the difference between the diffusivity of network-formers and network-modifying cations (Fig. 9.66; see also Baker, 1990; Huang et al., 2000; Zhang et al., 2010). In fact, even in a simple-system such as MgOeAl2O3, results from molecular dynamics simulation show that the O and Al diffusivity do not differ by much at the MgAl2O4 composition. However, as the Mg/Al increases to values greater than 1, the diffusivity difference increases, and that of Al3þ gets closer to the values for Mg2þ (Fig. 9.66B; see also Jahn, 2008). This

-9

A

B 3•10

Mg

Na

Diffusivity, m /s

2

Diffusivity, log D, m /s

-10

-9

2

-11 -12 -13

2.5•10

2•10

-9

-9

O

-14

1.5•10

-9

Al

Si

-15 5

6 7 4 -1 Temperature. 10 /T (K )

8

0 Al2O3

20

40

60 mol %

80

100 MgO

FIGURE 9.66 (A) Diffusivity versus temperature relationships for network-forming Si4þ and network-modifying Na2þ in rhyolitic magma compositions. (B) Diffusivity versus composition of MgOeAl2O3 melt to illustrate the large diffusivity difference between typical network-forming Al3þ and O2 and network-modifying Mg2þ. Modified from Smith (1974), Baker (1990), Jahn (2008).

9.6 Diffusion

679

change may lead to the suggestion that the excess Al3þ over that charge-balanced in tetrahedral coordination resides in oxygen polyhedra not greatly different from those where Mg2þ is located in the structure. Diffusive motion not only includes surmounting bond energy contributions, but also a contribution from the hindrance energy that is required to move through a silicate network. Intuitively, it might be proposed that the more polymerized an aluminosilicate network, the greater is this contribution. This suggestion is in accord with observations (Hofmann and Magaritz, 1977; Jambon, 1982; Shimizu and Kushiro, 1991; Mungall et al., 1999; Horbach et al., 2001; Noritake, 2021). Those energy effects are, however, relatively small. Furthermore, this behavior is not always what has been observed. For example, comparing Naþ and Cs2þ diffusion in magmatic liquids ranging from basalt with NBO/T slightly less than 1 and more felsic magma up to and including rhyolite with NBO/T near 0, the DCs decreases as the magma becomes more felsic (NBO/T decreases), whereas for DNa the opposite effects can be seen (Zhang et al., 2010; see also Fig.9.67). Diffusivity differences such as those illustrated in Fig. 9.67 document why multiple electronic cation properties and melt structural variables play roles in defining elemental diffusion in magmatic liquids. It is useful, therefore, to attempt to isolate these effects further by first separating the effect of melt structure and composition from properties of the elements themselves.

9.6.1.1 Major element self-diffusion, melt composition, and melt structure It should not come as a surprise that the same compositional variables that relate the main features of aluminosilicate melt structure to melt viscosity also can have a profound effect on diffusivity. The influence of melt structure on Al3þ diffusion was discussed earlier (Jahn, 2008; see also Fig. 9.66B). -20 A

-24

Na diffusion da

2

de

-28

sit

da

ci

e

te

-32 rh

yo

lit

-36

e

ci

te

e sit lt de sa an ba

an

Diffusivity, ln DNa, m /s

lt

sa

2

-21

Cs diffusion

ba

Diffusivity, ln DCs, m /s

B

-22

rhy

olit

e

-23 -24 -25

-40 5

6

7 8 9 10 4 -1 Temperature. 10 /T (K )

11

-26

6

7 8 4 -1 Temperature. 10 /T (K )

9

FIGURE 9.67 (A) Diffusivity versus temperature relationships for Cs2þ in magma compositions ranging from rhyolite to basalt. (B) Diffusivity versus temperature relationships for Na2þ in magma compositions ranging from rhyolite to basalt. For both network-modifying cations, the diffusivity increases the more mafic the melt, but the diffusivity of the larger Cs2þ cation is considerably slower than for the smaller Na2þ. Modified from Zhang et al. (2010).

680

Chapter 9 Transport properties

Melt structural control on Si4þ diffusion have been examined in numerical simulations (molecular dynamics) for melts on the Na2OeSiO2 joins (Horbach et al., 2001; Noritake, 2021) and on chemically more complex aluminosilicate melts (Li and Garofalini, 2004; Jahn, 2008). In such studies, a distinct relationship between Si4þ and O2 diffusion can be seen as a function of Na2O/SiO2 ratio and, therefore, NBO/Si of the melts (Fig. 9.68). The diffusion coefficients of both silicon and oxygen, DSi and DO, decrease as the network polymerization increases although DSi seems slightly smaller than DO for any composition and temperature (Fig. 9.68A and B). The temperature-dependence of the same diffusion coefficients and, therefore, the activation energy of viscous flow, also becomes greater as the NBO/Si of these melts increases (Noritake, 2021). Both diffusivity and activation energy of diffusive flow of O2 and Si4þ differ significantly from the diffusion behavior of Naþ (DNa), which does not seem significantly dependent on melt composition (polymerization; see Fig. 9.68C). However, the activation energy of diffusive flow of Naþ increases the more polymerized melt. Similar relationships were reported by Horbach et al. (2001) for diffusion behavior in the same system. This difference between diffusivity and activation energy may be related to the increased hindrance energy as the NBO/Si of a melt decreases. Analogous NBO/T-dependent diffusion behavior was reported by Henderson et al. (1985) for natural magmatic liquids. For a number of cations ranging from highly electropositive Cs to considerably more electronegative cations such as Fe and Eu, their diffusion coefficients always decrease the more depolymerized (greater NBO/T-values) the melts (Fig. 9.69). More complex behavior has been reported for activation energy of viscous flow where alkali metals exhibit greater activation energy the more mafic the magma (basalt vs. andesite and rhyolite), whereas for more highly charged cations (di- and trivalent cations), the activation energy is greater in felsic magmatic liquids (Henderson et al., 1985). Complex relations between NBO/T and cation diffusivity reflects the fact the network polymerization, NBO/T, is far from the only factor affecting this transport property. As also noted for melt viscosity above (Section 9.3.2), the Al/(Al þ Si) ratio and the proportion of network-modifying cations, predominantly Mþ and M2þ, the proportion and types of Mnþ cation serving to charge-balance tetrahedrally coordinated Al3þ, and the proportion of Mnþ cations relative to the proportion of Al3þ, all affect melt structure and can, therefore, influence the diffusivity of both network-forming and network-modifying cations. The latter effect was already noted in the simple-system, MgOeAl2O3 (Fig. 9.66). It has also been reported for Si4þ diffusivity in granite/dacite melts as a function of their (K2O þ Na2O þ CaO)/Al2O3 ratio (Baker, 1990) with minimum DSi-values near the meta-aluminous composition [(Na2O þ K2O þ CaO)/Al2O3 ¼ 1]. This behavior resembles, of course, that of viscosity, which exhibits a maximum value near the same composition (Fig. 9.43). The impact of bond strength on cation diffusivity is demonstrated for melt compositions along meta-aluminosilicate joins such as SiO2eNaAlO2 and SiO2eCaAl2O4 and even more so across from Na-aluminosilicate to Ca-aluminosilicate joins (Zhang et al., 2010). Whereas the changes with Al/ (Al þ Si) along individual meta-aluminosilicate joins to a considerable degree reflect just the decreasing (Si,Al)eO bond strength with increasing Al/(Al þ Si), and the effect is small, the effects of crossing from Na-to Ca-aluminosilicate (e.g., from NaAlSi3O8 to CaAl2Si2O8) on cation diffusion is much greater because of the different nature of the AleO bonds charge-balanced with Na þ as compared with Ca2þ (Zhang et al., 2010).24 These effects get even more complex in the absence of 24

These features were discussed in more detail in Sections (9.3.1.1) and (9.3.1.2) above. For more detail on structure of such melt compositions, the reader is referred to Chapter 5.

-7

2

Diffusivity, log DO, m /s

A -8

-9

NBO/Si=2

NBO/Si=1

-10 O diffusion

NBO/Si=0.67 NBO/Si=0.5

-11 3.0

3.5 4.0 4.5 5.0 4 -1 Temperature. 10 /T (K )

5.5

-7

2

Diffusivity, log DSi, m /s

B -8

-9

NBO/Si=2

NBO/Si=1

-10 Si diffusion -11 3.0

NBO/Si=0.67 NBO/Si=0.5

3.5 4.0 4.5 5.0 4 -1 Temperature. 10 /T (K )

5.5

2

Diffusivity, log DNa, m /s

-7

C

-8

NBO/Si=2 NBO/Si=1 NBO/Si=0.67 NBO/Si=0.5

-9

-10 Na diffusion -11 3.0

3.5 4.5 5.0 4.0 4 -1 Temperature. 10 /T (K )

5.5

FIGURE 9.68 Diffusivity versus temperature relationships for network-forming oxygen and silicon (A and B) and networkmodifying sodium (C) in Na2OeSiO2 melt as a function of the NBO/Si of the melts. Whereas Naþ diffusion seems relatively insensitive to melt polymerization, the network-forming Si4þ and O2 show rapidly decreasing diffusivity and increasing activation energy of diffusion with increasingly polymerized melts. Modified from Noritake (2021).

682

Chapter 9 Transport properties

FIGURE 9.69

-10

Cation diffusion in natural magma as a function of their degree of silicate polymerization, NBO/T.

Co Sr

2

Diffusivity, log D, m /s

Modified after Henderson et al. (1985).

Fe

-11

Cs

-12

-13 0

0.2

0.6 0.4 0.8 Melt polymerization, NBO/T

1.0

charge-balance of Al3þ such as observed, for example, in the temperature-dependence of Si, Al, O self-diffusion constants for melts along the SiO2eAl2O3 join (Pfeiderer et al., 2006). In this case, we have the unusual effect of the activation energy of diffusion being significantly temperature-dependent, a feature rarely seen among more typical melts compositionally relevant to magmatic liquids. This behavior also differs from that of melt viscosity along this join, which display Arrhenian temperaturedependence (Langstaff et al., 2013; see also Fig. 9.41). Most likely, this difference reflects significant changes of SiO2eAl2O3 melt structure with temperature (Florian et al., 1995) affect viscosity and Si, Al, O self-diffusion differently although exactly what these differences might be is not clear.

9.6.1.2 Trace element diffusion and cation properties Electronic properties of the cations affect their diffusivity (Jambon, 1982; Lowry et al., 1982; Baker, 1990; Behrens and Hahn, 2009; Ni, 2012) as does the structure of melts through which the diffusion takes place (Lowry et al., 1982; Henderson et al., 1985; see also Zhang et al., 2010, for comprehensive review). Properties of cations such as their ionic radius and electrical charge both affect the diffusivity in systematic ways. For example, in qualitative terms, the diffusivity decreases with increasing atomic number (and, therefore, cation radius), whereas their activation energies of diffusion tend to increase in the same direction (Behrens and Hahn, 2009; see also Fig. 9.70). In more detail, it appears that cations such as the alkali metals tend to show an increased activation energy of diffusion with increasing ionic radius, independently of magma composition, whereas trace element activation energy of diffusive flow of transition metals exhibit the opposite trend (Lowry et al., 1982; Jambon, 1982; see also Fig. 9.71). There is, however, a clear positive correlation between activation energy and increased ionic radius at constant electric charge and with increased electric charge at constant ionic radius

9.6 Diffusion

A

-11 -12 -13 -14 -15

Rb Sr Ba Cr Ni Zn Y La Nd Sm Eu Gd Yb Sn Zr Nb Hf

Trace elements

B

400 Activation energy, kJ/mol

2

Diffusivity, log D, m /s

-10

683

300

200

100

0

Rb Sr Ba Cr Ni Zn Y La Nd Sm Eu Gd Yb Sn Zr Nb Hf

Trace elements

FIGURE 9.70 Diffusivity (A) and activation energy of diffusive flow (B) of trace elements shown with increasing electronic charge and ionization potential to the right in anhydrous trachyte composition melt. Modified from Behrens and Hahn (2009).

FIGURE 9.71 (A) Activation energy of trace and major element cations in basalt and andesite composition melt as a function of their ionic radius. (B) Diffusivity in basalt composition melt of M-cations with different formal electrical charge as indicated as a function of their ionic radius. Modified from Lowry et al. (1982), Henderson et al. (1985).

684

Chapter 9 Transport properties

(Jambon, 1982; see also Fig. 9.71A). It appears, though, as if the influence of cation properties on activation energy diminishes with increased electrical charge. However, the diffusion itself seems quite dependent on the formal charge (Henderson et al., 1985; see also Fig. 9.71B).

9.6.2 Diffusion, composition, and pressure Most magmatic processes take place at pressure above ambient. Characterization of the effect of pressure on diffusion, be it self-diffusion and chemical diffusion, is important, therefore, for the same reason that many other magma properties need to be described as a function of pressure. While the influence of temperature on diffusion commonly can be described in terms of Arrhenian behavior, pressure effects often are characterized in terms of an activation volume, DVa, that typically is in the 105 to 106 m3/mol range (Watson, 1981; see also Ni et al., 2015, for review). The dependence of diffusion coefficients, D, on temperature and pressure then takes the form (Ni et al., 2015):   Ea þ PDVa D ¼ Do exp  ; (9.16) RT where D is the diffusion coefficient, Ea is activation energy, DVa is activation volume, P is pressure, and T is temperature. The R is, of course, the gas constant. Current information of pressure effects on diffusion has been reported from results of numerical simulation and experimental determination. In terms of total amount of information as well as the nature of how to establish what governs pressure effects, information from results of numerical simulation is more common (Angell et al., 1982; Bryce et al., 1997; Lacks et al., 2007; De Koker, 2010; Adjaoud et al., 2011; Karki et al., 2011, 2018; Verma et al., 2012; Dufils et al., 2018). Although the quantitative reliability of results from numerical simulations can be difficult to establish, in some cases, the results have been benchmarked against experimental data (Spera et al., 2011; Verma et al., 2012; Dufils et al., 2018), which enhances the reliability. This prevalence of numerical simulation information might be because experimental determination of pressure effects on diffusive flow is both technically challenging and time-consuming. Those challenges notwithstanding, experimental data also are available for a number of compositions (Watson, 1979, 1981; Shimizu and Kushiro, 1991; Tinker et al., 2003). Moreover, trace element diffusion data with element concentration at trace levels can only be obtained with experiments (Watson, 1981; Baker, 1990; Mungall and Dingwell, 1997; Nakamura and Kushiro, 1998).

9.6.2.1 Major element self-diffusion, cation properties, temperature, and pressure In this section, the self-diffusion data of major elements in various melt compositions at high pressure will be discussed first. This is so because that information often can be linked directly to melt structure and can, therefore, be employed to advance a better understanding of what melt structural variables govern diffusion on silicate melts and magma. With that understanding in hand, the presentation of trace element diffusion as a function of pressure will understood better. The latter group of data will, therefore, be discussed after the presentation of major element self-diffusion. Among existing high-pressure data on diffusion of major elements in silicate melts, a series of measurements at 0.1 MPa and 1 GPa for major elements in compositions ranging from nominally granite to dacite have been reported (Baker, 1990; see Fig. 9.72). In those experiments, melt

9.6 Diffusion

685

FIGURE 9.72 Diffusivity versus temperature relationships for network-forming aluminum and silicon (A and B) and networkmodifying Fe (C), Mg (D), and Ca (E) as at ambient pressure and at 1 GPa. Modified from Baker (1990).

compositions were defined by their SiO2 content (65, 70, and 75 wt% SiO2). However, it is difficult to extract a complete bulk composition from the data provided, so the relationships in Fig. 9.72 cannot be discussed in terms of melt structural features although there very likely is a positive correlation between the SiO2 concentrations and the NBO/Si of the magmatic liquid, for example.25 These concerns notwithstanding, it appears difficult to distinguish the diffusivities of Si4þ and Al3þ between the three SiO2 contents in the data summarized in Fig. 9.72. From the average of the three compositions, the activation energy from the temperature-dependent total diffusion coefficient (incorporating diffusion data for all elements in Fig. 9.72) changes from 356 to 244 kJ/mol between 0.1 MPa and 1 GPa and the diffusivity decreases by up to an order of magnitude, but also depends on temperature (Fig. 9.72). 25

The structure of magmatic liquids can be estimated from their bulk chemical composition to pressures of a few GPa provided that there are insignificant changes in the oxygen coordination surrounding the major cations. Instructions as to how to accomplish this can be found in Mysen (1987) and Mysen and Richet (2019), Chapter 18. Some such information can also be found in Chapter 5.

686

Chapter 9 Transport properties

In compositionally simple systems designed to characterize how individual components and, therefore, structural parameters, affect pressure-dependent melt diffusion, most results are from numerical simulations for effects of NBO/Si (Zhang et al., 2010) and Al/(Al þ Si) (Bryce et al., 1999) together with experimental data for specific metal oxide silicate compositions such as CaMgSi2O6 and Na2Si4O9 to high pressure (Shimizu and Kushiro, 1984, 1991; Rubie et al., 1993; Poe et al., 1997; Reid et al., 2001). In depolymerized melts such as those of CaMgSi2O6 composition (NBO/Si ¼ 2), the diffusivity increases with increasing pressure whether for network-modifiers (Ca2þ, Mg2þ) or network-formers (O2, Si4þ) (Shimizu and Kushiro, 1984, 1991; see Fig. 9.73A). The diffusivity difference between network-formers and network-modifiers is about three orders of magnitude with the Ca2þ and Mg2þ diffusion faster than those of O2 and Si4þ. This difference does not seem to vary much in the 0.1 MPae2 GPa pressure range shown in Fig. 9.73A. An extension of the pressure-dependent diffusivity in CaMgSi2O6 melt to higher pressure (Reid et al., 2001) indicates that both oxygen and silicon diffusion reaches a minimum at pressures near 10 GPa before a further increase results in reversed pressure dependence (Fig. 9.73B). This reversal, which also implies change from negative to positive activation volume, might be a reflection of possible coordination changes in the CaMgSiO6 melt structure. By using, for example, structural information from other silicate melts to similar and higher pressures (Lee et al., 2012), one might suggest that both the networkformers (Si4þ) and network-modifiers (Ca2þ, Mg2þ) undergo coordination changes in this pressure environment. That suggestion is consistent with results of numerical simulation of coordination changes of cations in CaMgSi2O6 and MgSiO3 melts (Shimoda et al., 2005; Ghosh et al., 2014). There likely also would be SieOeSi angle compression as the pressure is increased. Such angle compression leads to weakening of the SieO bonds (Ross and Meagher, 1984). Such structural changes would result in increased diffusion rates of network-formers such as Si4þ so that the diffusivity difference between network-formers and network-modifiers would decrease. Additional results of molecular dynamics calculation of Mg, Ca, Si, and O diffusion in CaMgSi2O6 melt to pressures beyond those of the core-mantle boundary have been reported.26 Those results suggest a turnover from positive to negative pressure dependence of network-forming ions (Si and O) at pressures near 20 GPa. The DSi and DO both decrease throughout the pressure range from about 20 to 160 GPa at 3000e5000K temperature (Fig. 9.74; see also Verma et al., 2012). The diffusivity turnover near 20 GPa in the calculations by Verma et al. (2012) is in qualitative accord with the experimental results of Reid et al. (2001) although the latter authors reported the minimum to be near 10 and not 20 GPa. The simulation results from Verma et al. (2012), calculated at 2500K in this lower pressure range, also fall within a factor or 2 or 3 of the experimental results of Reid et al. (2001). In light of this relatively good agreement with the experimental data in the pressure regime were simulation and experimental data overlap, it would seem reasonable to conclude that the higher-pressure data probably are fairly accurate.27 26

The pressure at the core-mantle boundary is about 136 GPa. In these calculations (Verma et al., 2012), the characteristic lengths, l, as employed in the StokeseEinstein equation (Einstein, 1905) converted to the jump distance which might be used in the Eyring equation (Eq. (9.3)), for example, ranges be˚ at ambient pressure, but decreases by at least 50% at pressures above 40 GPa, results resembling those tween 1.2 and 2 A reported for molten Mg2SiO4 to 32 GPa from molecular dynamics calculations by Adjaoud et al. (2011). The difference between the distances of Ca and Mg on the one hand and Si and O on the other also becomes much smaller with increasing ˚ and 40 GPa compared with 0.8 A ˚ at ambient pressure). It is not possible to establish, however, whether pressure (about 0.4A this change reflects different structural environments of diffusion or whether the change is an artifact of the calculations. 27

9.6 Diffusion

687

FIGURE 9.73 Pressure dependence of cation diffusion in CaMgSi2O6 melt. (A) Data comparison of network-forming Si and O with network-modifying Ca and Mg at pressures below 2 GPa. (B) Data to near 16 GPa showing the change in diffusivity of network-forming components (Si and O) near 10 GPa. Modified from Shimizu and Kushiro (1984), (1991), Reid et al. (2001).

A

2

-8

6000K

-9

10

-8

B

6000K

10

-9

K

-10

-7

00

10

Si diffusion

10

30

10

Diffusivity, DO, m /s

2

10

-7

0K 300

Diffusivity, DSi, m /s

10

O diffusion

-10

0

20

40

60 80 100 120 140 160 Pressure, GPa

10

0

20

40

60 80 100 120 140 160 Pressure, GPa

FIGURE 9.74 Calculated pressure dependence of Si (A) and O (B) diffusion in CaMgSi2O6 melt to pressures near those of the core-mantle boundary at two different temperatures as indicated. Modified from Verma et al. (2012).

688

Chapter 9 Transport properties

Even though there is a significant amount of information on diffusive properties of CaMgSi2O6 melt, this information does not contain all that is needed to characterize relationships between diffusion, melt structure, and pressure. That information does not, for example, include effects of the NBO/Si on the pressure-dependent diffusivity behavior. Some such data may be extracted from the results of the molecular dynamics simulations of melts in the MgOeSiO2 system as a function of MgO/SiO2 ratio and pressure (Lacks et al., 2007). From these latter results, oxygen diffusion increases with pressures to about 8e15 GPa before additional pressure causes decreasing DO (Fig. 9.75). The pressure of this maximum increases as the melts become increasingly polymerized (their NBO/Si decreases). Interestingly, the difference between pressure dependence of DO, DSi, and DMg, for lowNBO/Si and high-NBO/Si melts diminishes rapidly with increasing pressure so that while the calculated difference at ambient pressure is about 1.5 orders of magnitude between DSi,O and DMg, at 15 GPa, this difference is only a factor of 2 (Fig. 9.75B and C). This difference decreases further with additional pressure increase (Lacks et al., 2007). As also noted for diffusion in other melt compositions, these changes likely reflect the changes in oxygen coordination of Si4þ and Mg2þ with increasing pressure (Gaudio et al., 2008; Ghosh et al., 2014). From the Ghosh et al. (2014) and Stixrude and Karki (2005) calculations of MgSiO3 melt (NBO/Si ¼ 2) structure indicates more than 50% of the Si4þ with oxygen coordination numbers exceeding 4 at 40 GPa, for example. Another interesting feature of the pressure-dependent DMg and DCa as a function of Mg/(Mg þ Ca) of CaOeMgOeSiO2 melts is the rapidly diminishing difference between DMg and DCa with increasing pressure (Lacks et al., 2007; Zhang et al., 2010). An implication of this behavior is that once in the deep upper mantle and beyond, it is likely that diffusivities of network-modifying cations such as alkali metals and alkaline earth might be quite similar, and the difference between those and those of Si and O (and perhaps Al) also becomes quite small. The diffusion of oxygen with increasing pressure in aluminosilicate melts can exhibit a complex evolution, at least to 15 GPa (Poe et al., 1997; Bryce et al., 1997). Whereas Na2Si4O9 melt (NBO/ Si ¼ 0.5) shows continuously increasing DO in this pressure range, by adding NaAlO2 to reach melt NBO/T ¼ 0.25, the oxygen diffusion slows down, and the activation energy increases. However, the vDo/vP changes from positive to negative near 8 GPa (Fig. 9.76). With the addition of even more NaAlO2 to form NaAlSi3O8 melt (NBO/T ¼ 0), this trend evolves further. The vDo/vP increases even more, the activation energy below about 5 GPa increases further, and the maximum Do-value is at lower pressure (w5 GPa) (Fig. 9.76). It was proposed (Poe et al., 1997) that the changes at pressures below the oxygen diffusion turnover reflect the increased aluminosilicate melt polymerization as NaAlO2 was added, whereas the vDo/vP turnover resulted from Al3þ shifting to higher coordination states. Those conclusions are in semiquantitative accord with the results of numerical calculations on diffusivity and oxygen coordination of Al3þ in NaAlSi2O6 as well as other SiO2eNAlO2 melts (Angell et al., 1982; Bryce et al., 1997, 1999; see also Fig. 9.77). There are only minor changes of diffusion constants with pressure as the Al/(Al þ Si) of the melts is increased. In contrast, the networkmodifying Naþ exhibits a continuous diffusion decrease with increasing pressure. The Naþ diffusivity does, therefore, approach the diffusion values for oxygen, aluminum and silicon the higher the pressure (Fig. 9.77). This behavior seems analogous to the diffusion in MgOeSiO2 and CaOe MgOeSiO2 melts (Lacks et al., 2007; Zhang et al., 2010, Fig. 9.75), and probably reflects the coordination changes of Si4þ and Al3þ in the 10e20 GPa pressure range (e.g., Lee et al., 2012).

9.6 Diffusion

60

FIGURE 9.75

A

Calculated pressure-dependent diffusion in MgOeSiO2 composition melts as a function of their NBO/Si ratio. (A) Oxygen diffusion. (B) Silicon diffusion. (D) Magnesium diffusion.

NBO/Si=4

2

Diffusivity, DO•10 m m /s

50 40

10

MgO-SiO2 melts O diffusion

NBO/Si=2

30

Data from Lacks et al. (2007).

20

NBO/Si=1 NBO/Si=0.2

10 NBO/Si=0

0 0

10

20

30

40

50

60

Pressure, GPa 60

B

2

Diffusivity, DSi•10 m m /s

50 40

10

NBO/Si=4

30

MgO-SiO2 melts Si diffusion

NBO/Si=2

20

NBO/Si=1 NBO/Si=0.2

10

NBO/Si=0

0 0

160

10

20

30 Pressure, GPa

40

50

60

C

NBO/Si=4

140

2

Diffusivity, DMg•10 m m /s

689

10

120 100 80 60

MgO-SiO2 melts Mg diffusion

NBO/Si=2

NBO/Si=1

40

NBO/Si=0.2

20 0 0

10

20

30 Pressure, GPa

40

50

60

690

Chapter 9 Transport properties

FIGURE 9.76 Pressure-dependent diffusion in Na2OeAl2O3eSiO2 composition melts illustrating the effect of Al content and melt polymerization on the pressure at which the oxygen diffusivity changes from an increase to a de crease with increasing pressure.

-9

Na2Si4O9

O diffusion

2

Diffusivity, DO, m /s

10

Modified from Poe et al. (1997).

10

Na3AlSi7O17

-10

NaAlSi3O8

10

FIGURE 9.77

-11

2

4

6

8 10 12 Pressure, GPa

14

16

-17

Pressure-dependent diffusion in NaAlSi2O6 composition melts showing the diffusivity maxima for network-forming components (Si, Al, O) as compared with continuously decreasing diffusivity of network-modifying cation, Naþ. Bryce et al. (1997).

-19 2

Diffusivity, ln D, m /s

Modified from results of calculations by

-18

-20 +

Na

3+

-21

Al

2-

O 4+ Si

NaAlSi2O6 melt

-22

-23

-24

0

10

40 20 30 Pressure, GPa

50

60

9.6 Diffusion

691

9.6.2.2 Trace element diffusion, cation properties, temperature, and pressure Most trace elements are network-modifiers. One might expect, therefore, that their diffusion coefficients decreased with increasing pressure for reasons qualitatively similar to the behavior of major network-modifying components such as Na, Ca, and Mg, discussed in the previous section. This feature was reported early on by Watson (1981) in an experimental study that included Csþ diffusion in a CaOeNa2OeAl2O3eSiO2 melt [NBO/T ¼ 0.81, Al/(Al þ Si) ¼ 0.17]. He found the DCs to decrease monotonously between ambient pressure and 1.8 GPa (Fig. 9.78). The negative activation volume derived from this relationship changed only by 30% between 1100 and 1300 C (volume values near 10 cm3/mol) while the activation energies changed by less than 10% across the 0.1 MPae1.8 GPa pressure range (activation energy near 160 kJ/mol). This behavior differed significantly from that of the major element component, Ca2þ. The DCa and the activation volume of Ca2þ diffusion, although negatively pressure-dependent, decreased rapidly with increasing temperature (DVa ¼ 2.24 to 11.9 cm3/mol between 1400 and 1100 C and activation energy, Ea, increasing from 110 to 215 kJ/ mol between 0.1 MPa and 2.0 GPa). One has to assume that this difference between the diffusivity of Cs2þ and Ca2þ reflect different preferences for specific oxygen to form CseO and CaeO bonds in the melts (steric hindrance; see Kohn and Schofield, 1994)28 and perhaps also competing distribution of Al3þ among the Qn-species in the melt governed by the different ionization potentials of Ca2þ and Csþ (see, for example, Merzbacher and White, 1991; Mysen et al., 1981, 2003). The diffusivity of other trace elements in silicates melts might also be better understood in light of the observations in the early Watson (1981) experiments. It is clear, for example, that in the comprehensive study by Behrens and Hahn (2009) at 0.5 GPa who used trachyte and phonolite melts (Fig. 9.79) that the diffusion constant for any trace element at fixed temperature and pressure decreases with increasing ionic radius and increasing electrical charge. It is not surprising, though, that regardless of trace element of interest, the diffusivity in the phonolite melt in the Behrens and Hahn (2009) study (NBO/T ¼ 1.28) is more than an order of magnitude faster than in the trachyte melt (NBO/T ¼ 0.10) (Fig. 9.79). The fact that the proportion of Al3þ charge balanced by alkali metals is about 80% in phonolite magma, whereas in trachyte melt it is about 40%, could also contribute to the different diffusion constants for the elements in the two melts. There exist also a few data points for Th and U diffusion in haplogranite melt at ambient pressure and at 1 GPa (Mungall and Dingwell, 1997). Although this study was aimed primarily on the effects of dissolved H2O on actinide diffusion (see next section), a few data were recorded with dry melts. From that information, the activation energies of diffusion in haplogranite melt, HPG8, of Th and U at both ambient pressure and 1 GPa are the same (364e368 kJ/mol, with uncertainties near  40 kJ/mol). However, the activation volumes might have differed slightly with DVa(Th) ¼ 5.7 cm3/mol and DVa(U) ¼ 4.2 cm3/mol. More detailed data exist for wide range of other trace elements (alkali metals, alkaline earths, rare earth elements, and actinides) in both CaMgSi2O6 (NBO/Si ¼ 2) and NaAlSi2O6 (NBO/T ¼ 0) melt as a function of pressure (Nakamura and Kushiro, 1998; see also Fig. 9.80A, B). For rare earth element diffusion, for example, there is a general and positive correlation between diffusion coefficients for both melt compositions and the ionic radius of the rare earth elements. However, whereas for NaAlSi2O6 melt the DREE increases rapidly with increasing pressure and the dependence of ionic 28

In general, the more electronegative a cation, the stronger is its preference for forming bonding to nonbridging oxygen in the least polymerized Qn-species available (Mysen, 2007).

692

Chapter 9 Transport properties

-9.5

A

B 1400˚C

Diffusivity, log DCa, m /s

1300

2

2

Diffusivity, log DCs, m /s

-9.0

-9.5 130

0˚C

-10.0

1200

˚C

-10.5

110

0˚C

˚C

-10.0

120

0˚C

-10.5

11

00

-11.0

Ca diffusion

Cs diffusion

˚C

-11.0 0

0.5

1.0 1.5 Pressure, GPa

2.0

0

1.0 2.0 Pressure, GPa

3.0

FIGURE 9.78 Pressure-induced relationships for Cs (A) and Ca (B) diffusion in Na2OeCaOeAl2O3eSiO2 melts as a function of different temperatures as indicated on individual curves. Modified from Watson (1981).

FIGURE 9.79

Modified from Behrens and Hahn (2009).

-10

2

Diffusivity, log D, m /s

Diffusivity of trace elements shown with increasing electronic charge and ionization potential to the right in anhydrous trachyte and phonolite composition melts.

-11

Phonolite melt (NBO/T=1.28)

-12 Trachyte melt (NBO/T=0.1)

-13 -14 -15

Rb Sr Ba Cr Ni Zn Y La Nd Sm Eu Gd Yb Sn Zr Nb Hf

Trace elements radius also increases with increasing pressure, the exact opposite relationship was reported for DREE in CaMgSi2O6 composition melt (Fig. 9.80B). Moreover, the pressure-dependent diffusion coefficient for NaAlSi2O6 (jadeite) composition melt was clearly positive for cations with electrical charge greater than 1þ, whereas for alkali metals with a charge of 1þ, a pressure dependence was barely discernible (Fig. 9.80C).

2.5

a

Diffusivity, D•10 m /s

2.0 GP

12

2

2

a

1.5 GP 1

1.25 GPa 0.75 GPa Sm Nd

0.5 Er Lu Yb

Dy

1.0

Pr

La

Ce

Gd

A Ionic radius, Å

1.1

3

GP

a

10

2

Diffusivity, D•10 m /s

1.0

2

1.25 G

Pa

Sm Nd Gd

Ce Er

1

La

Pr

Yb Dy

Lu

B 1.0

Ionic radius, Å

1.1

Rb Sr -11

Ba

2

Diffusivity, D, m /s

10

-12

10

La Sm Dy Lu U Nb Th Zr -13

C

10

0.5

1.0 1.5 Pressure,GPa

2.0

FIGURE 9.80 Trace element diffusion in NaAlSi2O6 and CaMgSi2O6 composition melts as a function of pressure (A) Diffusivity of rare earth elements in NaAlSi2O6 composition melts as a function of their ionic radius at different pressures as indicated on individual curves. (B) Diffusivity of rare earth elements in CaMgSi2O6 composition melts as a function of their ionic radius at different pressures as indicated on individual curves. (C) Diffusivity of trace elements separated by their formal electrical charge in NaAlSi2O6 composition melts as a function of pressure. Modified from Nakamura and Kushiro (1998).

694

Chapter 9 Transport properties

In summary, it appears clear from existing diffusion data that the general trends to be expected for network-modifying trace element qualitatively is that which would be expected for any networkmodifying cation in a silicate melt be it in a compositionally simple silicate melt or compositionally more complex magmatic liquid. Pressure effects tend to vary with melt composition and ionization potential as well. These factors need to be taken into consideration, therefore, when considering calculation based on trace element diffusion in magmatic liquids in the Earth’s interior. Regardless of details, the diffusivity always increases the more mafic a magma. Moreover, increasing pressure enhances the diffusivity in felsic magma, whereas for basaltic liquids, for example, increasing pressure results in decreasing diffusivity. However, there are systematic changes as a function of pressure, composition of the melt, and the ionization potential of the trace element.

9.6.3 Volatiles and diffusion Volatiles such as H2O, CO2, and halogens (primarily F and Cl) dissolved in magmatic liquids affect the melt structure (see Chapters 7 and 8). As a result, there will be an effect on the diffusivity of other components caused by volatiles in melt solution. This statement applies whether these are major, minor, or trace elements components (Watson, 1981; Baker and Watson, 1988; Mungall et al., 1999; Baker and Balcone-Boissard, 2009; Behrens and Hahn, 2009; Gonzales-Garcia et al., 2017; Holycross and Watson, 2018). Not only are volatiles in magma important, the diffusivity of the volatiles, themselves, in magmatic liquids also is important because this behavior affects volcanic processes such as bubble growth and style of eruption, for example (Sparks et al., 1994; Stevenson and Wilson, 1997; Gardner et al., 2000; Lensky et al., 2004; Zhang et al., 2007; Moretti et al., 2018). In this section, these issues will be addressed beginning with the influence of volatiles on the diffusivity of other components.

9.6.3.1 Diffusion and volatiles in magmatic liquids and The main volatiles of interest are H2O, CO2, and F. There also exist a few data point on the effect of Cl. Among those volatiles, the role of H2O is of particular interest in felsic magmatic systems because felsic magmatism tends to involve the most H2O (Kushiro, 1972; Mandeville et al., 1996; Bouhifd et al., 2006).

9.6.3.1.1 Effect of H2O As discussed in previous sections, the extent of silicate melt polymerization has profound impact on diffusion (see Section (9.5.1)). Solution of H2O in silicate melts results in silicate depolymerization (increased NBO/T; see Chapter 7). It follows, therefore, that solution of H2O in melts likely would result in increased diffusivity. This is exactly what has been observed. For example, in an early experimental study of diffusion of Ca2þ, Na2þ, and Csþ in an obsidian composition melt with NBO/ Tw0 and Al/(Al þ Si) ¼ 0.17 (typical for felsic magma such as this), at fixed temperature and pressure, increased H2O results in increased diffusion coefficients (Watson, 1981; see also Fig. 9.81A). As is often the case for other properties of hydrous silicate melts, the extent of H2O-influence decreases as the amount of H2O in solution increases. Not only does the diffusion coefficient increase with increasing H2O concentration in magmatic liquids, the activation energy decreases, and apparently more so for diffusion of alkali metals than for alkaline earths, for example (Fig. 9.81B and C).

-9

A

2

Diffusivity, log D, m /s

Na

-11 Ca Cs

-13

-15 Obsidian melt

-17 1 2 3 4 5 6 H2O concentration in melt, wt%

B

2

Diffusivity, log DCs, m /s

-12 -13 -14 An

-15

hyd

rou

-16

s(

0.1

MP

a)

Obsidian melt Cs diffusion 9

8

10 4

Temperature, 10 /T (K-1)

C

2

Diffusivity, log DCa, m /s

-11

-12

-13 Anh

ydro

-14

us (

0.1

MPa

)

Obsidian melt Ca diffusion

-15 8

9 10 4 Temperature, 10 /T (K-1)

FIGURE 9.81 Diffusion in obsidian melt. (A) Na, Ca, and Cs diffusion as a function of H2O content of melt. (B) Cs diffusion as a function of temperature and H2O content in obsidian composition melt. (C) Ca diffusion as a function of temperature in obsidian melt at different H2O concentrations as indicated on individual curves. Modified from Watson (1981).

696

Chapter 9 Transport properties

In experimental diffusion studies covering a wider range of elements including alkali metals, alkaline earths, HFSE’s, transition metals and rare earth elements (Koepke and Behrens, 2001; Behrens and Hahn, 2009; Gonzales-Garcia et al., 2017), qualitatively the same relationships exist as those reported for Naþ, Csþ, and Ca2þ by Watson (1981) summarized in Fig. 9.81 (Figs. 9.82e9.84). For example, the relationship between major element diffusion and magma composition expressed, for example, in terms of SiO2 content, remains whether or not the H2O is dissolved in the magmatic liquid (Gonzales-Garcia et al., 2017; see also Fig. 9.82A and B). It is striking, though, that the DSi and DMg both are more sensitive to the SiO2 content of the magma, and, therefore, melt polymerization, NBO/T, with H2O in solution compared with anhydrous conditions. Furthermore, as would perhaps be expected, the diffusivity for both cations, as well as diffusivity of other major elements (see GonzalesGarcia et al., 2017), increase the greater the H2O content of the magma. This observation is the same as that found for the diffusion of any other element, whether network-former or network-modifier, major or trace element (see, for example, Watson, 1979, 1981; Baker and Bossany, 1994; Mungall et al., 1999; Koepke and Behrens, 2001; Holycross and Watson, 2018). For any and all network-modifying cations and regardless of magma type, the diffusivity of these elements always increases with increasing H2O content of the magma (Behrens and Hahn, 2009, Fig. 9.83). Moreover, the hierarchy of diffusion constants decreasing as a magma becomes more felsic, and, therefore more polymerized, is retained in the hydrous systems (Fig. 9.83). As is evident from the relationship between log D and 1/T (e.g., Fig. 9.82), the activation energy of diffusion also becomes smaller with increasing H2O content of the magma regardless of whether major or trace elements are considered (Fig. 9.83). It also is clear from the trace element diffusion data of Behrens and Hahn (2009), for example, that the extent to which diffusion coefficients vary with H2O -11.4

-11.4 B 2

Diffusivity of Mg, log DMg, m /s

2

Diffusivity of Si, log DSi, m /s

A

-11.8

-12.2

-12.6

-13.0 58

Anhydrous

60 62 64 66 68 SiO2 concentration in melt, wt%

70

-11.8

-12.2

Anhydrous

-12.6

-13.0 58

60 62 64 66 68 SiO2 concentration in melt, wt%

70

FIGURE 9.82 Interdiffusion of Si (A) and Mg (B) between shoshonite and rhyolite magmatic liquids at 1200 C as a function of the SiO2 content of the melts for anhydrous magma and for magma with 1 and 2 wt% H2O as indicated on individual curves. Modified from Gonzales-Garcia et al. (2017).

9.6 Diffusion

A

2

Diffusivity, log D, m /s

-10 -11 -12 -13 -14 -15

Anh

ydr

ous

Trachyte melt

Rb Sr Ba Cr Ni Zn Y La Nd Sm Eu Gd Yb Sn Zr Nb Hf

B

2

Diffusivity, log D, m /s

-10

-11 Phonolite

Trac

hyte

Rhy

olite

-13

-14

Rb Sr Ba Cr Ni Zn Y La Nd Sm Eu Gd Yb Sn Zr Nb Hf

Trace elements C

Activation energy, kJ/mol

400

300

200

ite ol us on ro Ph hyd n A ite O ol H2 on % Ph wt 75 1. Trachyte s Anhydrou

100

0

Rb Sr Ba Cr Ni Zn Y La Nd Sm Eu Gd Yb Sn Zr Nb Hf

Trace elements

FIGURE 9.83 (A) Diffusivity of trace elements shown with increasing electronic charge and ionization potential to the right in anhydrous and hydrous (1.13 wt% H2O) trachyte composition melts. (B) Diffusivity of trace elements shown with increasing electronic charge and ionization potential to the right in hydrous 1.7e2.0 wt% H2O phonolite, trachyte, and rhyolite composition melt. (C) Activation energy of diffusion of trace elements shown with increasing electronic charge and ionization potential to the right in anhydrous and hydrous phonolite and trachyte magma with H2O content shown on individual curves. Modified from Behrens and Hahn (2009).

Trace elements

-12

697

698

Chapter 9 Transport properties

FIGURE 9.84

Modified from Koepke and Behrens (2001).

-10 Andesite melt (4-5 wt% H2O, 1400˚C)

2

Diffusivity of trace elements (low field strength, transition metals, rare earth elements, and high-field strength trace elements) in hydrous (w5 wt% H2O) andesite composition melt at 0.5 GPA pressure.

Diffusivity, log D, m /s

-9.0

-11.0

-12

-13 0

0.2

0.6 0.4 0.8 1.0 -2 Ionic field stength, Å

1.2

1.4

content depends on the bulk composition of the magmatic liquid and on the electronic nature of the diffusing element. These latter features are well illustrated, for example, for hydrous andesite and granitoid melts (Figs. 9.82e9.84) (Watson, 1981; Mungall et al., 1999; Koepke and Behrens, 2001; Behrens and Hahn, 2009).

9.6.3.1.2 Effect of halogens Halogens such as chlorine and fluorine can be important in magmatic processes, in particular in subduction zone settings (e.g., Scambelluri and Philippot, 2001; Beollomo et al., 2007; Zhang et al., 2007; Barnes et al., 2018). An understanding of their influence on properties of magmatic liquids is, therefore, important. Furthermore, as halogen solubility in silicate melts can be considerable even at low pressure (e.g., Dolejs and Baker, 2005), effects of halogens on magma properties, in contrast to H2O and CO2, can be considerable even at shallow depths and surface conditions where CO2 and H2O effects would be small because of their low solubility in magmatic liquids under such low-pressure conditions. In silicate melts such as peralkaline dacite and rhyolite magma, interdiffusion (Baker, 1993; Baker and Bossanyi, 1994) resulted in diffusion coefficients and activation energy, expressed as a function of X/(X þ O) (X ¼ F and OH), that define a single relationship whether H2O or F alone or in combination (Fig. 9.85). Although there is some scatter in the experimental data, one might suggest that in general terms dissolved fluorine and H2O have the same effect on the melt structural factors that govern major element diffusivity. This may be because both volatile components cause depolymerization of the aluminosilicate network of magmatic liquids.29 The most evident feature is depolymerization of the 29

For a detailed review of existing experimental data on solubility mechanisms of halogens and H2O in aluminosilicate melts, the reader is referred to Mysen and Richet (Chapters 15 and 17).

9.6 Diffusion

260

Si interdiffusion

Activation energy, kJ/mol

Activation energy, kJ/mol

B

A

260

Volatile-free Chlorine

220

699

Fluorine OH

180

140

Si interdiffusion

220 Volatile-free Chlorine

180

Fluorine

140 100 0.00

0.02

0.04 0.06 0.08 X/(X+O), X=OH, F, Cl

0.10

0.8

1.0 1.2 1.4 (Na2O+K2O+CaO)/Al2O3

FIGURE 9.85 Silicon interdiffusion between dacite and rhyolite composition melt at 1 GPa (A) As a function halogen and H2O content, and (B) As a function of peralkalinitiy [(Na2O þ K2O þ CaO)/Al2O3] with volatile-free, Cl-, and Fbearing melts. Modified from Baker (1993), Baker and Bossanyi (1994).

silicate melt structure. Both F and H2O dissolved in magma results in increasing NBO/T. Moreover, because addition of either H2O, F or Cl to felsic magmatic liquids seems to have comparable effect on the diffusion of major elements such as Si4þ, Baker (1993) derived a relationship between the activation energy, Ea, and the proportion, X/(X þ O), where XeOH, F, or Cl (Fig. 9.85): 1636X þ 214:22: (9.18) XþO However, the magma compositional extent for which this expression is applicable is not known. The peralkalinity of magmatic liquids is another important variable that can cause changing diffusivity. For peralkaline [(Na2O þ K2O þ CaO)/Al2O3 > 1] and peraluminous [(Na2O þ K2O þ CaO)/Al2O3 < 1] magmatic liquids, the activation energy is less than for metaaluminous [(Na2O þ K2O þ CaO)/Al2O3 ¼ 1] melt compositions (Fig. 9.85B). It would seem likely that this observation reflects the fact that whenever (NA2O þ K2O þ CaO)/Al2O3 differs from 1, nonbridging oxygens are formed. That, in turn, leads to the decreased activation energy of Si diffusion seen in Fig. 9.85B. An unusual feature of mixed halogen þ H2O in solution in magmatic liquids is the increased activation energy compared with the activation energy with only H2O dissolved in magma (Baker et al., 2002). For example, in the meta-aluminous granite melt examined by Baker et al. (2002), the Zr4þ diffusion with 4.4 wt% H2O in solution is 140.1 kJ/mol, whereas by adding Cl or F to this melt system, the energy increased by as much as 30%e40%. The extent to which this effect can be observed depends, however, on the total H2O concentration in solution in the felsic magmatic liquid. This behavior may be related to possible interaction between halogens and H2O, perhaps similar to that Ea ¼ 

700

Chapter 9 Transport properties

which might explain the viscous behavior of similar magma compositions discussed in Section (9.4.2.4.2).

9.6.3.1.3 Effect of carbon dioxide Despite the observation that CO2 is the second-most abundant volatile in the Earth (Jambon, 1994) and beneath the continents probably the most abundant (Zhang and Duan, 2009), relatively little information exists on the effect of CO2 on diffusion in magmatic liquids. If melt polymerization was the dominant control of diffusivity, one would expect diffusion to slow down and activation energy to increase with dissolved CO2. This so because solution of CO2 in silicate melts results in melt polymerization whenever all or a portion of the dissolved CO2 is dissolved to form CO2 3 groups (Brooker et al., 1999; Guillot and Sator, 2011; Morizet et al., 2015). This expectation is in accord with results of molecular dynamics calculations (Ghosh and Karki, 2017). From the numerical simulations of an MgSiO3 melt with 16.1 wt% total CO2 in solution, the log D of the three major element components (Si, O, and Mg) as well as that of carbon, itself, versus 1/T exhibit Arrhenius behavior (Fig. 9.86). The slope of these linear relations increases in the order Mg < C < O < Si. Of course, oxygen in this environment includes that bound in both silicate species and CO2 3 groups, a species that form complexes with metal cations, and which is isolated from the silicate network (Morizet et al., 2015). This structural situation likely would drive the DO toward greater values. The diffusion constant in CO2-saturated MgSiO3 melt also are slightly smaller and the activity coefficients of diffusion slightly greater compared with the results for volatile-free MgSiO3 composition melt (see Table 1 in Ghosh and Karki, 2017). These changes likely reflect the increased polymerization of the MgSiO3 melt upon dissolution of CO2 to form CO2 3 in the melt structure (see Chapter 8).

100

A MgSiO3 melt

10 5.0

1.0 0.5

0.1 1.5

10 C

-9

-9

2

Diffusivity, D•10 , m /s

MgSiO3 melt

2

Diffusivity, D•10 , m /s

50

B

50

100

2.5 3.5 4 -1 Temperature, 10 /T (K )

4.5

Si

5.0

Mg O

1.0 0.5

0.1 0

40

80 Pressure, GPa

120

FIGURE 9.86 Calculated silicon, magnesium, and carbon diffusion in MgSiO3 composition melt with 16.1 wt% CO2 (solid lines) and CO2 free (dashed lines). (A) As a function of temperature at ambient pressure, and V, as a function of pressure at 3000 K. Modified from Ghosh and Karki (2017).

9.6 Diffusion

701

The decreasing diffusion constant of Si, O, Mg, and C with increasing pressure from the numerical simulations by Ghosh and Karki (2017) (Fig. 9.86B) likely reflects both the compaction of the structure with pressure as well increasing oxygen coordination numbers of both Si4þ and Mg2þ. As these coordination numbers increase, the difference between the diffusion coefficients of the individual components diminishes (see also Section 9.5.2).

9.6.3.2 Diffusion of volatiles in melts Volatiles can transfer components to melting regions in the Earth’s interior such as, for example above subducting plates near convergent plate boundaries (Mysen et al., 1978; Keppler, 1996; Brenan et al., 1998; Ni et al., 2017). The supply of volatiles, through diffusion in the magmatic liquids also leads to enhanced and different crystallization, bubble growth, and degassing during volcanic ascent and eruption (Eggler and Rosenhauer, 1978; Lensky et al., 2004; Blundy et al., 2008; Watson, 2017; Moretti et al., 2018). In multicomponent volatile-bearing melt systems, fractionation of the volatile components also is affected by diffusive behavior (Eggler and Kadik, 1979; Witham et al., 2012; Watson, 2017). Kinetics of diffusive motion among species has been proposed as possible geospeedometers (Huppert and Sparks, 1984; Zhang et al., 1997, 2007). It is, therefore, critical to characterize diffusivity of volatiles in magmatic liquids as well as the mechanisms that govern these transport processes.

9.6.3.2.1 Noble gas diffusion Characterization of diffusion of noble gases in magmatic liquids and other silicate melts is a useful starting point as this information sheds light on how a neutral and nonreactive species move through melt structure (Roselieb et al., 1992; Doremus, 1995; Zhang et al., 2010). Diffusion of noble gases may also govern isotopic evolution (Watson, 2017), which, in turn, affects models of evolution of volatiles in the Earth (Marty, 2012). In the simplest of silicate compositions, SiO2, noble gas diffusion through its glass and supercooled melt follows the typical Arrhenius behavior (Carroll and Stolper, 1991; Behrens, 2010; see also Fig. 9.87). As the atomic radius increases, the diffusion constant through amorphous SiO2 decreases (Fig. 9.87). Moreover, by increasing pressure, which one might expect would enhance the hindrance to particle diffusion, the diffusion coefficients do indeed decrease. For the ambient-pressure diffusion of Ar and Kr through an NaAlSi2O6 melt30, their diffusion coefficients decrease with increasing pressure, for example (Fig. 9.87B). The diffusion features shown for amorphous SiO2 (Fig. 9.87) are retained for other highly or fully polymerized melts such as those of KAlSi3O8, NaAlSi3O8 and rhyolite composition (Carroll, 1991; Carroll et al., 1993; Behrens, 2010) although there are differences in activation energy depending on atomic radius of the noble gas (Carroll, 1991; Behrens, 2010; see also Fig. 9.87C). Noble gas diffusion also depends on other structural/compositional parameters. As an example, although the NBO/T of rhyolite, NaAlSi3O8, and SiO2 composition melts for all practical purposes are the same (NBO/Tw0), the relationship between activation energy and atomic radius in the rhyolite composition is about 20 kJ/mol smaller than the Ea for the SiO2 and NaAlSi3O8 composition (Fig. 9.87C). Most likely, this 30 The only structural difference between SiO2 and NaAlSi2O6 melt at ambient pressure is the increased Al/(Al þ Si) of the NaAlSi2O6 melt because the melt structure along the SiO2eNaAlO2 remains the same (Taylor and Brown, 1979; Neuville and Mysen, 1996).

702

Chapter 9 Transport properties

FIGURE 9.87

-8 A 2

Diffusion coefficient, D, m /s

Noble gas diffusion in polymerization silicate melts. (A) Ne and He diffusivity in SiO2 melt as a function of temperature. (B) Ar and Kr diffusion in NaAlSi3O8 melt as a function of pressure. (C) Comparison of activation energy od noble gas and H2O diffusion in SiO2, NaAlSi3O8 and rhyolite composition melts as a function of atomic radius of the diffusing species. Modified from Carroll and Stolper (1991), Carroll et al. (1993), Behrens (2010).

-9 -10 -11

He SiO2 melt

-12 -13

Ne

-14 1.0

2.0 3.0 1.5 2.5 4 -1 Temperature, 10 /T (K )

B

-13.0

2

Diffusion coefficient, D, m /s

3.5

Ar

-13.5

-14.0 NaAlSi2O6 melt -14.5 -15.0

Kr -15.5 0.0

0.2

0.6

0.4 Pressure, GPa

400 Xe

Activation energy, kJ/mol

C

300 Kr Ar

200 H2O 100

0 1.0

Ne He

1.2

1.4 1.6 Atomic radius, Å

1.8

2.0

9.6 Diffusion

703

difference results from some of the Al3þ in the rhyolite composition being charge-balanced with alkaline earths, which weakens the (Si,Al)eO bonds compared with the bond strength when charge balanced with alkali metals only (Smyth and Bish, 1988). By increasing melt depolymerization, the diffusivity of the noble gases increase (Behrens, 2010; Nowak et al., 2004; Spickenbom et al., 2010) as seen both in natural melt systems and in simple model melts (Lux, 1987; Behrens, 2010). These relationships are well demonstrated in a simple-system such NaAlSi3O8þNa2O as a function of their added Na2O and, therefore, increasing melt NBO/T (Spickenbom et al., 2010; see also Fig. 9.88). Translated to magmatic liquids, relationships such as illustrated in Fig. 9.88 imply that trace element diffusivity increases as a magma becomes increasingly mafic such as such as from rhyolite, dacite, andesite, to tholeiite magma, for example (Fig. 9.88A). An effect analogous to that of adding Na2O to NaAlSi3O8 melt seen in Fig. 9.88B has been demonstrated by dissolving H2O in the melts and magmas (Behrens and Zhang, 2001; Zhang et al., 2007 31). In this latter case, a number of Ar diffusion data were least squares fitted to an expression of the form;     17367 P 855:2 P  1:9448 þ 0:2712 DAr ¼ exp  13:99  þ CH2 O ; (9.19) T T T T where P and T are pressure (MPa) and temperature (Kelvin), respectively, and CH2 O is the concentration of H2O (wt%). Although this expression does a good job in fitting the data within the compositional range that it was calibrated, it must be remembered that it is not clear how well it may apply to melt compositions outside this range. From experimental data such as those in Fig. 9.88, it is clear that melt polymerization is a critical variable in the control of noble gas diffusivity. The relationship between diffusion constants and their atomic radius remains, however, as a magmatic liquid becomes more mafic, and, therefore, more depolymerized (Lux, 1987; Amalberti et al., 2016, 2018). Just as was observed for noble gas diffusivity in SiO2 melt (e.g., Carroll and Stolper, 1991), in basalt melt, the diffusivity decreases systematically as the atomic radius of the noble gas (and therefore, atomic mass) increases (Fig. 9.89). The diffusion through basalt melt is, however, as much as eight orders of magnitude faster than through SiO2 melt (Carroll and Stolper, 1991) and five to six orders of magnitude faster that in NaAlSi3O8 and KAlSi3O8 melt (Carroll, 1991). These large differences, which reflect the large differences in the aluminosilicate network structure of fully polymerized felsic magmas and tholeiitic melt compositions likely reflect the greater ease by which diffusion through a network channel consisting of weak M-O bonds (M: alkali metal or alkaline earth) compared with the much more tightly held fully polymerized and, therefore, three-dimensionally interconnected tectosilicate network.

9.6.3.2.2 H2O diffusion The diffusion behavior of H2O in silicate melts is central to our understanding of igneous processes because H2O has profound effects on numerous melt properties relevant to the physics and chemistry of the magma and magmatic evolution (e.g., Kushiro, 1972, 1981; Gaetani et al., 1993; Richet and Whittington, 2000; Richet et al., 1996; Robert et al., 2015). Numerous experimental studies have been 31 Zhang et al. (2007) is a very useful review paper on the behavior of volatiles (H2O, CO2, noble gases) in silicate melts and provides a nice summary of the solubility and diffusion behavior and how these properties can be employed to discuss the role of volatiles during volcanic eruptions.

Chapter 9 Transport properties

A

B

-10.0

NBO/Si=0.198 NBO/Si=0.160 NBO/Si=0.127 NBO/Si=0.100 NBO/Si=0.077

de

-10.5

R

sit

e

hy

ol

2

An

Diffusivity, log DAr m /s

2

Diffusivity, log DAr m /s

-10.0

ite

Da

cit

e

-11.0 -11.5

NBO/Si=0.048 NBO/Si=0.019 NBO/Si=0.000

-11.0

Th

ole

-12.0 -12.5 5.50

-10.5

iite

6.00

6.50

7.00 4

-11.5

5.50

7.50

6.00

-1

6.50

7.00 4

increasing n-value

-9.5

NaAlSi3O8+nNa2O

704

7.50

-1

Temperature, 10 /T(K )

Temperature, 10 /T(K )

FIGURE 9.88 Argon diffusion in melts. (A) Ar diffusivity as a function of temperature in magmatic liquids from tholeiite to rhyolite as indicated on individual curves. (B) Ar diffusion in NaAlSi3O8þadded Na2O to obtain diffusivity as a function of NBO/T of melts as indicated. Modified from Nowak et al. (2004), Spickenbom et al. (2010).

FIGURE 9.89

6.0

Noble gas diffusion in basalt melt as a function of their atomic radius.

4.0

He

Modified from Lux (1987).

2.0

9

2

Diffusivity, D•10 m /s

Ne

1.0 0.8 0.6

Ar Kr

0.4

Basalt melt

Xe

0.2 1.0

1.2

1.6 1.4 1.8 Atomic radius, Å

2.0

9.6 Diffusion

705

carried out, therefore, to determine the diffusivity of H2O in magmatic liquids. Information exists for melt compositions ranging from basalt (Zhang and Stolper, 1991; Okumura and Nakashima, 2006; Zhang et al., 2017), to andesitic, rhyolitic, or granitic compositions (Lapham et al., 1984; Behrens and Nowak, 1997; Okumura and Nakashima, 2004; Liu et al., 2004; Behrens and Zhang, 2009; Behrens et al., 2004; Ni et al., 2009, 2013). A focus of felsic magma compositions is because H2O is particularly important in the petrogenesis of such magma (Kushiro, 1972; Mysen and Boettcher, 1975; Gaetani et al., 1993; Pichavant et al., 1992; Scaillet et al., 1996). In general, the diffusion constant for H2O, DH2O, in magmatic liquids decreases the more felsic the melt and the greater the H2O concentration in the magma (Freda et al., 2003; Schmidt et al., 2013; Zhang and Ni, 2010; Zhang et al., 2017; see also Fig. 9.90A and B). Moreover, the activation energy of diffusive flow for a given H2O content and fixed pressure also increases the more felsic the magmatic liquid (Okumura and Nakashima, 2006; Zhang and Ni, 2010). In fact, expressed in terms of the extent of polymerization of the magmatic liquid, the greater the NBO/T, the greater is the activation energy of diffusion (Okumura and Nakashima, 2006). Notably, the diffusion constant for H2O in basaltic magma is approximately the same as that of the noble gas, Xe (Zhang and Stolper, 1991), which is interesting because the atomic radius of Ar is approximately the same as that of H2O and not Xe (Fig. 9.91). The diffusivity behavior differs, however, from that of the activation energy of diffusive flow, in which case the Ea for H2O is between that of Ne and Ar (Fig. 9.87C). As the H2O content of magmatic liquids decreases toward 0, the diffusivity decreases, a feature also seen in H2O-bearing amorphous SiO2 as well in ternary aluminosilicate melts (Behrens and Nowak, 1997; Behrens, 2010; see also Fig. 9.92). This observation seems to hold, therefore, regardless of melt composition or magma type. These latter variations have led to the suggestion that more than one diffusion mechanism describes the diffusivity of H2O in melts and magma. Such a suggestion is -8

100

Activation energy, kJ/mol

-9

Ba

sa

lt m

elt

An

de

-10

sit

em

Da

cite

elt

me

lt

Rhy

olite

-11 5.0

B

90

H2O diffusion

2

Diffusivity,log DH2O m /s

A

me

lt

H2O diffusion phonolite melt

80

70

60

50 5.5 6.0 6.5 4 -1 Temperature, 10 /T(K )

7.0

2

3 4 5 6 7 H2O concentration in melt, wt%

FIGURE 9.90 (A) Diffusion of H2O in melts from rhyolitic to basaltic composition as a function of temperature. (B) Activation energy of H2O diffusion in phonolite melt as a function of H2O content. Modified from Schmidt et al. (2013).

706

Chapter 9 Transport properties

FIGURE 9.91

He

also from Karsten et al. (1982), Zhang et al. (1991).

basalt

2

Modified from Zhang and Stolper (1991), with data

Ne

-20 Diffusivity, ln DH2O m /s

Diffusion of H2O in basalt and rhyolite melt as a function of temperature and compared with noble gas diffusivity at fixed temperature.

melt

Ar Kr

-22

Xe

-24 rhyolite melt

(Karsten et al.

, 1982; Zhan

-26 5.6

g et al., 1991

)

5.8 6.0 6.2 4 -1 Temperature, 10 /T(K )

6.4

consistent with proposed solution mechanisms of H2O in silicate and aluminosilicate melts. As originally suggested by Goranson (1931) and expanded upon by Wasserburg (1957) and subsequently shown to work at least for the H2O solution mechanism of H2O in three-dimensionally interconnected SiO2 melts (Scholze, 1959), at least some of the dissolved H2O interacts SieOeSi bridges in the melt structure to form to SieOH bonds. This solution mechanism can be described with the simple equilibrium among oxygen-bearing species in a hydrous melt (Stolper, 1982):  H2 Omelt þ O2 melt H2OH melt; 2

(9.20) 

where O denotes the oxygen in the silicate melt structure and OH denotes SieOH bond and H2Omelt water dissolved as molecular H2O. Results from experiments using Fourier Transform Infrared Spectroscopy (FTIR) as well as NMR spectroscopy and numerical simulation, have added addition support to this concept (Bartholomew et al., 1980; Stolper, 1982; Eckert et al., 1988; Pohlmann et al., 2004; Behrens and Yamashita, 2008; Cody et al., 2020). In an experimental study that combined solution mechanism and characterization of diffusion of H2O in andesitic melt compositions, Ni et al. (2009) determined the equilibrium constant for Eq. (9.20), K9.20, as a function of temperature and combined with this with the diffusion data to arrive at an expression that describes the bulk H2O diffusion constant, Dtotal, as a function of the molecular H2O content in the melt, Dmelt, the equilibrium constant, K9.20, and the mol fraction of H2O in the melt, Xmelt: 0 1 B C 2Xmelt  1 C: Dtotal ¼ Dmelt B   @1 þ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A 4 4Xmelt ðXmelt  1Þ 1  þ1 K9:20

(9.21)

9.6 Diffusion

707

The relationship between the total diffusion constant and those of the molecular H2O and the OHgroups can then be described as (Ni et al., 2013): Dtotal ¼ DH2OðmeltÞ

vXH2OðmeltÞ vXOHðmeltÞ þ DOHðmeltÞ ; vXmelt 2vXmelt

(9.22)

where XH2OðmeltÞ and XOHðmeltÞ are the mol fractions of molecular H2O and OH-groups, respectively, in the melt. An expression such as Eq. (9.22) can explain relationships such as those between total H2O concentration and the diffusion constant of total H2O illustrated in Fig. 9.92. The treatment summarized in Eqs. (9.21e9.22) also leads to an explanation of the different diffusivity behavior of H2O compared with those of noble gases in melt solution (Figs. 9.87 and 9.91). The treatment also provides diffusion coefficients for molecular H2O and OH-groups linked to network-forming components in melts (Ni et al., 2013; see also Fig. 9.93). This treatment does not, however, handle diffusion of H2O dissolved to form isolated M-OH groups where M could be an alkali metal or an alkaline earth. Such solution mechanisms become increasingly important the more depolymerized (more mafic) a melt (Xue and Kanzaki, 2004, 2008; Cody et al., 2005). The latter complication notwithstanding, it is clear that molecular H2O in silicate melts diffuses about two orders of magnitude faster than OH-groups in (Si,Al)eOH bonds. The fact that the DOH increases as a magmatic liquid becomes more felsic (more polymerized) (Zhang et al., 2017; see also Fig. 9.93B) likely is a result of the observation that the abundance ratio of OH-bonding in hydrous melt (Si,Al)eOH/M-OH, increases as the melt becomes more felsic (Xue and Kanzaki, 2004; Cody et al., 2005) and the bond energy of (Si,Al)eOH bonds are greater than M-OH bonds by a factor of several (Smyth and Bish, 1988). Moreover, the observation that the Dmelt is quite sensitive to temperature and that this temperature-dependence diminishes with increasing H2O concentration (and, therefore, the FIGURE 9.92

-5

Modified from Behrens and Nowak (1997).

1200˚C 0.5 GPa

2

Diffusivity, log D, m /s

Diffusion of H2O in NaAlSi3O8eKAlSi3O8eSiO2 melts at 1200 C and 0.5 GPa as a function of their H2O content.

-6

-7

-8

0

1 2 3 4 5 6 H2O concentration in melt, wt%

7

708

Chapter 9 Transport properties

-8.0

A

-8.5

B

-9.0

-8.5

bas

alt

-9.5

ba

me

lt

sa

lt m

-9.0

elt

-10.0 -9.5

-10

5.4

5.6

an

de

-10.5

Basalt melt

sit

em

elt

5.8

6.0

6.2

-11.0 5.0

5.5

6.0

6.5

FIGURE 9.93 (A) Diffusion of molecular H2O and OH groups in basalt melt as a function of temperature. (B) Diffusion of OH groups in basalt and andesite melt and diffusion of Na in basalt melt as a function of temperature. Modified from Zhang et al. (2017).

activation energy of fluid flow) (e.g., Schmidt et al., 2013) probably reflects the observation that Eq. (9.20) also is sensitive to temperature and total H2O content (Zhang et al., 1991). The diffusivity of H2O in magmatic liquids summarized in Figs. 9.90e9.93 reflects both the complex solution mechanisms of H2O in silicate melts and the fact that this behavior is sensitive to the bulk melt composition.32 In order to advance our understanding of how those factors might affect the diffusion of H2O, examination of Dmelt for H2O is needed, beginning perhaps with the study by Moulson and Roberts (1961), who determined H2O diffusion in amorphous SiO2 in the 600e1000 C temperature range at 0.09 MPa H2O pressure (Fig. 9.94). They concluded from the log D versus 1/T relationship that the activation energy of H2O diffusion was about 78 kJ/mol. This value compares fairly well with that of Behrens (2010) who reported that the activation energy at 0.2 GPa pressure is w61 kJ/mol. The amount of experimental data on H2O diffusion in depolymerized melts appears include less than a handful of reports (Scholze and Mulfinger, 1959; Nowak, 1997; Nowak and Behrens, 1997). Among these, information for binary metal oxide-SiO2 melts appears limited to the study by Scholze and Mulfinger (1959), who reported that both the diffusion and activation energy of H2O diffusion in such melts depended on both the degree of melt polymerization, NBO/Si, and on the ionization potential of the metal cation in the metal oxide silicate melts (Fig. 9.95). With the metal/Si abundance ratio replaced with NBO/Si of the melt in Fig. 9.95, the diffusivity increases and the activation energy of H2O diffusion decreases with increasing NBO/Si (more depolymerized) of the melts. It appears also, however, that for a given NBO/Si-value, both the diffusivity decreases and the activation energy of 32

These issues were reviewed extensively in Chapters 14 and 15 of Mysen and Richet (2019). Interested readers may consult those chapters for details.

9.6 Diffusion

709

FIGURE 9.94

-8.5

Diffusion of H2O in SiO2 melt as a function of temperature. Modified from Moulson and Roberts (1961).

2

Diffusivity, log DH2O, m /s

-9.0

-9.5

-10.0 SiO2+H2O H2O diffusion

-10.5

-11.0 7.0

8.0 9.0 10.0 4 -1 Temperature, 10 /T (K )

A Na

140 Activation energy, kJ/mol

2

B

Li K

-9.2 Diffusivity, log D, m /s

11.0

-9.4 Rb

M2O-SiO2 melts

-9.6

-9.8

Rb K

120 M2O-SiO2 melts Na

100

80

Li

-10.0 0.0

0.5

1.0 NBO/Si

1.5

2.0

0.0

0.5

1.0 NBO/Si

1.5

2.0

FIGURE 9.95 Diffusivity (A) and activation energy of diffusion (B) of metal cations in binary alkali silicate melts. Data are identified on individual curves. Modified from Scholze and Mulfinger (1959).

710

Chapter 9 Transport properties

diffusion seem to increase with decreasing Z/r2 of the metal cation, at least for Na2OeSiO2, K2OeSiO2, and Rb2OeSiO2 melts. These trends probably reflect different Qn-species abundance in these melts. The much smaller Liþ cation very likely occupies a different oxygen coordination sphere than the larger alkali metals (Shannon and Prewitt, 1969) so that diffusion in Li2OeSiO2 melts might not easily be compared with diffusion in the other alkali silicate melts. There does not seem to be experimental data with which to isolate effects of Al/(Al þ Si) and the nature of charge balance of tetrahedrally coordinated Al3þ on the diffusion of H2O in aluminosilicate melts. One might surmise, however, that as a meta-aluminosilicate melt becomes increasingly aluminous, the diffusivity would increase and activation energy would decrease because of the diminished (Si,Al)eO bond energy with increasing Al/(Al þ Si). Moreover, by increasing the ionization potential of the charge-balancing cation, it is likely that the diffusivity and activation energy both increase because the increased Z/r2 leads to increased structural disorder of aluminosilicate melts (Seifert et al., 1982; Lee and Stebbins, 1999). This suggestion is based on the fact that their melt viscosities decrease and given the inverse relationship between viscosity and diffusivity from the Eyring equation (Eq. (9.3)), this conclusion follows.

9.6.3.2.3 Halogen diffusion Halogens can be important in igneous processes, including, for example, magmatism near convergent plate boundaries (Pichavant et al., 1987; Aiuppa, 2009). Experimentally determined diffusion data of halogens are, however, relatively scarce, but some information can be found for basalt and phonolite liquids (Alletti et al., 2007; Balcone-Boissard et al., 2009; Bo¨hm and Schmidt, 2013) as well as for simple alkali aluminosilicate melts (Dingwell and Scarfe, 1984, 1985). There is information on F, Cl, and Br diffusion (DF, DCl, and DBr) in basalt melt (Allettii et al., 2007). The diffusion constants for F and Br in such magmatic liquids differ by approximately a factor of 4. The difference between DF and DCl is smaller (Fig. 9.96A). From the different slopes of the log D FIGURE 9.96

-9.8

Diffusivity of halogens in basalt composition melt (as indicated on curves) as a function of temperature.

-10.0 2

Diffusivity, log D, m /s

Modified from Alletti et al. (2007).

-10.2

-10.4

F

-10.6

Cl -10.8

Br

Basalt melt

-11.0 6.00

6.20

6.40 4

-1

Temperature, 10 /T (K )

9.6 Diffusion

711

versus 1/T relationship in Fig. 9.96, it appears that whereas the activation energy of F and Br diffusion is approximately the same (218  34 and 199  33 kJ/mol for F and Br, respectively), the slope of the chlorine relationship is much steeper, which results in Ea ¼ 277  8 kJ/mol. A somewhat similar relationship can be seen in the temperature-dependent Cl and F diffusion data in a sodium-rich phonolite melt (Balcone-Boissard et al., 2009). Here, the two activation energies were reported to be 133  15 and 216  54 kJ/mol for F and Cl, respectively. In this latter study, it was notable, however, that for a K-rich phonolite (K2O/Na2O ¼ 1.6 as compared with K2O/Na2O ¼ 0.5 for the Narich phonolite melt) the Ea ¼ 215  30 and 164  33 kJ/mol (Balcone-Boissard et al., 2009). The different diffusivity of F and Cl in basalt and Na-phonolite magma likely reflects the different solution mechanisms of F and Cl in silicate melts (Dalou et al., 2015). Whereas Cl predominantly forms metal chloride complexes thus leading to melt polymerization, for fluorine, the solution mechanism also involves breakage of (Si,Al)eO bridges in the aluminosilicate structure thus resulting in melt depolymerization (Stebbins and Du, 2001; Stebbins and Zeng, 2000; Dalou et al., 2015). This structural difference does not, however, explain the different activation energy behavior in the K-rich phonolite. It remains interesting, though, that the DCl is greater than DF even though the difference is smaller in K-rich phonolite than in the Na-rich phonolite melt (Balcone-Boissard et al., 2009). Further, the log D versus 1/T relations for the K-rich phonolite melt deviate significantly from linearity. It is possible that it is not the K/Na ratio causing this effect, but perhaps the Al/(Al þ Si) and how the tetrahedrally coordinated Al3þ is charge-balanced because increasing Al/(Al þ Si) results in increasing diffusivity with approximately the same activation energy (Dingwell and Scarfe, 1985). There exists little or no information on diffusion and solution mechanism of heavier halogens in silicate melts. It is only known that the solubility in a given melt decreases systematically as a function of atomic mass (Bureau et al., 2000). This information is not, however, sufficient to explain the similar diffusion behavior of F and Br, but the different behavior of Cl (Fig. 9.96). Addition of H2O to magmatic liquids affects the diffusion behavior of the halogens (Bo¨hm and Schmidt, 2013). The diffusivity of both Cl and F increases in hydrous melts (Fig. 9.97). However, the effect seems greater for DCl than DF. This different behavior again likely reflects the different solution mechanisms of Cl and F in hydrous melts (Dalou and Mysen, 2015). Whereas F forms SieF and AleF bonds in replacement of SieOH and AleOH bonds in melts and magmas, the solution of chlorine in hydrous melts results in an exchange of Hþ for Mnþ, a feature that is a more efficient means by which to depolymerize the melt structure than the manner in which fluorine is dissolved in hydrous magma (Dalou and Mysen, 2015).

9.6.3.2.4 CO2 diffusion Carbon dioxide is the second-most abundant volatile component in the silicate earth (Jambon, 1994) and often is considered the most important in the upper mantle away from subduction zone settings (Zhang and Duan, 2009). However, its solubility in magmatic liquids is comparatively low, in particular at pressures near the Earth’s surface (see Chapter 8, Sections 8.1.1 and 8.11.2). Carbon dioxide exsolution is, therefore, an important contributor to near-surface degassing of magmatic liquids (Eggler and Kadik, 1979; Bottinga and Javoy, 1989; Watson, 2017). In a comprehensive experimental study of diffusion in magmatic liquids ranging from rhyolite to basaltic in composition, Nowak et al. (2004) reported CO2 diffusion and, perhaps surprisingly, concluded that the bulk CO2 diffusion in magmatic liquids does not change significantly as a function of melt polymerization. In this respect, CO2 diffusion differed, therefore, from the diffusion behavior

Chapter 9 Transport properties

-10.5

Phonolite melt Fluorine diffusion

2

2.1 -11.5

wt%

-11.5

H2 O

-12.0

an

hyd

-12.5

rou

s

2.

4

-12.0

wt

%

H

2

-12.5

O

an

hy

dr

ou

-13.0

s

-13.5

-13.0

-13.5 6.5

B Phonolite melt Chlorine diffusion

2

-11.0

Diffusivity, log D, m /s

-11.0

A

Diffusivity, log D, m /s

712

7.0

7.5

8.0

8.5 4

9.0

-14.0 6.5

9.5

7.0

7.5

8.0

8.5 4

-1

9.0

9.5

-1

Temperature, 10 /T (K )

Temperature, 10 /T (K )

FIGURE 9.97 Halogen diffusion in anhydrous and hydrous phonolite composition melt. (A) Chlorine diffusion as a function of temperature in anhydrous and 2.1 wt% H2O-containing phonolite melt. (B) Fluorine diffusion as a function of temperature in anhydrous and 2.4 wt% H2O-containing phonolite melt. Modified from Bo¨hm and Schmidt (2013).

of Ar (Fig. 9.98). However, a portion of the CO2, is dissolved in the form of CO2 3 complexes. The fraction of these complexes relative to the total amount of CO2 in solution increased rapidly with increasing NBO/T of the melt (see Chapter 8, Section 8.1.2 for more information on the solution mechanisms of carbon dioxide in silicate melts). The equilibrium: 2CO2 ðtotalÞ þ O2 ¼ CO2 ðmolecularÞ þ CO2 3 ðmeltÞ; 2

(9.23) 33

describes the relations between molecular CO2 and CO3 groups in the magmatic liquids. It follows that the diffusion coefficients of the two melt species in the magmatic liquid is related to that total CO2 diffusivity as (Nowak et al., 2004): DCO2 ðtotalÞ ¼ DCO2 ðmolecularÞXCO2 ðmolecularÞ þ DCO2 ð1  XCO2 ðmolecularÞÞ; 3

(9.24)

where X is mol fraction. From this treatment, it follows that diffusion constant, DCO2 ðmolecularÞ, must decrease as the magmatic liquids become more mafic. It is interesting, in light of the data in Fig. 9.98, that in chemically simpler systems such as, for example NaAlSi3O8þNa2O (Sierralta et al., 2002; Spickenbom et al., 2010), the DCO2 ðtotalÞ increased with increasing NBO/T of the melts (Fig. 9.99) even though the activation energy of diffusion did not show meaningful variation (Fig. 9.99B). There does, therefore, seem to be conflict between the 33

Eq. (9.23) shifts to the left with increasing temperature and decreasing pressure (Nowak et al., 2003; Guillot and Sator, 2011; Konschak and Keppler, 2014).

9.6 Diffusion

FIGURE 9.98

-10.5

Ar

andesite melt

dacitic andesite melt

-13.0

-14.5 -15.0 0.0

rhyolite melt

-13.5

andesitic tholeiite melt

-12.0

2-

Modified from Behrens et al. (2004).

hawaiite melt

tholeiite melt

CO3

dacite melt

2

Diffusivity, log D, m /s

-11.5

-12.5

Diffusion of Ar, total CO2 and CO2 3 groups in melts from rhyolite to hawaiite compositions identified by their NBO/T-values.

total carbon as CO2

-11.0

-14.0

713

0.1

0.2

0.3

0.5

0.4

0.6

0.7

NBO/T of melt

300

A

-10.8 -11.0 -11.2 NaAlSi3O8-nNa2O melt

Activation energy, kJ/mol

2

Diffusivity, log D, m /s

-10.6

B

250 200 150 100 50

NaAlSi3O8-nNa2O melt

-11.4 0.00

0.04 0.08 NBO/T

0.12

0 0.00

0.04

0.08 NBO/T

0.12

FIGURE 9.99 (A) CO2 diffusion inNaAlSi3O8 þ nH2O composition melts expressed as a function of NBO/T of the melts. (B) Activation energy of diffusion CO2 diffusion inNaAlSi3O8þnH2O composition melts expressed as a function of NBO/T of the melts. Modified from Spickennbom et al. (2010).

714

Chapter 9 Transport properties

experimental data for natural magma compositions from Nowak et al. (2004) in those in the chemically simpler system, Na2OeAl2O3eSiO2 by Spickenbom et al. (2010). The difference could, of course, be related to different Al/(Al þ Si) and perhaps different forms of charge-balance of Al3þ in tetrahedral coordination. Bulk Al/(Al þ Si) seem to be correlated positively with DCO2 (Spickenbom et al., 2010), for example. However, experimental data needed for evaluation of such ideas are not yet available. Carbon dioxide in most magmatic liquids typically coexist with some H2O although the CO2/H2O proportion often depends on tectonic settings. Diffusivity data of CO2 in hydrous magmatic liquids are, therefore, needed. In the example in Fig. 9.100 showing DCO2 as a function of H2O content and temperature, DCO2 increases with H2O content (Watson, 1991). The activation energy of CO2 diffusion decreases with increasing H2O content given the decreasing slope of the curves in Fig. 9.100. In light of the fact that solution of H2O results in melt depolymerization (see Chapter 8), the increased CO2 diffusivity with increasing H2O content likely is also a result of the melt depolymerization caused by H2O. This feature is consistent, for example, with the CO2 diffusion data for NaAlSi3O8 þ H2O and NaAlSi3O8 þ Na2O (Sierralta et al., 2002; see also Fig. 9.101). The slightly smaller effect on DCO2 by H2O compared with Na2O accords with the fact that some portion of the dissolved H2O exists in molecular form in the melts. In molecular form, H2O does not cause silicate melt depolymerization. Moreover, it cannot be ruled out that with mixed CO2 þ H2O melt systems, some of the dissolved carbon dioxide may also form HCO3 complexes (Mysen, 2015). Carbon dioxide diffusion in basalt melt decreases as a function of increased pressure (Watson et al., 1982; see Fig. 9.102). This behavior is consistent with the fact that in basalt melt, CO2 is dissolved as CO2 3 groups, which exist as isolated complexes associated with alkali metals or alkaline earths (Morizet et al., 2015). Their motion through melts would be expected to encounter increased hindrance with increasing pressure. It follows, therefore, that their diffusion coefficients increase with increasing pressure as seen both in Fig. 9.102 (Watson et al., 1982) and in the high-pressure results of calculations of CO2 diffusion in MgSiO3 melt by Ghosh and Karki (2017). It is likely that this behavior remains if FIGURE 9.100 CO2 diffusion in hydrous obsidian melt (H2O contents shown in figure) as a function of temperature. Modified after Watson et al. (1991).

9.6 Diffusion

FIGURE 9.101

2

2

Diffusivity of CO2, log DCO , m /s

-10.6 -10.8

715

CO2 diffusion in NaAlSi3O8þnH2O and NaAlSi3O8þH2O composition melts as a function of their NBO/T at 1250 C and 0.5 GPa.

1250˚C/0.5 GPa

-11.0

lSi3O

NaA

O +Na2

Modified from Sierralta et al. (2002).

8

H 2O

-11.2

+ i 3O 8 AlS

Na

-11.4 -11.6 -11.8 -12.0 0.00

0.04

0.08 0.12 NBO/T of melt

0.16

H2O also is added to the magmatic liquids because addition of H2O, if anything, would result in increased compaction of the melt structure (see also Chapter 10).

9.6.3.2.5 Sulfur diffusion Diffusion of sulfur in magmatic systems not only depends on bulk chemical composition, temperature, and pressure (e.g., Baker and Rutherford, 1996; Freda et al., 2005), redox conditions is also important because sulfur in magmatic liquids can exist both in reduced (as S2) and oxidized (as S6þ) form.34 At the oxygen fugacity conditions typical for basalt petrogenesis (Carmichael and Ghiorso, 1990), S2 dominates (O’Neill and Mavrogenes, 2002; Jugo et al., 2010; Botcharnikov et al., 2011), whereas under more oxidizing conditions such as those in subduction zone settings (Kelley and Cottrell, 2009), oxidized sulfur likely dominates in magma (Scaillet et al., 1998; Binder and Keppler, 2011). Sulfur diffusivity depends on the oxidation state (Behrens and Stelling, 2011; see also Fig. 9.103) with oxidized sulfur diffusing somewhat slower than reduced sulfur (less than an order of magnitude; see Fig. 9.103). In addition, it must be kept in mind that sulfur diffusion, being linked to melt structure of the magmatic liquid through which it may diffuse (Watson, 1994), also depends on the composition of magmatic liquids. Similar to the diffusion behavior of other volatile components, the sulfur diffusivity decreases as the magma becomes more felsic (see review by Watson, 1994). In view of the fact that sulfur in basaltic and related magmatic liquids tend to exist in its reduced state, S2, whereas sulfur exists predominantly in its oxidized form in felsic magma, the different sulfur diffusion coefficients might even vary by more than the order of magnitude suggested in the review by Watson (1994). This transformation in magmatic liquids takes place at an fO2 equivalent to that near the QFM (quartz-fayalite-magnetite) oxygen buffer [see also Chapter 8, Sections (8.3.1) and (8.3.2) and Fig. 8.19]. 34

716

Chapter 9 Transport properties

FIGURE 9.102 CO2 diffusion in Na2OeAl2O3eSiO2 composition melts as a function of pressure.

-10.4 -10.6

2

2

Diffusivity, log DCO , m /s

Modified after Watson et al. (1982).

-10.8 -11.0 -11.2 Na2O-Al2O3-SiO2 melt CO2 diffusion

-11.4 -11.6 -11.8 0.0

FIGURE 9.103

0.5

1.0 1.5 2.0 Pressure, GPa

2.5

-10

Diffusion of reduced and oxidized sulfur (S and S6þ) in Na2Si3O7 composition melt as a function of temperature.

Modified from Behrens and Stelling (2011).

Diffusion coefficient, log D (m2/s)

2

Na3SiO7 melt Sulfur diffusion

-11

-12 S 2-

-13

S 6+

-14 0.60

0.65

0.70

0.75 3

-1

Temperature, 1/T•10 (K )

0.80

9.7 Electrical conductivity

717

In hydrous silicate melt systems, the sulfur diffusivity can increase by more than an order of magnitude (Baker and Rutherford, 1996). Furthermore, in hydrous andesite melt, the activation energies of sulfur diffusion under both oxidizing and reducing conditions range between 115 kJ/mol for S2 compared with 458 kJ/mol in nominally anhydrous NaAlSi3O8 melt (Watson, 1994; Winther et al., 1998). Activation energies of sulfur diffusion are in the range of SieO and AleO bond energies (Smyth and Bish, 1988). One might suggest, therefore, that sulfur diffusion involves bond disruption and formation in the silicate network. That would also be consistent with sulfate and sulfide solution mechanisms in silicate melts (see Mysen and Richet, 2019; Chapter 16), which makes it is clear that 2 the solution mechanisms of both SO2 groups are linked to the structure of the silicate 4 and S network. This conclusion is further substantiated by the experiments from Zhang et al. (2007), who suggested that the effect of dissolved H2O on sulfur solubility can be expressed an equation of the form:   27692  651:6CH2O DS ðms = sÞ ¼ 2:72$104 exp  ; (9.25) T for the diffusivity of sulfur in basalt melt. In Eq. (9.25), CH2O is concentration of H2O (wt%) and T is temperature (Kelvin). Of course, in reality, the redox state of sulfur also should enter into such an expression, but as a first example of melt effects, it may suffice.

9.7 Electrical conductivity Electromagnetic methods are commonly employed for surveys of fluid and magma distribution in the Earth’s interior (Gough, 1992; Jones, 1999; Poirier et al., 1998; Heise et al., 2010; Ni et al., 2011). Electromagnetic methods also can be helpful to decide whether or not fluids and melts form interconnected networks (Scarlato et al., 2004; ten Grotenhuis et al., 2005; Watson and Roberts, 2011; Pommier, 2014; Laumonier et al., 2017). For example, in a series of experiments by ten Grotenhuis et al. (2005), the electrical conductivity of the bulk sample increased by more than an order of magnitude as the melt distribution changed from situated at triple junctions with melt fraction near 0.01 to wetting all grain boundaries by gradually increasing melt fractions from 0.01 to 0.1 (Fig. 9.104). Even when the melt fraction is near 0.1, however, the electrical conductivity is an order of magnitude smaller than that of 100% melt (Fig. 9.104). Analogous observations might be made for distribution of fluids along grain boundaries with implications, for example, for fluid migration in subduction zone settings (e.g., Mysen et al., 1978; Schwarz et al., 1997; Mibe et al., 1999; Pommier, 2014; Iwamori et al., 2021). Experimental data on relationships between conductivity of silicate-saturated fluids of relevant compositional variations in deep crust and the mantle of the earth is, however, not widely available. A few such data exist (Frantz and Marshall, 1984; Reynard et al., 2011; Shimojuka et al., 2014; Guo and Keppler, 2019; Klumbach and Keppler, 2020), but the existing conductivity data base is insufficient for comprehensive analysis of how fluid distribution and composition, pressure, temperature can be related quantitatively to electrical conductivity in the Earth’s interior.

718

Chapter 9 Transport properties

FIGURE 9.104 Electrical conductivity of partially molten peridotite as a function of melt fraction. Modified from ten Grotenhuis et al. (2005).

In this chapter, therefore, the focus is electrical conductivity of silicate melts. This focus does not rule out an importance of fluids (see also Chapter 11), but the absence of sufficient experimental and theoretical data for a substantive discussion makes a comprehensive discussion difficult.35 Electrical conductivity (s, measured in S/m) is an expression of the rate at which charge transport occurs. For the most part, this transfer appears linked to the motion of ions, which means that often there are links between diffusion and electrical conductivity and viscosity and electrical conductivity (see, for example, Zhang et al., 2011; Nemilov, 2011; Mills et al., 2012; Noritake et al., 2012). More generally, the NernsteEinstein equation relates conductivity of component to its diffusivity (Nernst, 1888; Einstein, 1905; see also Eq. (9.1)). In fact, for a number of magma compositions ranging from peridotite and komatiite to andesite in composition, Dufils et al. (2018) found that the NernsteEinstein relation works quite well although it seems that there is a small off-set from the 1:1 relationship. This off set seems constant for magma compositions between basalt and andesite, but for more ultramafic compositions, the offset appears to diminish somewhat.36 Pressure and temperature effects on conductance typically take the same form, therefore, as its links between network-modifying cation diffusion, temperature, and pressure. There is, thus, an Arrhenius equation similar to that of diffusion (see also Ni et al., 2015, for detailed review of these features) that commonly describes relationships between conductance, temperature, and pressure:   Ea þ PDVa s ¼ so exp  : (9.26) RT Here, s is electrical conductivity, Ea is activation energy and DVa activation volume.

35 For additional information on experimental data on the behavior of fluids, interested readers are directed to experimental studies of electrical conductivity by, for example, Ni et al. (2011), Sinmyo et al. (2017), and Watanabe et al. (2021). 36 We note that the Haven factor, HR, is incorporated in this calculation (see also Eq. (9.1b)).

9.7 Electrical conductivity

719

9.7.1 Electrical conductivity, composition, and temperature Despite the utility and need for laboratory data with which to calibrate natural electromagnetic measurements, conductance data of natural magmatic liquids are relatively scarce (Gruener et al., 2001; Gaillard, 2004; Gaillard et al., 2005; Pommier et al., 2010). However, within the existing data base, systematic relationships between electrical conductivity and type of igneous rocks do exist. For example, from the linear temperature-dependence of electrical resistivity, the activation energy of conductivity37 of natural magmatic liquids increases the more mafic the magma (Fig. 9.105) much as does the diffusivity of network-modifying cations as seen in its positive correlation with NBO/T of melts and magma, for example (Fig. 9.69). It is not surprising, therefore, that in a study of the relationship between the proportion of nonbridging oxygen relative to total oxygen budget in silicate melts, NBO/O, Gruener et al. (2001) found that the electrical conductivity increases the greater the proportion of nonbridging oxygen (Fig. 9.106). In terms of natural magmatic liquids, the more mafic the magma, the greater are both the proportions NBO/T and NBO/O (see Mysen and Richet, 2019; Chapter 18, for review of the structure of natural magmatic liquids). This relationship is evident in the evolution of electrical conductivity of different igneous rocks. The electrical conductivity is greatest for peridotitic and komatiitic magma and smallest for rhyolite magma (Fig. 9.107; see also Guillot and Sator, 2007). Relationships such as summarized in Figs. 9.105e9.107, reflect the fact that the electrical conductivity is related to the ease by which charge transfer through a melt is accomplished with aid of motion of network-modifying cations. In all but felsic magma such as rhyolite, alkaline earths are the dominant network-modifying cations (see Mysen and Richet, 2019, Fig. 18.5). It may not be surprising, therefore, that by comparing the electrical conductivity of natural magmatic liquids, not only does it increase the more felsic the magma, but the proportion of alkali metals relative to alkaline earths serving as charge carriers also increases (Guillot and Sator, 2007; see also Figs. 9.107 and 9.108). In view of the observation that the alkali-oxygen bond energies are smaller than those of alkaline eartheoxygen (Smyth and Bish, 1988), the lower activation energy of conductance and conductivity itself of felsic magmas would be a natural consequence. In order to develop a deeper understanding of how electrical conductivity of silicate melts is governed by their structure, data from simple binary and ternary metal oxide silicate and metal oxide aluminosilicate melts are needed (Bockris et al., 1948, 1952; Tickle, 1967; Hunold and Bru¨ckner, 1980; Satherley and Smedley, 1985; Gruener et al., 2001; Malki and Echegut, 2004; Kim and Sohn, 2012). Among these reports, those of Bockris et al. (1952), Tickle (1967), and Satherley and Smedley (1985) addressed conductance in binary metal oxide silicate melts. The results from those experimental studies were in close agreements. Aluminosilicate and chemically more complex melts were examined by Gruener et al. (2001), Malki and Echegut (2004), and Kim and Sohn (2012). In a compilation of data from a range of metal oxide silicate melts, Satherley and Smedley (1985) observed that with conductivity expressed as a function of NBO/Si of the melt, the data fall on the same line (Fig. 9.109). It is notable, though, that the effect of increasing NBO/Si becomes less and dependent on silicate depolymerization (increasing NBO/Si) as it increases. In light of the evolution of Qn-species abundance with increasing NBO/Si of melts (see Chapter 5; Section (5.2.3)), it would seem that as the proportion of highly polymerized species diminishes with increasing bulk melt NBO/Si, so does the 37

Note that resistivity, r (ohm m) is the inverse of electrical conductivity, s (S/m) so that s ¼ 1/r.

720

Chapter 9 Transport properties

250

Latite

Rhyolite

Andesite

Phonolite

Tephrite

50

phonotephrite

100

Alkali olivine basalt

150

Tholeiite

Activation energy, kJ/mol

200

0

FIGURE 9.105 Activation energy of electrical conductivity of a range of typical magmatic liquids. Modified from Pommier et al. (2010).

FIGURE 9.106 Electrical conductivity of CaOeAl2O3eSiO2 melt and glass as a function of the proportion of nonbridging oxygen relative to total oxygen, NBO/O, as a function of temperature as indicated. Modified from Gruener et al. (2001).

9.7 Electrical conductivity

721

FIGURE 9.107 Calculated electrical conductivity of magmatic liquids ranging from ultramafic to felsic as a function of temperature. Modified from Guillot and Sator (2007).

FIGURE 9.108 Calculated electrical conductivity of reflecting Naþ(A) and Ca2þ(B) in a range of natural magmatic liquids ranging from basalt to rhyolite as a function of temperature. Modified from Guillot and Sator (2007).

722

Chapter 9 Transport properties

FIGURE 9.109 Electrical conductivity of a range of magmatic liquids and simple silicate melts as a function of their total alkali content. Modified from Satherley and Smedley (1985), see Satherley and Smedley (1985), for detailed references to melt compositions and sources.

Electrical conductivity, logσ, S/m

4

2

0

-2

-4 0

10

20 30 40 50 Total alkali content, mol %

60

effect of NBO/Si on electrical conductivity. It is likely that, along the line of discussion of these issues by Pommier et al. (2008), this effect at least in part reflects decreased strain energy as the melt becomes increasingly depolymerized. In the data bases containing information on electrical conductivity of binary metal oxide silicate melts, there is a slightly nonlinear relationship between the logarithm of conductivity (and resistivity) and temperature, 1/T (Fig. 9.110). Moreover, the more electronegative the metal cation, the greater is the equivalent conductance (Bockris et al., 1952; Tickle, 1967; see also Fig. 9.110B).38 Interestingly, Bockris et al. (1952) reported that the activation energy of electrical conductivity of different alkali silicate melts is the same, but is about 50% of the value for alkaline earth silicate melts. This difference likely reflects how the activation energy increases as the more tightly bonded alkaline earth cations are charge carriers. The mixed alkali effect (Day, 1976) is another feature of conductivity of alkali silicate melts seen as two or more network-modifying cations are mixed. Among K2OeNa2OeSiO2 and K2OeNa2OeAl2O3eSiO2 melts, for example, the mixed alkali effect on melt conductivity as well as activation energy of electrical energy are significant (Kim, 1995, 1996; see also Fig. 9.111). It is also notable that the mixed alkali effect is more pronounced in glasses at temperatures below their glass transition than for melts (Kim, 1995, 1996). Another compositional variable affecting the electrical conductivity is the ratio of metal oxide to Al2O3 for which data exist for alkali aluminosilicate melts and glasses (Hunold and Bru¨ckner, 1980). Just as was the case for diffusion and viscosity (see Sections (9.3.1.1) and (9.5.1.1)), the conductance Equivalent conductance, L, is defined as L ¼ 1/rC, where r is resistivity and C is the gram equivalent of the metal cations under consideration.

38

9.7 Electrical conductivity

NBO/T of melt 0.5 1.0

60 i=0.

O/S

NB

0.5 .80

/Si=0

NBO

0

1.0 O/Si=

0.0

NB

i=1.18

NBO/S

i=1.40 NBO/S i=1.58 NBO/S i=1.78 NBO/S i=1.980 NBO/S i=2.3 NBO/S

5.0

B Equivalent conductance at 1400˚C

Electrical resistivity, logΩ, ohm

2.5

2.0

A

1.0

-0.5

723

6.0 7.0 8.0 4 -1 Temperature, 10 /T (K )

200 160 120

80 40

10 20 30 40 50 60 Alkali oxide concentration in melt, mol %

9.0

FIGURE 9.110 (A) Electrical conductivity as a function of temperature of Na2OeSiO2 melts as a function of their NBO/Si. (B) Equivalent conductance at 1400 C of alkali silicate melts as indicated on individual curves. Modified after Tickle (1967).

70

A

B Electrical conductivity, logσ, S/m

Activation energy, kJ/mol

1.7 60

50

40

30

20 0.0

0.2

0.4 0.6 K2O/Na2O

0.8

1.0

1.5 1400˚C

1.3 1200˚C

1.1 0.9 1000˚C

0.7

0.0

0.25

0.50

0.75

1.00

K2O/Na2O

FIGURE 9.111 Electrical conductance of alkali aluminosilicate melts as a function of K2O/Na2O abundance ration. (A) Activation energy at different SiO2 contents as indicated. (B) Electrical conductance at different temperatures as indicated. Modified after Kim (1996).

724

Chapter 9 Transport properties

in Na2OeAl2O3eSiO2 glasses and melts exhibit a maximum slightly to the peraluminous side of the Al2O3/Na2O ¼ 1 (meta-aluminosilicate) compositions. Interestingly, the intensity of this minimum appears more pronounced for the glasses than for the melts (Fig. 9.112). Hunold and Bru¨ckner (1980) also found that the electrical conductivity of glasses exhibit Arrhenius behavior, whereas at the higher temperatures above the glass transition, this temperature-dependence (log s vs. 1/T) is not linear. Similar behavior was subsequently reported by Tickle (1967), Kim (1995, 1996), and Malki and Echegut (2004) for ternary aluminosilicate and binary metal oxide silicate melts. One might speculate that these changes reflect changes in the proportion of various metal cations that charge balance Al3þ in tetrahedral coordination. Such reasoning has been employed, for example, to explain increasing entropy of mixing and configurational heat capacity with increasing temperature of aluminosilicate melts (see Chapter 4, Section (4.2.3) for more discussion of such thermodynamic phenomena). This nonlinear conductivity behavior with temperature above the glass transition (Fig. 9.110) would suggest that the charge transfer mechanism(s) change as a function of temperature. Interestingly, in their study of natural magmatic compositions, Pommier et al. (2010) did not report deviations from Arrhenian behavior. Reasons for this apparent difference between electrical conductivity in chemically complex magmatic liquids and that in simple-system melts are not clear, but may just reflect compensating factors governing the electrical conductivity of natural magma.

9.7.2 Electrical conductivity and pressure In light of the positive correlation between electrical conductivity and diffusivity of networkmodifying cations from the NernsteEinstein relationship (Nernst, 1888; Einstein, 1905; see also Eq. (9.1)), one might anticipate that electrical conductivity also decreases with increasing pressure. This feature assumes, however, that the oxygen coordination numbers around those metal cations does FIGURE 9.112

Modified after Hunold and Bru¨ckner (1980).

Electrical conductivity, logσ, S/m

Electrical conductivity of alkali aluminosilicate glasses and melts at temperatures indicated on individual graphs as a function of their Al2O3/Na2O abundance ratio.

2 850˚C

0

-2

250˚C

-4

-6

0

20˚C

1.0 0.5 1.5 Al2O3/Na2O abundance ratio, by mole

9.7 Electrical conductivity

725

not change with pressure, which, of course, it does (Bryce et al., 1999; De Koker, 2010; Noritake et al., 2012; Karki et al., 2018). Experimental data on pressure effects of electrical conductivity, have been restricted to several GPa (Tyburczy and Waff, 1983, 1985; Satherley and Smedley, 1985; Gaillard, 2004; Pommier et al., 2008). In addition, results from a few molecular dynamics simulation studies of transport properties of melts to higher pressure have been reported (Mookherjee et al., 2008; Noritake et al., 2012; Karki et al., 2018). The electrical conductivity of magmatic liquids compositionally ranging from basalt to rhyolite retain the differences between magma compositions with increasing pressure (Fig. 9.113). In other words, the conductivity increases as the magma becomes increasingly mafic at least to several GPa pressure (Tyburczy and Waff, 1983, 1985; Pommier et al., 2008). The rate of change with pressure, (vs/vP)T, does, however, decrease the more mafic (and, therefore, the nigher the NBO/T) of the magmatic liquid, a feature also seen in the pressure evolution of electrical conductivity of melts in the simpler system, Na2OeSiO2 (Tyburczy and Waff, 1983, 1985; Satherley and Smedley, 1985; Gaillard, 2004; Pommier et al., 2008; see also review of data by Ni et al., 2015) as well as in results of numerical simulations of the (vs/vP)T of magmatic liquids (Dufils et al., 2018). The activation energy of electrical conductivity also increases with increasing pressure as can be observed, for example, in the increased slope of the log s versus 1/T relationship (Fig. 9.113B), a feature that is consistent with the concept that the hindrance energy contribution to activation energy increases with increasing pressure. This pressure effect is, however, likely to diminish with increasing pressure as the compressibility of melts and magma decreases with increasing pressure (see also Chapter 10). It is clear from the experimental data, however, that the NBO/T is not only variable governing the pressure dependence. This can be seen in the (vs/vP)T behavior of the alkali-rich tephritic and phonolitic magmatic liquids (Fig. 9.114). It is possible that this feature is in response to how tetrahedrally coordinated Al3þ in the magmatic liquid structures is chargeebalanced. Among the magma compositions for which data are shown in Fig. 9.114, the phonolite magma has the highest proportion of Al3þ charge-balanced with alkali metals.39 Extension of conductivity data of melts to pressures greater than about 3 GPa relies exclusively on results of numerical simulations (Ghosh and Karki, 2017; Karki et al., 2018). From such results, the electrical conductivity appears to continue its increase with pressure until it approaches 20 GPa followed by a conductivity decrease with a further pressure increase (Fig. 9.115). Such an evolution, probably is driven by Mg2þ being the charge carrier in the MgSiO3 melt of those studies. The decreasing electrical conductivity with pressure above w20 GPa likely reflects the increased oxygen coordination number for Mg2þ as the pressure is increased (Ghosh and Karki, 2017) in much the same manner as diffusion and melt viscosity vary with pressure as discussed earlier in this chapter (Sections (9.3.1.4), (9.3.2.3), and (9.5.2)).

9.7.3 Electrical conductivity and volatiles Characterization of electrical conductivity of hydrous magmatic liquids and crystal þ liquid mixtures is particularly relevant for understanding the behavior of magmatism in subduction 39 This preference results from the increased stability of aluminate complexes in aluminosilicate melts the more electropositive the charge-balancing cation (Navrotsky et al., 1982). Alkali metals are more electropositive than alkaline earths, for example, and within each group the cations become more electropositive the greater their ionic radius.

726

Chapter 9 Transport properties

1

A Electrical conductivity, logσ, S/m

Electrical conductivity, logσ, S/m

2

1 Basalt melt Rhyolite melt Andesite melt

0

-1

-2 10

20

30

40

50

60

B

0.5 0.1 M

Pa

0.48 G

Pa

0 2.1

1.28 0 Pa 1.7 G GPa .65 GP a Pa

9G

Basalt melt

-0.5

-1 5.9

Pressure, GPa

6.1 6.3 6.5 6.7 4 -1 Temperature, 10 /T (K )

6.9

FIGURE 9.113 Electrical conductivity of magmatic liquids as a function of pressure and temperature. (A) Electrical conductivity of basalt, andesite, and rhyolite melt as a function of pressure. (B) Electrical conductivity of basalt melt as a function of temperature at different pressures as indicated on individual curves. Modified from Tubyrcszy and Waff (1983), Ni et al. (2015).

FIGURE 9.114

Modified after Pommier et al. (2008).

0.8 Electrical conductivity, logσ, S/m

Comparison of the effect of pressure on electrical conductivity of trachyte and phonolite melts.

0.6 Tephrite

0.4

melt

0.2 0.0 Phonolite

melt

-0.2 -0.4 0

100

200 Pressure, MPa

300

400

9.7 Electrical conductivity

727

Electrical conductivity, logσ, S/m

FIGURE 9.115 Calculated electrical conductivity of MgSiO3 melt as a function of pressure.

3

Modified from Ghosh and Karki (2017).

2

1

0

20

40

100 60 80 Pressure, GPa

120

140

zones, in general, and the evolution of felsic magma chambers in particular (Ni et al., 2011; Laumonier et al., 2015; Guo et al., 2016). Electrical conductivity data from volatile-bearing silicate melts and magma have been reported predominantly for H2O-bearing melt systems (Gaillard, 2004; Pommier et al., 2008; Fanara and Behrens, 2011; Ni et al., 2011a). This emphasis on H2O is because the H2O content in the magma can have significant effect on not only on the electrical conductivity of the magmatic liquid (e.g., Guo et al., 2016), but also on how the proportions of crystals and gas bubbles evolve as a function of the H2O in a magma chamber (Laumonier et al., 2015). An expression has been proposed for the electrical conductivity of magma, smagma, that incorporates proportion of crystals and melt, Xcryst and Xmelt, together with conductivity of the melt and crystals, smelt and scryst. Presumably, any effect of volatiles dissolved in the magma would be incorporated in the smelt-values (Glover et al., 2000; Pommier et al., 2008):
 log 1Xm =ð1Xmelt Þ m þ smelt Xmelt ; (9.27) smagma ¼ scryst Xcryst ½ ð melt Þ and m is the so-called Archie cementation component, which was set to m ¼ 1.05 by Pommier et al. (2008), for example. In comparison, among electrical conductivity data to evaluate effects of other volatiles, CO2 appears to be the only such component. Electrical conductivity of CO2-bearing magma is most relevant to deep upper mantle melting where CO2-rich environments give rise to partial melts ranging from carbonatitic to nephelinitic (see Chapter 2; Sections (2.2.5) and (2.2.7)). Given the significant structural and compositional differences between silicate and carbonatite melt, conductivity data for carbonatite magma is needed to model deep mantle melting.

728

Chapter 9 Transport properties

9.7.3.1 Electrical conductivity and H2O From an experimental perspective, conductivity measurements of volatile-bearing melts for carried out mostly in the presence of H2O. Such data exist to pressures near 10 GPa (Gaillard, 2004; Fanara and Behrens, 2011; Ni et al., 2011a,b; Poe et al., 2012; Guo et al., 2016, 2017). Subordinate amounts of experimental data describing effects of CO2 on magma conductivity also exist (Guo et al., 2021). Results of numerical simulation of conductivity of CO2-rich silicate melts have been reported for conditions to much higher pressure (Ghosh and Karki, 2017). There are also scattered data on electrical conductivity of carbonatite magma at high pressure and temperature (Gaillard et al., 2008). In a review of conductivity data of hydrous magma, Guo et al. (2016) summarized the effect of increasing H2O concentration in magmatic liquids compositionally ranging from hydrous rhyolite and dacite to hydrous basalt and phonolite (Fig. 9.116). Of course, experiments need to be conducted at significant pressures to retain the needed proportions of H2O in the liquid. This means, as can be seen in Fig. 9.116 as well, that pressure effects on conductivity also play a role in the data reflecting the presence of H2O. Those considerations notwithstanding, it would seem that, in general, electrical conductivity of all magma types increases with increasing H2O content, The more felsic (smaller NBO/ T-values) the magma, the more rapidly will the conductivity increase with increasing H2O content. This composition dependence most likely exists because the more felsic a magma, the more effectively will dissolved H2O affect its structure and, therefore, its properties. The activation energy of electrical conductivity decreases as the magma becomes more H2O rich.

9.7.3.2 Electrical conductivity and CO2 From limited experimental data of how CO2 and combinations of CO2 and H2O affect electrical conductivity of nephelinitic magmatic liquid, it has been suggested that increasing CO2 content in FIGURE 9.116

Modified from Guo et al. (2017).

2 Electrical conductivity, logσ, S/m

Influence of H2O on electrical conductivity of various magmatic liquids as indicated on individual curves.

a

/2 GP

400˚C

elt, 1 asalt m

B

1

t, 1350˚C/0.2

phonolite mel

GPa Pa

/1 G

0

-1 0.0

lite rhyo

˚C 000

t, 1

mel

6.0 2.0 4.0 H2O content of melt, wt%

8.0

2.0 2.0 1.0 1.0 0.0 Nephelinite melt

-0.5 -1.0

729

100

A

Activation energy, kJ/mol

Electrical conductivity, logσ, S/m

9.7 Electrical conductivity

B

90 80 70 60

Nephelinite melt

50 6

8 10 12 4 -1 Temperature, 10 /T (K )

14

0

1

2 3 4 5 6 CO2 concentration in melt, wt%

FIGURE 9.117 Effect of CO2 on electrical conductivity. (A) Effect of CO2 on electrical conductivity of nephelinite melt. (B) Effect of CO2 on activation energy of electrical conductivity of nephelinite melt. Modified after Guo et al. (2021).

hydrous magma leads to increased electrical conductivity and decreased activation energy of viscous flow (Guo et al., 2021). It is notable, however, that both the conductivity and activation energy (and activation volume as well) seem to pass through minimum values at intermediate CO2 contents (Fig. 9.117). In the report providing the data summarized in Fig. 9.117, the CO2 solubility in the magmatic liquid was not provided. It is possible, however, that there might have been exsolution of CO2 because the CO2 solubility in silicate melts under these pressure conditions normally is only on the order of a few wt%. There might, therefore, have been exsolution of CO2 at the highest CO2 content of these experiments. Such an effect might be the underlying cause of the minima and maxima in conductivity and activation energy of viscous flow in the nepheliniteeH2OeCO2 magmatic liquid shown in Fig. 9.117. Partial melting of peridotite þ CO2 in the middle and deeper portions of the upper mantle, 35e40 GPa pressure, results in an initial melt of carbonatitic composition (Eggler, 1974; Brey et al., 2006, 2008; Litasov et al., 2014). The very different composition of carbonatite compared with silicate magma results in significantly more conductive carbonatite melt even though the activation energy of carbonate melt conductivity is not greatly affected by carbonate composition (Gaillard et al., 2008; see Fig. 9.118). The conductivity of carbonatite melt is also two to three orders of magnitude greater than that of molten silicate and, of course, many additional orders of magnitude greater than crystalline mantle materials (Fig. 9.119). This effect is, however, a gradual function of increasing CO2 concentration in the melt (Ghosh and Karki, 2017) so that with increasing degree of melting, which leads to a gradual change from carbonatitic to CO2-rich silicate magma (Brey et al., 2008), the conductivity also will gradually decrease. The different electrical conductivity of silicate and carbonatite magma must, of course, also be taken into consideration when modeling electromagnetic observations in terms of degree of melting of peridotite in the presence of volatiles at various depths in the Earth’s mantle.

730

Chapter 9 Transport properties

FIGURE 9.118 (A) Electrical conductivity of various carbonate melts as indicated. (B) Activation energy of electrical conductivity of various carbonate melts as indicated. Modified from Gaillard et al. (2008).

FIGURE 9.119

Modified from Gaillard et al. (2008).

3.0 Molten carbonates

Electrical conductivity, logσ, S/m

Relationship between temperature and electrical conductivity of carbonate melt, molten silicate, hydrous olivine and dry olivine as identified on individual curves.

2.0 1.0 cates

Molten sili

0.0 -1.0

olivine

-2.0

Hydrous

-3.0

Dry oli

vine

-4.5 -2.0 900

1000

1100 1200 Temperature, ˚C

1300

1400

9.8 Concluding remarks

731

9.8 Concluding remarks The transport properties dominating materials transfer in the Earth are viscosity, diffusion, and electrical conductivity. Characterization of magma viscosity is needed for our understanding of transport processes ranging from magma aggregation, ascent, and eruption, to exsolution of bubbles during decompression in volcanic conduits. Those features also will govern the nature of volcanic eruptions. Diffusion operates mostly on smaller scales in which the diffusive transport affects crystallization, exsolution of volatiles from magma, and, at times, isotope fractionation during fluid exsolution. Electrical conductivity is a principal tool with which to characterize melt and fluid distribution a crystalline matrix. The melt properties governing transport processes can be linked to each other via functional relationships. Often, they also can be described in terms of the same melt structural variables and, therefore, bulk chemical composition of magmatic liquids. Pressure and temperature are the other variables causing transport property variability. Magma and melt viscosity, which is inversely correlated with diffusivity of network-forming components (Si4þ, Al3þ, and O2), depends on magma composition, temperature and pressure. At ambient pressure, magma viscosity decreases systematically as the composition becomes more mafic (from rhyolitic to basaltic and komatiitic compositions). Pressure effects on magma viscosity changes from negative to positive in the same order of magma types until sufficiently high pressures are reached where coordination transformation of network-forming components (Si4þ and Al3þ) is reached. The diffusivity of the same compositional variables follows the inverse relationship to pressure. Pressure-induced coordination transformations in the melts at high pressure results in the diffusivity of individual components approaching one another. Activation energy of viscous flow, which is linked to oxygen bonded to Si4þ and Al3þ in magma and melts, decreases as the Al/(Al þ Si) of a magmatic liquid becomes larger. However, the impact of this compositional variable also depends on how tetrahedrally coordinated Al3þ is charge balanced by alkali metals and alkaline earths. In depolymerized melts and magmas (which includes most natural magmatic liquids), a further complication follows from the observation that Al3þ tends to favor fully polymerized structural units in the melts. This preference implies that the more mafic a magma, and therefore, the less polymerized, the greater is this effect. As magmatic liquids become more mafic, this feature is further enhanced by the compositional variables causing charge-balance of tetrahedrally coordinated Al2þ to change from alkali-rich to become dominated by alkaline earths. The transport of network-modifiers such as alkali metals and alkaline earths is decoupled from that of network-formers. The impact of network-modifiers on melt viscosity is much less than that of network-formers because the metal-oxygen bond energy of network-modifiers is only a small fraction of the (Si,Al)eO bond energy. The transport behavior of the former components is, however, central to our understanding of diffusion in silicate melts and magma because most elements of geochemical (and geophysical) interest are network-modifiers. Their transfer behavior also is relevant to our understanding of electrical conductivity because charge transfer usually is accomplished via motion of network-modifying cations. At low pressure, the activation energies of network-modifying cation diffusion and electrical conductivity differ by several orders of magnitude from that of network-formers. However, at pressure corresponding to depths exceeding perhaps 300 km in the Earth, the coordination numbers of oxygen

732

Chapter 9 Transport properties

surrounding network-forming cations (predominantly Si4þ and Al3þ) increase rapidly, which cause bond energy decrease and their activation energy to resemble those of all other cations in the silicate melts. Under such deep Earth conditions, transport properties, be they viscosity, diffusion, or conductivity, also begin to resemble one another. The effects on transport properties by volatiles such as H2O, halogens, and CO2, primarily are those that affect silicate polymerization of silicate melts and magma. The influence of H2O and halogens on magma transport behavior is mostly evident in and near subduction zone settings, whereas CO2 is more important in the upper mantle elsewhere. The effects can be large, up to several orders of magnitude, in the pressure regime from the crust to the uppermost mantle, but become much less important at greater depth, where the melt structure and, therefore, the relationship between magma composition and transport properties become less, often by several orders of magnitude.

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Ardia, P., Giordano, D., Schmidt, M.W., 2008. A model for the viscosity of rhyolite as a function of H2O-content and pressure: a calibration based on centrifuge piston cylinder experiments. Geochem. Cosmochim. Acta 72, 6103e6123. Askarpour, V., Manghnani, M.H., Richet, P., 1993. Elastic properties of diopside, anorthite, and grossular glasses and liquids: a Brillouin scattering study up to 1400 K. J. Geophys. Res. 98, 17683e17689. Baasner, A., Schmidt, B.C., Webb, S.L., 2013. Compositional dependence of the rheology of halogen (F, Cl) bearing aluminosilicate melts. Chem. Geol. 346, 172e183. Bacon, L.R., 1936. Measurements of absolute viscosity by the falling sphere method. J. Franklin Inst. 221, 251e273. Bagdassarov, N.S., Dingwell, D.B., Wilding, M.C., 1996. Rhyolite magma degassing: an experimental study of melt vesiculation. Bull. Volcanol. 57, 587e601. Baker, D.R., 1990. Chemical interdiffusion in dacite and rhyolite: anhydrous measurements at 1 atm and 10 kbar, application of transition theory, and diffusion in zoned magma chambers. Contrib. Mineral. Petrol. 104, 407e423. Baker, D.R., 1993. The effect of F and Cl on the interdiffusion of peralkaline intermediate and silicic melts. Am. Mineral. 78, 316e324. Baker, D.R., 1996. Granitic melt viscosities: empirical and configurational entropy models for their calculation. Am. Mineral. 81, 126e134. Baker, D.R., Watson, E.B., 1988. Interdiffusion of major and trace elements in compositionally complex Cl- and F-bearing silicate melts. J. Non-cryst. Solids 102, 62e70. Baker, D.R., Balcone-Boissard, H., 2009. Halogen diffusion in magmatic systems; our current state of knowledge. Chem. Geol. 263, 82e88. Baker, D.R., Bossanyi, H., 1994. The combined effect of F and H2O on interdiffusion between peralkaline dacitic and rhyolitic melts. Contrib. Mineral. Petrol. 117, 203e214. Baker, D.R., Vaillancourt, J., 1995. The low viscosities of F þ H2O-bearing granitic melts and implications for melt extraction and transport. Earth Planet Sci. Lett. 132, 199e211. Baker, D.R., Conte, A.M., Freda, C., Ottolini, L., 2002. The effect of halogens on Zr diffusion and zircon dissolution in hydrous metaluminous granitic melts. Contrib. Mineral. Petrol. 142, 666e678. Balcone-Boissard, H., Baker, D.R., Villemant, B., Boudon, G., 2009. F and Cl diffusion in phonolitic melts; influence of the Na/K ratio. Chem. Geol. 263, 89e98. Barnes, J.D., Manning, C.E., Scambelluri, M., 2018. The behavior of halogens during subduction-zone processes. In: Harlov, D.R., Aranovich, L. (Eds.), The Role of Halogens in Terrestrial and Extraterrestrial Geochemical Processes. Springer, Cham, Switzerland, pp. 545e590. Bartels, A., Behrens, H., Holtz, F., Schmidt, B.C., 2015. The effect of lithium on the viscosity of pegmatite forming liquids. Chem. Geol. 410, 1e11. Bartholomew, R.F., Butler, B.L., Hoover, H.L., Wu, C.-K., 1980. Infrared spectra of water-containing glasses. J. Am. Ceram. Soc. 63, 481e485. Behrens, H., 2010. Ar, CO2 and H2O diffusion in silica glasses at 2 kbar pressure. Chem. Geol. 272, 40e48. Behrens, H., Yamashita, S., 2008. Water speciation in hydrous sodium tetrasilicate and hexasilicate melts: Constraint from high temperature NIR spectroscopy. Chem. Geol. 256, 306e315. Behrens, H., Zhang, Y., 2001. Ar diffusion in hydrous silicic melts: implications for volatile diffusion mechanisms and fractionation. Earth Planet Sci. Lett. 192, 363e376. Bercovici, D., Karato, S., 2003. Whole-mantle convection and the transition-zone water filter. Nature 425, 39e44. Behrens, H., Hahn, M., 2009. Trace element diffusion and viscous flow in potassium-rich trachytic and phonolitic melts. Chem. Geol. 259, 63e77. Behrens, H., Nowak, M., 1997. The mechanisms of water diffusion in polymerized silicate melts. Contrib. Mineral. Petrol. 126, 377e385.

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Watanabe, N., Yamaya, Y., Kitamura, K., Mogi, T., 2021. Viscosity-dependent empirical formula for electrical conductivity of H2O-NaCl fluids at elevated temperatures and high salinity. Fluid Phase Equil. 549. https:// doi.org/10.1016/j.fluid.2021.113187. Watson, E.B., 1979. Diffusion of cesium ions in H2O-saturated granitic melt. Science 205, 1259e1260. Watson, E.B., 1981. Diffusion in magmas at depth in the Earth: the effects of pressure and dissolved H2O. Earth Planet Sci. Lett. 52, 291e301. Watson, E.B., 1982. Basalt contamination by continental crust: some experiments and models. Contrib. Mineral. Petrol. 80, 73e87. Watson, E.B., 1991. Diffusion of dissolved CO2 and Cl and hydrous silicic to intermediate magmas. Geochem. Cosmochim. Acta 55, 1897e1902. Watson, E.B., 1994. Diffusion in volatile-bearing magmas. Rev. Mineral. 30, 371e411. Watson, E.B., 2017. Diffusive fractionation of volatiles and their isotopes during bubble growth in magmas. Contrib. Mineral. Petrol. 172 (8), 61. https://doi.org/10.1007/s00410-017-1384-7. Watson, E.B., Wark, D.A., 1997. Diffusion of dissolved SiO2 in H2O at 1 GPa, with implications for mass transport in the crust and upper mantle. Contrib. Mineral. Petrol. 130, 66e80. Watson, H.C., Roberts, J.J., 2011. Connectivity of core forming melts; experimental constraints from electrical conductivity and X-ray tomography. Phys. Earth Planet. In. 186, 172e182. Watson, E.B., Sneeringer, M.A., Ross, A., 1982. Diffusion of dissolved carbonate in magmas: experimental results and applications. Earth Planet Sci. Lett. 61, 346e358. Webb, S.L., Courtial, P., 1996. Compressibility of melts in the CaO-Al2O3-SiO2 system. Geochem. Cosmochim. Acta 60, 75e86. Webb, S.L., Banaszak, M., Kohler, U., Rausch, S., Raschke, G., 2007. The viscosity of Na2O-CaO-Al2O3-SiO2 melts. Eur. J. Mineral 19, 681e692. Webb, S.L., Muller, E., Buttner, H., 2004. Anomalous rheology of peraluminous melts. Am. Mineral. 89, 812e818. Whittington, A., Richet, P., Holtz, F., 2000. Water and the viscosity of depolymerized aluminosilicate melts. Geochem. Cosmochim. Acta 64, 3725e3736. Whittington, A., Richet, P., Behrens, H., Holtz, F., Scaillet, B., 2004. Experimental Temperature-X(h2o)-Viscosity Relationship for Leucogranites and Comparison with Synthetic Silicic Liquids, vol. 95. Transactions of the Royal Society of Edinburgh-Earth Sciences, pp. 59e71. Whittington, A., Richet, P., Linard, Y., Holtz, F., 2001. The viscosity of hydrous phonolites and trachytes. Chem. Geol. 174, 209e223. Whittington, A.G., Bouhifd, M.A., Richet, P., 2009. The viscosity of hydrous NaAlSi3O8 and granitic melts: configurational entropy models. Am. Mineral. 94, 1e16. Winkler, A., Horbach, J., Kob, W., Binder, K., 2004. Structure and diffusion in amorphous aluminum silicate: a molecular dynamics simulation. J. Chem. Phys. 120, 384. Winther, K.T., Watson, E.B., Korenowski, G.M., 1998. Magmatic Sulfur Compounds and Sulfur Diffusion in Albite Melt at 1 GPa and 1300e1500C, vol. 83. Amer. Mineral., pp. 1141e1151 Witham, F., Blundy, J., Kohn, S.C., Lesne, P., Dixon, J., Churakov, S.V., Botcharnikov, R., 2012. SolEx: a model for mixed COHSCl-volatile solubilities and exsolved gas compositions in basalt. Comput. Geosci. 45, 87e97. Wu, G., Yazhenskikh, E., Hack, K., Wosch, E., Mu¨ller, M., 2015a. Viscosity model for oxide melts relevant to fuel slags. Part 1: pure oxides and binary systems in the system SiO2eAl2O3eCaOeMgOeNa2OeK2O. Fuel Process. Technol. 137, 93e103. Wu, T., He, S.P., Liang, Y.J., Wang, Q., 2015b. Molecular dynamics simulation of the structure and properties for the CaO-SiO2 and CaO-Al2O3 systems. J. Non-cryst. Solids 411, 145e151.

References

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Wyllie, P.J., Tuttle, O.F., 1964. Experimental investigation of silicate systems containing two volatile components. III. The effects of SO3, P2O5, HCl, and Li2O in addition to H2O on the melting temperatures of albite and granite. Am. J. Sci. 262, 930e939. Xue, Y., Kanzaki, M., 2004. Dissolution mechanisms of water in depolymerized silicate melts: constraints from 1H and 29Si NMR spectroscopy and ab initio calculations. Geochem. Cosmochim. Acta 68, 5027e5057. Xue, Y., Kanzaki, M., 2008. Structure of hydrous aluminosilicate glasses along the diopsideeanorthite join: a comprehensive one- and two-dimensional 1H and 27Al NMR study. Geochem. Cosmochim. Acta 72, 2331e2348. Yoder, H.S., Tilley, C.E., 1962. Origin of basaltic magma: an experimental study of natural and synthetic rock systems. J. Petrol. 3, 342e532. Zelenski, M., Kamenetsky, V.S., Mavrogenes, J.A., Gurenko, A.A., Danyushevsky, L.V., 2018. Silicate-sulfide liquid immiscibility in modern arc basalt (Tolbachik volcano, Kamchatka): Part I. Occurrence and compositions of sulfide melts. Chem. Geol. 478, 102e111. Zimova, M., Webb, S.L., 2007. The combined effects of chlorine and fluorine on the viscosity of aluminosilicate melts. Geochem. Cosmochim. Acta 71, 1553e1562. Zhang, C., Duan, Z., 2009. A model for C-O-H fluid in the Earth’s mantle. Geochem. Cosmochim. Acta 73, 2089e2102. Zhang, G.H., Yan, B.J., Chou, K.C., Li, F.S., 2011. Relation between viscosity and electrical conductivity of silicate melts. Metall. Mater. Trans. B Process Metall. Mater. Process. Sci. 42, 261e264. Zhang, L., Guo, X., Wang, Q., Ding, J., Ni, H., 2017. Diffusion of hydrous species in model basaltic melt. Geochem. Cosmochim. Acta 215, 377e386. Zhang, Y., Ni, H., 2010. Diffusion of H, C, and O components in silicate melts. Rev. Mineral. Geochem. 72, 171e225. Zhang, Y., Ni, H., Chen, Y., 2010. Diffusion data in silicate melts. Rev. Mineral. 72, 311e408. Zhang, Y., Stolper, E.M., 1991. Water diffusion in a basaltic melt. In: AGU-MSA 1991 Spring Meeting. Anonymous. American Geophysical Union, Washington, DC, United States, p. 312. Zhang, Y., Stolper, E.M., Wasserburg, G.J., 1991. Diffusion of a multi-species component and its role in oxygen and water transport in silicates. Earth Planet Sci. Lett. 103, 228e240. Zhang, Y., Xu, Z., Zhu, M., Wang, H., 2007. Silicate melt properties and volcanic eruptions. Rev. Geophys. 45. https://doi.org/10.1029/2006RG000216. Zhang, Y.X., Jenkins, J., Xu, Z.J., 1997. Kinetics of the reaction H2OþO ¼ arrow 2OH in rhyolitic glasses upon cooling: geospeedometry and comparison with glass transition. Geochem. Cosmochim. Acta 61, 2167e2173. Zhao, G., Mu, H.F., Tan, X.M., Wang, D.H., Yang, C.L., 2014. Structural and dynamical properties of MgSiO3 melt over the pressure range 200e500 GPa: ab initio molecular dynamics. J. Non-cryst. Solids 385, 169e174.

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CHAPTER

Equation-of-state of magmatic liquids

10

10.1 Introduction Formation, aggregation, ascent, eruption, and crystallization of magma depend on its equation-of-state (EOS). Magma density governs, for example, whether partial melts in the Earth’s mantle will, in fact, ascend to the surface be it in the Earth or within other planets and moons (Stolper et al., 1981; Ohtani et al., 1995; Agee, 1998, 2008a,b). Density differences in the Earth’s crust often result in magma ascent stagnation at shallow depths thus resulting in magma chambers at a few km depth (Ryan, 1994; Gonzales-Mettado et al., 2008). A number of experimental investigations has led to the conclusion, that partial melts in the deeper portion of the Earth’s upper mantle may be denser than the surrounding crystalline peridotite. This idea, first proposed about 40 years ago (Stolper et al., 1981), initially was based on the observation that the compressibility of basaltic melts, at least at pressures near ambient, is about an order of magnitude greater than that of peridotite minerals (olivine, pyroxenes, spinel, and garnet). It was suggested, therefore, that at depths between perhaps 100 and 200 km in the upper mantle, the density of basaltic magma would exceed that of the surrounding mantle peridotite (Fig. 10.1). Since that time, data from experimental studies have aimed at adding deeper understanding of density and compressibility of magma and shown this crossover to be likely (Agee and Walker, 1988, 1993; Ohtani et al., 1993; Suzuki et al., 1995; Agee, 1998; Suzuki and Ohtani, 2003; Guillot and Sator, 2007; Villeumier et al., 2009). It seems clear, therefore, that a density crossover of magma and surrounding deep upper mantle and below is possible. However, factors that include magma composition, dissolved volatiles, and compressibility as a function of pressure, temperature, and composition of the magma will affect the depth where possible density turnovers may occur. For example, in a study with magma compositions ranging from Midocean Ridge Basalt (MORB) to peridotitic melts, Agee (1998) concluded that there would likely be a density crossover for MORB and komatiite magma at pressures near 8 GPa (w250 km depth) by comparing magma density with that of peridotite comprised primarily of olivine and pyroxenes. With garnet-rich peridotite, the crossover depth would increase, perhaps to pressures corresponding to those of the transition zone in the mantle. For a peridotite magma composition, the depths would increase by 20% or so. With a silicate perovskite-rich mantle,1 the crossover of basalt to

1

Silicate perovskite (Mg,Fe)SiO3 recently was named bridgmanite (Tschauner et al., 2014). The CasiO3 perovskite is now named davemaoite (Tschauner et al., 2021; Fei, 2021). Mass Transport in Magmatic Systems. https://doi.org/10.1016/B978-0-12-821201-1.00011-0 Copyright © 2023 Elsevier Inc. All rights reserved.

755

756

Chapter 10 Equation-of-state of magmatic liquids

FIGURE 10.1 Relationship between density of olivine, diopside, garnet and calculated density trajectory of basalt melt in the upper mantle. The basalt melt density trajectory was based on bulk modulus and its pressure derivative as determined at ambient pressure (shown on diagram). Modified from Stolper et al. (1981).

komatiite composition magma would occur between 40 and 60 GPa pressure. There would not be a density crossover with a peridotite composition melt (Agee, 1998). All those suggested density crossover pressures depend significantly on the values chosen for magma density, bulk modulus, and its pressure derivative. Those considerations notwithstanding, it would not seem unreasonable that a density crossover where magma would be denser than the surrounding peridotite may occur at depths near the boundary between the upper mantle and the transition zone in the Earth. Analogous arguments have been advanced for density crossover in the lunar mantle (Circone and Agee, 1996; Agee, 1998) as well as the mantles of terrestrial planets (Ohtani et al., 1995; Elkins-Tanton et al., 2008; Tro¨nnes et al., 2019). Another challenge facing students of magma transport in planetary interiors is an understanding of how density contrasts between ascending magma and surrounding crystalline materials govern the ascent, stagnation to form magma chambers, or eruption of magmatic liquids (Ryan, 1987, 1994; Cashman, 2004; Gonzales-Mellado et al., 2008). Critical variables in the assessment of these processes also include magma density and compressibility together magma viscosity (see Chapter 9). The density contrast between felsic magma (andesitic, dacitic, and rhyolitic compositions) and surrounding crystalline crust led Ryan (1994) to conclude, for example, that there is a depth of neutral buoyancy between about 1 and 8 km depth (depending on local environment including composition of the

10.2 Equation-of-state (EOS) of glass versus melt

757

FIGURE 10.2 Depth of mantle storage of magmatic liquids whesn reaching the depth of neutral buoyancy in Hawaii, in midocean rift systems and Iceland. Modified from Ryan (1994).

magma itself) where the density of magma and that of the surrounding crystalline crust is the same (Fig. 10.2). This density neutrality can lead to stagnation of magma ascent. Interestingly, this is the depth of many magma chambers containing felsic liquids (Martel et al., 1998; Huber et al., 2019). Of course, concentration of volatiles such as CO2 and H2O can affect these conditions. Decompressiondriven release of volatiles with consequent density changes can complicate this situation further (Dingwell, 1995, 1996; Mysen, 2002). In light of properties and processes such as illustrated earlier, the need for EOS data of magma requires experimental data on magma density, volume, compressibility, and thermal expansion. More broadly, such data are necessary to describe mass transport, driven by density differences between magma and country rock (buoyancy), throughout the history of the Earth. Those relationships form the basis for the EOS discussion of magmatic liquids in this Chapter.

10.2 Equation-of-state (EOS) of glass versus melt Ahead of a discussion of the equation-of-state of silicate melts such as magmatic liquids, it is necessary to address whether the EOS of glass, which is sometimes employed as proxy for the EOS of magmatic liquid (e.g., Gaudio et al., 2008; Murakami and Bass, 2011; Wu et al., 2014; Murakami, 2018), the extent to which volume behavior in temperature-pressure-composition space of silicate

758

Chapter 10 Equation-of-state of magmatic liquids

glasses may approximate the volume behavior of silicate melts, including that of magmatic liquids.2 General features of the glass transition and the glass transition temperature, Tg, were discussed in Chapter 5 (Section 5.2) and will not be repeated here. Suffice to state that the temperature at which a material is transformed from melt to glass is that where the relaxation time of the melt exceeds that of the method used to determine a glass property of interest (see, for example, Chapter 5, Fig. 5.3). Thermodynamic, rheological, and volume properties of melts in glasses operate on essentially the same time scale (Dingwell, 1995; Toplis and Richet, 2000; Sipp and Richet, 2002). The glass transition temperature determined with any of these methods is, therefore, for all practical purposes the same. The glass transition temperature depends on melt composition. It also can be is somewhat dependent on pressure (Rosenhauer et al., 1979). Pressure effects seem comparatively small and can be slightly negative or slightly positive depending on melt composition. This temperature, in turn, varies with bulk melt composition as well as volatiles that may be in solution (Askarpour et al., 1993; Knoche et al., 1994; Richet and Toplis, 2001). It follows, therefore, that Tg depends on the degree of melt polymerization (e.g., Knoche et al., 1994). Although the glass transition temperature tends to decrease as a melt becomes more depolymerized (Knoche et al., 1994), in chemically more complex natural magmatic liquids, additional compositional variables such as Al/(Al þ Si), how Al3þ is charge-balanced in tetrahedral coordination, and proportion of various alkali metals to alkaline earths affect this temperature (Richet and Bottinga, 1986, 1995; Webb, 1992; Knoche et al., 1992; Askarpour et al., 1993; Romano et al., 1994; Dingwell, 1995; Gottsman and Dingwell, 2002). A simple relationship to melt polymerization is not meaningful, therefore, for magmatic liquids. As an example, the temperature-dependent molar volumes, vV/vT, of glass and melt compositions from trachyte to basanite are distinctly different with a discontinuity in vV/vT at the glass transition temperature (Potuzak and Dingwell, 2006, Fig. 10.3). There are differences both in actual molar volume as well as the vV/vT of glass as compared with melts of the same bulk composition. The volume change below the glass transition temperature appears linearly dependent on temperature, whereas above this temperature, the rate of volume change increases and is a nonlinear function of temperature. It is also clear that the density of glass formed by temperature-quenching while at high pressure, differs significantly from the density of the same magmatic liquid recorded while at high temperature and pressure (Fujii and Kushiro, 1977; see also Fig. 10.4). In fact, at least to the 1.5 GPa maximum pressure in the experimental study of tholeiite basaltic melt and glass in Fig. 10.4, the density of glass formed by temperature-quenching melt while at high pressure is greater than that of the melt while at high temperature and pressure. Interestingly, though, this density difference diminishes with increasing pressure, which may suggest that the compressibility of the basalt magma overtakes the quench effect as pressure is increased. Moreover, the density of glass subjected to high pressure while at ambient temperature differs significantly from that of a glass temperature-quenched from high temperature while at high pressure (Seifert et al., 1983; Bouhifd et al., 2001). A more quantitative view of how melt and glass volumes differ depending on their composition can be seen in the behavior of glasses and melts in the simple Na2OeSiO2 system, for example (Knoche 2 Density, r, and molar volume, V, are related via the simple expression, V ¼ molecular weight/r. see also Section 10.3 for a discussion of the most important relationships employed in discussion of equation-of-state of materials including melts and glasses.

10.2 Equation-of-state (EOS) of glass versus melt

759

FIGURE 10.3 Temperature-dependent molar volumes of magma and its glass for different igneous rocks as indicated on individual curves. The glass transition temperature is also indicated with arrow. Modified from Potuzak and Dingwell (2006).

FIGURE 10.4 Density of tholeiite magma determined at temperature and pressure as a function of pressure. Also shown (in dashed lines) is the density of the glass from the same magma determined after temperature quenching while at high pressure. Modified from Fujii and Kushiro (1977).

760

Chapter 10 Equation-of-state of magmatic liquids

FIGURE 10.5 (A) Molar volume of glass and melt in the system NaOeSiO2. The 20 C and 520 C curves indicate molar volume of glass as a function of composition, whereas the 1400 C indicates the molar volume of Na2OeSiO2 melt. (B) Thermal expansion, vV/vT, as a function of composition for Na2OeSiO2 glass at temperatures indicated as a function of composition. Modified from Knoche et al. (1994).

et al., 1994). The molar volume of Na2OeSiO2 glass does not change much, or increases slightly, with increasing Na/Si ratio, and therefore, increasing NBO/Si, of the glass (Fig. 10.5). However, this behavior differs significantly from that of the melts in the same system, which exhibit rapidly increasing molar volume decrease with increasing NBO/Si. The thermal expansivity, vV/vT, below and above the glass transition also differs. The vV/vT of high-temperature melts is more sensitive to composition (and NBO/Si) than their glasses (Fig. 10.5B). The contrasting volume behavior of glasses and their melts is even more pronounced when Al2O3 is added to the system (see review by Dingwell, 1995). For example, for compositions between the feldspar endmembers, CaAl2Si2O8 and NaAlSiO3, thermal expansivity of melts and their glasses does not vary much (Fig. 10.6). However, that behavior changes dramatically when comparing the behavior of melts and their glasses along joins such as CaAl2Si2O8eCaMgSi2O6 and NaAlSiO3eCaMgSi2O6 (Dingwell, 1995). The thermal expansivity of the glasses of those compositions seems essentially invariant with composition, whereas in the molten state the thermal expansion increases dramatically with increasing CaAl2Si2O8 and NaAlSiO3 components (Fig. 10.6). This behavior differs from that of the CaMgSi2O6 endmember, itself, where the density and volume of glasses and their melts differ little (Askarpour et al., 1993). The large differences between glass and melt within those joins likely reflect complex mixing behavior of structurally quite different endmember melts. The feldspar compositions are essentially fully polymerized (Taylor and Brown, 1979a,b), whereas the CaMgSi2O6 glass and melt compositions have NBO/Si ¼ 2 (Etchepare, 1972). The existence of up to three different cations for possible charge-balance of tetrahedrally coordinated Al3þ (Navrotsky et al., 1982; Lee and Stabbins, 2000) adds to this structural and, therefore, EOS complexity. The different volume behavior of melts and their glasses likely reflects the fact that in silicate and aluminosilicate melts (including magmatic liquids), thermal expansion reflects the expansivity of the

10.2 Equation-of-state (EOS) of glass versus melt

761

FIGURE 10.6 Thermal expansion coefficient, a¼(1/V) (vV/vT), of melts and glass and melt (as indicated on curves) for composition along the joins NaAlSi3O8eCaAl2Si2O8, CaAl2Si2O8eCaMgSi2O6, and CaMgSi2O6eNaAlSi3O8 as indicated on diagram. Modified from Dingwell (1995).

silicate network, whereas for glasses, which is not equilibrium state, such structural effect cannot be seen. In fact, the difference between glasses and melts likely also is reflected in the observation that glasses compressed to high temperature retain some of their compression when returned to ambient conditions, whereas this is not so for their melts (Seifert et al., 1983). The different volume behavior of melts and their glasses illustrates why EOS of glass is a poor proxy for silicate melts. The formation history of a glass affects its response to pressure, for example. Quenching rates is one of the parameters causing changes in the physical behavior of a glass. For example, the faster the quenching rate, the higher is the temperature at which the glass structure is frozen in (Moynihan, 1995). Furthermore, volume properties determined at ambient conditions of a glass quenched from high temperature at high pressure differ from that of a glass decompressed at high temperature (e.g., Fujii and Kushiro, 1977; Seifert et al., 1983). Information obtained in such a manner differs from that which can be determined by subjecting a glass to high pressure at ambient temperature (Wu et al., 2014). None of the data thus obtained would provide useful information with which to characterize the EOS of magma and other silicate melts while at the relevant temperatures and pressures. In this chapter we will, therefore, focus on the EOS of silicate melts and magmatic liquid with only cursory reference to their glassy states.

762

Chapter 10 Equation-of-state of magmatic liquids

10.3 Functional relationships Prior to a discussion of the EOS of magma, it is useful to summarize the most commonly employed relationships to describe this behavior. The variable most often determined experimentally is the density, r. At ambient pressure, density most typically is determined by Archimedean methods. With a glass, simple tools such as Berman type balance, for example, can be used with small sample sizes (Berman, 1939), whereas density of silicate melts at the high temperatures typically is obtained by bobs suspended in melts in a high-temperature furnace (e.g., Bockris et al., 1956). Typically, the so-called double-bob method is used (e.g., Lange and Carmichael, 1987). Here, the density of a melt at temperature, T, is: rðTÞ ¼

B1 ðTÞ  B2 ðTÞ : VðTÞ  V2 ðTÞ

(10.1)

In this equation, B1 and B2 and V1 and V2 are buoyancy and volume of bobs 1 and 2, respectively. Density measurements carried out at high temperature and high pressure often are accomplished with the so-called melt-float method in which case small spheres of known densities are observed to sink or float in the silicate melt so that density of the melt can be bracketed (e.g., Agee and Walker, 1988). Alternatively, by determining the settling or floating velocity of at least two spheres of different densities in a molten sample, Stokes law can be employed: rmelt ¼ rsphere 

9vh ; 2r 2 g

(10.2)

with correction for friction effects from the walls of the sample chamber, whose diameter commonly is on the mm-scale. This effect becomes bigger the smaller the diameter of the sample container (Faxen, 1922; Leach et al., 2009). In Eq. (10.2), rmelt and rsphere are densities of the melt and sphere, respectively, v is sinking or floating velocity, h is melt viscosity. r is the radius of a sphere, and g is the gravitational constant. By using two different spheres, two equations of the type in Eq. (10.2) can be solved simultaneously for melt density and melt viscosity (e.g., Fujii and Kushiro, 1977). A third method sometimes used for in situ density measurements at high temperature and high pressure involves the determination of intensity of X-rays passing through a melt sample (e.g., Katayama et al., 1996; Suzuki et al., 2005; Sanloup et al., 2013). By using a reference standard such as diamond, for example, melt density can be obtained from the expression (Suzuki et al., 2005): rmelt ¼

lnIdiamond  lnImelt  þ mdiamond rdiamond :
0 0 2mmelt d lnImelt  lnIdiamond

(10.3)

In this equation, Idiamond and Imelt, are the X-ray intensities after passing through the melt and the 0 0 diamond, respectively, and Idiamond and Imelt the intensities before passing through the melt and the diamond. The mmelt and mdiamond are the absorption coefficients for melt and diamond, and rmelt and rdiamond the densities of melt and diamond, respectively. A comparison of density-pressure relations of peridotite melt obtained in this way with density determined with other methods such as the sink-float method, for example (Agee, 1998; Suzuki and Ohtani, 2003), illustrate how well this density measurement method compares with density results using more conventional density measurement

10.3 Functional relationships

763

FIGURE 10.7 Density-pressure curves of peridotite composition melts determined with the X-ray absorption method (solid line; Suzuki et al., 2005) compared with the density obtained with the “sink-float” method (dashed line: Agee and Walker, 1993). Modified from Suzuki et al. (2005).

techniques (Fig. 10.7). An interesting byproduct of the use of this method by Sanloup et al. (2013) was a positive correlation of the first diffraction peak in the X-ray diffractogram of her in-situ, hightemperature/high-pressure density measurements of basalt melt. Once calibrated, those latter X-ray diffraction data could be used for in situ density measurements while the same was at high temperature and pressure in a multianvil device (e.g., Crepisson et al., 2014; Sanloup, 2016). A more convenient way to describe EOS is by molar volume, Vmelt, which is related to density as: Vmelt ¼

Mmelt ; rmelt

(10.4)

where Mmelt is the molecular weight. For melts, gram formula weight (gfw) is commonly used instead of molecular weight because molecular weight is not a meaningful quantity for melts without specifying additional compositional parameters (number of oxygens is often used for this purpose). Molar volume can also be determined directly. For example, the ClausiuseClapeyron equation describing the slope of the melting (solidus) temperature of a materials as a function of pressure, vT/ vP, incorporates the volume difference between melt and solid on the solidus, DV, and either the enthalpy difference, DH, or entropy difference, DS between melt and solid: DV DV ¼ : (10.5) DS TDH Of course, the volumes of both melt and solid also depend on pressure and temperature, so those variables also need to be considered. The temperature and pressure dependencies of molar volume are described by the compressibility often denoted as b and thermal expansivity, a, respectively: vT = vP ¼

b¼ 

vV ; VvP

(10.6)

764

Chapter 10 Equation-of-state of magmatic liquids

and, vV : (10.7) VvT The bulk modulus, K ¼ 1/b, is often used instead of compressibility. The bulk modulus is determined isothermally, bT, or isentropically, bS. Whereas for crystalline oxides, compressibility and thermal expansion are approximately linear functions of pressure and temperature, for melts, deviations from linearity is common because the melt structure deforms nonlinearly. This nonlinearity is increasingly pronounced the more polymerized a silicate melt. It follows from this observation that although it is often assumed that the bulk modulus of melt is a linear function of pressure, the accuracy of this assumption deviates more and more the more felsic a magma. Therefore, it is common practice to use relationships between the bulk modulus, K, and its pressure derivative, K0 ¼ vK/vP, in order to make the best possible fit to experimental data on melt densities (e.g., Herzberg, 1987; Miller et al., 1991; Agee, 1998; Courtial et al., 1997; Suzuki et al., 1998). The molar volume, thermal expansion, and compressibility can be linked directly with sonic velocity measurements via an expression such as (e.g., Rivers and Carmichael, 1987; Kress and Carmichael, 1991) a¼

V¼

b ; 1 Ta2 þ c2 Cp

(10.8)

where c is sonic velocity and Cp is heat capacity. Melt density also has been derived directly from sound velocity (Polian and Grimditch, 1993; Zha et al., 1994): ZP   rðPÞ ¼ rðP0 Þ þ g Vp2  4 = 3VS2 vP;

(10.9)

P0

where rðPÞ and rðP0 Þ are densities at pressure, P, and at reference pressure, P0, the g is the ratio of the isothermal to adiabatic bulk modulus. Finally, another very useful variable is partial molar volume of individual components in chemically more complex melts and magmatic liquids. The partial molar volume, V i ; is defined as: V i ¼ vV=vni ;

(10.10)

where V is the molar volume of the melt system, and ni denotes the concentration change (in moles) of component, i. The partial molar volume, V i ; in principle could be linked to molar volume of a melt or a glass via the simple summation: V¼

i X i¼1

where Xi is mol fraction of component, i.

Xi V i ;

(10.11)

10.3 Functional relationships

765

Ideally, Eq. (10.11) could be used to calculate the molar volume of silicate melts and magma provided, however, the vV/vni is independent of composition, temperature, pressure or any other variable affecting the state of a melt system. Unfortunately, this is not the case because the melt structural roles of some components such as in particular Fe3þ, Al3þ, and Ti4þ, depend on all those variables (See Chapter 5, Sections (5.3.2), (5.3.5), and (5.4.2.1)). In addition, the structural roles of those three components depend on their concentration, and abundance of network-modifying and, for Al3þ and Fe3þ, the electronic properties3 of charge-balancing metal cations (Dingwell, 1992; Lee and Stebbins, 2000; Mysen et al., 1984; Johnson et al., 1999; Mysen and Neuville, 1995; Farges, 1999). In addition, the number of oxygens in the oxygen coordination spheres surrounding these cations (oxygen coordination number) depends on both temperature and pressure (Lee et al., 2012). Modifications of Eq. (10.11) have been proposed to try to accommodate partial various molar volumes of Ti4þ, Fe3þ, and Al3þ, which may not be the same for all compositional environments (Bottinga et al., 1982; Lange and Carmichael, 1987, 1989; see also Chapter 5, Sections (5.3.4), (5.3.5), and (5.3.2.1) for more discussion of the structural roles of these cations in silicate melts). For example, Lange and Carmichael (1987) proposed to accommodate Ti4þ with the modification: V¼

i X i¼1

Xi V i ; þ XNa XTi V NaTi ;

(10.12)

where V NaTi is the partial molar volume of TiO2 in Na-bearing silicate melt. This is, however, a simplification because the partial molar volume of TiO2 depends on the kind of network-modifiers, in particular whether the dominant modifiers are alkali metals or alkaline earths (Dingwell, 1992; see also Mysen and Richet, 2019, Chapter 12, for a detailed review of the structural behavior of Ti4þ in silicate melts). The partial. molar volume of Ti4þ in silicate melts also depends on temperature and TiO2 concentration because its structural behavior changes as a function of its concentration. Aluminum in silicate melts also has variable partial volume depending on how it is chargebalanced in tetrahedral coordination (see Chapter 5, Section (5.3.4)). This volume behavior was noted as early as 1972, when Bottinga and Weill (1972) developed their model for melt viscosity. The structural behavior of Al3þ in aluminosilicate melts was incorporated in the melt volume model by Bottinga et al. (1982, 1983) who proposed an expression such as: ! P i X j¼1 Xj Kj c Xi V i ; þXk V þ Xk P V¼ ; (10.13) j¼1 Xj i¼1 where Vc is a constant, Xj is the mol fraction of the component, j, requiring charge-balance and Kj are the constants associated with the components requiring charge-balance. The component, j, can be either Al3þ or Fe3þ, for example. Finally, temperature and pressure effects on the partial molar volume of oxide components could be taken into consideration by adding temperature and pressure elements to form an expression such as:

3 The term “electronic properties” is often used instead “ionization potential,” for example. In both cases, in this chapter as well as elsewhere in this Book, when using this term, it refers to the ratio, Z/r2, where Z is formal electric charge and r is the ionic radius. The latter radius throughout this Book is that from Shannon and Prewitt (1969).

766

VT ¼

Chapter 10 Equation-of-state of magmatic liquids

i X i¼1



   Xi V i;TðreferenceÞ þ vV i = vT T  Treference þ V i;PðreferenceÞ þ vV i = vP P  Preference ; (10.14)

where the subscript reference refers to reference partial molar volume,  temperature,  and pressure. Of course, even an expression such as (10.14) implicitly assumes that vV i vT and vV i vP are constant in the temperature and pressure intervals, (T-Treference) and (P-Preference), respectively. However, vV i = vT  and V i vP can vary with pressure, and temperature, respectively, in light of the numerous structural expansion and compression mechanisms in existence in silicate melts.4 Finally, none of the suggested expressions take into considerations mixed alkali effects. Of course, to determine all these variables for each and every melt and magma compositions of interest is unrealistic. It is, therefore, necessary to characterize what structural features affect the variables and to build models and expressions with this in mind. A somewhat different approach to how EOS of magma that can be calculated from melt composition was proposed by Ghiorso (2004a). From a calibration based on published EOS data summarized in Ghiorso (2004a,b) he stated that his model can be used to about 40 GPa and 2500 C. Interested readers are referred to the original Ghiorso-papers for a detailed description of this model (Ghiorso, 2004a,b,c; Ghiorso and Kress, 2004). It is too complex and comprehensive for a summary in this chapter.

10.4 Equation-of-state of magmatic liquids Density and volume of magmatic liquids as a function of chemical composition, temperature, and pressure, have been subject to considerable experimental study because density contrasts between magma and crystals in magma suspension, and between magma and country rock together with viscosity behavior described in Chapter 9, are all critical to our understanding of the physics and chemistry of magmatic transport processes. Here, as in previous Chapters, we will first summarize data from natural magma compositions, and then, from the behavior in chemically simpler model systems, address how chemical composition controls melt structural features particularly relevant to our understanding of the EOS of natural magma.

10.4.1 EOS of natural magma, composition, and temperature An expression such as Eq. (10.11) to a first approximation addresses effects of bulk chemical composition on the molar volume of magmatic liquids. Therefore, before addressing more detailed experimental data, a broad overview of molar volume information from results of calculations using Earthchem.org as a source of magma compositions. From those calculations, the molar volume of natural magmatic liquids show distinct distribution, at times resembling a Gaussian distribution, within tholeiite, andesite, phonolite, and rhyolite magma (Fig. 10.8). The average molar volume for each group of rocks increases the more felsic the magma The complex structural behavior of Al3þ and consequent effects on EOS of aluminosilicate melts (including natural magmatic liquids) were reviewed in detail in Chapters 8 and 9 of Mysen and Richet (2019). 4

10.4 Equation-of-state of magmatic liquids

767

(24.2  0.8, 25.9  0.8, 27.9  1.1, and 27.9  0.5 cm3/mol for tholeiite, andesite, phonolite, and rhyolite melt compositions, respectively). Instead of using rock names as a discriminant, we can employ the degree of melt polymerization, NBO/T, which at ambient pressure can be calculated from bulk composition of the magma.5 Expressed in terms of molar volume as a function of NBO/T of the magmatic liquids, their molar volumes decrease systematically with increasing degree of melt polymerization Fig. 10.8. An evolution based on the NBO/T-values is evident at least in part because the partial molar volume of nonbridging oxygens is smaller than that of bridging oxygens (Bottinga and Richet, 1995) so that the greater the NBO/T of magmatic liquids, the smaller their molar volume. The volume relationship of natural magmatic liquids for any NBO/T-value does show a spread of about 1e2 cm3/mol (Fig. 10.8B). This spread may exist because even though a major control on melt volumes is the proportion of nonbridging oxygens, other factors such as alumina content, the type of charge-compensation of tetrahedrally coordinated Al3þ, and the electronic properties of the networkmodifying cations also contribute to melt structure and, therefore physical and chemical properties of magmatic liquids. A simple relationship between volume and Al/(Al þ Si) ratio alone does not show much of a correlation even at constant bulk melt NBO/T (Fig. 10.8C). This lack of significant relationship with Al/(Al þ Si) most likely reflects the fact that the electronic properties of the charge-balancing cations has important influence on the partial molar volume of Al2O3 in melts, a feature seen clearly in volume relationships of ternary aluminosilicate melts.6 Additional refinements not taken into consideration in the data summary in Fig. 10.8C is that most, and perhaps all of the Al3þ resides in Q4 species in aluminosilicate melts such as natural magmatic liquids, but the details of this distribution vary as a function of the nature of the charge-balancing cations as well the overall degree of melt polymerization, NBO/T (Mysen et al., 1981, 2003; Merzbacher et al., 1990). Moreover, as the partial molar volume of each of the Qn-species must be different because of their different number of bridging and nonbridging oxygens, any variation in Qn-species abundance driven by overall NBO/T, different network-modifying cations or Al3þ charge-balance will cause the molar volume to change. It follows from these structural considerations that relationships between molar volume of magmatic liquids and their Al/(Al þ Si) also will depend on the bulk composition of the magma. The general volume/density trends of magmatic liquids summarized in Fig. 10.8, can be seen in more detailed experimental work on density of magma as a function of their composition and temperature (Lange and Carmichael, 1987, 1990; Toplis et al., 1994; Courtial et al., 1997; Potuzak and Dingwell, 2006; Guo et al., 2014). Effects of pressure will be addressed in Section 10.4.2 immediately following the current section.

Details of how the NBO/T-values are calculated from chemical composition of silicate melts can be seen in Section (5.3.1) of Chapter 5. Such calculations can be conducted with confidence at or near ambient pressure where there is sufficient melt structural information available for this purpose, and where coordination transformation of the cations in the magmatic liquids do not take place. It must be recalled, however, once coordination transformations occur, which typically begins ate a few GPa pressure (Mysen and Virgo, 1985; Lee et al., 2012), the NBO/T-calculations become much less certain because of the much less comprehensive data base on effect of pressure on silicate melt structure for compositions relevant to magmatic liquids. 6 This feature was discussed for ternary aluminosilicate melts in Chapter 8 of Mysen and Richet (2019), and, in particular, is summarized in their Fig. 8.27. Readers interested in these details are referred to that information. 5

FIGURE 10.8 Molar volume of magma as a function of magma composition calculated with the method of Bottinga et al. (1982) from magma compositions from Earthchem.org. (A) Distribution of molar volumes of a few examples of magma types. (B) Molar volumes of magma as a function of their melt NBO/T. (C) As a function of their Al/ (Al þ Si) in the NBO/T-range between 0.24 and 0.26. Modified from Mysen and Richet (2005).

10.4 Equation-of-state of magmatic liquids

769

FIGURE 10.9 Density of magma as a function of temperature and oxygen fugacity. (A) Densities of magma types as indicated on diagram of various magmatic liquids as a function of temperature in the fO2-range between that of the IW (iron-wu¨stite) and MH (magnetite-hematite) oxygen buffer. (B) Calculated density-temperature relations of various magma types as indicated. (A) Modified from Lange and Carmichael (1987). (B) Modified from Guillot and Sator (2007).

Although the availability of density data of natural magmatic liquids is nowhere as comprehensive as indicated by the results of calculations in Fig. 10.8, in general, similar trends as the calculated results in Fig. 10.8 can be seen. For example, decreasing density as magma becomes more felsic remains in the experimental data base of natural magma (Courtial et al., 1997; Lange and Carmichael, 1987; Guillot and Sator, 2007; and review by Ghiorso, 2004b; see also Figs. 10.9 and 10.10). Magma of peridotite composition always is the densest among the main types of magmatic liquids with its density increasing further as its Mg/(Mg þ Fe) decreases. This latter compositional effect would be expected, of course, given the greater atomic mass of Fe compared with Mg. In fact, even within the relatively narrow composition range and NBO/T-values from komatiite to peridotite, the magma density at any temperature varies by several percent depending on the Mg/(Mg þ Fe) (Fig. 10.10). Temperature-dependent magma density often increases nearly linearly with increasing temperature, but it is also clear that as a magmatic liquid becomes more felsic the rate of change of magma density with temperature decreases (Fig. 10.11). It is no surprise, therefore, that as fractional crystallization proceeds and temperature decreases while the magma composition shifts toward the more felsic, the magma becomes less and less dense (Lange and Carmichael, 1990; see also Fig. 10.12).

770

Chapter 10 Equation-of-state of magmatic liquids

FIGURE 10.10 Density of various mafic and ultramafic magma, showing in particular the effect of Fe concentration, as a function of temperature. Modified from Courtial et al. (1997).

There are two factors driving this trend. Even though as crystallization and the temperature decreases, increasing magma density would result, the compositional changes toward felsic magma resulting from crystallization have greater effect on magma density than the lowering of the temperature thus leading to the overall density decrease shown in Fig. 10.12. The redox ratio of iron also affects magma density (Lange and Carmichael, 1987; Kress and Carmichael, 1991; Toplis et al., 1994). Increasing in Fe3þ/SFe caused by increasing oxygen fugacity, for example, results in decreased magma density (Fig. 10.11). The þ/SFe increase leads to lower NBO/ T. In fact, the general rule is that the more polymerized a silicate melt, be it a simple system melt or natural magma, its molar volume increases as the magma becomes increasing felsic (and has lower NBO/T-values). This effect is also well illustrated in the relationship between mol fraction of networkmodifying cations and the molar volume of the magma (Fig. 10.13). The linear relationship in Fig. 10.13 does not seem to depend on the type or proportions of network-modifying cations. This is surprising in light of the observation (Kress and Carmichael, 1991) that there is a negative correlation between molar volume per cation and the ionization potential, Z/r2, of the cation (Fig. 10.13B). Granted that there is some scatter in the latter data, but given the relationship in Fig. 10.13B, one might not expect quite as good a correlation as that shown in Fig. 10.13A. Whether this is because simplifications in the numerical simulations that yield the results in Fig. 10.13A or whether this is because

10.4 Equation-of-state of magmatic liquids

771

FIGURE 10.11 Density-temperature evolution of increasingly felsic magma (from basalt to rhyolite; Figures A to C) as a function of temperature in the oxygen fugacity range between four orders of magnitude above to two orders of magnitude below that defined by the nickel-nickel oxide (NNO) buffer. Modified from Lange and Carmichael (1990).

772

Chapter 10 Equation-of-state of magmatic liquids

FIGURE 10.12 Comparison of temperature-dependent basalt magma density with no crystallization and with equilibrium crystallization from temperatures of the liquidus relying on phase equilibrium model described by Ghiorso et al. (1983) Modified from Lange and Carmichael (1990).

of compensating effects in the chemically complex natural magmatic liquids cannot be determined from available information. Even though it is sometimes suggested that the thermal expansion coefficient does not depend on temperature (Lange and Carmichael, 1987, 1990; Courtial et al., 1997), other data such as those used to illustrate volume effects in Fig. 10.3 (see also Potuzak and Dingwell, 2006) indicate that vV/vT actually may decrease with increasing temperature. The latter suggestion would seem reasonable given that expansion of the oxygen polyhedra of silicate melts are not the same regardless of cation type and oxygen ligand number.7 In fact, that is exactly what can be seen in the relationship between thermal expansion and cation ionization potential in Figs. 10.14 and 10.15. Partial molar volumes of individual components are linked molar volumes of silicate melts, be they simple system melts or complex natural magma, via expressions such as discussed under Eqs. (10.10)e(10.14). The discussion in Section 10.3 emphasized the fact that in many magmatic liquids, the partial molar volumes of major oxide components also depend on composition of the magma. In fact, given our knowledge of silicate melt structure, in principle, one might expect that partial molar volumes of all components in silicate melts depend on the composition. For example, the steric hindrance causing specific network-modifying cations to exhibit preferences for specific nonbridging oxygen in the various Qn-species has been reported from 17O MAS NMR spectra of silicate melts (Lee et al., 2005). These differences affect the energetics of metal-nonbridging oxygen 7 This feature has been well demonstrated for crystalline silicates (Hazen and Finger, 1979, 1982). Given the greater flexibility and more open structures of molten silicates and the widely different metal-oxygen bond distances and bond energies, different thermal expansion among different oxygen polyhedra would be expected.

10.4 Equation-of-state of magmatic liquids

773

FIGURE 10.13 Thermal expansion and compressibility as a function of network-modifier. (A) Molar volume of various magmatic liquids as indicated as a function of the mol fraction of network-modifying cation (Ca, Mg, Na, K). (B) Cation compressibility as a function of their ionization potential as defined on horizontal axis. (A) Modified from Guillot and Sator (2007). (B) Modified from Kress and Carmichael (1991).

FIGURE 10.14 Thermal expansion as a function of cation field strength of network-modifying cations in magma as determined by Lange and Carmichael (1990).

774

Chapter 10 Equation-of-state of magmatic liquids

FIGURE 10.15 Volume evolution magmatic liquid of caused by alkaline earths and alkali metals added to haplogranite magma composition. (A) Molar volume as a function of ionization potential of alkali oxides and alkaline earths as indicated on individual curves. (B) Thermal expansion as a function of ionization potential of alkali oxides and alkaline earths as indicated on individual curves. Modified from Knoche et al. (1995).

bonds. These energetic differences, in turn, should result in partial molar volume changes because different magmatic liquids will have different nonbridging oxygen bonds with those different bond energies. That structural feature, in turn, affects the flexibility of the oxygen coordination spheres. This flexibility in the end affects the partial molar volume of the oxides of interest. The influence of bulk chemical composition on partial molar volumes of the various major element oxides (e.g., Lange and Carmichael, 1987, 1990; Kress and Carmichael, 1991) likely also is seen in their temperature- and pressure-dependence. It is notable, for example, that both the partial molar volume and its thermal expansion coefficient can be correlated with their ionization potential, Z/r2, of the cation of interest (Bottinga et al., 1982; Lange and Carmichael, 1990; Knoche et al., 1995; see also Fig. 10.14).8 The partial molar volume decreases and its thermal expansion coefficient increases with increasing Z/r2 of the alkali metal and alkaline earth metal because the more electronegative the cation (higher Z/r2), the stronger is the preference for nonbridging oxygen in the least polymerized of the Qnspecies in the melt. The more depolymerized this species, the greater is its contribution to volume and thermal expansion from the metal-oxygen bonds. The partial molar volume variability of Al2O3 as a function of the electronic properties of the charge-balance of tetrahedrally coordinated Al3þ can be profound (Fig. 10.16). For example, the

8

The partial volume behavior of Al3þ, Ti4þ, and Fe3þ is not discussed here because of the complex and varied nature of their oxygen environments as discussed above.

10.4 Equation-of-state of magmatic liquids

775

FIGURE 10.16 Molar volumes of melts as indicated on curves as a function of their alkalinity index as defined on the horizontal axis. Modified from Knoche et al. (1995).

V Al2 O3 in peraluminous granite melt increases with decreasing peralkalinity index,9 whereas on the peralkaline side of the meta-aluminous join, the V Al2 O3 is insensitive to increasing peralkalinity index. However, when adding up to 20 mol% MgO to the haplogranite melt, for any peralkalinity index value, V Al2 O3 is at least 7% smaller. Moreover, in peraluminous melts, the V Al2 O3 decreases rapidly with increasingly peraluminous compositions (Fig. 10.16). Those trends demonstrate, therefore, how sensitive the V Al2 O3 is to magma composition. It is also noted here that the relative stability of aluminate complexes with different metal cations have different 9

The peralkalinity index is used to describe whether there are excess alkalis plus alkaline earth over that required for Al3þ charge balance, equal to or less than that needed for this purpose. The index, using molar proportions, is defined as [S(Mþ2O þ 0.5 M2þO)]/Al2O3, where Mþ is an alkali metal and M2þ is an alkaline earth. This index does not, however, provide any information on exactly how this charge balance is accomplished. This was discussed in Chapter 5, Section (5.3.2).

776

Chapter 10 Equation-of-state of magmatic liquids

thermodynamic stabilities. This difference, in turn, affects the relative proportions of the aluminate complexes in the magma as well as their thermal and compressional coefficients. Variations of the V Al2 O3 such as illustrated with the data from Knoche et al. (1995) in Fig. 10.16 cannot be accounted for with any of the proposed corrections schemes for Al2O3 contributions to the molar volume of magmatic liquids discussed in Section 10.3. That requires characterization of the linkage between variables such as illustrated in Fig. 10.16 and the partial molar volume of Al2O3 in melts and magmatic liquids. It seems reasonable to assume that effects of temperature and pressure on V Al2 O3 in magmatic liquids likely cause even greater variations in the resulting molar volume of a magma. In fact, from the partial molar volume variations summarized earlier, it seems reasonable to conclude that until we understand how to characterize EOS in terms of how melt and magma structure govern the EOS, one should be extremely careful trying to use fixed molar volume of oxides to compute molar volumes of magmatic liquids and their response to temperature and pressure.

10.4.2 EOS of natural magma and pressure EOS of magmatic liquids at both high temperature and high pressure is central to characterization of crystal settling or flotation, magma separation, and magma ascent processes in the Earth, its moon, and the terrestrial planets. In the Earth’s crust, the most relevant data involve the behavior of basalt to rhyolitic magma EOS relative to those of felsic minerals such as feldspars and quartz (Fujii and Kushiro, 1977; Murase, 1982; Sharpe et al., 1983). At the higher temperatures and pressures and more mafic magmatic liquids in the Earth’s mantle, density, volume, and compressibility contrasts between mafic to ultramafic magma and olivine, pyroxenes, and garnet in the upper mantle and their higherpressure polymorphs in the transition zone and the lower mantle, govern whether or not such magma will rise or sink (Stolper et al., 1981; Rigden et al., 1984; Agee and Walker, 1988; Miller et al., 1991; Ohtani et al., 1998; Ohtani and Maeda, 2001; Suzuki et al., 1995; Suzuki and Ohtani, 2003; Sakamaki et al., 2010). Significant experimental work also has been reported for those relationships in the lunar mantle (Circone and Agee, 1996; Smith and Agee, 1997; Agee, 1998; van der Kaden et al., 2015). To a more limited extent, EOS data exist for magma buoyancy in the interior of other terrestrial mantles (Ohtani et al., 1995; Bertka and Fei, 1998).

10.4.2.1 EOS of magmatic liquids in the Earth’s crust Density and volume data in the composition, temperature, and pressure environment of the Earth’s crust are centered on basaltic and more felsic magma and the relationship between their EOS and those of the major crustal mineral assemblages involving dominantly feldspar compositions, quartz, and femic minmerals such as olivine, pyroxenes and amphiboles. For example, in a study of Kilauea (1921) olivine tholeiite magmatic liquid, Fujii and Kushiro (1977) determined its melt density to 2.0 GPa and the density of the glass formed upon temperature-quenching of this melt to 3.0 GPa (Fig. 10.17). There are two interesting features of those data. First, the density of the magmatic liquid determined in situ while the melt was at high temperature and pressure, and that of its glass formed by temperaturequenching while at high pressure, both show a density discontinuity between 1 and 1.5 GPa.10 10

It is important to remember in this discussion that comments made in Section 10.3 that the pressure/temperature history of glass formation will affect its equation-of-state, including the density information such as illustrated in Fig. 10.17.

10.4 Equation-of-state of magmatic liquids

777

FIGURE 10.17 Density of olivine tholeiite magma and its glass as a function of pressure together with the density evolution of plagioclase with anorthite content indicated (dashed lines). Modified from Fujii and Kushiro (1977).

Interestingly, the density discontinuity of the magma determined in situ about twice as large as that of its glass. Second, there is a large difference between the melt density and that if its temperaturequenched glass ranging from about 10% at ambient pressure (2.61 and 2.85 g/cm3 for melt and glass, respectively) to slightly more than 5% near 1 GPa to essentially no difference at pressures greater than about 1.5 GPa (Fig. 10.17). In an attempt to explain this density behavior, Kushiro (1980) noticed that in the density evolution with pressure of the crystalline equivalent of this tholeiite composition, the transition from a gabbro mineralogy to granulite mineralogy takes place in the same pressure-temperature range as that where the discontinuous density change was observed in the melt and its glass. He proposed that rearrangements of the melt structure somewhat resembling that which takes place in the crystalline materials in the pressure range of the density discontinuity. Another feature of interest in the data in Fig. 10.17 is the crossover of plagioclase density with the tholeiite melt density at pressures less than about 0.6 GPa ( 60 , the liquid will tend to remain at triple junctions such as illustrated schematically in Fig. 11.6. The wetting angle also affects the relationships between porosity and permeability (von Bargen and Waff, 1986; Wark et al., 2003). For given porosity, the smaller the wetting angle, the greater the permeability. In the example of these relationships using permeability of silicate melt in quartzite (Fig. 11.7), for q-values less than 60 and a porosity of 0.02 (2%), a 40 wetting angle decrease from 60 to q ¼ 20 causes the permeability to increase by approximately a factor of 5. A similar 40 angle decrease with 3% porosity (f ¼ 0.03) leads to the permeability to increase by more than 10 orders of magnitude. The q-value and, therefore, the ratio of the two interface energies, ggss , is linked to the solubility in sl the liquid phase of one or more of the components in the solid (Takei and Shimizu, 2003). For example, using experimental data on wetting angles and dissolved components in aqueous fluid in contact with olivine at mantle pressures and temperature, a tripling of the solute in aqueous solvent results in a 25% lowering of the wetting angle of this fluid and peridotite minerals in the 1e8 GPa range (Fig. 11.8). The relationships of solubility and wetting angle in Fig. 11.8 likely reflect the fact that the speciation of components dissolved in aqueous fluids near the interface with mantle mineral surfaces with increasing pressure become increasingly similar to the silicate speciation in the mantle minerals as the silicate solubility in the fluid increases. Such features are seen in the pressure-dependent silicate solubility in aqueous fluids in model mantle system MgOeSiO2, for example (Mysen et al., 2013), which, therefore, lead to decreases dihedral (wetting) angle with increasing pressure (Fig. 11.8). This increasing structural similarity of aqueous fluid and forsterite near at and near the fluid/forsterite

FIGURE 11.5 Effect of deformation in melt distribution in olivine þ basalt melt. (A) Relationship between melt pocket length and melt pocket area. (B) Relationship between area-normalized orientation of melt pockets (degree) as a function of differential stress. (C) Cumulative melt pocket area as a function of melt pocket length as a function of differential stress indicated on individual curves. Modified from Daines and Kohlstedt (1997).

828

Chapter 11 Mass transport

FIGURE 11.6 Example of triple junction with melt and its dihedral angle, q, in contact with olivine. Modified from Cmiral et al. (1998).

FIGURE 11.7 Results of modeling permeability, k, as a function of melt fraction, f, in a partially molten system for different dihedral angles, q, as indicated on individual curves. Modified from von Bargen et al. (1986).

11.2 Porosity, permeability, and transport

829

FIGURE 11.8 Solubility in aqueous fluid (A) and dihedral angles (expressed as the ratio, r ¼ 1/(2cos(q/2)) in forsterite-H2O systems (B) as a function of pressure. Modified from Takei and Shimizu (2003).

interface results in lowering of gsl and, therefore, a decreased q.3 Similar wetting angle developments can be seen when adding small fractions of component that are highly soluble in aqueous fluids to a simple SiO2eH2O system. As an example, the quartz-aqueous fluid dihedral angle decreases with dissolved feldspar component in the aqueous fluid (e.g., Holness, 1995). This effect probably is because the solubility of feldspar components in the fluids is considerably greater than that of just SiO2 (Anderson and Burnham, 1965, 1983). The idealized form of the relationship in Eq. (11.3) is rarely, if ever, a realistic representation of the distribution of liquid (malt and fluid) in a crystalline rock matrix because in rocks, multiple different minerals and different grain size coexist with the liquid phase. As a first step toward more appropriate representation, consider a situation with liquid-filled pores in a two-phase solid environment (solids 1 and 2) (Fig. 11.9). Here, the following relations hold (Wark and Watson, 1998): gs1l g g ¼ s2l ¼ ss ; (11.4) sinq2 sinq1 sinq3

3 The solute in aqueous fluid in equilibrium with forsterite at pressures less than 2e3 GPa is predominantly SiO2, but at higher pressures the Mg/Si ratio in the fluid increases as a positive function of increasing pressure (Kawamoto et al., 2004) until a second critical endpoint near 6e8 GPa is approached (Mibe et al., 2007). The increasing rate of solubility and wetting angle in the higher-pressure regime in Fig. 11.8 probably reflects this approach to the second critical endpoint in the Mg2SiO4eH2O system.

830

Chapter 11 Mass transport

FIGURE 11.9 Definition of triple junctions as associated angles for two different solid phases, 1 and 2, in contact with fluid at the triple junction. Angle q3, is the dihedral angle of the melt in contact with solids, 1 and 2. Modified from Wark and Watson (1998).

Here, the dihedral angle, q3, depends on whether liquid is in contact with (and in equilibrium with) solids 1 or 2 as compared with the situation where liquid is in contact with only one solid phase such as in Fig. 11.6, for example.

11.2.2.1 Wetting angle and composition Whether the liquid is a silicate melt (magma) or fluid such as in the CO2eH2O or contains a salt such as chloride, for example, in general, different wetting angle will result. In general, the angle is smaller in rock/magma environments than in rock/fluid environments (Fig. 11.10; see also Holness, 1997). This difference should not be much of a surprise because the composition and structure of magmatic liquids tend to show much closer resemblance to crystalline silicates than composition and structure of fluids (see also Chapters 5 and 6). It follows, therefore, that the interface energy, gsl, in Eq. (11.3) is much smaller for magmatic liquids than for fluids. In the following I will, therefore, separate the discussion of relationships between composition in fluid-bearing and silicate melt-bearing systems.

11.2.2.1.1 Wetting angle and fluid composition Experimental data that describe the distribution of aqueous fluid (H2O is the only fluid component) in a monocrystalline matrix include the dihedral angle of H2O in contact with major crustal minerals such as quartz, plagioclase, calcite and dolomite (Watson and Brenan, 1987; Hay and Evans, 1988; Laporte and Watson, 1991; Holness, 1992, 1993, 1995; Nakamura and Watson, 2001; Yoshino et al., 2002). Wetting behavior by H2O for additional minerals such as those relevant to mantle mineral assemblages include olivine, pyroxenes, and garnet and their high-pressure polymorphs (Watson et al., 1987, 1990;

11.2 Porosity, permeability, and transport

831

FIGURE 11.10 Summary of dihedral angles in solid þ fluid and solid þ silicate melt systems. Modified from Holness (1997).

Mibe et al., 1998, 1999, 2003; Ono et al., 2002; Yoshino et al., 2007; Matsukage et al., 2017; Liu et al., 2018).4 It is also likely that in some of the experimental studies conducted under upper mantle pressure conditions, the fluid may actually be supercritical.5 This suggestion may apply, for example, to the experimental data reported by Yoshino et al. (2007) and Matsukage et al. (2017). These experiments were reported to be with hydrous melts, but the pressure-temperature conditions of those experiments very likely were greater than those that define the critical points in the chemical systems investigated. For this reason, their data will be included in this section on wetting/dihedral angle and fluid composition even though in the original reports, the authors in both cases referred to this as hydrous liquid. In the simplest of systems, quartz-H2O (fluid), at crustal pressures, the dihedral angle, q, is slightly above 60 . However, this angle decreases rapidly with pressure increasing to those of the deep continental crust and uppermost mantle (Fig. 11.11; see also Watson et al., 1990; Holness, 1992). Interestingly, at fixed total pressure, Watson et al. (1990) also noticed that q decreased as a linear function of temperature and at 1 GPa pressure crosses the 60 threshold at temperatures near 1100 C (Fig. 11.11B). Those pressure and temperature conditions are very near the second critical endpoint in 4

These high pressure polymorphs include majorite garnet, wadsleyite, ringwoodite, silicate perovskite (bridgmanite and davmaoite), and magnesiowu¨stite. 5 In silicate-H2O systems, a fluid is supercritical under pressure-temperature conditions where there is complete miscibility between H2O-rich melt and silicate-rich fluids (above the critical endpoint, c.p.). For systems such as basalt-H2O (eclogiteH2O) and peridotite-H2O, the c.p. typically has been placed between about 4 and 5 GPa and 800e900 C and 1100e1200 C, for basalt-H2O and peridotite-H2O, respectively (Kessel et al., 2005; Mibe et al., 2007).

832

Chapter 11 Mass transport

FIGURE 11.11 Dihedral angle in dunite (olivine)dfluid systems. (A) Dihedral angle in dunite-H2O at 1200 C as a function of pressure. (B) Dihedral angle in dunite-H2O and dunite-CO2 at 1 GPa as a function of temperature. Modified from Watson et al. (1990).

the SiO2eH2O system (Kennedy et al., 1962).6 It is possible, therefore, that the decreased dihedral angle could be linked to the rapidly increasing quartz solubility as the temperature and pressure approached those of the supercriticality just below 1100 C at pressures near 1 GPa. A positive solubility influence on the wetting angle of H2O in systems dominated by silica, may also explain why this angle decreases profoundly as a K- or Na-feldspar components (up to near 7 and 4 wt%, respectively) are added to the SiO2eH2O system (Holness, 1995). As can be seen in Fig. 11.12, solution of a K-feldspar component, in particular, caused a rapid angle reduction with increasing temperature at fixed pressure (0.4 GPa). By adding a mixture of a few percent K- and Na-feldspar component, q also decreased, but at a slower rate than with K-feldspar alone (Holness, 1995). It is possible that this difference is in response to different solubility behavior of those two feldspar components in aqueous fluids under the pressure and temperature conditions of the experiments in Fig. 11.12. The pressure-temperature coordinates of dihedral angle evolution at 0.4 GPa pressure in Fig. 11.12 is well below the pressure-temperature coordinates of the critical endpoint that has been assigned responsibility for the rapidly decreasing q at 1 GPa for the simpler SiO2eH2O system (Fig. 11.11). Moreover, for the pure SiO2eH2O system, the dihedral angle actually increases between about 400 and 600 C before a decrease with further temperature increase is observed (Fig. 11.12A). It is not altogether clear why this latter angle behavior was observed because the temperature effect of SiO2 solubility in H2O under these conditions does not change significantly at different temperatures (Anderson and Burnham, 1965; Manning, 1994). 6

The actual pressure-temperature coordinates of second critical endpoint for the SiO2eH2O system are 0.97 GPa and 1082 C (Kennedy et al., 1962).

11.2 Porosity, permeability, and transport

833

FIGURE 11.12 (A) Dihedral angles in aqueous quartz-rich systems as a function of temperature at 0.4 GPa pressure. Curve marked “quartz þ H2O” is for pure quartz, whereas those marked “quartz þ Na-feldspar þ Kfeldspar þ H2O” and “quartz þ K-feldspar þ H2O” show the dihedral angle evolution with small amounts of the feldspar components added. (B) Dihedral angle in quartzeH2OeCO2 systems at 1 GPa and 950e1150 C as a function of fluid composition. (A) Modified from Holness (1995). (B) Modified from Watson and Brenan (1987).

By adding a second fluid component to H2O such as, for example, CO2 (Watson and Brenan, 1987; Holness, 1992; Holness and Graham, 1995), the dihedral angle, q, increases rapidly with increasing CO2 content at fixed temperature and pressure reaching value near 100 for the pure SiO2eCO2 system (Fig. 11.12B). This large dihedral angle for fluid in the SiO2eCO2 system is consistent with the much lower solubility of SiO2 in CO2 fluid than in H2O fluid (Newton and Manning, 2000). The lack of a pressure effect on q in the SiO2eCO2 system (Holness, 1992; see also Fig. 11.13) would likely imply that in contrast to silica solubility in H2O fluid (e.g., Manning, 1994), the silica solubility in CO2 fluid probably is not significantly pressure-dependent (Newton and Manning, 2000; Shmulovich et al., 2001, 2006). The dihedral angle in mixed fluid systems such as SiO2eH2OeCO2, on the other hand, not only decreases with decreasing CO2/(CO2þH2O) ratio at constant temperature and pressure (Watson and Brenan, 1987; see also Fig. 11.12B), there is also an angle decrease with increasing pressure at pressures above about 0.6 GPa (Fig. 11.13). The lack of pressure-dependent angle changes below about 0.6 GPa is in accord with what would be expected from the continuously decreasing solubility of SiO2 in mixed CO2þH2O fluids as these become more CO2-rich (Newton and Manning, 2000). However, the changing pressure-effect on q from lack of pressure-dependent angle variation below w0.6 GPa to decreasing q with pressure above 0.6 GPa (Fig. 11.13) might suggest more complex activity-composition relations in CO2eH2O fluids at the higher pressures (Eggler and Kadik, 1979; Shmulovich et al., 1980). The experimental data from Eggler and Kadik (1979) suggest, for example,

834

Chapter 11 Mass transport

FIGURE 11.13 Evolution of dihedral angle in quartz þ CO2 and quartz þ H2O þ CO2 with 50 mol% CO2 at 800 C as a function of pressure. Modified after Holness (1992).

that the activity coefficient of H2O in CO2eH2O fluids increases much more rapidly with decreasing mol fraction of H2O in CO2eH2O in fluids at pressures above 0.6e0.7 GPa than at lower pressures. It is possible that this could lead to enhanced SiO2 solubility in such fluids at those higher pressures, thus leading to the decreased wetting angle in this pressure regime as shown in Fig. 11.13. Addition of alkali chloride to H2O results in lowered dihedral angles as a function of alkali chloride concentration at constant temperature and pressure (Watson and Brenan, 1987; Laporte and Watson, 1991; Holness, 1992; Holness and Graham, 1995). Alkaline earth chlorides such as MgCl2 or CaCl2, on the other hand, do not appear to affect the angle greatly, and may, in fact, result in a slight angle increase (Lee et al., 1991). Most experimental studies of wetting angle and salinity have focused on NaCl where the dihedral angle decreases rapidly with increased salinity, but where, however, the extent of this decrease also depends on pressure and the kind of solid in contact with the saline solutions (Fig. 11.14). In the calciteeH2OeNaCl system, for example, the dihedral angle is more sensitive to NaCl at pressures less than about 150 MPa than at higher pressure (Holness and Graham, 1991, 1995). In fact, Holness and Graham (1991) reported a near linear angle decrease as a function of NaCl concentration with perhaps a slight temperature-dependence of this relationship. This low-pressure effect does not, however, extend to higher pressures, where it has been suggested (Holness and Graham, 1995), that the qdecrease becomes less sensitive to increasing NaCl concentration to such an extent that near 40e45 wt % NaCl, q no longer appears to change (Fig. 11.14A). Complex relations between dihedral angle, NaCl concentration, and pressure in the SiO2eH2OeNaCl system (Fig. 11.14B) likely reflect analogously complex SiO2 solubility behavior in

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FIGURE 11.14 (A) Evolution of the dihedral angle of brine (H2O þ NaCl) in contact with calcite below and above 0.25 GPa at 650 C as a function of brine composition (chloride content). (B) Evolution of dihedral angle in quartz þ H2O and quartz þ H2O þ NaCl at 800 C as a function of pressure. (A) Modified from Holness and Graham (1995). (B) Modified after Holness (1992).

H2OeNaCl fluids (Newton and Manning, 2000). Whereas at pressures less than about 300 MPa, there is an SiO2 solubility maximum in solutions with approximately 10e20 mol % NaCl, at higher pressures, this maximum disappears. It would seem likely that this effect is reflected in the changing pressure-dependent dihedral angle distribution in SiO2eH2OeNaCl as a function of NaCl concentration at different pressures (Fig. 11.14B). Although plagioclase is a major component of crustal mineral assemblages, experimental studies of fluid wetting angles, q, involving plagioclase are rare. In one study with anorthite and anorthite-rich plagioclase (Yoshino et al., 2002), there is a general trend of decreasing q with increasing anorthite component in the plagioclase (Fig. 11.15A). Within the pressure-temperature stability field of crystalline anorthite in the CaAl2Si2O8eH2O system (Boettcher, 1970; see also dashed line in Fig. 11.15B), the q ¼ 60 from about 1.2 GPa at the intersection between the q ¼ 60 curve and the breakdown of anorthite to zoisite þ kyanite þ H2O near 700 C/1.2 GPa to about 1200 C and 0.8 GPa where the 60 isopleth intersects the incongruent melting curve of anorthite (Boettcher, 1970): anorthite þ vapor ¼ corundum þ liquid.

(11.5)

From the limited q-data for aqueous fluid in contact with anorthite (Yoshino et al., 2002; see also Fig. 11.15A), it is possible that the pressure-temperature trajectory of the 60 -isopleths (thick line for the anorthite-H2O system in Fig. 11.15B) shifts to higher temperatures and pressures when the anorthite component of the plagioclase decreases. It must be emphasized, however, that the experimental data extend from pure anorthite to only about 95% of the anorthite component (An) in plagioclase, so extrapolation to lower An component concentrations in plagioclase is very uncertain. It

836

Chapter 11 Mass transport

FIGURE 11.15 Dihedral angle in plagioclase-H2O fluid systems. (A) Dihedral angle as a function of plagioclase composition in the 0.8e1.2 and 800e1000 C pressure and temperature ranges, respectively. (B) Pressure-temperature relations of various dihedral angles as indicated for the system anorthite-H2O with the limiting stability relations in the CaAl2Si2O8eH2O system. Modified from Yoshino et al. (2002) and Boettcher (1970).

may be, for example, that solution mechanisms of plagioclase in aqueous fluids change as the albite component increases because the solution behavior of NaAlSi3O8 in H2O fluid may be quite different from that of CaAl2Si2O8 in H2O. Although such solubility data for CaAl2Si2O8 do not appear to exist, from the solubility behavior of Ca3Al2Si3O12 in aqueous fluids (Newton and Manning, 2007), it would seem that the Ca2Al2Si2O8 solubility likely is considerably less than that of NaAlSi3O8 (Anderson and Burnham, 1983). Such different solubilities depending on plagioclase composition would mean that the increasing wetting angle of in the plagioclase-H2O system in the initial high-An component composition range (Fig. 11.15) is likely to change to lowering of q as the plagioclase becomes more albitic. The wetting angle of carbonate minerals (calcite, dolomite, magnesite) in H2OeCO2 fluid environments for the most part exceeds the 60 C limit (Holness and Graham, 1995). There is, however, an intermediate XCO2 ¼ CO2/(CO2þH2O) value in the CaCO3eH2OeCO2 system with XCO2 between about 0.2 and 0.6 where q < 60 C (Fig. 11.16) This minimum appears, however, also to depend on pressure, so there is a rather narrow XCO2-pressure environment (w50e200 MPa) where q < 60 (Fig. 11.16B). For carbonates other than calcite, existing experimental data indicate that the wetting angle always exceeds 60 C. This situation likely changes with temperature, and probably also when chlorides are added to the solution (Holness and Graham, 1995). The q-data for H2OeCO2eNaCl fluids in an olivine matrix within the pressure range of the upper mantle appear considerably more extensive than for any of the typical crustal minerals such as quartz, feldspar, and carbonates discussed in previous paragraphs (Watson and Brenan, 1987; Mibe et al., 1998, 1999; Yoshino et al., 2007; Liu et al., 2018). Under crustal pressure and temperature conditions,

11.2 Porosity, permeability, and transport

837

FIGURE 11.16 Dihedral angle of fluid in carbonateeH2OeCO2 systems. (A) Dihedral angles for various carbonate minerals indicated with H2O þ CO2 fluid as a function of fluid composition at 0.1 GPa and 650 C. (B) Dihedral angle contours in the calcilateeH2OeCO2 system as a function of pressure and fluid composition at temperatures near 650 C. Modified from Holness and Graham (1995).

the dihedral angle in the olivine-H2O system exceeds 60 (Mibe et al., 1998, 1999). It does, however, decrease relatively rapidly with increasing temperature whether at crustal or upper mantle pressures, and decreases particularly rapidly at mantle pressure and temperature conditions where the olivineH2O system approaches and perhaps exceeds the supercritical conditions (Mibe et al., 1998, 1999; Yoshino et al., 2007; Huang et al., 2020; see also Fig. 11.17). As for other systems discussed above, the q-angle evolution in the olivine-H2O system with pressure (and possibly temperature) reflects increases silicate solubility in H2O fluid in the MgOeSiO2 system with increasing pressure (Zhang and Frantz, 2000; Newton and Manning, 2002; Kawamoto et al., 2004) with attendant changes of the silicate structural species in the fluids as temperature and pressure change (Mysen et al., 2013). The observation that the Mg/Si ratio in fluids the MgOeSiO2eH2O system increases rapidly with pressure at pressures above about 2e3 GPa (Kawamoto et al., 2004) does not seem to affect the pressure-dependent evolution of the dihedral angle because q remains a linear function of pressure to at least 7 GPa (Yoshino et al., 2007, Fig. 11.17C). This observation would suggest that the main structural feature governing this angle and, therefore, the surface energy of the fluid/solid interface in this system, is the silicate abundance and silicate speciation in the fluid. However, it is also to be remembered that other data (Takei and Shimizu, 2003, Fig. 11.8) would imply a non-linear evolution with pressure of the dihedral angle between aqueous fluid and olivine crystals in this pressure range. It is not clear why these differences (Figs. 11.8 and 11.17) exist. Addition of CO2 or chloride to aqueous fluid in equilibrium with olivine, leads to changes in wetting angles that are qualitatively similar to those in fluids in contact with other silicate minerals

FIGURE 11.17 Dihedral angles of aqueous fluid and hydrous melt an olivine matrix (see also text, however, for a discussion of whether or not the hydrous melt at high pressure may be a supercritical fluid) as a function of temperature and pressure. (A) Dihedral angle of aqueous fluid in the olivine-H2O system as a function of temperature at pressures indicated. (B) Dihedral angle of aqueous fluid in the olivine-H2O system as a function of pressure at temperatures indicated. (C) Dihedral angle of aqueous fluid in the olivine-hydrous melt system as a function of pressure at temperatures indicated, but see also text for discussion of melt versus supercritical fluid. (A, B) Modified from Mibe et al. (1999). (C) Modified from Yoshino et al. (2007).

11.2 Porosity, permeability, and transport

839

(Watson and Brenan, 1987; Huang et al., 2020). This angle increases as the CO2 content increases and more rapidly the higher the CO2 concentration in the fluid (Fig. 11.18). Although little is known about the solubility behavior of olivine in CO2-rich fluids under mantle pressure and temperature conditions, the general trend seen in Fig. 11.18 would lead to the suggestion that there are but minor chemical interactions between the CO2 and the olivine. Therefore, it would seem that at least in the uppermost mantle, the wetting angle in the olivineeH2OeCO2 system remains greater than 60 . This situation changes at higher pressures as the 60 limit is crossed between 2 and 3 GPa with XCO2 in the 0.33e0.5 range (Fig. 11.18B). This crossover probably occurs at even higher CO2 concentrations at higher pressure, but relevant experimental data do not appear to exist. A few q-data also exist for H2O-chloride solutions in contact with major mantle minerals (Liu et al., 2018). In the olivineeH2OeNaCl system, for example, the dihedral angle of fluid in contact with olivine decreases rapidly from above 70 in pure H2O at 1 GPa and 800 C to less than 60 with less than 10 mol% NaCl in solution (Fig. 11.19). However, there appears to be little or no angle change between about 10 and 50 mol% NaCl in aqueous solution (Fig. 11.19). This situation likely reflects complex solubility behavior of olivine in NaCleH2O fluids perhaps involving a combination of chloride complexing as well as formation of silicate complexes. Formation of Mg-bearing chloride complexes in the fluid is possible because forsterite solubility in saline fluids increases with increasing chloride concentration (Macris et al., 2020; see also Chapter 6, Section 6.4.3). The wetting angle of pyroxenes þ H2O and garnet þ H2O are significantly greater than those of the main upper mantle mineral phase, olivine (Ono et al., 2002; Mibe et al., 2003; Liu et al., 2018). From the summary of existing q-data by Liu et al. (2018), the angles in both the clinopyroxene-H2O and

FIGURE 11.18 (A) Dihedral angle in olivineeH2OeCO2 at 1 GPa as a function of fluid composition. (B) Dihedral angle in olivine þ orthopyroxene þ magnesiteeH2OeCO2 at 3 GPa as a function of fluid temperature. Modified from Huang et al. (2020).

840

Chapter 11 Mass transport

FIGURE 11.19 Dihedral angle in olivineeH2OeNaCl at 1 GPa and 800 C as a function of fluid composition. Modified from Huang et al. (2020).

garnet-H2O systems remain at or above 60 at least to pressures near 10 GPa (Fig. 11.20). In fact, from the experimental data of Mibe et al. (2003), it would appear that clinopyroxene-H2O and garnet-H2O angles remain essentially identical and more or less independent of pressure, at least to the approximately 5 GPa pressure in the Mibe et al. (2003) experimental study (Fig. 11.21A). Those results differ slightly, however, from those of Matsukage et al. (2017) (Fig. 11.21B and C). From the latter experimental results, the dihedral angle in the garnet-H2O environment increases with pressure to a maximum value at pressures near 12 GPa (Fig. 11.21B). The actual dihedral angle at those pressures was, however, reported to be significantly dependent on temperature, with q < 60 at temperatures above approximately 900 C, whereas that of clinopyroxene remained at or above 60 in the same temperature range (Fig. 11.21C). Th clinopyroxene-H2O and garnet-H2O dihedral angle behavior led to the conclusion that in eclogite þ H2O systems in a subducting slab containing dominantly basalt composition,7 the wetting angle of H2O would remain at or above 60 at least to depths between 200 and 300 km (Matsukage et al., 2017). There appears, however, to be a reversal for this q-trend with pressure at higher pressures (Liu et al., 2018). Under those higher-pressure conditions, the q of both the clinopyroxene-H2O and garnet-H2O systems decreases below 60 and increasingly so with increasing temperature (Fig. 11.21D). However, under these latter conditions, pressure seems to have less effect than temperature (Matsukage et al., 2017; see also Fig. 11.21C and D).

7

Basalt compositions at subsolidus temperatures of hydrous basalt composition at pressures above about1.5e2.0 GPa will be comprised of eclogite mineralogy [jadeitic clinopyroxene and (almandine þ pyrope)-rich garnet (Yoder and Tilley, 1962; Green and Ringwood, 1967)].

11.2 Porosity, permeability, and transport

841

FIGURE 11.20 Dihedral angle of aqueous fluid in contact with various mantle minerals and mineral assemblages as a function of pressure at temperatures indicated on individual curves. Modified from Liu et al. (2018).

It is possible that the significantly negative q-evolution with temperature of aqueous fluids in garnet and clinopyroxene systems may reflect approach of garnet-H2O and clinopyroxene-H2O to a second critical endpoints. Such a feature would be analogous to, for example, the behavior suggested for the temperature-dependent q-evolution of the aqueous fluid in the quartz-H2O system (Watson et al., 1990; Holness, 1995; see also Figs. 11.11 and 11.12). However, experimental data relevant to this suggestion of temperature/pressure effects of wetting angle resulting from silicate solubility changes in aqueous fluid do not appear to exist even though a critical endpoint of eclogite mineral assemblages (Kessel et al., 2005), about 6 GPa, is near that where the dihedral angle of fluid in contact with garnet and clinopyroxene decreases quickly with increasing temperature (Fig. 11.21C and D). Such a solubility evolution of those silicate components in aqueous fluid would suggest that the wetting angles of aqueous fluid in this system also could decrease rapidly as the second critical endpoint is reached. In light of the experimental results in Fig. 11.21, the dihedral angle near the pressure and temperature conditions of the eclogite-H2O critical endpoint could easily be less than 60 . However, confirmation of such suggestions requires experimental data that are not yet available.

11.2.3 Dihedral angles and H2O distribution in the earth The temperature and pressure effects on wetting angles of mantle minerals by H2O can have profound effects on properties of fluid-bearing upper mantle materials. In addition, whether or not there is fluid connectivity will affect mass transport behavior (Watson, 1991; Brenan, 1993; Iizuka et al., 1998; Bebout et al., 1999; Kawamoto et al., 2014) as well as seismic and electric properties of H2O-bearing rock systems (Wiens et al., 2006; Reynard et al., 2011; Yoshino and Katsura, 2013; Ogawa et al., 2014). The wetting properties of aqueous fluids in the mantle and crust also will impact on the extent

842

Chapter 11 Mass transport

FIGURE 11.21 Dihedral angles of aqueous fluid in contact with mantle minerals as a function of pressure and temperature. (A) Clinopyroxene and garnet in contact with aqueous fluid as a function of pressure at temperatures indicated. (B) Dihedral angle-pressure curves at temperatures indicated for garnet and clinopyroxene. (C) Dihedral angle of aqueous fluid in contact with clinopyroxene as a function of pressure in the 700e1000 C temperature range. D. Dihedral angle of aqueous fluid in contact with majorite garnet in the 17e19 GPa range as a function of temperature. Modified from Mibe et al. (2003), Matsukage et al. (2017), Liu et al. (2018).

to which H2O can influence metamorphic and magmatic processes because H2O affects both subsolidus and supersolidus phase relations of crustal and mantle mineral assemblages (Kushiro, 1972; Kirby and Scholz, 1984; Iwamori, 1998; Gaetani and Grove, 1998; Schmidt and Poli, 1998; Hacker, 2006; Iwamori et al., 2007; Malaspina et al., 2010; Evans and Powell, 2015; Mann et al., 2015 Nakao et al., 2018; Huang et al., 2020).

11.2 Porosity, permeability, and transport

843

11.2.3.1 Dihedral angles and properties The properties of rocks in the Earth’s interior are most often discussed in the context of influence of volatiles include melting behavior (see Chapters 1 and 2) and metasomatism by fluids (see also Chapter 6), together with physical properties such as electrical and seismic properties (Connolly, 2005; Hier-Majumder and Abbott, 2010; Reynard et al., 2011; Shimojuku et al., 2012; Yoshino and Katsura, 2013; see also Chapter 9). However, the equation-of-state of solid and molten materials in the Earth’s interior also varies with the composition and abundance of fluids such as H2O and CO2 and mixtures of these two components (see Chapter 10).

11.2.3.1.1 Geochemical properties and processes The geochemical properties of materials subject to fluid infiltration include trace and major element abundance. Fluid infiltration can also cause isotopic changes (Watson, 1991; Brenan, 1993; Iizuka et al., 1998; Brenan et al., 1998; Lupulescu and Watson, 1999; Manning, 2004; Foustoukos and Mysen, 2012; Dalou et al., 2015; Labidi et al., 2016). Water is the transport agent most frequently subjected to experimental study perhaps because H2O is the volatile component that affects rock properties the most profoundly and also because of the large solubility of numerous geochemically important elements in H2O at high temperature and pressure. The proportion of H2O permeating a rock volume is also important. It has been shown, for example, that the diffusivity of halogens through a rock sample containing H2O can vary by orders of magnitude depending on the volume of H2O (Brenan, 1993). Watson (1991) documented how the diffusion constant for Fe in H2O and (H2O þ CO2)-bearing systems depends on both the proportion of fluid and its H2O/CO2 ratio (Fig. 11.22). It is evident from those experimental results that whether pure H2O or a 1:1 mixture of H2O:CO2, the volume of fluid is a critical parameter affecting the diffusivity of elements such as Cl and Fe through a hydrous rock. This effect very likely reflects the extent to which the fluid connectivity affects the fluid permeability and, therefore, the bulk rock diffusion constant of, in this latter cases, Fe and Cl. It is also evident from the Fe diffusivity data that the proportion of CO2 relative H2O plays an important role (Fig. 11.22A and B). This effect likely is because of both the decreasing solubility of iron in fluid as its H2O content decreases and CO2 increases, and because the wetting angle of the fluid in contact with solids in the sample decreases in the same direction of CO2/H2O abundance ratio, thus lowering the bulk diffusivity of iron through the rock sample. Brenan (1993) observed analogous effects for Cl diffusivity as a function of volume fraction of H2O in the sample (Fig. 11.22C). Increasing volume of H2O and decreasing CO2/H2O of the fluid enhance the permeability thus leading to enhanced diffusivity of Cl. In other words, the fluid parameters affecting wetting angles and permeability all influence diffusivity through the rock. It is quite likely that analogous behavior would be encountered for transport of all elements by aqueous fluids when their solubility behavior resembles those of Cl and Fe as in the experimental data in Fig. 11.22. Silica metasomatic alteration via SiO2 transport in aqueous solution illustrates how permeability of H2O can have a major effect on bulk composition and, therefore, physical and chemical properties of rocks in the Earth. The large SiO2 solubility in H2O fluid at high temperature and pressure is well known (e.g., Manning, 1994), as is permeability of H2O through mantle and crustal rocks as discussed above (see also Mysen et al., 1978; Iwamori, 1998; Yoshida et al., 2020; Huang et al., 2020). As a result, from permeability experiments in the 2.5e4 GPa pressure range, Iizuka et al. (1998) calculated, for example, the extent to which a peridotite mantle wedge overlying a dehydrating basaltic subducting plate will grow additional orthopyroxene from the reaction (Fig. 11.23): Mg2 SiO4 ðperidotiteÞ þ SiO2 ðfluidÞ ¼ 2MgSiO3 ðperidotiteÞ.

(11.6)

FIGURE 11.22 Diffusion of iron is olivine-H2OeCO2 (A and B) and chlorine diffusion in quartzeH2OeCO2 as a fluid concentrations. (A) Evolution of Fe diffusion in olivine-H2O as a function of concentration of aqueous fluid expressed relative to diffusion in fluid-free olivine. (B) Evolution of Fe diffusion in olivineeH2OeCIO2 as a function of concentration of aqueous fluid expressed relative to diffusion in fluid-free olivine. (C) Chlorine diffusion in quartz-H2O and quartzeH2OeCO2 systems as a function of total fluid concentration. Modified from Watson (1991), Brenan (1993).

11.2 Porosity, permeability, and transport

845

FIGURE 11.23 Calculated orthopyroxene growth range in mantle wedge above dehydrating (amphibole-bearing) subducting slab as a function of time since dehydration of mslab materials. Modified from Iizuka et al. (1998).

Such metasomatic alteration of a mantle wedge overlying subducting plates will have profound effects on physical and chemical properties of the mantle wedge. Such chemical alteration will also affect the composition of potential partial melts from such metasomatically-enriched peridotite. It is quite likely, for example, that magma formed by partial melting of a hydrous pyroxenite source formed by metasomatic alteration in the mantle wedge would be considerably more felsic than that from a hydrous peridotite source (see also Chapter 2). The melting temperatures and melting intervals of such a metasomatically altered wedge above dehydrating subducting plates also will be affected (see Chapter 1). Another example is the evolution of fluid-sensitive trace elements such as Be, B, and Li where Brenan et al. (1998) determined their solubility in aqueous fluids derived from dehydration of hydrous minerals in the subducting plate. Those minerals were lawsonite and amphibole, the stability of which in a hydrous basalt composition was taken from Schmidt and Poli (1998).8 An example of estimated changes in B/Be ratio of fluid as a function of the depth in a subduction zone where such fluid might be released, is shown in Fig. 11.24 (Brenan et al., 1998). Decreased B/Be abundance ratio in the fluid with depth in subduction zones reflects decreasing H2O concentration in the subducting slab with depth (Schmidt and Poli, 1998), decreasing H2O/CO2 abundance ratio in the fluid with increasing pressure (Connolly, 2005) and changing phase relations in the dehydrating slab with changing pressure and activity of H2O (Schmidt and Poli, 1998). The B/Be (as well as other trace element ratios; e.g., Manning, 2004; Rustioni et al., 2021) thus generated by dehydration and migration of aqueous fluid to 8 An updated version of these estimate was published by Schmidt and Poli (2014). However, those data do not affect the conclusions such as summarized in Fig. 11.24. Another geophysically-based approach to the H2O distribution in subduction zones can be found in van Keken et al. (2011).

846

Chapter 11 Mass transport

FIGURE 11.24 B/Be-values of fluid released from dehydrating, amphibole-bearing subducting slab as a function of slab depth expressed relative to initial value. Modified from Brenan et al. (1998).

melting regions in mantle wedges found in island arc lavas were found consistent with a supply of such trace elements to the source region of melting in the mantle wedge to form those magmatic liquids (e.g., Morris et al., 1990; Moriguti and Nakamura, 1998).

11.2.3.1.2 Geophysical properties and processes The two major properties most commonly employed to model fluid (and melt) distribution in the Earth’s interior are electrical and seismic properties. For example, electrical properties as a function of fluid fraction and fluid salinity have been calibrated experimentally (Shimojuku et al., 2012; Guo et al., 2015; Sun et al., 2020; Huang et al., 2021). Seismic properties have not been examined in similar detail although some information exist for wave velocities as a function of what has been referred to as “grain wetness,” a factor taken as a measure of the extent to which all grain boundaries have been wetted by H2O fluid (Yoshino et al., 2005). It is interesting, though, that there seem to be simple linear relations between electrical conductivity and P and S wave attenuation in subduction zones (Fig. 11.25; see also Pommier, 2014). Fluid connectivity, which is known to govern electrical conductivity (e.g., Sun et al., 2020), also could be correlated with seismic properties of fluid-bearing materials in the Earth’s interior. In fact, seismic velocities in subduction zones have been used to estimate total H2O content (Carlson and Miller, 2003; Hacker and Abers, 2004). Moreover, a slight velocity drop with H2O content in H2Obearing quartz aggregates has been reported (Fig. 11.26; see also Ishikawa and Matsumoto, 2014). This H2O effect appears to decrease some with increasing pressure and temperature (Ishikawa and Matsumoto, 2014). Finally, the correlation between electrical conductivity and seismic velocity in subduction zones (Fig. 11.25) could well be because both properties are positively linked to fluid and melt content. Various models have been proposed to describe relationships between electrical conductivity and porosity in crystal-fluid systems (Archie, 1942; Waff, 1974).

11.2 Porosity, permeability, and transport

847

FIGURE 11.25 Relationship between electrical conductivity and P-wave attenuation from a variety of fore-arc and back-arc subduction zones. See Pommier (2014) for detailed description of the individual locations together with relevant citations. Modified from Pommier (2014).

For fluid-bearing rock samples, the electrical conductivity of the bulk rock is related to that of the fluid as; f: ssolidþfluid ¼ C$sfluid $4n ;

(11.7)

where C is a constant, f is porosity and the exponent, n, which commonly is in the 0.5e1.5 range (ten Grothuis et al., 2005; Shimojuku et al., 2012). The electrical conductivity of H2O-bearing quartzite, log s, is linearly dependent on temperature, 1/T, so that from the simple Arrhenius formulation9: logs ¼ logs0  DE=RT;

(11.8)

4the slopes in Fig. 11.27 yield activation energy of electrical conductivity. The decreasing slope with increasing porosity implies that the activation energy of bulk rock conductivity diminishes the greater the porosity. This would be expected given that increasing permeability follows from increasing porosity, a relationship that does, in fact, follow Archie’s Law [Eq. (11.7), see also Fig. 11.27B]. The activation energy of electrical conductivity decreases further when salts such as NaCl are dissolved in the aqueous solution in contact with solids (Fig. 11.28). It also increases the greater the salinity (Sun et al., 2020). Because wetting angles decrease as salinity of aqueous solution increases 9 Details of relationships between electrical conductivity and temperature in silicate melts and magma were discussed in Chapter 9 (Section 9.7.1). Linear relations between log s (conductivity) and DE (activation energy) of most magmatic liquids were explained by the observation that conductivity typically is network-modifying cations serving as charge-carriers whereas magma viscosity, for example, depends primarily on transport by network-formers, the average activation energy of which is a nonlinear function of temperature, whereas that of network-modifiers is.

848

Chapter 11 Mass transport

FIGURE 11.26 Experimentally-determined P-wave velocity in quartz-H2O aggregates determined at 25 C with H2O contents as indicated on individual curves as a function of pressure. Temperature data also are reported in the citation. Modified from Ishikawa and Matsumoto (2014).

FIGURE 11.27 Electrical conductivity of H2O-bearing quartzite determined at 1 GPa. (A) As a function of temperature for porosities (F) indicated. (B) As a function of porosity, f, at two different temperatures. The fitted lines are from Aerchie’s Law [Eqn. 11.1] with n-values in Archie’s Law as indicated on individual curves. Modified from Shimojuku et al. (2012).

(e.g., Glover, 2015; Guo et al., 2015; Liu et al., 2018), it follows that the porosity increases with increasing salinity. From the increased porosity in Eq. (11.1), the permeability also increases the more saline an aqueous solution. Such a development would enhance electrical conductivity both of the

11.2 Porosity, permeability, and transport

849

FIGURE 11.28 Electrical conductivity in clinopyroxeneeH2OeNaCl at conditions indicated on figure as a function of temperature and fluid composition as indicated on individual curves at fixed porosity, F, as shown. Modified from Liu et al. (2018).

saline fluid and the saline bulk rock (Fogo et al., 1954; Guo and Keppler, 2019). The increased conductivity and decrease in activation energy of electrical conductivity with increasing porosity and increasing fluid salinity, therefore, would be expected. There exist high-conductivity layers in the Earth’s deep crust (Guo et al., 2018). High-conductivity layers also have been reported from subduction zones (Wanamaker et al., 2009; Guo and Keppler, 2019). As illustrated in Fig. 11.29, the high electrical conductivity in high-conductivity crustal layers could result from on the order of 1% aqueous fluid with significant salinity. From experimental data on electrical conductivity in forsterite þ H2O mixtures, Huang et al. (2021) concluded that the high electrical conductivity often reported from the mantle wedge above subducting plates could be accommodated by 5e10 volume % aqueous fluid in the wedge. Of course, were the fluid saline, as is often suggested (Kawamoto et al., 2014; Kumagai et al., 2014), the volume fraction of fluid could be smaller. A significantly smaller fraction (perhaps less than 1%) would be consistent with modeling results from Iwamori (2007), for example. Water concentrations in the 0. 5e1 wt% range in the source regions of andesitic magma in this mantle wedge would also be consistent with results of melting experiments on hydrous peridotite mantle (Till et al., 2011).

11.2.4 Wetting angles and partial melts Wetting angles between silicate melts (magma) and crystalline materials in general are considerably smaller than between the same crystalline materials and fluids as seen in the summary in Fig. 11.10, (Holness, 1997). The often different wetting angles in fluid-versus magma-containing environments likely are because of the greater compositional and structural similarity between silicate minerals and silicate melts (magmatic liquid) than between silicate minerals and fluids, but that such differences

850

Chapter 11 Mass transport

FIGURE 11.29 Comparison between estimated and determined electrical conductivity with fluid fraction for various geographic locations. (A) Electrical conductivity as a function of H2O þ NaCl fluid fraction for different NaCl concentrations. (B) Electrical conductivity of forsterite þ H2O as a function of fluid volume and compared with conductivity anomalies in mantle wedges above subducting plates. (A) Modified from Sun et al. (2020). (B) Modified from Huang et al. (2021).

diminished when temperature and pressure conditions approached those of second critical endpoints. Under those latter conditions with supercritical fluids at temperatures and pressures above the critical point, melts and fluids are completely miscible and cannot necessarily be distinguished from one another (see also footnote 2 in this chapter for further summary of those relations). Neither could their contribution to electrical conductivity. Wetting angles of partial melts in the Earth’s interior not only depend on the temperature and pressure, but also vary with melt composition, mineral compositions, and mineral assemblages (Jurewicz and Watson, 1985; Laporte, 1994; Laporte and Watson, 1995; Lupulescu and Watson, 1999; Maumus et al., 2004; Yoshino et al., 2009). In addition, interfacial energies and, therefore, wetting angles [see Eqn. 11.1)] of anisotropic minerals in rock-forming mineral assemblages can be significantly different from one another (Waff and Faul, 1992; Lupulescu and Watson, 1999). The aforementioned possible angle variations notwithstanding, there are certain systematic relationships. For example, the wetting angle of olivine in partially molten peridotite is a systematic function of increasing temperature over a relatively wide pressure interval that does not appear to affect the angle (Fig. 11.30A; see also Yoshino et al., 2009). Of course, increasing pressure also results in compositional changes of partial melts (see Chapter 2; Sections 2.1.2 and 2.1.3). For example, partial melts from peridotite tend to become increasingly depolymerized (increasing NBO/T) as pressure is increased. This is what also was observed in the experiments by Yoshino et al. (2009) where the dihedral angle of partial melts decreases the greater the NBO/T of the melt (Fig. 11.30B). There is, therefore, a systematic decrease in the wetting angle as the partial melts become increasingly depolymerized (Fig. 11.30B). This evolution could reflect the fact that the more depolymerized the partial melt, the more similar are structural elements of the crystalline materials and the melt itself. That, in

11.2 Porosity, permeability, and transport

851

FIGURE 11.30 Dihedral angles of partial melts from peridotite. (A) Dihedral angle as a function of temperature in the 1e5 GPa pressure range. (B) Dihedral angle as a function as a function of the degree of polymerization, NBO/ T, of the partial melt. Modified from Yoshino et al. (2009).

turn, results in decreases of the solid-liquid interfacial energy, which is the principal reason for decreased wetting angle.17 Features such as summarized in Fig. 11.30, were discussed in some detail for simpler silicate systems such as alkali silicate and alkaline earth silicates in contact with olivine (Wanamaker and Kohlstedt, 1991). In the compositionally simple systems in the latter study, the dihedral angle of melt in contact with olivine increased systematically with increasing SiO2 content of the melt (Fig. 11.31). There is, of course, a simple positive relationship between SiO2 concentration and the degree of polymerization, NBO/Si, of simple silicate melts.10 It is also important to keep in mind, however, that the electronic properties of the metal cations affect the wetting angle. The more electronegative this cation, the smaller is the angle. One might argue that this latter relationship could be linked to how disproportion equilibria among Qn species in silicate melts depend on the electronic properties of the of the metal cation (see also Chapter 5, Section 5.3.3). The more electronegative the cation, the greater is the concentration of depolymerized silicate species (Qn species).11 This enhanced structural similarity with the olivine structural might cause the dihedral angle between olivine and silicate melts to decrease with increasingly electronegative metal cations in the melt. 17 In general, partial melts from a peridotite mantle source becomes increasingly depolymerized the greater the depth of melting. One might surmise, therefore, that the wetting angle between mantle melts and crystalline residue also decreases with increasing depth in th mantle. 10 Details of relationships between silicate melt composition and melt polymerization were discussed in Chapter 5, Section 5. 2.1. 11 In order to maintain the same bulk melt silicate polymerization, increased concentration of depolymerized Qn-species is associated with increased abundance of more polymerized silicate species [see Eqn. (5.10)].

852

Chapter 11 Mass transport

FIGURE 11.31 Dihedral angle of K-silicate melts in contact with olivine crystals for different crystallographic surfaces as indicated as a function of SiO2 concentration in melt. Modified from Wanamaker and Kohlstedt (1991).

Another interesting feature of the data in Fig. 11.31 is different dihedral angles between partial melts and individual crystallographic orientations of the olivine surfaces. This observation implies that the surface energy of the different olivine surfaces are different, which, is, of course, exactly as would be expected for any nonisotropic solid material. It is reasonable to expect that such relationships would be dependent not only on the SiO2 content (and, therefore, NBO/Si) of the melt, but also on pressure and temperature as these latter variables affect the surface energy of melts in contact with the various crystalline surfaces. Relationships between silicate melt polymerization and wetting angle, q, not only reflect bulk chemical variations such as proportions of SiO2 and Al2O3 relative to network-modifying cations, such relationship also are consistent with the effect of H2O dissolved in magmatic liquids on the wetting angle, the porosity, and permeability (Khitarov et al., 1979; Fujii et al., 1986; Minarik and Brenan, 1994; Hirth and Kohlstedt, 1996; Yoshino et al., 2007).12 Although there are limited data on this subject, in light of well-established relationships between NBO/T and wetting angle, it would appear that provided that the effect of dissolved H2O on melt polymerization can be established, this variable can then be linked to wetting angle and related properties. As an example, Laporte (1994) found that this angle is about 20 for quartz-feldspar-H2O melts in contact with quartz and quartz þ feldspar, whereas for natural anhydrous felsic magma with similar model mineralogy the wetting angle is between 50 and 60 (Jurewicz and Watson, 1985).

12

Increasing H2O content of silicate melts as well the proportion of network-modifying cations relative to the concentration of SiO2þAl2O3in melts result in increasing depolymerization, NBO/T, of the melts (see Chapters 5 and 7).

11.2 Porosity, permeability, and transport

853

It is also notable that in the latter study, the wetting angle of a granitic composition melt in contact with quartz is near 60 , whereas such melt in contact with feldspar þ quartz and feldspar þ feldspar results in systematic decrease in the wetting angle (Fig. 11.32). We recall that similar trends were reported in experiments on wetting angle of hydrous fluid in equilibrium with quartz and with quartz þ feldspar compositions. In this latter case, wetting angles decreased as felspar compositions were added (Holness, 1995; see also Fig. 11.12). Therefore, as the composition and structural entities of silicate melts or aqueous fluid become more similar to the composition and structure of the crystalline materials in contact with the fluid or melt, the wetting angle decreases. More likely than not, it is such structural similarities that drives this wetting angle trend.

FIGURE 11.32 Observed angles of melt in contact with two different crystal surfaces as indicated on individual diagrams. Modified from Jurewicz and Watson (1985).

854

Chapter 11 Mass transport

11.2.5 Melt/mineral dihedral angle, porosity, and properties Just as when fluid filling the pore space in crystalline materials affects the properties of fluid-bearing rocks, silicate melts and magma in the pore space serve to change physical and chemical properties of partially molten rocks at high temperature and pressure at temperatures and temperatures above the glass transition (Walsh, 1969; Faul et al., 2004; Maumus et al., 2004, 2005; ten Grotenhuis et al., 2005; Hier-Majumder, 2008; Hier-Majumder and Abbott, 2010; Wang et al., 2015; Iwamori et al., 2021).13 Interpretation of natural observations in combination with experimental data have led to models that describe melt distribution in the Earth’s interior together with models to describe magma aggregation and ascent (McKenzie, 1985, 1989; Iwamori and Zhao, 2000; Connolly et al., 2009; Wimert and Hier-Majumder, 2012; Zhang et al., 2014; Laumonier et al., 2017). An example of how porosity and permeability govern melt aggregation and ascent can be illustrated by using Eq. (11.1) in combination with viscosity and density relations of partially magma and the crystalline materials in partially molten rock (Maumus et al., 2004). By using n ¼ 2 and C ¼ 3000 in together with a grain size in the 1e10 mm range and porosity, f ¼ 0.03, Maumus et al. (2004) computed the permeability of such partially molten rocks to be in the range 3$1015 to 3$1013 m2. Then, with a density contrast, Dr ¼ 600 kg/m3 a melt viscosity of 2$103 Pa s and a partially molten layer of 10 km, the time scale of the melt segregation is on the order of 50 million years and ascent velocity on the order of 1 m/year. However, both the ascent rate and time scale are linear functions of the physical variables (McKenzie, 1985), so those rate and time scales can easily be adjusted by changing magma viscosity and density contrasts. Magma viscosity, for example, can be adjusted by up to many orders of magnitude by changing magma composition (e.g., from basalt to komatiite) and fluid content (see Chapter 9, Section 9.4). Seismic properties are sensitive to the presence of melt. Moreover, whether or not the melts form an interconnected network (“contiguity”) also plays a role in how melt fractions in partially molten rocks affect their seismic properties (Wimert and Hier-Majumder, 2012). Contiguity has been related to porosity in a nonlinear manner (Takei, 2002; Wimert and Hier-Majumder, 2012). As a melt fraction increases, for example, the contiguity diminishes (von Bargen and Waff, 1986; Yoshino et al., 2005; see also Fig. 11.33). Relationships such as those in Fig. 11.33A help explain the changes in seismic wave velocities, VP and VS (Fig. 11.33B and C). Of course, magma composition is an additional variable that will affect those relationships because it governs wetting angles, porosity, and contiguity. Moreover, grain size and grain size distribution, as well as anisotropic crystal structure will also influence these relations. Finally, but very importantly, the stress field results in deformation of partially molten rocks. In the end those variables also affect seismic (and other physical) properties (Takei, 2005; Wimert and Hier-Majumder, 2012).14

13

Below the glass transition, magmatic liquids are transformed to glass. The physical properties of silicate glass differ from those of their melts in major ways (see Chapter 10, Section 10.1, for example). Such glass in the pore space of rocks would have very different influence of rock properties compared with the effect of melt. However, this environment is not discussed here because the focus here is transport of mass and glass in nature is not an efficient mass transport medium. 14 Closely related to information such as in Fig. 11.33 is the behavior of the shear modulus of partially molten rocks as a function of temperature and the melt fraction even at melt fraction on the order of hundreds of ppm. Once the system is relaxed, as seen for olivine with and without small proportions of melt, the shear modulus deviates from simple linear relations to temperature (as seen in the unrelaxed state). This deviation is greater in the presence of melts than in its absence.

11.2 Porosity, permeability, and transport

855

FIGURE 11.33 Melt fraction, contiguity and seismic wave velocities. (A) Contiguity of partially molten peridotite in contact with basalt as a function of melt fraction calculated by Wimert and Hier-Majumber (2012) (solid dots) and for partial melt of peridotite determined experimentally by Yoshino et al. (2005) (open symbols). (B) Relative change of seismic wave velocity as a function of melt fraction from Wimert and Hier-Majumber (2012). (C) Relative change of seismic wave velocity as a function of contiguity from Wimert and Hier-Majumber (2012). Modified from Wimert and Hier-Majumber (2012).

856

Chapter 11 Mass transport

Electrical conductivity of partially molten rocks is a sensitive function of melt fraction, melt geometry, and melt composition so that by using effective medium theory (Kirkpatrick, 1973), Watanabe and Kurita (1993) reported the following equation to link electrical conductivity of individual components (melt and minerals) and their distribution geometry in a partially molten rock to electrical conductivity: i X

si  s (11.9) si  s ¼ 0: 1þg i¼1 s In Eq. (11.9), si and s are the electrical conductivity of component, i, and bulk electrical conductivity, respectively. The Xi is the volume fraction of component, i, and g as an expression of geometry of the melt distribution. For a silicate system with melt in equilibrium with olivine, there is, therefore, systematically increasing conductivity as the melt fraction increases (Fig. 11.34). With even a small melt fraction such as between 1% and 10% in the example in Fig. 11.34, the electrical conductance is the 0.02e0.71 S/m range. Such electrical conductivity is between three and four orders of magnitude greater than that of crystalline forsterite. This conductance is, however, less than that of the pure melt by about one to two orders of magnitude (ten Grotenhuis et al., 2005). The electrical conductivity partially molten rocks also is a function of temperature, even for a fixed melt fraction (Tyburczy and Waff, 1983; Pommier et al., 2010; Yoshino et al., 2010; Laumonier et al., 2017), a feature also reported for chlorine brine systems, for example (Watanabe and Kurito, 1993). The linear relationship expected from Eq. (11.8) does indeed seem to hold although there appears to be a small dependence of the slope of the conductivity versus temperature relations at given pressure (Fig. 11.35). It is also clear that the electrical conductivity increases systematically with increasing melt fraction, a feature conceptually similar to the increases electrical conductivity in fluid-bearing Xi

FIGURE 11.34 Electrical conductivity of olivine þ basalt melt as a function of melt fraction. Modified from ten Grotenhuis et al. (2005).

11.2 Porosity, permeability, and transport

857

FIGURE 11.35 (A) Electrical conductivity of olivine þ basalt melt at 1.5 GPa as a function of temperature for volume % basalt melt as indicated. (B) Electrical conductivity of olivine þ basalt melt as a function of temperature for volume % basalt melt as indicated. (A) Modified from Laumonier et al. (2017). (B) Modified from Yoshino et al. (2010).

silicate systems, where the proportion of fluid enhanced the electrical conductivity (Fig. 11.29). In effect, therefore, the activation energy of conductance of a partially molten rock decreases with increasing volume fraction of melt to about 4 vol%. At higher volume fraction, the activation energy actually seems to increase, a feature that may related to changes in melt geometry or perhaps changing electrical conductivity of the melt itself. It also seems clear that the relationship between volume fraction of melt and conductance depends on the melt composition even within the broad compositional range of basalt melt (Fig. 11.35B). This feature also is seen clearly in the effect of H2O content of partial melts (Fig. 11.36; see also Yoshino and Katsura, 2013). Increasing H2O content enhances conductivity of the melt itself. It also causes increased grain boundary wetting characteristics. The effect of H2O contents of partial melts, therefore, should not be surprising. Electrical conductivity of the Earth’s interior has been employed to deduce fraction of melts in various regions of unusually high conductivity (see, for example, Fig. 11.29). Further manifestation of this latter feature is illustrated in the data from a few tectonic settings superimposed on the conductivity data in Fig. 11.36. The proportion of H2O can be incorporated in this discussion because the electrical conductivity of magmatic liquids is sensitive to H2O contents (Yoshino and Katsura, 2013). Enhanced conductivity of partially molten mantle rocks with high H2O concentration would be particularly relevant to melting in the mantle wedge above subducting plates (e.g., Iwamori and Zhao, 2000; Gaetani and Grove, 2003; Kawamoto et al., 2009, 2013). Of course, the fluid released from dehydrating slabs in subduction zones tends to be quite saline (Kumagai et al., 2014). Saline fluids dissolved together with H2O in magma during partial melting likely would affect the wetting characteristics of such melts further because salinity of aqueous fluids affect wetting angles, for example

858

Chapter 11 Mass transport

FIGURE 11.36 Electrical conductivity of partially molten peridotite as a function of melt fraction with different proportions of H2O in melt as indicated on individual curves and compared with electrical conductivity of various upper mantle locations. Modified by Yoshino and Katsura (2013).

(Huang et al., 2019) although less is known about wetting characteristics of partial melts with chlorides in solution. Under the assumption, based on data above (Fig. 11.30), that the NBO/T of the magma exerts important control of wetting characteristics of magmatic liquids, one might suggest that dissolved chlorine in hydrous magma may not have the same profound effect on wetting angles as chlorine in aqueous solutions, whereas fluorine, in contrast, might have effects on wetting angles resembling that of H2O.15 However, it appears that as of now, that experimental data relevant to effects of saline aqueous fluids in subduction zone partial melts on wetting angles have not been reported. Moreover, as the CO2/H2O ratio of fluid from subducting crust increases with increasing depth, in particular perhaps at depths greater than about 100 km, the partial melts formed in the presence of such fluids will be increasingly CO-rich. Increasing CO2 content results in increased degree of polymerization (decreased NBO/T), which would imply that as the depth of magma formation, aggregation, and ascent in subduction zones becomes greater, their wetting angle increases. Increased wetting angle by magma and fluid with depth in subduction zones have been suggested as a possible cause of volcanic fronts (Mibe et al., 1998; Huang et al., 2020). Electrical conductivity profiles through the mantle have been used to deduce distribution of H2O in the mantle, for example (Fig. 11.37A and B). The data in Fig. 11.37B are particularly interesting because they would be consistent with enhanced concentration of hydrous melt and perhaps a separate, H2O-rich fluid, near the boundary between the upper mantle and the top of the transition zone (Bercovici and Karato, 2003). However, the interpretation of the data in Fig. 11.37A are not consistent with such a model (Yoshino and Katsura, 2013). These suggestions are based on the relationships between the NBO/T of magmatic liquids and dissolved Cl and F. Chlorine does not have a major effect on NBO/T, whereas fluorine does [see Chapter 8, Sections 8.7.1e8.7.4].

15

11.2 Porosity, permeability, and transport

859

FIGURE 11.37 Electrical conductivity with depth using olivine þ H2O with concentrations as indicated. (A) Evolution using the model of Yoshino et al. (2009). (B) Evolution using the models of various Karato publications (see Yoshino and Katsura, 2013) for details of those citations. Modified from Yoshino and Katsura (2013).

11.2.6 Permeability and porosity in carbonate and sulfide-bearing silicate systems Wetting angles, porosity, and permeability of melts other than silicate melts in equilibrium with mantle peridotite mineral assemblages are important in part because carbonatite magma would be the initial magma composition formed by partial melting of peridotite-CO2 at pressures in excess of about 3 GPa (Brey et al., 2008; Ghosh et al., 2009, 2014), whereas alkali carbonatite magma may form under crustal conditions via immiscibility between silicate and carbonatite magma compositions (Visser and Koster van Groos, 1979).16 Sulfide and metal-rich magma on the other hand may not be important in the modern mantle. However, characterization of processes leading to formation of the core of the Earth and terrestrial mantles depends on understanding the control of wetting angle, porosity, and permeability of sulfide and metallic melts in contact with mantle mineral assemblages (Rubie et al., 2011; Walte et al., 2011; Bouhifd et al., 2017).

11.2.6.1 Wetting angles of carbonatite magma in the earth Some experimental data exist for wetting angles (q) of carbonatite melt in contact with olivine (Hunter and McKenzie, 1989; Watson et al., 1990). For dolomite composition melt (CaMgCO3), for example, the q is about 30 as described by the median value of the cumulative frequency versus angle curve in 16

The reader is referred to Chapter 2, Sections 2.3.4 and 2.3.5 (Figs. 2.21, 2.22, and 2.28) for detailed discussion of melting relations of peridotite þ CO2 under such conditions. Those melting relations are particularly important in the continental upper mantle where the principal volatile component is CO2 and, therefore, the initial melt could be carbonatitic. The carbonatite magma under those conditions would be an alkaline earth carbonatite. In comparison, carbonatite formed in the Earth’s crust is alkali carbonatite and perhaps formed by immiscibility between carbonatite and silicate magma (Visser and Koster van Groos, 1979).

860

Chapter 11 Mass transport

Fig. 11.38A. This dihedral angle does not differ much from those of other carbonate melts, which Watson et al. (1990) placed between 28 and 30 (Fig. 11.38B). It is striking that these angles actually are less than those of silicate melts in contact with silicate mineral assemblages regardless of their composition and, furthermore, much smaller than those of CO2 and H2OeCO2 fluids (Watson and Brenan, 1987; Holness, 1992; see also Figs. 11.13 and 11.38C). It is not clear, however, why this is given that at least at crustal pressures, there is immiscibility between alkali carbonate and silicate melts (Visser and Koster van Groos, 1979), a feature that would suggest limited silicate solubility at least in alkali carbonate melts. Low silicate solubility in carbonatite magma may diminish structural similarities between partial melts and surrounding crystalline peridotite. So, if enhanced structural similarities would lead to decreased dihedral angles (as discussed above), one might suggest that the wetting angle of carbonatite partial melt in a peridotite mantle would be greater than those of silicate magma. This is, for example, what happens with aqueous fluids with and without CO2 (Fig. 11.38C). There must, therefore, be other characteristics near the melt/crystal surface structures of these melts and the adjoining silicate mineral(s) that affect the solid-liquid interfacial energy necessary to reach such small wetting angles as summarized in Fig. 11.38C. Carbonatite magma in the mantle not only exhibits small wetting angles compared with silicate magma (typically in the 40e60 range; see Section 11.2.4), such magma also is less dense (perhaps by as much as 1 g/cm3 density difference from upper mantle crystalline peridotite (see Genge et al., 1995; Ohtani et al., 1995) and less viscous than silicate magma by as much as two to three orders of magnitude compared with basalt melt, for example (Kono et al., 2014). It follows from fluid dynamics treatments such as discussed by McKenzie (1985) that separation velocity of carbonatite magma in the upper mantle is about three orders of magnitude faster than basalt melt and even greater than that compared with more felsic magma (Fig. 11.39).

11.2.6.2 Wetting angles of sulfide/metal melts Sulfide and metal melt wetting angles in the interior of the Earth (e.g., Gaetani and Grove, 1999; Mungall and Su, 2005; Bagdassarov et al., 2009) are important to aid in characterization of environments of transition metal enrichments in the crust and the mantle via partitioning into sulfide-rich transition metal-sulfide melts (e.g., Rajamani and Naldrett, 1978; Mungall and Brenan, 2014; Wood et al., 2014; Kiseeva and Wood, 2015). Such wetting angle data, combined with the wetting angle of molten iron and iron alloys against deep mantle mineral assemblages (bridgmanite and magnesiowu¨stite), also are central to model of formation of the core of terrestrial planets (Ballhaus and Ellis, 1996; Minarik et al., 1996; Shannon and Agee, 1998; Takafuji et al., 2004; Yoshino et al., 2004; Terasaki et al., 2007 Mann et al., 2008; Holzheid et al., 2000, 2013). The dihedral angle of sulfide melts against upper mantle mineral assemblages in general exceeds 60 (Minarik et al., 1996; Gaetani and Grove, 1999; Ballhaus and Ellis, 1996; Holzheid et al., 2000, Rose and Brenan, 2001). In fact, for sulfide melts there is an apparent essentially linear relationship between dihedral angle and proportion of the total anions (S2 and O2) (Fig. 11.40A) indicating perhaps the proportion of oxygen in such melts near the interface between silicate minerals and sulfide melt is a critical variable governing the melt-minerals interfacial energy (Rose and Brenan, 2001). It is also evident that the proportion of nonferrous metals in the sulfide melt does have an impact on the dihedral angle (Fig. 11.40B). However, those relationships are significantly dependent on the oxygen fugacity (fO2). The more oxidizing the environment, the smaller is the dihedral angle. Of course, one might expect increasing oxygen contents of these melts with increasing oxygen fugacity.

FIGURE 11.38 (A) Cumulative frequency distribution of dihedral angle for CaMg(CO3)2 melt in contact with olivine and 3 GPa and 1300 C. (B) Dihedral angle of various carbonate melts in contact with olivine in the 0.5e3 GPa and 1200e1400 C, pressure and temperature ranges, respectively. (C) Dihedral angle of various carbonate and basalt melts as well as fluids as indicated in contact with olivine in the 0.5e3 GPa and 1200e1400 C, pressure and temperature ranges, respectively. (A) Modified from Hunter and McKenzie (1989). (B, C) Modified from Watson et al. (1990).

862

Chapter 11 Mass transport

FIGURE 11.39 Calculated separation velocity (ascent velocity) of various magmatic liquids from mantle sources as a function of rock porosity with magma viscosity (h) and density contrast with country rocks (Dr) as indicated. Modified from McKenzie (1985).

It also appears that the relationship between dihedral angle and proportion of nonferrous metals diminishes as the conditions become more oxidizing (Fig. 11.40B). This relationship may be expressed in terms of a formalized redox reaction of the form (Rose and Brenan, 2001): gas

M1x Osulfide melt þ 0:5S2

gas

¼ M1x OSsulfide melt þ 0:5O2 .

(11.10)

It is to be expected, therefore, that the wetting angle decreases as a systematic function of the oxygen content of the sulfide melt (Fig. 11.40C). The extent to which the information summarized above can be applied to modeling formation of cores of terrestrial planets (and perhaps the Moon) depends on both the composition of the coreforming material as well on the data reported above extrapolated to conditions involving lower mantle mineral assemblages at lower mantle pressures. Such extrapolation does not, however, necessary imply that the Earth’s core was formed at its current depth because separation of corematerials from silicate materials may not necessarily have occurred at the depth of the cores as they exist today (e.g., Rubie et al., 2011, 2015; Badro et al., 2014). The Earth’s core is not FeS, but likely consists of several percent Ni, Si, O, C, and perhaps H, for example, and considerably less S than implied by an FeS stoichiometry (e.g., Morard et al., 2013). Iron is, nevertheless, the main component (e.g., Fisher et al., 2017). At the time of core formation, this material likely existed initially perhaps as liquid droplets that aggregated into larger volumes that may or may not have been interconnected depending on wetting angles, porosity, and permeability.

FIGURE 11.40 Dihedral angle between sulfide and metal melts in contact with various mantle minerals. (A) Effect of the ratio of all anions/all cations of sulfide melts versus olivine. (B) Effect of non-Fe metal concentration of sulfide melts on their dihedral angle in contact with olivine as a function of oxygen fugacity, fO2. (C) Dihedral angle of sulfide melts with oxygen concentrations as indicated in contact with various mantle minerals as indicated on diagram. Modified from Rose and Brenan (2001), Holzheid et al. (2000), Terasaki et al. (2007).

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The latter issue can be addressed with experiments comprised of molten, Fe-rich metals with various added components in contact with mantle minerals under appropriate temperature, pressure, and redox conditions (Ballhaus and Ellis, 1996; Minarik et al., 1996; Shannon and Agee, 1998; Takafuji et al., 2004; Ghanbarzadeh et al., 2017; Roberts et al., 2007; Mann et al., 2008; Watson et al., 2011; Holzheid et al., 2013). In an early such study, Ballhaus and Ellis (1996) determined dihedral angles for iron sulfide and of metal melts with small fractions of a percent Ni, Co, and C (carbonsaturated at 2 GPa and 1580 C) in contact with olivine. They determined the dihedral angles as a function of the metal/Si ratio of the iron-bearing metals (Fig. 11.41). Regardless of metal/sulfur ratio, the dihedral angle increased as the melt got more metal-rich. In fact, with M/S < 1 (presumably with some oxygen in the melt), q was near 60 , but increased rapidly with increasing M/S (Fig. 11.41) at least at the conditions of those experiments. Moreover, dissolving Si in such Fe-rich melts results in an angle increase (Mann et al., 2008), whereas solution of oxygen resulted in an angle decrease even under upper mantle pressure and temperature conditions (Gaetani and Grove, 1999; Terasaki et al., 2005; see also Fig. 11.41B). Pressure also affects the (metal and sulfide)/mineral dihedral angle significantly (Shannon and Agee, 1998; Takafuji et al., 2004; Holzheid et al., 2013) so that under sufficiently high oxygen and sulfur fugacity the dihedral angle between reasonable core composition metallic melts and lower mantle minerals such as silicate perovskite (bridgmanite and davemaoite) would decrease below 60 as a function of pressure (Fig. 11.42; see also Shannon and Agee, 1998; Takafuji et al., 2004; Terasaki et al., 2007). In short, it appears that core-forming metal and/or metal-sulfide melt may have formed, aggregated, and settled via percolation through a deep silicate crystalline mantle, even with a small fraction of melt, at the time of the Earth’s core-forming stage. With a core melt containing a few percent oxygen such a core-forming process would be more favored (Rubie et al., 2003, 2004; Wood

FIGURE 11.41 (A) Dihedral angle of sulfide and metal melts (as indicated on diagram) in contact with olivine at 2 GPa, 1350e1570 C as a function of the metal/sulfur ratio. (B) Dihedral angle of Fe alloys with additives as indicated in contact with olivine between ambient pressure and 5 GPa in the 1600e1730 C (see Mann et al., 2008, for details). (A) Modified by Ballhaus and Ellis (1996). (B) Modified from Mann et al. (2008).

11.3 Concluding remarks

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FIGURE 11.42 Wetting angle of FeS melt in contact with various mantle minerals within their respective depth (pressure) ranges in the mantle as indicated. Modified from Holzheid et al. (2013).

et al., 2006). This process might be somewhat similar to that which leads to the formation of the core of Mars and Mercury (Solomon, 2003; Malavergne et al., 2010; Terasaki et al., 2005).

11.3 Concluding remarks Mass transport occurs through the interior of the Earth and is accomplished with magma and fluid passing through cracks and with percolation through channels along grain boundaries. Percolation is the main mechanism at any depth greater than a few km or at any pressure above which it is sufficient to close open cracks in rocks. Percolation velocity is linked to permeation, which in turn is governed by rock porosity. Finally, porosity is controlled by wetting angles, q, at the interface between melt and fluid and those of mineral surfaces of surrounding rocks. How wetting angles are linked to porosity and permeability and how such information can be employed to model mass transport by magma and fluid movement through the Earth is the central theme of this discussion. Characterization of such mass transport is central to our understanding of formation and evolution of the Earth from the earliest separation of a core from silicate mantle to modern magmatic activity. In a hydrostatic environment with a single isotropic crystalline material in contact with fluid or melt, the ratio of interfacial energies of contacting crystalline surfaces and that of the crystal/melt or fluid, defines the wetting angle, q. This wetting angle, in turn, depends on composition of crystals, melts, and fluids in addition to temperature and pressure. When q < 60 , the fluid or melt will wet all grain boundaries of an isotropic crystalline material in a hydrostatic environment, whereas when greater than 60 , melts and fluids do not wet the surfaces. Of course, with anisotropic crystal structures, the wetting angles for individual crystal surfaces will vary depending on the properties of the specific surface. Different crystals in contact with melt and fluid also will affect the bulk wetting angle. Finally, deformation can cause significant changes of q and its distribution in a partially molten or fluid-rich environment in the interior of the Earth, the Moon, and terrestrial planets.

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For fluids that in the Earth typically consist of H2O, CO2, and salts such as chlorides, the q is the greatest for CO2 fluids and the smallest for brines (H2O þ salt). Essentially all CO2 fluids in contact with silicate minerals exhibit q > 60 and would not, therefore result in wetting of grain boundaries. This could be the situation during granulite metamorphism, for example, where the principal fluid remaining in granulite facies rocks is CO2. In the continental upper mantle, CO2 also is the dominant fluid so wetting by fluid in such tectonic settings is not likely. With H2O and H2O þ chlorides, however, the q < 60 so complete wetting of grain boundaries becomes common. This situation exists under lower grade metamorphism and during fluid transport in the upper portions of subduction zones (typically 60 so that it has been proposed that core formation in the Earth and terrestrial planets is not likely to reflect percolation of metal and/or sulfide melts through a crystalline matrix. Oxide-rich metallic melts, governed by high oxygen fugacity conditions, in contact with silicate perovskite at lower mantle pressures can, however, exhibit q-values less than 60 . Instead, separation of such melts from silicate magma to form metallic melt volumes that eventually aggregated to form a separate core under lower mantle pressure conditions would be a more likely process. One might surmise that similar processes governed core formation in other terrestrial planets and perhaps also the Earth’s Moon.

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