High Temperature Gas-Solid Reactions in Earth and Planetary Processes 9781501511790, 9781946850003

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REVIEWS in MINERALOGY and GEOCHEMISTRY Volume 84

2018

High Temperature Gas–Solid Reactions

in Earth and Planetary Processes EDITORS Penelope L. King

The Australian National University, Australia

Bruce J. Fegley, Jr.

Massachusetts Institute of Technology, USA

Terry Seward

Victoria University, New Zealand

Series Editor: Ian Swainson MINERALOGICAL SOCIETY of AMERICA GEOCHEMICAL SOCIETY

Reviews in Mineralogy and Geochemistry, Volume 84

High Temperature Gas–Solid Reactions in Earth and Planetary Processes

ISSN 1529-6466 (print) ISSN 1943-2666 (online) ISBN 978-1-946850-00-3

Copyright 2018

The MINERALOGICAL SOCIETY of AMERICA 3635 Concorde Parkway, Suite 500 Chantilly, Virginia, 20151-1125, U.S.A. www.minsocam.org www.degruyter.com The appearance of the code at the bottom of the first page of each chapter in this volume indicates the copyright owner’s consent that copies of the article can be made for personal use or internal use or for the personal use or internal use of specific clients, provided the original publication is cited. The consent is given on the condition, however, that the copier pay the stated per-copy fee through the Copyright Clearance Center, Inc. for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to other types of copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. For permission to reprint entire articles in these cases and the like, consult the Administrator of the Mineralogical Society of America as to the royalty due to the Society.

High Temperature Gas–Solid Reactions

in Earth and Planetary Processes 84

Reviews in Mineralogy and Geochemistry

iii

84

PREFACE Gas mixtures play a crucial role in distributing elements between different parts of Earth and planet-forming systems over a range of settings and temperatures. Despite the fundamental role of gases in geochemical cycles and their prevalence both in the crust and the early solar system, we are unaware of any reviews on this topic. This volume arose from an interest in promoting further research into the role of gases in geologic systems on Earth and beyond, with an aim to illuminate the gaps in our knowledge. We focus on high temperature interactions here because at low temperatures, low density, very low dielectric constant gas mixtures rather loosely 'physisorb' onto natural materials. In contrast, at higher temperatures solids volatilize and condense, lose/gain volatile components and heterogeneous chemisorption reactions occur between gases and solid surfaces. These reactions have previously had very little attention, but recent research has laid foundations for understanding these processes and their application to Earth and planetary environments. The volume is divided into five main topics that are outlined below. 1. Experimental and analytical approaches to characterising gas–solid reactions. 2. Modelling approaches to examining gas-solid reactions. 3. Terrestrial volcanic systems. 4. Planetary systems. 5. Industrial processes. Penelope King, Australian National University, Canberra, Australia Bruce Fegley, Washington University at St. Louis, St. Louis, USA Terry Seward, Victoria University of Wellington, Wellington, New Zealand

DEDICATION As in all of science, this volume builds on the work of our predecessors. We would like to dedicate the volume to the following researchers who have impacted not only our research approaches, but also our lives. C.W. Burnham (1922–2015)

W.S. Fyfe (1927–2013)

B.W. Chappell (1936–2012)

J.R. Holloway (1940–2017)

M.E. Fleet (1938–2017)

A.J.R. White (1931–2009)

1529-6466/18/0084-0000$00.00 (print) 1943-2666/18/0084-0000$00.00 (online)

http://dx.doi.org/10.2138/rmg.2018.84.0

High Temperature Gas–Solid Reactions

in Earth and Planetary Processes 84

1

Reviews in Mineralogy and Geochemistry

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TABLE OF CONTENTS Gas–Solid Reactions: Theory, Experiments and Case Studies Relevant to Earth and Planetary Processes

Penelope L. King, Vincent W. Wheeler, Christian J. Renggli, Andrew B. Palm, Siobhan A. Wilson, Anna L. Harrison, Bree Morgan, Hanna Nekvasil, Ulrike Troitzsch, Terrence Mernagh, Lindsey Yue, Alicia Bayon, Nicholas J. DiFrancesco, Riley Baile, Peter Kreider, Wojciech Lipiński NOTATION USED IN EQUATIONS........................................................................................2 INTRODUCTION.....................................................................................................................3 FLUIDS, GASES AND VAPORS.............................................................................................3 Crustal systems...............................................................................................................4 Silicate magmatic systems..............................................................................................5 Other settings for gas–solid reactions............................................................................7 TYPES OF HIGH TEMPERATURE GAS–SOLID REACTIONS...........................................7 Vaporization/condensation reactions..............................................................................8 Gas release or uptake reactions......................................................................................9 Catalysis reactions........................................................................................................10 Challenges in modeling gas–solid systems..................................................................10 A FRAMEWORK FOR UNDERSTANDING GAS–SOLID REACTIONS..........................11 FACTORS THAT INFLUENCE GAS–SOLID REACTIONS—WITH EMPHASIS ON THE SOLID...................................................................................................................12 Transport of gases.........................................................................................................13 Adsorption of a gas on a solid surface..........................................................................14 Solid state processes in surface–mediated gas–solid reactions....................................16 Dynamic evolution of the 3D solid architecture during gas–solid reactions................17 REACTION RATES................................................................................................................20 MODELING COMPLEX REACTIONS AND TRANSPORT PHENOMENA IN HIGH TEMPERATURE GAS–SOLID REACTIONS....................................................26 Multi-scale phenomena and homogenization...............................................................27 PRESERVATION OF GAS–SOLID REACTION PRODUCTS.............................................30 CASE STUDIES......................................................................................................................31 Case Study 1: Magmatic gas condensation in volcanic settings on planetary bodies..31 v

High Temperature Gas–Solid Reactions ‒ Table of Contents Case Study 2: CO2 uptake (carbonation) reactions and heat transfer...........................35 Case Study 3: Experimental and modeling study of mass, energy and momentum transfer in carbonation–decarbonation reactions.............................37 Case Study 4: Electron transfer via dehydrogenation–oxidation in amphiboles..........40 Case Study 5: Chemisorption reactions between SO2 and common silicate minerals.41 Case Study 6: Chemisorption reactions between S–Cl gas and common silicate minerals...................................................................................48 SUMMARY.............................................................................................................................49 ACKNOWLEDGMENTS........................................................................................................49 REFERENCES........................................................................................................................49

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Molecular Clusters and Solvation in Volcanic and Hydrothermal Vapors Kono H. Lemke, Terry M. Seward

INTRODUCTION...................................................................................................................57 THE MOLECULAR STRUCTURE OF WATER VAPOR (STEAM AND LOW DENSITY SUPERCRITICAL WATER)....................................................................60 Neutral Clusters............................................................................................................60 SOLVATION IN WATER VAPOR (SOLVATION IN AND ON NEUTRAL WATER CLUSTERS).......................................................................................65 The hydrated proton and hydroxide ions......................................................................65 THE ION PRODUCT CONSTANT, KW, OF STEAM............................................................70 SODIUM CHLORIDE IN STEAM/LOW DENSITY WATER VAPOR.................................73 SOLVATION OF METALS IN WATER VAPOR....................................................................74 EPILOGUE..............................................................................................................................79 ACKNOWLEDGMENTS........................................................................................................79 REFERENCES........................................................................................................................79

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Reaction Mechanisms and Solid–Gas Phase Reactions: Theory and Density Functional Theory Simulations James D. Kubicki, Heath D. Watts

INTRODUCTION...................................................................................................................86 Problems in determining reaction mechanisms............................................................86 BACKGROUND THEORY.....................................................................................................87 Experimental data related to reaction mechanisms......................................................87 Rate Laws.....................................................................................................................89 Transition State Theory................................................................................................91 QUANTUM MECHANICAL CALCULATIONS..................................................................93 Independence of model results.....................................................................................93 Example Calculations—Model Anorthite Interactions with SO2........................................................ 94 COMPUTATIONAL METHODS—VASP, ENERGY MINIMIZATIONS, AND MOLECULAR DYNAMICS SIMULATIONS...........................................................96 INITIAL ANORTHITE MODELS FOR HYPOTHESIS TESTING......................................97 RESULTS FOR ANORTHITE REACTIONS WITH SO2, OR SO2 AND H2O......................98 Hypothesis 1: Results...................................................................................................98 vi

High Temperature Gas–Solid Reactions ‒ Table of Contents Hypothesis 2: Results...................................................................................................99 Hypothesis 3: Results...................................................................................................99 SUMMARY...........................................................................................................................100 REFERENCES......................................................................................................................100

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Analytical Techniques for Probing Small-Scale Layers that Preserve Information on Gas–Solid Interactions Kim N. Dalby, Jeff. A. Berger, Helen E.A. Brand, Julie M. Cairney, Katja Eder, Stephen M. Eggins, Anna Herring, Richard L. Hervig, Peter B. Krieder, Terrence P. Mernagh, Andrew B. Palm, Christian J. Renggli, Ulrike Troitzsch, Lindsey Yue, Penelope L. King HISTORICAL DEVELOPMENTS OF ANALYTICAL TECHNIQUES APPLIED TO GAS–SOLID INTERACTIONS.................................................................104 Since the last MSA volume........................................................................................104 Some definitions.........................................................................................................104 THE MOST COMMON SAMPLE PREPARATION CHALLENGES................................107 Coating thickness.......................................................................................................107 Coating Stability.........................................................................................................108 CONFOCAL MICROSCOPY...............................................................................................111 A SHORT INTRODUCTION AND DEVELOPMENT HISTORY OF CONFOCAL MICROSCOPY......................................................................................111 APPLICATIONS OF CONFOCAL MICROSCOPY TO GAS–SOLID CHARACTERIZATION........................................................................111 ATOMIC FORCE MICROSCOPY (AFM)...........................................................................113 A SHORT INTRODUCTION AND DEVELOPMENT HISTORY OF AFM......................113 AFM BASICS........................................................................................................................113 APPLICATION OF AFM TO GAS–SOLID CHARACTERIZATION................................114 Glasses and coatings...................................................................................................115 Minerals......................................................................................................................115 RECENT DEVELOPMENTS IN AFM THAT OPEN UP APPLICATION.........................115 AFM-IR......................................................................................................................115 High P and T...............................................................................................................115 X-RAY COMPUTED TOMOGRAPHY (XCT)....................................................................116 A SHORT INTRODUCTION AND DEVELOPMENT HISTORY OF X-RAY COMPUTED TOMOGRAPHY (XCT)..........................................................116 APPLICATIONS OF XCT TO GAS–SOLID REACTIONS................................................117 THERMOGRAVIMETRIC ANALYSIS (TGA)...................................................................119 A SHORT INTRODUCTION AND DEVELOPMENT HISTORY OF THERMAL GRAVIMETRIC ANALYSIS, DIFFERENTIAL SCANNING CALORIMETRY, AND DIFFERENTIAL THERMAL ANALYSIS...................................119 IN SITU POWDER X-RAY DIFFRACTION (XRD) USING SYNCHROTRON RADIATION...........................................................................120 A SHORT INTRODUCTION AND DEVELOPMENT HISTORY OF IN SITU POWDER X-RAY DIFFRACTION (XRD)...................................................120 XRD BASICS........................................................................................................................120 XRD DATA INTERPRETATION..........................................................................................121 Phase identification.....................................................................................................121 Crystal structure refinement with the Rietveld method..............................................122 Microstructure refinement with whole powder pattern modelling.............................122 vii

High Temperature Gas–Solid Reactions ‒ Table of Contents Quantitative phase analysis........................................................................................122 Parametric Rietveld refinement..................................................................................123 POWDER DIFFRACTION AT A SYNCHROTRON............................................................123 In situ synchrotron powder X-ray diffraction (XRD) of gas–solid reactions.............124 Reaction rates during decarbonation via in situ synchrotron XRD...........................125 X-RAY PHOTOELECTRON SPECTROSCOPY (XPS) OR ELECTRON SPECTROSCOPY FOR CHEMICAL ANALYSIS (ESCA).................127 X-RAY PHOTOELECTRON SPECTROSCOPY (XPS) HISTORY....................................127 XPS BASICS.........................................................................................................................127 XPS SAMPLE PREPARATION AND THE ADVENTITIOUS CARBON PROBLEM........................................................131 DATA COLLECTION AND INTERPRETATION................................................................132 APPLICATION OF XPS TO GAS–SOLID REACTIONS...................................................133 The identification of the oxidation states of surface species......................................133 The characterization of sorption reactions on mineral surfaces.................................133 The characterization of alteration and weathering of mineral surfaces......................133 The studies of silicate bulk atomic structure in glasses..............................................134 RECENT DEVELOPMENTS IN XPS THAT OPEN UP APPLICATIONS TO GAS–SOLID REACTIONS.........................................................................................134 Ambient pressure XPS...............................................................................................134 Cryogenic XPS...........................................................................................................134 TRANSMISSION ELECTRON MICROSCOPY (TEM) AND SCANNING ELECTRON MICROSCOPY (SEM) TECHNIQUES.................................135 ELECTRON MICROSCOPY (EM) HISTORY....................................................................135 EM BASICS...........................................................................................................................136 Sources.......................................................................................................................138 Lens systems...............................................................................................................138 Detectors.....................................................................................................................139 Detectors in TEM.......................................................................................................139 Detectors in SEM.......................................................................................................139 Detectors in TEM and SEM.......................................................................................140 Common extras...........................................................................................................140 EM SAMPLE PREPARATION.............................................................................................142 APPLICATIONS OF EM TO GAS–SOLID REACTIONS..................................................143 Mineral and surface coatings......................................................................................143 LASER ABLATION-INDUCTIVELY COUPLED PLASMA MASS SPECTROMETRY (LA-ICPMS).......................................................................................145 LA-ICPMS HISTORY...........................................................................................................145 A SHORT HISTORY OF THE DEVELOPMENT AND TRENDS IN LA-ICPMS.............147 WHY LASER WAVELENGTH, PULSE LENGTH AND ENERGY DENSITY MATTER.............................................................................................................................147 Quantification.............................................................................................................148 COMMON ANALYTICAL ARTEFACTS AND CHALLENGES.......................................149 APPLICATIONS OF LA-ICPMS TO GAS–SOLID REACTIONS.....................................150 PARTICLE-INDUCED X-RAY EMISSION SPECTROMETRY (PIXE)...........................151 A SHORT INTRODUCTION AND DEVELOPMENT HISTORY OF PARTICLE INDUCED X-RAY EMISSION SPECTROMETRY (PIXE)...................151 PIXE BASICS........................................................................................................................151 PIXE SAMPLE PREPARATION..........................................................................................152 PIXE DATA INTERPRETATION.........................................................................................152 viii

High Temperature Gas–Solid Reactions ‒ Table of Contents ADVANTAGES AND DISADVANTAGES OF PIXE ANALYSIS......................................153 SECONDARY ION MASS SPECTROMETRY (SIMS)......................................................154 A SHORT INTRODUCTION AND DEVELOPMENT HISTORY OF SECONDARY ION MASS SPECTROMETRY (SIMS).............................................154 SIMS DEPTH PROFILING: DESCRIPTION, RESOLUTION, QUANTIFICATION, SIDE EFFECTS..................................................................................................................154 NANOSIMS...........................................................................................................................157 ATOM PROBE TOMOGRAPHY (APT)..............................................................................158 A SHORT INTRODUCTION AND DEVELOPMENT HISTORY OF ATOM PROBE TOMOGRAPHY (APT).....................................................................158 APT BASICS.........................................................................................................................158 APT SAMPLE PREPARATION...........................................................................................159 APPLICATIONS OF APT TO GAS–SOLID REACTIONS.................................................160 ACKNOWLEDGMENTS......................................................................................................161 REFERENCES......................................................................................................................162

5



Using Infrared and Raman Spectroscopy to Analyze Gas–Solid Reactions Terrence P. Mernagh, Penelope L. King, Paul F. McMillan, Jeff. A. Berger, Kim N. Dalby

LIST AND DEFINITION OF THE ACRONYMS, ABBREVIATIONS AND SYMBOLS USED IN THIS CHAPTER..................................................................177 INTRODUCTION.................................................................................................................178 MOLECULAR AND SOLID STATE VIBRATIONS...........................................................179 INFRARED SPECTROSCOPY............................................................................................182 INFRARED SPECTROMETER INSTRUMENTATION.....................................................182 TRANSMISSION IR SPECTROSCOPY..............................................................................184 Transmission IR analysis set-up and use ...................................................................184 REFLECTANCE IR SPECTROSCOPY...............................................................................186 Specular (bidirectional) and grazing angle reflectance IR spectroscopy....................189 Attenuated total reflection (ATR) IR spectroscopy....................................................191 Diffuse reflectance FTIR Spectroscopy (DRIFTS): biconical reflectance.................192 Directional-hemispherical reflection spectroscopy....................................................192 Mixed absorption–reflection spectroscopy.................................................................193 EMISSION SPECTROSCOPY.............................................................................................194 INFRARED SPECTROSCOPY APPLIED TO PRODUCTS OF GAS–SOLID REACTIONS.........................................................................................195 IR spectroscopy of powders.......................................................................................195 Microbeam-reflectance IR spectroscopy of minerals in rocks...................................198 Reflectance IR spectroscopy of coatings on substrates..............................................198 Polarized IR spectroscopy of crystallographically oriented and unoriented minerals..........................................................................................202 IR spectroscopy of dissolved volatiles in natural glasses...........................................204 RAMAN SPECTROSCOPY.................................................................................................204 Introduction................................................................................................................204 Classical and Quantum Mechanical Interpretation of the Raman Effect...................203 Challenges for Raman spectroscopy applied to mineral identification and quantitative analysis..........................................................................................206 ix

High Temperature Gas–Solid Reactions ‒ Table of Contents ENHANCEMENT OF THE INHERENTLY WEAK RAMAN SIGNAL FOR STUDIES OF MINERAL SURFACES AND GAS–SOLID INTERACTIONS.......208 Resonance Raman (RR) Scattering ..........................................................................208 Surface-enhanced Raman Scattering (SERS).............................................................208 Tip-enhanced Raman scattering (TERS) ...................................................................212 RAMAN SPECTROSCOPY APPLIED TO GAS–SOLID REACTIONS AND RELATED GEOLOGICAL SYSTEMS....................................................................213 Mineral and Surface Coatings....................................................................................213 Vesicular Glass and Volcanic Ash...............................................................................217 ADVANTAGES AND DISADVANTAGES OF RAMAN SPECTROSCOPIC TECHNIQUES FOR ANALYSIS OF GAS-SOLID REACTIONS...................................220 ACKNOWLEDGMENTS......................................................................................................220 REFERENCES......................................................................................................................220

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SO2 Gas Reactions with Silicate Glasses Christian J. Renggli, Penelope L. King

INTRODUCTION.................................................................................................................229 GLASS PROPERTIES...........................................................................................................230 EXPERIMENTAL TECHNIQUES.......................................................................................233 SO2(g) REACTIONS WITH Fe-FREE SILICATE GLASSES...............................................235 Mineralogy of phases formed on Fe-free glass substrates.........................................235 Textures of sulfate coatings on Fe-free glass substrates.............................................235 Compositional changes in the Fe-free glass substrate ...............................................239 SO2(g) REACTIONS WITH Fe-BEARING GLASSES.........................................................240 Mineralogy of phases formed on Fe-bearing glass substrates....................................240 Textures of sulfate coatings on Fe-bearing glass substrates.......................................241 Compositional changes in the Fe-bearing glass substrate..........................................243 DISCUSSION........................................................................................................................245 Role of the fugacities of SO2(g) and O2(g) on reactions with silicate glasses................246 Reaction rates.............................................................................................................249 Summary and outlook................................................................................................250 ACKNOWLEDGMENTS......................................................................................................251 REFERENCES......................................................................................................................252

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Unravelling the Consequences of SO2–Basalt Reactions for Geochemical Fractionation and Mineral Formation Andrew B. Palm, Penelope L. King, Christian J. Renggli, Richard L. Hervig, Kim N. Dalby, Anna Herring, Terrence P. Mernagh, Stephen M. Eggins, Ulrike Troitzsch, Levi Beeching, Leslie Kinsley, Paul Guagliardo

LIST OF ABBREVIATIONS USED.....................................................................................257 INTRODUCTION.................................................................................................................258 EXPERIMENTAL METHODS.............................................................................................259 ANALYTICAL METHODS..................................................................................................260 RESULTS...............................................................................................................................261 Textural observations—Reflected light and scanning electron microscopy (SEM)...261 Three-dimensional architecture—X-ray computed tomography (X-ray CT)............263 Surface chemistry—SEM–EDXS and X-ray photoelectron spectroscopy (XPS).....264 x

High Temperature Gas–Solid Reactions ‒ Table of Contents Mineralogy and molecular species—FTIR and Raman spectroscopy.......................265 Chemical profiling and isotopic mapping—nanoSIMS, LA-ICPMS, and SIMS.......267 DISCUSSION........................................................................................................................272 Element fractionation in SO2–basalt reactions...........................................................274 Future Work................................................................................................................279 CONCLUSIONS....................................................................................................................280 ACKNOWLEDGMENTS......................................................................................................281 REFERENCES......................................................................................................................281

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High Temperature Reactions between Gases and Ash Particles in Volcanic Eruption Plumes Pierre Delmelle, Fabian B. Wadsworth, Elena C. Maters, Paul M. Ayris

INTRODUCTION.................................................................................................................285 ERUPTION PLUME: GENERATION, COMPOSITION AND TEMPERATURE......................................................................................................288 Generation..................................................................................................................288 Composition...............................................................................................................288 Temperature................................................................................................................290 METHOD OF INVESTIGATING THE HIGH TEMPERATURE REACTIONS OF VOLCANIC GASES ON ASH...........................................................................................291 Aluminosilicate glass as a proxy for volcanic ash......................................................291 Experimental apparatus..............................................................................................291 Post-experiment analysis............................................................................................292 HIGH TEMPERATURE UPTAKE AND REACTION OF SULFUR DIOXIDE AND HYDROGEN CHLORIDE GASES WITH ALUMINOSILICATE GLASS...........292 Sulfur dioxide uptake and reaction.............................................................................293 Hydrogen chloride uptake and reaction......................................................................298 Effect of mixed gas atmospheres................................................................................299 MODELING THE UPTAKE OF SULFUR DIOXIDE AND HYDROGEN CHLORIDE GASES ON VOLCANIC ASH.....................................301 Constraints on Ca and Na diffusion............................................................................301 Application to eruption plumes..................................................................................303 SUMMARY AND CONCLUSIONS.....................................................................................303 ACKNOWLEDGMENTS......................................................................................................305 REFERENCES......................................................................................................................305

9

Gas–Solid Reactions in Arc Volcanoes: Ancient and Modern Richard W. Henley, Terry M. Seward

INTRODUCTION.................................................................................................................309 VOLCANIC GAS EXPANSION...........................................................................................312 FUMAROLE GAS CHEMISTRY.........................................................................................315 Gas phase species distributions..................................................................................317 SUBLIMATE MINERAL DEPOSITION: CLOSED SYSTEM GAS–SOLID REACTIONS..............................................................324 ROCK ALTERATION IN VOLCANOES: xi

High Temperature Gas–Solid Reactions ‒ Table of Contents OPEN SYSTEM GAS–SOLID REACTIONS...................................................................329 DISCUSSION........................................................................................................................341 ACKNOWLEDGMENTS......................................................................................................343 SUPPLEMENTARY INFORMATION.................................................................................344 REFERENCES......................................................................................................................344

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Gas–Solid Interactions on Venus and Other Solar System Bodies Mikhail Yu. Zolotov

INTRODUCTION.................................................................................................................351 VENUS..................................................................................................................................352 The atmosphere and surface materials.......................................................................352 Approaches.................................................................................................................354 Reactions of minerals with specific atmospheric gases..............................................356 Venus’ history and gas–solid interactions..................................................................373 Summary and further efforts......................................................................................375 MARS....................................................................................................................................377 High-temperature interactions....................................................................................378 IO .........................................................................................................................................380 CONCLUSIONS....................................................................................................................381 ACKNOWLEDGMENTS......................................................................................................382 REFERENCES......................................................................................................................382

11

Thermodynamics of Element Volatility and its Application to Planetary Processes Paolo A. Sossi, Bruce Fegley, Jr.

INTRODUCTION.................................................................................................................393 THERMODYNAMICS OF EVAPORATION/CONDENSATION OF METAL OXIDES IN SIMPLE, COMPLEX AND NATURAL SYSTEMS................396 Equilibrium evaporation/condensation.......................................................................396 Kinetic Evaporation....................................................................................................414 EVAPORATION IN THE PRESENCE OF MAJOR VOLATILES H, C, S AND HALOGENS.................................................................................................425 Overview....................................................................................................................425 Calculations in a multicomponent gas mixture..........................................................427 Zn-bearing gases.........................................................................................................428 Factors governing the stability of gas species............................................................429 VOLATILITY DURING PLANETARY FORMATION.......................................................432 Overview....................................................................................................................432 Planetary Bodies.........................................................................................................434 The Earth....................................................................................................................436 The Moon and Vesta...................................................................................................438 CONCLUSIONS....................................................................................................................440 ACKNOWLEDGMENTS......................................................................................................442 REFERENCES......................................................................................................................443 xii

High Temperature Gas–Solid Reactions ‒ Table of Contents

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Kinetics of Gas–Solid Reactions in the Solar System and Beyond Hiroko Nagahara

INTRODUCTION.................................................................................................................461 THEORETICAL BASIS OF ELEMENTAL FRACTIONATION DURING HIGH TEMPERATURE EVAPORATION AND CONDENSATION...............................462 Chemical equilibrium around stellar environments....................................................462 Hertz-Knudsen relation..............................................................................................464 Condensation and evaporation coefficients................................................................466 Evaporation and condensation of crystals..................................................................467 Anisotropy for evaporation and condensation of crystals..........................................468 Mode of evaporation and condensation in multicomponent systems.........................468 EXPERIMENTAL METHODS FOR EVAPORATION AND CONDENSATION OF COSMOCHEMICALLY IMPORTANT MINERALS.................................................469 Evaporation experiments............................................................................................469 Condensation experiments..........................................................................................472 High temperature gas reaction experiments...............................................................472 EVAPORATION OF COSMOCHEMICALLY IMPORTANT MINERALS........................476 Forsterite.....................................................................................................................476 Mg–Fe olivine solid solution......................................................................................481 Al2O3.......................................................................................................................................................................................................................481 Fe................................................................................................................................483 Enstatite......................................................................................................................484 FeS..............................................................................................................................485 Plagioclase..................................................................................................................486 Amorphous SiO..........................................................................................................487 CONDENSATION OF COSMOCHEMICALLY IMPORTANT MINERALS....................489 Forsterite.....................................................................................................................489 Al2O3.......................................................................................................................................................................................................................489 Metallic iron...............................................................................................................490 Enstatite......................................................................................................................491 FeS..............................................................................................................................491 Olivine........................................................................................................................491 Spinel..........................................................................................................................492 CONCLUSIONS....................................................................................................................493 ACKNOWLEDGMENTS......................................................................................................493 REFERENCES......................................................................................................................494

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High-Temperature Gas–Solid Reactions in Industrial Processes Peter Kreider, Wojciech Lipiński

INTRODUCTION.................................................................................................................499 DEFINING HIGH-TEMPERATURE....................................................................................499 GAS–SOLID HETEROGENEOUS REACTIONS...............................................................501 INDUSTRIAL CONTEXT....................................................................................................504 xiii

High Temperature Gas–Solid Reactions ‒ Table of Contents Metals.........................................................................................................................506 Minerals......................................................................................................................508 Chemicals and petrochemicals...................................................................................509 SOLAR THERMOCHEMICAL REACTIONS....................................................................511 ACKNOWLEDGMENTS......................................................................................................512 REFERENCES......................................................................................................................512

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Reviews in Mineralogy & Geochemistry Vol. 84 pp. 1–56, 2018 Copyright © Mineralogical Society of America

Gas–Solid Reactions: Theory, Experiments and Case Studies Relevant to Earth and Planetary Processes Penelope L. King1, Vincent M. Wheeler2, Christian J. Renggli1 Andrew B. Palm1, Siobhan A. Wilson3, Anna L. Harrison4 Bree Morgan5, Hanna Nekvasil6, Ulrike Troitzsch1 Terrence Mernagh1, Lindsey Yue2, Alicia Bayon7 Nicholas J. DiFrancesco6, Riley Baile1, Peter Kreider2 Wojciech Lipiński2 1

Research School of Earth Sciences The Australian National University Canberra ACT 2601 Australia 2 Research School of Engineering The Australian National University Canberra ACT 2601 Australia

3

Department of Earth and Atmospheric Sciences University of Alberta Edmonton, AB T6G 2E3 Canada 4

Department of Earth Sciences University College London London, WC1E 6BT UK 5

School of Geosciences The University of Sydney Camperdown, NSW 2006 Australia 6

Department of Geosciences SUNY Stony Brook Stony Brook, NY 11794–2100 USA 7

CSIRO Energy GPO Box 330 Newcastle NSW 2300 Australia

1529-6466/18/0084-0001$10.00 (print) 1943-6266/18/0084-0001$10.00 (online)

http://dx.doi.org/10.2138/rmg.2018.84.1

King et al.

2

NOTATION USED IN EQUATIONS  α

conversion fraction

Nj

moles of j

specific interfacial surface area

∇

differential operator in three-dimensions

C

number of components

W

temperature dependent collision integral (Lennard– Jones potential)

cp

critical point

P

pressure

Dij

molecular diffusion of gases i, j

pg

local gas pressure

DK g

Knudsen diffusion of gas

p

number of phases

A

D

effective diffusion of a mixed gas i in porous media

ɸ

phase (solid, liquid, gas, supercritical fluid)

dpore

pore diameter

φ

porosity

Ea

activation energy in the Arrhenius equation

power per volume delivered by heat transfer

G

pre–exponential factor in the Arrhenius equation

q q rad

DG[R]

Gibbs free energy change for reaction R

R

gas constant

∆G

Gibbs free energy change for reaction R in the standard state

R

chemical reaction or mass transport phenomenon (subscript)

DHTmax

enthalpy at the maximum temperature where two competing reactions have equal Gibbs free energy of reaction

R0

initial radius of a sphere before reaction

e

volume fraction

rc n

radius of a reacting sphere during reaction at time n

e−

electron

g rads

rate of adsorption of a gas

eff i

o [ R]

φ j

radiative heat flux vector

f(a)

function to describe a rate of reaction

r

rate of transport of a reacting phase j

fj

fugacity of gas species j

r

density

f

force per volume acting on the material

si,j

average collision diameter of gases i and j

F

degrees of freedom

sj

solid species j

' j

gj

gas species j

s

g > cp

supercritical fluid

t

time

H Φj

enthalpy of species j in phase ɸ

tn

time after time step n

I

number of intensive variables

T

temperature

κ

effective permeability

c

tortuosity

k

mass transfer coefficient (reaction rate constant)

t

total time for reaction

kB

Boltzmann constant

τ

stress tensor

keff

effective thermal conductivity

m

effective viscosity of the gas

K

equilibrium constant

v

velocity vector

lj

liquid species j

V

volume

l

mean free path length of the gas

Vm

molar volume

m gj

mean flux of gas j

Vp

vapor

Mg j

molar mass for gas j

wj

mass fraction of species j

transferred

W

power per unit volume delivered by mass transfer

number of electrons transferred

x

formal charge on an atom

X

volatile species

x+n + M ( ) M is a multivalent metal with formal charge x and n electrons multi

n

g

solid species j modified

Gas–Solid Reactions Relevant to Earth and Planetary Processes

3

INTRODUCTION High temperature gas–solid reactions interactions are ubiquitous in and on the Earth and other planetary bodies (Fig. 1). In these natural systems, gases are elusive. Like a hurricane’s wind that leaves a path of destruction but no trace of wind after the event, the gas that initiated a gas–solid reaction may be conspicuously absent. Because gases effectively escape from geologic systems, gas–solid reactions may only be recorded by their stable, or metastable, solid reaction products. In this chapter, we seek to unravel the evidence and approaches that can be used to examine gas–solid reactions, especially through their solid reaction products. We define the major types of gas–solid reactions, paying particular attention to surface-mediated reactions. Factors that influence gas–solid reactions are presented followed by models for transfer of mass, energy and momentum. We then examine case studies in which different experimental, analytical and modeling approaches have been used to investigate gas–solid reactions. We highlight the evidence for these reactions such as unusual phase assemblages including salts (e.g., sulfates and chlorides), chemical anomalies and textural features. a. Natural settings for gas-solid reactions Early solar system

Volcanic plume Fumerole Ore deposit Magma

b. Anthropogenic settings for gas-solid reactions

Meteorite Impact

Particulate emissions

e.g., smelters, construction, transport, energy plants

Gas sequestration or extraction

Figure 1. (a) Natural settings for gas–solid reactions include the early solar system (Sossi and Fegley 2018, this volume; Nagahara 2018, this volume); magmatic systems (Delmelle et al. 2018, this volume; Henley and Seward 2018, this volume) and impact events. (b) Anthropogenic settings for gas–solid reactions include locations where particulates are emitted with gases at high temperature and gas sequestration or extraction settings (e.g., Kreider and Lipiński 2018, this volume).

FLUIDS, GASES AND VAPORS

Fig. 1

In the geosciences, there has been some ambiguity in the use of the terms fluid, gas and vapor. Here, we adopt the generic term for ‘fluid’, where it is a type of matter with no shear modulus that responds to force by movement. A ‘gas’ is a state of matter where particles (molecules or atoms) are relatively small compared to the distance between them; an ideal gas is a low density phase with negligible forces between particles. Gas particles are generally in constant, independent and random motion (i.e., Brownian motion) and they travel until they collide with another particle where they may either be deflected or interact. Ideal gases follow relatively simple rules for interaction, whereas real gases have more complex interactions (e.g., Atkins et al. 2018). Here, ‘gas’ (g) is used for fluids with gas-like properties: typically with densities less than 0.5 g cm–3, compared to liquid water which has a density near ~1.0 g cm–3 at room conditions, and silicate melts with densities greater than 2.0 g cm–3. The term ‘gas’ is particularly useful when the pressure and temperature conditions relative to the critical point are unknown. In contrast, it is possible to use the term ‘supercritical fluid’ (g > cp) for a single phase mobile phase with a density between liquid and gas in the case where it is known that the phase exists at pressure and temperature conditions above the critical endpoint (cp). We use the term ‘vapor’ (Vp) for a gas that coexists with a condensed phase (i.e., a liquid or solid), which is a convenient way to indicate that the vapor was derived from a single phase.

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4

The use of these terms is illustrated in Figure 2 for a model substance that contracts upon freezing (unlike water). The phase relations are shown in three-dimensional (3D) space for pressure, temperature and volume in Figure 2a. Two dimensional cross-sections are also included showing isochoric (constant volume; Fig. 2b), isothermal (constant temperature; Fig. 2c) and isobaric (constant pressure; Fig. 2d) sections. The gas phase exists not only above cp, but also at conditions where pressures are low and temperatures and volume are high. Water in the gas phase shows similar relations except (Fig. 3a) that it expands upon freezing (e.g., Atkins et al. 2018).

Crustal systems

Figure 2. (a) P–V–T diagram showing the surfaces for a substance that contracts upon freezing (i.e., not water), modified from Cengel and Boles (2014). s–solid, l–liquid, g–gas at conditions below the critical point and g>cp–gas at conditions greater than the critical point. (b) Isochoric section (constant V). (c) Isothermal section (constant T). (d) Isobaric section (constant P).

Gases play a crucial role in distributing elements between different parts of planet-forming systems (Fig. 1) over a range of settings and temperatures (Delmelle et al. 2018, this volume; Henley and Seward 2018, this volume; Palm et al. 2018, this volume; Renggli and King 2018, this volume; Sossi and Fegley 2018, this volume). Within the crust, H2O-rich gas may move between the grains in a rock or sediment, facilitated by pressure gradients, gas buoyancy and/or tectonic forces. As gases move in the subsurface at high temperatures, they may be trapped as inclusions in a thermally annealing rock, or react with the rock and create new minerals (e.g., Eugster and Skippen 1967). Gases trapped in magmas may create overpressure resulting in fracturing and brecciation, for example, in the subvolcanic porphyry environment (Burnham 1985); in explosive volcanic eruptions (Sparks 1978) and in the metamorphic environment (Eugster and Skippen 1967). To understand the stability and prevalence of gases in the crust, it is instructive to examine the density of water and that of water with dissolved constituents as a function of pressure (P) and temperature (T). Water is the most abundant gas phase in most high temperature systems on Earth and it commonly combines with other gases (e.g., CO2, CH4, H2S, SO2) and may dissolve solids such as NaCl and SiO2 (e.g., Kennedy et al. 1962). At shallow crustal temperatures and pressures ( 970 ºC to form anhydrite. These observations are consistent with the aforementioned contrast in the Vm values of CaO, CaCO3 calcite and CaSO4anhydrite.

a. Themal annealing & fluid entrapment

b.

0.5 µm, SEM

c.

2 µm, SEM

Figure 10. (a) Schematic diagram showing how thermal annealing and fluid entrapment result in grain coarsening, formation of near triple-point boundaries and trapping of fluid inclusions (modified extensively after Szekely et al. 1976). (b) Field emission-SEM image of mineral replacement textures after full pseudomorphic conversion of calcite (CaCO3) to porous lime (CaO) at 850 ºC showing in gas–mineral reactions oriented attachment of nanoparticles (reproduced from Figure 3 in Rodriguez-Navarro et al. 2009). (c) Field emission-SEM image showing loss of reactive surface area and porosity in CaO following sintering at 1150 ºC (reproduced from Figure 3 in Rodriguez-Navarro et al. 2009).

Passivation of the surface. Gas–solid reactions may eventually completely coverFig. 10 the reacting solid with one or more solid reaction products (e.g., Figs. 4, 6 and 10b, c). A classic example of passivation is the oxidation of metal to form rust. If a solid product is porous and permeable (e.g., Figs. 4 and 7), as is commonly the case due to the large changes in Vm, then the gas may still be transported to the unreacted core of the solid reactant, thereby sustaining the reaction (e.g., Kreider and Lipiński 2018, this volume). Sustained reactions with positive volume changes are reported in environments rich in magmatic gases and allow for effective transport of large quantities of sulfur in the subsurface that is required to form porphyry and skarn ore deposits (Henley et al. 2015, 2017). Alternately, permeability may be created by deformation and fracturing of the product layer providing access to the surface of the reactant (e.g., Renggli and King 2018, this volume). It is important to note that permeability does not necessarily increase with enhancements to porosity. This is in part because two types of porosity are generated during chemisorption reactions and other types of replacement reactions: intergranular porosity, which creates pore spaces between solid grains, and intragranular porosity, which creates isolated pores and fluid inclusions. However, both types of porosity may be lost during annealing at high temperature or during ‘textural equilibration’ (Fig. 10a), an annealing process that is driven by minimization of interfacial energy associated with the high surface area of a porous mineral (Ruiz–Agudo et al. 2014). If pore spaces are destroyed or isolated, a reaction becomes self–limiting by generating a passivating layer of the solid product(s) that coat the solid reactant and hinders gas transport to any remaining reactant.

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King et al.

The degree to which an altered layer is passivating depends in part on the structural similarity between the solid product and the unaltered solid reactant (e.g., Cubillas et al. 2005). When structurally similar, the growth of the solid product will be epitaxial (i.e., it will form with some degree of crystallographic continuity in the case of a mineral reactant) and its structure will build up layer–by–layer to completely cover the surface of the solid reactant as the reaction progresses. Epitaxial replacement tends to be quite common in mineral replacement reactions in aqueous systems (e.g., replacement of K-feldspar by albite; Norberg et al. 2011). As described above in many high temperature gas–solid reactions, structural and volume differences commonly exist between solid reactants and product(s) causing the salt products to grow as discontinuous, discrete islands (e.g., Delmelle et al. 2018, this volume; Palm et al. 2018, this volume; Renggli and King 2018, this volume; below). Such coatings provide permeable pathways for continued interaction between the gas and solid reactants (e.g., Kreider and Lipiński 2018, this volume). In addition, these salt–rich coatings may be underlain by impermeable, silicarich and alumina-rich or aluminosilicate layers that result from the depletion of cations as a reaction progresses (Li et al. 2010; Palm et al. 2018, this volume; Renggli and King 2018, this volume). The Si–Al–O–rich layers may eventually block either diffusing cations or reactive surface sites, limiting the progress of the reaction in a manner similar to what has been widely reported for silica– rich residues found in aqueous systems (Ruiz–Agudo et al. 2012, 2014; Schott et al. 2012). These processes result in a rim of alteration products around the solid reactant, which can be represented simplistically by the Shrinking Core model discussed in more detail below. REACTION RATES As discussed and illustrated above (e.g., Figs. 4, 7, 8), reactions between gases and solids require a mechanism for transport of reagent gases to the reactive solid surface and for gaseous products to be transported away. Depending on the relative rates of reaction and transport, the overall rate of reaction is controlled by either the intrinsic kinetics of gas–solid reaction (i.e., it is ‘reaction-controlled’) or by the rate of transport (i.e., it is ‘transport-controlled’). The overall reaction can shift from reaction- to transport-controlled as the solid products (i.e., mineral or amorphous phase(s)) build up to encase the solid reactant. In this case, the reaction becomes limited by the rate of diffusion through the solid product where the unreacted solid is passivated by an alteration zone of a secondary solid product. Simple gas–solid reactions such as calcite–SO2 (Fegley and Prinn 1989) have been successfully modeled using the Arrhenius equation: − Ea dα (26) = Γ e RT dt where a is the conversion fraction (e.g., amount of gas consumed or amount of product produced), a is a pre-exponential factor, Ea is the activation energy, T is the absolute temperature and R is the gas constant. This is a so-called ‘zero-order’ model (Table 3), and it works well for isolated particles reacting with a diffusive gas film with no impediments to the reaction. However, Arrhenius models do not adequately describe systems that dynamically evolve in terms of temperature, gas and solid composition and 3D solid architecture (i.e. buildup of a product that impedes access of the gas to the reactant solid) (Lyakhov et al. 1985; Maciejewski and Reller 1987; Galwey and Brown 1999). In most geologic cases, different strategies are needed to model gas–solid reactions.

Gas–Solid Reactions Relevant to Earth and Planetary Processes

21

Table 3. Conversion-time expressions for different kinetic models (from Galwey and Brown 1999; Levenspiel 2004; symbols given in text). α*



g(α) Reaction order control Zero-order control (gas-film control, shrinking core)

a −ln (1 − α )

First-order reaction

 rc   +1 

n

1 − e  R0

Nucleation and growth model: Avrami-Erofe’ev, sigmoidal a-time Nucleation and growth, n = order of reaction

−ln (1 − α )

1

n

 rc   +1 

n

1 − e  R0

Reaction control (Geometrical model) Shrinking Sphere (Contracting Vol.) Small particle, Stokes regime

1 − (1 − α )

1

Shrinking Core for constant sized spheres (Contracting Area)

1 − (1 − α )

1

3

2

r  1−  c   R0 

3

r  1−  c   R0 

2

Product diffusion control (Ginstling–Brounshtein) Shrinking Core for constant sized spheres (Contracting Area)

1 − (1 − α )

2

3

2 α 3

−

Gas film diffusion control Shrinking Sphere (Contracting Vol.) Small particle, Stokes regime

1 − (1 − α )

2

Shrinking Sphere (Contracting Vol.) Large particle, turbulent regime

1 − (1 − α )

1

* Note that

rc = R0

3

3

(1 − kt ) , where k is a reaction rate constant.

Another approach is to use a generalized rate equation (Levenspiel 2004): − Ea dα 1 dα (27) = Γ e RT f ( α ) ; f ( α ) = dt k dt where f(a) is a differential form of a reaction model that describes the conversion fraction and k is a rate constant (Galwey and Brown 1999). The g(a) function is the integral form of the reaction α dα model: g ( α ) =∫ and it is generally more convenient to use when plotting reaction conversion f (α) 0 as a function of time. Equations for g(a) for several different reaction models are reported in Table 3.

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Types of reaction models. Reaction models are ideally developed based on the physics of the reaction pathway in the system, but they may also be derived empirically (e.g., Brown et al. 1980; Galwey and Brown 1999). For example, some studies work from a set of possible initial reaction models and attempt to fit the data (or a selected range of data) to determine the best g(a). Several models have been developed to address gas–solid reactions. The first-order reaction model, also known as progressive conversion, assumes a reacting particle has unchanging size, with the reaction occurring throughout the entire particle simultaneously (Levenspiel 2004). Here, the rate does not depend on the concentration of the solid reactant, and it is assumed that the diffusion coefficient and coefficients of mass transfer do not change. First-order reaction models are commonly used for these types of reactions that are typified by either gas release/ uptake reactions (e.g., Figs. 6b, 10b,c) or where molecular diffusion dominates (Fig. 7a). This type of process is modeled by a first-order kinetic model where g(a) = −ln(1 − a) (Table 3) if gas phase transport is fast relative to reaction rate (Galwey and Brown 1999). Johnson and Fegley (2003) successfully used a first-order reaction model combined with the Arrhenius equation to explain decomposition rates of tremolite powder (Ca2Mg5Si8O22(OH)2; Fig. 11a,b). Those authors measured the mass loss during decomposition and dehydroxylation of tremolite (fraction reacted, α) over a range of temperatures and times (Fig. 11a). These data were then fit using a first-order reaction model (in this case, it is the same as a nucleation and growth model or Avrami-Erofe’ev model with an exponent of unity; Table 3). The data were then used to model the potential solid phases on Venus’s gas-rich surface (Johnson and Fegley 2003). Temperature (°C)

a.

0.8 0.6

800

700

b.

-4

-6 -6

0.4

0

2

4

6

-8

-10

Symbols - Samples Open – powder Solid – crystal

0.2 0.0

900

-2

log(rate) (hr‒1)

Fraction reacted, α

1.0

1200 1100 1000 0

Lowland surface temperature on Venus 740K

-12 -14 8

Reduced time (t/t0.5)

10

8

9

10

11

12

13

14

10,000 / T (K-1)

Figure 11. Decomposition kinetic data for tremolite [Ca2Mg5Si8O22(OH)2)] modified from Johnson and Fegley (2003). (a) Reduced time plots showing fraction reacted, α, calculated based on the mass loss where reduced time is time normalized to 50% decomposition time. Data is for a range of powder and crystal experiments run at different temperatures discussed by the authors. (b) Reaction Fig. rate 11 constants versus 10,000/T shown in an Arrhenius plot. The open symbols represent powders run in slightly different conditions and the solid diamonds are for tremolite crystals. The solid line is a linear regression through the powder data with 95% confidence intervals for the regression shown by the dashed lines. [Used by permission of Elsevier, from Johnson and Fegley (2003), Icarus, Vol 164, Fig. 4b, p. 322 and Fig. 5, p. 323.]

In contrast to the system described above, many geologic systems involve small gas volumes and changing surfaces (i.e., dominantly Knudsen diffusion or diffusion in porous media; Figs. 7b,c). In these cases it is necessary to apply other models that include the ‘Shrinking Sphere’ (contracting volume) and ‘Shrinking Core’ (contracting area) methods for modeling gas–solid reactions (Yagi and Kunii 1955; Szekely et al. 1976; Galwey and Brown 1999; Levenspiel 2004).

Gas–Solid Reactions Relevant to Earth and Planetary Processes

23

Shrinking Sphere models. These models represent reaction rates of a particle that shrinks in size during reaction with an homogeneous ‘film’ of surrounding gas, where any product layer either does not form or is removed (Fig.12a; Table 3) (Szekely et al. 1976; Levenspiel 2004). Shrinking Sphere models assume that the radius (r) of the solid reactant decreases with time (t) as a reaction progresses (i.e., in Fig. 12: rc → rc2 with rc > rc2 over time, t → t2). The Shrinking Sphere models may be applied to gas release reactions where the solid shrinks in volume, including decomposition reactions; for example, the loss of H2O gas from a hydrous sulfate mineral (e.g., see Table 4) or vaporization reactions. Also, Shrinking Sphere models are applied to surface–mediated reactions where the product forms and is subsequently removed from the surface of the solid reactant; for example, solids that are vaporized as gases, or effectively removed as solid flakes (e.g., in a turbulent volcanic plume). Shrinking Sphere models have two main forms: ‘transport–controlled’ models that are controlled by ‘film’ or gas diffusion (either Stokes or turbulent gas regimes) and ‘reaction controlled’ or geometrical models (Fig. 12b, Table 3). The extent of conversion of a solid reactant to a solid product is typically plotted against the ratio of the reaction time and the time required for complete conversion (τ; Fig. 12b).

a. Shrinking Sphere models R0=rc

time t1 Reaction front

Gas film

rc1

time t2

rc2

Product removed

b. Reaction progress for a single sphere Fraction reacted, α

1.0 0.8 0.6 0.4 0.2

Reaction control Turbulent regime, Gas film diffusion control Stokes (laminar) regime, Gas film diffusion control

0.0 0.0 0.2 0.4 0.6 0.8 Time for complete reaction, t/τ

1.0

Figure 12. Schematic representation of the Shrinking Sphere model (modified after Levenspiel 2004). Fig. 12(a) Grey (interior with R0 = rc) represents the reactant, the black line represents the reaction front and the dotted line indicates the extent of the gas film. Over time, the sphere shrinks; for example, after time t1, the sphere shrinks to radius rc1. (b) Fractional conversion of the solid reactant to the solid product (a) versus fractional time, defined as the ratio of the reaction time, t, to the time required for complete conversion, τ. The black line represents the behavior of a chemical reaction-controlled process, the dashed line represents the behavior of a turbulent film-diffusion controlled process, and the dotted line indicates a Stokes regime (laminar) filmdiffusion controlled process. The equations for these different processes are given in Table 3.

Shrinking Core models. Shrinking Core models (Szekely et al. 1976; Levenspiel 2004; Teir et al. 2007) represent the reaction of a particle of unchanging overall size that is converted from a solid reactant to a solid product, leaving a progressively smaller unreacted core of the solid reactant beneath the product layer (Fig. 13; Table 3). Examples of Shrinking Core reactions include (1) oxidation of Fe-alloy to produce wüstite (Eqn. 14) during entry of a micro-meteorite into Earth’s atmosphere (Fig. 6b; Tomkins et al. 2016), (2) oxidation of a grain of pyrite on exposure to O2 gas (e.g., Nicholson et al. 1990), or (3) formation of carbonates from (hydr)oxide or silicate minerals during reaction with CO2 (Case Studies 2 and 3).

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Table 4. Equilibrium constants and melting [or decomposition] points in air of common K-, Na-, Ca-, Mg- sulfates and chloridesa Meas. ln K b

Chemistry Mineral name Formula

Calc. ln K c

Melting moi / RT c [decomposition] temperature, °C

Sulfates K Na Ca

–1.78

–532.39

1069 d

0.58

–417.57

200 d

–0.29

–512.35

884 d

Na6(SO4)2(CO3)

–0.77

–1449.4

[392] [e]

Gypsum

CaSO4·2H2O

–4.58

–725.56

1460 d

Bassanite

CaSO4·0.5H2O

Anhydrite

CaSO4

Epsomite

MgSO4·7H2O

Hexahydrite

Arcanite

K2SO4

Mercallite

KHSO4

Thenardite

Na2SO4

Burkeite

–1.87 –0.3

1460 d –4.36

–533.73

1460 d

–2.13

–1.88

–1157.83

1137 d

MgSO4·6H2O

–2

–1.63

–1061.60

1137 d

Kieserite

MgSO4·H2O

0.2

–0.12

–579.80

1137 d

K–Na

Aphthitalite

NaK3(SO4)2

–3.80

–1057.05

709 f

K/Na–Ca

Polyhalite

K2Ca2Mg(SO4)4·2H2O

–13.74

–2282.5

[233] [g]

Syngenite

K2Ca(SO4)2·H2O

–7.45

–1164.8

[227] [h,i]

Eugsterite

Na4Ca(SO4)3·2H2O

–5.67

–1751.45

[150] [j]

Glauberite

Na2Ca(SO4)2

–5.24

–1047.45

520 k

Langbeinite

K2Mg(SO4)3

Löweite

Na12Mg7(SO4)13·15H2O

Blödite

Na2Mg(SO4)2·4H2O

K

Sylvitex

KCl

Na

Halitex

NaCl

Mg

K/Na–Mg

944 l [227] [m] –2.35

–1383.6

[107] [m]

0.894

0.90

–164.84

771 d

1.56

1.57

–154.99

802 d

–2.38 Halides

Villiaumite

NaF

Mg

Bischofite

MgCl2·6H2O

K–Mg

Carnallitex

Ca–Mg

KMgCl3·6H2O x

Tachyhydrite CaMg2Cl6·12H2O

–0.375

996 d

p

4.29

4.45

–853.1

[100] [d]

4.1

4.33

–1020.3

[230] [n]

16.32

17.38

–2015.9

[150] [o]

(a) We omitted salts that decompose at low temperatures (650°

Gwater flow

Magmatic reservoir

b. Waning 250°

Subsurface salt products flooded by groundwater

50° 150°

~4km

Hydrostatic Lithostatic

Waning reservoir

Figure 15. (a) Schematic cross-section through an active volcanic system showing the locations of high temperature gas–solid reactions in both the subvolcanic system and volcanic plume (modified after Henley et al. 2015). Gas expansion from a magma reservoir at depth expands into the crust (1000 °C; Fig. 17a) with little air contamination and is therefore considered to be a reasonable representation of a magmatic gas (de Moor et al. 2013). The high temperature gas was collected in a silica tube to sample a range of sublimates over a temperature gradient (Fig. 17a–c) by Zelenski et al. (2013). They found that silica/silicates and oxides formed at 750–1100 °C, and native chalcogens such as S, Se and Te at the lowest temperatures (1000°C

0

~150°C

200

c.

200 mm

c.

d. Temperature (°C)

b.

Erta Ale silica tube sulfides sulfates halides fluorosilicates S, Se, Te

400

600

800

1000

Distance (mm)

Momotombo (basaltic andesite)

1200 Erta Ale  silica tube

1000 800

Piton de la Fournaise (alkali basalt) Merapi (andesite)

600 400

Initial T

200 0

tungstates

Mt St Helens (dacite)

Assumed final T 0

200

400

600

800

Distance (mm)

1000 800 700

600 500

400

300

Temperature (°C)

200

100

0

Figure 17. (a) Silica glass tube inserted in a high temperature fumerole at Erta Ale by Zelenski et al. (2013). Fig. 17 Annotations to the original figure show the transfer of mass, energy and momentum along the thermal gradient in the tube. (b) Temperature recorded initially in the tube and assumed for deposition by Zelenski et al. (2013). (c) Phases identified by Zelenski et al. (2013) along the silica tube as a function of distance (figure modified from theirs). (d) Phases identified at other volcanoes as a function of temperature based on data from WilliamsJones et al. (2002) and using the same mineral groups as the Erta Ale example (Fig. 17a–c). [Figs. 17a–c used by permission of Elsevier, from Zelenski et al. (2013) Chem Geol Vol. 357, Fig. 4a, p. 99, Fig. 7a, c, p. 103.]

Gas–Solid Reactions Relevant to Earth and Planetary Processes

33

Experimental simulation of sublimate formation. The formation of sublimates has been replicated by laboratory chemical vapor transport (CVT) and chemical vapor deposition (CVD) experiments (Schrön 1989a,b, 2013; Binnewies 2012). Such experiments involve a gas phase that moves along a thermal gradient to a lower temperature sink where a solid is deposited, or alternately involve cycling gas and/or temperature in the apparatus. Recent laboratory CVT–CVD reactions were applied to simulate element transport on the surface of Mars where there are abundant halides and iron oxides mixed with basaltic rocks (e.g., Clark and van Hart 1981). DiFrancesco et al. (2015, 2016) and DiFrancesco (2018) modified a sealed silica tube set-up to explore the nature of gas-deposited phases formed from degassing an analog martian magma. In these experiments, a multicomponent gas source was created by dissolving S and Cl in a martian basaltic composition at elevated pressure and at relatively oxidized conditions (nickel–nickel oxide buffer), then quenching the mixture to form a volatile-rich glass. At high pressure, the gas solubility is significant and so the resultant glass is significantly volatile-oversaturated at 101.3 kPa; thus, when it is remelted in the hot zone of a furnace it produces a multicomponent gas containing S- and Cl-bearing species. This approach simulates concentrated gas in surface and near-surface magma bodies due to the ascent of gas bubbles from deeper portions of a magma plumbing system. Figure 18a shows a schematic of the setup used in these experiments (DiFrancesco et al. 2016), which is similar to that of Ustunisik et al. (2011, 2015). Examples of the gas-deposited materials after quenching include silica, iron oxides (hematite and maghemite), halides (halite, sylvite, and molysite), iron sulfides (pyrrhotite and pyrite) and native S (Figs. 18b–e).

a.

Sealed  silica  tube

250

b.

2 mm 500 °C

Po

200

Distance (mm)

400‐500 °C

d.

Fe,Na, K  chlorides Phases  deposited  at lower  temp‐ erature

150

20 µm, SEM

e.

100

Halite

c.

500 °C

100 °C Sulfur

1 mm

50 Source  capsule 1200

800

400 0

0

20 µm, SEM

Temperature (°C) Figure 18. (a) Thermal gradient and silica glass tube showing a source capsule and phases deposited at lower temperature. In this case, the source capsule contained an S and Cl-rich basalt (Irvine composition from Gusev Crater, Mars) which was placed in the hot-zone of a furnace resulting in the degassing of volatile and metal species. At lower temperatures within the tube new minerals deposit. (b) Enlargements of the region in the tube near 500°C containing well formed octahedra of Fe2O3 (maghemite) adhered to the tube by a composite of FeCl3 (molysite), NaCl (halite) and KCl (sylvite). At ~400 oC, a ring of orange fine-grained material was formed. (c) Microscope view of the maghemite. (d) BSE image of coexisting phases gas-deposited phases at 400–500 °C from gases evolved from an Irvine composition with high S (~2.4 wt.%) and Cl contents (~1.3 wt.%). The iron sulfide was likely pyrrhotite (Po). (e) Native S precipitated at the cool end of the tube (~100 °C).

Fig. 

34

King et al.

Thermodynamic models to simulate volcanic gas condensation. Thermodynamic models are another tool for investigating these condensation reactions and enable the researcher to model many natural gas and solid species. In this regard, a Gibbs free energy minimization approach have been used (Symonds and Reed 1993; Néron et al. 2012; Renggli et al. 2017; Henley and Seward 2018, this volume), although these methods only point to potential reaction products because equilibrium is rarely achieved as indicated above. Results of Gibbs free energy calculations reveal that metals are not only transported as chlorides in the gas phase such as discussed above, but also as sulfides, fluorides, hydroxides, tungstates and elemental species, with varying relative abundances upon cooling and decompression of the volcanic gas. The concentration of chlorine and water in the gas phase are particularly important because they readily form gas phase metal-chloride and metal-hydroxide compounds (Renggli et al. 2017). To evaluate trace element transport under the different conditions of the Earth versus the Moon, Renggli et al. (2017) examined volcanic gas composition calculated to occur on the Moon at 10–6 bar and a gas sampled at Erta Ale volcano at 1 bar (de Moor et al. 2013). The volcanic gas from the Moon was highly reduced with an oxygen fugacity (fO2) of two log-units below the iron–wüstite buffer (IW – 2 log f O2 units), whereas the terrestrial gas from Erta Ale volcano had an f O2 at the fayalite–magnetite–quartz buffer which corresponds to IW + 3.6 log f O2 units (Renggli et al. 2017). Given equal concentrations of metals, lead is the most efficiently transported metal in both gases, followed by Cu and Fe (Fig. 19). In the lunar gas at 10–6 bar all three metals are transported as elemental species at T > 1000 °C,

Fig. 19 Figure 19. Calculated mole fractions of different metal species in the solid (solid lines) and gas (dotted lines) determined using Gibbs free energy minimization calculations for both lunar gas compositions (10–6 bar) and a gas sampled at Erta Ale volcano (1 bar). (a) Calculated Fe-species in the lunar composition; (b) Calculated Fe-species at Erta Ale; (c) Calculated Pb-species in the lunar gas; (d) Calculated Pb-species at Erta Ale; (e) Calculated Cu-species in the lunar gas; (f) Calculated Cu at Erta Ale. [Used by permission of Elsevier, from Renggli et al. (2017) Geochim Cosmochim Acta Vol. 206, Fig. 3d–f, p. 302, Fig. 4d–f, p. 303.]

Gas–Solid Reactions Relevant to Earth and Planetary Processes

35

whereas in the terrestrial gas the metals are predominantly transported as chloride species. The lunar volcanic gases have lower Cl and H2O concentrations and total pressure and thus have a lower capacity for transporting metals (Renggli et al. 2017). The solids which are calculated to precipitate from these gases include sulfides, oxides, native metals, chlorides and fluorides (Fig. 19). Future work could include examining sulfosalts and fluorosilicates that are common at volcanoes and determining their thermodynamic properties.

Case Study 2: CO2 uptake (carbonation) reactions and heat transfer Mineral carbonation is an example of a gas uptake reaction and it is one of several methods for transferring gaseous CO2 to form carbonate minerals. Mineral carbonation is used in industrial applications (e.g., construction materials), it is potentially useful in reducing anthropogenic CO2 emissions in the atmosphere (Boynton 1980, Rodriguez-Navarro et al. 2009, Biasin et al. 2015, Valverde and Medina 2017) and is important on Venus (Zolotov 2018, this volume). Much of the mineral carbonation literature focuses on Carbon Capture Utilization and Storage (CCUS) by injection of highly reactive, high-density supercritical fluids containing CO2 and H2O into sedimentary reservoirs (e.g., DePaolo et al. 2013). As shown in Figure 3b, CO2-rich fluids are denser than pure water gas and under certain conditions they are negatively buoyant; thus, given a ready source of energy, they can be pumped into deep geologic reservoirs where they react and are stored in rocks (e.g., Oelkers et al. 2008). In contrast to high-density CO2 mixtures, this chapter (and the entire volume) instead focuses on the low-density gaseous phase at high temperature. Mineral carbonation from gaseous CO2 follows the form of Reaction (2), for example using forsterite, where the latter may react following:

Mg2SiO 4 ( s) + 2CO2 ( g )  2MgCO3 ( s) + SiO2 ( s)

(32)

We note that the reaction may alternately produce MgSiO3 instead of SiO2. Examples of many different carbonation reactions are given in Table 5. For long term carbon storage, Ca- or Mg-carbonates are favored because they are stable and less soluble in water than K or Na carbonates (Table 4). However, carbonation rates for silicate minerals (different for each reaction) reacting with low density, dry-CO2 gas are very slow, especially at room temperature, and require the addition of H2O gas or the availability of thin films of H2O on solid surfaces (e.g., Loring et al. 2011, 2012; Schaef et al. 2013). The carbonation reaction rates increase as a function of temperature until the carbonate mineral decomposes: MgCO3 (s)  MgO(s) + CO2 ( g )

(33)

In addition to providing a mechanism for CO2 uptake, carbonation reactions have also been evaluated for their heat transfer capacity. Here we summarize the work by Lackner et al. (1995) who examined a range of CO2 + mineral reactions (Table 5) using data on the Gibbs free energies of the reactants and reaction products (Robie and Hemingway 1995). For Reaction (32), the Gibbs free energy is calculated following:  a2 a 2  ∆G[32] = ∆G[o32] + RT ln  MgCO3 SiO 2  aMgSiO fCO  4 2  

(34)

where ∆GRo is the Gibbs free energy of the standard state for the reaction to form the silicate or carbonate from the oxides. For a negative value of ∆G[32] the reaction proceeds spontaneously to the right forming MgCO3. Similarly for Reaction (33):

King et al.

36

a f ∆G[33] = ∆G[o33] + RT ln  MgO CO2  aMgCO 3 

  

(35)

Heat transfer in carbonation reactions is most effective at temperatures where reaction rates are optimized (where CO2 is taken up rather than released). Thus, the maximum temperature for a reaction from the oxides to proceed spontaneously is given by: DG[32] = DG[33] (Table 5). For the maximum temperature, the calculated enthalpy of reaction (DHTmax; Table 5) shows that considerable heat may be released during the carbonation process. In particular, carbonation–decarbonation of lime, CaO, has high potential for cyclic storage and release of heat because DHTmax is large (–167 kJ mol−1; Table 5). Furthermore, only moderate heat energy (DQ) is required to heat the CaO + CO2 to the higher temperature of Tmax and Tdeh, normalized to one mole of CO2 (Table 5). Table 5. Dehydration and decomposition temperatures, DHTmax and DQ for carbonation reactions (from Lackner et al. 1995) Tdeh °C

Mineral and Carbonation Reaction Calcium oxide CaCO3 CaO + CO2

→

Tmax °C

∆HTmax ∆Q kJ mol−1 kJ mol−1

888

–167

87

418

–148

121

407

–115

34

260

–92

40

242

–88

24

281

–87

37

Clinoenstatite (pyroxene) MgCO3 + SiO2 MgSiO3 + CO2

201

–81

23

Anorthite (feldspar) CaAl2Si2O8 + CO2

165

–81

39

164

–71

19

888

–68

114

192

–67

28

439

201

–44

64

Magnesium hydroxide MgCO3 + H2O Mg(OH)2 + CO2

265

407

–37

46

Tremolite (amphibole) 1 /7 Ca2Mg5Si8O22(OH)2 + CO2 2 /7 CaCO3 + 5/7 MgCO3 + 8/7 SiO2 + 1/7 H2O

566

164

–37

72

Chrysotile (serpentine) 1 /3 Mg3Si2O5(OH)4 + CO2

535

407

–35

78

Anorthite glass CaAl2Si2O8 (gl) + CO2

→ CaCO

+ Al2O3 + 2 SiO2

3

Magnesium oxide MgO + CO2 MgCO3

→

Pyrope (garnet) 1 /3 Mg3Al2Si3O12 + CO2 Forsterite (olivine) Mg2SiO4 + CO2 Wollastonite CaSiO3 + CO2

→ MgCO

3

→ MgCO

3

→ CaCO

+ 1/3 Al2O3 + SiO2

+ SiO2

+ SiO2

3

→

→ CaCO

Diopside (pyroxene) 1 /2 CaMg(SiO3)2 + CO2 Calcium hydroxide Ca(OH)2 + CO2

3

→

1

→ CaCO

Grossular (garnet) 1 /3 Ca3Al2Si3O12 + CO2

3

+ Al2O3 + 2 SiO2

/2 CaCO3 + 1/2 MgCO3 + SiO2

→ CaCO

Talc 1 /3 Mg3Si4O10(OH)2 + CO2

518

+ H2O 3

+ 1/3 Al2O3 + SiO2

→ MgCO

3

+ 4/3 SiO2 + 1/3 H2O

→

→

→ MgCO

3

+ 2/3 SiO2 + 2/3 H2O

Gas–Solid Reactions Relevant to Earth and Planetary Processes

37

The consequences of the large heat transfer during carbonation–decarbonation of CaO is evaluated further next using some of the methods developed above.

Case Study 3: Experimental and modeling study of mass, energy and momentum transfer in carbonation–decarbonation reactions Due to its significant DHTmax and the ease of obtaining CaO by calcining limestone, the CaObased carbonation–decarbonation reaction pair has been developed into an engineering process known as ‘Ca-looping CO2 capture’ (Fig. 20). The feasibility of Ca-looping CO2 capture has been tested on the large scale at pilot plants in the USA (Ohio State University; Wang et al. 2010) and Taiwan (Industrial Technology Research Institute; Chang et al. 2013). In these facilities, the CO2 is stored and recycled through the system and heat is captured. Although some energy is still required; this is likely solved by renewable energy technologies, which are currently predicted to provide ample high-temperature heat (e.g., Bader and Lipiński 2017). However, the process is non-ideal because the reactivity of CaO is reduced over time by sintering and the effect of any impurities is unknown. To examine thermochemical cycling technology, the intrinsic, gas–solid reaction kinetics at the heart of these systems must be well understood (e.g., Blamey et al. 2010) and the energy transfer must be coupled with the mass transfer (Fig. 20). Several recent studies on CO2 uptake by minerals have attempted to combine chemical reaction mechanisms with 3D porosity (e.g., review in Noiriel and Daval 2017). Here we highlight the study by Yue (2018) because it combines both thermal transport modeling with intrinsic chemical reaction models. In other words, their study included the full transfer of mass, energy and momentum to describe the Ca-looping CO2 capture process (Fig. 20).

Decarbonation CaO Mass transfer Eq 36-39

+ CO2 Energy transfer Eq 29, 40

Momentum transfer Eq 31

Carbonation CaCO3 + Heat Figure 20. Schematic diagram showing the transfer processes involved in a carbonation–decarbonation reaction as modelled in the text. The diagram shows mass, energy and momentum transfer vectors. The 3D architecture is treated as a Shrinking Core model.

Yue (2018) undertook thermogravimetric analysis (TGA) to monitor the mass of CaCO Fig. 20 3 spheres (Fig. 21a) with a range of diameters (1, 2.5 and 5 mm) in a controlled gas atmosphere as the sample was subjected to a prescribed temperature program. The TGA technique is described in more detail in Dalby et al. (2018, this volume). Yue (2018) analyzed weight loss during temperature cycling simultaneously with mass spectrometry of the effluent gas (Fig. 22). The samples were cycled three times beginning with a calcination period (1273 K) followed by a carbonation period (873 K) with ramping up and down at a rate of 20 K min−1 (Fig. 22). Flowing gas with three different CO2 concentrations was used (100%, 50%, and 25% CO2 by volume in N2), with a total gas flow rate of 20 mL min−1.

King et al.

38

c. CaO-rich product

a. CaCO3-rich reactant

50 µm

b. CaO-rich product

50 µm

1 mm

Figure 21. (a) Backscattered electron (BSE) image of the CaCO3-rich reactant; (b) BSE image of the CaO-rich product; (c) full BSE view of the CaO-rich product showing the porosity that has developed in the interior portions of the sample. 1273

100 1073

90 80 70

673

60

473

50

Fig. 21

873

20

40

60

80

100

120

273

Figure 22. Example TGA results for one cycle of a decarbonation run showing the weight loss between 80 and 100 minutes at temperatures in excess of 873 K at 101.3 kPa and the evolution of CO2, measured by mass spectrometry, at the beginning of that time period.

Results on the calcium-looping CO2 capture processes show large changes in mineralogy and 3D architecture (Yue 2018). Backscattered electron images of carbonation–decarbonation Fig. 22and cycling experiments confirm that during calcination the grainsize of the spheres decreases intergranular porosity develops (Fig. 21a–c). To investigate this further, Yue (2018) constructed a numerical model that includes mass and energy transfer coupled to reversible chemical kinetics. Enough detail will be given here to demonstrate the application of the general theory presented in the previous section on transport phenomena contained in this chapter. The conservation of species can be written for the four components under consideration: two solids (CaCO3–calcite and CaO) and two gases (CO2 and air). Conservation of mass in the solid phase can be stated rather simply for calcite:

d s s s s ε ρ wCaCO3 = −rCaCO 3 dt

(36)

d s s s s ε ρ wCaO =rCaO dt

(37)

(

)

and for calcium oxide:

(

)

The term on the right-hand side of these equations is the reaction term that provides a source or sink of calcite or calcium oxide. It represents the intrinsic chemical reaction rate and depends on composition and morphology, temperature, and CO2 partial pressure. Evaluation

Gas–Solid Reactions Relevant to Earth and Planetary Processes

39

of the term requires a kinetic rate expression in terms of these physical quantities. A survey of expressions used in the literature is found in Galwey and Brown (1999). Conservation of mass in the gas phase requires accounting for the bulk and diffusive transport of the gas through the porous solid material. Conservation of species for CO2 can be stated as:

d g g g g g g g v g = ∇ ⋅ ρg DCO A ε ρ wCO2 + ∇ ⋅ εgρg wCO ∇wCO + m CO 2 2 2 2 dt

(

)

(

)

(

)

(38)

The terms on the right-hand side represent the mass transfer mechanisms discussed with respect to generic conservation of mass (Eqn. 28). From left to right they represent Brownian g diffusion (i.e. diffusion via random motion of molecules in the gas), where DCO is the 2 g diffusion coefficient, and mass lost or gained across the gas–solid interface, where m CO is 2 the mass flux and A is the surface area per unit volume. A similar expression for air can be formulated without the gas–solid flux term:

d g g g g g g g v = ∇ ⋅ ρg Dair ε ρ wair + ∇ ⋅ εgρg wair ∇wair dt

(

)

(

)

(

)

(39)

Conservation of momentum in the fluid phase is given by Darcy’s law (Eqn. 31). A single conservation of energy statement for the two-phase effective medium was employed. Thus, local thermal equilibrium (LTE) was assumed and a single temperature T was assigned to each location in space:

  g g g  d s s s s g g g g g g  ∑ε ρ w j H j + ∑ε ρ w j H j  + ∇ ⋅  ε ρ v ∑w j H j  dt  j j j     = ∇ ⋅  ∑H gj D gj ∇ ρg w gj  j

(



)  + ∇ ⋅ ( k 

eff

∇T ) − ∇ ⋅ q rad

(40)

(41)

where q rad refers to the vector for radiative heat transfer and keff refers to the effective thermal conductivity. A rigorous analysis of this assumption was not carried out, but can be justified using the conditions described in the work of Kaviany (1991). Four mechanisms of energy transfer are represented in Equation (40). The first is the bulk movement of energy-carrying gas by advection as represented by the second term on the left-hand side. The energy carried by gas transported by Brownian diffusion is described by the first term on the right-hand side. Finally, thermal diffusion (conduction with a conductivity keff) and radiative absorption are given by the last two terms, respectively. The radiation term appearing in Equation (40) is of particular importance to the energy transfer. A full discussion of its evaluation is beyond the scope of this chapter, but can be found in the original work of Yue and Lipiński (2015a,b). Expressions for closure relationships, the gas state equation, boundary and initial conditions, and effective property determination are necessary for the solution of the model but are not included here. What is the ultimate result of this modeling? Yue (2018) was able to create a model that takes into account the mass, energy and momentum transfer (the latter simplified using Darcy’s Law; Eqn. 31) that is coupled to reversible chemical kinetics. This model is able to reproduce the behavior of a complex calcium-looping CO2 capture system as it is cycled through temperature. Such information is necessary to evaluate the ideal efficiency of the calcium-looping CO2 capture process, to determine what variables may be fine-tuned to improve efficiency (e.g., porosity development in the starting CaO could be investigated; Fig. 21).

King et al.

40

Case Study 4: Electron transfer via dehydrogenation–oxidation in amphiboles There is a substantial literature on the use of mineral assemblages as sensors for the intensive parameters of magmas; for example, hydrous phases such as micas and amphiboles (e.g., Wones and Eugster 1965; Wones 1981; Munoz 1984). Many of these studies focus on interactions between the solid mineral and a melt or fluid. However, mineral compositions may be reset at high temperature in the presence of the gas phase only; for instance, there is substantial literature showing how oxides change composition as a function of both temperature and oxygen fugacity (fO2) in the presence of a gas phase (Darken and Gurry 1945; Buddington and Lindsley 1964) and some studies of micas (e.g., Righter et al. 2002). Amphiboles provide a convenient example for exploring the competing role of melt and gas reactions because both have been investigated (Fig. 23). Experiments crystallizing amphibole within its stability field at high pressure and temperature (the Am ‘in’ field in Fig. 23a) show that it inherits its H and Fe3+/Fetotal from the melt (e.g., water activity, fH2 and/or fO2; Popp et al. 1995; King et al. 2000). If the amphibole ascends rapidly to the surface (i and iii in Fig. 23a) then the crystal is preserved as it formed (e.g., an example from Soufrière Hills volcano in Fig. 26b). In contrast, if the amphibole takes a slow ascent path to the solidus (ii in Fig. 23) it may breakdown to form an anhydrous rim of pyroxene, plagioclase and magnetite at pressures below the amphibole stability field (e.g., Rutherford and Hill 1993). An example of such an amphibole from Soufrière Hills is shown in Fig. 23c. After reaching the solidus, the amphibole may ascend and cool slowly or in a low f H2 environment (e.g., air) in which case it can lose H2 in a gas–solid reaction following a version of Equation (13):

1 H + ( in solid ) + Fe 2+ H 2 g + Fe3+ Am  Am 2 ()

(41)

This reaction involves transfer of an electron and is therefore coupled with iron oxidation as observed in the two redder amphiboles from Soufrière Hills (Figs. 23c and d).

P (MPa)

Am+ S+G

b.

Magma

a.

Am records melt  fH2/fO2/aH2O

Am+ S+L

c.

S+L

S+G

Super‐solidus ascent

i. Fast – No Am rims ii. Slow – Am rims

d.

Subsolidus ascent

iii. Fast or high fH2 – Am preserved iv. Slow or low fH2 – H2‐loss: D/H & Fe3+ increase

750

790

830

870

Temperature (°C)

910

950

Figure 23. (a) Schematic pressure–temperature diagram showing the stability of amphibole (Am), solids (S), gas (G) and liquid (L, melt). Amphibole forms in the magma in the amophibole stability region above the Am ‘in’ curve. It is brought to the surface either fast (i) or slowly (ii) where the latter may result in anhydrous rims forming. If ascent and cooling is slow (iv), it may also be accompanied by H2-loss that causes D/H and Fe3+ to increase. (b) An example of an amphibole from Soufrière Hills (Buckley et al. 2006) that has been rapidly transported to the surface (i + iii). (c) An amphibole from Soufrière Hills (Buckley et al. 2006) that Fig. 23 has developed a rim and also become dehydrogenated–oxidized (ii + iv). (d) An amphibole from Soufrière Hills (Buckley et al. 2006) that has been brought to the solidus rapidly and also become dehydrogenated–oxidized (i + iv). For photographs in (b) through (d), the field of view is ~3mm across. [Figures 23b–c used by permission of Springer Nature, from Buckley et al. (2006) Contrib Mineral Petrol Vol. 151, Fig. 1a–c, p. 124.]

Gas–Solid Reactions Relevant to Earth and Planetary Processes

41

Reaction (46) and the potential loss of H2O also, has been explored experimentally by heating amphiboles in air (e.g., Miyagi et al. 1998; King et al. 2009). Miyagi et al. (1998) showed significant reddening of amphibole color (e.g., iv in Fig. 23a and Figs. 23c,d). They related a large increase in the deuterium (D) to protium (H) ratio to both H2 and H2O degassing following Rayleigh distillation at temperatures above 400 °C. Similar experiments were carried out by King et al. (2009) who attributed the changes in D/H entirely to H2-loss via Rayleigh fractionation at 800 °C and showed that initial homogeneities in the natural starting materials caused deviations from this trend. They compared their experimental results to amphiboles from slowly cooled and/or oxidized volcanic rocks (lava flows and cinder cones; King et al. 1999) and found that the D/H versus total H2O contents in these natural samples could be explained entirely by H2-loss via Rayleigh fractionation at 700–900 °C. Using the same amphiboles, Wagner et al. (2008) showed that dehydrogenation of the amphiboles results in oxidation, confirming Equation (41). This example of how amphibole transfers electrons through dehydrogenation-oxidation at high temperature is applicable to other H-bearing phases such as biotites (e.g., Feeley and Sharp 1996; Righter et al. 2002). This example shows the power of including stable isotopes in a toolbox for understanding the full geologic history of materials, including magmatic, ascent and cooling processes.

Case Study 5: Chemisorption reactions between SO2 and common silicate minerals It is well known that SO2, an important reactive component in magmatic gases, readily forms sulfate (and oxide minerals) upon reaction with silicates and carbonates at high temperatures (MacRae 1974; Burnett et al. 1997; Li et al. 2010; Ayris et al. 2013; Schmauss and Keppler 2014; Delmelle et al. 2018, this volume; Kubicki and Watts 2018, this volume; Palm et al. 2018, this volume; Renggli and King 2018, this volume; Zolotov 2018, this volume). In the anhydrous system, these reactions generally follow the form (modified after Burnham 1979b): 2SO2 ( g ) + M -silicate → MSO 4 + Sreduced + silicate ± oxide

(42)

where M is a cation, SO2 contains S4+ and this disproportionates to form S6+ in the sulfate mineral and a reduced sulfur species in the gas or solid phase (e.g., S2–, a reduced sulfur radical, S– or S0). In this Case Study, we examine experiments undertaken at 101.3kPa using pure SO2 similar to those described previously (Henley et al. 2015, 2017; Palm et al. 2018, this volume; Renggli and King 2018, this volume). Polished wafers of minerals were suspended in the hot zone of a vertical gas-mixing furnace with a 20 mL min−1 flow of SO2. Minerals were introduced to the hot furnace under an Ar flow that was replaced by SO2 for the duration of the experiment. The reaction was terminated by flushing the furnace with Ar before lifting the sample out of the furnace for immediate storage in a desiccator. This open system set-up has the advantage of allowing control and monitoring of gas flow rates and gas fugacities so that reaction equations and kinetics may be determined. The high flow rates also remove gas-phase product species, which are likely removed from the system. In contrast to the closed system approaches described in Case Study 1 or used by Burnett et al. (1997) and Li et al. (2010), the open system consumes larger volumes of gas. To characterize the mineralogy of the reaction products we primarily relied upon Raman spectroscopy and determined the chemistry using scanning electron microprobe X-ray maps of the reaction products. Below, we discuss the experimental results and apply Gibbs free energy minimization techniques to explore the variables which control SO2–mineral reactions. For each SO2–mineral reaction we used thermodynamic data appropriate for the 500–1000 °C range (Roine 2015), assuming that minerals are pure endmembers. As a starting point, we assume a 9:1 molar ratio of SO2:mineral and the gas phase species considered include O2, S-oxides (SO2, SO, S2O and SO3) and S-gases (S2, S3, S4, S5, S6, S7 and S8). Solid species were varied as appropriate based on the predicted and observed reaction products and as described further below. We included the corresponding oxides

King et al.

42

of any sulfates formed in the model (e.g., CaO if CaSO4 formed) in order to include decomposition reactions (e.g., Table 4; Stern 2001) from sulfate to oxides and SO3 following: MSO 4 → MO + SO3 ( g )

(43)

For Na2SO4, we considered both the gas and solid forms because it can be a gas at the conditions of our experiments (Stern and Weise 1966). The consequences and validity of some of these assumptions are discussed further below. Feldspars. Feldspars are the most abundant mineral in the crust, commonly found as phenocrysts in volcanic rocks, thus how they react with SO2 has wide application in a variety of settings on Earth and other planetary bodies. Calcium-rich feldspar, anorthite (CaAl2Si2O8), reacts with SO2 to effectively produce CaSO4, SiO2, Al2SiO5 and S2 (Burnham 1979b; Henley et al. 2015). The proposed reaction is: 4 CaAl2Si2O8(s) + 6 SO2(g) → 4 CaSO4(s) + 4 Al2SiO5(s) + 4 SiO2(s) + S2(g)

(44)

Significantly, one mole of CaAl2Si2O8 produces one mole of CaSO4. The mole fraction of reactants and products calculated by Gibbs free energy minimization as described above are shown in Figure 24a. The condition where the concentration of the CaSO4 product is equal to the CaAl2Si2O8 reactant is labeled using a star annotated with Ca, referred to as Ca*. At temperatures between 500 °C and the temperature of Ca* (~ 840 °C), CaSO4 > CaAl2Si2O8, whereas between 840 °C and 1000 °C, CaAl2Si2O8 < CaSO4. If we choose a greater concentration of SO2 in the initial starting composition, then Ca* moves to lower mole fraction and higher temperatures. Thus, our arbitrary choice of starting composition has a significant role on the model output. For this reason, the temperatures should be viewed as relative only and we don’t report temperatures in the text henceforth. Nonetheless, the modeling shows that the reaction is thermodynamically favored at low temperatures: most of the CaAl2Si2O8 is consumed and CaSO4 is extensively produced within a several hundred degree interval below Ca*. We may also use Figure 24a to confirm that SO2 and S2 are the major S-species involved in the reaction.

101

a.

Mole fraction

100

Al2SiO5 CaSO4 CaAl2Si2O8

10‒1

SiO2

S2(g)

b.

SO2(g)

SiO2

Al2SiO5 (K/Na)2SO4 K

KAlSi3O8 Na

NaAlSi3O8 S 2(g)

S2O(g)

10‒2

S8(g) 500

600

S7(g)

SO(g)

SO(g)

10‒4 10‒5

S2O(g)

S3(g)

S5(g)

10‒3

10‒6

SO2(g)

Ca

S6(g) 700

S4(g)

800

Temperature (°C)

S3(g)

SO3(g)

SO3(g)

S4(g) to S8(g) not shown 900

500

600

700

800

Temperature (°C)

900

1000

Figure 24. (a) Mole fraction of species versus temperature derived from a Gibbs free energy minimization model for SO2 + anorthite (CaAl2Si2O8) at 101.3 kPa. For this diagram and subsequent diagrams, the models were run using SO2:mineral = 9:1 moles and only major products are shown with the oxides removed for clarity; (b) Results of a Gibbs free energy minimization model for SO2 + NaAlSi3O8 + KAlSi3O8. Here and in subsequent diagrams the reaction products S4, S5, S6, S7 and S8 (S4 to S8) are not shown for clarity.

Fig. 2

Gas–Solid Reactions Relevant to Earth and Planetary Processes

43

Table 6. Products of pure SO2 + silicate mineral experiments at 101.3 kPa. Phase

Temp (°C)

Time (hr)

Reaction product

Ref.

Balanced reaction(s)

Feldspars Labradorite An60 Na0.4Ca0.6Al1.6Si2.4O8

600

336

CaSO4

H15

800

several

CaSO4

H15

K-feldspar KAlSi3O8

600

24

none

P&B

4 CaAl2Si2O8(s) + 6 SO2(g) → 4 CaSO4(s) + 4 Al2SiO5(s) + 4 SiO2(s) + S2(g)

(44)

8 KAlSi3O8(s) + 6 SO2(g) → K2SO4(s) + 4 Al2SiO5(s) + 20 SiO2(s) + S2(g)

(46)

Garnet and muscovite Grossular Ca3Al2(SiO4)3

750

96

CaSO4

H17

4 Ca3Al2(SiO4)3(s) + 18 SO2(g) → 12 CaSO4(s) + 8 SiO2(s) + 4 Al2SiO5(s) + 3 S2(g) (47)

Muscovite KAl2(Si3AlO10)(OH)2

600

24

none

P&B

Not applicable

Pyroxenes and amphibole Diopside CaMgSi2O6

600

0.16

CaSO4

CR

600

24

CaSO4 + MgSO4 + Fe2O3

P&B

CaSO4

H17

750

Augite (Ca,Na)(Mg,Fe,Al) (Si,Al)2O6

Actinolite Ca2(Mg,Fe)5Si8O22(OH)2

96

800

1–96

CaSO4

CR

600

24

CaSO4 + Na2SO4 + Fe2O3 + Al-phase

P&B

800

168, 360

CaSO4

H&C

600

24

(Ca,Mg)SO4

P&B

2 CaMgSi2O6(s) + 6 SO2(g) → 2 CaSO4(s) + 2 MgSO4(s) + 4 SiO2(s) + S2(g) 4 CaMgSi2O6(s) + 6 SO2(g) → 4 CaSO4(s) + 4 MgSiO3(s) + 4 SiO2(s) + S2(g) 4 CaMgSi2O6(s) + 6 SO2(g) → 4 MgSO4(s) + 4 CaSiO3(s) + 4 SiO2(s) + S2(g)

8 NaAlSi2O6(s) + 6 SO2(g) → 4 Na2SO4(s) + 16 SiO2(s) + 4 Al2O3(s) + S2(g) 2 CaMgSi2O6(s) + 6 SO2(g) → 2 CaSO4(s) + 2 MgSO4(s) + 4 SiO2(s) + S2(g) 8 FeSiO3(s) + 2 SO2(g) → 4 Fe2O3(s) + 8 SiO2(s) + S2(g)

(48) (49) (50)

(51) (52) (53)

Ca2Mg5Si8O22(OH)2+ 10.5 SO2(g) → 2 CaSO4 + 8 SiO2(s) + 5 MgSO4 + 1.75 S2(g) + H2O (54)

Olivine Olivine (Mg,Fe)SiO4

600

24

MgSO4 + Fe2O3

P&B

800

360

MgSO4 + Fe2O3

H&C

2 Mg2SiO4(s) + 6 SO2(g) → 4 MgSO4(s) + 2 SiO2(s) + S2(g) (55) 4 Fe2SiO4(s) + 2 SO2(g) → 4 Fe2O3(s) + 4 SiO2(s) + S2(g) (56)

* alteration minerals in starting material; # CR – unpublished Renggli and King; H15 – Henley et al. (2015); H17 – Henley et al. (2017); P&B –unpublished Palm, Baile and King; RH – unpublished Henley and Clark at the Australian National University.

In contrast to CaAl2Si2O8 (anorthite), there are few NaAlSi3O8 (albite) experiments. Our experiments on albite glass produce Na2SO4 (Renggli and King 2018, this volume), but other workers using a K2S2O8 source that likely produced SO3 (Renggli and King 2018, this volume) either did not observe sulfate (Burnett et al. 1997) or very little (Li et al. 2010). Similarly, K-feldspar (KAlSi3O8), plus muscovite experiments did not produce sulfates (Table 6). We suspect that K2SO4 formed in previous experiments may have formed from either K2S2O8 or K-bearing clay minerals. For NaAlSi3O8 and KAlSi3O8, the reaction products are similar to those for CaAl2Si2O8: 8 NaAlSi3O8(s) + 6 SO2(g) → 4 Na2SO4(s) + 4 Al2SiO5(s) + 20 SiO2(s) + S2(g)

(45)

8 KAlSi3O8(s) + 6 SO2(g) → 4 K2SO4(s) + 4 Al2SiO5(s) + 20 SiO2(s) + S2(g)

(46)

King et al.

44

except that two moles of Na- or K-feldspar are required to produce one mole of sulfate, in contrast to the CaAl2Si2O8 ratio of 1:1. This difference is consistent with less (or minimal) sulfate observed on the Na- and K-feldspars (Table 6, Burnett et al. 1997; Li et al. 2010). The larger size of K may inhibit the reaction progress and account for the lack of K2SO4 (e.g., Palm et al. 2018, this volume). In addition, significant SiO2 is produced from the reaction with Naand K-feldspar, and SiO2 products may form a barrier to diffusing cations from the feldspar substrate, effectively halting the reaction. The thermodynamic modeling is consistent with the lower abundances of sulfate products observed in the Na- and K-feldspar relative to the Ca-feldspar. The amount of Na- and K-feldspar consumed relative to the Na- and K-sulfate produced below their respective Na* and K* temperatures (Fig. 24b) is much less than the Ca* temperature for Ca-feldspar (Fig. 24a). Garnet. There are several lines of evidence to suggest that garnet may be affected by gas– solid reactions. First, garnet is a common mineral at granulite and amphibolite facies where fluids may have gas-like densities (Fig. 3). Second, it is found in gas pockets in peraluminous rhyolites (e.g., Burt et al. 1982). Third, Ca-rich garnet (grossular) is common in calc-silicate rocks and skarns including the Cu–Au skarn from Ertsburg, Indonesia, where ore metal and sulfides are associated with assemblages including grossular, anhydrite, anorthite and diopside (Henley et al. 2017). Using an experimental approach, Henley et al. (2017) demonstrated that reaction of grossular garnet with SO2 at 750 °C resulted in the formation of anhydrite; an example of the reaction products is shown in Figure 25a. Anhydrite forms unusual layered crystals that appear embedded in the substrate with a texture reminiscent of icebergs. We provide one possible equation for this reaction in Table 6: Equation (47). In Figure 25b, we show the simple SO2 + grossular garnet reaction to form anhydrite; noting that the addition of other Ca-silicate phases does not significantly change the relations. Relative to the reaction with anorthite, the grossular reaction is favored for a greater range of temperatures (Ca* is at higher temperature). As discussed by Henley et al. (2017) the reaction has an important role in producing reduced S required for ore deposition in skarn deposits.

a. Grossular

b.

101

SO2(g)

100

Mole fraction

CaSO4

SiO2 CaSO 4

Al2SiO5

10‒1

S2O(g)

10‒2

SO(g)

Ca3Al2Si8O12

S3(g)

10‒3

2  m

Ca

S2(g)

10‒4

10‒6

SO3(g)

S4(g) to S8(g) not shown

10‒5 500

600

700

800

Temperature (°C)

900

1000

Figure 25. (a) BSE image showing CaSO4 formed on grossular after reaction with SO2 at 750 °C at 101.3 kPa for 96 hours (Table 6); (b) Mole fraction of species versus temperature derived from a Gibbs free energy minimization model for SO2 + grossular garnet (Ca3Al2Si8O12).

Pyroxenes. Pyroxenes may interact with gases as the primary components of basalts and Fig. 25 ultramafic rocks, they are found as sublimates at some volcanoes (e.g., Ca-Fe-pyroxene and NaFe-pyroxene, aegerine at Erta Ale: Zelenski et al. 2013, Case Study 1). Pyroxenes are common in metamorphic rocks that are associated with gases including amphibolite–granulite facies rocks and calc-silicate metamorphic rocks. Diopside (CaMgSi2O6) + SO2 reactions were first investigated by Fegley and Prinn (1989) who used a SO2–CO2 mixture (nom. 1 vol.%) forming

Gas–Solid Reactions Relevant to Earth and Planetary Processes

45

layers of CaSO4 crystals at 833 °C over 48 hours. Subsequent studies are summarized in Zolotov (2018, this volume) and also found CaSO4; however, most other experiments have used mixed gases or pressures greater than 101.3 kPa and are thus not directly relevant to this Case Study. Our experiments on diopside with pure SO2 at 600–800 °C and 0.16–96 hours identified CaSO4 as the dominant solid product, with additional MgSO4 (and Fe2O3) found only in a 24 hour run at 600 °C (Fig. 26a–d). The textures of the sulfates range from continuous layers of crystals through to concentrated ‘pools’ containing a collection of crystals, as shown in Figure 26a–d. Our observation that CaSO4 is more abundant than MgSO4 as a product phase may be due to the instability of MgSO4 during sample storage and preparation, issues in identifying MgSO4 using scanning electron microscopy (SEM) and Raman spectroscopy, or a result of inhomogeneity or differences in starting materials. To explore the reaction products of diopside + SO2 reactions, we again turn to potential reaction equations. These are given in Table 6 (Eqns. 48–50) showing that diopside may react to form SiO2 and S2 and a range of sulfate and silicate mineral products: CaSO4 + MgSO4 or CaSO4 + MgSiO3 or CaSiO3 + MgSO4. Thermodynamic modeling in Figure 26e illustrates the reaction to form solely SiO2 + S2 + CaSO4 + MgSO4. The dominance of CaSO4 is explained by the greater temperature range over which it exists (higher temperature Ca* and higher mole fraction) relative to MgSO4 (lower temperature Mg* and lower mole fraction). The model predicts that CaSO4 is likely to form even more readily than MgSO4 if Ca- and Mg-pyroxenes also form (wollastonite, CaSiO3 and enstatite, MgSiO3 respectively; Fig. 26f). Similar calculations were made by Zolotov (1985) and a recent summary is given in Zolotov (2018, this volume; his Figs. 4, 5, 11). The thermodynamic modeling results both permit the formation of MgSO4 and provide an explanation for the abundance of CaSO4 over MgSO4. We note that further work is still required to evaluate the other potential factors such as sample preservation and reactant inhomogeneity.

a. Diopside

c.

Ca‐sulfate

20µm

Mg‐sulfate

b. 20µm

e.

100

Mole fraction

d.

20µm 101

SiO2

10‒1

S2(g)

S2O(g)

Mg

10‒2

SO2(g)

S4(g)

10‒5

S8(g) S7(g) 500

600

MgSO4

S6(g)

700

MgSiO3 CaSiO3

800

900

CaMgSi2O6

Ca

SO(g)

Mg MgSO4

SO3(g)

1000 500

SiO2

S2O(g)

SO3(g)

S4(g) to S8(g) not shown

Temperature (°C)

Mg

CaSO4

S3(g) S3(g)

S5(g)

10‒4

20µm

S2(g)

SO(g)

10‒3

10‒6

Ca

CaMgSi2O6

S

f.

SO2(g)

CaSO4

Ca

600

700

800

Temperature (°C)

900

1000

Figure 26. (a) BSE image showing CaSO4 and MgSO4 formed on diopside after reaction with SO2 at 600 °C Fig 26 for 24 hours at 101.3 kPa (Table 6); (b) SEM S X-ray map of the image shown in (a); (c) SEM Ca X-ray map of the image shown in (a); (d) SEM Mg X-ray map of the image shown in (a); (e) Mole fraction of species versus temperature derived from a Gibbs free energy minimization model for SO2 + CaMgSi2O6 considering the products CaSO4 + MgSO4; (f) Mole fraction of species versus temperature derived from a Gibbs free energy minimization model for SO2 + CaMgSi2O6 considering the products CaSO4, MgSO4, CaSiO3 and MgSiO3.

King et al.

46

Augite (pyroxene with formula (Ca,Na)(Mg,Fe,Al)(Si,Al)2O6) has also been reacted with SO2 at 600–800 °C (Table 6). As is the case for diopside, CaSO4 is the dominant product, forming large plate-like crystals (Fig. 27a–c). In contrast to the diopside, the augite also formed Na2SO4, hematite (Fe2O3) and a submicron Al-phase. To explore the formation of Na-sulfate and Fe2O3 we used the bulk composition of the augite to model the SO2 reaction with endmember pyroxenes: CaMgSi2O6, FeSiO3 and NaAl2Si2O6 (Table 6; Eqns. 51–53). These reactions are shown graphically in Fig. 27d using approximate mole fractions of the endmembers (0.73 CaMgSi2O6, 0.20 FeSiO3 and 0.07 NaAl2Si2O6) to roughly model the solid solution in the augite; recognizing that this approach ignores thermodynamic mixing parameters, but provides useful constraints on the potential reactions. The Gibbs free energy minimization calculations show that for temperatures below Ca*, CaSO4 is calculated to be the dominant sulfate. Interestingly, despite the low Na content in the pyroxene, Na2SO4 is predicted to be abundant and stable for the * entire range of temperatures. The formation of Fe2O3 is favored at temperatures below Feox that tend to be at the lower end of the range. We note that formation of FeO is predicted to be * favorable at temperatures higher than Feox , but the oxidizing environment in the SO2 means that it effectively forms hematite (Fe2O3) and magnetite (Fe3O4).

Na2SO4 10µm

CaSO4

10µm

Fe‐ox

d.

b.

Ca

c.

Mole fraction

a. Augite

101

10‒2

0.2FeSiO3 Fe3O4 Na2SO4

Mg

S2O(g)

10‒6

S3(g)

SO(g)

10‒5

Fe

Al2O3

Ca

10‒3 10‒4

10µm

SO2(g)

SiO2 100 CaSO4 S2(g) 0.73CaMgSi2O6 Fe2O3 Feox 10‒1

S4(g) to S8(g) not shown 500

600

SO3(g) 700

800

Temperature (°C)

900

1000

Figure 27. (a) BSE image showing CaSO4, NaSO4 and Fe-oxide formed on augite after reaction with SO2 at 600°C for 24 hours at 101.3 kPa (Table 6); (b) SEM Ca X-ray map of the image shown in (a); (c) SEM Fe X-ray map of the image shown in (a); (d) Mole fraction of species versus temperature derived from a Gibbs free energy minimization model for molar 9.0 SO2 + 0.73 CaMgSi2O6 + 0.20 FeSiO3 + 0.07 NaAl2Si2O6. Fig. 27

Amphibole. Actinolite, an amphibole with the formula Ca2(Mg,Fe)5Si8O22(OH)2, is representative of a large mineral group, found in many metamorphic and igneous rocks. Experiments between SO2 and actinolite reveal mound-like CaSO4 on the surface of actinolite reactant (Fig. 28a–c)—we cannot rule out hydration of these crystals due to dehydrogenation or dehydration of the amphibole (e.g., Case Study 4). Nonetheless, we have used thermodynamic models to examine the formation of anhydrous CaSO4 and MgSO4 using tremolite (Ca2Mg5Si8O22(OH)2) as a reactant because thermodynamic data is available for tremolite, but not actinolite (Eqn. 54; Fig. 28d). These models provide a rationale for the dominance of CaSO4 over MgSO4 as a product for the entire temperature range modeled (Fig. 28d). Olivine. Olivine is found as phenocrysts in volcanic rocks and, as we write, is being erupted from Kilaeau volcano amidst large concentrations of SO2-rich magmatic gas. Olivine is also an important mineral on planetary surfaces that are rich in sulfates such as Mars (Hoefen et al. 2003; King et al. 2004; King and McSween 2005) and Venus (Zolotov 2018, this volume). Our results for SO2 + olivine experiments at 600 and 800 °C show that MgSO4 and Fe2O3 form on the surfaces of olivine (Table 6). The olivine appears to have formed subgrains and developed elongate porosity associated with elongate Fe2O3 (Fig. 29a). The subgrains are reminiscent of the surface topography observed on olivine heat-treated under CO–CO2 gas at high temperature (Fig. 29b). We have not identified MgSiO3 in these run products; although thermodynamic modelling predicts that it should form (Zolotov 2018, this volume). We provide reactions for these observations in Table 6 (Eqns. 55 and 56) assuming that MgSiO3 is absent.

Gas–Solid Reactions Relevant to Earth and Planetary Processes

CaSO4 10µm

Ca

c.

10µm

Mole fraction

d.

101

SO2(g)

100

H2O

SiO2

SO(g)

10‒2

Fe‐oxide Fe

10‒6

b.

a. Actinolite

10µm

101

d.

CaSO4 Ca

c.

10µm

100

SO2(g)

SiO2

H2 O

10‒1 Mg

Ca2Mg5Si8O22(OH)2

10‒5

Fe

10‒6

Ca

S2(g) S2O(g) SO(g) S3(g)

MgSO4

10‒4

10µm

CaSO4

10‒2

10‒3

Fe‐oxide

SO3(g)

S4(g) to S8(g) not shown 00:00 600 500

700

800

Temperature (°C)

900

1000

Fig. 28

S3(g)

10‒3

10‒5

Ca

S2(g) S2O(g)

Ca2Mg5Si8O22(OH)2

10‒1 Mg

MgSO4

10‒4

10µm

CaSO4

Mole fraction

b.

a. Actinolite

47

SO3(g)

S4(g) to S8(g) not shown 00:00 600 500

700

800

Temperature (°C)

900

1000

Figure 28. (a) BSE image showing CaSO4 and Fe-oxide formed on actinolite after reaction with SO2 at 600°C for 24 hours at 101.3 kPa (Table 6); (b) SEM Ca X-ray map of the image shown in (a); (c) SEM Fe X-ray map of the image shown in (a); (d) Mole fraction of species versus temperature derived from a Gibbs free energy minimization model for SO2 + tremolite, Ca2Mg5Si8O22(OH)2, a proxy for actinolite.

Thermodynamic modeling was undertaken for olivine representative of the starting Fig. 28 to material (San Carlos olivine: 0.9 moles forsterite and 0.1 moles fayalite), in an attempt model the solid solution although (as above) mixing parameters were not applied (Fig. 29c). We tested how MgSiO3 affects the calculations and it has a minimal role because it is nearconstant in concentration if it is included in calculations. The results show that iron oxides form in significant quantities relative to Fe2SiO4 at all temperatures. In contrast, MgSO4 does not form from Mg2SiO4 except at low temperatures below the range calculated (Fig. 29c). This calculation does not agree with the experimental observations where limited MgSO4 was observed. We postulate that the formation of the iron oxides, porosity development and subgrain boundary formation has destabilized the olivine to develop reactive surfaces that enable for the disequilibrium formation of MgSO4 in the experiments.

a. BSE image

San Carlos Olivine

c. Mole fraction

MgSO4

SO2(g) 0.90Mg2SiO4 SiO2

100

b. AFM deflection image

Fe2O3

101

10‒1

Fe3O4

10‒2 FeSO4

10‒3

2µm

600 °C, SO2

900 °C, 10:90 CO:CO2

S3(g)

10‒5 10‒6

S2O(g) S2(g) 0.10Fe2SiO4 SO(g) MgSO4

10‒4

5µm

Fe2O3

S4(g) to S8(g) not shown 500

600

SO3(g) 700

800

Temperature (°C)

900

1000

Figure 29. (a) BSE image showing MgSO4 and Fe-oxide formed on olivine after reaction with SO2 at 600 °C for 24 hours at 101.3 kPa (Table 6); (b) AFM deflection image of a resurfaced olivine crystal that was prepared at 900 °C, 10:90 CO:CO2 (modified after King et al. 2017 and sourced at https://pubs.acs.org/doi/ full/10.1021/acsearthspacechem.6b00016. Further permissions related to this figure should be directed to the ACS.); (c) Mole fraction of species versus temperature derived from a Gibbs free energy minimization model for SO2 + 0.90 Mg2SiO4 and 0.10 Fe2SiO4.

Fig. 29 Recap of mineral–SO2 reactions and limitations of our assumptions. In summary, the literature, our experiments and thermodynamic modeling show CaSO4 is strongly favored as a product of Ca-bearing mineral + SO2 reactions. Iron oxides form in some reactions although Fe-bearing minerals have not been extensively examined. In addition, Na- and Mg-sulfate

King et al.

48

minerals may form; however these tend to be less favorable reactions in our Fe-free samples; future work is required to evaluate Fe-bearing minerals (see Renggli and King 2018, this volume for some approaches used for glass–SO2 reactions). We provide thermodynamic calculations that are consistent with the reaction products. However, we remind the reader that our experiments were carried out assuming a molar ratio of SO2:mineral of 9:1 and assuming that equilibrium occurs. The SO2:mineral ratio likely decreases * and the mole fraction over the course of an experiment and the location of Ca*, Mg*, Na* and Feox of each species strongly depend on SO2:mineral. Our experiments were not likely to have reached equilibrium, nor was that our purpose, but the assumption was made in order to model these reactions using Gibbs free energy minimization. Our aim in using thermodynamic approaches was to point towards possible reaction products (not quantitative amounts or temperature constraints). Future work, could apply some of the approaches presented above to extract reaction rate constants, examine the diffusion of cations in the context of both crystallography and atomscale processes and use isotopic techniques to better probe these reactions.

Case Study 6: Chemisorption reactions between S–Cl gas and common silicate minerals Experimental studies of mixed gases reacting with silicate minerals are summarized by Zolotov (2018, this volume). Here, we revisit the system presented in Case Study 1 to simulate martian lavas. DiFrancesco et al. (2015) assessed the reaction of magmatic gas with the surfaces of minerals by modifying the experimental set-up described in Case Study 1. A target mineral, wrapped in a Pt wire or placed in a gold mesh bag, was placed in a silica glass capillary at a specific temperature in the furnace above a volatile-saturated glass that was reheated to release a S–Cl gas. Within 48 hours, the stream of S gases and Cl gases resulted in significant reactions. Olivine starting material (Fig. 30a) became oxidized at 800 °C (Fig. 30b) likely by evolved SO2 (known to be quite oxidizing; see Fig. 1 in Renggli and King 2018, this volume). At 400 °C, Mgsulfate was identified on the reacted olivine (Fig. 30c,d). In contrast, augite (Fig. 30e) reacted at 400 °C, showed significant precipitation of sulfates and chlorides, particularly in pits in the mineral surface (Fig. 30f,g). Because these minerals were reacted in the same magmatic gases, the results demonstrate the differences between the products of direct condensation (Case Study 1) and those produced by surface-mediated chemisorption reactions. In the condensation experiments, Mg and Ca were not transported by the gas because they were not observed as precipitates or in bulk analyses of the gas-deposited minerals. In contrast, on the surfaces of the plagioclase and augite targets, Ca-sulfate formed as the result of surface-mediated chemisorption reactions. a.

e.

b.

c.

1mm

1mm 1mm

1mm f.

1mm g.

d.

20 µm SEM Counts 400 300 200 100

Fe 2

Counts

20 µm SEM

400 300 200 100

S

Mg O

4

S

6

keV

6

keV

Ca

O Si 2

4

Figure 30. Minerals pre- and post-alteration in a S–Cl-rich gas. (a) A typical unaltered olivine. (b) Olivine post-reaction at 800 °C in the S–Cl gas stream. (c) Olivine post-reaction in the S–Cl gas at 400°C. (d) SEM image of Mg-sulfate on olivine reacted at 400 °C identified using the EDS spectrum— inset. (e) Typical unaltered augite. (f) Augite after reaction at 400 °C with high S gas. (g) SEM image of Ca-sulfate on augite reacted at 400 °C with high S gas, identified using the EDS spectrum—inset.

Fig. 30

Gas–Solid Reactions Relevant to Earth and Planetary Processes

49

Experimental techniques such as these closed system experiments, combined with open system experiments, promise new insights into the products of multi-component magmatic gas interacting with solids, including both condensation and chemisorption processes. Future progress will pair experimental studies with thermodynamic analysis (e.g., Case Studies 1 and 5), transfer modelling (like Case Study 3), together with an understanding of the electron transfer reactions (Case Study 4) and computational chemistry to provide a full understanding of these disequilibrium systems.

SUMMARY In this chapter we have shown that gas–solid reactions occur in a range of Earth and planetary settings. Because gas transport is effective, we should expect to find traces of these reactions in many rocks. Nonetheless, gas–solid reactions have received little attention because in the past these reactions have been difficult to decipher. In part, this has arisen because reaction products commonly evolve over time (Figs. 4, 11–13; Tables 1–3); reaction products may dissolve (e.g., salts; Figs. 15 and 16; Table 4) or escape (gas products), and host rocks may brecciate, anneal or become modified during typical geologic processes (Figs. 3b, 9, 10, 15, 17 and 23). This chapter provides a conceptual framework using techniques from chemistry, physics and chemical engineering to help constrain how reaction processes in Earth and planetary systems may be modelled (e.g., Fig. 14; Tables 1–3). Case studies show that these approaches can be merged to explain phenomena encountered in nature, but previously viewed as too difficult to constrain. We also show how standard approaches, such as equilibrium thermodynamics, may have limitations, but remain useful for predicting gas−solid reaction products (e.g., Figs. 24–29), particularly if paired with homogenization approaches (Fig. 14) as well as energy and momentum transfer models (Case Study 3). Finally, we show that there is much to explore in this relatively young field of research, as illustrated further in the following chapters in this volume.

ACKNOWLEDGMENTS We are grateful for helpful and insightful reviews from Misha Zolotov and David Ellis. Bruce Fegley is thanked for review, editorial comments and for providing Figure 6a. This work was supported by Australian Research Council funding to King, Renggli, Palm, Troitzsch and Baile (DP150104604 and FT130101524). Renggli was supported by an ANU PhD scholarship and Palm by the Kerry and John Lovering Scholarship. Lipiński was supported by Australian Research Council (FT140101213). This contribution benefited from discussions with David Lescinsky, Steve Eggins, Marc Norman, Dima Kamenetsky, Don Burt, the late Allan White, late C. Wayne Burnham, and the late John Holloway. Richard Henley was involved in initial discussions and, he, David Clark and the ANU Experimental Petrology Group are thanked for assistance with the reconnaissance experiments in Table 5. Carolyn Parcheta and Tina Neal (both at the USGS, Hawaii Volcano Observatory) are thanked for helping to provide Figure 5. The authors acknowledge the facilities and technical assistance of the Australian Microscopy and Microanalysis Research Facility at the Centre of Advanced Microscopy.

REFERENCES Africano F, Rompaey GV, Bernard A, Guern FL (2002) Deposition of trace elements from high temperature gases of Satsuma-Iwojima volcano. Earth Planets Space 54:275–286 Agrinier P, Deutsch A, Schärer U, Martinez I (2001) Fast back-reactions of shock-released CO2 from carbonates: an experimental approach. Geochim Cosmochim Acta 65:2615–2632 Allard P, Aiuppa A, Loyer H, Carrot F, Gaudry A, Pinte G, Michel A, Dongarrà G (2000) Acid gas and metal emission rates during long-lived basalt degassing at Stromboli Volcano. Geophys Res Lett 27:1207–1210

50

King et al.

Alletti M, Baker DR, Freda C (2007) Halogen diffusion in a basaltic melt. Geochim Cosmochim Acta 71:3570–3580 Altree-Williams A, Pring A, Ngothai Y, Brugger J (2015) Textural and compositional complexities resulting from coupled dissolution-reprecipitation reactions in geomaterials. Earth Sci Rev 150:628–651 Anderson GM, Burnham CW (1983) Feldspar solubility and the transport of aluminum under metamorphic conditions. Am J Sci 283A:283–297 Asaduzzaman A, Laref S, Deymier P, Runge K, Cheng H-P, Muralidharan K, Derek M (2013) A first-principles characterization of water adsorption on forsterite grains. Philos Trans R Soc London Ser A 371:20110582 Asaduzzaman A, Muralidharan K, Ganguly J (2015) Incorporation of water into olivine during nebular condensation: Insights from density functional theory and thermodynamics, and implications for phyllosilicate formation and terrestrial water inventory. Meteorit Planet Sci 50:578–589 Atkins P, de Paula J, Keeler J (2018) Physical Chemistry, 11th ed. Oxford University Press Ayris PM, Lee AF, Wilson K, Kueppers U, Dingwell DB, Delmelle P (2013) SO2 sequestration in large volcanic eruptions: High-temperature scavenging by tephra. Geochim Cosmochim Acta 110:58–69 Bader R, Lipiński W (2017) Solar thermal processing. In: Advances in Concentrating Solar Thermal Research and Technology. Blanco MJ, Santigosa LR (eds) Elsevier, Cambridge MA USA, p 403–459 Balić-Žunić T, Garavelli A, Jakobsson SP, Jonasson K, Katerinopoulos A, Acquafredda KKP (2016a) Fumarolic minerals: An overview of active European volcanoes. In: Updates in Volcanology. Nemeth K (ed), IntechOpen, p 267–322, doi: 10.5772/61961 Balić-Žunić T, Birkedal R, Katerinopoulou A, Comodi P (2016b) Dehydration of blödite, Na2Mg(SO4)2.4H2O, and leonite, K2Mg(SO4)2.4H2O. Eur J Mineral 28:33–42 Berger JA, King PL, Green A, Craig MA, Spilde MN, Wright SP, Kunkel TS, Lee RJ (2015) Effect of halite coatings on thermal infrared spectra. J Geophys Res Solid Earth 120:2162–2178 Biasin A, Segre CU, Strumendo M (2015) CaCO3 crystallite evolution during CaO carbonation: critical crystallite size and rate constant measurement by in-situ synchrotron radiation X-ray Powder Diffraction. Cryst Growth Des 15:5188–5201 Binnewies M (ed) (2012) Chemical Vapor Transport Reactions. Walter de Gruyter, Berlin Bird RB, Stewart WE, Lightfoot EN (2007) Transport Phenomena, 2nd ed, John Wiley & Sons, New York Blamey J, Anthony EJ, Wang J, Fennell PS (2010) The calcium looping cycle for large-scale CO2 capture. Prog Energy Combust Sci 36:260–279 Blount CW, Dickson FW (1969) The solubility of anhydrite (CaSO4) in NaCl–H2O from 100 to 450 °C and 1–1000 bars. Geochim Cosmochim Acta 33: 227–245 Borovička J, Koten P, Spurný P, Boček J, Štork R (2005) A survey of meteor spectra and orbits: evidence for three populations of Na-free meteoroids. Icarus 174:15–30 Bowers TS, Helgeson HC (1983) Calculation of the thermodynamic and geochemical consequences of nonideal mixing in the system H2O–CO2–NaCl on phase relations in geologic systems: metamorphic equilibria at high pressures and temperatures. Am Mineral 68:1059–1075 Boynton RS (1980) Chemistry and Technology of Lime and Limestone, 2nd ed. John Wiley & Sons, New York Brindley GW, Maroney DN, Udagawa S (1961) High-temperature reactions of clay mineral mixtures and their ceramic properties, III. J Am Ceram Soc 44:42–47 Brindley GW, Udagawa S (1960) High-temperature reactions of clay mineral mixtures and their ceramic properties, I. J Am Ceram Soc 43:59–65 Brown G, Brindley GW (1984) Crystal Structures of Clay Minerals and Their X-Ray Identification. 2nd Ed, Mineral Soc, London UK Brown ME, Dollimore D, Galwey AK (1980) Reactions in the solid state. In: Comprehensive Chemical Kinetics, Vol. 22. Bamford CH, Tipper CFH (eds.), Elsevier, Amsterdam. Buckley VJE, Sparks RSJ, Wood BJ (2006) Hornblende dehydration reactions during magma ascent at Soufrière Hills Volcano, Montserrat. Contrib Mineral Petrol 151:121–140 Buddington AF, Lindsley DH (1964) Iron–titanium oxide minerals and synthetic equivalents. J Petrol 5:310–357 Bunsen R (1851) Über die Processe der vulkanischen Gesteinsbildungen Islands. Ann Phys 159:197–272 Burkhard DJM (2001) Crystallization and oxidation of Kilauea basalt glass: Processes during reheating experiments. J Petrol 42:507–527 Burkhard DJ, Scherer T (2006) Surface oxidation of basalt glass/liquid. J Non-Cryst Solids 352:241–247 Burnham CW (1967) Hydrothermal fluids at the magmatic stage. In: Geochemistry of Hydrothermal Ore Deposits, 1st ed. Barnes HL (ed) Rinehart and Winston, New York, p 34–76 Burnham CW (1979a) Magmas and hydrothermal fluids. In: Geochemistry of Hydrothermal Ore Deposits, 2nd ed. Barnes HL (ed) John Wiley & Sons, New York, p 71–136 Burnham CW (1979b) The importance of volatile constituents. In: The Evolution of the Igneous Rocks: Fiftieth Anniversary Perspectives. Yoder HSJ (ed) Princeton University Press, Princeton, p 439–482 Burnham CW (1985) Energy release in subvolcanic environments: Implications for breccia formation. Econ Geol 80:1515–1522 Burnham CW, Ohmoto H (1980) Late-stage processes of felsic magmatism. Soc Min Geol Jpn Spec Issue 8:1–11 Burnett DS, Goreva J, Epstein S, Haldemann SL, Johnson AR (1997) SO2-rock interaction on Io 2. Interaction with pure SO2. J Geophys Res Atmospheres 102:19371–19382

Gas–Solid Reactions Relevant to Earth and Planetary Processes

51

Burt DM, Sheridan MF, Bikun JV, Christiansen EH (1982) Topaz rhyolites–Distribution, origin and significance for exploration. Econ Geol 77: 1818–1836 Cengel YA, Boles MA (2014) Thermodynamics: An Engineering Approach, 8th ed, WCB/McGraw-Hill Education, Boston Censi P, Sortino F, Zuddas P, Saiano F, Brusca L, Chiavetta S, Falcone EE (2017) Rare earths behaviour during the deposition of volcanic sublimates. J Volcanol Geotherm Res 331:53–63 Chang M-H, Huang C-M, Liu W-H, Chen W-C, Cheng J-Y, Chen W, Wen T-W, Ouyang S, Shen C-H, Hsu H-W (2013) Design and experimental investigation of calcium looping process for 3-kWth and 1.9-MWth facilities. Chem Eng Technol 36:1525–1532 Chapman S, Cowling TG (1970) The Mathematical Theory of Non-Uniform Gases, 3rd ed, Cambridge University Press, Cambridge UK Chase Jr MW (1998) NIST–JANAF Thermochemical Tables, 4th ed. J Phys Chem Ref Data, Monogr 9 Chipera SJ, Vaniman DT (2007) Experimental stability of magnesium sulfate hydrates that may be present on Mars. Geochim Cosmochim Acta 71:241–250 Clark BC, Van Hart DC (1981) The salt on Mars. Icarus 45:370–378 Coats WA, Redfern JP (1963) Thermogravimetric Analysis. A Review. The Analyst 88:1–906 Cooper RF, Fanselow JB, Poker DB (1996a) The mechanism of oxidation of a basaltic glass: Chemical diffusion of network-modifying cations. Geochim Cosmochim Acta 60:3253–3265 Cooper RF, Fanselow JB, Weber JKR, Merkley DR, Poker DB (1996b) Dynamics of oxidation of a Fe2+-bearing aluminosilicate (basaltic) melt. Science 274:1173–1176 Court RW, Sephton MA (2011) The contribution of sulphur dioxide from ablating micrometeorites to the atmospheres of Earth and Mars. Geochim Cosmochim Acta 75:1704–1717 Cubillas P, Köhler S, Prieto M, Causserand C, Oelkers EH (2005) How do mineral coatings affect dissolution rates? An experimental study of coupled CaCO3 dissolution–CdCO3 precipitation. Geochim Cosmochim Acta 69:5459–5476 Dalby KN, Berger JA, Brand HEA, Eder K, Eggins SM, Herring A, Hervig RL, Kreider PB, Mernagh TP, Palm A, Renggli CJ, Troitzsch U, Yue L, King PL (2018) Analytical techniques for probing gases and small-scale layers that preserve information on gas–solid interactions. Rev Mineral Geochem 84:103–175 Darken LS, Gurry RW (1945) The system iron-oxygen. I. The wüstite field and related equilibria. J Am Chem Soc 67:1398–1412 de Moor JM, Fischer TP, Sharp ZD, King PL, Wilke M, Botcharnikov RE, Cottrell E, Zelenski M, Marty B, Klimm K, Rivard C, Ayalew D, Ramirez C, Kelley KA (2013) Sulfur degassing at Erta Ale (Ethiopia) and Masaya (Nicaragua) volcanoes: Implications for degassing processes and oxygen fugacities of basaltic systems. Geochem Geophys Geosyst 14:4076–4108 Delmelle P, Wadsworth FB, Maters EC, Ayris PM (2018) High temperature reactions between gases and ash particles in volcanic eruption plumes. Rev Mineral Geochem 84:285–308 DePaolo DJ, Cole DR, Navrotsky A, Bourg IC (2013) Geochemistry of Geologic CO2 Sequestration. De Gruyter, Berlin, Boston DiFrancesco NJ, Nekvasil H, Jaret SJ, Lindsley DH, Rogers AD (2015) Simulating a martian fumarole: understanding the effects of a degassing martian magma on surrounding rock, Lunar Planet Sci Conf 46:2305 DiFrancesco NJ, Nekvasil H, Lindsley DH, Rogers AD (2016) Modifying martian surface chemistry: chlorides as sublimates from volcanic degassing on Mars. Lunar Planet Sci Conf 47:1517 DiFrancesco NJ (2018) Evolution of the Crust on the Moon and Mars. PhD dissertation, SUNY Stony Brook, NY USA Doremus RH (2002) Diffusion of Reactive Molecules in Solids and Melts. John Wiley & Sons, New York Du H (2000) Thermodynamic assessment of the K2SO4–Na2SO4–MgSO4–CaSO4 system. J Phase Equilib 21:6–18 Emons HH, Seyfarth HH, Stegmann, E (1971) Zur Kristallographie von Doppelsalzen aus Calciumsulfat und Natriumsulfat. Cryst Res Technol 6:85–95 Eugster HP, Skippen GB (1967) Igneous and metamorphic equilibria involving gas equilibria. Res Geochem 2:492–526 Feeley TC, Sharp ZD (1996) Chemical and hydrogen isotope evidence for in situ dehydrogenation of biotite in silicic magma chambers. Geology 24:1021–1024 Fegley B, Prinn RG (1989) Estimation of the rate of volcanism on Venus from reaction rate measurements. Nature 337:55–58 Fenter P, Sturchio NC (2004) Mineral-water interfacial structures revealed by synchrotron X-ray scattering. Prog Surf Sci 77:171–258 Freeman AG (1966) The dehydroxylation behavior of amphiboles. Mineral Mag 35:953–957 Freyer D, Voigt W (2003) Crystallization and phase stability of CaSO4 and CaSO4-based salts. Monatsh Chem/Chem Mon 134:693–719 Freyer D, Voigt W, Köhnke K (1998) The phase diagram of the system Na2SO4–CaSO4. Eur J Solid State Inorg Chem 35:595–606 Frogner P, Gíslason SR, Óskarsson N (2001) Fertilizing potential of volcanic ash in ocean surface water. Geology 29:487–490 Galwey AK, Brown ME (1999) Thermal Decomposition of Ionic Solids. Elsevier, Amsterdam Gbor PK, Jia CQ (2004) Critical evaluation of coupling particle size distribution with the shrinking core model. Chem Eng Sci 59:1979–1987

52

King et al.

Getahun A, Reed MH, Symonds R (1996) Mount St. Augustine volcano fumarole wall rock alteration: mineralogy, zoning, composition and numerical models of its formation process. J Volcanol Geotherm Res 71:73–107 Giggenbach WF (1975) A simple method for the collection and analysis of volcanic gas samples. Bull Volcanol 39:132–145 Gislason SR, Hassenkam T, Nedel S, Bovet N, Eiriksdottir ES, Alfredsson HA, Hem CP, Balogh ZI, Dideriksen K, Oskarsson N, Sigfusson B, Larsen G, Stipp SLS (2011) Characterization of Eyjafjallajökull volcanic ash particles and a protocol for rapid risk assessment. Proc Natl Acad Sci USA 108:7307–7312 Gordon RS, Kingery WD (1967) Thermal decomposition of brucite: II, Kinetics of decomposition in vacuum. J Am Ceram Soc 50:8–14 Grabowsky S, Luger P, Buschmann J, Schneider T, Schirmeister T, Sobolev AN, Jayatilaka D (2012) The significance of ionic bonding in sulfur dioxide: Bond orders from X-ray diffraction data. Angew Chem Int Ed 51:6776–6779 Gupta SC, Ahrens TJ, Yang W (2001) Shock-induced vaporization of anhydrite and global cooling from the K/T impact. Earth Planet Sci Lett 188:399–412 Hack AC, Thompson AB (2011) Density and viscosity of hydrous magmas and related fluids and their role in subduction zone processes. J Petrol 52:1333–1362 Harrison AL, Dipple GM, Power IM, Mayer KU (2015) Influence of surface passivation and water content on mineral reactions in unsaturated porous media: Implications for brucite carbonation and CO2 sequestration. Geochim Cosmochim Acta 148:477–495 Harvie CE, Møller N, Weare JH (1984) The prediction of mineral solubilities in natural waters: The Na–K–Mg– Ca–H–Cl–SO4–OH–HCO3–CO3–CO2–H2O system to high ionic strengths at 25 °C. Geochim Cosmochim Acta 48:723–751 Hazen RM, Downs RT (eds) (2000) High-Temperature and High-Pressure Crystal Chemistry. Mineralogical Society of America, Washington DC Henley RW, Seward TM (2018) Gas–solid reactions in arc volcanoes: Ancient and modern. Rev Mineral Geochem 84:309–349 Henley RW, King PL, Wykes JL, Renggli CJ, Brink FJ, Clark DA, Troitzsch U (2015) Porphyry copper deposit formation by sub-volcanic sulphur dioxide flux and chemisorption. Nat Geosci 8:210–215 Henley RW, Brink FJ, King PL, Leys C, Ganguly J, Mernagh T, Middleton J, Renggli CJ, Sieber M, Troitzsch U, Turner M (2017) High temperature gas–solid reactions in calc-silicate Cu–Au skarn formation; Ertsberg, Papua Province, Indonesia. Contrib Mineral Petrol 172:106 Hinkley TK, Lamothe PJ, Wilson SA, Finnegan DL, Gerlach TM (1999) Metal emissions from Kilauea, and a suggested revision of the estimated worldwide metal output by quiescent degassing of volcanoes. Earth Planet Sci Lett 170:315–325 Hirschfelder JO, Curtiss CF, Bird RB (1964) Molecular Theory of Gases and Liquids (corrected printing). John Wiley & Sons, New York Hoefen TM, Clark RN, Bandfield JL, Smith MD, Pearl JC, Christensen PR (2003) Discovery of olivine in the Nili Fossae region of Mars. Sci 302:627–630 Homma S, Ogata S, Koga J, Matsumoto S (2005) Gas–solid reaction model for a shrinking spherical particle with unreacted shrinking core. Chem Eng Sci 60:4971–4980 Hong Y, Fegley B (1998) Experimental studies of magnetite formation in the solar nebula. Meteorit Planet Sci 33:1101–1112 Hyde BC, King PL, Dyar MD, Spilde MN, Ali AMl (2011) Methods to analyze metastable and microparticulate hydrated and hydrous iron sulfate minerals. Am Mineral 96:1856–1869 Ismail AF, Khulbe KC, Matsuura T (2015) Gas Separation Membranes: Polymeric and Inorganic. Springer, New York Jakobsen HA (2014) Chemical Reactor Modeling: Multiphase Reactive Flows, 2nd ed. Springer, New York Johnson A, Canil D (2011) The degassing behavior of Au, Tl, As, Pb, Re, Cd and Bi from silicate liquids: Experiments and applications. Geochim Cosmochim Acta 75:1773–1784 Johnson NM, Fegley Jr B (2003) Tremolite decomposition on Venus II. Products, kinetics, and mechanism. Icarus 164:317–333 Kaviany M (1991) Principles of Heat Transfer in Porous Media. Springer, New York Keene DJ, Davidson JH, Lipiński W (2013) A model of transient heat and mass transfer in a heterogeneous medium of ceria undergoing nonstoichiometric reduction. J Heat Transf 135:052701 Kennedy GC, Wasserburg GJ, Heard HC, Newton RC (1962) The upper three-phase region in the system SiO2–H2O. Am J Sci 260:501–521 King HE, Stimpfl M, Deymier P, Drake MJ, Catlow CRA, Putnis A, de Leeuw NH (2010) Computer simulations of water interactions with low-coordinated forsterite surface sites: Implications for the origin of water in the inner solar system. Earth Planet Sci Lett 300:11–18 King HE, Plümper O, Putnis CV, O’Neill HStC, Klemme S, Putnis A (2017) Mineral surface rearrangement at high temperatures: implications for extraterrestrial mineral grain reactivity. ACS Earth Space Chem 1:113–121 King PL, McSween Jr HY (2005) Effects of H2O, pH, and oxidation state on the stability of Fe minerals on Mars. J Geophys Res Planets 110:E12S10 King PL, Hervig RL, Holloway JR, Vennemann T, Righter K (1999) Oxy-substitution and dehydrogenation in mantlederived amphiboles. Geochim Cosmochim Acta 63:3635–3651

Gas–Solid Reactions Relevant to Earth and Planetary Processes

53

King PL, Holloway JR, Hervig RL, Delaney JS, Dyar MD (2000) Partitioning of H and Fe3+/Fetotal between amphibole and basaltic melt as a function of oxygen fugacity. Earth Planet Sci Lett 178:97–112 King PL, Lescinsky DT, Nesbitt HW (2004) The composition and evolution of primordial solutions on Mars, with application to other planetary bodies. Geochim Cosmochim Acta 68:4993–5008 King PL, Guan Y, Vennemann TW, Leshin LA, Sharp ZD (2009) The role of dehydrogenation on the hydrogen contents and δD values of kaersutites. Lunar Planet Sci Conf 40:2322 Kloprogge JT, Ding Z, Martens WN, Schuiling RD, Duong LV, Frost RL (2004) Thermal decomposition of syngenite, K2Ca(SO4)2·H2O. Thermochim Acta 417:143–155 Koretsky CM, Sverjensky DA, Sahai N (1998) A model of surface site types on oxide and silicate minerals based on crystal chemistry; implications for site types and densities, multi-site adsorption, surface infrared spectroscopy, and dissolution kinetics. Am J Sci 298:349–438 Kornacki AS, Fegley B (1986) The abundance and relative volatility of refractory trace elements in Allende Ca,Al-rich inclusions: implications for chemical and physical processes in the solar nebula. Earth Planet Sci Lett 79:217–234 Korotkov JA, Mikhailov EF, Andreev GA, Eltsov BI, Polyakov JA, Shestakov BG, Kechina GD (1980) Method of dehydrating carnallite. U.S. Patent 4,224,291 Kreider P, Lipiński W (2018) High-temperature gas–solid reactions in industrial processes. Rev Mineral Geochem 84:499–514 Kubicki JD, Watts HD (2018) Reaction mechanisms and solid–gas phase reactions: Theory and density functional theory simulations. Rev Mineral Geochem 84:85–101 Lackner KS, Wendt CH, Butt DP, Joyce EL, Sharp DH (1995) Carbon dioxide disposal in carbonate minerals. Energy 20:1153–1170 Lamoreaux RH, Hildenbrand DL (1984) High temperature vaporization behavior of oxides. I. Alkali metal binary oxides. J Phys Chem Ref Data 13:151–173 Lamoreaux RH, Hildenbrand DL, Brewer L (1987) High–temperature vaporization behavior of oxides II. Oxides of Be, Mg, Ca, Sr, Ba, B, Al, Ga, In, Tl, Si, Ge, Sn, Pb, Zn, Cd, and Hg. J Phys Chem Ref Data 16:419–443 Landau LD, Lifshitz EM (1987) Fluid Mechanics. Pergamon Press, New York Larocque ACL, Stimac JA, Siebe C, Greengrass K, Chapman R, Mejia SR (2008) Deposition of a high-sulfidation Au assemblage from a magmatic volatile phase, Volcán Popocatépetl, Mexico. J Volcanol Geotherm Res 170:51–60 Lemke KH, Seward TM (2018) Molecular clusters and solvation in volcanic and hydrothermal vapors. Rev Geochem 84:57–83 Levenspiel O (2004) Chemical Reaction Engineering. John Wiley & Sons, New York Li EY, Chareev, DA, Shilobreeva, SN, Grichuk DV, Tyutyunnik OA (2010) Experimental study of sulfur dioxide interaction with silicates and aluminosilicates at temperatures of 650 and 850 °C. Geochem Int 48:1039–1046 Lindberg D, Backman R, Chartrand P (2006) Thermodynamic evaluation and optimization of the (Na2SO4 + K2SO4 + Na2S2O7 + K2S2O7) system. J Chem Thermodyn 38:1568–1583 Loring JS, Thompson CJ, Wang Z, Joly AG, Sklarew DS, Schaef HT, Ilton ES, Rosso KM, Felmy AR (2011) In situ infrared spectroscopic study of forsterite carbonation in wet supercritical CO2. Environ Sci Technol 45:6204–6210 Loring JS, Thompson CJ, Zhang C, Wang Z, J, Schaef HT, Rosso KM (2012) In situ infrared spectroscopic study of brucite carbonation in dry to water-saturated supercritical carbon dioxide. J Phys Chem A 116:4768–4777 Lukyanova EV, Zotov AV (2017) Determination of the NaFaq association constant for the NaF–NaCl–H2O system at 25–75 °C by means of potentiometry. Rus J Phys Chem A, 91:672–677 Lyakhov N, Maciejewski M, Reller A (1985) Theoretical considerations on the temperature and pressure dependence of the kinetics of reversible thermal decomposition processes of solids. J Solid State Chem 58:398–400. Maciejewski M, Reller A (1987) How (UN) realiable are kinetic data of reversible solid-state decomposition processes? Thermochim Acta 110:145–152 MacKenzie JM, Canil D (2008) Volatile heavy metal mobility in silicate liquids: Implications for volcanic degassing and eruption prediction. Earth Planet Sci Lett 269:488–496 MacRae ND (1974) Sulfurization of basalt under thermal metamorphic conditions to produced cordierite-bearing rocks. Can J Earth Sci 11:246–253 Manning CE (1994) The solubility of quartz in H2O in the lower crust and upper mantle. Geochim Cosmochim Acta 58:4831–4839 Mantha NM, Schindler M, Murayama M, Hochella MF (2012) Silica- and sulfate-bearing rock coatings in smelter areas: Products of chemical weathering and atmospheric pollution I. Formation and mineralogical composition. Geochim Cosmochim Acta 85:254–274 Maters EC, Delmelle P, Rossi MJ, Ayris PM, Bernard A (2016) Controls on the surface chemical reactivity of volcanic ash investigated with probe gases. Earth Planet Sci Lett 450:254–262 Matteucci S, Yampolskii Y, Freeman BD, Pinnau I (2006) Transport of gases and vapors in glassy and rubbery polymers. In: Materials Science of Membranes for Gas and Vapor Separation. John Wiley & Sons, Chichester UK, p 1–47 Melchiori T, Canu P (2014) Improving the quantitative description of reacting porous solids: Critical analysis of the shrinking core model by comparison to the generalized grain model. Ind Eng Chem Res 53:8980–8995 Mehrotra BN (1989) Structural transformations and phase stabilization in Na2SO4–Na2CO3 system. Phase Trans, 16:431–436 Miyagi I, Matsubaya O, Nakashima S (1998) Change in D/H ratio, water content and color during dehydration of hornblende. Geochem J 32:33–48

54

King et al.

Modest MF (2013) Radiative Heat Transfer. Academic Press, New York Morey GW (1964) Phase-equilibrium Relations of the Common Rock-forming Oxides Except Water. US Govt Print Office, Washington Morgan B, Wilson SA, Madsen IC, Gozukara YM, Habsuda J (2015) Increased thermal stability of nesquehonite (MgCO3·3H2O) in the presence of humidity and CO2: Implications for low-temperature CO2 storage. Int J Greenh Gas Control 39:366–376 Moulijn JA, van Leeuwen PWNM, van Santen RA (1993) Catalysis: An Integrated Approach to Homogeneous, Heterogeneous and Industrial Catalysis. Elsevier, Amsterdam Moune S, Gauthier PJ, Gislason SR, Sigmarsson O (2006) Trace element degassing and enrichment in the eruptive plume of the 2000 eruption of Hekla volcano, Iceland. Geochim Cosmochim Acta 70:461–479 Mueller SB, Ayris PM, Wadsworth FB, Kueppers U, Casas AS, Delmelle P, Taddeucci J, Jacob M, Dingwell DB (2017) Ash aggregation enhanced by deposition and redistribution of salt on the surface of volcanic ash in eruption plumes. Sc Rep 7:45762 Munoz JL (1984) F–OH and Cl–OH in micas with applications to hydrothermal ore deposits. In: Micas. Vol 13. Bailey SW (ed), Mineral Soc Am, Blacksburg VA, p 469–493 Nagahara H (2018) Kinetics of gas–solid reactions in the Solar System and beyond. Rev Mineral Geochem 84:461–497 Néron A, Lantagne G, Marcos B (2012) Computation of complex and constrained equilibria by minimization of the Gibbs free energy. Chem Eng Sci 82:260–271 Newton GH, Chen SL, Kramlich JC (1989) Role of porosity loss in limiting SO2 capture by calcium based sorbents. AIChE J 35:988–994 Nicholson RV, Gillham RW, Reardon EJ (1990) Pyrite oxidation in carbonate-buffered solution: 2. Rate control by oxide coatings. Geochim Cosmochim Acta 54:395–402 Norberg N, Neusser G, Wirth R, Harlov D (2011) Microstructural evolution during experimental albitization of K-rich alkali feldspar. Contrib Mineral Petrol 162:531–546 Noiriel C, Daval D (2017) Pore-scale geochemical reactivity associated with CO2 storage: new frontiers at the fluid– solid interface. Acc Chem Res 50:759–768 Norris CA, Wood BJ (2017) Earth’s volatile contents established by melting and vaporization. Nature 549:507–510 Oelkers EH, Gislason SR, Matter J (2008) Mineral carbonation of CO2. Elements 4:333–337 Olsson J, Bovet N, Makovicky E, Bechgaard K, Balogh Z, Stipp SLS (2012) Olivine reactivity with CO2 and H2O on a microscale: Implications for carbon sequestration. Geochim Cosmochim Acta 77:86–97 Olsson J, Stipp SLS, Dalby KN, Gislason SR (2013) Rapid release of metal salts and nutrients from the 2011 Grímsvötn, Iceland volcanic ash. Geochim Cosmochim Acta 123:134–149 Óskarsson N (1980) The interaction between volcanic gases and tephra: fluorine adhering to tephra of the 1970 Hekla eruption. J Volcanol Geotherm Res 8:251–266 Oppenheimer C, Scaillet B, Martin RS (2011) Sulfur degassing from volcanoes: Source conditions, surveillance, plume chemistry and Earth system impacts. Rev Mineral Geochem 73:363–421 Oppenheimer C, Fischer TP, Scaillet B (2014) Volcanic degassing: Process and impact. In Treatise on Geochemistry (2nd ed.) Holland HD, Turekian KK (eds), Elsevier, Oxford, p 111–179 Palm AB, King PL, Renggli CJ, Hervig RL, Dalby KN, Herring A, Mernagh TP, Eggins SM, Troitzsch U, Beeching L, Kinsley L, Guagliardo P (2018) Unravelling the consequences of SO2–basalt reactions for geochemical fractionation and mineral formation. Rev Mineral Geochem 84:257–283 Pathak AD, Nedea SV, Zondag HA, Rindt CCM, Smeulders DMJ (2016) A DFT based equilibrium study of a chemical mixture tachyhydrite and their lower hydrates for long term heat storage. J Phys Conf Ser 745:032003 Pokrovski GS, Borisova AY, Bychkov AY (2013) Speciation and transport of metals and metalloids in geological vapors. Rev Mineral Geochem 76:165–218 Popp RK, Virgo D, Yoder Jr HS, Hoering TC, Phillips MW (1995) An experimental study of phase equilibria and Fe oxycomponent in kaersutitic amphibole: Implications for the ƒH2 and aH2O in the upper mantle. Am Mineral 80:534–548 Putnis A (2015) Transient porosity resulting from fluid-mineral interaction and its consequences. Rev Mineral Geochem 80:1–23 Raimondeau S, Vlachos DG (2002) Recent developments on multiscale, hierarchical modeling of chemical reactors. Chem Eng J 90:3–23 Renggli CJ, King PL (2018) SO2 gas reactions with silicate glasses. Rev Mineral Geochem 84:229–255 Renggli CJ, King PL, Henley RW, Norman MD (2017) Volcanic gas composition, metal dispersion and deposition during explosive volcanic eruptions on the Moon. Geochim Cosmochim Acta 206:296–311 Righter K, Dyar MD, Delaney JS, Vennemann TW, Hervig RL, King PL (2002) Distribution of OH−, O2−, Cl− and F− in biotite from volcanic rocks and correlations with octahedral cations. Am Mineral 87:142–153 Robie RA, Hemingway BS (1995) Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar (105 Pascals) pressure and at higher temperatures. United States Geological Survey, US Government Printing Office, Washington DC Robock A, Oppenheimer C (2004) Volcanism and the Earth’s Atmosphere. American Geophysical Union, Washington DC Rodriguez-Navarro C, Ruiz-Agudo E, Luque A, Rodriguez-Navarro A, Ortega-Huertas M (2009) Thermal decomposition of calcite: Mechanisms of formation and textural evolution of CaO nanocrystals. Am Mineral 94:578–593 Roine A (2015) Outotec HSC Chemistry 8.1. Outotec Research Center, Finland

Gas–Solid Reactions Relevant to Earth and Planetary Processes

55

Rose WI (1977) Scavenging of volcanic aerosol by ash: Atmospheric and volcanologic implications. Geology 5:621–624 Ross NL (2000) Framework structures. Rev Mineral Geochem 41:257–287 Rowe JJ, Morey GW, Silber CC (1967) The ternary system K2SO4–MgSO4–CaSO4. J Inorg Nucl Chem 29:925–942 Ruiz-Agudo E, Putnis CV, Rodriguez-Navarro C, Putnis A (2012) Mechanism of leached layer formation during chemical weathering of silicate minerals. Geology 40:947–950 Ruiz-Agudo E, Putnis CV, Putnis A (2014) Coupled dissolution and precipitation at mineral-fluid interfaces. Chem Geol 383:132–146 Rumble J (2017) CRC Handbook of Chemistry and Physics, 98th ed. Taylor & Francis Ltd., New York Ruscic B (2010) Active Thermochemical Tables. https://atct.anl.gov/index.html Ruscic B, Feller D, Peterson KA (2014) Active thermochemical tables: dissociation energies of several homonuclear first-row diatomics and related thermochemical values. Theor Chem Acc 133:1415 Rutherford MJ, Hill PM (1993) Magma ascent rates from amphibole breakdown: An experimental study applied to the 1980–1986 Mount St. Helens eruptions. J Geophys Res 98:19667–19685 Safari V, Arzpeyma G, Rashchi F, Mostoufi N (2009) A shrinking particle—shrinking core model for leaching of a zinc ore containing silica. Int J Miner Process 93:79–83 Salmi T, Grénman H, Wärnå J, Murzin DY (2013) New modelling approach to liquid–solid reaction kinetics: From ideal particles to real particles. Chem Eng Res Des 91:1876–1889 Schaef HT, McGrail BP, Loring JL, Bowden ME, Arey BW, Rosso KM (2013) Forsterite [Mg2SiO4)] carbonation in wet supercritical CO2: An in situ high-pressure X-ray Diffraction study. Environ Sci Technol 47:174–181 Schmauss D, Keppler H (2014) Adsorption of sulfur dioxide on volcanic ashes. Am Mineral 99:1085–1094 Schott J, Pokrovsky OS, Spalla O, Devreux F, Gloter A, Mielczarski JA (2012) Formation, growth and transformation of leached layers during silicate minerals dissolution: The example of wollastonite. Geochim Cosmochim Acta 98:259–281 Schrön W (1989a) Solid–gas–equilibria in geo- and cosmochemistry; 1. Geochemistry. Eur J Mineral 1:739–763 Schrön W (1989b) Solid–gas–equilibria in geo- and cosmochemistry; 2. Cosmochemistry. Eur J Miner 1:765–782 Schrön W (2013) Chemical fluid transport (CFT). Chem Erde – Geochem 73:421–428 Sharp ZD (2017) Nebular ingassing as a source of volatiles to the terrestrial planets. Chem Geol 448:137–150 Shaw DJ (1980) Introduction to Colloid and Surface Chemistry. Butterworths Canada Ltd, Calgary Somorjai GA, Van Hove MA (1989) Adsorbate-induced restructuring of surfaces. Prog Surf Sci 30:201–231 Sossi PA, Fegley B (2018) Thermodynamics of element volatility and its application to planetary processes. Rev Mineral Geochem 84:393–459 Sparks RSJ (1978) The dynamics of bubble formation and growth in magmas: a review and analysis. J Volc Geotherm Res 3:1–37 Steefel CI, Beckingham LE, Landrot G (2015) Micro-continuum approaches for modeling pore-scale geochemical processes. Rev Mineral Geochem 80:217–246 Stefánsson A, Dreisner T, Bénézeth P (2013) Thermodynamics of Geothermal Fluids. Rev Mineral Geochem Vol. 76 Steiger M, Linnow K, Ehrhardt D, Rohde M (2011) Decomposition reactions of magnesium sulfate hydrates and phase equilibria in the MgSO4–H2O and Na+–Mg2+–Cl––SO42––H2O systems with implications for Mars. Geochim Cosmochim Acta 75:3600–3626 Stern KH (2001) High Temperature Properties and Thermal Decomposition of Inorganic Salts with Oxyanions. CRC Press, Boca Raton FL Stern KH, Weise EL (1966) High temperature properties and decomposition of inorganic salts. Part 1. Sulfates. National Bureau of Standards, US Government Printing Office, Washington DC Stocker TF, Qin D, Plattner G-K et al. (2013) Technical summary. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Stocker TF, Qin D, Plattner G-K et al. (eds) Cambridge University Press, Cambridge, UK, p 33–115 Suttle MD, Genge MJ, Folco L, Russell SS (2017) The thermal decomposition of fine-grained micrometeorites, observations from mid-IR spectroscopy. Geochim Cosmochim Acta 206:112–136 Symonds RB, Reed MH (1993) Calculation of multicomponent chemical equilibria in gas–solid–liquid systems; calculation methods, thermochemical data, and applications to studies of high-temperature volcanic gases with examples from Mount St. Helens. Am J Sci 293:758–864 Symonds RB, Rose WI, Reed MH, Lichte FE, Finnegan DL (1987) Volatilization, transport and sublimation of metallic and non-metallic elements in high temperature gases at Merapi Volcano, Indonesia. Geochim Cosmochim Acta 51:2083–2101 Symonds RB, Rose WI, Bluth GJS, Gerlach TM (1994) Volcanic-gas studies: Methods, results, and applications. In: Volatiles in Magmas. Vol 30. Carroll MR, Holloway JR (eds). Mineral Soc Am, Blacksburg VA, p 1–66 Szekely J, Evans JW, Sohn HY (1976) Gas–Solid Reactions. Academic Press, New York Teir S, Kuusik R, Fogelholm C-J, Zevenhoven R (2007) Production of magnesium carbonates from serpentinite for long-term storage of CO2. Int J Miner Process 85:1–15 Tomkins AG, Bowlt L, Genge M, Wilson SA, Brand HEA, Wykes JL (2016) Ancient micrometeorites suggestive of an oxygen-rich Archaean upper atmosphere. Nature 533:235–238 Triolo I, Mottana A, Giampaolo C (1988) Synthesis and thermal behaviour of syngenite. Terra Cogn 8:79 Ustunisik G, Nekvasil H, Lindsley DH (2011) Differential degassing of H2O, CI, F, and S: Potential effects on lunar apatite. Am Mineral 96:1650–1653

56

King et al.

Ustunisik G, Nekvasil H, Lindsley DH, McCubbin FM (2015) Degassing pathways of Cl, F-, H-, and S-bearing magmas near the lunar surface: Implications for the composition and Cl isotopic values of lunar apatite. Am Mineral 100:1717–1727 Valverde MJ, Medina S (2017) Limestone calcination under calcium-looping conditions for CO2 capture and thermochemical energy storage in the presence of H2O: an in situ XRD analysis. Phys Chem Chem Phys 19:7587–7596 Varekamp JC, Luhr JF, Prestegaar KL (1984) The 1982 eruptions of El Chichon Volcano (Chiapas, Mexico): character of the eruptions, ash-fall deposits, and gas phase. J Volcanol Geotherm Res 23: 9–68 Vattuone L, Smerieri M, Savio L, Asaduzzaman AM, Muralidharan K, Drake MJ, Rocca M (2013) Accretion disk origin of Earth’s water. Philos Trans R Soc London, Ser. A 371:1–11 Vlastélic I, Menard G, Gannoun A, Piro J-L, Staudacher T, Famin V (2013) Magma degassing during the April 2007 collapse of Piton de la Fournaise: The record of semi-volatile trace elements (Li, B, Cu, In, Sn, Cd, Re, Tl, Bi). J Volcanol Geotherm Res 254:94–107 Wagner C, Deloule E, Fialin M, King PL (2008) Dehydrogenation of kaersutitic amphibole under electron beam excitation recorded by changes in Fe3+/ΣFe ratios: An EMP and SIMS study. Am Mineral 93:1273–1281 Wang W, Ramkumar S, Li S, Wong D, Iyer M, Sakadjian BB, Statnick RM, Fan L-S (2010) Subpilot demonstration of the carbonation−calcination reaction (CCR) process: High-temperature CO2 and sulfur capture from coal-fired power plants. Ind Eng Chem Res 49:5094–5101 Welty J, Wicks CE, Rorrer GL, Wilson RE (2007) Fundamentals of Momentum, Heat and Mass Transfer. WileyVCH, New York Williams-Jones AE, Migdisov AA, Archibald SM, Xiao Z (2002) Vapor-transport of ore metals. In: Water-Rock Interactions, Ore Deposits, and Environmental Geochemistry: A Tribute to David Crerar, Spec Pub 7. Hellmann R, Scott AW (eds) The Geochemical Society, St-Louis MO, p 279–306 Williams-Jones AE, Heinrich CA (2005) 100th anniversary special paper: Vapor transport of metals and the formation of magmatic-hydrothermal ore deposits. Econ Geol 100:1287–1312 Wilson SA, Bish DL (2012) Stability of Mg-sulfate minerals in the presence of smectites: possible mineralogical controls on H2O cycling and biomarker preservation on Mars. Geochim Cosmochim Acta 96:120–133 Wones DR (1981) Mafic silicates as indicators of intensive variables in granitic magmas. Min Geol 31:191–212 Wones DR, Eugster HP (1965) Stability of biotite: Experiment, theory, and application. Am Mineral 50:1228–1272 Wood JR (1975) Thermodynamics of brine–salt equilibria—I. The systems NaCl–KCl–MgCl2–CaCl2–H2O and NaCl–MgSO4–H2O at 25 °C. Geochim Cosmochim Acta 39:1147–1163 Xu H, Guo X, Bai J (2017) Thermal behavior of polyhalite: a high-temperature synchrotron XRD study. Phys Chem Miner 44:125–135 Yagi S, Kunii D (1955) Studies on combustion of carbon particles in flames and fluidized beds. Symp Int Combust 5:231–244 Yue L (2018) Thermal Transport Phenomena in Carbonate Particles Undergoing Chemical Looping. PhD Australian National University, Canberra Australia Yue L, Lipiński W (2015a) A numerical model of transient thermal transport phenomena in a high-temperature solid– gas reacting system for CO2 capture applications. Int J Heat Mass Transf 85:1058–1068 Yue L, Lipiński W (2015b) Thermal transport model of a sorbent particle undergoing calcination-carbonation cycling. AIChE J 61:2647–2656 Zelenski ME, Fischer TP, de Moor JM, Marty B, Zimmermann L, Ayalew D, Nekrasov AN, Karandashev VK (2013) Trace elements in the gas emissions from the Erta Ale volcano, Afar, Ethiopia. Chem Geol 357:95–116 Zelenski M, Malik N, Taran Y (2014) Emissions of trace elements during the 2012–2013 effusive eruption of Tolbachik volcano, Kamchatka: enrichment factors, partition coefficients and aerosol contribution. J Volcanol Geotherm Res 285:136–149 Zhang Y (2010) Diffusion in minerals and melts: Theoretical background. Rev Mineral Geochem 72:5–59 Zolotov MY (1985) Sulfur-containing gases in the Venus atmosphere and stability of carbonates. Lunar Planet Sci Conf 16:942–943 Zolotov MY (2018) Gas–solid interactions on Venus and other Solar System bodies. Rev Mineral Geochem 84:351–392

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Molecular Clusters and Solvation in Volcanic and Hydrothermal Vapors Kono H. Lemke Department of Earth Sciences University of Hong Kong Pokfulam Road Hong Kong SAR China

Terry M. Seward SGEES Victoria University of Wellington Wellington 6140 New Zealand INTRODUCTION Throughout the Earth’s crust from magmatic/volcanic to lower temperature hydrothermal environments, low density aqueous fluids play a fundamental role in its chemical evolution. These gas-like fluids contain a periodic table of elements but their molecular chemistry has been little studied. Even the gas-phase molecular chemistry of the solvent itself, steam or low density supercritical water, is poorly known. These low density, gas-like aqueous fluids are important reactive, chemical transport media (Henley and Seward 2018, this volume) throughout the crust and may exit into the Earth’s ocean–atmosphere system, contributing to ocean and atmospheric chemistry throughout geologic time. The importance of high temperature gas–solid reactions in crustal evolution and ore deposit formation has recently been emphasized by Henley et al. (2017) in their study of the enormous skarn deposits associated with the giant Grasberg porphyry deposit at Ertsberg in Indonesia. Low-density water solvent (steam or water vapor) at elevated temperatures is not a hydrogen bonded dielectric continuum as is liquid water at temperatures above about 150 °C (see for example Seward and Driesner 2004, and references therein). Water vapor is comprised of aggregates of waters molecules held together by hydrogen bonding with the cluster sizes and geometries defined by the water gas density (or pressure) at a given temperature. We present new data on the size, energetics (stabilities) and geometries of molecular water clusters in water vapor as well as data on the solvation of both ionic and molecular species in the water cluster environment. We discuss the solvation of the proton, or more correctly, the hydrated proton, by water clusters, which comprise the basis for our understanding of pH and the equilibrium ion product constant, Kw, of water vapor. The solvation of a number of dissolved species relevant to high temperature natural systems, including NaCl, H2S and HS− is also discussed. We also present new data on the cluster solvation of Au+ as well as the simple monochloridogold(I) complex, AuCl°, in water vapor at elevated temperatures. These observations provide fundamental molecular insight into the reactivity and transport chemistry of high temperature water vapor in the Earth´s crust but our observations are only a reconnaissance because so little is known. 1529-6466/18/0084-0002$05.00 (print) 1943-6266/18/0084-0002$05.00 (online)

http://dx.doi.org/10.2138/rmg.2018.84.02

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The topic of gas-phase (molecular and ionic) chemistry is a relatively new and an exciting domain of research in the Earth Sciences. Despite being a new field of geochemistry, it has attracted considerable attention, from both within and outside the Earth Sciences, by the experimental community (Casey and Swaddle 2003; Casey and Rustad 2007) and now increasingly from the theoretical chemistry community (Zhao and Truhlar 2010). Research on gas-phase ions over the past three decades has opened up exciting new possibilities for geochemists to examine the structure and stability of solvated gaseous ions, which makes it possible to understand why gaseous ions behave fundamentally differently from their bulk (liquid) analogues, and distinguish between intrinsic properties of ion(-molecule) clusters and properties resulting from their solvation environment. For example, the concept of vapor pH is directly linked to the formation of solvated proton clusters (or hydroxide water clusters), that exist with fundamentally different bonding motifs (see Fig. 1), i.e. Eigen vs Zundel, exterior vs interior ion positions, and dynamically transform as the solvation shell grows and evolves from cluster-size towards structures with bulk-like environments

Figure 1. Structures of protonated Eigen and Zundel water cluster ions, and hydroxide water clusters with first and second shell water solvation.

Probing solvated ion clusters using mass spectrometry, and more recently, in combination with structure-sensitive infrared (IR) spectroscopic techniques, has helped to reveal the nature of ion-water interactions in gas-phase clusters (Robertson and Johnson 2003). For example, the solvation of the hydroxide ion in water vapor stands out as an interesting case where completion of the first solvation shell with OH−(H2O)3 and emergence of a second solvation shell in OH−(H2O)4 is marked by changes in IR bands caused by inter-water hydrogen bonding (Robertson et al 2003). Interestingly, solvated fluoride anions display comparable spectral shifts as the solvation shell evolves to include a strongly bound water–water network beginning in F−(H2O)5 with spectral features typical of internally solvated ions. Larger halide ions such as Cl−, Br− and I−, on the other hand, display IR spectral features characteristic of surfacesolvated ions, in other words, the primary solvation shell is only partially filled with the halide ion positioned at the water cluster surface (e.g. Robertson and Johnson 2003; Likhoyot et al. 2005). We will later see that these solvation motifs play a key role in the positioning of ions at water–vapor interfaces, with important implications for the partitioning of molecular ions across phase boundaries during film, bubble and droplet formation in high temperature vapor. The experimental study of gaseous ions provides obvious advantages over bulk phase studies, because the former can resolve spectroscopic signatures that stem from single, double and higher-order ion aggregates whereas solution phase methods often yield averaged signals and rarely provide direct evidence for ion clustering. However, ion cluster studies are also attended by challenges, and these are predominantly due to trade-offs as to how mass spectrometric facilities are linked to laser spectroscopic systems, but also the role that ambient blackbody radiation has on the stability of a cluster. There are some exciting new developments in cryogenically cooled mass spectrometers that will overcome some of these difficulties and permit the probing of cluster structures as a function of temperature (Guo et al. 2004). The past decade has seen an explosion

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in the number of mass spectrometric/IR laser spectroscopic investigations of solvated molecular ions, and this is in part due to recent developments in tunable optical parametric oscillator/ amplifier (OPO/OPA) laser systems and a growing number of mass spectrometric facilities with mass selection and storage capabilities, such as time-of-flight (TOF-MS) and Fourier-transform ion cyclotron resonance (FT-ICR-MS) mass spectrometry. The challenge of transferring molecular ions from the solution into the gas-phase, without causing any significant changes to the molecular structure and distribution, has been addressed by probing concentration and pH-dependent changes in ion cluster populations following electrospray ionization (Schröder et al. 2011, Schröder 2012). From a computational perspective, larger clusters (> 80 H2O) have been intractable using reliable high level theory, primarily because of their size and configurational complexity, but also because these systems require appropriate theory to accurately describe interactions ranging from relativistically driven metal-metal bonding to dispersion dominated weak interactions in the solvation shell (Zhao et al. 2006; Zhao and Truhlar 2008, 2010). Consequently, density functional theory (DFT) with continuum methods (PCM), and explicit first shell solvation, are the work-horse methods used in most simulations of microsolvated clusters, however, scattered evidence indicates that this approach is impractical and often fails to predict the correct properties for solvated ion clusters. Some of these problems are now being overcome, such as for instance, finding the global minimum of a solvated (> 50 waters) ion cluster which is still a formidable task but can be achieved using artificial bee colony (Zhang and Dolg 2016), basin hopping type optimizations (Wales et al. 2007) and genetic algorithm based techniques (Schulz and Hartke 2002). The main focus of this review is on the gas-phase physical geochemistry of single ions, ion pairs and polynuclear ions solvated with geochemically relevant molecules (e.g. H2O, NH3, H2S, CO2 etc.) using insights from mass spectrometry (e.g. FT-ICR-MS) and vibrational spectroscopy with tunable IR laser sources. The combination of FT-MS and IR spectroscopy can provide valuable information on the structure of the ion core and solvation shell; however, this approach entails several challenges, in particular the ability to control the temperature in the vicinity of the ion detector/ICR cell still remains an obstacle. Ions with large solvation shells generally require cryogenic cooling, and thus, if these ions are exposed to a controlled blackbody field generated within the mass spectrometer, IR spectra can be obtained for mass-selected ions with temperature-dependent solvation shell structures. Other mass spectrometric techniques, such as HPMS, complement FT-ICR MS IRMPD measurements and provide important thermodynamic information on the interaction of solvent molecules with ions (Meot-Ner 2005, and refs. therein). The interpretation of mass spectrometric and IRMPD spectra builds critically on results from molecular simulations, and this task becomes increasingly challenging as the size of the cluster increases. This problem is further compounded when inter-water hydrogen bonding in the solvation shell around an ion gives rise to closely spaced ( 10) water clusters (Pradzynski et al. 2012). These findings are crucial for understanding droplet nucleation phenomena in water vapor, aerosols, clouds and atmospheric chemistry processes occurring at the nanodroplet interior and surfaces.

THE MOLECULAR STRUCTURE OF WATER VAPOR (STEAM AND LOW DENSITY SUPERCRITICAL WATER) Neutral Clusters The dimer and small ring structures: The first experimental account of the water dimer, (H2O)2, dates back to 1957 and reported OH-stretching and bending vibrations in the 1600–3500 cm−1 spectral region using cryogenic matrices (Van Thiel et al. 1957). Subsequent IR spectroscopic (Liu et al. 1996a; Braly et al. 2000a,b), thermal conductivity (Curtiss and Blander 1979, 1988) and quantum chemical studies (Xantheas 1994; Feyereisen et al. 1996; Xantheas et al. 2002; Lemke and Seward 2008a, Mukhopadhyay et al. 2018, and refs therein) of (H2O)2 (and smaller water clusters) have yielded valuable insight into the structure and stability of the simple dimer, and as of this review, there are around 1700 publications that have examined the water dimer both experimentally and theoretically. Figure 2 below presents a van’t Hoff plot for the water clustering reaction (H2O)n + (H2O) = (H2O)n+1 generating ring-type (H2O)3 (2,3), (H2O)4 (3,4) and (H2O)5 (4,5) clusters and these results have been obtained at the CCSD(T)/CBS limit level of theory.

Figure 2. left: Van’t Hoff plot for (H2O)n + (H2O) = (H2O)n+1 clustering reaction together with equilibrium thermal conductivity (TC) measurements for water dimerization (1,2) reaction (Curtiss 1979). right: water cluster geometries and CCSD(T)/CBS level stepwise clustering enthalpies (kcal/mol) and entropies (cal/mol/K) shown in brackets. Also shown for reference are data for the H2S dimer (brown) taken from Lemke (2017).

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Given the importance of smaller water clusters, it seems appropriate to briefly comment on the thermodynamic properties of these species. In Figure 2, values for the stepwise water clustering equilibria are shown as a function of temperature from 298 K up to ~640 K, and it is seen that all clustering reactions exhibit positive slopes (i.e. negative clustering enthalpies) over the full temperature range, corresponding to a decrease in cluster stability with increasing temperature. The magnitude of this decrease in stability, however, differs from cluster to cluster, indicating, for instance, that the water dimer would play a more significant role as a molecular species in water vapor at higher temperatures, whereas higher clusters would undergo full dissociation to their constituent monomers and play a less important role in water vapor. In fact, Slanina and coworkers (Slanina 1988; Slanina et al. 2006) have examined temperature effects for several water clustering equilibria and concluded that water clusters disassociate with increasing temperature, in particular at hydrothermal temperatures. It was also noted that water clusters would play a more important role in low-temperature saturated vapor over ice or liquid water, given the increasing thermodynamic favor for water clustering at lower temperatures. However, because water vapor pressures are significantly higher along the two phase curve, particularly in the vicinity of the critical point of water, a large fraction of the monomer population will likely interconvert to the water dimer and larger clusters. In Figure 3 below, the partial pressures of water clusters with n = 2–4 are presented as a function of temperature for vapor saturation conditions.

Figure 3. Abundance profiles of water clusters (H2O)n with n = 2–4 in equilibrium with H2O (liquid) along the liquid–vapor phase boundary from 298 to 646 K. Note the initial dip in cluster abundance at lower temperatures, inflection at 350 (n = 2), 360 (n = 3) and 380 K (n = 4) followed by a steady increase in water cluster abundance with increasing temperature up to the critical region.

Our calculations demonstrate that the (exponentially) increasing water monomer pressure along the liquid vapor phase boundary suffices to enhance the stability of water clusters, in particular, in the case of the water dimer; results from CCSD(T)/aVTZ calculations predict that approximately 40% of the vapor phase is composed of water dimers, with noticeable contributions from (H2O)3 and (H2O)4 that steadily increase with increasing temperature; it is also worth noting that our predicted levels of trimer and tetramer clusters are not necessarily a good diagnostic for the abundance of larger clusters in water vapor because water cluster beginning with n > 6 form three-dimensional structures that possess higher stabilities compared with ring-like (H2O)3, (H2O)4 and (H2O)5. Cluster structures that so far have not been examined for their ability to exist in ambient over even high-temperature aqueous vapors, in spite of their well-known stability, include compact (H2O)6 species and as discussed further below, cubic (H2O)8 and the magic number dodecahedral (H2O)20 clusters.

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Medium sized water clusters, n = 4–10. Saykally and coworkers (Pugliano and Saykally 1992; Cruzan et al. 1996; Liu et al. 1996a,b,c; Gregory et al. 1997) reported the first account of the structure and spectra of the larger water clusters (H2O)n with n = 3–6, using far-IR vibrationaltunneling (VRT) spectroscopy. Huisken et al. (1996) subsequently reported the first experiments to observe water OH-stretching bands in (H2O)n (n = 3–5) by recording infrared predissociation (IRPD) spectra in the spectral region 3300–3800 cm−1 of mass-selected water clusters. These studies were followed up by an experimental investigation of the three-dimensional forms of (H2O)6 by Saykally and coworkers (Liu et al. 1996a). Several important points evolve from these studies which show that the lowest energy conformers of the water hexamer adopt threedimensional structures (e.g. prisms, cages, books, boats, etc). However, smaller water clusters (n = 2–5) maintain linear or cyclic configurations, and the stability ranking of the five lowestenergy (H2O)6 structures changes when vibrational zero-point energies are taken into account; i.e. the cage configuration of (H2O)6 is favored over the prism form when ZPE effects are considered. Buck et al. (1998) measured the first IR predissociation spectra for larger water clusters (H2O)n (n = 8–10) using supersonic expansion techniques, vibrational predissociation spectroscopy and theoretical MP2/DZP calculations and found that (H2O)8–10 adopt microcrystalline structures based on small water octamers in which water molecules occupy the vertices of a cube. The most stable water nonamer (n = 9) and decamer (n = 10) structures, on the other hand, are derived from cubic (H2O)8 by insertion of one and two two-coordinated molecules into the cube edges. Therefore one might expect that IRMPD fingerprint spectra of (H2O)9 and (H2O)10 to retain features of the cubic octamer, while also showing characteristic red-shifted OH-stretching bands associated with these “newly” inserted singly and doubly coordinated water molecules. Figure 4 shows an example of IR-predissociation spectra (Buck and Huisken 2000) of water clusters having n = 7–20 as well as the IR absorption spectrum of liquid water at 298 K;

Figure 4. IR photo dissociation (IRPD) spectra of mass-selected water clusters (H2O)n with n = 7–20 in the OH stretching region (modified from Buck and Huisken 2000) together with the broad OH stretch band in ordinary liquid water at 298 K shown in grey (Maréchal 2011).

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these data have been added to illustrate the breadth of the interwater OH-stretching bands in bulk water (Maréchal 2011). It may be seen that the octa-, nona- and decamer water clusters exhibit characteristic spectral bands around 3050–3150, 3550–3620 and 3720 cm−1, and a large absorption gap exists from around 3200 to 3500 cm−1. For the water octamer, the 3720 cm−1 spectral feature is assigned to free OH-stretching modes in water molecules at cube vertices, while broader features at 3050–3150 and 3550–3620 cm−1 are attributable to symmetric and asymmetric OH stretching modes of hydrogen-bonded water molecules, respectively; note, these are red-shifted by several hundred wavenumbers, relative to gas phase water. A comparison of experimentally measured OH vibrational spectra with reported ab inito results (Maeda and Ohno 2007) indicates that interactions in larger water clusters require dispersion sensitive ab initio theory, such as MP2, DFT-Dn or M0X-2X functionals, in order to accurately reproduce the OH-stretching frequencies for (H2O)8–10 and in larger water clusters. Large water clusters, n > 10. Although a detailed discussion of larger (n > 10) water cluster structures and energies is beyond the scope of this review, we provide an introductory overview of some of the key molecular features of larger water clusters with more than 10 water molecules. This is meaningful given the central role that size and structure have on physicochemical properties (i.e. melting, boiling/condensation and critical points) of water clusters and nanodroplets (Johnston and Molinero 2012). More recently, water clusters and nanodroplets have received growing interest from atmospheric chemists due to cluster surface–interior transfer processes of water molecules (Jungwirth and Tobias 2006; Buch et al. 2007). These structural transitions from an all-surface configuration where all water molecules reside at the cluster surface, to an interior configuration, where at least one fully solvated H2O molecule exists inside a water cluster, play an important role in ion transfer processes between the cluster surface and interior. This structural transition, from all-surface to interior, is reported to occur at n = 17 for water clusters, and has been predicted using CCSD(T)/aug-cc-pVTZ single point energies with MP2/aug-cc-pVTZ zero-point energy corrections (Yoo et al. 2010). A preliminary conclusion from these studies is that even high-level MP2 calculations are of insufficient accuracy to predict the energetic ordering among water clusters, such as (H2O)16 and (H2O)17, and instead, require costly CCSD(T) computations with triple-zeta size basis sets in order to successfully explore the potental energy surface (PES) of each cluster. This problem is further complicated due to the high number of isomeric forms that exist for (H2O)16 and (H2O)17; for example, both clusters have 500 distinct minima structures on the TIP4P PES, spanning an energy range of less than 20 kcal/mol. As noted in Yoo et al. (2010), the main theoretical problem lies in determining accurate energetic rankings for water clusters, and this task has proven to be extremely difficult due to the structural complexity and the exponentially increasing number of isomers that exist for larger water clusters. VRT- and IRPD-based spectroscopic methods have helped to identity water clusters up to the decamer, however, there are to the best of our knowledge, no experimental results available for (H2O)n with n > 10, with the exception of one study that reported IRMPD spectra for methanol-doped water clusters (H2O)n(CH3OH) with n = 15–20 (Huisken et al. 1998). As a consequence, structural and energetic information for larger clusters are usually obtained using a combination of global optimization techniques and density functional methods.  

Over the past decade, several new and promising approaches have been developed for resolving likely global minima water clusters structures. One such approach is the basin hopping/Monte Carlo minimization technique developed by Wales and coworkers (Wales and Hodges 1998; Wales and Scheraga 1999) in which the potential energy surface of water cluster are systematically explored using a Monte Carlo minimization approach in combination with pair potential functions. (e.g. for the TIP4P, TIP5P liquid water models, Mahoney and Jorgensen 2000). Alternative approaches to this problem include particle swarm optimization techniques (Lv et al. 2014), artificial bee colony (Zhang and Dolg 2016) and genetic algorithms (Guimarães et al. 2002), all of which have proven to provide valuable

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insight into the nature of the potential energy surface of molecular clusters, and in a particular water cluster. Global minima structures of water clusters with up to 24 water molecules, which have been determined using an artificial bee colony algorithms in conjunction with the TIP4P water model as part of this review, are shown in Figure 5. These optimization techniques, together with suitable DFT and MP2 computations, are among the most useful tools for water cluster structure determinations where spectroscopic data are not available, and, in particular, for large clusters with small energy differences among low-lying isomers. However, due to the mode of interaction and large number of isomers, computations of structures and energetic properties of larger water clusters is still a formidable task. For example, until recently, the nature of interactions and the complexity of the potential energy landscape led to the use of less accurate methods (B3LYP, PBE and BP86). This problem has in part been addressed following the introduction of new Minnesota DFT methods capable of modeling weak interaction in larger clusters, such M05–2X, M06–2X (Zhao et al. 2006) and the Grimme dispersion-sensitive functionals mPW2PLYP-D (Grimme 2006a), B2PLYP-D (Grimme 2006b) and B2PLYP-D3 (Grimme et al. 2011). Although these functionals can provide useful structural information and energetic trends, they very often fail to deliver reliable IR spectroscopic and thermodynamic properties because the intermolecular part of the PES in water clusters is typically anharmonic and cannot be accurately modeled with unique frequency scaling factors (Temelso and Shields 2011). The steady improvement in both HPC performance and implementation of faster ab inito methods, however, now permits structures and spectroscopic characterization of weakly bound water cluster systems, enabling global minima prediction for clusters with 20 water molecules with sub-kcal/mol accuracy (Yoo et al. 2010); this is achieved by using MP2 or coupled cluster theory CCSD(T). Correlation-based methods in conjunction with Dunning-style basis sets are the gold standard for water cluster simulations, and are capable of predicting individual vibrational modes (interand intramolecular) in small water clusters to within several wavenumbers (Howard et al. 2014). This approach however, becomes impractical for clusters with a large number of nearly

Figure 5. Equilibrium structures of water clusters (H2O)n with n = 10–24 obtained from swarm optimization and M06–2X/aVDZ density functional calculations; note, 16-s is the largest all-surface species. i.e. all H2O molecules reside on the cluster surface, and converts upon addition of H2O, to an internally solvated cluster 17-I with interior water.

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isoenergetic isomers because CCSD(T) calculations scale as N 7 with electron number and are prohibitively expensive relative to B97D, B2PLYP or even MP2 (both functionals employ MP2-like correlation that scale as N 5). For selected clusters, it is often possible to identify the global minimum configuration by comparing experimentally determined properties such as optical absorption, PES or IR vibrational spectra with those determined theoretically. For example, global minima structures of larger water clusters (H2O)n with n = 15–20 are identified by comparing characteristic features of IR-predissociation spectra of methanol-doped water clusters (H2O)n(CH3OH) with MP2 IR spectroscopic simulations of water clusters in which the hydrogen-bonded methanol molecule at the cluster surface is replaced with a structurally equivalent water molecule (Buck and Huisken 2000; Jungwirth and Tobias 2006)

SOLVATION IN WATER VAPOR (SOLVATION IN AND ON NEUTRAL WATER CLUSTERS) The hydrated proton and hydroxide ions Magmatic and volcanic gases as well as steam produced by boiling in hydrothermal systems are low density aqueous media in which both ionic and molecular species are solvated (“dissolved”) by water clusters, thus facilitating transport of volatile components such as SO2, H2S, CO2, NH3, N2, NaCl as well as ionic species such as H3O+. Metal complexes are also stable in these low-density aqueous solutions which play a role in metal transport and deposition (ore deposits) in the Earth’s crust. Hydronium ion (H3O+) hydration by water clusters in steam and low density supercritical water vapor “determines” the pH of such low density aqueous media at elevated temperatures, which in turn, affects the reactivity of water vapor, with particular reference to gas–solid interaction in the Earth’s crust. The last decade has seen a sharp increase in the study of large water clusters with up to 1000 H2O molecules and 1–3 nanometer size ranges (Devlin et al. 2000. Buch et al. 2004). The drive to study these cluster systems stems from a desire to understand the composition and structure of cluster, droplet (and bubble) surfaces (Vácha et al. 2007, Buch et al. 2007) and the role such surfaces can play in vapor-liquid isotope exchange reactions, seawater spray and aerosol chemistry, and molecular speciation during bubble formation (boiling) and droplet nucleation in vapor. Studies of water clusters have also become relevant in the context of interpreting results of water droplet zeta-potential measurement and droplet titration experiments, as these indicate a propensity of some ions to concentrate at water cluster surfaces (Buch et al. 2007). For instance, a number of recent reports have demonstrated enhanced autoionization of water molecules at solution-gas interfaces resulting in acidic (pH  55. The second important feature observed for the proton–hydroxide water clusters is the propensity for both ions to partition to the water cluster surface, which clearly differs from proton and hydroxide surface

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solvation processes that take place at air/liquid water interfaces (Jungwirth and Tobias 2006). For the air/liquid water interface, there is clear evidence, both from experiment and from ab initio calculations (Jungwirth and Tobias 2006, and references therein), that the hydronium ion prefers surface solvation, whereas hydroxide ions reside in the solution interior and exhibit a near-surface propensity at most (Vacha et al. 2007). Extending our current DFT simulation results to the aqueous vapor environment, we may therefore expect that water cluster (droplet) ionization reactions exhibit pronounced cluster-size dependencies leading to a characteristic size distribution of proton–hydroxide water clusters reflective of temperature and water monomer pressure. These theoretical results also indicate that for a given cluster-size, the proton and hydroxide ions will surface-solvate either as contact ion pairs (n = 20–55) or as solvent-separated ion pairs (n > 70), posing interesting questions about charge separation and surface versus interior solvation motifs in larger water clusters upon ionization.

SODIUM CHLORIDE IN STEAM/LOW DENSITY WATER VAPOR Of particular interest in high-temperature, low-density aqueous systems (i.e. in steam and supercritical aqueous fluids having gas-like densities) is the well-known solubility of many inorganic compounds (Palmer et al. 2004) in such media. In natural volcanic gas and magmatic volatile systems, NaCl and other halogen compounds (e.g. HF, HCl, NH4Cl, HBr) are ubiquitous and NaCl and HCl in particular, play an important role solid–gas reactions in low-pressure magmatic and volcanic gas environments. The vapor pressure of crystalline NaCl (melting point 800.7 °C; boiling point 1465 °C: CRC Handbook 2013) in the absence of water is low, varying from 4.9 × 10–8 bar at 500 °C but then rising to 3.8 × 10–4 bar at 790 °C, just below the NaCl melting point (Zimm and Mayer 1944; Ewing and Stern 1974; Dortmund Data Bank 2018). However, the concentration of NaCl is many orders of magnitude higher in steam or low density, supercritical water than in a “dry” system without water as demonstrated by various experimental studies (Martynova 1964; Styrikovich et al. 1966; Galobardes et al. 1981; Armellini and Tester 1993) and further summarized by Palmer et al. (2004). These earlier studies were motivated by a need to understand NaCl volatility/solubility in steam and salt transport in steam and related corrosion problems in power generation systems. The solubility of NaCl in water vapor is a function of the density of the “steam” phase, temperature and pressure but reliable solubility data are sparse at low steam densities and the molecular details are not well known. However, some insight is provided by a number of computational studies (e.g. Pitzer 1983; Fernandez-Prini 1998; Suleimenov et al. 2006). It is well known that sodium and chloride ions are extensively ion paired in aqueous (liquid) electrolyte solutions at elevated temperatures up to 600 °C and moderate pressures up to 1000 bar (Quist and Marshall 1968). It has also generally been accepted that NaCl ion pairing defines molecular speciation in steam as well. In their thermodynamic study of NaCl in steam, Pitzer and Pabalan (1986) considered that NaCl–water clusters (their successive hydration model) were responsible for the observed solubilities. More recently, Suleimenov et al. (2006) employed CBS-QB3 level theory (Montgomery et al. 1999) to obtain gas-phase Gibbs energies (for optimized cluster geometries) of various NaCl–H2O clusters as a function of temperature and pressure which together with thermodynamic data for halite and water, permitted the calculation of NaCl solubility in steam. Other ab initio studies pertaining NaCl–water clusters as well as metal complex–water clusters such as AgCl(H2O)n (e.g. Godinho et al. 2006) have been carried out but are not relevant to high temperature water vapor. Figure 12 shows the solubility of NaCl in water vapor at 450 °C as a function of pressure (or density). With increasing pressure or water vapor density, higher order clusters (i.e. NaCl(H2O)6 and NaCl(H2O)8) predominate and account for NaCl solubility in steam at 450 °C at pressures greater than 100 bar. At pressures  500 °C (Likholyot et al. 2005). In addition, Pitzer (1983) has demonstrated (using mass spectrometrically derived thermodynamic data for Na+ and Cl− hydration together with NaCl solubility in steam and a general Born model approach) that there is an increase in ionic species in low density (e.g. 0.01–0.10 g/cm3) steam containing NaCl with increasing temperature from 400 to 800 °C, although NaCl ion pairs still comprise a significant portion of the total dissolved salt. Our dilemma then, is that there are few experimental or theoretical studies of simple 1:1 and 2:1 salts in water solvent having gas-like density at high temperatures pertinent to magmatic and volcanic gas systems or to steam in lower temperature hydrothermal/geothermal systems and from which we can gain molecular insight into gas–solid equilibria and reactivity at these extreme conditions.

SOLVATION OF METALS IN WATER VAPOR A major problem in gas-phase metal transport is the difficulty of assessing how metals and metal complexes bond to water clusters, and consequently the large uncertainty as to their abundance in water vapor. A brief review of the existing experimental data reported for gas phase metals shows that metals such as copper and gold are extremely partitioned into the vapor-phase upon boiling, however, there are only limited data available on the concentrations and structures of metal water clusters in different water vapor environments. Indeed, an understanding of the stability of metal-water clusters under typical hydrothermal conditions may provide a new perspective on metal ore formation from low-density aqueous fluids. Experimental studies of

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hydrated metal clusters using electrospray ionization mass spectrometry and high temperature studies of metal halide complexes in water vapor, have established a conceptual bridge between metal ion cluster observed in high vacuum environments and the occurrence of a metal-charged vapors in nature (Schröder 2012). Subsequent experimental studies of solvated metal species have shown that the formation and stability of, for instance, gaseous gold (Mei et al. 2017) and copper complexes (Mei et al. 2018) is directly related to the size and structure of the solvation shell surrounding the metal core. One important conclusion from above mentioned studies is that a wide range of hydrated metal-water clusters would exist in the vapor phase at any given temperature and pressure, probably with one dominant global minimum configuration and a large number of coexisting local minima (for instance, the octa-hydrated gold cation has around 10 distinct minimum structures within a 1 kcal/mol energy range). There is a general consensus, from experimental and ab initio studies, that the gold(I) ion binds water with two H2O molecules attached directly to the metal center. However, there is less of a consensus on the minimum energy structures adopted by Au(I) and chloride complexed Au(I) in larger water clusters or even nano-sized water droplets. The following section of this review will therefore give an account of the current understanding of gold solvation in water clusters, without a ligand and in the presence of a halide ion such as Cl−. Gold in water vapor and the cluster solvation of Au+. Several laboratories have reported mass spectrometric and vibrational spectra of charged gold–water clusters in an attempt to characterize the water network surrounding the gold atom. For instance, for the Au(I)–water system, Li et al. (2012) reported results from IRMPD spectroscopic studies of mass-selected Au+(H2O)n clusters with n = 1–8, showing that Au+ retains two water molecules into its primary solvation shell forming a linear O–Au+–O configuration. Subsequent water molecules attach to the H2O–Au+–OH2 core forming the second solvation shell, which is complete at n = 6. The structure of the Au+(H2O)n cluster system was also described in detail using ab initio molecular dynamics simulations (Camellone and Marx 2012), MP2 and CCSD(T) level of theory calculations with up to six water molecules (Lee et al. 2005a,b) and DFT calculations at the PBE99 level of theory for larger Au+(H2O)n clusters with up to 10 water molecules (Reveles et al. 2007). Interestingly, results from the above simulations and those obtained from mass spectrometric studies of Au+(H2O)n (Magnera et al. 1989; Poisson et al. 2002) indicate that the second water solvation energy is larger (by around 5–6 kcal/mol) than the first solvation energy, a feature rooted in electronic and hybridization effects in Au+–water clusters. In brief, the first two water molecules bind strongly to Au+ at around ~40 and 45 kcal/mol, followed by a decrease in the binding energy from 23 to 16 kcal/mol for solvation by 3–6 H2O molecules, and remain constant at condensation level values of ~10 kcal/mol for n = 7–10; the role of charge transfer in Au+(H2O)n clusters has been examined in detail by Lee et al. (2005), who described various contributions from 6s- and 5d-orbital hybridizations to the overall stability of mono-cationic Au+(H2O). It is also noteworthy to briefly comment on how the water solvation shell contributes to the overall structure and stability of polynuclear gold clusters. A brief review of recent mass spectrometric and molecular simulation results for [Aum]+(H2O)n is given below. One interesting aspect of water solvated poly nuclear gold clusters is a potential connection between the stability of a polynuclear gold cluster and the emergence of nanosized gold particles in water vapor, as well as the influence of water desorption processes, at higher temperatures, on the onset of gold nucleation and precipitation in the gas-phase. For instance, gas phase microsolvated gold clusters would likely undergo a two-step water desorption process in which more loosely bound 2nd shell water molecules are released from the solvated core, followed by desolvation of more strongly bound water molecules that are in direct contact with Au atoms. For example, structures and water desorption energetics in [Aum]+(H2O)n have been probed using TOF mass spectrometry and complimented with DFT and MP2 calculations (Nagata et al. 2017). Thermal effects were examined by observing changes in TOF mass spectra in the temperature range 300–1000 K, including shifts in the intensity and

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distribution of hydrated gold cluster. In brief, these results showed that [Aum] +(H2O)nclusters incrementally release water molecules upon heating with characteristic intensity distributions (m/z m × 197 + n × 18 a.u.). For example, for pentanuclear [Au5]+(H2O)n, desolvation is complete at 600 K, whereas smaller hydrates of [Au5]+(H2O)n exhibit characteristic intensity maxima at 350 K (n = 4), 420 K (n = 3), 480 K (n = 2) and 540 K (n =1). In other words, smaller solvation shells remain stable at elevated temperature and conversely, lower temperatures favor larger solvation environments. Interestingly, water dissociation energies for [Au2]+(H2O) n incrementally increase with decreasing water shell cluster size (n = 4–1), whereas water binding energies in the mono-solvated clusters [Aum]+(H2O) decrease with increasing gold cluster size (m = 2–8). In the case of octa-nuclear gold, water binding energies shift form 14 kcal/mol (n = 1), 9 kcal/mol (n = 2), 8 kcal/mol (n = 3) to 6 kcal/mol (n = 4), and these sizedependent trends in water binding energies can be directly traced to the size of [Aum]+ core, and shifts in charge density of the ion core; a related study also reported MP2 and DFT level water binding energies for tri-nuclear [Au3]+(H2O), (13.4 kcal/mol) Ag-doped [Ag2Au]+(H2O) (10.8 kcal/mol) and [Ag3]+(H2O) (11.3 kcal/mol) (Fleischer et al. 2013). From the above experimental and theoretical studies, it evolves that poly nuclear gold clusters, such as [Au5]+(H2O)n and larger [Aum]+(H2O)n species exist over a wide temperature range much like pure water clusters. Important yet unexplored aspects of poly nuclear Au cluster are whether the higher water partial pressures (and those of other volatiles) in natural hydrothermal systems would give rise to an expanded solvation shell, contributing towards a fully dissolved gas-phase gold cluster, and more importantly, how gold cluster abundances would balance, in response to changes in temperature and the significantly higher water vapor pressures in gas-like ore fluids compared against typical UHV conditions used in mass spectrometric studies. A final point of interest related to the transport of Au in low-density ore fluids, is the propensity of Au+ ions, Au complexes and larger gold clusters to partition to water cluster (and nanodroplet) surfaces and/or interiors. In fact, the propensity of metals to surface-solvate or reside in the interior of a water cluster or droplet would have important consequences for metal complexation/clustering processes and the fractionation of isotopes given the fundamentally different thermodynamic properties of surface and bulk hydrated metal species. These themes have been discussed in detail for smaller ions, with reference to IR spectroscopy and quantum chemical calculations and it is now well known that the hydrated proton resides at the vapor/solution interface, giving rise to an acidic cluster surface, whereas the hydroxide ion partitions into the cluster interior resulting in an alkaline nearsurface layer and a neutral pH in the deeper bulk region (Jungwirth and Tobias 2006). The surface, near-surface or bulk propensity of metal ions, complexes or clusters in water clusters and droplets remains unresolved at present, however this issue can be addressed in future using IR spectroscopy, mass spectrometry and a combination of molecular simulation tools. Solvation of the AuCl complex in water vapor. Following our discussion on the structure and energetic properties of solvated gold ions and clusters, it is meaningful to provide a brief review of the gas-phase stability of halide-complexed gold species, particularly because, halide ions represent a core class of ligands that bind strongly to gold ions and occur ubiquitously in ore vapor environments. Complexation of gold with halide ions, but also other ligands, such as H2S/HS−, is a central topic in hydrothermal geochemistry, and its consequences for the mobility of Au have been discussed in detail, both for the bulk solution environment, and for ore vapors (Stefansson and Seward 2003; Seward et al. 2014; Hurtig and Williams-Jones 2014, Lemke 2014b). However, unlike for the ligand-free case, Au complexation with halide ions gives rise to a fundamentally different solvation environment around the halogen (in part due to weak X−–H interactions) and also induces a restructuring of the solvation shell near the gold atom. The solvation of AuCl in water vapor is an important topic for geochemists, however, there are still knowledge gaps regarding the speciation of mono- and poly nuclear gold in small water clusters and even more so for more complex mixed solvent systems.

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The AuCl complex is a geochemically important species with an affinity to partition into aqueous vapors (Archibald et al. 2001; Hurtig and Williams-Jones 2014), however, these thermodynamic studies provide no direct insight into the solvation shell structure and stability of AuCl(H2O)n in water vapor. There are to our knowledge no theoretical or experimental data in the literature for the structure and vapor phase stability of microsolvated AuCl(H2O)n, either as a function solvation shell size or temperature. From ab initio calculations, we now know that the global minimum structure of AuCl(H2O)n is a near-linear complex, with the chloride ion and water molecule occupying terminal positions; for smaller solvation numbers (n), water molecules attach onto the water terminus given the higher water–water binding energy versus the reduced binding energy of the chloride water cluster system. As noted in the work of Reveles et al. (2007), the primary solvation shell of monovalent gold typically contains two water molecules. We have expanded on this work, and list results from a set of preliminary DFT computations at the M06/aVDZ level of theory for AuCl(H2O)n clusters with primary and secondary solvation shells, and provide detail of the structures, i.e. global minima configurations, as well as trends for the incremental binding energies; Figures 13 and 14 show the global and local minima of AuCl(H2O)n with up to 10 water molecules, and a van’t Hoff plot for the stepwise solvation of AuCl with up to 9 water molecules; corresponding water binding enthalpies, free energies and equilibrium constants for solvated AuCl at 298 K and elevated temperatures are listed in Table 2. As seen in Figure 13, AuCl with an expanded water solvation shell (n = 5–10) prefers exterior solvation on a water cluster surface, similarly as in the case of the larger halides (Likholyot et al. 2005). This surface solvation feature is highlighted in Figure 13, which shows the mono-solvated complex AuCl(H2O) bound onto a water tetramer ring for n = 5, a book-like water hexamer for n = 7 and in the case of AuCl(H2O)10, the AuCl(H2O) complex occupies the edge-sites of a stacked water decamer. Table 2 also shows that the entropic contribution to the solvation free energy is approximately constant at condensation entropy values for n = 2–9 (or equivalent to a ~9–11 kcal/mol TΔS contribution at 298 K). We have also carried out supplementary calculations to determine the relative strengths of interactions between AuCl, H2O, NH3 and H2S, in other words, the affinity of these volatiles to bind to Au and their capacity to form an interconnected network around the AuCl core. For example, we found that the CCSD(T)/aVDZ binding energies in AuCl(H2O), AuCl(H2S) and AuCl(NH3) shift from −25.1, −40.3 to −48.9 kcal/mol, indicating a strong affinity of AuCl for solvation with

Figure 13. M06/aVDZ equilibrium geometries for AuCl(H2O)1–10 with Au–Cl distances given below each cluster; global minima obtained from swarm-based structure searches using TIP4P water Au–Cl force field parameters.

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Figure 14. Van’t Hoff plot for the incremental solvation of AuCl with first water listed as 0,1; attachment of additional H2O molecules up to solvation step 8,9 shown as colored lines; the slope of the linear fits provide values of –ΔH which yield enthalpies for each successive solvation of AuCl(H2O)n with n = 0–9.

Table 2. Incremental solvation energies of AuCl at the M06/aVDZ level of theory at 298 and 500 K at 1 bar, where the units for ΔEe are in kcal/mol; ΔG, ΔH are kcal/mol and for ΔS, cal/mol/K. n, n + 1

ΔEe

0,1 1,2 2,3

ΔH298 K

ΔS298 K

ΔG298 K

ln K298 K

ΔG500 K

−24.5

−23.1

−29.9

−11.9

−10.3

−26.1

−14.2

23.9

−8.1

8.2

−2.5

4.3

2.8

−2.8

−14.3

−12.8

−32.7

−3.1

5.2

3.6

−3.6

ln K500 K

3,4

−11.2

−9.7

−32.3

−0.1

0.1

6.5

−6.5

4,5

−11.7

−9.9

−36.2

0.9

−1.5

8.2

−8.2

5,6

−8.0

−6.6

−33.2

3.3

−5.6

10.0

−10.1

6,7

−14.4

−12.3

−36.1

−1.5

2.6

5.7

−5.8

7,8

−13.1

−11.2

−34.2

−1.0

1.7

5.9

−5.9

8,9

−8.9

−7.5

−34.8

2.9

−4.9

9.9

−10.0

the ammonia molecule; interestingly, the AuCl(NH3) binding energy is nearly double that of AuCl(H2O), and therefore solvation of AuCl is significantly more favorable than the formation of the corresponding hydrogen sulphide or even H2O-bearing complex, with the only caveat that hydrogen-bond NH3 networks are less stable than those formed by water. Finally, a wide range of hybridization and electronic effects will influence the magnitude and trends in the sequential solvation energies of AuCl, and these concepts will be of importance in understanding the solvation behavior of polynuclear gold chloride cluster in water vapor both with and without NH3 and H2S.

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EPILOGUE In this chapter, we have presented new data on the molecular structure of steam and water vapor and discussed various aspects of evolving cluster geometry and size as a function of temperature. We have then considered proton solvation in water vapor and shown that the hydronium ion occupies a surface coordinated position on water clusters which leads to an “acidic” nano-layer overlying a given molecular water cluster. New data on the ion-product constant of water vapor as a function of cluster size and temperature are also presented and this further encourages consideration of the molecular framework with which to consider the pH of water vapor at high temperatures. We note, for example, the values (Table 1) of pKw(500 K) ranging from 3.2 to 6.0 for water cluster sizes (n = 10–45) in comparison to the liquid water value of pKw(500 K) = 11.2. The solvation of solute species in/on water clusters has also been considered by investigating the solvation of reduced sulfur (H2S and HS−) and a transition metal ion and complex (Au+ and AuCl). H2S was shown to prefer a surface hydration environment on water clusters resulting in a nano-scale phase separation comprising the water cluster core and an H2S surface. Similarly, the simple AuCl complex is surface solvated on water clusters in water vapor. These and other observations discussed in our chapter emphasize the labile nature of high temperature water vapor with cluster surface enhanced availability of solute species, including charged species (e.g. protons). The much diminished pKw of low density water solvent at high temperatures as well as the surface enhanced acidity of gas phase water clusters will also have fundamental implications for hydrolytic reactions and metal complex stability in water vapor. Of particular interest as well is the solvation of SO2 by molecular water clusters in water vapor under conditions relevant to gas–solid (e.g. SO2–feldspar) sulfidation reactions in high temperature porphyry and skarn deposits which give rise to ubiquitous anhydrite and the precipitation of sulfide minerals (Henley et al. 2017). Over the past decade, there has been an accelerated progress in the field of gas phase physical chemistry, and in particular, researchers have made considerable advances in the field of cluster mass spectrometry and infrared spectroscopy. These advances have also been catalyzed by faster and more accurate ab initio tools and an improved capability to now study clusters one molecule at a time up to nanometer size ranges. Nevertheless, the study of neutral and ionic clusters in low-density water solvent under conditions relevant to the Earth’s crust still remains a largely unexplored field of research.

ACKNOWLEDGMENTS This work was supported by HK General Research Fund No. HKU 17302714. Computing time for this study was provided to K.H.L. by the HKU High Performance Computing (HPC) and Grid Computing Center.

REFERENCES Archibald SM, Migdisov AA, Williams-Jones AE (2001) The stability of Au-chloride complexes in water vapor at elevated temperatures and pressures. Geochim Cosmochim Acta 65:4413–4423 Armellini FJ, Tester JW (1993) Solubility of sodium chloride and sulfate in sub- and supercritical water vapor from 450–550°. Fluid Phase Equil 84:123–142 Ayotte P, Bailey CG, Weddle GH Johnson MA (1998) Vibrational spectroscopy of small Br−(H2O)n and I−(H2O)n clusters: infrared characterization of the ionic hydrogen bond. J Phys Chem A 102:3067–3071 Barone V (2004) Vibrational zero-point energies and thermodynamic functions beyond the harmonic approximation. J Chem Phys 120:3059–3065 Braly LB, Liu K, Brown MG, Keutsch RS, Fellers RS, Saykally RJ (2000a) Terahertz laser spectroscopy of the water dimer intermolecular vibrations. II (H2O)2 J Chem Phys 112:10314–10326

80

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Braly LB, Cruzan JD, Liu K, Fellers RS, Saykally RJ (2000b) Terahertz laser spectroscopy of the water dimer intermolecular vibrations. I (D2O)2 J Chem Phys 112:10293–102313 Buch V, Sigurd B, Devlin JP, Buck U, Kazimirski JK (2004) Solid water clusters in the size range of tens–thousands of H2O: a combined computational/spectroscopic outlook. Int Rev Phys Chem 23:375–433 Buch V, Milet A, Vácha R, Jungwirth P, Devlin JP (2007) Water surface is acidic. Proc Nat Acad Sci 104:7342–7347 Buck U, Huisken F (2000) Infrared spectroscopy of size-selected water and methanol clusters. Chem Rev 100:3863–3890 Buck U, Ettischer I, Melzer M, Buch V, Sadlej J (1998) Structure and spectra of three-dimensional (H2O)n clusters, n = 8, 9, 10. Phys Rev Lett 80:2578 Buck U, Huisken F (2000) Infrared spectroscopy of size-selected water and methanol clusters. Chem Rev 100:3863–3890 Camellone MF, Marx D (2012) Solvation of Au+ versus Au0 in aqueous solution: electronic structure governs solvation shell patterns. Phys Chem Chem Phys 14:937–944 Casey WH, Rustad JR (2007) Reaction dynamics, molecular clusters, and aqueous geochemistry. Ann Rev Earth Planet Sci 35:21–46 Casey WH, Swaddle TW (2003) Why small? The use of small inorganic clusters to understand mineral surface and dissolution reactions in geochemistry. Rev Geophys 41:1008 Chang HC, Wu CC, Kuo JL (2005) Recent advances in understanding the structures of medium-sized protonated water clusters. Int Rev Phy Chem 24:553–78 CRC Handbook of Chemistry and Physics (2013) (WM Haynes, editor), 94th Edition. CRC Press LLC, Boca Raton FL, USA, 4–89 Dortmund Data Bank (DDBST GmbH) (2018)(www.ddbst.com/en/EED/PCP/VAP/ C4911.php) Cruzan JD, Braly LB, Liu K, Brown MG, Loeser JG, Saykally RJ (1996) Quantifying hydrogen bond cooperativity in water: VRT spectroscopy of the water tetramer. Science 271:59–62 Curtiss LA, Blander M (1988) Thermodynamic properties of gas-phase hydrogen-bonded complexes. Chem Rev 88:827–841 Curtiss LA, Frurip DJ, Blander M (1979) Studies of molecular association in H2O and D2O vapors by measurement of thermal conductivity. J Chem Phys 71:2703–2711 Devlin JP, Joyce C, Buch V (2000) Infrared spectra and structures of large water clusters. J Phys Chem A 104:1974–1977 Do H, Besley NA (2012) Structural optimization of molecular clusters with density functional theory combined with basin hopping. J Chem Phys 137:134106 Douberly GE, Walters RS, Cui J, Jordan KD, Duncan MA (2010) Infrared spectroscopy of small protonated water clusters H+(H2O)n (n = 2–5): isomers, argon tagging, and deuteration. J Phys Chem A 114:4570–4579 Ewing CT Stern KH (1974) Equilibrium vaporization rates and vapor pressures of solid and liquid sodium chloride, potassium chloride, potassium bromide, cesium iodide and lithium fluoride. J Phys Chem 78:1998–2005 Fernandez-Prini R (1998) Ionic aggregates in steam. 2. Standard chemical potentials. J Phys Chem 102;257–262 Feyereisen MW, Feller D, Dixon DA (1996) Hydrogen bond energy of the water dimer. J Phy Chem 100:2993–2997 Fleischer I, Popolan DM, Krstić M, Bonačić-Koutecký V and Bernhardt TM (2013) Composition dependent selectivity in the coadsorption of H2O and CO on pure and binary silver–gold clusters. Chem Phys Lett 565:74–79 Galobardes JF, van Hare DR Rogers LB (1981) Solubility of sodium chloride in dry steam. J Chem Eng Data 26:363–366 Godinho SSMC, Cabral do Couto P, Costa Cabral BJ (2006) Photochemistry of AgCl–water clusters: Comparison with Cl−–water clusters. Chem Phys Lett 419:340–345 Gregory JK, Clary DC, Liu K, Brown MG, Saykally RJ (1997) The water dipole moment in water clusters. Science 275:814–817 Grimme S (2006a) Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J Comp Chem 27:1787–1799 Grimme S (2006b) Semiempirical hybrid density functional with perturbative second-order correlation. J Chem Phys 124:034108 Grimme S, Ehrlich S, Goerigk L (2011) Effect of the damping function in dispersion corrected density functional theory. J Comp Chem 32:1456–1465 Guimarães FF, Belchior JC, Johnston RL, Roberts C (2002) Global optimization analysis of water clusters (H2O)n (11 ⩽ n ⩽ 13) through a genetic evolutionary approach. J Chem Phys 116:8327–8333 Guo X, Duursma M, Al-Khalili A, McDonnell LA, Heeren RM (2004) Design and performance of a new FT-ICR cell operating at a temperature range of 77–438 K Int J Mass Spectr 231:37–45 Headrick JM, Diken EG, Walters RS, Hammer NI, Christie RA, Cui J, Myshakin EM, Duncan MA, Johnson MA, Jordan KD (2005) Spectral signatures of hydrated proton vibrations in water clusters. Science 308:1765–1769 Henley RW, Seward TM (2018) Gas–solid reactions in arc volcanoes: Ancient and modern. Rev Mineral Geochem 84:309–349 Henley RW, Brink FJ, King PL, Leys C, Ganguly J, Mernagh T, Middleton J, Renggli CJ, Sieber M, Troitzsch U, Turner M (2017) High temperature gas–solid reactions in calc-silicate Cu-Au skarn formation; Ertsberg, Papua Province, Indonesia. Contrib Mineral Petrol 7211–7212 Hodges MP, Wales DJ (2000) Global minima of protonated water clusters. Chem Phys Lett 324:279–288 Holzapfel WB (1969) Effect of pressure and temperature on the conductivity and ionic dissociation of water up to 100 kbar and 1000 oC J Chem Phys 50:4424–4428

Molecular Clusters & Solvation in Volcanic & Hydrothermal Vapors

81

Howard C, Gray JL, Hardwick AJ, Nguyen LT, Tschumper GS (2014) Getting down to the fundamentals of hydrogen bonding: anharmonic vibrational frequencies of (HF)2 and (H2O)2 from ab initio electronic structure computations. J Chem Theory Comp 10:5426–5435 Huisken F, Kaloudis M, Kulcke A (1996) Infrared spectroscopy of small size-selected water clusters. J Chem Phys 104:17–25 Huisken F, Mohammad-Pooran S, Werhahn O (1998) Vibrational spectroscopy of single methanol molecules attached to liquid water clusters. Chem Phys 239:11–22 Hurtig NC, Williams-Jones AE (2014) An experimental study of the transport of gold through hydration of AuCl in aqueous vapour and vapour-like fluids. Geochim Cosmochim Acta 127:305–325 Johnston JC, Molinero V (2012) Crystallization, melting, and structure of water nanoparticles at atmospherically relevant temperatures. J Am Chem Soc 134:6650–6659 Jungwirth P, Tobias DJ (2002) Ions at the air/water interface. J Phys Chem B 106:6361–6373 Jungwirth P, Tobias DJ (2006) Specific ion effects at the air/water interface. Chem Rev 106:1259–1281 Kebarle P (1977) Ion thermochemistry and solvation from gas phase ion equilibria. Ann Rev Phys Chem 28:445–476 Keutsch FN, Saykally RJ (2001) Water clusters: untangling the mysteries of the liquid, one molecule at a time. Proc Nat Acad Sci 98:10533–10540 Klots CE (1984) The pH of steam. J Phys Chem 88:4407–4410 Kozack RE Jordan PC (1993) Structure of H+(H2O)n clusters near the magic number n = 21. J Chem Phys 99:2978–2984 Lau YK, Ikuta S, Kebarle P (1982) Thermodynamics and kinetics of the gas-phase reactions—H3O+(H2O)n−1 + H2O = H3O+(H2O)n. J Am Chem Soc 104:1462–1469 Lemke KH (2014a) Structures and thermodynamic properties of (C2H6)n (n = 2–8) by M06–2X and DFT-D theory: Implications for Titan’s atmospheric chemistry. Chem Phys Lett 601:194–199 Lemke KH (2014b) Gold chloride clusters with Au (III) and Au (I) probed by FT-ICR mass spectrometry and MP2 theory. Phys Chem Chem Phys 16:7813–7822 Lemke KH (2017) Structure and binding energy of the H2S dimer at the CCSD (T) complete basis set limit. J Chem Phys 146:234301 Lemke KH, Seward TM (2008a) Ab initio investigation of the structure, stability, and atmospheric distribution of molecular clusters containing H2O, CO2, and N2O. J Geophys Res Atmos16:113 Lemke KH, Seward TM (2008b) Solvation processes in steam: Ab initio calculations of ion–solvent structures and clustering equilibria. Geochim Cosmochim Acta 72:3293–3310 Lemke KH, Seward TM (2013) Thermodynamic properties of carbon dioxide clusters by M06–2X and dispersioncorrected B2PLYP-D theory. Chem Phys Lett 573:19–23 Lee HM, Kim KS (2001) Structures and spectra of iodide–water clusters I−(H2O)n=1–6: An ab initio study. J Chem Phys 114:4461–4471 Lee HM, Kim D, Kim KS (2002) Structures, spectra, and electronic properties of halide-water pentamers and hexamers, X−(H2O)5,6 (X= F, Cl, Br, I): Ab initio study. J Chem Phys 116:5509–5520 Lee HM, Diefenbach M, Suh SB, Tarakeshwar P, Kim KS (2005a) Why the hydration energy of Au+ is larger for the second water molecule than the first one: Skewed orbitals overlap. J Chem Phys 123:074328 Lee HM, Min SK, Lee EC, Min JH, Odde S, Kim KS (2005b) Hydrated copper and gold monovalent cations: Ab initio study. J Chem Phys 122:064314 Likholyot A, Hovey JK, Seward TM (2005) Experimental and theoretical study of hydration of halide ions. Geochim Cosmochim Acta 69:2949–2958 Likholyot A, Lemke KH, Hovey JK, Seward TM (2007) Mass spectrometric and quantum chemical determination of proton water clustering equilibria. Geochim Cosmochim Acta 71:2436–2447 Li Y, Wang G, Wang C, Zhou M (2012) Coordination and solvation of the Au+ cation: infrared photodissociation spectroscopy of mass-selected Au(H2O)n+ (n = 1–8) complexes. J Phys Chem A 116:10793–10801 Liu K, Cruzan JD, Saykally RJ (1996a) Water clusters. Science 271:929–933 Liu K, Brown MG, Cruzan JD, Saykally RJ (1996b) Vibration-rotation tunneling spectra of the water pentamer: Structure and dynamics. Science 271:62–64 Liu K, Brown MG, Carter C, Saykally RJ, Gregory JK, Clary DC (1996c) Characterization of a cage form of the water hexamer. Nature 381:501 Lukashov YuM, Komissarov KB, Golubev BP, Smirnov SN, Svistunov EP (1975) Electrolytic properties of monomonovalent electrolytes at high parameters of state. Teploenergetika 12:78–81 Lv ZL, Xu K, Cheng Y, Chen XR and Cai LC (2014) Ab initio investigation of the lower energy candidate structures for (H2O)5+ water cluster. J Chem Phys 141:054309 Maeda S, Ohno K (2007) Structures of water octamers (H2O)8: Exploration on ab initio potential energy surfaces by the scaled hypersphere search method. J Phys Chem A 111:4527–4534 Maeda S, Ohno K (2008) Microsolvation of hydrogen sulfide: Exploration of H2S(H2O)n and SH−.H3O+.(H2O)n−1 (n = 5−7) cluster structures on ab initio potential energy surfaces by the scaled hypersphere search method. J Phys Chem A 112:2962–2968 Mahoney MW, Jorgensen WL (2000) A five-site model for liquid water and the reproduction of the density anomaly by rigid, nonpolarizable potential functions, J Chem Phys 112:8910–8922

82

Lemke & Seward

Magnera TF, David DE, Michl J (1989) Gas-phase water and hydroxyl binding energies for monopositive first-row transition metal ions. J Am Chem Soc 111:4100–4101 Maréchal Y (2011) The molecular structure of liquid water delivered by absorption spectroscopy in the whole IR region completed with thermodynamics data. J Mol Struc 1004:146–155 Masamura M (2003) Structures, energetics, and spectra of Br−(H2O)n clusters n = 1–6: ab initio study. J Chem Phys 118:6336–6347 Mei Y, Liu W, Brugger J, Migdisov AA, Williams-Jones AE (2017) Hydration is the key for gold transport in CO2– HCl–H2O vapor. Earth and Space Chem 1:368–375 Mei Y, Liu W, Migdiov AA, Brugger J, Williams-Jones AE (2018) CuCl complexation in the vapor phase: insights from ab initio molecular dynamics simulations. Geofluids 2018 Meot-Ner, M (2005) The ionic hydrogen bond. Chem Rev 105:213–284 Miyazaki M, Fujii A, Ebata T, Mikami N (2004) Infrared spectroscopic evidence for protonated water clusters forming nanoscale cages. Science 304:1134–1137 Mizuse K, Fujii A (2013) Infrared spectroscopy of large protonated water clusters H+(H2O)20–50 cooled by inert gas attachment. Chem Phys 419:2–7 Montgomery Jr JA, Frisch MJ, Ochterski JW and Petersson GA (1999) A complete basis set model chemistry. VI Use of density functional geometries and frequencies. J Chem Phys 110:2822–2827 Mukhopadhyay A, Xantheas SS, Saykally RJ (2018) The water dimer II: Theoretical investigations. Chem Phys Lett 700:163–175 Nagata T, Mafuné F (2017) Thermal analysis of hydrated gold cluster cations in the gas phase. J Phys Chem C 121:16291–16299 Palmer DA, Simonson JM, Jensen JP (2004) Partitioning of electrolytes to steam and their solubilities in steam. In: Aqueous Systems at Elevated Temperatures and Pressures: Physical Chemistry in Water, Steam and Hydrothermal Solutions (DA Palmer, R Fernandez-Prini and AH Harvey, eds.), Elsevier, p 409–430 Perlt E, Domaros M, Kirchner B, Ludwig R, Weinhold F (2017) Predicting the ionic product of water. Sci Rep 7:10244 Pitzer KS (1983) Thermodynamics of sodium chloride solutions in steam. J Phys Chem 87:1120–1125 Pitzer KS, Pabalan RT (1986) Thermodynamics of NaCl in steam. Geochim Cosmochim Acta 50:1445–1454 Poisson L, Lepetit F, Mestdagh JM, Visticot JP (2002) Multifragmentation of the Au(H2O)n ≤ 10+ cluster ions by collision with helium. J Phys Chem A 106:5455–5462 Pradzynski CC, Forck RM, Zeuch T, Slavíček P and Buck U (2012) A fully size-resolved perspective on the crystallization of water clusters. Science 337:1529–1532 Pugliano N Saykally RJ (1992) Measurement of quantum tunneling between chiral isomers of the cyclic water trimer. Science 257:1937–1940 Quist AS, Marshall WL (1968) Electrical conductances of aqueous sodium chloride solutions from 0 to 800°and at pressures to 4000 bars. J Phys Chem 72:684–703 Reveles JU, Calaminici P, Beltrán MR, Köster AM, Khanna SN (2007) H2O nucleation around Au+. J Am Chem Soc 129:15565–15571 Robertson WH, Johnson MA (2003) Molecular aspects of halide ion hydration: The cluster approach. Ann Rev Phys Chem 54:173–213 Robertson WH, Diken EG, Price EA, Shin JW, Johnson MA (2003) Spectroscopic determination of the OH− solvation shell in the OH− (H2O)n clusters. Science 299:1367–1372 Rocher-Casterline BE, Ch’ng LC, Mollner AK, Reisler H (2011) Determination of the bond dissociation energy (D0) of the water dimer (H2O)2 by velocity map imaging. J Chem Phys 134:211101 Rosenbauer RJ, Bischoff JL (1987) Pressure-composition relations for co-existing gases and liquids and the critical points in the system NaCl–H2O at 450, 475 and 500 °C Geochim Cosmochim Acta 51:2349–2354 Slanina Z (1988) A theoretical evaluation of water oligomer populations in the Earth’s atmosphere. J Atmos Chem 6:185–190 Slanina Z, Uhlík F, Lee SL, Nagase S (2006) Computational modelling for the clustering degree in the saturated steam and the water-containing complexes in the atmosphere. J Quant Spect Rad Trans 97:415–423 Schröder D (2012) Ion clustering in electrospray mass spectrometry of brine and other electrolyte solutions. Phys Chem Chem Phys 14:6382–6390 Schröder D, Ducháčková L, Tarábek J, Karwowska M, Fijalkowski KJ, Ončák M, Slavíček P (2011). Direct observation of triple ions in aqueous solutions of nickel (II) sulfate: a molecular link between the gas phase and bulk behavior. J Am Chem Soc 133:2444–2451 Schulz F, Hartke B (2002). Dodecahedral clathrate structures and magic numbers in alkali cation microhydration clusters. Chem Phys Chem 3:98–106 Seward TM, Driesner T (2004) Hydrothermal solution structure: experiments and computer simulations. In: Aqueous Systems at Elevated Temperatures and Pressures (pp. 149–182); Elsevier, Amsterdam (DA Palmer R FernandezPrini, AH Harvey, eds.), chap. 5, pp. 149–182

Molecular Clusters & Solvation in Volcanic & Hydrothermal Vapors

83

Seward TM, Williams-Jones AE, Migdisov AA (2014) The chemistry of metal transport and deposition by ore forming hydrothermal fluids. In: The Treatise on Geochemistry (2nd edn., vol. 13) (HD Holland and KK Turekian, eds.), Elsevier, Oxford, p 29–57 Shin JW, Hammer NI, Diken EG, Johnson MA, Walters RS, Jaeger TD, Duncan MA, Christie RA, Jordan KD (2004) Infrared signature of structures associated with the H+(H2O)n (n = 6 to 27) clusters. Science 304:1137–1140 Smith A, Vincent MA, Hillier IH (1999) Mechanism of acid dissociation in water clusters: electronic structure studies of (H2O)nHX (n= 4, 7; X= OH, F HS, HSO3, OOSO2H, OOHSO2). J Phys Chem A 103:1132–1139 Stefansson A, Seward TM (2003) The stability of chloridogold(I) complexes in aqueous solutions from 300 to 600 °C and 500 to 1800 bar. Geochim Cosmochim Acta 67:4559–4576 Suleimenov OM, Seward TM (1997) A spectrophotometric study of hydrogen sulphide ionisation in aqueous solutions to 350 oC Geochim Cosmochim Acta 61:5187–5198 Suleimenov OM, Bastrakov EN, Shvarov YuV, Seward TM (2006) Sodium chloride–water clusters in steam: classical, quantum chemical and thermodynamic computational approach. Geochim Cosmochim Acta (Goldschmidt Conference Abstracts), A623 Tanger IV JC, Pitzer KS (1989) Calculation of the ionization constant of H2O to 2,273 K and 500 MPa. AIChE J 35:1631–1638 Temelso B, Shields GC (2011). The role of anharmonicity in hydrogen-bonded systems: the case of water clusters. J Chem Theory Comp 7:2804–2817 Vácha R, Buch V, Milet A, Devlin JP Jungwirth P (2007) Autoionization at the surface of neat water: is the top layer pH neutral, basic, or acidic? Phys Chem Chem Phys 9:4736–4747 Van Thiel M, Becker ED, Pimentel GC (1957) Infrared studies of hydrogen bonding of water by the matrix isolation technique. J Chem Phys 27:486–490 Wales DJ Hodges MP (1998) Global minima of water clusters (H2O)n, n ≤ 21, described by an empirical potential. Chem Phys Lett 286:65–72 Wales DJ, Scheraga HA (1999) Global optimization of clusters, crystals, and biomolecules. Science 285:1368–1372 Wales DJ, Doye JP, Miller MA, Mortenson PN, Walsh TR (2007) Energy landscapes: from clusters to biomolecules. Adv Chem Phys115: 1–111 Wu CC, Lin CK, Chang HC, Jiang JC, Kuo JL, Klein ML (2005) Protonated clathrate cages enclosing neutral water molecules: H+(H2O)21 and H+(H2O)28. J Chem Phys 122:074315 Xantheas SS (1994) Ab initio studies of cyclic water clusters (H2O)n, n = 1–6. II Analysis of many-body interactions. J Chem Phys 100:7523–7534 Xantheas SS, Burnham CJ, Harrison RJ (2002) Development of transferable interaction models for water. II Accurate energetics of the first few water clusters from first principles. J Chem Phys 116:1493–1499 Yang X, Castleman Jr AW (1989) Large protonated water clusters H+(H2O)n (1  60): the production and reactivity of clathrate-like structures under thermal conditions. J Am Chem Soc 111:6845–6846 Yoo S, Apra E, Zeng XC, Xantheas SS (2010) High-level ab initio electronic structure calculations of water clusters (H2O)16 and (H2O)17: A new global minimum for (H2O)16. J Phys Chem Lett 1:3122–3127 Zhang J, Dolg M (2016) Global optimization of clusters of rigid molecules using the artificial bee colony algorithm. Phys Chem Chem Phys 18:3003–3010 Zhao Y, Truhlar DG (2008) The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor Chem Acc 20:215–241 Zhao Y, Truhlar DG (2010) The Minnesota density functionals and their applications to problems in mineralogy and geochemistry. Rev Min Geochem 71:19–37 Zhao Y, Schultz NE, Truhlar DG (2006) Design of density functionals by combining the method of constraint satisfaction with parametrization for thermochemistry, thermochemical kinetics, and noncovalent interactions. J Chem Theor Comp 2:364–382 Zimm BH Mayer JE (1944) Vapor pressures, heats of vaporization and entropies of some alkali halides. J Chem Phys 12:362–369

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Reviews in Mineralogy & Geochemistry Vol. 84 pp. 85–101, 2018 Copyright © Mineralogical Society of America

Reaction Mechanisms and Solid–Gas Phase Reactions: Theory and Density Functional Theory Simulations James D. Kubicki and Heath D. Watts Department of Geological Sciences The University of Texas at El Paso El Paso, Texas USA [email protected], [email protected]

Geochemistry was dominated by thermodynamic theory for much of its first century of existence (Anderson and Crerar 1993; Nordstrum 2006). Interest in high temperature igneous and metamorphic processes combined with the presumption of long time periods that are available for geochemical reactions justified the assumption of equilibrium thermodynamics. Consequently, geochemists were interested in reactants and products, i.e., examining A, B, and C in reactions like A + B → C without concern for what happens in between as represented by the arrow. In fact, for many geochemical reactions, the reactants and products can be treated as components without direct knowledge of the actual molecular-level structure. For example, in thermodynamic treatments of solutions H4SiO4(aq) is represented as SiO2(aq), even though O=Si=O molecules do not exist in solution. It is now clear that even many high-temperature processes do not reach equilibrium (Rubie and Brearly 1987; Han et al. 2015), so understanding the kinetics of geochemical processes and all the species involved has been a growing focus since the 1980s (Stumm et al. 1987). A comparison of the two approaches is outlined in Figure 1. Recent interest in surface geochemical processes such as chemical weathering, oxidation of sulfides, and transport of elements via water flow has demanded that kinetics and speciation be invoked in geochemical studies because most systems do not come close to approaching

Figure 1. The top three boxes show the components, system of study, and what the observer finds from a thermodynamic study (e.g., A + B → C). The bottom three boxes show the more-detailed information that it is possible to obtain from a kinetics or reaction mechanism experiment (e.g., A + D → AD + B → D + AB + E → C + E). See the section Problems in determining reaction mechanisms in chapter text for further details. Am-SiO2(s) is amorphous silica.

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equilibrium in human time frames at Earth surface temperatures. In addition, recognition of the role of biota (hence the “E” for enzyme in Fig. 1), especially microbes, in geochemical processes has buttressed the need for kinetics data. In geochemistry, “kinetics” has commonly come to mean rates of reactions. Large volumes of studies have been published collecting rate data in the laboratory or in the field (e.g., White and Brantley 2003). However, far fewer studies have been focused on determining the reaction mechanisms involved that control the observed rates. This situation stands in stark contrast to the field of organic chemistry, where textbooks are filled with reaction mechanisms, which detail the step-by-step processes leading to synthesis of organic compounds. Just as in other fields of chemistry, however, knowledge of geochemical reaction mechanisms helps to provide information about how to extrapolate rates from one set of conditions to another and to allow for more intelligent engineering of systems to minimize negative impacts (e.g., acid mine drainage) or maximize benefits (e.g., soil productivity). For example, the toxic effects and biodegradability of some elements and compounds are generally influenced by their bioavailability (i.e., biological uptake). When compounds are less bioavailable, their toxicity will be mitigated even when the compound has a high inherent toxicity. This was demonstrated (Steinberg et al. 1987) for 1,2-dibromoethane (EDB) in soils as aged EDB became absorbed into micropores; adsorption dramatically decreased the EDB biodegradation rate compared to that of freshly added EDB. This type of process plays out naturally and effects the preservation of natural organic matter (Keil et al. 1994; Torn et al. 1997), which has enormous consequences for C cycling, climate, and fossil fuel preservation.

Problems in determining reaction mechanisms If one agrees that knowledge of the reaction mechanism is useful, then why are there so few studies that attempt to determine geochemical reaction mechanisms? First, chemical reactions in general and geochemical reactions in particular are commonly the net result of several elementary reactions—i.e., reactions involving the chemical species as written. For example, instead of the net overall reaction: A+B→C one could find the equivalent set of elementary reactions: A + D → AD AD + B → D + AB AB + E → C + E The reaction intermediates AD and AB cancel out as they are consumed after being produced, and the enzyme, E, plays a role in catalyzing the reaction but is neither consumed nor produced in it. When one looks at a common chemical weathering reaction such as microcline to kaolinite, 2 KAlSi3O8 + 9 H2O + 2 H+ → Al2Si2O5(OH)4 + 2 K+ + 4 H4SiO4

(Faure 1998)

one can see there may be many elementary steps involved in producing the overall reaction (Criscenti et al. 2006). Not only is this more complicated than determining the stoichiometry of the overall reaction, but also many species may be present in concentrations below detection limits or exist as transient species that one does not find unless he/she is looking for them. Even if one can define the elementary reactions that are involved, one then needs to determine how these reactions occur and which one is the rate-determining step in the overall reaction. The rate-determining step will be the slowest step in sequential reactions and the fastest step in a set of parallel reactions. Many geochemical reactions are slow (especially on the chemical scale where “slow” can mean milliseconds) and thus difficult to study kinetically in the laboratory. Often conditions

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of T or pH are altered to speed up the reaction to get faster kinetics (Dove 1999; Rosso and Rimstidt 2000), but this leaves open the question of whether the kinetics and mechanisms are similar at other T and pH conditions (Brantley 2008). As an added complication, Nature has decided that the key step in the elementary reaction, formation of the transition state or activated complex, is extremely transitory and not readily observable except in cases where femtosecond spectroscopy may be applied (Kemp 2016). In situ techniques (e.g., reviewed in King et al. 2018, this volume) are not the norm in geochemical kinetics studies, so commonly there is little to no data on the reaction intermediates and potential transition state complexes involved with a reaction. For these reasons, most published studies on geochemical reaction mechanisms have been computational in nature where a reaction mechanism is presumed and the resulting kinetic parameters are compared to observed values (Casey et al. 1990). This chapter will describe the basics of chemical kinetics while referencing other sources for more details on the concepts presented. We focus on application to mineral–gas reactions kinetics so the interested reader can see the connection between theory and this particular application. The final component of the chapter describes techniques for modeling mineral–gas reaction kinetics with quantum mechanical calculations and provides an example.

BACKGROUND THEORY Experimental data related to reaction mechanisms To begin understanding reaction mechanisms, we start with the kinetic theory of gases. This is because we assume that molecules must be close together in order to react with one another, so we must understand how the molecules move. In thermodynamics, we measure a temperature of a system, which is an average of the kinetic energy of all the atoms in the system of interest. However, not all the atoms in a system have the same kinetic energy, they have a distribution of energies, and their distribution is described by the Maxwell–Boltzmann equation: = f (ν )

( m / 2 pk BT )3/ 2 4 πν 2 exp( − mν 2 / 2k BT )

(1)

Here, ν is the velocity, m is the molar mass, kB is the Boltzmann constant, and T is temperature. If one uses the molar mass 44 for CO2 and T of 300 and 1000 K, their respective temperature-dependent distributions shown in Figure 2a are the result. First note that even near room temperature (300 K = 27 °C), velocities of molecules can be very high—approximately 1000 m⋅s−1 near the high-end tail and over 300 m⋅s−1 at the maximum of the distribution. Perhaps one could use this as an excuse when pulled over for speeding—“Sorry officer, the gas molecules behind my car were pushing me at 300 m⋅s−1 (650 miles per hour)!” Other molecular motions are also very rapid such as vibrations that occur in the picosecond range and rotations that occur in the nanosecond time range. Obviously, the winds on Earth do not constantly blow at hundreds of kiolmeters per hour, so this high molecular velocity is dampened by some factor. The velocities are randomized, rather than organized, so gas-phase molecules do not spontaneously form directional winds (e.g., the molecules in Figure 2b move in random directions not left-to-right.). In addition, the molecules are constantly colliding with one another, so they are changing velocity (direction and speed), which does not allow them to perform organized motion (i.e., work). (This reminds us of many people we have known.) The average distance a molecule travels between collisions, the mean-free path, is approximately 150 nm at 25 °C and 1 atm pressure. This means that the average time between molecular collisions is approximately 5 x 10−10 s or a billion collisions per second! In liquid and solid states, these translation motions can be slowed down dramatically to almost zero in crystals, but the rates of vibrations and rotations can still be high.

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b. 300 K

1000 K

c.

The Ca and O atoms of two Caanorthite-O=S=O bonds are labeled.

O

Ca

O

Ca

Figure 2. a. Maxwell–Boltzmann probability distribution for CO2 at 300 and 1000 K, b. SO2, O2, and H2O molecules in a periodic box, and c. Model showing SO2 molecules interacting with anorthite surface. The Ca and O atoms of two Caanorthite–OSO bonds are labeled.

With so many collisions occurring, one may wonder why chemical reactions are not constantly occurring. Elementary thermodynamics tells us that two species will not react if the sum of their Gibbs free energies (G) is less than the G of any products that might form. This explains why the thermodynamically stable O=O and N≡N molecules are so common in Earth’s atmosphere. Even when A + B → C has a ∆G