Micas: Crystal Chemistry & Metamorphic Petrology 9781501509070, 9780939950584

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MICAS: CRYSTAL CHEMISTRY AND METAMORPHIC PETROLOGY Editors Annibale Mottana Francesco Paolo Sassi James B. Thompson, Jr. Stephen Guggenheim

Università degli Studi Roma Tre Università di Padova Harvard Universi ti/ Universitì/ of Illinois at Chicago

FRONT COVER: Perspective view of TOT layers in Biotite down [100] ([001] is vertical), produced by Crystalfyhiker, Red tetrahedra contain Si and Al, green and white octahedra contain Mg and Fe, respectively, and yellow spheres represents the K interlayer cations. Courtesy of Mickey Gunter, University of Idaho, Moscow. [Data: S.R. Bohlen et al. (1980) Crystal chemistry of a metamorphic biotite and its significance in water barometry. Am Mineral 65: 55-62] BACK COVER: A view down [001] of lepitdolite-2M2, showing tetrahedrally coordinated Si,Al (blue) joined with bridging oxygens (red thermal ellipsoids) in the T-Layer and ordered, octahedrally coordinated A l (gray) and Li (yellow) in the O-layer. The interlayer cation I sl2-coordinator K (green). Courtesy of Bob Downs, University of Arizona, Tucson. [Data: S. Guggenheim (1981) Cation ordering in lepidolite. Am Mineral 66:1221-1232]

Series Editor for MSA: Paul H. Ribbe Virginia Polytechnic Institute and State University M n : » J M L © C T C A L ¡ M C K T Y of A M E M C A W a Ä g t a W s ,

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M I N E R A L O G I C A L S O C I E T Y OF A M E R I C A 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.

REVIEWS IN MINERALOGY AND GEOCHEMISTRY ( F o r m e r l y : R E V I E W S IN M I N E R A L O G Y )

ISSN 1529-6466

Volume 46

MICAS: Crystal Chemistry and Metamorphic Petrology ISBN 0-939950-58-8 ** This volume is the eighth of a series of review volumes published jointly under the banner of the Mineralogical Society of America and the Geochemical Society. The newly titled Reviews in Mineralogy and Geochemistry has been numbered contiguously with the previous series, Reviews in Mineralogy. Additional copies of this volume as well as others in this series may be obtained at moderate cost from: THE M I N E R A L O G I C A L S O C I E T Y OF A M E R I C A 1 0 1 5 EIGHTEENTH STREET, N W , SUITE 6 0 1 WASHINGTON, D C 2 0 0 3 6 U . S A .

MICAS: Crystal Chemistry and Metamorphic Petrology Reviews in Mineralogy and Geochemistry Volume 46 2002 FORWARD The editors and contributing editors of this volume participated in a short course on micas in Rome late in the year 2000. It was organized by Prof. Annibale Mottana and several colleagues (details in the Preface below) and underwritten by the Italian National Acadmey, Accademai Nationale dei Lincei (ANL). The Academy subsequently joined with the Mineralogical Society of America (MSA) in publishing this volume. MSA is grateful for their generous involvement. I am particularly thankful to Prof. Mottana for Herculean efforts in supervising the editing of twelve manuscripts from six countries and submitting a single package containing everything needed to compile this volume! This was a uniquely positive experience fro me as Series editor for MSA. Assembling this volume was made tolerable by the exceptional efforts of Steve Guggenheim. During recovery from spinal surgery he spent three weeks painstakingly (no pun) correcting grammar and wording of the many authors from whom English is not their first language. Special thanks to him and the gracious and patient authors who suffered the extra work of assimilating both Steve's suggestions and mine, above and beyond those of their reviewers and the editors. MSA's Executive Director, Alex Speer, made all the contractual arrangements with ANL. This is the second of what we hope will be many co-operative projects with international colleagues and members of MSA. The first was in the year 2000: "Transformation Processes in Minerals," RiMG 39, the proceedings of a short course at Cambridge University in partnership with four European scientific societies. Paul H. Ribbe, Series editor Blacksburg, Virginia April 20, 2002

PREFACE Micas are among the most common minerals in the Earth crust: 4.5% by volume. They are widespread in most if not all metamorphic rocks (abundance: 11%), and common also in sediment and sedimentary and igneous rocks. Characteristically, micas form in the uppermost greenschist facies and remain stable to the lower crust, including anatectic rocks (the only exception: granulite facies racks). Moreover, some micas are stable in sediments and diagenetic rocks and crystallize in many types of lavas. In contrast, they are also present in association with minerals originating from the very deepest parts of the mantle—they are the most common minerals accompanying diamond in kimberlites. The number of research papers dedicated to micas is enormous, but knowledge of them is limited and not as extensive as that of other rock-forming minerals, for reasons mostly relating to their complex layer texture that makes obtaining crystals suitable for careful studies with the modern methods time-consuming, painstaking work. Micas were reviewed extensively in 1984 (Reviews in Mineralogy 13, S.W. Bailey, editor). At that time, "Micas" volume covered most if not all aspects of mica knowledge, thus producing a long shelf-life for this book. Yet, or perhaps because of that iii 1529-6466/02/0046-0000305.00

DOI: 10.2138/rmg.2002.46.0

excellent review, mica research was vigorously renewed, and a vast array of new data has been gathered over the past 15 years. These data now need to be organized and reviewed. Furthermore, a Committee nominated by the International Mineralogical Association in the late 1970s concluded its long-lasting work (Rieder et al. 1998) by suggesting a new classification scheme which has stimulated a new chemical and structural research on micas. To make a very long story short: the extraordinarily large, but intrinsically vague, micas nomenclature developed during the past two centuries has been reduced from >300 to just 37 species names and 6 series (see page xiii, preceding Chapter 1); the new nomenclature shows wide gaps that require data involving new chemical and structural work; the suggestion of using adjectival modifiers for those varieties that deviate away from end-member compositions requires the need fro new and accurate measurements, particularly fro certain light elements and volatiles; the use of polytype suffixes based on the modified Gard symbolism created better ways of determining precise stacking sequences. This resulted in new polytypes being discovered. Indeed, all this has happened over the past few years in an almost tumultuous way. It was on the basis of these developments that four scientists (B. Zanettin, A. Mottana, F.P. Sassi and C. Cipriani) applied to Accademia Nazionale dei Lincei—the Italian National Academy—for a meeting on micas. An international meeting was convened in Rome on November 2-3, 2000 with the title Advances on Micas (Problems, Methods, Applications in Geodynamics). The topics of this meeting were the crystalchemical, petrological, and historical aspects if the micas. The organizers were both Academy members (C. Cipriani, A. Mottana, F.P. Sassi, W. Schreyer, J.B. Thompson Jr., and B. Zanettin) and Italian scientist well-known for their studies on layer silicates (Professors M.F. Brigatti and G. Ferraris). Financial support in addition to that by the Academy was provided by C.N.R. (the Italian National Research Council), M.U.R.S.T. (the Italian Ministry for University, Scientific Research and Technology) and the University of Rome III. Approximately 200 scientists attended the meeting, most of them Italians, but, with a sizeable international participation. Thirteen invited plenary lectures and six oral presentations were given, and fourteen posters were displayed. The amount of information presented was large, although the organizers made it very clear that the meeting was to be limited to only a few of the major topics of micas studies. Other studies are promised for a later meeting. Oral and poster presentations on novel aspects of mica research are being printed in the European Journal of Mineralogy, as apart of an individual thematic issue: indeed thirteen papers have appeared in the November 2001 issue. The plenary lectures, which consisted mostly of reviews, are presented in expanded detail in this volume. This book is the first a co-operative project between Accademia Nazionale dei Lincei and Mineralogical Society of America. Hopefully, future projects will involve reviews of the remaining aspects of mica research, and other aspects of mineralogy and geochemistry. The entire meeting was made successful through a co-operative effort. The editing of this book was achieved by a co-operative effort of two Italian Academy members from one side, and by two American scientists from the other side, one of them (JBT) being also a member of Lincei Academy. The entire editing process benefited from the goodwill of many referees, both from those attending Rome meeting and from several who did not. In all the reviewers were distinguished expert of the international iv

community o f mica scholars. Their work, as w e l l as our editing work, were aided greatly b y RiMG Series Editor, Professor Paul Ribbe, w h o continuously supported the efforts with all his professional experience and friendly advice. W e , the co-editors, thank them all very warmly, but take upon ourselves all remaining shortcomings: w e are aware that some shortcomings m a y be present in spite o f all our efforts to avoid them Moreover, w e are aware that there are puzzling aspects o f micas that are unresolved. Please consider all these possible avenues for future research! Annibale Mottana (Rome) Francesco Paolo Sassi (Padua) James B. Thompson, Jr. (Cambridge, Mass.) Stephen Guggenheim (Chicago)

v

MICAS: C R Y S T A L C H E M I S T R Y and M E T A M O R P H I C P E T R O L O G Y Editors: A Mottana,

F P Sassi, J B Thompson, Jr & S Guggenheim Table of Contents

1

Mica Crystal Chemistry and the Influence of Pressure, Temperature, and Solid Solution on Atonlistic Models M a r i a F r a n c a Brigatti, S t e p h e n G u g g e n h e i m

OVERVIEW Treatment of the data and definition of the parameters used End-member crystal chemistry: New end members and new data since 1984 Synthetic micas with unusual properties EFFECT OF COMPOSITION ON S T R U C T U R E , Tetrahedral sheet Tetrahedral rotation and interlayer region Tetrahedral cation ordering Octahedral coordination and long-range octahedral ordering Crystal chemistry of micas in plutonic rocks ATOMISTIC MODELS INVOLVING HIGH-TEMPERATURE STUDIES OF THE MICAS Studies of samples having undergone heat treatment Dehydroxylation process for dioctahedral phyllosilicates Dehydroxylation models for lran\-vacanl 2: 1 layers Dehydroxylation models for cis-vacant 2: 1 layers Compalison o f N a - r i c h vs. K-rich dioctahedral forms Heat-treated trioctahedral samples: The 0 , 0 H , F site and in siiu high-temperature studies Heat-treated trioctahedral samples: Polytype comparisons ACKNOWLEDGMENTS \ P P h N n : \ I: DERIVATIONS Derivation of "tetrahedral cation displacement", T 1[sp Derivation o f f IE,. AE,, AF,3 Derivation of a Explanation of O K O I Explanation of EM 0(4j APPENDIX II: TABLES 1-4 Table la. Structural details of trioctahedral true micas-1 Ivi, space group C2/m Table lb. Structural details of trioctahedral true micas-1M, space group C2 Table Ie. Structural details of trioctahedral true micas-2M'], space group C2/c Table Id. Structural details oftrioctahedral true micas-2M,. space groups Ce. CI Table Ie. Structural details of trioctahedral true micas-2M,. space group C2!c Table If. Structural details of trioctahedral true micas-3T, space group Pi,12 Table 2a. Structural details of trioctahedral true micas-I/W, Mspace groups C2/m and C2 Table 2b. Structural details of trioctahedral true micas-lM, space group C2/c Table 2c. Structural details of trioctahedral true micas-2M, space group C2/e Table 2d. Structural details of trioctahedral true micas-3T, space group P 3 ; 12 Table 3a. Structural details of trioctahedral brittle micas Table 3b. Structural details of dioctahedral brittle micas Table 4. Structural details of boromuscovite-I M a n d -2M') calculated from the Rietveld structure refinement by Liang et al. (1995) REFERENCES

Vll

l 3 .4 ll 11 ll 19 25 27 37 39 39 .41 43 44 .49 50 51 51 52 52 52 53 54 54 55 55 70

12

74 74 74 76 78

84

84 86 88 88 90

2

Behavior of Micas at High Pressure and High Temperature Pier F r a n c e s c o Zanazzi, A l e s s a n d r o P a v e s e

INTRODUCTION Investigative techniques for the study of the thennoelastic behavior of micas p- V and P- V- T equations of state Dioctahedral micas Trioctahedral micas ACKNOWLEDGMENTS REFERENCES

3

99 100 101 103 108 ] 14 114

Structural Features of Micas G i o v a n n i F e r r a r i s , G a b r i e l l a Ivaldi

INTRODUCTION NOMENCLATURE AND NOTATION MODULARITY OF MICA STRUCTURE The mica module C L O S E S T - P A C K I N G aspects Closest-packing and polytypism C O M P O S I T I O N A L ASPECTS S Y M M E T R Y ASPECTS Metric (lattice) symmetry Structural symmetry Symmetry and cation sites T w o kinds of mica layer: Ml and M 2 I a y e r s The interlayer configuration Possible ordering schemes in the M D O polytypes The phengite case DISTORTIONS The misfit Geometric parameters describing distortions Ditngonal rotation Other distortions Effects of the distortions on the stacking mode FURTHER STRUCTURAL MODIFICATION Pressure, temperature and chemical influence Thickness of the mica module Ditrigonal rotation and interlayer coordination Effective coordination number (ECoN) CONCLUSIONS APPENDIX I: M I C A S T R U C T U R E A N D P O L Y S O M A T I C SERIES Layer silicates as members of modular series? Mica modules in polysomatic series The heterophyllosicate polysomatic series The palysepiole polysomatic series Conclusions A P P E N D I X II: O B L I Q U E T E X T U R E E L E C T R O N DIFFRACTION (OTED) ACKNOWLEDGMENTS REFERENCES

vili

117 1 ]7 118 118 ]20 121 122 124 ]24 124 125 127 128 129 130 130 130 131 131 132 133 135 135 135 137 138 138 140 140 140 140 142 143 144 148 148

4

Crystallographic Basis ofPolytypism and Twinning in Micas M a s s i m o N e s p o l o , SlavomiJ D u r o v i c

IN1RODUCTION NOTATION A N D DEFINITIONS The mica layer and its constituents Axial settings, indices and lattice parameters Symbols Symmetry and symmetry operations THE UNIT LAYERS OF MICA Alternative unit layers MICA POLYTYPES AND THEIR CHARACTERIZATION Micas as O D structures SYMBOLIC DESCRIPTION OF MICA POLYTYPES Orientational symbols Rotational symbols RETICULAR CLASSIFICATION OF POLYTYPES: SPACE ORIENTATION AND S Y M B O L DEFINITION LOCAL AND GLOBAL S Y M M E 1 R Y OF MICA POLYTYPES FROM THEIR STACKING S y M B O L S Derivation of MDO polytypes The symmetry analysis from a polytype symbol RELATIONS O F H O M O M O R P H Y AND CLASSIFICATION OF MDO POLYTYPES BASIC S 1 R U C T U R E S AND POLYTYPOIDS. SIZE LIMIT FOR THE DEFINITION OF "POLYTYPE" Abstract polytypes Basic structures HI REM observations and some implications IDEAL S P A C E - G R O U P TYPES OF MICA POLYTYPES AND DESYMME1RIZATION OF LAYERS IN POLYTYPES CHOICE OF THE AXIAL SETTING G E O M E 1 R I C A L CLASSIFICATION OF RECIPROCAL LATTICE ROWS SUPERPOSITION S1RUCTURES, FAMILY S 1 R U C T U R E AND FAMILY REFLECTIONS Family structure and family reflections of mica polytypes REFLECTION CONDITIONS NON-FAMILY REFLECTIONS AND O R T H O G O N A L PLANES HIDDEN S Y M M E 1 R Y OF THE MICAS: THE R H O M B O H E D R A L LATTICE TWINNING OF MICAS: THEORY Choice of the twin elements Effect of twinning by selective merohedry on the diffraction pattern Diffraction patterns from twins Allotwinning Tessellation of the hp lattice Plesiotwinning TWINNING O F MICAS. ANALYSIS OF THE GEOME1RY OF THE DIFFRACTION PATTERN Symbolic description of orientation of twinned mica individuals. Limiting symmetry Derivation of twin diffraction patterns Derivation of allotwin diffraction patterns IDENTIFICATION OF M D O POLYTYPES FROM THEIR DIFFRACTION PATTERNS Theoretical background Identification procedure IDENTIFICATION OF N O N - M O O POLYTYPES: THE PERIODIC INTENSITY DISTRIBUTION FUNCTION PID in tenns of TS unit layers Derivation of PID from the diffraction pattern ix

155 156 157 158 158 159 159 160 164 164 172 172 175 178 178 180 180 184 189 191 192 193 193 193 204 206 209 212 213 214 216 217 219 220 223 224 224 230 233 235 237 243 244 244 245 247 249 251

EXPERIMENTAL INVESTIGATION OF MICA SINGLE CRYSTALS FOR TWIN / POLYTYPE IDENTIFICATION Morphological study Surface microtopography Two-dimensional XRD study Diffractometer study APPLICATIONS AND EXAMPLES 24-layer subfamily: A Series I Class b biotite from Ambulawa. Ceylon HA , (subfamily A Series 0.Class a3) oxyhinmc from Ruiz Peak, New Mexico 1M-2M] oxyblOtlte allotwm Z T = 4 from RUiZ Peak, New Mexico {3,6}[7 {3,6}] biotite plesiotwin from Sambagawa, Japan APPENDIX A. TWINNING: DEFINITION AND CLASSIFICATION APPENDIX B. COMPUTATION OF T H E PID FROM A STACKING S E Q U E N C E CANDIDATE Symlnetry of the PID ACKNOWLEDGMENTS REFERENCES

5

252 252 252 254 256 257 257 258 262 262 267 270 271 272 272

Investigations o f Micas Using Advanced Transmission Electron Microscopy Toshihiro Kogure

INTRODUCTION TEMS AND RELATED TECHNIQUES FOR THE INVESTIGATION OF MICA Transmission electron microscopy New recording media for beam-sensitive specimens Sample preparation techniques Image processing and simulation ANALYSES OF POLYTYPES DEFECT STRUCTURES CONCLUSION ACKNOWLEDGMENTS REFERENCES

6

281 281 281 286 287 288 289 299 310 310 310

Optical and Mossbauer Spectroscopy of Iron in Micas M. D a r b y D y a r

INTRODUCTION OPTICAL SPECTROSCOPY Current instrumentation Review of existing work Sunlmary MOSSBAUER SPECTROSCOPY (MS) Current instrumentation Recoil-free fraction effects Thickness effects Texture effects and other sources of error Techniques for fitting Mossbauer spectra Review of existing Mossbauer data Sumlnary COMPARISON OF TECHNIQUES CONCLUSIONS ACKNOWLEDGMENTS APPENDIX: Other techniques for measurement of Fe V/LFe in Micas X-ray ray photoelectron spectroscopy (XPS) Electron energy-loss spectroscopy (EELS) X-Ray absorption spectroscopy (XAS) REFERENCES X

313 315 315 316 320 320 320 320 321 322 323 325 333 334 336 337 337 337 338 338 340

7

Infrared Spectroscopy of Micas Anton Beran

INTRODUCTION LATTICE VIBRATIONS Far-IR region Mid-IR region OH STRETCHING VIERATIONS Polarized measurements Quantitative water determination Hydrogen bonding Cation ordering OH-F replacement Dehydroxylation mechanisms Excess hydroxyl NHj groups ACKNOWLEDGMENTS REFERENCES

8

351 352 352 353 359 359 360 360 362 365 366 367 367 367 367

X-Ray Absorption Spectroscopy of the Micas Annibale Mottana, Augusto Marcelli, G i a n n a n t o n i o Cibin, and M. D a r b y D y a r

INTRODUCTION OVERVIEW OF THE XAS METHOD EXAFS XANES Experimental spectra recording Optimization of spectra Systematics ACKNOWLEDGMENTS REFERENCES

9

371 373 375 376 384 387 395 404 405

Constraints on Studies of Metamorphic K-Na White Micas Charles

V.

Guidotti,

Francesco

P.

Sassi

INTRODUCTION EFFECTS OF P E T R O L O G I C F A C T O R S ON W H I T E MICA C H E M I S T R y Important compOSitional variations Controls of mica composition by petrologic factors M A X I M I Z I N G I N F O R M A T I O N F R O M MICA S T U D I E S : SAMPLE SELECTION CONSTRAINTS Petrologic studies Minéralogie studies DISCUSSION C o m m o n failings in petrology studies C o m m o n failings in mineralogy studies "Standard starting points" for the compositional variations of rock-forming dioctahedral and trioctahedral micas ACKNOWLEDGMENTS REFERENCES

XI

41 3 41 4 414 41 8 423 424 428 440 440 441 44 1 443 444

10

Modal Spaces for Pelitic Schists James

B. T h o m p s o n ,

Jr.

INTRODUCTION NOTATIONS AND CONVENTIONS THE ASSEMBLAGE QUARTZ-MUSCOVITE-BIOTITE-CHLORITE-GARNET THE ASSEMBLAGE QUARTZ-MUSCOVITE-CHLORITEGARNET-CHLORITOID ASSEMBLAGES CONTAINING CHLORITOID AND BIOTITE OTHER MODAL SPACES ACKNOWLEDGMENTS APPENDIX: INDEPENDENT NET-TRANSFER REACTIONS REFERENCES

11

449 450 451 454 455 458 458 460 462

Phyllosilicates in Very Low-Grade Metamorphism: Transformation to Micas Peter Arkai

INTRODUCTION MAIN METHODS OF STUDYING LOW-TEMPERATURE TRANSFORMATIONS OF PHYLLOSILICATES XRD techniques TEM techniques MAIN TRENDS OF PHYLLOSILICATE EVOLUTION AT LOW TEMPERATURE CURRENT PROBLEMS IN STUDYING PHYLLOSILICATE EVOLUTION AT THE LOWER CRYSTALLITE-SIZE LIMITS OF MINERALS REACTION PROGRESS OF PHYLLOSILICATES THROUGH SERIES OF METASTABLE STAGES CONCLUDING REMARKS ACKNOWLEDGMENTS REFERENCES

12

Micas: Historical Curzio

463 464 465 466 467 469 472 473 474 474

Perspective

Cipriani

INTRODUCTION PRESCIENTIFIC ERA THE EIGHTEENTH C E N T U R y THE NINETEENTH C E N T U R y Physical properties Crystallography Chemical composition THE TWENTIETH CENTURY Crystal chemistry Synthesis POLYTYPES SYSTEMATICS CONCLUSIONS REFERENCES APPENDIX I Present-day nomenclature of the mica group and its derivation APPENDIX II Other works consulted in preparation of this historical review

XII

479 479 480 483 483 485 486 491 491 494 494 49 5 496 497 498 499

Nomenclature of Micas MICA SIMPLIFIED FORMULA: /Af 2 . 3 Di.0 T4 OwA2 where /

= Cs, K, Na, NH4, Rb, Ba, Ca

M

= Li, Fe (2+, 3+), Mg, Mn, Zn, Al, Cr, V, Ti

•

= vacancy

T

= Be, Al, B, Fe(3+), Si

A

= Cl, F, OH, O, S

MICA SERIES NAMES:

biotite glauconite illite lepidolite phengite zinnwaldite

TRUE MICAS

BRITTLE MICAS

Dioctahedral

Trioctahedral

Dioctahedral

muscovite

annite

margante chernykhite

brammallite

aluminoceladonite phlogopite

Trioctahedral

INTERLAYERDEFICIENT MICAS Dioctahedral

Trioctahedral

clintonite

illite

wonesite

bityite

glauconite

ferro-aluminoceladonite celadonite

siderophyllite

anandite

eastonite

kinoshitalite

ferroceladonite

hendricksite

roscoelite

montdorite

chromphyllite

tainiolite

boromuscovite

polylithionite

paragonite

trilithionite

nanpingite

masutomilite

tob elite

norrishite tetra-ferri-annite tetra-ferriphlogopite aspidolite preiswerkite ephesite

1

Mica Crystal Chemistry and the Influence of Pressure, Temperature, and Solid Solution on Atomistic Models Maria Franca Brigarti Dipartimento di Scienze della Terra Università di Modena e Reggio Emilia, Via S. Eufemia, 19 1-41100 Modena, Italy [email protected]

Stephen Guggenheim Department of Earth and Environmental Sciences University of Illinois at Chicago 845 West Taylor Street, M/C 186 Chicago, Illinois 60607 [email protected]

OVERVIEW The 2:1 mica layer is composed of two opposing tetrahedral (T) sheets with an octahedral (M) sheet between to form a "TMT" layer (Fig. la). The mica structure has a general formula of A M2-3 T4 O10 X2 [in natural micas: A = interlayer cations, usually K, Na, Ca, Ba, and rarely Rb, Cs, NH4, H3O, and Sr; M = octahedral cations, generally Mg, Fe +, Al, and Fe3+, but other cations such as Li, Ti, V, Cr, Mn, Co, Ni, Cu, and Zn can occur also in mica species; T = tetrahedral cations, generally Si, Al and Fe3+ and rarely B and Be; X = (OH), F, CI, O, S]. Vacant positions (symbol: • ) are also common in the mica structure (Rieder et al. 1998). In the tetrahedral sheet, individual TO4 tetrahedra are linked with neighboring TO4 by sharing three corners each (i.e., the basal oxygen atoms) to form an infinite two-dimensional "hexagonal" mesh pattern (Fig. lb). The fourth oxygen atom (i.e., the apical oxygen atom) forms a corner of the octahedral coordination unit around the M cations. Thus, each octahedral anion atom-coordination unit is comprised of four apical oxygen atoms (two from the upper and two from the lower tetrahedral sheet) and by two (OH) or F, CI, O and S anions [the X anions, usually indicated as the OH or 0(4) site]. The OH site is at the same level as the apical oxygen but not shared with tetrahedra. In the octahedral sheet, individual octahedra are linked laterally by sharing octahedral edges (Fig. lc). The smallest structural unit contains three octahedral sites. Structures with all three sites occupied are known as trioctahedral, whereas, if only two octahedra are occupied [usually M(2)] and one is vacant [usually M(l)], the structure is defined as dioctahedral. The 2:1 layers, which are negatively charged, are compensated and bonded together by positively charged interlayer cations of the A site. The layer charge ideally is -1.0 for true micas and -2.0 for brittle micas. Thus, in true micas, the layer charge is compensated by monovalent A cations, whereas in brittle micas it is compensated primarily by divalent A cations. In this section, we consider and discuss the structural and chemical features of more than 200 micas. Most are true micas (146 trioctahedral and 55 dioctahedral). Brittle-mica crystal-structure refinements number about twenty, of which only three are dioctahedral (Tables 1-4, at the end of the chapter). Of the six simple polytypes first derived by Smith and Yoder (1956) and reported by Bailey (1984a, p. 7), only five (i.e., 1M, 2M h 3T, 2M2, and 2O) have been found and studied by three-dimensional crystal-structure refinements.

1529-6466/02/0046-0001 $ 10.00

DOI: 10.2138/rmg.2002.46.01

2

b

4

6(11

>

^

r-4

WW

Figure 1. (a) The 2:1 layer; (b) the "hexagonal" tetrahedral ring; (c) the octahedral sheet. For site nomenclature see text, a and b are unit cell parameters.

Most of the trioctahedral true-mica structures are IM polytypes and a few are 2M\, 2Mi, and 3 T polytypes. In dioctahedral micas, the 2M\ sequence dominates, although 37" and IM structures have been found. Brittle mica crystal-structure refinements indicate that the IM polytype is generally trioctahedral whereas the 2M\ polytype is dioctahedral. The 2O structure has been found for the trioctahedral brittle mica, anandite (Giuseppetti and Tadini 1972; Filut et al. 1985) and recently was reported for a phlogopite from Kola Peninsula (Ferraris et al. 2000). The greatest number of the reported structures were refined from single-crystal X-ray diffraction data, with only a few obtained from electron and neutron diffraction experiments. Subsequent sections of this paper present short reviews pertaining to the description of phyllosilicates, an emphasis of the literature since the publication of MICAS, Reviews in Mineralogy', Volume 13, edited by S.W. Bailey (1984a), and a new analysis of the crystal chemistry of the micas. New formulae are presented to clarify how crystal chemistry affects the mica structure. Derivations of these formulae are provided in Appendix I. Also, please refer to other chapters in this volume that cover related topics. For example, see Zanazzi and Pavese for the behavior of micas at high pressure and high temperature.

Mica Crystal Chemistry and Influence ofP-T-X

on Atomistic Models

3

Treatment of the data and definition of the parameters used To achieve standardization, all data in Tables 1-4 (Appendix II) were re-calculated from unit-cell parameters and atomic coordinates reported by the authors of the original articles. Information concerning rock type and sample composition was obtained from the original works as well. Suspect refinements are discussed separately or not reported. Of more than 200 reported crystal-structure refinements, about twenty refinements show an agreement factor, R, greater that 9.0%. These structures are considered of poor quality and are not considered further. Several authors used symbols and orientations that differ from convention to describe geometric arrangements of the layer and the stacking sequence of mica polytypes (e.g., Radoslovich 1961; Durovic 1994; Dornberger-Schiff et al. 1982). To make inter-structure comparisons of features easier, however, it is advantageous to define briefly the site nomenclature adopted and the parameters used to describe and characterize layer geometry. The direction defined by the stacking of 2:1 units defines the [001] direction (i.e., the c axis), whereas the periodicity of the infinite two-dimensional sheets defines [100] and [010] directions (i.e., a and b translations). The actual value of the repeat distance in the [001] direction, as well as lateral a and b parameters, depends on several factors, such as the layer stereochemistry and polytypism (i.e., c ~ 10 A x n, where n identifies the number of layers involved in the stacking sequence). The sitenomenclature scheme adopted here starts from the nomenclature generally used for the 2:1 layer of the 1M polytype in C2!m symmetry: T denotes the four-coordinated site, M(l) and M(2) indicate six-coordinated sites with (OH) groups in trans- and cisorientation, respectively, A refers to the interlayer cation, O(l) and 0(2) represent the basal tetrahedral oxygen atoms, 0(3) is the apical oxygen atom, and 0(4) refers to the (OH), F, CI, S or O anions (Fig. la). The number of sites per unit cell is: T = 8; M(l) = 2; M(2) = 4; A = 2; O(l) = 8; 0(2) = 4; 0(3) = 8; 0(4) = 4. The site nomenclature for other structural variants can be derived from this nomenclature by changes that relate to spacegroup differences and to the number of 2:1 layers per unit cell. The definition of parameters reported in Tables 1-4 (Appendix II) follows. For a more extensive review on definition and structural significance of these parameters, see Bailey (1984b) and references therein. Cation-anion bond lengths: (i) tetrahedral (T-O); (ii) octahedral (M-0,0H,F,C1,S) for both M(l) and M(2) sites; and (iii) interlayer (A-O). Mean bond lengths were compared to those of the original papers and vacant-site distances determined (i.e., vacancy-to-anion distances). The tetrahedral Oapkai-T-Obasai angles were used to obtain the tetrahedral flattening angle, x = X-.i Oapicai-T-ObaSai)i/3. The internal angles of the tetrahedral ring were used to determine the tetrahedral rotation angle, a = Zf^a, / 6 where a ; = |120° - is/^H and tj>i is the angle between basal edges of neighboring tetrahedra articulated in the ring. Basal oxygen-plane corrugation, Az, was determined by Az = (zObaSai(max) - zObaSai(mm)) x c sinp. The thickness of the tetrahedral and octahedral sheets was calculated from oxygen z coordinates of each polyhedron, including the OH group (or other X anions). The interlayer separation was obtained by considering the tetrahedral basal oxygen z coordinates of adjacent 2:1 layers. The octahedral flattening angle y was calculated from

4

Brigatti & G u g g e n h e i m

V|/

~C0S

_A octahedral thickness | Ux(M-0,0H,F,C1,S>J

Tetrahedral cation atomic coordinates, taken from the original reference, were transformed from fractional to Cartesian to calculate the Layer Offset, the Intralayer Shift, and the Overall Shift. The Layer Offset is based on the displacement of the tetrahedral sheet across the interlayer from one 2:1 layer to the next, which should be equal to zero in the ideal mica structure. The Intralayer Shift is the over-shift of the upper tetrahedral sheet relative to the lower tetrahedral sheet of the same 2:1 layer. The Overall Shift relates to both effects. In true micas, the tetrahedral mean bond distance varies from 1.57(1) A in boromuscovite-2Aii (Liang et al. 1995; Table 4) to 1.750(2) A in an ordered (A1 vs. Si) ephesite-2Aii (Slade et al. 1987; Table Id); in brittle micas, the (T-O) mean bond distance varies from 1.620(2) to 1.799(2) A, both values are from anandite-20 (Filut et al. 1985; Table 3a). Octahedral mean bond length ranges from about 1.882(1) A in an ordered ferroan polylithionite-lAi (Guggenheim and Bailey 1977; Brigatti et al. 2000b; Table lb) to 2.236(1) A in anandite 2 O (Filut et al. 1985; Table 3a). The radius of the vacant M(l) site in dioctahedral micas ((M(l)-O)) varies from 2.190 to 2.259 A. The shortest (A-OXnner distance occurs in clintonite ( ( A - O ) ^ ! = 2.397(2) A; Alietti et al. 1997, Table 3a), whereas the longest distance occurs in nanpingite and synthetic Cs-tetra-ferri-annite ((AO) inner of ~ 3.370 A; Ni and Hughes 1996 and Mellini et al. 1996, Tables l c and la, respectively). These data show the great variability in bond distances which may be ascribed not only to the local composition but also to the constraints of closest packing within the layer and the confinement of the octahedra between two opposing tetrahedral sheets. We consider the compositional and topological relationships in the following analysis. End-member crystal chemistry: New end members and new data since 1984 Boromuscovite. Boromuscovite was first reported by Foord et al. (1991). The mineral, precipitated from a late-stage hydrothermal fluid (T: 350-400°C; P: 1-2 kbar), occurred in the New Spaulding Pocket, Little Three Mine pegmatite dike (Ramona district, San Diego County, California), as a fine-grained coating of quartz, polylithionite, microcline and topaz. The mineral was found also in elbaite pegmatite at Recice near Move Mesto na Morave, western Moravia, Czech Republic (Liang et al. 1995; Novak et al. 1999). Relatively high B contents were also reported for muscovite and polylithionite from polylithionite-rich pegmatites of Rozna and Dobra Voda, Czech Republic (Cerny et al. 1995), for polylithionite-2Aii from Recice (Novak et al. 1999), and for muscovite from metapegmatite at Stoffhutte, Koralpe, Austria (Ertl and Brandstatter 1998). Boromuscovite (Foord et al. 1991) has the general structural formula of KAl 2 D(Si3B) Oio(OH) 2 , in which [4]A1 is replaced by ™B relative to muscovite. The composition of Little Three Mine boromuscovite is (K0.89Rb0.02Ca0.01XAl1.93Li0.01Mg0.01XSi3.06B0.77Al0.17) O9.82F0.i6(OH)2.02, whereas the composition of Recice boromuscovite shows a slightly lower [41B content: (Ko.89Nao.oi)(Ali.99Lio.oi)(Si3.ioBo.68Alo.22)OioFo.o2(OH)i.98. The unit cell parameters, very similar in natural and synthetic crystals (Schreyer and Jung 1997), are significantly smaller than those reported for muscovite (a = 5.075(1), b = 8.794(4), c = 19.82(3) A, /3 = 95.59(3)° and a = 5.077(1), b = 8.775(3), c = 10.061(2) A , / ? = 101.31(2)° for Little Three Mine boromuscovite-2Aii and boromuscovite-\M, respectively). A boromuscovite structure determination is complicated by the fine-grained nature

Mica Crystal Chemistry and Influence ofP-T-X on Atomistic Models

5

of the mineral and by the presence of the mixture of 1M and 2M\ polytypes. Nonetheless the crystal-structure determination of a mixture of 83 wt % boromuscovite-2Aii and 17 wt % boromuscovite-lAi from Recice was attempted using a coupled Rietveld-staticstructure energy-minimization method (Liang et al. 1995). Although the high standard deviation for calculated parameters suggests caution in the analysis of crystal chemical details, Liang et al. (1995) indicated that: (i) boron is uniformly distributed between the two polytypes, (ii) (T-O) distances correspond well with the B-content at the corresponding T-sites, namely (T-O) distances linearly decrease as B occupancy increases, and (iii) in the 2M\ polytype, slight differences between (T(l)-O) and (T(2)O) distances may imply a B preference for the T(l) site (Table 4). The U B MAS NMR spectra showed a single, symmetric and narrow line (about 150 Hz wide) at 20.7 ppm. The width was interpreted as possibly relating to the coordination for B with a nearsymmetrical disposition of anions (Novak et al. 1999). Clintonite. Clintonite is the trioctahedral brittle mica with ideal composition of Ca(Mg2Al)(SiAl3)Oio(OH)2. This structure violates the Al-avoidance principle of Loewenstein (1954). It crystallizes in LhO-saturated Ca-, Al-rich, Si-poor systems under wide P-T conditions. Clintonite, usually found in metasomatic aureoles of carbonate rocks, is rare in nature because crystallization is limited to environments characterized by both alumina-rich and silica-poor bulk-rock chemistry and very low CO2 and K activities (Bucher-Nurminen 1976; Olesch and Seifert 1976; Kato et al. 1997; Grew et al. 1999). The 1M polytype and 1 Mj sequences are the most common forms. The 2M\ form is rare (Akhundov et al. 1961) and no 37" forms have been reported. Many 1M crystals are twinned by ±120° rotation about the normal to the {001} cleavage. Such twinning causes extra spots on precession photographs that simulate an apparent three-layer periodicity (MacKinney et al. 1988). Subsequent to an extensive review of brittle micas (Guggenheim 1984), additional crystal-chemical details of clintonite-\M (space group C2/m) were reported by MacKinney et al. (1988) and Alietti et al. (1997). These studies confirmed that natural clintonite crystals do not vary extensively in composition: (i) the octahedral sites contain predominant Mg and Al with Fe2+ to [4]A1 + [12] K. A representative formula is Ko.75(AlL75,R?+25)(Si3.5oAlo.5o)Oio

(OH)2.

Bailey (1986) suggested that the layer charge m a y vary between -0.6 to -0.9, although the upper limit of -0.8 was extrapolated f r o m the data of Hower and Mowatt (1966). The lower limit of -0.6 was judged as a reasonable minimum without leading to possible expandability of the structure. The general term "illite" (Grim et al. 1937) is for a clay mineral that is a discrete and non-expandable mica of detrital or authigenic origin, where the exact nature of the mica is unknown. Finally, the third use is for the micaceous component of an interstratified system, such as "illite-smectite". Material that includes an expandable component is referred to as "illitic material" and not illite. Rieder et al. (1998) recognized the wide variation in possible compositions for illite and defined a series name for illite. The layer charge with an upper limit of -0.85 for illite was determined so that muscovite f r o m metamorphic regimes, which generally has a layer charge f r o m -0.85 to -1.0, does not require reassessment. Approximate variations in octahedral occupancy (per octahedral site) are A1/(A1 + Fe 3+ ) f r o m 0.6 to 1.0 and R 2 + /(R 2 + + R 3 + ) of (A) = 1.607+4.201 • 10~2

[4]

Al + 7.68-10~2[41Fe

(correlation coefficient, r = 0.965) In the regression analysis, structures containing B, Be, and Ge in tetrahedral sites were not considered, as well as structures with symmetry lower than ideal owing to tetrahedral cation ordering (differences in (T-O) values greater than 5CT). Only structures containing tetrahedral Si, Al, and Fe were examined. Geometrical considerations of tetrahedral distortion parameters have been considered earlier (e.g., Drits 1969, 1975; Takeuchi 1975; Appelo 1978; Lee and Guggenheim 1981; Weiss et al. 1992). We further discuss these relationships here and relate them to layer composition on the basis of data from a large number of structure determinations. A crystal chemical study of the x parameter is complex. In an ideal tetrahedron x is equal to arcos (-1/3) = 109.47°. For non-ideal cases, however, x was found to be affected by tetrahedral content, increasing as Si increases (Takeuchi 1975) relative to Al. The x value can deviate from its ideal value as a function of the relative position along c for the basal oxygen atoms with respect to the tetrahedral cation and with respect to the mean basal-edge length and the mean tetrahedral-edge value. These conclusions are based on the linearized topology of the tetrahedron. Several simple models of deformation are considered here (Fig. 2) and only modes (3) and (4) were found to affect the x value. All dependences (over displacement from an ideal undeformed configuration) of order

Mica Cn/stal Chemistn/

and Influence ofP-T-X

on Atomistic

Models

13

1 , 2 , 5 , 5, 7 : x = c o s t = 1 0 9 . 4 7 ° 3: x = 1 0 9 . 4 7 ° - 8 8 . 2 1 x k / e 4: x = 1 0 9 . 4 7 ° + 1 8 . 0 1 x k / e Figure 2. Geometrical considerations over the dependence of x from tetrahedron vertex and center displacement. The relationships in the legend have been obtained from a linearized geometrical model, k and e indicate the displacement and the tetrahedron edge length, respectively.

greater than one are ignored. The model, thus, provides results in good agreement with structural data only if displacements are small relative to the characteristic length of the system (i.e., the tetrahedral edge). Figure 3 shows the variations of x vs. [41Si content. Although the increase of x with Si is confirmed, there are two different linear trends, one trend for true and one trend for brittle micas. Brittle micas show x values greater than expected if just the composition of the tetrahedron is considered. Although this simple model ignores cation ordering, on the basis of geometrical considerations derived before (Fig. 2), the higher x values may be explained by the increase in the electrostatic attraction of basal oxygen atoms by the high-charge interlayer cation and by the concomitant increase in repulsion between the interlayer cation and the tetrahedral cation. Note, for example, that kinoshitalite usually tends to approach true micas in composition. Samples of kinoshitalite and ferrokinoshitalite (Guggenheim and Kato 1984; Brigatti and Poppi 1993; Guggenheim and Frimmel 1999) contain significant amounts of monovalent K in substitution for Ba, whereas, kinoshitalite refined by Gnos and Armbruster (2000), marked by an arrow in Figure 3, has nearly complete interlayer Ba occupancy and a larger x value. [41

To better relate how the interlayer cation affects x, we have developed a simple electrostatic model. The model is comprised of four tetrahedral oxygen atoms, with the tetrahedral and the interlayer cations located at the center of the tetrahedron and in the

14

Brigatti & Guggenheim

112.0

110.0

0.0

1.0

2.0 3.0 Si (apfu)

4.0

5.0

Figure 3. Relationships between the tetrahedral flattening angle, x, and Si content in tetrahedral coordination as determined by microprobe analysis. Symbols used: tilled circle = annite; tilled circle, x-hair = magnesian annite; open circle = phlogopite; open circle, x-hair = ferroan phlogopite; tilled circle, dotted = tetra-ferri-annite; open circle, dotted = tetra-ferriphlogopite; open square = polylithionite; filled square = trilithionite; filled square, x-hair = siderophyllite; open square, x-hair = ferroan polylithionite; filled hexagon, x-hair = norrishite; crosses = preiswerkite; open diamond = muscovite; open diamond, xhair = nanpingite; filled diamond = paragonite; filled diamond x-hair = boromuscovite; open triangle up = clintonite; filled triangle up, x-hair = ferrokinoshitalite; filled triangle up = kinoshitalite. The sample arrowed is kinoshitalite by Gnos and Armbruster (2000). For details see text.

middle of the interlayer, respectively. The oxygen atoms were placed at the vertices of an undistorted tetrahedron with a tetrahedral volume equal to that as considered above. A uniform displacement along the [001] direction was then imposed on the basal oxygen atom plane and the electrostatic energy associated with the system was then derived as a function of this displacement. Finally, the displacement which minimizes the electrostatic energy of the system was calculated and compared with the value obtained for a system identical to that described, but differing in the formal charge of the interlayer cation which was arbitrarily set equal to one. Therefore, the model takes into consideration the differences in energy between the two configurations described, not the total energy. The displacement obtained was used to "isolate" the x value from the influence of the divalent interlayer cation. The x values of tetrahedrally disordered brittle micas which was thus "isolated" (i.e., x*) follow the same trend defined for true micas, confirming the influence of interlayer cations on x (Fig. 4). Unlike other models reported in the literature (e.g., Giese 1984), our model introduces only the Coulombic term and does not consider the repulsive energy or van der Waals interactions. This simplification, as Giese (1984) correctly noted, does not produce correct energy values. For this reason, energy differences between structural systems, which are characterized by the same repulsive energy, were considered. The charge at each position was determined from chemical data and from structural constraints.

Mica Cn/stal

Chemistn/

and Influence

ofP-T-X

on Atomistic

Models

116.0

114.0

112.0

110.0

108.0

106.0

104.0

Si (apfu) Figure 4. Relationship between x* and Si tetrahedral c o n t e n t . x* refers to the x value "isolated" from the influence of the interlayer cation for the brittle micas clintonite and kinoshitalite. Regression equation: x* ( , : j = 2.920 x [ 4 I S i + 101.98. r = 0.950. Symbols and samples as in Figure 3.

bond energy [(e")2/ A]

Figure 5. B o n d energy between tetrahedral cation and tetrahedral basal oxygen atoms compared with the bond energy between interlayer cation and tetrahedral basal oxygen atoms. Symbols and samples as in Figure 3.

16

Brigatti & G u g g e n h e i m

Figure 5 relates the bond energy between the tetrahedral basal oxygen atoms vs. tetrahedral cations ((T-Obasai)) and between the basal oxygen atoms vs. interlayer cations ((A-Obasai)), respectively. In brittle mica species, the distance between the tetrahedral cation and the basal oxygen atom plane increases, owing to the interaction with the interlayer cation. In this way the increase in (T-Obasai) bond energy is partly compensated by a decrease in bond energy between the cation and the oxygen atoms of the basal plane. The displacement of the tetrahedral cation from its ideal position can be evaluated (see Appendix I for derivation) from the tetrahedral displacement parameter, Tdisp.: T idisp. --

L i - basal (À)

Figure 7. Plot of x vs. (0-0) b a s a l . Symbols and samples as in Figure 3.

In addition, x reflects an adjustment for the misfit between the tetrahedral sheet and the octahedral sheet (the regression coefficient, r, of x vs. the difference between mean basal tetrahedral edges and mean octahedral triads is r = 0.92). Furthermore, as the mean (O-O) basal distance decreases, the tetrahedral cation moves away from the basal oxygen-atom plane. Thus, x increases in value (Fig. 7). The deviation of the parameters for clintonite and kinoshitalite from the trend for true micas further suggests that there is a significant influence of the interlayer cation on the value of x. In conclusion (i) x increases as the distance between the tetrahedral cation and the basal oxygen-atom plane increases from its ideal value; (ii) x increases as ( O - O ) b a s a i decreases, thus reflecting a dimensional adjustment between the tetrahedral sheet and octahedral sheet; and (iii) x increases with content. Differences between x values of brittle micas from the true micas are related in part to electrostatic features. It is useful to understand why the tetrahedral cation moves from its ideal position. Drits (1969) stated that "the position of the tetrahedral cation depends not only on the degree of substitution of Si by A1 in the tetrahedra (Brown and Bailey 1963), but also in the position and distribution in compensating positive charges." This assumption is related to electrostatic forces in the following way (see Appendix I for derivation): -3AE; = - ÜL

icalJ

IS + 2 - d T

Í AE, =

Jo

qT

qT

[t-O

IS/ 2 + d T

q T - ( q

b j

A

/ 4 )

apical

^apical)

IS + 2/3-(T-O a p l c i l )J

qT-(qA/4) •J(lS/2 + (T - 0 a p l c a l ) / 3 ) 2 + ( 0 a p l c a l - 0 a p l c a l ) 2

18

Brigatti & Guggenheim

where qT and qA are the tetrahedral and interlayer charges, respectively; IS is the interlayer separation; dTKob is the distance of the tetrahedral cation from the basal oxygen atom plane; (OapiCai-Oapicai) is the distance between apical oxygen atoms; and T-OapiCai is the distance between the tetrahedral cation and apical oxygen atom. Ei relates the electrostatic energy between the tetrahedral cation and the basal oxygen atoms. E2 is the electrostatic energy between the tetrahedral cation and interlayer cation. E3 considers the repulsion between tetrahedral cations of two opposing tetrahedra across the interlayer (Fig. 8). AEi (AE?, AE3) is the variation of Ei (E?, E3) values in the actual structure and in an ideal structure with the tetrahedral cation ideally spaced from the basal and apical oxygen atoms. AEi, AE2, and AE3 were derived by considering the set of charges represented in Figure 9. This specific arrangement of charges was developed to describe the electrostatic interactions between the basal oxygen atoms of the tetrahedron and interlayer cation. All planes of atoms (i.e., the plane of interlayer cations, the plane of basal oxygen atoms and the plane of tetrahedral cations) can be described through a rigid displacement of the simple charge distribution in Figure 9, thus the energy involving the oxygen-atom plane differs, to a first approximation, from the energy related to the distribution in Figure 9 by just a scale factor. The objective of our model is to describe the factors influencing the interlayer cation displacement from its "ideal" position. However, we consider the difference in energy between the actual structure configuration and that characterized by a tetrahedral cation-basal oxygen atom plane distance, which is equal to (T—Oapicai)/3. All terms in energy which do not include that distance, are therefore excluded in this derivation because they must be equal in both the configurations considered. In conclusion, differences in energy among configurations which vary for very small displacements of charge can be very useful. Our model considers van der Waals and repulsion energies equal in both configurations to simplify the calculation. 0.20

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 AE! [(e ) 2 / A ] Figure 8. Relationship between AE2 + AE3 vs. AEj. For the definition of energy E 1; E2, and E3> see text. Regression equation [(AE2 + AE3) = -1.099 AEJ + 1.26 x 10~3; r = 0.997). Symbols and samples as in Figure 3.

Mica Cn/stal Chemistn/ and Influence ofP-T-X

on Atomistic

Models

19

Figure 9. The set of charges used to derive AEi, AE2, and AE3.

Figure 8 clearly shows that an increase in the electrostatic energy associated with an increase in the tetrahedral cation-basal oxygen atom distance is compensated by a reduction in the repulsion between the interlayer cation and the tetrahedral cation and the tetrahedral-tetrahedral cations (sited in adjacent layers). Given the high correlation coefficient (r = 0.997), the relation may be useful as a predictive tool. The basal oxygen atom plane corrugation effect (Ar) produces an out-of-plane twisting of tetrahedra about the bridging basal oxygen atom in the [110] tetrahedral chain and a shortening of the distance between apical oxygens along the octahedral edge parallel to the (001) plane. Lee and Guggenheim (1981) demonstrated that the corrugation of the basal oxygen atom plane reflects differences in distance between apical oxygen atoms linked to octahedra of different size. Thus A: is limited in trioctahedral micas with M ( l ) « M(2) in size, whereas it shows higher values in dioctahedral micas with M ( l ) » M(2) in size. Differences in A: are related to the linkage of the tetrahedral sheet by apical oxygen with octahedral sites different in size. A strong relationship between A: and AM [AM = ( M - 0 ) m a x - (M-0) m i n ] for a structure is evident in Figure 10. This result confirms that differences in octahedral site dimensions play an important role over tetrahedral basal oxygen-plane corrugation [regression equation: Ar ( A) = 0.647 x AM; r = 0.984]. Figure 11 shows the effect of A1 octahedral content ( [ 6 Al) on AT. Where [61A1 occupancy is less than 1 apfu, A: is approximately zero (trioctahedral true and trioctahedral brittle micas). In trioctahedral Li-rich micas (polylithionite, trilithionite and siderophillite) and in preiswerkite, [61A1 occupancy is nearly 1 apfu and A: is as large as 0.15 A. A A: of

w

=2.581 + 8.836-10"

x

m

A l + 0.164

[41

Fe

whereas the mean length of the octahedral triads is well fitted by the following expression ([61A1, [61Fe2+ in apfu, r = 0.940): (0-0>„[lla,e,M(i> = 0 and EMi2l,M(i> = 0 correspond to C'2/m symmetry. Symbols as in Figure 19 (from Brigatti et al. 2000b).

occupied by a cation whose average charge is smaller and whose average size is larger than that found in M(2), was detected for kinoshitalite, ferrokinoshitalite and clintonite (see the "new species and new data" section). Anandite-20, (Ba0.96K0.003Na0.01)(Fe;;o:Feo:,1Mgo.45Mni;o4Mno;o4)(Fe-;:,sSi 2.62)OloSo.84Clo.l6Fo.04(OH)o.96, has octahedral Fe-Mg ordering with two Fe-poor octahedra near the cell comers and two Fe-rich octahedra near the C-face center (Filut et al. 1985). The Fe-Mg ordering requires that hydroxyl groups are associated with the Fe-poor octahedra, whereas S replaces (OH) in the Fe-rich octahedra. Bityite-2Mi, (Ca0.95Na0.02)(Li0.55n0.45Al2.04Fe(;;i)(All.34Si2.02Be0.64)Ol0(OH)2, has the trans-M(l) site occupied by Li and vacancies, and the two ci',s-M(2) sites are occupied by Al cations (Lin and Guggenheim 1983). Coexistence of dioctahedral [with M(1 (-vacant sites] and trioctahedral [with Li-filled M(l) sites] sheets was suggested to explain the two patterns of O-H vector orientation. The topology of each octahedron is influenced not only by local composition but also by the constraints of closest packing within the sheet. Several authors (e.g., Toraya 1981; Lin and Guggenheim 1983; Weiss et al. 1985, 1992) examined the relationships between composition and the octahedral topology (i.e., variations in the octahedral dimensions and in octahedral distortions). In agreement with the observation of Hazen and Wones (1972), who suggested that octahedral flattening is controlled by the octahedral cation radius, Toraya (1981) suggested for IM silicate and germanate micas, that the octahedral flattening angle, y , gradually decreases with decreasing misfit between the tetrahedral and octahedral sheets. He noted also that the tetrahedral lateral dimensions remain constant. Toraya also showed that the degree of octahedral flattening,

Mica Cn/stal Chemistn/ and Influence ofP-T-X

on Atomistic

Models

33

which reflects variations in octahedral thickness and lateral octahedral dimensions, is related to lateral misfit between the sheets of tetrahedra and octahedra and, therefore, by a . Lin and Guggenheim (1983) related the counter-rotation of upper and lower octahedral oxygen triads (the co angle of Appelo 1978) to the difference between the ( M ( l ) - O ) and ( M ( 2 ) - 0 ) distances. They demonstrated that y is significantly affected by the field strength of adjacent octahedral cations and less affected either by the octahedral cation size or by the misfit between the tetrahedral and octahedral sheets. They also observed that octahedral flattening and octahedral counter-rotation produce opposing effects. Octahedral flattening increases mean values of the upper and lower triads, and thus increases lateral dimensions of the octahedra, whereas the overall effect of counterrotation is the reduction of the lateral octahedral size. Weiss et al. (1985) also showed that octahedral flattening and the counter-rotation of the upper and lower anion triads are related to the interaction in the "whole" sheet rather than an individual octahedron, and suggested geometrical models to predict the octahedral topology by composition.

63.0

62.0

O f? D • i t D • •

61.0

° ^>

•

60.0

59.0

A

0

"

.

mi*

*

®

58.0

57.0 2.000

2.050

2.100

2.150

2.200

2.250

2.300

(A) Figure 21. Variation of \|/ Mill vs. (M(l)-O) bond distance. Symbols and samples as in Figure 3.

Figure 21 shows the variation of y vs. the mean bond distance for the trans M ( l ) site. Both y and (M( 1 ) - 0 ) increase from trioctahedral micas to dioctahedral micas. As noted previously, the distortion of an octahedral site is not a simple function of the size of the cation residing in the octahedron. In fact, distortions in the vacant site in dioctahedral micas and in the M( 1) site in Li-rich micas are caused by the decrease in length of the shared edges of the M ( l ) octahedron with respect to the mean edge value of M(l). M ( l ) is required to share edges with smaller adjacent octahedra containing cations with high field strength. In Figure 21, plotted values for the trioctahedral micas (excluding Li-rich) show scatter, but the general trend suggests that y decreases as the site size increases. From a geometrical point of view (in space group C2!m), a displacement of 0(4) along [001] affects each octahedron in the same way, i.e., ( M ( l ) - O ) and ( M ( 2 ) - 0 ) mean bond

34

Brigatti & Guggenheim

0(4) t Oct.

C

d 1

Figure 22. (a) \|/ = cos toct / 2(M-0); (b) deformation induced on M ( l ) by a displacement of the 0(4) oxygen atom along the [001] direction; (c) deformation induced on M(2) by a displacement of the 0(4) oxygen atom along [001] direction; (d) deformation produced on octahedra by a displacement in (001) plane which produces the Cl!m symmetry requirement.

distances decrease equally, whereas \|/m(d and \|/m(2) values increase equally [modes (b) and (c), Fig. 22]. Differences between M(l) and M(2) are explained by mode (d) (Fig. 22), with a displacement of the 0(4) atom toward M(2). In this way, the (M(l)-O) distance, and the \|/m(d value increase at nearly two times the rate at which (M(2)-0) and yM(2) decrease. Mode (d), therefore, does not affect (M-O) [(M-O) = «M( l)-O) + 2 x (M(2)-0))/3] and (y) [(y) = (\|/m(d + 2x \|/m(2))/3] mean values. The results provided by the geometrical model (see Appendix I) can be compared to the trend observed for the structures in Figure 23. The parameter otcor (i.e., the difference between the value of the observed octahedral thickness and the thickness of an ideal octahedron whose edge is equal to S(0-0)msharcd) is defined here as:

JL

°t cor - °t - ^ • (O - O }unshaiecl where ot is the observed octahedral thickness and E (O-O)unshared is the mean value of the M( 1 )and M(2) unshared edges [i.e, the mean octahedral triad value: £ (0-0)msharcd = ((O-OXmsharedMd) + 2 X (O-OXmsharedMR))^]. The resulting equation of regression is = -34.352-otcor/ 2(C)—0}unshared + 54.779 (r = 0.982). The trend in Figure 23 indicates that the y mean value depends nearly entirely on the displacement of the 0(4) atom along the [001] direction. The first-order constant in the regression equation (i.e., -34.352) is greater than the calculated value from the

Mica Cn/stal Chemistn/

and Influence ofP-T-X

on Atomistic

Models

35

60.0

59.5

A V

58.0

-0.14

-0.13

-0.12 ot

cor /
o u ter| versus pressure, normalized to their values at room conditions, pg (tilled circles): paragonite (Comodi and Zanazzi 1997): ms (empty circles): muscovite (Comodi and Zanazzi 1995). Subscripts i and o stand for inner and outer: HP and RP for high pressure and room pressure, respectively. (b)|i l m e r- < K-0> o u ter| versus temperature, normalized to their values at room conditions, pg (open circles): paragonite (Comodi and Zanazzi 2000): ms (tilled circles): muscovite (Guggenheim et al. 1987). Subscripts i and o stand for inner and outer: HT and RT for high temperature and room temperature, respectively.

The modest number of experimental studies on the behavior of micas as a function of pressure and/or temperature and the difficulty in the experiments that leads to lack of precision, make a statistically reliable comparison between trioctahedral and dioctahedral micas difficult. The main differences between the two originate from the octahedral sheet behavior. Differences between the two forms would be expected between the rearrangements of the 2:1 layers uponP and/or T. Based on the current data, and assuming a K-bearing interlayer sheet, the following conclusions can be drawn: 1. Dioctahedral micas are less thermally stable, and have larger bulk thermal expansion than trioctahedral micas, presumably as a consequence of the vacant Ml site.

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2. Dioctahedral micas have a slightly larger bulk modulus than trioctahedral micas (i.e. are slightly stiffer), because of the presence of trivalent cations instead of divalent cations in octahedral coordination. This produces a larger polyhedral bulk modulus (Hazen and Finger 1982).

Na(pg)x

Na(mu) Figure 6. Bulk modulus as a function of interlayer cation size, calculated using the interlayer chemical composition. Na(Pg): paragonite (Comodi and Zanazzi 1997); Na(mu): Na-rich muscovite (Comodi and Zanazzi 1995); K(phl): phlogopite (Hazen and Finger 1978); K(mu): K-muscovite (Comodi and Zanazzi 1995); Cs(Cs-tfa): Cstetra-ferri-annite (Comodi et al. 1999); Rb(Rb-tfa): Rb-tetra-ferri-annite (Comodi et al. 2001).

K(phl)

Rb(Rb-tfa) K(mu)

Cs(Cs-tfa)

_i 1.4

J 1.8

2.0

ionic radius (A)

ACKNOWLEDGMENTS We are grateful to Steve Guggenheim for reviewing this chapter and for his comments on the manuscript. REFERENCES Abbott RN (1994) Energy calculations bearing on the dehydroxylation of muscovite. Can Mineral 32:87-92 Ahrens TJ (1987) Shock wave techniques for geophysics and planetary physics. ln\ CG Sammis, TL Henyey (eds) Methods of experimental physics, p 185-235. Academic Press. San Diego. CA Ahsbahs H (1987) X-ray diffraction on single crystals at high pressure. Prog Crystal Growth and Charact 14:263-302 Aleksandrov KS. Ryzhova TV (1961) Elastic properties of rock-forming minerals. II. Layered silicates. Izv Acad Sci USSR. Phys Solid Earth. Engl Transl 1165-1168 Amisano Canesi A. (1995) Studio cristallografico di minerali di altissima pressione del complesso Brossasco-Isasca (Dora Maira Meridionale): PhD dissertation. University of Torino Amisano Canesi A. Ivaldi G. Chiari G. Ferraris G (1994) Crystal structure of phengite-3 T\ thermal dependence and stability at high P/T. Abstracts 16th General Meeting IMA. Abstr, 10 Anderson OL (1995) Equations of state for geophysics and ceramic sciences. Oxford University Press. Oxford. U K Anderson OL and Isaak DG (1995) Elastic constants of mantle minerals at high temperature. In Mineral Physics and Crystallography: A Handbook of Physical Constants. Ahrens TJ (ed) A G U Reference Shelf 2 Angel RJ (2001) Equations of state. Rev Mineral Geochem 41:35-59 Angel RJ. Downs RT. Finger LW (2001) Diffractometry. Rev Mineral Geochem 41:556-559 Barnett JD. Block S and Piermarini GJ (1973) A n optical fluorescence system for quantitative pressure measurement in the diamond-anvil cell. Rev Sci Instrum 44:1-9 Birch F (1986) Equation of state and thermodynamic parameters of NaCl to 300 kbar in the hightemperature domain. J Geophys Res 83:1257-1268 Bridgman P W (1949) Linear compressions to 30.000 kg/cm 2 , including relatively incompressible substances. Proc A m Acad Arts Sci 77:189-234

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and High

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Catti M, Ferraris G, Ivaldi G (1989) Thermal strain analysis in the crystal structure of muscovite at 700°C. Eur J Mineral 1:625-632 Catti M, Ferraris G, Hull S, Pavese A (1994): Powder neutron diffraction study of 2M\ muscovite at room pressure and at 2 GPa. Eur J Mineral 6:171-178 Chung DDL, De Haven PW, Arnold H, Ghosh D (1993). X-ray diffraction at elevated temperatures, VCH Ed., New York Comodi P, Zanazzi PF (1995) High-pressure structural study of muscovite. Phys Chem Minerals 22:170177 Comodi P, Zanazzi PF (1997) Pressure dependence of structural parameters of paragonite. Phys Chem Minerals 24:274-280 Comodi P, Zanazzi PF (2000) Structural thermal behavior of paragonite and its dehydroxylate: A hightemperature single-crystal study. Phys Chem Minerals 27:377-385 Comodi P, Zanazzi PF, Weiss Z, Rieder M, Drabek M (1999) Cs-tetra-ferri-annite: High-pressure and hightemperature behavior of a potential nuclear waste disposal phase. Am Mineral 84:325-332 Comodi P, Drabek M, Montagnoli M, Rieder M, Weiss Z, Zanazzi PF (2001) Pressure-induced phase transition in a n e w synthetic Rb-mica. FIST-Geoitalia2001, Chieti, Sept. 5-8 2001 Donnay G, Donnay JDH, Takeda H (1964) Trioctahedral one-layer micas. II. Prediction of the structure from composition and cell dimensions. Acta Crystallogr 17:1374-1381 Duffy TS, Wang Y (1998) Pressure-volume-temperature equations of state. Rev Mineral xx 425-457 Faust J, Knittle E (1994) The equation of state, amorphization, and high-pressure phase diagram of muscovite. J Geophys Res 99:19785-19792 Flux S, Chatterjee ND, Langer K (1984) Pressure induced [4] (Al,Si)-ordering in dioctahedral micas? Contrib Mineral Petrol 85:294-297 Franzini M (1969) The A and B layers and the crystal structure of sheet silicates. Contrib Mineral Petrol 21:203-224 Guidotti CV (1984) Micas in metamorphic rocks. Rev Mineral 13:357-467 Guggenheim S, Chang YH, Koster van Groos AF (1987) Muscovite dehydroxylation: High-temperature studies. Am Mineral 72:537-550 Giiven N (1971) The crystal structures of 2Mi phengite and 2Mi muscovite. ZKristallogr 134:196-212 Hazen RM and Finger LW (1978) The crystal structures and compressibilities of layer minerals at high pressure. II. Phlogopite and chlorite. Am Mineral 63:293-296 Hazen RM and Finger LW (1982) Comparative Crystal Chemistry. John Wiley and Sons, New York. Hewitt DA, Wones DR (1984) Experimental phase relations of the micas. Rev Mineral 13:357-467 Hogg CS, Meads RE (1975) A Mossbauer study of thermal decomposition of biotites. Mineral Mag 40:7988 Holzapfel WB (1996) Physics of solids under strong compression. Reports Progress Phys 59:29-90 Jackson I and Rigden SM (1996) Analysis of P-V-T data—Constraints on the thermoelastic properties of high pressure minerals. Phys Earth Planet Int 96:85-112 Jeanloz R (1988) Universal equation of state. Phys Rev B 38:805-807 Kumar M (1995) High pressure equation of state for solids. Physica B 212:391-394 Kumar M and Bedi SS (1996) A comparative study of Birch and Kumar equations of state under high pressure. Phys Stat Sol B 196:303-307 Mazzucato E, Artioli G, Gualtieri A (1999) High temperature dehydroxylation of muscovite-2M]: a kinetic study by in situ XRPD. Phys Chem Minerals 26:375-381 Mookherjee M, Redfern SAT, Hewat A (2000) Structural response of phengite 2M\ to temperature: an in situ neutron diffraction study. EMPG VIII, Bergamo, April 16-19, Abstracts, p 75 Moriarty JA (1995) First-principles equations of state for Al, Cu, Mo and Pb to ultrahigh pressures. High Press Res 13:343-365 Muller F, Drits VA, Plangon A, Besson G (2000a) Dehydroxylation of Fe 3+ , Mg-rich dioctahedral micas: (I) structural transformation. Clay Minerals 35:491-504 Muller F, Drits VA, Tsipursky SI, Plangon A (2000b) Dehydroxylation of Fe 3+ , Mg-rich dioctahedral micas: (II) cation migration. Clay Mineral 35:505-514 Pavese A, Ferraris G, Prencipe M, Ibberson R (1997) Cation site ordering in phengite-3 T from the DoraMaira massif (western Alps): a variable-temperature neutron powder diffraction study. Eur J Mineral 9:1183-1190 Pavese A, Ferraris G, Pischedda V, Ibberson R (1999a) Tetrahedral order in phengite-2M] upon heating, from powder neutron diffraction, and thermodynamic consequences. Eur J Mineral 11:309-320 Pavese A, Ferraris G, Pischedda V, Mezouar M (1999b) Synchrotron powder diffraction study of phengite 3T from the Dora-Maira massif: P-V-T equation of state and penological consequences. Phys Chem Minerals 26:460-467

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Pavese A, Ferraris G, Pischedda V, Radaelli P (2000) Further powder neutron diffraction on phengite-3 T\ cation ordering and methodological thoughts. Mineral Mag 64:11-18 Pavese A, Ferraris G, Pischedda V, Fauth F (2001) Ml-site occupancy in 3T and 2M\ phengites by low temperature neutron powder diffraction: Reality or artefact? Eur J Mineral (in press) Poirier JP, Tarantola A (1998) A logarithmic equation of state. Phys Earth Planet Int 109:1-8 Rancouxt DG, Turne P, Lalonde AE (1993) Kinetics of the (Fe2++ OH-) m i c a -> (Fe 3+ +0 2 ~) m i ca + H oxidation reaction in bulk single-crystal biotite studied by Mössbauer spectroscopy. Phys Chem Minerals 20:276-284 Russell RL, Guggenheim S (1999) Crystal structures of near-end-member phlogopite at high temperature and heat treated Fe-rich phlogopite: the influence of the 0 , 0 H , F site. Can Mineral 37:711-720 Sassi F P, Guidotti C, Rieder M, De Pieri R (1994) On the occurrence of metamorphic 1M\ phengites: some thoughts onpolytypism and crystallization conditions of 3T phengites. Eur J Mineral 6:151-160 Saxena SK, Zhang J (1990) Thermochemical and pressure-volume-temperature systematics of data on solids, examples: tungsten andMgO. Phys Chem Minerals 17:45-51 Sekine T, Rubin AM, Ahrens TJ (1991) Shock wave equation of state of muscovite. J Geophys Res 96:19675-19680 Shinmei T, Tomioka N, Fujino K, Kuroda K, Irifune T (1999) In situ X-ray diffraction study of enstatite up to 12 GPa and 1473 K and equation of state. Am Mineral 84:1588-1594 Smyth JR, Jacobsen SD, Swope RJ, Angel RJ, Arlt T, Domanik K, Holloway JR (2000) Crystal structures and compressibilities of synthetic 2M1 and 3T phengite micas. Eur J Mineral 12:955-963 Symmes GH (1986) The thermal expansion of natural muscovite, paragonite, margarite, pyrophyllite, phlogopite, and two chlorites: The significance of high T/P volume studies on calculated phase equilibria. B.A. Thesis, Amherst College, Amherst, Massachusetts Takeda H and Morosin B (1975) Comparison of observed and predicted structural parameters of mica at high temperature. Acta Crystallogr B31:2444-2452 Tripathi RP, Chandra U, Chandra R, Lokanathan S (1978) A Mössbauer study of the effects of heating biotite, phlogopite and vermiculite. J Inorg Nucl Chem 40:1293-1298 Tutti F, Dubrovinsky LS, Nygren M (2000) High-temperature study and thermal expansion of phlogopite. Phys Chem Minerals 27:599-603 Udagawa S, Urabe K, Hasu H (1974) The crystal structure of muscovite dehydroxylate. Japan Assoc Mineral Petrol Econ Geol 69:381-389 Utsumi W, Weidner DJ, Liebermann RC (1998) Volume measurements of MgO at high pressure and temperature. In MH Manghnani, Y Yagi (eds) Properties of Earth and Planetary Materials at High Pressure and Temperature, p 327-334, Am Geophys Union, Washington, DC Vaughan MT, Guggenheim S (1986) Elasticity of muscovite and its relationship to crystal structure. J Geophys Res 91:4657-4664 Velde B (1980) Cell dimension, polymorph type, and infrared spectra of synthetic white micas: the importance of ordering. Am Mineral 65:1277-1282 Vinet P, Ferrante J, Smith JR, Rose JH (1986) A universal equation of state for solids. J Phys C 19:L467L473 Vinet P, Smyth JR, Ferrante J, Rose JH (1987) Temperature effects on the universal equation of state of solids. Phys Rev B 35:1945-1953 Vinet P, Rose JH, Ferrante J, Smyth JR (1989) Universal features of the equation of state of solids. J Phys Cond Mater 1:941-1963 Wallace DC (1972) Thermodynamics of Crystals. John Wiley and Sons, New York. Zhang L, Ahsbahs H, Hafner S, Kutoglu A (1997) Single-crystal compression study and crystal structure of clinopyroxenes up to 10 GPa. Am Mineral 82:245-258 Zanazzi PF (1996) X-ray diffraction experiments in (moderate) high-P / high-T conditions; high-P and high-T crystal chemistry. High Pressure and High Temperature Research on Lithosphere and Mantle Materials. Proc Int'l School Earth Planetary Sei, Siena, December 3-9, 1995, p 107-120

3

Structural Features of Micas Giovanni Ferraris 1 and Gabriella Ivaldi 2 l2

' Dipartimento di Scienze Mineralogiche e Petrologiche Università di Torino 10125 Torino, Italy and Istituto di Geoscienze e Georisorse Consiglio Nazionale delle Ricerche 10125 Torino, Italy ferraris@dsmp. unito, it

ivaldi@dsmp. unito, it

INTRODUCTION The large number of mica species (end-members) and varieties is based on chemical variability and peculiar structural features like polytypism, local and global symmetry. In addition, mainly because of an inherent misfit between the constituent tetrahedral and octahedral sheets, in the specific mica structures several structural parameters undergo adjustments relative to their ideal values. Consequently, the mechanisms ruling distortions from ideal models must be considered when investigating a mica behavior under geological conditions. Micas are important rock-forming minerals and petrographers consider them mainly for their chemical aspects. The importance of the chemical composition is well known to all researchers dealing with minerals. To give emphasis to the chemical composition, the official classification of the micas (Rieder et al. 1998; Rieder 2001) allows exceptions (note the introduction of 'species that are not end member' in Rieder et al. 1998) to the rules which are normally used to define mineral species (Nickel and Grice 1998). However, as shown throughout this book, the role of structure features (including some aspects of polytypism) in determining fields of stability of micas and, therefore, in providing geological insights, is increasingly recognized as crucial. Thus, it seems justified that a chapter dedicated to the description of the general structural background of micas should be presented independently from specific cases, which are discussed in other chapters. This chapter is an introduction to the symmetry and geometric aspects of micas. Nevertheless, some less conventional topics not covered in other chapters are reported in appendices. Appendix I concerns the wide presence of mica-like modules in the growing group of natural, layer titanosilicates (Khomyakov 1995; Ferraris et al. 2001b,d) and other more or less exotic structures belonging to the expanding field of modular crystallography (Merlino 1997). Important results have been obtained by the obliquetexture electron diffraction method (OTED; cf. Zvyagin et al. 1996, and references therein). Only a few, limited treatments are in English. Thus, this method is discussed in Appendix II. NOMENCLATURE AND NOTATION Bailey (1984c) recommended a notation system for structural sites in micas. However, there is no agreement to the labeling of these sites; e.g., either an italic or roman font is used with or without parentheses to separate the alphanumeric parts. Following recent papers (Nespolo et al. 1999c: Nespolo 2001) and in agreement with the chapter of Nespolo and Durovic (this volume), the nomenclature of the OD theory of polytypes (Dornberger-Schiff et al. 1982; Durovic 1994) is here adopted to label sites, 1529-6466/02/0046-0003S05.00

D01:10.2138/rmg.2002.46.03

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planes, sheets and layers. Emphasis is given to symmetry aspects more than to structural and chemical features. Thus, rather than to a distinction between dioctahedral and trioctahedral micas, preference is given to a classification in homo-octahedral, mesooctahedral and hetero-octahedral families according to the layer symmetry [H(3)lm, P(3)lm and P(3)12; see Table 1 below] of the octahedral sheet in the TOT or 2:1 layer, here referred to as the M layer. Two types of M layers are introduced according to the position of the origin assigned to the reference system in the octahedral sheet: layer M l if the origin is in the octahedral trans site Ml, and layer M2 if the origin is in the octahedral cis sites Ml or M3. Trans and cis refer to the position of the OH groups (cf. Fig. 5 below). The distinction between M l and M2 is necessary also because of the different role played by these two types of layer in generating polytypes (Nespolo 2001). The introduction of the notation M l and M2 for the M layer follows directly from the letter "M" which is previously used to indicate the TOT layer (e.g., Takeuchi and Haga 1971), before the existence of two types of layer was recognized. Because the roman font is reserved for the layer, we adopt the italic font to indicate the octahedral sites, namely Ml, Ml and Mi. For the ordinal label 1, 2 and 3 see the below "Structural symmetry" below. Summarizing: roman font is used for planes (cf. Fig. 2 below), sheets (O octahedral, T tetrahedral) and layers (M, TOT); italics font is used for structural sites (M octahedral, T tetrahedral) and cations occupying them ( 7 octahedral, Z tetrahedral, /interlayer). MODULARITY OF MICA STRUCTURE Thanks to the pioneering paper on the biopyribole polysomatic series by Thompson (1978), the structure of micas, together with those of amphiboles and pyroxenes, lead to the development of the modern modular description of the crystal structures. According to the modular crystallography principles (Merlino 1997), the same structural modules (fragments) larger than single coordination polyhedra may occur in different structures. The emphasis on modules is not only important in describing series, it is also useful in describing aspects ranging from a single structure to classification, genesis, solid state reactions (e.g., Baronnet 1997; Ferraris et al. 2000), structural modeling, and defect structures (cf. chapter by Kogure, this volume). Micas are layer silicates (phyllosilicates) whose structure is based either on a brucite-like trioctahedral sheet [Mg(OH)2 which in micas becomes Mg304(0H)2] or a gibbsite-like dioctahedral sheet [Al(OH)3 which in micas becomes Al204(0H)2]. This module is sandwiched between a pair of oppositely oriented tetrahedral sheets. The latter sheet consists of Si(Al)-tetrahedra which share three of their four oxygen apices to form a two-dimensional hexagonal net (Fig. 1). In micas, the association of these two types of sheet produces an M layer, which is often referred as the 2:1 or TOT layer. As mentioned in the Introduction, the wide variety of micas (Rieder et al. 1998) derives not only from chemical composition but also from structural features such as the many (infinite, in principle) possibilities of stacking the M layer, particularly the special type of polymorphism known as polytypism, discussed by Nespolo and Durovic (this volume). The mica module The mica module, consisting of an M (TOT or 2:1) layer plus an interlayer cation, is conveniently considered to be built by eight atomic planes in the following sequence, starting from the bottom in Figure 2. • •

Obi Lower (I) plane of the basal (b) oxygen atoms (O) belonging to the tetrahedra; these oxygen atoms also participate in the coordination of the interlayer cation I. Z; Lower plane of the four-coordinated tetrahedral cations Z (these cations are

Structural Features of Micas

119

often indicated by T, but here this letter is used to indicate a tetrahedral site T and a tetrahedral sheet T). Oai Plane of the lower apical (a) oxygen atoms of the tetrahedra; these oxygen atoms are shared between one tetrahedral and one octahedral sheet. The O a i plane contains also hydroxyl (OH)" groups (and their substitutions) which belong only to the octahedral sheet. Y Plane of the octahedral cations Y which are often indicated by M (here this letter is used to indicate an octahedral site M and the M layer; the symbol O is used to indicate the sheet containing the M sites). O mi Plane of the upper (u) apical oxygen atoms (O a ) of the tetrahedra (cf. O „;). Z„ Upper (u) plane of the tetrahedral cations (cf. Z ; ). 0 b„ Upper (u) plane of the basal (b) oxygen atoms (Ob) belonging to the tetrahedra (cf. (>••). 1 Plane of the interlayer cations I (interlay er sites).

Figure 1. Ideal trioctahedral brucite-like (a) and dioctahedral gibbsite-like (b) sheets. Two ideal tetrahedral sheets (c) share their apical oxygen atoms with an octahedral sheet to ±orm an M layer (d) which is also known as 2:1 or TOT layer. Hydroxyl (OH)" groups are represented by black circles.

Planes are combined to form three types of sheets: Ob + Z + Oa form two tetrahedral sheets (T; and T„); O a + Y + O a form one octahedral (O) sheet. The whole M mica layer corresponds to the T/-0-T,, (also termed 2:1) sequence; this layer is also called the conventional mica layer and is often designated as the TOT layer. The interlayer cations are located between two successive M layers in the I plane and their coordination is discussed below. The separation between two I planes is about 10 A.

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The apical oxygen atoms and the hydroxyl (OH)" groups forming the O a plane (Fig. 2) are arranged according to a two-dimensional closest-packing of spheres; O a is also called the hydroxyl plane. In this plane, the packing is however not tight; in fact, the spacing between the oxygen anions is about 3.1 A compared to 2.6 A in a typical closestpacking of oxygen atoms (e.g., in olivine or spinel). Between two adjacent hydroxyl planes (Oai and Oa„), the octahedral and tetrahedral sites that are typical of a threedimensional closest-packing of spheres occur (Fig. 3). This type of tetrahedral sites is vacant in micas; the octahedral sites M instead are fully (trioctahedral micas) or partially.

o

o

o

O hu

V Y-

©

©

©

©

°ar z

r o,

Figure 2. Cross-section perpendicular to the M layer of the mica structure seen along [110]. Sequence and labeling of eight distinct building atomic planes are shown. Hydroxyl (OH)" groups are represented by black circles (see text tor explanation of labeling).

0

O

3

®

Q

0

CÎJ> ; OzJ

G»

0

& Ob

)

Q ®

( Oa )

0 ^

( Oa")

( Oa j

Figure 3. Projection of a closest-packing . ill sequence along the planes formed by apical oxygen atoms ( Positions of the octahedral (Ai) and tetrahedral (small circles) sites are shown. These tetrahedral sites are not occupied in the octahedral sheets of micas.

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Figure 4. Stacking of two closest-packing planes of spheres (plane A dark gray, plane B light gray) consisting of oxygen atoms and (OH)" groups. The primitive hexagonal cell (. f = . I,,) and the conventional C-centred orthohexagonal cell [(a, b) in the CI orientation according to Arnold (1996)] normally used tor phyllosilicates are shown. Cells are shown also for a closest-packing of equal spheres [smaller (ah, bh) cells]. Each ?z-th plane of spheres (e.g. B) is ±a/3 staggered relative to the (iz-l )-th plane (A). The interstitial sites between the spheres appear either as open holes or as gray 'triangles'. Each interstice is surrounded by three packing spheres in its plane; between the two planes A and B tetrahedral and octahedral sites occur (Fig. 3).

(dioctahedral micas) occupied by 7cations. Note (Fig. 4) that in the Oa plane each (OH)" group is surrounded by six oxygen ions which, in turn, are surrounded by three (OH)" groups, and three oxygen atoms. The distances (~2.7 A) between the anions within the basal Oj plane are closer to the expected value for a closest-packing of oxygen ions (~2.6 A). However, relative to real closest-packing, the Oi, plane shows vacancies. In tact, this plane can be formally derived from a closest-packing of spheres by removing one third of the spheres which, otherwise, in a (001) projection would occupy the center of the hexagonal rings (Fig. 1). The same configuration of the Oi, plane is obtained by removing the (OH)" groups in Figure 4. The Oi, plane shows ideal closest-packing without vacancies if the maximum value (30°) of the ditrigonal rotation occurs (cf. the paragraph "Ditrigonal rotation" and Fig. 8 below). Closest-packing and polytypism The pseudo-closest-packing feature of the Oa planes is key to the understanding of widespread polytypism of micas (Bailey 1984a). A plane closest-packing of equal spheres (Fig. 4) is based upon a plane hexagonal Bravais lattice with cell parameter ah which is equal to the diameter of the packed sphere. In the plane, each sphere is in contact with six translationally equivalent spheres and two translationally independent sets of small vacant sites; each of these two sets (open circles and gray 'triangles' in Fig. 4) contains three translationally equivalent vacant sites. To maintain a closest-packing arrangement in three dimensions, the stacking of two successive planes of spheres (A and B) implies that the upper plane (e.g., B) is staggered (shifted) in such a way that its spheres overlie one set of vacant sites belonging to the lower plane (A). Owing to the hexagonal symmetry in the plane, six equivalent staggers are possible along six directions separated by 60° (cf. Ferraris 2002).

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The possibility of multiple staggering is the basis for different periodicities along c, a structural aspect known as polytypism (Verma and Krishna 1966). In the case of micas (and, generally, of phyllosilicates) there are two types of packing spheres: oxygen ions and (OH)" groups. A larger, orthohexagonal C-centered cell (a,b) must be chosen, as shown in Figure 4, and the typical closest-packing stagger between O a ; and Omi corresponds to an ±a/3 shift (intralayer stagger). Note that, in module, the parameter a in micas corresponds to the parameter bh of the orthohexagonal cell in a standard closestpacking plane of equal spheres. The ±a/3 stagger between Oai and Oau reflects in the mutual postion of the T; and T„ sheets as shown in Figure 5. Particularly in K-micas (Radoslovich 1960) and in dioctahedral micas (Bailey 1975) the intralayer stagger may slightly differ from ±a/3. This effect is related either to the size of the / cation or to the distortion of the vacant Ml site, as defined below.

Figure 5. Reference axes ill the M layer plane. Hydroxyl (OH)" groups are represented by black circles. The OH groups are in Trans position in A/1 and in cis position in A/2 and A/3. The stagger (offset) ±a/3 between lower and upper T sheets is shown. The T\u and Tin tetrahedra are translationally independent; the same for the A/1. A/2 and A/A octahedra.

To build the crystal structures of the mica polytypes, the M layer is stacked along c in steps of about 10 A. Commonly, at least in the homo-octahedral (i.e., all octahedra are equal in content and size; cf. below) approximation, the derivation of the mica polytypes is achieved by considering rotations between adjacent M layers (Smith and Yoder 1956) rather than stacking directions. These rotations are performed around the normal to the layer and leave the layer unchanged if multiples are of 60°. The insertion between two O¿, planes of interlayer cations / is possible only if each (ideally) hexagonal ring of the atomic plane Os,„ belonging to the /7th layer, faces an (ideally) hexagonal ring of the plane O« belonging to the (n+l)th layer. Because this structural requirement can be achieved by different relative rotations between two adjacent layers, different mica polytypes are possible. COMPOSITIONAL ASPECTS Ideally, the crystal-chemical formula of micas can be written as /(73..rDr)[Z40io]^2

Structural Features of Micas

123

(Rieder et al. 1998). Labels represent the following chemical elements and groups [the commonest elements and groups are shown in bold face and their ionic radii (A) according to Shannon (1976) are given in parentheses]. • 1 = Cs, K (1.38), Na (1.02), NIL,, Rb, Ba, Ca (1.00), • . • 7 = Li (0.76), Fe2+ (0.78), Fe3+ (0.645), Mg (0.72), Mn2+, Mn3+, Zn, Al (0.535), Cr, V, Ti (0.605), Na (unpublished results on the occurrence of an analogue of tainiolite with octahedral Na instead of Li). In the crystal-chemical formula, the coefficient 3-x together with the symbol of vacancy ( • ) means that in principle the occupancy of the octahedral sheet (O) can span from 2/3 (x = 1, dioctahedral micas) to all the available sites (x = 0, trioctahedral micas). Actually, not many exampfes of intermediate di/trioctahedral micas are known. Some of the examples might leave doubts on their 'intermediate' nature because of unsatisfactory chemical (cf. below) and/or structural data. A 2M 2 lepidolite with (Lio.35Alo.10no.55) in Ml (Takeda et al. 1971) and a Li-Berich mica bityite with (Lio.55Do.45) in Ml (Lin and Guggenheim 1983) should be true octahedrally intermediate micas. Cases as the Ail-deficient Li-rich micas refined by Brigatti et al. (2000), where the maximum vacancy in Ml is 0.23, look more like octahedrally-deficient trioctahedral micas than intermediate di-/trioctahedral micas. On chemical basis only, a Si-rich mica with slightly less than two Y cations has recently been reported (Burchard 2000). • Z = Be, Al (0.39), B, Fe34" (0.49), Si (0.26), Ti (?) (no vacancies have been reported). • A = CI, F, OH, O, S (no vacancies have been reported). It should be noted that: 1. The same site may be occupied (either in an ordered or a disordered way) by different ions. 2. At least two elements (Al and Fe3+) may occupy both octahedral and tetrahedral sites; as mentioned above, Na is reported also in octahedral coordination. 3. The same element (e.g., Fe) may be present in different oxidation states. 4. Most of the recent chemical data are obtained by electron microprobe analysis; consequently, they are often incomplete because oxidation state, light elements and water (hydrogen) are not analyzed [cf. Dyar (this volume) and Pavese et al. (2002) for a recent case of synergic use of neutron-diffraction data and Mossabauer spectroscopy]. Features 1-4 imply that the crystal-chemical formula of a mica cannot be established on the basis of a chemical analysis only (even if it is complete); detailed structural knowledge is necessary. Structurally, the occupancy of a site can be obtained by combining chemical constraints (chemical analysis) with other information like the following. Scattering power of a site (Sp). If a site is fully occupied by two elements with scattering power S\ and S2 and occupancy x and l-x, respectively, the distribution of the elements can be obtained by solving the equation Sp = x51 + (l-x)52. This procedure cannot be applied without further information when (1) vacancy and/or more than two elements occur in the same site; (2) the difference in the scattering power is small as, with X-ray diffraction, in the common cases of substituting elements differing by only one electron (Na-Mg, Mg-Al, Al-Si, Mn-Fe). If suitable wavelengths are available (e.g., synchrotron radiation) anomalous scattering may be used to recognize different atoms that randomly occupy the same site. For case (2), neutron-diffraction data would represent the best solution; but, for powder-diffraction data, cf. a discussion in Pavese et al. (2000). Note that the occurrence of stacking faults in the structure may create peculiar problem in the refinement procedure (Nespolo and Ferraris 2001).

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Distributions of the bond lengths. Good quality structural data allow the use of the average bond length of a coordination polyhedron to determine quantitatively the fraction of occupying atoms. In micas, a reasonable determination of the tetrahedral Si (x a ) and A1 (xA!) fractional contents as a function of the average tetrahedral bond lengths (Z-0) av can be obtained by the equation (Z-0) av = 0.163 \xaiA x® + xAi )] + 1.608 (Hazen and Burnham 1973; cf. Brigatti and Guggenheim (this volume) for an equation which also takes into account tetrahedral Fe). SYMMETRY ASPECTS Metric (lattice) symmetry Because of the pseudo-closest-packing nature of the atomic planes mentioned above, the two-dimensional Bravais lattice of both the T and the O sheets (Fig. 1), idealized and undeformed according to the Pauling (1930) structural model of micas, is hexagonal 6mm. Both sheets can be described in terms of a primitive hexagonal lattice, defined by two hexagonal axes A\ and A2, or of a C-centered orthohexagonal lattice defined by the two shortest perpendicular translation vectors, a and b, between which the orthohexagonal relation b = a^l3 ideally holds (Fig. 5; Nespolo et al. 1997a, 1998). The two-dimensional lattice of the real sheets, as well as of the whole M layer they form, is no longer hexagonal. The A\ and A2 axes are no longer exactly identical in length and their interaxial angle is no longer exactly 120°: they define a lattice that is only pseudo-hexagonal and corresponds to a centered rectangular lattice whose a and b axes only approximately obey the orthohexagonal relation b = a^3. Structural symmetry The T sheet In an ideal T sheet (Fig. 1), the tetrahedra are regular polyhedra and their centers (Z cations) coincide with the nodes of a hexagonal plane lattice; the corresponding point group symmetry is 6mm. The layer symmetry (X-symmetry) of this sheet is P(6)mm; the symmetry of the direction without periodicity, which is perpendicular to the layer, is shown in parentheses according to the layer group notation (Dornbenger-Schiff 1959). In each T sheet there are two translationally independent tetrahedral sites (Fig. 5). On the whole there are four T sites in the M layer: Tlu, T2u, Til and Til (u = upper; I = lower). Following Bailey (1984), tetrahedral sitesin the upper sheet that, in the (001) projection, are at -1/3[010], +1/3[310] and -1/3[310] from the upper OH group are labeled 71, whereas those at +1/3[010], -1/3[310] and +1/3[310] are labeled 72. The same definition applies to the lower T sites with respect to the lower OH group. The O sheet. In the O sheet (Fig. 5) the number of translationally independent M sites is three: one site (Ail) has two (OH)" groups in trans configuration, whereas the other two sites (Ml and MS) have two (OH)" groups in cis configuration. The definition of Ml and Mi is however not straightforward. Bailey (1984c) suggested labeling M3 the site on the left of the (pseudo)-mirror plane, but most authors have labeled that site as Ml. Here we retain the definition prevailing in the literature, calling Ml (MS) the site with negative (positive) y coordinate in the layer-fixed reference, namely on the left (right) of the (pseudo)mirror plane looking down the positive direction of the c axis. Families of micas according to the symmetry of the O sheet. The type of occupancy (number of electrons in the site, if the exact cation composition of the site is unknown) of the three M octahedral sites defines the three following families of micas as introduced by OD theory (Dornberger-Schiff et al. 1982; Durovic 1994). The X-symmetry of the O sheet is different in the three families (Table 1): homo-octahedral family (the three M sites have the same cation occupancy), meso-octahedral family (two M sites are identical,

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125

one is different), and hetero-octahedral family (the three M sites are differently occupied). The distinction in three families is based on structural features and reflects the symmetry of the O sheet; it is operatively determined on the basis of the number of electrons filling each of the three M sites, and it is used by the OD theory to fix unequivocally the origin in the layer. Table 1 contains a comparison of the common division of the mica families into tri- and dioctahedral classifications.

Table 1. Families of micas based on the symmetry of the octahedral sheet. Comparison with dioctahedral and trioctahedral classification is given. (Modified after Durovic 1994). Family

Asymmetry

Trioctahedral

Dioctahedral

Homo-octahedral

H[3)\m

•••

—

Meso- octahedral

P(3)lm

Hetero- octahedral

P(3)12

• •A

• • * = different electron occupancy of the M sites; • = vacancy

Dioctahedral/trioctahedral distinction. As mentioned above, the O sheet of micas is traditionally described with reference to the minerals brucite (brucite-like sheet or trioctahedral sheet, namely homo-octahedral sheet) and gibbsite (gibbsite-like sheet or dioctahedral sheet, namely meso-octahedral sheet). This description is helpful to emphasize the modular nature of the mica layer; however, whereas the brucite-like sheet corresponds to the highest symmetry (homo-octahedral), the gibbsite- sheet does not correspond to the lower symmetry, being only meso-octahedral. Symmetry of the O sheet. The plane point group symmetry of thejdeal O sheet (Fig. 1) is 3m (a subgroup of 6mm) and its layer-symmetry is either H{'i)\m (brucite-like sheet) or P(3)lm (gibbsite-like sheet). In fact, the symmetry of the two types of octahedral sheets differs at least for the following reasons. 1. In the ideal brucite-like sheet (Fig. 1) all the octahedral sites are metrically equivalent; each oxygen atom has coordination number three and the O-H bonds of the hydroxyl (OH)" groups are perpendicular to the sheet. 2. In the ideal gibbsite-like sheet (Fig. 1) only 2/3 of the octahedral sites are occupied by the same cation and the other 1/3 is vacant; each oxygen atom has coordination number two and the O-H bond is parallel to the sheet and directed towards the vacant site. Symmetry of the M layer. Because Oai and Oau correspond to two successive planes of a (pseudo)-closest-packing of spheres, Tl and Tu of an M layer are ±a/3 staggered (Fig. 5); consequently, both in the brucite-like and in the gibbsite-like case, the X-symmetry of the entire M layer is lowered to C12/m(l). Symmetry and cation sites Mainly because of a dimensional misfit between the T and O sheets (cf. below), in real mica structures the Pauling model (in which there are no structural distortions) is too abstract and must be replaced at least by a model which takes into account a rotation of the tetrahedra within the (001) plane. This ditrigonal rotation is discussed below; the resulting model has been called the trigonal model by Nespolo et al. (1999c).

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In the homo-octahedral family, the three M sites are by definition identical in content and size. Any difference in one of the M sites violates the H centering, lowering the symmetry of the O sheet to that of the meso-octahedral family. A difference between the other two M sites destroys also the inversion center and lowers the symmetry of the O sheet to that of the hetero-octahedral family. From the practical viewpoint, differences among the M sites are often small and must be evaluated on statistical grounds. As discussed by Bailey (1984c) for the specific case of micas [cf. an application in AmisanoCanesi et al. (1994)], if io](OH)2. Therefore, besides ditrigonal rotation, the chemical composition can contribute to match the dimensions between the T and O sheets. As seen in the paragraph "Compositional aspects," whereas in the T sites practically only Al and Si (sometimes Fe3 ) can occur, a larger variety of cations, with octahedral ionic radii ranging from 0.535 A (Al) to 0.76 A (Li), can occur in the M sites. An appropriate distribution of cations can therefore favor the fitting between T and O sheets. The introduction of chemical substitutions at least in part contributes to various types of polyhedral distortions. These, besides the discussed ditrigonal rotation, are classified here below (Fig. 10). Some specific structural reasons for the appearance of

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133

Figure 10. Definition of the octahedral flattening (\|/), octahedral thickness (/..). tetrahedral elongation (x), tetrahedral tilting (Ar) and octahedral counter-rotation (o) which is related to as shown in the text.

these distortions are given here but more details can be found in Brigatti and Guggenheim (this volume). Tetrahedral elongation. This distortion is also known as tetrahedral thickening and implies an expansion for the tetrahedra in the direction perpendicular to the T sheet and a lateral compression (Radoslovich and Norrish 1962). The effect is measured by the angle x = E,_i,3(Oj-r-O a ), /3 (Tidcai = 109.47°). It is particularly active in dioctahedral micas where it is related to the presence of the vacant octahedral site (Lee and Guggenheim 1981). Tetrahedral tilting. Practically, this distortion is only found in dioctahedral micas because is caused by a great difference between the sizes of the octahedral sites. The tetrahedra rotate around a direction parallel to the (001) plane detennining a departure from coplanarity of the Os oxygen atoms (out-of-plane tilting). This tilting produces a corrugation of the basal plane which is measured by the parameter = [-OS(max) - -0«min)]csilip.

Octahedral flattening (or thickening). This distortion is measured by the angle y between the body diagonal and the base of the octahedron (Domiay et al. 1964). Given the thickness t0 of the O sheet and the average octahedral distance (7-0), y is calculated as y = cos_1[?o/(2 (7-0))]. Because yideai = 54.73°, a flattening results in a larger value of y ; vice versa for a thickening. Counter-rotation co. This distortion (Newnliam 1961) is measured as the angle of rotation between the two triangular octahedral faces parallel to (001) belonging to the same octahedron; it is calculated by co = |(s i + 8 3 + 8 5)/3 - 60°| = (82 + 84 + 8 s)/3 - 60°| (CDidcai = 60° and 0°). The angles s, correspond to the O-YO angles measured in the projection of the octahedron onto (001); in a regular octahedron s, = 60°. Generally, for all micas this effect is related to the difference in size of neighboring octahedra (Lin and Guggenheim 1983). These distortions are not independent variables. In tact, besides specific aspects in part mentioned above, all of them are to some extent correlated with chemical substitutions and T/O misfit. Several correlations have been proposed, particularly for the ditrigonal rotation (e.g., Lin and Guggenheim 1983; McCauley and Newnliam 1971; Toraya 1981; Weiss et al. 1985). Effects of the distortions on the stacking mode All the distortions decrease in the order hetero-octahedral > meso-octaliedral > homo-octahedral, because of the corresponding reduction in the size difference of

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different octahedra. All octahedra in micas are more or less distorted (they should thus more rigorously be tenned trigonal antiprisms) and the distortions can be fully described by the flattening y and the counter-rotation co (Weiss and Rieder 1997). It has been shown (Weiss and Wiewiora 1986; Weiss and Rieder 1997) that the ditrigonal rotation is most effective in influencing the diffraction intensities, in particular 20/ and 13/ reflections (i.e., the second ellipse in the OTED described in Appendix II); instead the counter-rotation affects mainly the basal diffractions.

Figure 11. Adjacent basal (), oxygen atoms in the case of 1M and 2O polytypes, that show 0° and 180° rotations between adjacent M layers (left), and (right) of 2Mi, 3T, 2M2 and 6H polytypes where instead the rotation between adjacent M layers is +120= (2AU, 37) or ±60'' (2jI/2 and 6H). The tetrahedral tilting Az (Fig. 10) is exaggerated.

Az and stability of polytypes. The tetrahedral tilting A: seems to have the most marked influence on the relative stability of the IM and 2M\ polytypes, the latter becoming energetically favored when A: increases (Appelo 1978 and 1979, Abbott and Burnham 1988). A general influence of A: * 0 on the relative stability of different polytypes can also be expected on geometric grounds by considering the interlayer configuration (Fig. 11) for different values of the n x 60° rotation between adjacent M layers (Giiven 1971, Soboleva 1987). For polytypes based on 0° or 180° rotations (the MDO polytypes are W and 2O), both the Oj planes delimiting the interlayer region have negative A: in correspondence of the / cation. For polytypes based on ±120° (2M\ and 37) or ±60° (2M2 and 6H) rotations, the two Ob sheets delimiting the interlayer region have opposite signs of Ar in correspondence of the / cation. In presence of a large Ar, the polytypes based on 0° and 180° rotations offer too a large cavity for the / cation and, e.g., 2M\ (but also 37) is favored relative to 1M. At high Ar, (2/7+1) x 60° rotations become favored and the relative stability of 2Mi and 2O seems then to depend on the ditrigonal rotation of the tetraliedra (Bailey 1984c; Abbott and Burnham 1988).

/ •1

r~7\ I\ / \ j• { / j \

\

V

*

;

•

lYj-Jy i/ \ /

k/L B

Figure 12. Stacking of the M octahedral sites for subfamily A and subfamily B polytypes. These sites lie on the same perpendicular to (001) in subfamily B but not in subfamily A polytypes.

Structural Features of Micas

135

Relative rotation of two adjacent M layers. This plays a role in stabilizing polytypes also in connection with the relative positions of the M sites. In fact (Fig. 12), whereas for a 2n x 60° rotation (subfamily A) the octahedral sites in two adjacent M layers are staggered by ±a/3 and thus not overlapped in the (001) projection, in the case of a (2n+l) x 60° rotation (subfamily B) they are staggered ±b!3 and thus lie on the same perpendicular to (001) [Soboleva 1987; cf. also the polytypic stacking discussed in terms of configurations I and II of the octahedral cations in Bailey (1984a)]. Although a direct influence of the relative positions of octahedral cations belonging to adjacent layers is hardly conceivable, because of the large separation (~10 A), the stacking of octahedra along the perpendicular becomes an indirect destabilizing factor through its effect on tetrahedral tilting Az. This would be clear in the case of a hypothetical 2O dioctahedral mica, where the large and vacant octahedral sites would stack on the same perpendicular. As a consequence, tetrahedra on the opposite sides of the / cations are tilted in the same direction, increasing the repulsion between approaching Oj atoms. In the other two MDO subfamily B dioctahedral polytypes (2Mj and 6H), the stacking along a perpendicular alternates vacant and filled octahedral sites, reducing the O4-O4 repulsion with respect to the 2O polytype. Dioctahedral 2M2, although rare, has been found (Zhukhlistov et al. 1973), whereas neither 2O nor 6H have been discovered so far in dioctahedral micas. The complete absence of the 6H polytype in any family of mica likely derives both from energetic factors (e.g., odd rotations) and kinetic reasons (low probability of formation and inheritance of a 6-layer period with hexagonal symmetry; Nespolo 2001). FURTHER STRUCTURAL MODIFICATION Pressure, temperature and chemical influence Generally pressure (P) and temperature (7) have a major influence on the distortions of coordination polyhedra (cf. Zanazzi and Pavese, this volume). The tetrahedral dimensions are the ones least sensitive to P and T, whereas the compressibility and expansion of the octahedra are large, so the fit between tetrahedral and octahedral sheets improves with increasing T (larger O sheet) and worsen with increasing P (smaller O sheet). Therefore, in a first approximation, P and T shows an opposite behavior (Hazen and Finger 1982). The knowledge of the P-V-T equation of state would allow the calculation of the isochor, i.e., the P - r p a t h which maintains constant the cell volume (cf. Pavese et al. 1999b) and, reasonably, also the distortions. For a rough estimate of the isochor, the values of the expansion at constant P (isobar) and of the compression at constant T (isotherm) can be combined (e.g., Comodi and Zanazzi 1995; Mellini and Zanazzi 1989). The main effect of P and T are on the interlayer because the /-Oj bonds are weak. Both the effect of modifying the length of the c parameter and the ditrigonal rotation are discussed below. Note that any change in the T/O match because of P and T variations modifies the ditrigonal rotation and consequently the interlayer coordination. Other sources of change for the /-Oj distances are tetrahedral substitutions (which modify the length I of the tetrahedral edge). Summarizing, for a given I, the parameter c modifies mainly under the following factors: 1. temperature T (expansion —» longer c); 2. pressure P (compression —» shorter c); 3. ditrigonal rotation a (/-Oj distances are modified). Thickness of the mica module As mentioned at the beginning of this chapter, a mica module is intended to consist of an M layer plus the interlayer cation. The use of the module thickness tm = c$m$!n (n is the number of M layers in a unit cell) allows the comparison of data from different polytypes.

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10.02 y = 0.134x + 10.392 9.98

9.94

Figure 13. Decreasing trend of the mica module thickness (top) and ditrigonal rotation a vs the increasing content of Si in 2A/i (rhombi and crosses) and 3 T (open triangles and circles) natural phengitic micas. To obtain a the knowledge of the crystal structure is necessary. The values corresponding to samples with known structure are indicated by rhombi (2U,) and circles (37). The values at 3.8ISi represent the only two synthetic phengites which are included because their crystal structures are known (Smyth et al. 2000). R represents the correlation coefficients of the shown regression lines.

9.90

9.86 2.8

3.0

3.4

3,2

3.6

3.8

4.0

Si 14,0 •

-12.724x + 50.158

12,0

r.2- : 0.84

10.0 •

8.0 6.0

•

4,0 2.0 0.0 2.9

3.1

3.3

3.5

3.7

3.9

Si

Sinking effect of the I cation. The smaller the ditrigonal rotation a, the larger is the more or less hexagonal cavity where the interlayer cation / can sink; consequently a shorter c parameter is expected. This effect has been observed by several authors. Guidotti et al. (2000) noted that a shorter c parameter is observed in the low pressure Fmrich muscovites [Fm = (Fe + Mg)/(Fe + Mg + Al)]. In fact, as expected from the values of the cation ionic radii, the Fm substitution for Al in muscovites (and the parallel Si/Al tetrahedral substitution) improves the T/O fit and, consequently, the ditrigonal rotation a decreases. Massomie and Schreyer (1986, 1989) and, recently, Schmidt et al. (2001) showed, in synthetic phengites, a contraction of the c parameter with the increase of the Si content. Ivaldi et al. (2001a) have found the same result on natural samples (Fig. 13; the thickness of the mica module tm instead of c is used). The ditrigonal rotation a behaves as tm. The decrease of the ditrigonal rotation a with the increase of the Si content is well explained by the improvement of the fit between the tetrahedral and octahedral sheets promoted by the aluminoceladonitic substitution (Mg for VIA1 and Si for IVA1). By decreasing a, more-hexagonal rings occur in the Os plane where the interlayer cation can sink.

Structural Features of Micas

137

Figure 14. A shift a (exaggerated) of the basal plane O b from the full line to the dashed line position reduces more (CD) the /-(),.„..,, distances than (AB) the /-( ) ,. , , ,, ones.

Interlayer separation and coordination. Ferraris and Ivaldi (1994b) showed that a variation of the interlayer separation influences the outer I-O b distances more greatly than the inner I-O b distances. This geometric effect appears clear in Figure 14. Therefore, an 'at first sight unexpected' behavior occurs under variation of P and/or T: the I-Obfimm-> distances, which represent shorter and thus stronger bonds, change by far more than the IOb(outa) ones, which instead represent longer and thus weaker bonds.

Figure 15. Undistorted (a) hexagonal ring of a T sheet showing that all basal (), atoms have the same distance DA = / from the ring center /): I) represents the intersection of the drawing plane with the perpendicular to the ring. In a ring (b) with maximum ditrigonal rotation a, the inner (), atoms are closer {DC = 1131/2) to D than the outer (), atoms {DB = 2//31/2). The values of the internal ring angles are related to a as follows: BCB' = 120° + 2a, CBC' = 120° - 2a.

Ditrigonal rotation and interlayer coordination In presence of the ditrigonal rotation, six Os basal oxygen atoms are closer to (inner Ob oxygens) and six are farther from (outer Ob oxygens) the interlayer cation I. By increasing a from its minimum value (0°, absence of distortion) to its maximum value (30°), the distance d of the Ob oxygen atoms from the perpendicular to the layer containing /, expressed as a function of the tetrahedral edge /, changes (Fig. 15) from d = I to dimler = //31'" and d0UKr = 2//31'2. In other words, while the Obpmier) atoms decrease their undistorted distance from the perpendicular by (djimer - d)!d = -42.3%, the Ob(outa-) atoms move very little and increase the same distance by (d0UKr - d)/d = 15.5%. Therefore, the consequence of the ditrigonal rotation on the interlayer coordination is dramatic. Precisely:

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Ferraris & Ivaldi

Increase of the ditrigonal rotation. An increase of a (e.g., under compression) causes the difference between I-Ob(outer) and I-Ob(inner) distances to become larger. Thus both the trigonal antiprismatic (ideally octahedral) coordination (subfamily A polytypes such as 1 M , 2M\ and 3T ) and the trigonal prismatic coordination (subfamily B polytypes such as 2O, 2M2 and 6H) become more dominant. As far as the antiprismatic coordination is a stabilizing factor, the increase of the ditrigonal rotation at high P should not weaken a structure. Decrease of the ditrigonal rotation. A decrease of a (e.g., under expansion) causes the difference between I-Ob(outa-) and I-Ob(mner•> distances to become smaller: the interlayer coordination approaches the hexagonal prismatic coordination for both polytype subfamilies A and B. As far as the antiprismatic coordination is a stabilizing factor, the decrease of the ditrigonal rotation at high T should weaken a structure. Note that, under the combined causes which influence the 7-Oj distances and discussed above, overall decreases of the I-Ob(mner) has been reported in high-temperature refinements of micas (Catti et al. 1989, Guggenheim et al. 1987; Ivaldi et al. 1998; Russel and Guggenheim 1999; Takeda and Morosin 1975). Effective coordination number (ECoN) ECoN is a useful generalization of the classical definition of coordination number (number of anions in contact with a cation); it considers the lengths of the bonds (Hoppe 1979). For a cation X establishing R(X)j bonds with equal anions, ECoN is defined as [Nespolo et al. (1999a) on the basis of Hoppe et al. (1989)]: ECoN(X) = 25exp{l - [R{X),/R{X)avfy,

(1)

R(X)av represents a weighted average bond distance for the coordination polyhedron around the cation X and is defined as RaV(X) =£iR(X)iSxp{l

- [RWJRW^Ps/Zexpil

-

(2)

R(X)min being the shortest R(X)i distance (the exponent 6 is valid when the anion is O2")The sum over i is in principle extended to all the oxygen atoms; practically, however, note that the contribution falls to zero as R(X)t exceeds R(X)av [Eqn. (1)] or R(X)min [Eqn. (2)] by more than about 20%. ECoN defined by Equation (1) is a non-integer number approaching the Pauling's coordination number (i.e., the number of first neighbor anions) and equal to it for regular coordination polyhedra where R(X)j = R(X)av = R(X)min. Recently the method has been extended to distorted and hetero-ligand polyhedra (Nespolo et al. 2001). A correlation between ECoN calculated for the interlayer cation / and the ditrigonal rotation a can intuitively be expected from the discussion of this section. Such correlation has been investigated by Weiss et al. (1992) and found to be quite regular (Fig. 16). In fact, ECoN for / smoothly decreases from about 12 (null ditrigonal rotation) to 6 (for a ditrigonal rotation higher than about 16°). CONCLUSIONS Even if the discussion is still open, the basic features of the mica structure reasonably explain a wide range of the micas properties, from polytypism and twinning (Nespolo et al. 1997b; Nespolo et al. 1999b; details in Nespolo and Durovic', this volume) to chemical variability and stability in a range of geological conditions. The matter of stability fields is of paramount interest in Earth sciences and concerns both the occurrence of a polytype more than others and the capability for a mica of existing at high P and/or T values. For a list of references to occurrences of associated polytypes of

Structural Features of Micas

139

X Figure 16. Correlation between ECoN (effective coordination number) of the interlayer cation I and the ditrigonal rotation a in micas. [Modified afier Weiss et al.

(1992)].

5

10

15

20

a'

micas; cf. Ivaldi et al. (2001b) and Ferraris et al. (2001c). The following basic structural features play a role in structure stabilization. 1. The type of interlayer coordination, which is connected with the parity n of rotation (ti x 60°) between adjacent M layers, justifies a wider occurrence of family A polytypes (not limited to the MDO polytypes 1M, 2M\, 37) which show even rotations only. The amount of rotation between two adjacent M layers influences the relative stability of polytypes independently of the parity n. 2. A phengitic composition favors stability at high PIT values because the aluminoceladonitic substitution provides a good T/O fit and consequent small ditrigonal rotation a at high PIT also. 3. The argument of a small ditrigonal rotation a cannot stand alone (cf. the trioctahedral micas). It becomes effective as stabilizing factor at high P for dioctahedral micas because other aspects concur as: (1) the O-H bond points towards the vacant octahedral site and assumes a direction (almost) parallel to (001) thus minimizing its interaction with the interlay er cation; (2) the presence both of a pair of independent tetrahedral sites and of independent Ml and M3 octahedral sites in the 3Tpolytype which, with phengitic composition, is the most stable form of mica at high PIT. 4. In trioctahedral micas, the O-H bond is pushed away from the (001) Oi, plane and tends to lie along the perpendicular to this plane. Thus, some repulsive interaction with the interlay er cation occurs that weaken the stability of the structure. However, in oxidized (e.g., Ohta et al. 1982) or fluorinated micas (e.g., Takeda et al. 1971) this repulsion is reduced proportionally to the O2" -» OH" or F" -» OH" substitution. This is particularly evident in synthetic fluoro-micas (e.g., Takeda and Burnham 1969). 5. Geometric effects connected with the variation of the ditrigonal rotation a and of the interlayer separation are as important as energetic factors in determining the variation of the interlayer bonds under compression, dilatation and effects in a that produce changes in the coordination (i.e., sinking effect) of the interlayer cation. 6. The presence of two types of M layer, M l and M2, may play a role in the growth of long period polytypes (Nespolo 2001).

140

Ferraris & Ivaldi APPENDIX I: MICA STRUCTURE AND POLYSOMATIC SERIES

Layer silicates as members of modular series? The T and O sheets occurring in the mica structure are present in all layer silicates (phyllosilicates); the entire M (TOT) mica layer is present in 2:1 layer silicates only. The description of layer silicates is often given by emphasizing different stacking of T and O sheets, even if an explicit discussion in terms of modular series is absent from the literature. Several types of modular series have been defined (Makovicky 1997): Polysomatic (homologous accretional) series. The crystal structures of the members of these series are based on the same modules. Biopyriboles are a well known example (Thompson 1978). Merotypic series. Both common and peculiar modules are present in the crystal structures of the members. The case of bafertisite-derivative structures, belonging to the heterophyllosilicate group of titanosilicates, is described below. Plesiotypic series. The crystal structures of the members of these series are based on modules which have common features but may contain additional peculiar details. The family of serpentine-like structures (lizardite, chrysotile, antigorite, carlosturanite) is an example reported by Makovicky (1997). The members of this plesiotypic series are based on variously curled, reversed and/or interrupted TO (serpentine) layers. From a topologic viewpoint, namely without considering the actual composition of the M layer but only that of the interlayer, the following modules are necessary to obtain all the structures of the 2:1 layer silicates: 1. three types of M layer: homo- meso- and hetero-octahedral layers; 2. interlayer modules of different chemical and structural nature ranging from single cations (micas), to octahedral sheets (chlorites) and a mixture of layers and various chemical groups (interstratified clay minerals). The entire group of layer silicates could therefore be classified as a mero-plesiotypic series in the sense that both structural details and nature of the building modules varies. Mica modules in polysomatic series The M mica module occurs not only in biopyriboles, chlorites and interstratified clay minerals as mentioned above, but also in some other polysomatic series. Because these series represent different possibilities for the presence of mica-like structures in minerals, it seems useful to shortly describe some of them. The heterophyllosicate polysomatic series By analogy with phyllosilicates, a group of titanium silicates whose structures are based on TOT-like layers have been called heterophyllosilicates (Ferraris et al. 1997). In these structures, rows of Ti(Nb)-octahedra (hereafter, Ti-octahedra) are introduced in a T sheet along the direction which is parallel to a pyroxene tetrahedral chain (Fig. 17). HOH layers are thus obtained where H stands for hetero to indicate the presence of the Tioctahedra in a sheet corresponding to the T sheet of the layer silicates. Because the edges of the Ti-octahedra and Si-tetrahedra have close lengths dimensions, the insertion of the octahedra in a T sheet does not produce strain. As summarized by Ferraris (1997), three types of HOH layers (Fig. 18) are known so far. Bafertisite-like (HOH) B layer. A bafertisite module B, / 2 74[Ti2(0)4Si40i4](0,0H) 2 , is one-to-one intercalated with a one-chain-wide mica-like module

Structural Features of Micas

141

Figure 17. Different types of H sheets which are obtained by periodically introducing Ti-octahedra (light gray) in a tetrahedral T sheet: batertisite-like (B), astrophyllite-like (A) and nafertisite-like (N) H sheets.

M,/73[Si4Oi0](O,OH)2 (I and 7 represent interlayer cations and octahedral cations, respectively). Astrophyllite-like (HOH) i layer. With respect to the bafertisite-like layer, a second one-chain-wide mica-like module M is present between two bafertisite-like modules. Nafertisite-like (HOH^tv layer. With respect to the bafertisite-like layer, a second and a third one-chain-wide mica-like module M are present between two bafertisite-like modules [or, a second M module is added to (HOH),J. The series. Bafertisite (Guan et al. 1963, Pen and Shen 1963, Rastsvetaeva et al. 1991), astrophyllite (Woodrow 1967) and nafertisite (Ferraris et al. 1996) are members of a polysomatic series BmM,i which is based on B (bafertisite-like) and M (mica-like) modules and has a general formula /2+„74+3„[Ti2(O)4Si4+4„Oi4+i0„](O,OH)2+2„. In the formula, atoms belonging, even in part, to the H sheet are shown in square brackets; for n = 0,1 = Ba and 7 = (Fe,Mn) the tbnnula of bafertisite is obtained. The heterophyllosilicates have also been described by using differently defined B and M modules (Christiansen et al. 1999), a possibility which is not rare in modular crystallography (Merlino 1997).

142

Ferraris & Ivaldi

N

Figure 18. Baiertisite-like (B), astrophyllite-like (A) and nafertisite-like (N) HOH layers.

Seidozerite derivatives. The bafertisite-like module (HOH)g is the building fragment of several layer titanosilicates (seidozerite or bafertisite derivatives; Ferraris et al. 1997) where only the interlayer content varies. These titanosilicates are B^Ig members of the heterophyllosilicate series with a peculiar interlayer content. They are represented by the formula XT4[Ti2(0)4Si40i4](0,0H) ? , where X indicates the interlayer content which may consist of H2O, tetrahedral anions and cations. All the seidozerite derivatives are based on a common two-dimensional (sub)cell with a ~ 5.4 A and b~ 7 A, whereas the value of the stacking c parameter depends on the nature of X. The set of seidozerite derivatives forms a merotype [or mero-plesiotype (Ferraris 2001d) series]. In the seidozerite derivatives, (HOH)g represents the common building layer and the X inter-layer content is variable. The palysepiole polysomatic series The palysepiole polysomatic series PpSs (Ferraris et al. 1998) includes minerals whose structures contain one or both the types of TOT ribbons (modules) which are present in palygorskite and sepiolite; these ribbons are reminiscent of the TOT modules occurring in amphiboles (Fig. 19). The two modules are: • P = ^4 x (7 2+ ,i^ + ,n) 5 [Si8O20(OH)2] - «H2O (palygorskite module; in palygorskite 7 i s mainly Mg and n ~ 8); •

5 = 4(7 2+ ,^ + A)8[Sii2O30(OH)4]-mH2O (sepiolite mainly Mg and m ~ 12).

module;

in sepiolite ¥ is

The structures of sepiolite and palygorskite are based on chess-board arranged [001] T O T ribbons and intercalated channels. Each ribbon occurring in sepiolite, (TOT)s, is six pyroxene-chain wide and 50% wider than that occurring in palygorskite, (TOTIP, which in turn is four pyroxene-chain wide. A variable amount of alkali A cations and water molecules occurs in the channels. The third known mineral of the group, kalifersite, corresponds to the member P1S1 of the series and has formula K5(Fe73+,n2)[Si2o05o(OH)6] • 12H 2 0. Its structure is based on an alternation, in the [010] direction, of (TOT)s and (TOT)/, ribbons. Each of two types of [001] channels, which occur within the mixed palygorskite/sepiolite framework, is filled with a different strip of alkali-octahedra (not shown in Fig. 19).

Structural Features of Micas

P

SBHSSI

143

K Figure 19. View along [001] of the crystal structures of palygorskite (P), kalifersite (K) and sepiolite (S). Kalifersite is based on a chessboard arrangement of ribbons (TOT), (sepiolite) and (TOT)p (palygorskite). Cations and water molecules occurring in the channels are not shown.

Other modular structures Guggenheim and Eggleton (1987, 1988) described some modular 2:1 layer silicates in terms of fragments of the M (TOT) mica module, with or without interlayer cations. The modularity of these silicates originates by the inversion of part of the tetrahedral linkage. On the basis of the inversion fragments, the basic TOT layers may form either islands (e.g., stilpnomelane and zussmanite) or strips (where the octahedral sheets remains continuous as in ganophyllite and mimiesotaite, or discontinuous as in the above mentioned palysepioles). Conclusions TOT modules occur in different mineral structures and the following examples have been discussed in this Appendix. • Infinite two-dimensional layers occur in micas, talc, pyrophyllite, chlorites and interstratified clay minerals. • Slices of the mica (talc) structure cut perpendicularly to the layer are present in amphiboles and palysepioles; they are inclined on the layer in heterophyllosilicates, according to the description of Ferraris et al. (1996). It seems reasonable to connect variety and frequency of occurrence with structural stability. The wide range of conditions under which the TOT layer is stable on its own occurs in talc and pyrophyllite, built up by this layer only. The TOT layers are even able to survive through reactions generating other minerals [cf. Baromiet (1997) and Buseck (1992) and references therein] including other micas (cf. Ferraris et al. 2001a). Probably features other than crystal chemistry concur to explain the wide distribution and persistence of variously sliced mica modules. The high symmetry of the mica modules could be a key feature, in the sense that it favors different stacking and connections with other modules both of the same kind and different nature. Mica polytypes and twins are clear examples of symmetry-assisted structures. The flexibility of

144

Ferraris & Ivaldi

the T and O sheets and of the TOT layer as a whole has been widely discussed in this chapter. This flexibility is usefully exploited to match mica modules with other modules, a role which can be played also by closeness of polyhedral dimensions (cf. the heterophyllosilicates case). APPENDIX II: OBLIQUE TEXTURE ELECTRON DIFFRACTION (OTED) In addition to powder X-ray (Bailey 1988) and single-crystal X-ray diffraction methods, electron diffraction is widely used to characterize micas. In particular, the oblique-texture electron diffraction (OTED) method here described has been used to obtain important results from micro grained samples of layer silicates (cf. references below). A part some earlier sporadic papers, the OTED method was developed by Vainshtein (1956, 1964), following Pinsker (1953), and further improved during following years (Zvyagin 1967, Zvyagin et al. 1979, Vainshtein et al. 1992, Zvyagin et al. 1996). OTED has been used to obtain diffracted intensities for solving crystal structures (cf. quoted papers and Zhuklilistov et al. 1997), spite of the dynamic effects affecting the electron diffraction intensities. In the present context, however, we are interested in the application of OTED for polytype identification and follow Zvyagin (1967). The method is suitable for materials that show a very good cleavage where thin mounts can be prepared so that the cleavage planes are more or less perfectly parallel to the plane of the mount. c' c'

Figure 20. Cylindrical reciprocal lattice generated by rotation of reciprocal lattice rows around c* (left) and its elliptical intersection with the Ewald sphere (right) which, in the case of electron diffraction (only small Bragg angles are possible), can be approximated by a plane. At right, the effect of a non perfect planarity of the sample is shown by substituting the circles of the left figure with tori; the intersection of a torus with the Ewald sphere is an 'arc' (Fig. 22). Modified after Zvyagin (1967).

Let us suppose that the exploited cleavage is {001} and the cleavage lamellae are textured in a planar mount so that their orientations have a common perpendicular to (001), i.e., around c*. Under these conditions, each reciprocal row hkl (h and k are fixed) parallel to c* describes a so called cylindrical reciprocal lattice (Fig. 20). The nodes with the same hk indices are at a distance [(h/af + (k/b)~]m from c*. All the circles have their center on the rotation axis but not at the corresponding 00/ node, except when the lattice is orthogonal. The projection of these circles on the ab plane is shown in Figure 21 together with the hk

Structural Features of Micas

145

Figure 21. Distribution in the ab plane of the hkl reflections on concentric circles with radius [{h/af + (k//>)' | 1 '' in the case of a lattice with b = in1as occurs in layer silicates. Modified after Zvyagin (1967).

indices for the case of those layer silicates where the relations b = a^l3 holds. These circles correspond to the orbits which are defined in Figure 16 in the chapter by Nespolo and Durovic (this volume) in connection with the S, D and X classification of the rows (cf. below). However, whereas the orbits are the loci containing S, D or X rows with their individual nodes, in the cylindrical lattice one circle carries intensity contributed by all hkl nodes falling on that circle. Because of the small electron wavelength ( ~ 1 A ) and a substantial diffraction intensity limited to quite small Bragg angles around the incident beam, the Ewald sphere can locally be approximated by a plane. For a given inclination angle

(2)1

(2)1

(6)1

(6)1

- .,

,.

..,,

[ . . . ( . ) 2 . .]

2[310]

(2-p'),- ••>(2-j'),(2-i')

(4-p),.

••>(4-j),(4-i)

[• 2 . ( . ) • • • ]

2[iio]

< 1 - P %

(5-P),.

..,,

[ . . . ( . ) . .

2[oio]

[2 • • ( • ) • [ . . . ( . ) .

• •] 2

2]

and ipooi coincide with a and b axes respectively (y = 90°). To improve the clearness of the figure, the , , of the other three planes that would be equivalent in a truly hp lattice are not shown, but they can be easily traced (modified after Nespolo and Ferraris 2000).

Only the two-fold rotation about c of the twin lattice is a correct twin operation, in the sense that it restores the lattice, or a sublattice, of the individuals. If however coi^ 0, the c axis of the twin lattice is no longer exactly perpendicular to the (001) plane and the above rotations are defined only with respect to c* and not to c: none of them is thus a correct twin operation. The rotations about c* give simply the (approximate) relative rotations between pairs of twinned mica individuals, but are not true twin operations. Similar considerations apply also to the rotoinversion operations, s depends upon the obliquity of the twin but, at least in Li-poor trioctahedral micas, is sufficiently small to be neglected for practical purposes (Domiay et al. 1964; Nespolo et al. 1997a,b, 2000a). In Table 11 the complete scheme developed above is summarized for ease of consultation. Effect of twinning by selective merohedry on the diffraction pattern The above analysis does not consider the case of selective merohedry, which does not appear in the morphology of the twin but influences the diffraction pattern by relating lattice nodes corresponding to present reflections from one individual to nodes corresponding to non-space-group absences from another individual. Twinning by either syngonic or metric merohedry (for the definitions, see Appendix A) does not modify the geometry of the diffraction pattern. Instead, twinning by selective merohedry, i.e. when the twin operation belongs to the point group of the twin lattice but not to the point group of the family structure, produces an unusual diffraction pattern. The typical case is that of the 3Tpolytype orthogonal Series 1 subfamily A, space-group type P3i,2l2, which has an hP lattice. As shown above, the family structure is rhombohedral and the family reflections (S and D rows) obey the presence criterion / = iV"/2/3(mod N'). With respect to

Crystallographic Basis of Polytypism and Twinning in Micas

t. ¿i -a

i f| §)8 "H 3

tO 0 1 s 'S o •S- a SS Bg CO

S

N

CL,

c s

1

CÖ o

0O a (N

^ 13 8 •S § § «0 MOb$ A Cu © C!j

- 0& s.

X 00

X 00 (N

.g

I f

Crystallographic Basis of Polytypism and Twinning in Micas

227

O £ a> £o, &

?TD O £

?

#8

TD O 6

» ^ -H

Co ¿r> p

Co

á- a l I ) + cp = 60° -cp'

5 Takeuchi et al (1972) defined the vector r as r = mA]+vA2, i.e. with respect to a basis with interaxial angle 60°: correspondingly in the multiplicity of the mesh (Eq. 8) and in the length of the vector (Eq. 9) the term uv has opposite sign. Their definitions of (u, v) and n values correspond to reciprocal lattice values in our treatment. 6

The definition of the angles cp and cp' is given according to Takeuchi et al (1972).

Crystallographic

•°*

0

»

\

Basis of Polytypism

O m Q Q (f Q • • • • • 0*0 0» o • o •

a

and Twinning

in Miens

229

i

S} *oimo

• _ _ o cr:'*'••'• c^ 0 o o • o *b o#o 0»

a0*0» ¿rXPiVV)

A

£

2

ao

o«cv f c Vo t)'vO*OJ» o •o *o . • o* q--, 9a a/mi0/43 • o«o \ • cw o b * o • •'* ' • » ft • '•• • • O O .if O •6 0*i'0m U Q D ¿D 0» >\ cw •.t>»o / • dfc / o• •- O *o * 0 * 0 . (f » o T) \ / • / • • •• • • 0 rf o O^O Q» o * 0 «O / A | 7 * . - c V

k

»>

Figure 22. Overlap of two hp lattices rotated about an axis normal to the plane and passing through the origin by the angle (p of the compound tessellation {3, 6} [13 {3, 6}]. One node out of 13 is restored. Three hexagonal meshes containing each 13 nodes are also shown.

for the compound tessellation {3.6}[13{3.6}].

The relation between cp and cp' is derived taking into account that a node belonging to one set is related to the two nearest nodes of the other set by two reflection lines that intersect at the origin. For the regular tessellation, only one set of six nodes with the same r exists, each node being 60° apart: in this case cp = cp' = 0° (mod 60°). The space-fixed b orthohexagonal axis bisects the angle cp' as defined in Equation (15). The angles between b and the directions (ui,v) (81) and (z/n,v) (8n) are simply given by (Fig. 23): 81 = cp/2 = 30° - cp'/2

811 = -8i(mod 60°) = 81 + cp' = 30° + cp'/2

(16)

230

Nespolo & Durovic

In reciprocal space, nx 60° rotations relate nodes on the same type of row and of the same set (S; Di, Du, Xi, Xn); instead, non-crystallographic rotations relate nodes on the same type of row but of different sets (Di and Du; Xi and Xn) and do not restore nodes of the same set (cf. Fig. 16). If u and v (and thus also h and k) are not co-prime integers (i.e. they have a common factor), or if u+v = 0(mod 3) [i.e. k-h = 0(mod 3)], the lattice constructed on the mesh defined by the compound tessellation is multiple. The same lattice is described by a primitive mesh with smaller multiplicity and corresponding to u and v co-prime integers and u+v * 0(mod 3) Table 13 shows the features of compound tessellations {3, 6}[n{3, 6}] to r = 100Ä [Eqn. (12) assuming a = 5.3Ä], each of which describes a coincidence-site lattice (CSL) (Ranganathan 1961): the multiplicity n of its mesh is termed coincidence index or E factor and corresponds to the order of the subgroup of translation defining the twodimensional CSL with respect to the hp lattice. As shown in Table 13, the minimal value of the X factor for the hp lattice is 7 (see also Pleasants et al. 1996). Plesiotwinning If the obliquity is neglected (coy = co± = 0), micas have a hexagonal lattice (orthogonal polytypes) or sublattice (non-orthogonal polytypes). The twin lattice coincides with the lattice of the individual (orthogonal polytypes) or with its (pseudo)hexagonal sublattice (non-orthogonal polytypes) and can be described through the regular tessellation {3,6}. A different kind of oriented crystal association occurs, although less frequently, whose lattice is based on one of the compound tessellations {3, 6}[n{3, 6}], and thus has been termed plesiotwinning, from the Greek 7tXscno \(n>l for the hp lattice). The twin/plesiotwin index is thus 1 (twinning by merohedry)

Crystallographic Basis of Polytypism and Twinning in Micas

231

Table 13. Values of u, v (y=120°), //. K (y=60°) and corresponding angles (mod 60°) for the compound tessellation {3,

6}\n{3,

6}] up to r =

100A (assuming a = 5.3A).

n

r(Â)

Set

(«, v)

(H,K)

9

9'

81

1*

5.3

I, II

(1,1)

(1,1)

0°

0°

0°

0°

7

14.0

I II

(1,3) (2,3)

0,2) (2,1)

21°47'

38°13'

10°54'

49°06'

13

19.1

I

(1,4) (3,4)

0,3) (3,1)

32°12'

27°48'

16°06'

43054.

II

19

23.1

I

(2,5)

(2,3)

II

(3,5)

(3,2)

13°10'

46°50'

6°35'

53°25'

(1,6) (5,6)

0,5) (5,1)

42°06'

17°54'

21°03'

38°57'

II

(3,7) (4,7)

(3,4) (4,3)

9°26'

50°34'

4° 43'

55°17'

I

(1,7)

44049'

II

(6,7)

0,6) (6,1)

15°ir

22°25'

37035.

I

(3,8) (5,8)

(3,5) (5,3)

16°26'

43034'

II

8°13'

51°47'

I

(4,9)

(4,5)

II

(5,9)

(5,4)

7°20'

52°40'

3°40'

56°20'

I

(2,9)

II

(7,9)

(2,7) (7,2)

35°34'

2 4

17°47'

42°13'

31

29.5

37

32.2

43 49 61

34.8 37.1 41.4

67

43.4

73

45.3

79

47.1

91

50.6

I II I

I

(1,9) (8,9)

0,8) (8,1)

48°22'

11°38'

24°11'

35049'

II I II

(3,10) (7,10)

(3,7) (7,3)

26°00'

34°00'

13°00'

47°00'

I

(1,10) (9,10)

0,9) (9,1)

49035'

10°25'

24047'

35°13'

(5,11) (6,11)

(5,6)

6°or

53059'

27°00'

3°00'

II

(3,11) (8,11)

(3,8) (8,3)

29°25'

30°35'

45°18'

14°42'

40°21'

19°39'

39050'

20°10'

11°00'

49°00'

54°30'

5°30'

5°05'

54°55'

57°27'

2°33'

51°23'

8°37'

34°18'

25042'

25°02'

34°58'

47o29'

12°31'

34o32'

25°28'

42044'

17°16'

18°44'

41°16'

50°38'

9°22'

II I II

97

52.2

103

53.8

109

55.3

127

59.7

133

61.1

139 151

62.5 65.1

o26'

8n

I

(6,5)

I

(2,11)

(2,9)

II

(9,11)

(9,2)

I II

(5,12) (7,12)

(5,7) (7,5)

I

(6,13)

(6,7)

II

(7,13)

(7,6)

I

(1,12) (11,12)

(1,11)

II I II

(4,13) (9,13)

(11,1) (4,9) (9,4)

I II

(3,13) (10,13)

(3,10) (10,3)

I

(5,14)

(5,9)

II

(9,14)

(9,5)

R e g u l a r tessellation {3,6}.

or n (plesiotwinning) for orthogonal polytypes, and 3 (twinning by reticular merohedry) or 3n (plesiotwinning). For coy * 0 or ro± * 0 this description is not modified, but the lattice overlap is only approximated and corresponds to pseudo-merohedry (n = 1) and reticular pseudo-merohedry (n > 1): the rotations normal to S are cp±2s, and do not obey

232

Nespolo & Durovic

the law of Mallard. These rotations are useful to describe the CSL and the corresponding twin/plesiotwin indices but, as shown dealing specifically with twins, they are not correct twin/plesiotwin operations: the latter correspond instead to two-fold axes in the (001) plane or reflection planes almost normal to (001). The plesiotwin axes and plesiotwin planes have higher indices than the twin axes (Table 14). Note that plesiotwin planes correspond to crystal faces usually not developed in micas: consequently, reflection plesiotwins have a probability of occurrence lower than rotation plesiotwins. Table 13, continued 11

nA)

157

66.4

163

61.1

169

6S.9

1S1

71.3

193

73.6

199

74.S

211

77.0

Set

(«, v)

(H,K)

I

(1.13) (12,13)

(U2) (3.11)

II

(3.14) (11,14)

I

(7.15)

(7.8)

II

(S.15)

(S.7)

I

(4.15) (11,15)

(4.11)

II I

II I II I II I II I

217

78.1

223

79.1

229

S0.2

241

247

82.3

83.3

87.2

277

88.2

2S3

89.2

301

92.0

(9.7)

(U5) (14,15)

(U4)

(13.2) (14.1) (3.13) (13.3)

I

(8,17)

II

(9.17)

(S.9) (9.8)

I

(6,17)

(6.11)

II

(11,17)

(11.6)

I

(5,17) (12,17)

(5.12)

II I

(1,16)

(U5)

II

(15,16)

(15.1)

I

(3,17) (14,17)

(3.14)

(7,18) (11,18)

(7.11)

II I

II I II

271

(11.4) (7.9) (2.13)

II

I 85.3

(11.3)

(2,15) (13,15)

(3,16) (13,16)

II

259

(7.16) (9,16)

(12.1)

I II I II

(2,17) (15,17)

(12.5)

(14.3) (11.7) (2.15)

9

9'

81

8n

52°04'

7°56'

33°58'

26°02'

36°31'

23°29'

41°44'

18°16'

4°25'

55°35'

57°48'

2-12'

30°09'

29°51'

44-55'

15°05'

8°15'

51°45'

55°52'

4°08'

45°54'

14°06'

37°03'

22-57'

53°10'

6°50'

33°25'

26°35'

39°41'

20-19'

40°09'

19°51'

3°53'

56°07'

58°03'

1°57'

19°16'

40-44'

50-22'

9°38'

26°45'

33°15'

46°38'

13°22'

53°36'

6°24'

33°12'

26°48'

40°58'

19°02'

39°31'

20-29'

14°37'

45-23'

52-41'

7-19'

47039.

12°21'

36°11'

23-49'

28°47'

31°13'

45°37'

14°23'

3°29'

56°31'

58°16'

1-44'

17°17'

42-43'

5J-22'

8°38'

24-or

35°59'

48°00'

12°00'

36°58'

23°02'

41°31'

18°29'

6° 11'

53°23'

56°42'

3°18'

(15.2)

(5,18) (13,18)

(5.13)

(9,19) (10,19)

(9.10)

(7,19) (12,19)

(7.12)

(13.5) (10.9) (12.7)

I

(6,19)

(6.13)

II

(13,19)

(13.6)

I II

(4,19) (15,19)

(4.15) (15.4)

I

(9,20)

(9.11)

II

(11,20)

(11.9)

Crystallographic

Basis of Polytypism

and Twinning

in Miens

233

Table 13, concluded. 11

nA)

307

92.9

313

93.S

325

95.5

331

96.4

337

97.3

343

9S.2

349

99.0

(«, v) (us)

(H,K)

I II

(17,18)

(17,1)

I

(3.19)

(3,16)

II

(16,19)

(16,3)

Set

(U7)

9

9'

Si

8n

54-20'

5°40'

32°50'

27°10'

43°07'

16°53'

38°27'

21°33'

32°12'

27°48'

43054.

16°06'

I

(5,20)

II

(15,20)

I

(10,21)

(5.15) (15.5) (10,11)

II

(11,21)

(11,10)

3°09'

56°51'

58°26'

1°34'

I II

(8,21) (13,21)

(8,13) (13,8)

15°39'

44°21'

52°10'

7°50'

I II

(1.19) (18,19)

(US) (18,1)

54°38'

5°22'

32°41'

27°19'

I

(3,20)

(3,17)

II

(17,20)

(17,3)

44°01'

15°59'

38°22'

22°00'

Plesiotwimiing is a macroscopic phenomenon that differs from twinning not only in a geometrical definition but also from a physical viewpoint. Whereas for twins the twin index and the twin obliquity directly influence the probability of twin occurrences, for plesiotwins a similar lattice control is not recognized. In fact, the lowest plesiotwin index for micas is 7, which becomes 21 for non-orthogonal polytypes. The degree of restoration of lattice nodes is too small for a lattice control to be active. The plesiotwin formation is thus structurally controlled. Twins are usually believed to form in the early stages of crystal growth (Buerger 1945), but the formation of twins from macroscopic crystals is also known (e.g., Gaubert 1898; Schaskolsky, and Schubnikow 1933). When two or more nanocrystals interact, they can adjust their relative orientation until they reach a minimum energy configuration, corresponding either to a parallel growth or to a twin. When two macrocrystals interact, the energy barrier to the mutual adjustment is higher, especially at low temperature. If two macrocrystals coalesce or exsolve taking at first a relative orientation corresponding to an unstable atomic configuration at the interface, they tend to rotate until they reach a lower energy configuration. Parallel growth and twinning correspond to minimal interface energy, whereas plesiotwimiing corresponds to a lessdeep minimum. However, twin orientations are less numerous and are separated by larger angles, whereas plesiotwin orientations are more numerous and separated by smaller angles. In Figure 24 the plot E vs. cp for the hp lattice is given for E < 100 and 0° < cp < 60°. Between the two extreme values of cp corresponding to crystallographic rotations and to E = 1, several discrete valas appear, corresponding to E > 1 and to noncrystallographic rotations. Only limited adjustments may be necessary to reach plesiotwin orientations, which may thus represent a kind of compromise between the original unstable configuration and the too distant, although more stable, configuration of twins. This kind of origin is supported also by experiments of dispersion into a fluid and drying of flakes of crystals with layer structure: the result was simply a physical overlap of pairs of crystals, which however gave the same orientations of plesiotwins (Sueno et al. 1971; Takeuchi et al. 1972). TWINNING OF MICAS. ANALYSIS OF THE GEOMETRY OF THE DIFFRACTION PATTERN A simple and straightforward method to derive the orientations of the individuals in a mica twin or allotwin is introduced. The following analysis is entirely based on the

234

Nespolo & Durovic

CS J® L^ + ^ S

o "2 o bû öo

W to WW W es+Hes Ih Wes «es¡L, to v to to to ^ to to es ~L es es es L es es + es + to + + to + + to + + es 0 o n o o O ^ & b

-g fcs O O |ir> o O

O r 3OO-O — £ .S §

3

.s * o ^ ó &

Crystallographic

Basis of Polytypism

and Twinning

in

Miens

235

3(6-I)(6-J)...(6-P) transformation corresponds to reflecting the twin lattice across the (010) plane.

For polytypes in which layers are related only by proper motions 7 , like 3 T, two twins operations with the same rotational part and differing only for the proper/improper character of the motion produce the same twin lattice. The corresponding two twin laws are however different, and thus an orientation produced by an improper motion is hereafter distinguished by a small black circle (*) after the ZT symbol. The number of independent orientations of the w.r.l. of an individual is determined by its limiting symmetry, i.e. the lower symmetry between the ideal crystal lattice (as described by the Trigonal model) and the family structure. The limiting symmetry is given in Table 15, which is easily understood remembering that: 1) for mixed-rotation polytypes the family structure is defined only within the Pauling model and the limiting symmetry always coincides with the symmetry of the polytype lattice; 2) for orthogonal polytypes, the lattice is (pseudo) hexagonal: for both subfamilies the limiting symmetry coincides with that of the family structure; 3) subfamily B polytypes cannot belong to Class a; 4) non-orthogonal subfamily A polytypes belong to Class a for Series 0 but to Class b for Series > 0. 4.

Table 15. Limiting symmetry defining the number of independent lattice orientations. The (idealized) symmetries of the lattice and of the family structure are given. The limiting symmetry corresponds to the lower of the two. For mixed-rotation polytypes the family structure is defined only within the Pauling model and the limiting symmetry by definition coincides with the symmetry of the lattice. Orthogonal polytypes (hP)

Class a polytypes (mC)

Class b polytypes (hR)

subfamily A (hRf

hR

mC (iSeries 0)

hR (Series > 0)

subfamily B (hPf

hP

mixed-rotation (hPf

hP

hR mC

hR

^Trigonal model. ^Pauling model.

Class a polytypes. Each subfamily A Series 0 polytypes belong to Class a; mixedrotation polytypes may also belong to Class a. In both cases, the limiting symmetry is mC and the unique axis does not coincide with that of the family structure (b in the polytypes, c in the family structure). Each of the six possible orientations of the individuals correspond thus to independent orientations of the w.r.l. The possible composite twins are obtained by calculating the sequences of Z T symbols for sets of individuals from two to six. The orientation of the first individual is fixed (Z T = 3), and five possible orientations

7 A "motion" is an instruction assigning uniquely to each point of the point space an 'image' whereby all distances are left invariant. A motion is called proper (also: "first sort") or improper (also: "second sort") depending on whether the determinant of the matrix representing it is +1 or -1.

Crystallographic

Basis of Polytypism

and Twinning

in Micas

237

remain where m individuals (1 < m < 5) must be distributed. The number of twins is then: (17) Table 16 gives the 12 sequences of independent Z T symbols; the other 19 simply correspond to a rotation of the entire twinned edifice followed by a shift of the origin along c, eventually coupled with the inversion of the direction of the rotation of the individuals in the twin [reflection of the lattice across (010)], as in Z T = 341. Class b polytypes. Non-orthogonal polytypes belong to Class b in subfamily A Series > 0 and in subfamily B. The unique axis is a in the polytypes but c in the pseudorhombohedral lattice; the latter coincides with that of the family structure. The limiting symmetry is hR, which for subfamily A coincides both with the symmetry of the family structure and with the (pseudo) symmetry of the lattice. Only two orientations of the w.r.l. of the individual are independent, corresponding to the two parities of Z T symbols. A common symbol is thus used for the three equivalent orientations with the same parity, namely "U" (uneven) and "E" (even). Twinning by pseudo-merohedry involves individuals with the same orientation parity of Z T symbols and produces complete overlap of the w.r.l. of the individual (neglecting the obliquity). The reciprocal lattice of the twin is thus geometrically indistinguishable from the reciprocal lattice of the individual. The three twins ZT = 35, ZT = 31 and Zr = 351 are equivalent to the single crystal, when considering the geometry of their lattice, and are thus represented as Z T = U. Instead, twinning by reticular pseudo-merohedry involves individuals with an opposite orientation parity of the Z T symbols and, considering the lattice only, they are represented as Z T = UE. Orthogonal polytypes. In the Trigonal model, the lattice is hP (co = 0); in the true structure for orthorhombic polytypes the lattice is normally oC but pseudo-hP (co * 0). For subfamily B and mixed-rotation polytypes the limiting symmetry is hP and there is only one independent orientation of the w.r.l. Twinning is either by complete merohedry or by pseudo-merohedry and does not modify the geometry of the diffraction pattern. Subfamily A polytypes have an orthogonal lattice only if they belong to Series > 0 and have a 1:1:1 ratio of layers with the three orientations of the same parity (odd or even). The only example reported to date is 3 T, which is also the only possible orthogonal polytype in Series 1. Other subfamily A orthogonal polytypes may appear in Series > 1 but are at present unknown. The limiting symmetry is hR and the w.r.l. has two independent orientations, as for Class b polytypes, which correspond to the two settings (obverse/reverse) of the family structure. Twinning is by merohedry (co = 0, either complete or selective, depending on the twin law) or pseudo-merohedry (co * 0). The 37" polytype has three twin laws, two of which correspond to selective merohedry and invert the parity of the ZT symbol, namely ZT = U —> ZT = E (6'2'2) or ZT = E* (6'm'2); the third twin law (3'12!m') corresponds instead to complete merohedry and preserves the parity of the Z T symbol (Z T = U —> Z T = U*). Derivation of twin diffraction patterns The number and disposition of nodes on the reciprocal lattice rows parallel to c* are termed node features and are identified by a symbol I¡, where I is the number of nodes within the c*i repeat and j is a sequence number. Nespolo et al (2000a) introduced an orthogonal setting for the analysis of twins in terms of Iy, which is termed the twin setting. When dealing with a single polytype, the twin setting coincides with the C\ setting, which

Nespolo & Durovic

238

Table 16. Orientation of the individuals building a twin in Class a mica polytype. Angles in parenthesis express the counter clockwise rotations of the whole twinned edifice. "Shift" stands for the shift of the origin along c. (010) means reflection of the twin lattice across the (010).plane, which is equivalent to inverting the direction of rotation of the individuals in the twin, i.e. to the symbol transformation 3IJ.. .P —> 3(6-1 )(6-J)...(6-P). [After Nespolo et al. 2000a] Zr

Equivalent to

34 35 36 31

Unique Unique Unique 53(120°)

32 345 346 341 342 356 351 352 361 362 312

43(60°) Unique Unique 325(010) 453(60°) 134(240°) Unique 463(60°) 634(180°) 413(60°) 534(120°)

Zr

Equivalent to

3456 3451 3452 3461 3462 3412 3561 3562 3512 3612 34561

Unique Unique 4563(60°) Unique Unique 5634(120°) 1345(240°) 4613(60°) 5134(120°) 6345(180°) Unique

34562 34512 34612 35612 345612

45613(60°) 56134(120°) 61345(180°) 13456(240°) Unique

Equivalent to

Equivalent to

35(shift) 34( shift)

436(60°) 345(shift) 341(shift) 346(shift) 346 341(shift) 345(shift) Equivalent to

3456(shift)

3456(shift) 3451 (shift) 3461 (shift) 3451 (shift) 3456(shift) 3456 l(shift) 3456 l(shift) 3456 l(shift) 3456 l(shift)

346(shift) 346

346

Crystallographic

Basis of Polytypism

and Twinning

239

in Micas

is based on the cell of the twin lattice. To compare the geometry of the reciprocal lattice of polytypes with different periods, the twin setting is instead defined to have the shortest period along c* in the Ci setting among all the polytypes considered. The twin setting of the twin lattice is space-fixed and parallel to Ci, whereas that of the crystal lattice is crystal-fixed for each of the individuals building a twin. Since the first individual of the twin is space-fixed (Z T = 3 for Class a, or Z T = U for Class b and orthogonal polytypes), its twin setting is parallel to C\. The I index in the twin setting is labeled /T. Rotations between pairs of individuals are taken counter-clockwise in direct space, and thus clockwise in reciprocal space. The nx60° rotations about c*, which give the approximate rotations between pairs of individuals, overlap only R, belonging to the same type (S, D or X). Each of the R, is rotationally related to five other R, and along each of them a peculiar sequence of IT indices is obtained, which is termed a "Rotational Sequence". Each R, generates one rotational sequence, which is shortened to RS,P(rc), where: the superscript P indicates the polytype; i is the same index defining R,; n points to each of the six characters of the RS. RSi P corresponds to S rows and thus it is "000000" for all polytypes. The rc-th values of RS , p correspond to the l T indices of the nodes on the row which is related to R, by (rc-l)x60° clockwise rotation. The two RS,P corresponding to D-type rows ( R 2 - 3 ) on the one hand, and the six RS,P corresponding to X-type rows ( R 4 . 9 ) on the other, can be transformed into each other by cyclic permutations. Since the orientations of the single-crystal lattices and of the twin lattice are fixed and determined by Zt, also the starting point of each RS,P is fixed, and the nine RS, P are independent. The node features of the composite rows are obtained from the corresponding RS, P by considering their relation with the Z T symbols. A twin of N individuals (2 < N < 6) is identified by N Z T symbols. The lT index of the g-th node coming on ¿-th row from the j-th individual is given by: [li(i,j)]q = [RS ¡ p (n) ]q,n = [(Z T )j+4](mod 6).

(18) P

The node features of composite rows are completely defined by the nine RS and Z T symbols; therefore, there are only nine independent composite rows, for which the symbol C, is adopted. R, and C, share the same row features and thus the description of the reciprocal lattice in terms of the tessellation rhombus and of the minimal rhombus is the same for both the single-crystal lattice and the twin lattice. Because of the metric relations (Table 10), the /T of both C, and R, of the same type and belonging to the same central plane are related by: [/,(D,.)]?=[6-/,(D3_,.)]? (19) \}T (

X

i ) ] , = { 6 - ^ [ X (9-,)(mod6)

'

Knowing the /T of one D-type C, / R, and three X-type C, / R„ the /T of the remaining four C, / R, can be calculated. There are thus five truly geometrically independent C, / R, (one S-type, one D-type and three X-type), but nine translationally independent C, / R,. The distribution of Iy on the C, of a minimal rhombus is the information necessary to derive and identify the diffraction patterns of mica twins. A short comparative analysis of the four periodic basic structures (1M, 2M\, 2Mj and 37) is given below. For these four polytypes the twin setting has a period of c* 1/6 along c*: lT ( 2 M h 2M2) = lCi(2Mu 2M2), but lT (1M, 37) = 2 l C l ( \ M , 37). Table 17 gives the C, and RSPi. The definition of I¡, is given in Table 18. The rules for combining I / s of the individuals into composite I / s of the twin are given in Nespolo et al (2000a).

240

Nespolo & Durovic

1/1 Oí

o o o o o o

Í vi ai

o o o o o o

Ívi

o o o o o o

S oá

o o o o o o

m "S s. Je

o

Ei

p¿

0 CT„(E;e) where CT„(E;£) = -47t E a K S L L .m L ( e ) I m { ( - l ) n (T a H) n T a }li;miX^)In this expression, the term n = 0 represents the smoothly varying "atomic" cross section while the generic n term is the contribution to the photoabsorption cross section coming from processes in which the photoelectron has been scattered (n - 1) times by the surrounding atoms before returning to the photoabsorbing site. The unpolarized absorption coefficient, which is proportional to the total cross section, is given by (Benfatto et al. 1986): a F « hv {(/ + 1) M/>/+1 X/+i + 1 M /,/-i%/-i) where I is the orbital angular momentum of the core initial state (/ = 0 for a K level), My ± 1 is the atomic dipole transition matrix element for the photoabsorbing atom, and 1, = {(21 + 1) s i n V r 1 Z m Im { ( I + T ^ - ' T , } ^ is the quantity that contains the structural geometrical information. Here, 8 i s the phase shift of the absorbing atom. The total absorption coefficient can be expanded as a series a F = a 0 (1 +£ n > 2 %n) where the first element ao is the atomic absorption coefficient and the second term a i is always zero because H i m > i m = 0. For t h e ^ edge, in the plane-wave approximation, the expression for n = 2 is the usual backscattering amplitude, i.e., the EXAFS signal times the atomic part. Actually, the first multiple-scattering contribution is the a3 term, which can be written (Benfatto et al. 1989) as OC3 = OCo Z i i t j I m { P!(cos) fj(to) fj(6) exp(2i(8 i ° + kR tot ))/kr i ri j r j } where r;j is the distance between atoms i and j, f;(co) and fj(9) are the relative scattering amplitudes, which now depend on the angles in the triangle that joins the absorbing atom to the neighboring atoms located at sites r; and rj, and R to t= r; + r;j + rj. In this expression, cos4 standard in which the Cr 6+ is entirely in tetraliedral coordination, then it can be appraised that amount of [ 4 1 Cr in muscovite, if any, cannot exceed 0.4-0.5% of total Cr (cf. Lee et al. 1995). By contrast, if both Gaussian components are considered to be due to [61Cr3+, as in the uvarovite standard, and interpreted as a way to measure the distortions of the muscovite octahedral sites where Cr 3 is possibly hosted, then their relative

400

Mottana, Marcelli, Cibin & Dyar

intensities (1.3 and 1.2% nau [= normalized absorption units]) show that these two sites are very similar. Indeed, this is nothing more than an extension to Cr of the method for quantitatively determination of site distortion for octahedra centered by Ti4+ calibrated by Waychunas (1987). In the case of the already-mentioned Fe K pre-edge of tetra-ferriphlogopite, where Fe3+ is entirely in the tetrahedral site, the pre-edge is twice as strong and shifted to higher energy (ca. 2 eV) relative to annite, where Fe is mostly in the octahedral site (Fig. 2). This apparent irregularity can be explained by comparing the sharp single peak of tetraferriphlogopite, a synthetic endmember, and the broad, probably double peak of the Pikes Peak annite, the Fe of which is entirely octahedral, but partly Fe2+ and partly Fe3+. Clearly, the oxidation effect is more important than the coordination effect in determining the position of the Fe K pre-edge. However, the strong intensity of the tetraferriphlogopite peak also suggests that its Fe is constrained in a more tightly-bound coordination polyhedron than the annite one. Note, however, that there is an underlying problem in the pre-edge region that needs a more careful evaluation, and not only in these systems: this problem is the amount of quadrupolar effects present (see Giuli et al. 2001, for additional evaluation).

1560

1565

1570

1575

1580

1585

1590

1595

E (eV) Figure 20. Shift of the white-line in the FMS region of the Al A'-edye spectra of two synthetic micas as a result of two different coordination geometries: in phlogopite the Al atoms are entirely in a tetrahedral site geometry, and in polylithionite in an octahedral site geometry, as they are in the reference albite and grossular natural standards, respectively (Mottana et al. 1997, Fig. 3).

Coordination geometry also plays a role in shaping the FMS region of a XANES spectrum. This effect was clearly documented for the Al K edges of certain synthetic micas by Mottana et al. (1997), who showed that there is a shift of at least 2 eV between [41 A1 as in phlogopite and albite, and [61A1 as in polylithionite and grossular (Fig. 20). Moreover, they found that it is possible, although difficult, to recognize the concomitant presence in the spectra of two white-line features arising from contributions of the same atom occurring in two different geometries ([41A1 and [61A1 in zinnwaldite and

X-Ray Absorption

Spectroscopy of the Micas

401

preiswerkite: Mottana et al. 1997 Fig. 4). Thus, the FMS region of the XANES spectrum of a mineral with Al in two coordinations can be seen as the weighted combination of the contributions arising from the two Al atoms, although the general appearance of the spectrum (and its ensuing evaluation) is somewhat blurred by next nearest neighbor effects due to the presence of other atoms in the same sites substituting for the absorber Al (cf. the muscovite vs. bityite spectra: Mottana et al. 1997 Fig. 4). In the following we will document visually and sparingly comment upon a series of XANES spectra obtained at different K edges for the powders of a number of natural micas close to the end members. The present state of our investigation, which is still under way, compels us to defer to a later moment for drawing conclusions (Mottana et al., in preparation): micas are no simple systems, and XAS literature is already cluttered by faulty reasoning and wrong conclusions reached when hastily evaluating even simpler systems!

Mg K edge

Phlogopite

I

i

\

, .

Tetra-ferriphlogopite

,

Biotite

'.n/

'

.• .

:

Clintonite

1310

1320

E (eV) Figure 21. Experimental Mg A'-edye spectra for the powders of four natural tri-octahedral micas.

Figure 21 shows the experimental Mg K-edge spectra of three tri-octahedral micas (phlogopite, tetra-ferriphlogopite, and biotite) and one brittle mica (clintonite). All spectra are very similar and have no pre-edges, as magnesium is not a transition element. The FMS regions consist of three features, like the K edge of talc (Wong et al. 1995). However, the relative intensities of the three features differ significantly among the four spectra suggesting that there are substantial differences in the local order of their Mg that may be resolved via comparison with spectra taken for other absorbers. Note, moreover, that the three features in the clintonite spectrum are possibly doubled. Figure 22 shows the experimental Al K edge spectra of three tri-octahedral micas (phlogopite, annite, biotite) and one di-octahedral mica (muscovite). Again, Al is not a transition element, therefore the spectra have no distinct pre-edges. The FMS regions are apparently simpler than the ones occurring in the Mg ^-edge spectra above, but in fact

402

M o t t a n a , Marcelli, Cibin & D y a r

1550

1560

1570

1580

1590

1600

1610

1620

E(eV) Figure 22. Experimental A1 A'-edye spectra for the powders of three natural tri-octahedral and one natural di-octahedral mica.

they contain the same three features, although with strongly different intensities and energies (cf. Mottana et al. 1999). Possibly, the fact that non-precisely oriented powders were used affects the recorded features (cp. this muscovite spectrum with that in Fig. 7). The IMS regions are poor in features, but they display shifts and relative differences that are enormous, considering the similarity of the local structures that originate such differences. The significant role of the outer shells around the Al absorber appears to be well depicted here, but it will create great problems when interpreting the spectra from a quantitative viewpoint. Figure 23 shows the experimental Si K-edge spectra of five micas: four tri- and one di-octahedral one. Nowhere is there a pre-edge, and the entire XANES spectrum is dominated by the strong white-line of Si in tetrahedral coordination (cf. Li et al. 1994; Li et al. 1995a). The regions in between FMS and IMS (inset) undergo subtle but significant variations as a result of changes in the local and medium-range ordering occurring in the relevant structures for the volumes that surround the Si tetrahedra. Such variations may also occur in the energies of certain peaks, but this variation is also certainly due to the tri- vs. di-octahedral structure of the investigated mica (inset: cf. muscovite with the other micas). The experimental K K-edge spectra of the same five micas are shown in Figure 24. These XANES spectra are rather complex, both to record experimentally and to reckon with. The FMS regions have no strong white-lines, and only small differences show up in the intensities of their IMS regions (inset). However, their analysis suggests that the K coordination number is less than the expected 12, possibly 8 or even 6. In a case like this, only XANES simulations by the multiple-scattering code may be able to reveal safely the actual site geometry around the potassium atom. Finally, Figure 25 shows the experimental Fe K-edge spectra of two trioctahedral

X-Ray Absorption

Spectroscopy of the Micas

403

E(eV) Figure 23. Experimental Si A'-edye spectra for the powders of five natural micas. The strong differences displayed by a portion of their FMS and IMS regions is shown as inset.

micas (biotite and tetra-ferriphlogopite) and one brittle mica (clintonite). Iron is a transition element, therefore all spectra exhibit significant pre-edges (inset), each one of them having properties of its own. In particular, the tetra-ferriphlogopite pre-edge is a singlet (cf. Fig. 2), as is the clintonite one, but at 1 eV lower energy. Fe is tetrahedrallycoordinated in both micas, but in the former one it is Fe 3+ and in the latter one an additional contribution arising from Fe i + is likely. The biotite pre-edge is weak, because it mostly arises from octahedral Fe i + . The three pre-edges require a deconvolution of the same sort as the one previously demonstrated for the Cr pre-edge of muscovite (Fig. 19) in order to reveal all the information they contain. The FMS regions of these spectra are dominated by the Fe white-line, which undergoes energy variations accounting for differences in both coordination and oxidation state. The presence of significant variations in the medium- to long-range ordering occurring in these mica structures is made evident by their greatly different IMS regions (and also by their EXAFS regions: cf. Giulietal. 2001).

404

Mottana, Marcelli, Cibin & Dyar

E(eV> Figure 24. Experimental K A'-cdyc spectra for the powders of five natural micas. The strong differences displayed by a portion of their FMS and IMS regions are shown as an inset.

ACKNOWLEDGMENTS Our XAS work on minerals has enjoyed the support of numerous suggestions, discussions and contributions in many stages and levels over a number of years, the five more recent ones dedicated mostly to the micas. We thank all these colleagues, since it is by this form of synergy that we could carry out and develop our project over the years. A special thank goes to Maria Franca Brigatti, Jesús Chaboy, Paola De Cecco, Giancarlo Delia Ventura, Gabriele Giuli, Antonio Grilli, Cristina Lugli, Jeff Moore, Takatoshi Murata, Eleonora Paris, Marco Poppi, Agostillo Raco, Jean-Louis Robert, Claudia Romano, Michael Rowen, Francesca Tombolini, Hal Tompkins, Curtis Troxel, Joe Wong, Ziyu Wu and all others who allowed us to use for this review some of the data recorded together during painstaking sessions at the source. Most experimental XAS was carried out at SSRL, which is operated by Stanford University on behalf of D.O.E. Furthermore, M.D.D. acknowledges the insight and assistance of her collaborators at the N.S.L.S., Brookliaven National Laboratory: Jeremy Delaney, Tony Lanzirotti and Steve Sutton. Financial supports for our experimental work and for its evaluation and interpretation were granted by M.U.R.S.T. (Project COFIN 1999 "Phyllosilicates: crystalchemical, structural and petrologic aspects"), C.N.R. (Project 99.00688.CT05 "Igneous and metamorphic micas"), and I.N.F.N. (Project "DAONE-Light") in Italy, and by N.S.F.

X-Ray Absorption

Spectroscopy of the Micas

405

EAR-9909587 and EAR-9806182, and D.O.E.-Geosciences DE-FG02.92ER14244 in U.S.A. Critical readings by C.R. Natoli and a unknown referee improved the quality of this paper in a substantial maimer.

Fe K edge A;

Biotite Telra-ferriphlogopite Clintonite

a! y y

7105

7110

7200

7115

7120

7250

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