Table Of ContentREVIEWS In
MINERALOGY
Volume 10
JOHN M. FERRY, Editor
CHARACTERIZATION of
METAMORPHISM through
MINERAL EQUILIBRIA
The Authors:
Donald M. Burt Douglas Rumble III
Department of Geology Geophysical Laboratory
Arizona State University 2801 Upton Street, N.W.
Tempe, AZ 85287 Washington, D.C. 20008
Eric J. Essene Frank S. Spear
Department of Geological Sciences Department of Earth & Planetary Sciences
University of Michigan Massachusetts Institute of Technology
Ann Arbor, MI 48109 Cambridge, MA 02139
John M. Ferry James B. Thompson, Jr.
Department of Geology Department of Geological Sciences
Arizona State University Harvard University
Tempe, AZ 85287 Cambridge, MA 02138
Jack M. Rice Robert J. Tracy
Department of Geology Department of Geology & Geophysics
University of Oregon Yale University
Eugene, OR 97403 New Haven, CT 06520
Series Editor: Paul H. Ribbe
Department of Geological Sciences
Virginia Polytechnic Institute &
State University
Blacksburg, Virginia 24061
MINERALOGICAL SOCIETY OF AMERICA
COPYRIGHT 19112
MINERALOGICAL SOCIETY of AMERICA
Second Printing 1986
Printed by BookCraftcrs, Chelsea, Michigan
REVIEWS in MINERALOGY
(Formerly: SHORT COURSE NOTES)
ISSN 0275-0279
Volume ]0: CHARACTERIZATION of METAMORPIIJSM
lhrough MINERAI. EQUILIBRIA
ISBN 0-93'J'J50-12-X
ADDITIONAL COPIES of this volume as well as those listed below
may beobtained from the MINERALOGICAL SOCIETY of AMERICA,
1625 IStreet, N.W., Suite 414, Washington, D.C. 20006 U.S.A.
Reviews in Mineralogy Volume 9A: Amphiboles and Other Hydrous Pyriboles-Min-
eralogy, 1981; O.R.Veblen, Ed. 372pp. Seven chapters
Volume 1:Sulfide Mineralogy, 1974; P.H.Ribbe, Ed. 284 pp. on biopyribole mineralogy andpolysomatism; the crystal chem-
Six chapters on the structures of sulfides and sulfosalts; istry, structures andspectroscopy ofamphiboles; subsolidus re-
the crystal chemistry and chemical bonding of sulfides. synthe- lations; amphibole andserpentine asbestos-mineralogy, occur-
sis,phase equilibria, andpetrology. ISBN# 0-939950-01-4. rences. andhealth hazards. ISBN# 0-939950-10-3.
Volume 2:Feldspar Mineralogy, 2ndEdition, 1983; P.H.Ribbe, Volume 98: Amphiboles: Petrology and Experimental Phase
Ed.362pp. Thirteen chapters onfeldspar chemistry, struc- Relations, 1982; D.R.Veblen and P.H.Ribbe, Eds. 390 pp.
tureandnomenclature; Al,Siorder/disorder inrelation todomain Three chapters onphase relations of metamorphic amphi-
textures, diffraction patterns, lattice parameters and optical boles(occurrences andtheory); igneous amphiboles; experimen-
properties; determinative methods; subsolidus phase relations, talstudies. ISBN# 0-939950-11-1.
microstructures, kinetics andmechanisms ofexsolution, anddif-
fusion; color and interference colors; chemical properties; defor- Volume 10: Characterization of Metamorphism through Min-
mation. ISBN# 0-939950-14-6. erai Equilibria, 1982; J.M.Ferry, Ed. 397pp. Ninechap-
tersonanalgebraic approach tocomposition andreaction spaces
Volume 3: Oxide Minerals, 1976; O.Rumble III, Ed. 502 pp. andtheir manipulation; the Gibbs' formulation of phase equilib-
Eight chapters onexperimental studies, crystal chemistry, ria; geologic thermobarometry; buffering, infiltration, isotope
andstructures ofoxide minerals; oxide minerals inmetamorphic fractionation, compositional zoning andinclusions; characteriza-
andigneous terrestrial rocks, lunar rocks, andmeteorites. ISBN# tion01metamorphic fluids. ISBN# 0-939950-12-X.
0-939950-03-0.
Volume 11: Carbonates: Mineralogy and Chemistry, 1983; R.
Volume 4:Mineralogy and Geology of Natural Zeolites, 1977; J.Reeder, Ed.394pp. Ninechapters oncrystal chemistry,
F.A. Mumpton, Ed. 232 pp. Tenchapters on the crystal polymorphism, microstructures andphase relations oftherhom-
csheedmimisetnrytaryandandstrulocwtu-rgeradoef nmateutraamlorzpehoiclitesr,octkhseiranodccuclroresnecdehyin- dbioshseodlurtaiolnanadndorptrheocrihpoitmatbioicn; ctararbceonealteems;enttsheankdineistoictsopeosf CinaCse0d3-
drologic systems, their commercial properties and utilization. imentary carbonates; theoccurrence, solubility andsolidsolution
ISBN# 0-939950-04-9. behavior of Mg-calcites; geologic thermobarometry using meta-
morphic carbonates. ISBN# 0-939950-15-4.
Volume 5:Orthosilicates, 2nd Edition, 1982; P.H.Ribbe, Ed. Volume 12: Fluid Inclusions, 1984; by E. Roedder. 644 pp.
450pp. Liebau's "Classification ofSilicates" plus 12chap- Nineteen chapters providing an introduction to studies of
tersonsilicate garnets, olivines, spinels andhumites; zircon and alltypes offluid inclusions, gas, liquid ormelt, trapped inmate-
tthheeaaclutimniidneumorthsoiliscialicteaste,s;topatitza,nitaend(spshcoernees),ocfhlmoriistociedl,lansetoauusroliteqr,- driearlsslafnrodmingtheofegaertohlogaicnadlsppraoccee,ssaensd. tIhSeBirN#app0li-c9a3ti9o9n50-t1o6-t2h.e un-
thosilicates. Indexed. ISBN# 0-939950-13-8.
votume 13:Micas, 1984; S.W.Bailey, Ed. 584 pp. Thir-
Volume 6: Marine Minerals, 1979; R.G. Burns, Ed. 380 pp. teenchapters onstructures, crystal chemistry, spectroscopic and
Ten chapters on manganese and iron oxides, the silica optical properties, occurrences, paragenesis, geochemistry and
polymorphs, zeolites, clayminerals, marine phosphorites, barites petrology ofmicas. ISBN# 0-939950-17-0.
andplacer minerals; evaporite mineralogy andchemistry.ISBN#
0-939950-06-5. Volume 14: Microscopic to Macroscopic: Atomic Environ-
ments to Mineral Thermodynamics, 1985; S.W. Kieffer and
Volume 7: Pyroxenes, 1980; C.T. Prewitt, Ed. 525 pp. A. Navrotsky, Eds. 428 pp. Eleven chapters attempt to
Ninechapters onpyroxene crystal chemistry, spectroscopy, phase answer the question, "What minerals exist under given con-
equilibria, subsolidus phenomena andthermodynamics; compo- straints of pressure, temperature, andcomposition, and why?"
sition and mineralogy of terrestrial, lunar, andmeteoritic pyrox- Includes worked examples attheendofsome chapters. ISBN#
enes. ISBN# 0-939950-07-3. 0-939950-18-9.
Volume 15: Mathematical Crystallography, 1985; by M. B.
Volume 8: Kinetics of Geochemical Processes, 1981; A. C. aetsen, Jr. and G. V. Gibbs. Approx. 450 pp. Amatrix
Lasaga and R.J.Kirkpatrick, Eds. 398pp. Eight chapters and group theoretic treatment of the paint groups, Bravais lat-
on transition state theory and the rate laws of chemical reac- tices, andspace groups presented with numerous examples and
tions; kinetics of weathering, diagenesis, igneous crystallization problem sets, including solutions to common crystallographic
and geochemical cycles; diffusion in electrolytes; irreversible problems involving thegeometry andsymmetry ofcrystal struc-
thermodynamics. ISBN# 0-939950-08-1. tures. ISBN# 0-939950-19-7.
Volume 16: Stable Isotopes in High Temperature Geological
Processes, 1986;H. P.Taylor, Jr,.J.R.O'Neil, and). W,Valley,
Eds.Approx. 600pp.
Characterization of Metamorphism
through Mineral Equilibria
TABLE of CONTENTS
Page
Copyright and List of Other Volumes ii
Foreword iii
Preface and Acknowledgments iv
Chapter 1
COMPOSITION SPACE: An ALGEBRAIC and GEOMETRIC APPROACH
J.B. Thompson, Jr.
INTRODUCTION 1
COMPONENTS AND COMPOSITION SPACES 2
INDEPENDENTLY VARIABLE COMPONENTS 4
EXCHANGE AND ADDITIVE COMPONENTS 6
TRANSFORMATION OF COMPONENTS 7
CRYSTALLINE PHASES 20
REDUCED COMPOSITION SPACES 25
PROJECTED PHASE DIAGRAMS 29
ACKNOWLEDGMENTS 30
REFERENCES 31
Chapter 2
REACTION SPACE: An ALGEBRAIC and GEOMETRIC APPROACH
J.B. Thompson, Jr.
INTRODUCTION 33
PHASE COMPONENTS AND SYSTEM COMPONENTS 33
A REDUCTION MATRIX 34
OPEN-SYSTEM REACTIONS 35
EXCHANGE REACTIONS 36
NET TRANSFER REACTIONS 37
SOME SHORTCUTS 39
REACTION SPACE 40
REACTION POLYTOPES 42
USES OF REACTION SPACE 43
REACTIONS IN ANHYDROUS MAFIC ROCKS 44
THOLEIITE REACTION SPACE 47
SUMMARY .....•..• 50
vii
ACKNOWLEDGMENTS
51
REFERENCES
52
Chapter 3
LINEAR ALGEBRAIC MANIPULATION of N-DIMENSIONAL COMPOSITION SPACE
F.S. Spear, D. Rumble III, and J.M. Ferry
INTRODUCTION
53
REPRESENTATION OF MINERAL (OR ROCK) COMPOSITIONS IN COMPOSITION SPACE 53
TRANSFORMATION OF COORDINATE AXES . . . . . . . " 56
SOLUTION TO THE PROBLEM A·X = Y . 60
Matrix inversion 6l
Gauss-reduction 61
Cramer's rule 61
Korzhinskii's method 62
Pros and cons 62
APPLICATIONS . . . . .. .
63
Calculation of end-member mineral components
63
Calculation of rock norms
66
Balancing chemical reactions
66
Petrologic mixing problems
68
Projective analysis of composition space
68
Examples of projective analysis in metamorphic petrology
72
Projection involving predominantly pelitic assemblages
72
Projections in calcareous bulk compositions
74
Projective analysis of amphibolites
75
Jypes of information to be gained from graphical analysis
77
Pitfalls of graphical analysis
79
DEGENERACIES AND LINEAR DEPENDENCIES .....
82
Linear dependence of component sets
83
Linear dependence and the variance of a mineral assemblage
84
TREATMENT OF "EXTRA" COMPONENTS . .
85
LEAST-SQUARES MODELING IN PETROLOGY
87
Application of least-squares modeling to petrology
92
Balancing chemical reactions and the n-dimensional tie-line
problem
92
CONCLUSIONS . .
95
ACKNOWLEDGMENTS
96
REFERENCES
97
APPENDIX A: PROGRAM TETPLT: A FORTRAN program to plot stereoscopic
phase diagrams
99
APPENDIX B: PROGRAM LINEQU: A FORTRAN program to solve a system of
linear equations
104
viii
Chapter 4
ANALYTICAL FORMULATION of PHASE EQUILIBRIA: The GIBBS' METHOD
F.S. Spear, J.M. Ferry, and D. Rumble III
lOS
INTRODUCTION
l06
NOTATION
CONDITIONS OF HOMOGENEOUS EQUILIBRIUM: THE GIBBS-DUHEM EQUATION 110
113
CONDITIONS OF HETEROGENEOUS EQUILIBRIUM
114
THE ADDITION OF A NEW VARIABLE -- dX
117
PHASE COMPONENTS AND THE GIBBS METHOD
. .. . . l20
EXAMPLES
l2l
The system Al Si0
2 5 l22
The system Al2Si05-Si02-Fe203-FeTi03
l26
The system Si02-FeO-MgO
l3l
P-T-X derivatives
133
The AFM diagram
Derivatives with µH20 at constant P and T 133
137
Derivatives with P and T
l40
SUMMARY OF PROCEDURE
l40
LITERATURE REVIEW
l44
CONCLUSION
l45
ACKNOWLEDGMENTS
APPENDIX A: A NOTE ON SOLVING SYSTEMS OF EQUATIONS 146
APPENDIX B: INTEGRATING THE SLOPE EQUATIONS l48
. . . . . . .. .. l52
REFERENCES
Chapter 5
GEOLOGIC THERMOMETRY and BAROMETRY
E.J. Essene
l53
INTRODUCTION
155
THE CONCEPT OF A PETROGENETIC GRID
ASSUMPTIONS AND PRECAUTIONS IN THERMOBAROMETRY 156
159
EXCHANGE THERMOMETRY . . .
l59
Introduction
Intracrystalline exchange l59
Intercrystalline exchange l6l
Garnet-clinopyroxene l62
Garnet-bioti te 163
Isotopic thermometry 165
PHASE EQUILIBRIA FOR PETROGENETIC GRIDS l66
ix
Solvus thermometry
l67
Albite-K-feldspar
168
Ternary feldspars
168
Calcite-dolomite
l70
Enstatite-diopside
l71
Quadrilateral pyroxenes
l72
Solid-solid reactions
173
Andalusite-sillimanite-kyanite
174
Pyroxene/pyroxenoid-olivine-quartz
175
Pyroxene-plagioclase-quartz
l76
Garnet-plagioclase-Al2Si05-quartz
l77
Garnet-pZagiocZase-oZivine
178
Garnet-pZagioclase-orthopyroxene-quartz
l79
Garnet-cordierite-siZlimanite-quartz
180
Garnet-spinel-sillimanite-quartz
l8l
Garnet-rutile-ilmenite-silZimanite-quartz
181
SphaZerite-pyrrhotite-pyrite
l82
Reactions involving fluid species
183
FeO-Ti02-02 l84
CaO-Si02-C02 l86
K20-Al203-Si02-H20
187
CaO-Al203-Si02-H20
l88
K20-FeO-AZ203-Si02-H20-02
l89
OTHER METHODS .. . . . .. .. .. . .. .. .. .. .. .. .. .. .... .. .......... l89
Fluid inclusions
190
Illite crystallinity, vitrinite reflectance, and the conodont
color index
190
Illite crystallinity
19l
Vitrinite reflectance
191
Conodont color index
19l
CONCLUSIONS
192
ACKNOWLEDGMENTS
192
APPENDIX: ACTIVIT.Y-COMPOSITION RELATIONS FOR MINERAL SOLID
SOLUTIONS .. .. .. .. .. .. .. .. .. .. .... .. .... 194
Ideal activity-composition relations
194
Non-ideal activity-composition relations
194
REFERENCES . • • . . • . . . .
........................ 196
Chapter 6
CHARACTERIZATION of METAMORPHIC FLUID COMPOSITION
through MINERAL EQUILIBRIA
J.M. Ferry and D.M. Burt
INTRODUCTION . . . . . . .. .. .... ........ .. .. 207
Evidence for a fluid phase during metamorphism 207
The composition of metamorphic fluids: general statement 208
The system C-O-H-S 208
Dissolved chlorides 210
Species whose concentrations serve as monitors of process 210
Methods of investigating the composition of metamorphic fluids 2ll
QUALITATIVE CHARACTERIZATION OF METAMORPHIC FLUID COMPOSITION FROM
MINERAL EQUILIBRIA . . . . . . . . . • . . . . . . . . . . • . .. 213
x
Isobaric, isothermal µl-µ2 diagrams 213
Isothermal Ps-µi diagrams 216
Isobaric T-Xi diagrams 217
Exchange operators as components of the fluid 219
QUANTITATIVE CHARACTERIZATION OF METAMORPHIC FLUID COMPOSITION FROM
MINERAL EQUILIBRIA . . . • . . . . . . . . . . . . . . . . . . . . . 221
General statement 221
Pressure and temperature 223
Thermochemical data 223
Equations of state for participating mineral phases 224
Equation of state for the fluid phase 224
Bulk fluidsversusintergranularfilms 224
IdealC-O-H-S-Nfluidswhichare pure substances 225
Real C-O-H-S-Nfluidswhichare pure substances 225
Idealmixingin idealC-O-H-S-Nfluids 227
Idealmixingin real C-O-H-S-Nfluids 227
Non-idealmixingin real C-O-H-S-Nfluids 228
Aqueouselectrolytesolutions 232
Calculation of fluid composition 236
C-O-H-Sfluids 236
Aqueouselectrolitesolutions 237
Erroranalysis 239
Calculation of differences in chemical potentials of fluid
components between mineral assemblages 240
GRAPHICAL REPRESENTATION OF METAMORPHIC FLUID COMPOSITIONS . . . . .. 241
T-Xi and P-Xi diagrams 24l
Graphical representation of redox equilibria involving C-O-H
fluids 242
Graphical representation of mineral equilibria involving aqueous
electrolyte solutions 244
Application of the graphical representation of metamorphic fluid
composition 247
THE COMPOSITION OF METAMORPHIC FLUIDS: A REVIEW 247
C-O-H-S fluids 247
Metamorphosedcarbonaterocks 247
Pelitic.schists 25l
Metamorphosedmaficigneousrocks 252
Granulites 252
Halogens in metamorphic fluids 253
Fluorine 253
Chlorine 254
Nitrogen in metamorphic fluids 254
Aqueous metamorphic electrolyte solutions 255
ACKNOWLEDGMENTS . . . 256
APPENDIX 1: NOTATION 257
REFERENCES 258
xi
Chapter 7
BUFFERING, INFILTRATION, and the CONTROL of INTENSIVE
VARIABLES during METAMORPHISM
J.M. Rice and J.M. Ferry
INTRODUCTION
.... .. .. 263
The buffering process
265
BUFFERING, INFILTRATION, AND THE CONTROL OF FLUID COMPOSITION
268
Sources of fluids
268
Buffering and the internal control of fluid compositions
270
Infiltration and the external control of fluid compositions
280
Fluid composition controlled by combined infiltration and
buffering
287
Exothermic mineral-fluid reactions
287
Mineral proportions in isobaric univariant mineral
assemblages
Mineral proportions in isobaric invariant mineral 287
assemblages
291
Review of the literature
Discussion 297
30l
BUFFERING, INFILTRATION, AND THE CONTROL OF MINERAL COMPOSITION.
304
Buffering and the internal control of mineral composition
304
Infiltration and the external control of mineral composition
311
Mineral compositions controlled by combined infiltration and
buffering
Summary 313
315
BUFFERING, HEAT FLOW, AND THE CONTROL OF TEMPERATURE
General Statement .. .. .. .. 315
315
An example of the buffering of temperature
Discussion 317
319
Buffering of temperature and fluid composition during
metamorphism
319
Controls of temperature during metamorphism
320
BUFFERING AND THE CONTROL OF PRESSURE
32l
CONCLUDING REMARKS
322
ACKNOWLEDGMENTS
323
REFERENCES
324
Chapter 8
STABLE ISOTOPE FRACTIONATION during METAMORPHIC
DEVOLA TlLlZATION REACTIONS
D. Rumble III
INTRODUCTION
327
DEFINITION AND TECHNIQUES
327
ISOTOPE EXCHANGE REACTIONS
328
Isotope partitioning and geothermometry
328
xii
Attainment of isotope equilibrium during metamorphism 330
STABLE ISOTOPE FRACTIONATION BETWEEN FLUIDS AND MINERAL ASSEMBLAGES 333
MODELS OF FLUID-ROCK INTERACTION AND THEIR ISOTOPIC EFFECTS . . . . 337
Methods of computation 338
Rayleigh distillation 338
Infiltration 340
Combined Rayleigh distillation and infiltration 34l
Results of computations 342
Rayleigh distillation 343
Infil.tration 345
Combined Rayleigh distillation and infiltration 345
350
CONCLUSIONS . .
ACKNOWLEDGMENTS 35l
352
REFERENCES
Chapter 9
COMPOSITIONAL ZONING and INCLUSIONS in METAMORPHIC MINERALS
R.J. Tracy
INTRODUCTION . . . . . . . . . . . . 355
GROWTH ZONING • 357
Continuous growth zoning of garnet 357
Models of continuous growth zoning of garnet 357
compositional zoning in garnets from greenschist grade to
kyanite grade 36l
compositional zoning in garnets from the sillimanite +
muscovite zone 366
Discontinuous zoning in garnet 367
Growth zoning in other minerals 369
Inclusions in growth-zoned minerals 374
Summary: kinetic controls of growth zoning and inclusion
formation 376
.. . .
DIFFUSION ZONING 380
Diffusion zoning in garnet 380
Diffusion zoning in garnet-cordierite and garnet-biotite pairs 387
CONCLUDING REMARKS . 392
ACKNOWLEDGMENTS . . • . .., 393
REFERENCES 394
xiii
