1 Rigid Unit Modes in Framework Structures:
Theory, Experiment and Applications
Martin T. Dove, Kostya O. Trachenko, Matthew G. Tucker,
David A. Keen
INTRODUCTION .................................................... 1
FLEXIBILITY OF NETWORK STRUCTURES: SOME BASIC PRINCIPLES ........ 3
Engineering principles ....................................... 3
The role of symmetry ......................................... 4
THE SPECTRUM OF RIGID UNIT MODES IN SILICATES ................... 5
The "split-atom" method ...................................... 5
Three-dimensional distribution of RUMs ....................... 6
"Density of states" approach ................................. 7
Framework structures containing octahedra .................... 8
EXPERIMENTAL OBSERVATIONS 1: MEASUREMENTS OF DIFFUSE
SCATTERING IN ELECTRON DIFFRACTION .............................. 9
EXPERIMENTAL OBSERVATIONS 2: INELASTIC NEUTRON SCATTERING
MEASUREMENTS ................................................... 10
Single crystal measurements ................................. 10
Measurements on polycrystalline samples ..................... 11
EXPERIMENTAL OBSERVATIONS 3: STRUCTURE MODELLING USING
NEUTRON DIFFUSE SCATTERING DATA FROM POLYCRYSTALLINE SAMPLES ... 12
Total scattering measurements ............................... 12
The Reverse Monte Carlo method .............................. 13
Application of RMC modelling to the phase transition in
cristobalite ................................................ 15
Application of RMC modelling to the phase transition in
quartz ...................................................... 19
APPLICATIONS OF THE RIGID UNIT MODE (RUM) MODEL ................ 23
Displacive phase transitions ................................ 23
Theory of the transition temperature ........................ 25
Negative thermal expansion .................................. 26
Localised deformations in zeolites .......................... 27
RUMs in network glasses ..................................... 28
CONCLUSIONS .................................................... 28
ACKNOWLEDGMENTS ................................................ 30
REFERENCES ..................................................... 30
2 Strain and Elasticity at Structural Phase Transitions
in Minerals Michael
A. Carpenter
INTRODUCTION ................................................... 35
LATTICE GEOMETRY AND REFERENCE STATES .......................... 40
SYMMETRY-ADAPTED STRAIN, SYMMETRY-BREAKING STRAIN,
NON-SYMMETRY-BREAKING STRAIN AND SOME TENSOR FORMALITIES ....... 41
COUPLING BETWEEN STRAIN AND THE ORDER PARAMETER ................ 42
THERMODYNAMIC CONSEQUENCES OF STRAIN/ORDER PARAMETER
COUPLING ....................................................... 51
ELASTIC CONSTANT VARIATIONS .................................... 55
ACKNOWLEDGMENTS ................................................ 61
REFERENCES ..................................................... 61
3 Mesoscopic Twin Patterns in Ferroelastic and
Co-Elastic Minerals
Ekhard K. H. Salje
INTRODUCTION ................................................... 65
FERROELASTIC TWIN WALLS ........................................ 66
BENDING OF TWIN WALLS AND FORMATION OF NEEDLE DOMAINS .......... 71
Comparison with experimental observations ................... 72
NUCLEATION OF TWIN BOUNDARIES FOR RAPID TEMPERATURE QUENCH:
COMPUTER SIMULATION STUDIES .................................... 74
INTERSECTION OF A DOMAIN WALL WITH THE MINERAL SURFACE ......... 79
REFERENCES ..................................................... 82
4 High-Pressure Structural Phase Transitions
R.J. Angel
INTRODUCTION ................................................... 85
PRESSURE AND TEMPERATURE ....................................... 85
SPONTANEOUS STRAIN ............................................. 87
Experimental methods ........................................ 87
Fitting high-pressure lattice parameters .................... 89
Calculating strains ......................................... 91
ELASTICITY ..................................................... 93
OTHER TECHNIQUES ............................................... 96
ACKNOWLEDGMENTS ................................................ 96
APPENDIX ....................................................... 97
Fitting the high-symmetry data .............................. 97
Strain calculation .......................................... 99
REFERENCES .................................................... 102
5 Order-Disorder Phase Transitions
Simon A. T. Redfern
INTRODUCTION .................................................. 105
EQUILIBRIUM AND NON-EQUILIBRIUM THERMODYNAMICS ................ 107
The Bragg-Williams model ................................... 108
Landau theory .............................................. 112
Non-convergent ordering .................................... 117
Computer modelling of cation ordering ...................... 117
EXAMPLES OF REAL SYSTEMS ...................................... 119
Cation ordering in ilmenite-hematite ....................... 119
Thermodynamics and kinetics of non-convergent disordering
in olivine ................................................. 123
Modelling non-convergent order-disorder in spinel .......... 125
Bilinear coupling of Q and Qod in albite ................... 125
The Р6/mсс-Сссm transition in pure and K-bearing
cordierite: influence of chemical variation ................ 127
Ferroelasticity and order/disorder in leucite-related
frameworks ................................................. 128
CONCLUSIONS ................................................... 130
ACKNOWLEDGEMENTS .............................................. 130
REFERENCES .................................................... 130
6 Phase Transformations Induced by Solid Solution
Peter J. Heaney
INTRODUCTION .................................................. 135
CONCEPTS OF MORPHOTROPISM ..................................... 136
A brief historical background .............................. 136
Analogies between morphotropism and polymorphism ........... 137
PRINCIPLES OF MORPHOTROPIC TRANSITIONS ........................ 140
Types of atomic substitutions .............................. 140
Linear dependence of Tc on composition ..................... 141
Morphotropic phase diagrams (MPDs) ......................... 142
Quantum saturation, the plateau effect, and defect tails ... 144
Impurity-induced twinning .................................. 146
Incommensurate phases and solid solutions .................. 148
CASE STUDIES OF DISPLACIVE TRANSITIONS INDUCED BY SOLID
SOLUTION ...................................................... 149
Ferroelectric perovskites .................................. 149
Stabilized cubic zirconia .................................. 154
Lead phosphate analogs to palmierite ....................... 155
Cuproscheelite-sanmartinite solid solutions ................ 158
Substitutions in feldspar frameworks ....................... 160
Stuffed derivatives of quartz .............................. 164
GENERAL CONCLUSIONS ........................................... 166
ACKNOWLEDGMENTS ............................................... 167
REFERENCES .................................................... 167
7 Magnetic Transitions in Minerals
Richard J. Harrison
INTRODUCTION .................................................. 175
MAGNETIC ORDERING ............................................. 175
Driving force for magnetic ordering ........................ 175
Classification of ordered (collinear) magnetic structures .. 176
Models of magnetic ordering ................................ 176
CATION ORDERING ............................................... 179
Non-convergent cation ordering in oxide spinels ............ 180
Verwey transition in magnetite ............................. 181
Convergent cation ordering in rhombohedral oxides .......... 181
Magnetic consequences of cation ordering ................... 181
SELF-REVERSED THERMOREMANENT MAGNETIZATION (SR-TRM) ........... 189
Mechanisms of self reversal ................................ 189
Self-reversal in the ilmenite-hematite solid solution ...... 190
CHEMICAL REMANENT MAGNETIZATION (CRM) ......................... 195
Principles of CRM .......................................... 195
TRANSFORMATION OF γ-FeOOH → γ-Fe2O3 → α-Fe2O3 .................. 196
CLOSING REMARKS ............................................... 198
ACKNOWLEDGMENTS ............................................... 198
REFERENCES .................................................... 198
8 NMR Spectroscopy of Phase Transitions in Minerals
Brian L. Phillips
INTRODUCTION .................................................. 203
NMR SPECTROSCOPY .............................................. 203
Basic concepts of NMR spectroscopy ......................... 204
Chemical shifts ............................................ 205
Nuclear quadrupole effects ................................. 208
Dipole-dipole interactions ................................. 210
Dynamical effects .......................................... 211
Relaxation rates ........................................... 212
Summary .................................................... 212
STRUCTURAL PHASE TRANSITIONS .................................. 213
α-β transition in cristobalite ............................. 213
α-β quartz ................................................. 218
Cryolite (Na3AlF6) ......................................... 221
Order Parameters: The PĪ-lĪ transition in anorthite
(CaAl2Si2O8) ............................................... 224
Melanophlogite ............................................. 226
INCOMMENSURATE PHASES ......................................... 227
Sr2SiO4 .................................................... 227
Akermanite ................................................. 229
Tridymite .................................................. 230
ORDERING/DISORDERING TRANSITIONS .............................. 232
Si, Al ordering in framework aluminosilicates .............. 232
Cation ordering in spinels ................................. 235
CONCLUSIONS, ACKNOWLEDGMENTS .................................. 237
REFERENCES .................................................... 237
9 Insights into Phase Transformations
from Mossbauer Spectroscopy Catherine
A. McCammon
INTRODUCTION .................................................. 241
MÖSSBAUER PARAMETERS .......................................... 241
Isomer Shift ............................................... 243
Quadrupole splitting ....................................... 245
Hyperfine magnetic splitting ............................... 247
Relative Area .............................................. 249
INSTRUMENTATION ............................................... 251
APPLICATIONS .................................................. 252
Structural transformations ................................. 253
Electronic transitions ..................................... 255
Magnetic transitions ....................................... 255
CONCLUDING REMARKS ............................................ 256
REFERENCES .................................................... 256
APPENDIX ...................................................... 259
Worked example: Incommensurate-normal phase
transformation in Fe-doped akermanite ...................... 259
APPENDIX REFERENCES ........................................... 263
10 Hard Mode Spectroscopy of Phase Transitions
Ulii Bismayer
INTRODUCTION .................................................. 265
THE ANALYSIS OF PHONON SPECTRA ................................ 266
IR powder spectra .......................................... 266
Raman spectra .............................................. 267
EXAMPLES OF SHORT-RANGE ORDER IN STRUCTURAL PHASE
TRANSITIONS ................................................... 269
Precursor in Pb3(PO4)2 ..................................... 269
Phase transitions in synthetic titanite, natural titanite
and malayaite .............................................. 272
ACKNOWLEDGMENTS ............................................... 281
REFERENCES .................................................... 281
11 Synchrotron Studies of Phase Transformations
John B. Parise
INTRODUCTION AND OVERVIEW ..................................... 285
OVERVIEW: DIFFRACTION AND SPECTROSCOPIC TECHNIQUES FOR
STUDYING TRANSITIONS .......................................... 286
Overview of the diffraction-based science from bulk
samples .................................................... 288
SYNCHROTRON RADIATION SOURCES ................................. 289
General characteristics .................................... 289
Properties of undulators, wigglers and bending magnets ..... 290
Access ..................................................... 292
Web resources .............................................. 294
DIFFRACTION STUDIES AT SYNCHROTRON SOURCES .................... 294
General considerations ..................................... 294
Diffraction from single- and from micro-crystals ........... 294
Powder diffraction studies ................................. 296
Energy-dispersive (ED) studies ............................. 299
Tools for the collection and analysis of powder
diffraction data ........................................... 300
PHASE TRANSITIONS AND SYNCHROTRON RADIATION: CASE STUDIES ..... 301
Time resolved diffraction studies .......................... 301
Multiple simultaneous techniques - a more complete
picture of the phase transition ............................ 306
ACKNOWLEDGMENTS ............................................... 308
REFERENCES .................................................... 310
12 Radiation-Induced Amorphization
Rodney C. Ewing, Alkiviathes Meldrum LuMin Wang,
ShiXin Wang
INTRODUCTION .................................................. 319
History and applications ................................... 319
MECHANISMS OF RADIATION DAMAGE ................................ 320
EXPERIMENTAL METHODS .......................................... 322
Minerals containing U and Th ............................... 322
Actinide-doping ............................................ 323
Charged-particle irradiation ............................... 323
RADIATION DAMAGE IN MINERALS .................................. 326
Zircon ..................................................... 326
Monazite ................................................... 332
Thorite and huttonite ...................................... 334
Pyrochlore and zirconolite ................................. 334
Perovskite ................................................. 337
Titanite ................................................... 338
Apatite .................................................... 339
Olivine and spinel ......................................... 341
MODELS OF RADIATION DAMAGE MECHANISMS ......................... 342
Direct impact vs. defect accumulation models ............... 342
A modified model of direct impact amorphization ............ 345
Temperature-dependence of the amorphization dose ........... 346
The effects of ion mass and energy ......................... 347
SUSCEPTIBILITY TO RADIATION-INDUCED AMORPHIZATION ............. 348
GEOLOGIC APPLICATIONS ......................................... 350
ACKNOWLEDGMENTS ............................................... 353
REFERENCES .................................................... 354
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