Microfabrics as energy minimisers: Rotation recrystallisation as an example

Journal of Structural Geology

Volumn 33, Issue 3, 2011, Pages 220-243

  Ord, Alison ^a   Hobbs, Bruce ^a,b  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^b CSIRO   (Australia)

Author keywords

Deformation lamellae; Energy minimisation; Fractals; Microfabric; Microstructure; Rotation recrystallisation

Indexed keywords

CRYSTALLOGRAPHIC PREFERRED ORIENTATIONS; DEFORMATION GRADIENTS; ENERGY MINIMISATION; FRACTAL GEOMETRY; HELMHOLTZ ENERGY; INDEPENDENT COMPONENTS; INHOMOGENEOUS DEFORMATION; LOCAL GRADIENTS; MICROFABRIC; QUARTZ AGGREGATES; QUARTZ GRAINS; RECRYSTALLISATION; SELF-SIMILAR; STRAIN TENSOR;

FRACTAL DIMENSION; MICROSTRUCTURE; QUARTZ; RECRYSTALLIZATION (METALLURGY); ROTATION;

DEFORMATION;

DEFORMATION; GEOMETRY; MICROSTRUCTURE; PREFERRED ORIENTATION; RECRYSTALLIZATION; STRAIN ANALYSIS; TECTONIC ROTATION;

SANDER;

EID: 79951669979     PISSN: 01918141     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsg.2010.11.009     Document Type: Article

References (141)

1. Ardell A.J., Christie J.M., McCormick J.W. Dislocation images in quartz and the determination of Burgers vectors. The Philosophical Magazine 1974, 29:1399-1411.
2. Asaro R.J. Micromechanics of crystals and polycrystals. Advances in Applied Mechanics 1983, 23:1-115.
3. Baeta R.D., Ashbee K.H.G. Evidence of plastic deformation of quartz at atmospheric pressure. Abstracts, Fourth European Regional Conference on Electron Microscopy, Rome 1968, 427-428. D.S. Bocciarelli (Ed.).
4. Baeta R.D., Ashbee K.H.G. Slip systems in quartz: I. experiments. The American Mineralogist 1969, 54:1551-1573.
5. Baeta R.D., Ashbee K.H.G. Slip systems in quartz: II. interpretation. The American Mineralogist 1969, 54:1574-1582.
6. Ball J.M. Convexity conditions and existence theorems in nonlinear elasticity. Archive for Rational Mechanics and Analysis 1977, 63:337-403.
7. Ball J.M. Mathematical models of martensitic microstructure. Materials Science and Engineering A 2004, 378:61-69.
8. Ball J.M., James R.D. Fine phase mixtures as minimizers of energy. Archive for Rational Mechanics and Analysis 1987, 100:13-52.
9. Bestmann M., Prior D.J. Intragranular dynamic recrystallization in naturally deformed calcite marble: diffusion accommodated grain boundary sliding as a result of subgrain rotation recrystallization. Journal of Structural Geology 2003, 25:1597-1613.
10. Bhattacharya K. Microstructure of Martensite: Why It Forms and How It Gives Rise to the Shape-memory Effect 2003, Oxford University Press, 288 pp.
11. Biot M.A. Variational principles in irreversible thermodynamics with application to viscoelasticity. The Physical Review 1955, 97:1463-1469.
12. Biot M.A. Linear thermodynamics and the mechanics of solids. Proceedings Third U.S. National Congress of Applied Mechanics, Brown University, Providence, R.I 1958, 1-18. ASME, New York.
13. Bishop J.F.W., Hill R. A theory of the plastic distortion of a polycrystalline aggregate under combined stresses. Philosophical Magazine 1951, 42:414-427.
14. Bouchez J.L. Preferred orientations of quartz (a) axes in some tectonites - kinematic inferences. Tectonophysics 1978, 49:T25-T30.
15. Bouchez J.L., Lister G.S., Nicolas A. Fabric asymmetry and shear sense in movement zones. Geologische Rundschau 1983, 72:401-419.
16. Brodie K., Rutter E. The role of transiently fine-grained reaction products in syntectonic metamorphism: natural and experimental examples. Canadian Journal of Earth Sciences 1987, 24:556-564.
17. Bronkhorst C.A., Kalidindi S.R., Anand L. Polycrystalline plasticity and the evolution of crystallographic texture in FCC metals. Philosophical Transactions: Physical Sciences and Engineering 1992, 341:443-477.
18. Cahn J.W., Larche F. A simple model for coherent equilibrium. Acta Materialia 1984, 32:1915-1923.
19. Carstensen C., Hackl K., Mielke A. Non-convex potentials and microstructures in finite-strain plasticity. Proceedings of the Royal Society London A 2002, 458:299-317.
20. Choksi R., Del Piero G., Fonseca I., Owen D. Structured deformations as energy minimizers in models of fracture and hysteresis. Mathematics and Mechanics of Solids 1999, 4:321-356.
21. Christie J.M., Griggs D.T., Carter N.L. Experimental evidence of basal slip in quartz. The Journal Of Geology 1964, 72:734-756.
22. Cobbold P.R., Gapais D. Slip-system domains. I. Plane-strain kinematics of arrays of coherent bands with twinned fibre orientations. Tectonophysics 1986, 137:113-132.
23. Cross M.C., Hohenberg P.C. Pattern formation outside of equilibrium. Reviews of Modern Physics 1993, 65:851-1112.
24. de Ronde A.A., Heilbronner R., Stunitz H., Tullis J. Spatial correlation of deformation and mineral reaction in experimentally deformed plagioclase-olivine aggregates. Tectonophysics 2004, 389:93-109.
25. De Wit A., Borckmans P., Dewel G. Twist grain boundaries in three-dimensional lamellar Turing structures. Proceedings of the National Academy of Sciences USA 1997, 94:12765-12768.
26. Del Piero G., Truskinovsky L. Macro- and micro-cracking in one-dimensional elasticity. International Journal of Solids and Structures 2001, 38:1135-1148.
27. Dell'Angelo L.N., Tullis J. Fabric development in experimentally sheared quartzites. Tectonophysics 1989, 169:1-21.
28. Delle Piane C., Burlini L., Grobety B. Reaction-induced strain localization: torsion experiments on dolomite. Earth and Planetary Science Letters 2007, 256:36-46.
29. Delle Piane C., Wilson C.J.L., Burlini L. Dilatant plasticity in high-strain experiments on calcite-muscovite aggregates. Journal of Structural Geology 2009, 31:1084-1099.
30. Dillamore I.L., Roberts J.G., Bush A.C. Occurrence of shear bands in heavily rolled cubic metals. Metal Science 1979, 13:73-77.
31. Dmitrieva O., Dondl P.W., Muller S., Raabe D. Lamination microstructure in shear deformed copper single crystals. Acta Materialia 2009, 57:3439-3449.
32. Drury M.R., Humphreys F.J., White S.H. Large strain deformation studies using polycrystalline magnesium as a rock analog. 2. Dynamic recrystallization mechanisms at high-temperatures. Physics of the Earth and Planetary Interiors 1985, 40:208-222.
33. Epstein I.R., Pojman J.A. An Introduction to Nonlinear Chemical Dynamics 1998, Oxford University Press, New York, 392 pp.
34. Ericksen J.L. Equilibrium of bars. Journal of Elasticity 1975, 5:191-202.
35. Ericksen J.L. Introduction to the Thermodynamics of Solids 1998, Springer, New York, 189 pp.
36. Eshelby J.D. The elastic energy-momentum tensor. Journal of Elasticity 1975, 5:321-335.
37. Etchecopar A. A plane kinematic model of progressive deformation in a polycrystalline aggregate. Tectonophysics 1977, 39:121-139.
38. Etchecopar A., Vasseur G. A 3D kinematic model of fabric development in polycrystalline aggregates: comparisons with experimental and natural samples. Journal of Structural Geology 1987, 9:705-717.
39. Fairbairn H.W. Structural Petrology of Deformed Rocks 1949, Addison-Wesley, Cambridge, Mass, 344 pp.
40. Francfort G.A., Marigo J.-J. Revisiting brittle fracture as an energy minimization problem. Journal of the Mechanics and Physics of Solids 1998, 46:1319-1342.
41. Gapais D., Cobbold P.R. Slip system domains. 2. Kinematic aspects of fabric development in polycrystalline aggregates. Tectonophysics 1987, 138:289-309.
42. Garcia Celma A. Domainal and fabric heterogeneities in the Cap de Creus quartz mylonites. Journal of Structural Geology 1982, 4:443-455.
43. Gibbs J.W. Collected Works of J. Willard Gibbs 1906, vol. 1. Yale University Press, New Haven, 434 pp.
44. Glimm T., Hentschel H.G.E. On isoconcentration surfaces of three dimensional Turing patterns. The International Journal of Bifurcation and Chaos 2008, 18:391-406.
45. Groves G.W., Kelly A. Change of shape due to dislocation climb. Philosophical Magazine 1969, 19:977-986.
46. Guillope M., Poirier J.P. Dynamic recrystallisation during creep of single-crystalline halite - experimental study. Journal of Geophysical Research 1979, 84:5557-5567.
47. Hähner P., Bay K., Zaiser M. Fractal dislocation patterning during plastic deformation. Physical Review Letters 1998, 81:2470-2473.
48. Halfpenny A., Prior D., Wheeler J. Analysis of dynamic recrystallization and nucleation in a quartzite mylonite. Tectonophysics 2006, 427:3-14.
49. Hansen B.L., Bronkhorst C.A., Ortiz M. Dislocation subgrain structures and modeling the plastic hardening of metallic single crystals. Modelling and Simulation in Materials Science and Engineering 2010, 18. 055001.
50. Havner K.S. On lattice and material-frame rotations and crystal hardening in high-symmetry axial loading. Philosophical Magazine 2005, 85:2861-2894.
51. Heilbronner R., Tullis J. Evolution of c axis pole figures and grain size during dynamic recrystallization: results from experimentally sheared quartzite. Journal of Geophysical Research 2006, 111(B10202).
52. Hirth G., Tullis J. Dislocation creep regimes in quartz aggregates. Journal of Structural Geology 1992, 14:145-159.
53. Hobbs B.E. Microfabrics of tectonites from the Wyangala Dam area, New South Wales, Australia. Geological Society of America Bulletin 1966, 77:685-706.
54. Hobbs B.E. Recrystallisation of single crystals of quartz. Tectonophysics 1968, 6:353-401.
55. Hobbs, B.E., Ord, A., 2010. The development of microstructure within deforming-reactive systems. Geological Society of London, in press.
56. Hobbs B.E., Ord A., Spalla I., Gosso G., Zucalli M. The interaction of deformation and metamorphic reactions. Geological Society of London, Special Issue 2010, vol. 332. pp. 189-223.
57. Hobbs, B.E., Ord, A., Regenauer-Lieb, K. The continuum thermodynamics of deformed metamorphic rocks: a review. Journal of Structural Geology, in press.
58. Houlsby, G.T., Puzrin, A.M., 1999. An approach to plasticity based on generalised thermodynamics. Proc. Int. Symp. Hypoelasticity, Horton, Greece, pp. 233-245.
59. Houlsby G.T., Puzrin A.M. Principles of Hyperplasticity 2006, Springer-Verlag, London, 351 pp.
60. Hull D. Fractography 1999, Cambridge University Press, 366 pp.
61. Hunt B.W., Peletier M.A., Wadee M.A. The Maxwell stability criterion in pseudo-energy models of kink banding. Journal of Structural Geology 2001, 22:669-681.
62. Jeřábek P., Stünitz H., Heilbronner R., Lexa O., Schulmann K. Microstructural-deformation record of an orogen-parallel extension in the Vepor Unit, West Carpathians. Journal of Structural Geology 2007, 29:1722-1743.
63. Jessell M.W., Lister G.S. A simulation of the temperature-dependence of quartz fabrics. Deformation Mechanisms, Rheology and Tectonics 1990, 54:353-362.
64. Jiang Z.T., Prior D.J., Wheeler J. Albite crystallographic preferred orientation and grain misorientation distribution in a low-grade mylonite: implications for granular flow. Journal of Structural Geology 2000, 22:1663-1674.
65. Kagan Y.Y. Earthquake spatial distribution: the correlation dimension. Geophysical Journal International 2007, 168:1175-1194.
66. Kocks U.F. Polyslip in single crystals. Acta Metallurgica 1960, 8:345-352.
67. Kocks U.F., Tome C.N., Wenk H.-R. Texture and Anisotropy 1998, Cambridge University Press, Cambridge.
68. Koenig E., Chainais P. Multifractal analysis on the sphere. ICISP 2008, LNCS 5099 2008, 613-621. Springer-Verlag, Berlin. A. Elmoataz (Ed.).
69. Kohn K.V. The relaxation of a double-well energy. Continuum Mechanics and Thermodynamics 1991, 3:193-236.
70. Kondepudi D., Prigogine I. Modern Thermodynamics 1998, John Wiley, Chichester, 486 pp.
71. Kruhl J.H., Nega M. The fractal shape of sutured quartz boundaries: application as a geothermometer. Geologische Rundschau 1996, 85:34-43.
72. Law R.D., Searle M.P., Simpson R.L. Strain, deformation temperatures and vorticity of flow at the top of the Greater Himalayan Slab, Everest Massif, Tibet. Journal of the Geological Society, London 2004, vol. 161. pp. 305-320.
73. Linker M.F., Kirby S.H., Ord A., Christie J.M. Effects of compression direction on the plasticity and rheology of hydrolytically weakened synthetic quartz crystals at atmospheric pressure. Journal of Geophysical Research 1984, 89:4241-4255.
74. Lister G.S., Hobbs B.E. The simulation of fabric development during plastic deformation and its application to quartzite: the influence of deformation history. Journal of Structural Geology 1980, 2:355-370.
75. Lister G.S., Paterson M.S., Hobbs B.E. The simulation of fabric development in plastic deformation and its application to quartzite: the model. Tectonophysics 1978, 45:107-158.
76. Lloyd G.E., Law R.D., Mainprice D. Predicting seismic properties from three-dimensional microstructures - a new look at an old quartzite. Geological Society, London, Special Publications 2010, vol. 335. pp. 603-622.
77. Lyakhovsky V., Ben-Zion Y., Agnon A. Distributed damage, faulting and friction. Journal of Geophysical Research 1997, 102:27635-27649.
78. Lyakhovsky V., Ben-Zion Y. Scaling relations of earthquakes, aseismic deformation and evolving fault structures in a damage rheology model. Geophysical Journal International 2008, 172:651-662.
79. Lyakhovsky, V., Hamiel, Y., Ben-Zion, Y. A nonlocal visco-elastic damage model and dynamic fracturing. Journal of the Mechanics and Physics of Solids, submitted for publication.
80. Mamtani M.A. Strain-rate estimation using fractal analysis of quartz grains in naturally deformed rocks. Journal Geological Society of India 2010, 75:202-209.
81. Mamtani M.A., Greiling R.O. Serrated quartz grain boundaries, temperature and strain rate: Testing fractal techniques in a syntectonic granite. Geological Society, London, Special Publications 2010, vol. 332:35-48. M.I. Spalla, A.M. Marotta, G. Gosso (Eds.).
82. Mancktelow N. The influence of grain boundary fluids on the microstructure of quartz-feldspar mylonites. Journal of Structural Geology 2004, 26:47-69.
83. Mandelbrot B.B. The Fractal Geometry of Nature 1983, Freeman, New York, 468 pp.
84. Mangasarian O.L. Non-linear Programming. Classics in Applied Mathematics 1994, Society for Industrial and applied Mathematics, Philadelphia, 220 pp.
85. Marsden J.E., Hughes T.J.R. Mathematical Foundations of Elasticity 1983, Prentice-Hall, New Jersey, 556 pp.
86. McLaren A.C., Turner R.G., Boland J.N., Hobbs B.E. Dislocation structure of the deformation lamellae in synthetic quartz; a study by electron and optical microscopy. Contributions to Mineralogy and Petrology 1970, 29:104-115.
87. Means W.D. Application of the Mohr-circle construction to problems of in homogeneous deformation. Journal of Structural Geology 1983, 5:279-286.
88. Menegon L., Pennacchioni G., Heilbronner R., Pittarello L. Evolution of quartz microstructure and c-axis crystallographic preferred orientation within ductilely deformed granitoids (Arolla unit, Western Alps). Journal of Structural Geology 2008, 30:1332-1347.
89. Miehe C., Schotte J., Lambrecht M. Homogenisation of inelastic solid materials at finite strains based on incremental minimisation principles: application to the texture analysis of polycrystals. Journal of the Mechanics and Physics of Solids 2002, 50:2123-2167.
90. Miehe C., Lambrecht M., Gurses E. Analysis of material instabilities in inelastic solids by incremental energy minimisation and relaxation methods: evolving deformation microstructures in finite plasticity. Journal of the Mechanics and Physics of Solids 2004, 52:2725-2769.
91. Morrison-Smith D.J., Paterson M.S., Hobbs B.E. An electron microscope study of plastic deformation in single crystals of synthetic quartz. Tectonophysics 1976, 33:43-79.
92. Murdzek R. The box-counting method in the large scale structure of the universe. Romanian Journal of Physics 2007, 52:149-154.
93. Nadai A. Theory of Flow and Fracture of Solids 1950, McGraw-Hill, New York, 572 pp.
94. Nye J.F. Physical Properties of Crystals 1957, Clarendon Press, Oxford, 322 pp.
95. Oertel G. Construction of crossed girdles by superposing four subfabrics, each with a single maximum. Geologische Rundschau 1983, 72:451-467.
96. Oertel G.F. Stress and Deformation: a Handbook on Tensors in Geology 1996, Oxford University Press, 292 pp.
97. Ord, A., Kirby, S.H., 1982. Burgers vectors in deformed synthetic quartz. Australian Conference in Electron Microscopy and Cell Biology Abstracts, Canberra.
98. Ortiz M. Plastic yielding as a phase transition. Journal of Applied Mechanics 1999, 66:289-298.
99. Ortiz M., Repetto E.A. Nonconvex energy minimization and dislocation structures in ductile single crystals. Journal of the Mechanics and Physics of Solids 1999, 47:397-462.
100. Ortiz M., Repetto E.A., Stainier L. A theory of subgrain dislocation structures. Journal of the Mechanics and Physics of Solids 2000, 48:2077-2114.
101. Ortoleva P.J. Nonequilibrium reaction-diffusion structures in rigid and visco-elastic media: knots and unstable noninertial flows. Modelisation mathematique et analyse numerique 1989, 23:507-517.
102. Ortoleva P.J., Ross J. On a variety of wave phenomena in chemical reactions. Journal of Chemical Physics 1974, 59:5090-5107.
103. Ortoleva P.J., Merino E., Strickholm P. Kinetics of metamorphic layering in anisotropically stressed rock. American Journal of Science 1982, 282:617-643.
104. Paterson M.S. The ductility of rocks. The Orowan 65th Anniversary Volume 1969, 377-392. M.I.T. Press. A.S. Argon (Ed.).
105. Pauli C., Schmid S.M., Heilbronner R.P. Fabric domains in quartz mylonites: localised three dimensional analysis of microstructure and texture. Journal of Structural Geology 1996, 18:1183-1203.
106. Piercy G.R., Cahn R.W., Cottrell A.H. A study of primary and conjugate slip in crystals of alpha brass. Acta Metallurgica 1955, 3:331-338.
107. Pipkin A.C. Convexity conditions for strain-dependent energy functions for membranes. Archive for Rational Mechanics and Analysis 1993, 121:361-376.
108. Poirier J.P., Nicolas A. Deformation-induced recrystallization due to progressive misorientation of subgrains, with special reference to mantle peridotites. Journal of Geology 1975, 83:707-720.
109. Rice J. Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity. Journal of the Mechanics and Physics of Solids 1971, 19:433-455.
110. Rice J. Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanisms. Constitutive Equations in Plasticity 1975, 23-79. MIT Press, Cambridge, Mass. A.S. Argon (Ed.).
111. Rubie D.C. Reaction-enhanced ductility; the role of solid-solid univariant reactions in deformation of the crust and mantle. Tectonophysics 1983, 96:331-352.
112. Sander B. Uber Zusammenhange zwischen Teilbewegung und Gefuge in Gesteinen. Tschermaks mineralogische und petrographische Mitteilungen 1911, 30:281-314.
113. Sander B. Gefügekunde der Gesteine mit besonderer Berücksichtingung der Tektonite 1930, Springer, Vienna.
114. Sander B. An Introduction to the Study of Fabrics of Geological Bodies 1970, Pergamon Press, Oxford, (translation by Phillips, F.C., & Windsor, G. of Einführung in die Gefügekunde der geologischen Körper, 1948-1950, Vienna).
115. Schmid S.M. Textures of geological materials: computer model predictions versus empirical interpretations based on rock deformation experiments and field studies. Textures of Geological Materials 1994, 279-301. DGM Informationsges, Uberursel, Germany. H.J. Bunge (Ed.).
116. Schmid S.M., Casey M. Complete fabric analysis of some commonly observed quartz c-axis patterns. Geophysical Monograph 1986, vol. 36:263-286. American Geophysical Union. B.E. Hobbs, H.C. Heard (Eds.).
117. Schmid S.M., Paterson M.S., Boland J.N. High temperature flow and dynamic recrystallization in Carrara marble. Tectonophysics 1980, 65:245-280.
118. Silhavy M. Rank 1 perturbations of deformation gradients. International Journal of Solids and Structures 1991, 38:943-965.
119. Silhavy M. The Mechanics and Thermodynamics of Continuous Media 1997, Springer, Berlin, 504 pp.
120. Stipp M., Kunze K. Dynamic recrystallization near the brittle-plastic transition in naturally and experimentally deformed quartz aggregates. Tectonophysics 2008, 448:77-97.
121. Stipp M., Stunitz H., Heilbronner R., Schmid S.M. The eastern Tonale fault zone: a 'natural laboratory' for crystal plastic deformation of quartz over a temperature range from 250 to 700 degrees C. Journal of Structural Geology 2002, 24:1861-1884.
122. Stipp M., Tullis J., Scherwath M., Behrmann J.H. A new perspective on paleopiezometry: dynamically recrystallized grain size distributions indicate mechanism changes. Geology 2010, 38:759-762.
123. Streitenberger P., Forster D., Kolbe G., Veit P. The fractal geometry of grain boundaries in deformed and recovered zinc. Scripta Metallurgica et Materialia 1995, 33:546.
124. Stunitz H., Tullis J. Weakening and strain localization produced by syn-deformational reaction of plagioclase. International Journal of Earth Sciences 2001, 90:136-148.
125. Takahashi M., Nagahama H., Masuda T., Fujimura A. Fractal analysis of experimentally, dynamically recrystallized quartz grains and its possible application as a strain-rate meter. Journal of Structural Geology 1998, 20:269-275.
126. Taylor G.I. Plastic strains in metals. Journal Institute of Metals 1938, 62:307-324.
127. Tome C.N., Lebensohn R.A., Necker C.T. Mechanical anisotropy and grain interaction in recrystallized aluminum. Metallurgical and Materials Transactions A 2002, 33A:2635-2648.
128. Trepied L., Doukhan J.-C. Evidence of ā〈ā + 〉 dislocations in synthetic quartz crystals compressed along the axis. Bulletin de Mineralogie 1982, 105:176-180.
129. Trepied L., Doukhan J.C., Paquet J. Subgrain boundaries in quartz. Theoretical analysis and microscopic observations. Physics and Chemistry of Minerals 1980, 5:201-218.
130. Truskinovsky L., Zanzotto G. Ericksen's bar revisited: energy wiggles. Journal of the Mechanics and Physics of Solids 1996, 44:1371-1408.
131. Tungatt P.D., Humphreys F.J. An in-situ optical investigation of the deformation behaviour of sodium nitrate - an analogue for calcite. Tectonophysics 1981, 78:661-675.
132. Turner F.J., Weiss L.E. Structural Analysis of Metamorphic Tectonites 1963, McGraw Hill, New York, 545 pp.
133. Twiss R.J. Structure and significance of planar deformation features in synthetic quartz. Geology 1974, 2:329-332.
134. Twiss R.J. Some planar deformation features, slip systems, and submicroscopic structures in synthetic quartz. The Journal of Geology 1976, 84:701-772.
135. van Daalen M., Heilbronner R., Kunze K. Orientation analysis of localized shear deformation in quartz fibres at the brittle-ductile transition. Tectonophysics 1999, 303:83-107.
136. Vernon R.H. A Practical Guide to Rock Microstructure 2004, Cambridge University Press, Cambridge, 594 pp.
137. Wenk H.-R. A voyage through the deformed Earth with the self-consistent model. Modelling and Simulation in Materials Science and Engineering 1999, 7:699-722.
138. White S. The dislocation structures responsible for the optical effects in some naturally- deformed quartzes. Journal of Materials Science 1973, 8:490-499.
139. White S. Geological significance of recovery and recrystallization processes in quartz. Tectonophysics 1977, 39:143-170.
140. Wintsch R.P. The possible effects of deformation on chemical processes in metamorphic fault zones. Advances in Physical Geochemistry 1985, vol. 4:251-268. chap. 10. A.B. Thompson (Ed.).
141. Zhang G., Hynes A. Determination of position-gradient tensor from strain measurements and its implications for the displacement across a shear zone. Journal of Structural Geology 1995, 17:1587-1599.