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Atomic-scale models of dislocation cores in minerals: progress and prospects

Published online by Cambridge University Press:  05 July 2018

A. M. Walker*
Affiliation:
Department of Earth Sciences, University College London, Gower Street, London, WC1E 6BT, UK
P. Carrez
Affiliation:
Unité Matériaux et Transformations, UMR 8207 CNRS-Université Lille 1, Univ Lille Nord de France, F-59655 Villeneuve d'Ascq, France
P. Cordier
Affiliation:
Unité Matériaux et Transformations, UMR 8207 CNRS-Université Lille 1, Univ Lille Nord de France, F-59655 Villeneuve d'Ascq, France
*

Abstract

Recent advances in computer simulation at the atomic scale have made it possible to probe the structure and behaviour of the cores of dislocations in minerals. Such simulation offers the possibility to understand and predict the dislocation-mediated properties of minerals such as mechanisms of plastic deformation, pipe diffusion and crystal growth. In this review the three major methods available for the simulation of dislocation cores are described and compared. The methods are: (1) cluster-based models which combine continuum elastic theory of the extended crystal with an atomistic model of the core; (2) dipole models which seek to cancel the long-range elastic displacement caused by the dislocation by arranging for the simulation to contain several dislocations with zero net Burgers vector, thus allowing a fully periodic super-cell calculation; and (3) the Peierls-Nabarro approach which attempts to recast the problem so that it can be solved using only continuum-based methods, but parameterizes the model using results from atomic-scale calculations. The strengths of these methods are compared and illustrated by some of the recent studies of dislocations in mantle silicate minerals. Some of the unresolved problems in the field are discussed.

Type
Review
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 2010

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References

Asaro, R.J., Hirth, J.P., Barnett, D.M. and Lothe, J. (1973) A further synthesis of sextic and integral theories for dislocations and line forces in anisotropic media. Physica Status Solidi b, 60, 261271.CrossRefGoogle Scholar
Bigger, J.R.K., McInnes, D.A., Sutton, A.P., Payne, M.C., Stich, I., King-Smith, R.D., Bird, D.M. and Clarke, L.J. (1992) Atomic and electronic structures of the 90° partial dislocation in silicon. Physical Review Letters, 69, 22242227.CrossRefGoogle ScholarPubMed
Bilby, B.A. and Smith, E. (1956) Continuous distributions of dislocations. III. Proceedings of the Royal Society A, 236, 481505.Google Scholar
Bilby, B.A., Bullough, R. and Smith, E. (1955) Continuous distributions of dislocations: A new application of the methods of non-Riemannian geometry. Proceedings of the Royal Society A, 231, 263273.Google Scholar
Blumenau, A.T., Heggie, M.I., Fall, C.J., Jones, R. and Frauenheim, T. (2002) Dislocations in diamond: Core structures and energies. Physical Review B, 65, art. num. 205205.CrossRefGoogle Scholar
Braithwaite, J.S., Sushko, P.V., Wright, K. and Catlow, C.R.A. (2002) Hydrogen defects in forsterite: A test case for the embedded cluster method. Journal of Chemical Physics, 116, 26282635.CrossRefGoogle Scholar
Brodholt, J.P. (1997) Ab initio calculations on point defects in forsterite (Mg2SiO4) and implications for diffusion and creep. American Mineralogist, 82, 10491053.CrossRefGoogle Scholar
Brunner, D., Taeri-Baghbadrani, S., Sigle, W. and Rühle, M. (2001) Surprising results of a study on the plasticity in strontium titanate. Journal of the American Ceramic Society, 84, 11611163.CrossRefGoogle Scholar
Bulatov, V.V. and Kaxiras, E. (1997) Semidiscrete variational Peierls framework for dislocation core properties. Physical Review Letters, 78, 42214224.CrossRefGoogle Scholar
Burgers, J.M. (1939) Some considerations on the fields of stress connected with dislocations. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, 42, 293.Google Scholar
Burton, W.K., Cabrera, N. and Frank, F.C. (1949) Role of dislocations in crystal growth. Nature, 163, 398399.CrossRefGoogle Scholar
Cai, W., Bulatov, V.V., Chang, J., Li, J. and Yip, S. (2001) Anisotropic elastic interactions of a periodic dislocation array. Physical Review Letters, 86, 57275730.CrossRefGoogle ScholarPubMed
Cai, W., Bulatov, V.V., Chang, J., Li, J. and Yip, S. (2003) Periodic image effects in dislocation modelling. Philosophical Magazine, 83, 539567.CrossRefGoogle Scholar
Carrez, P., Cordier, D., Mainprice, D. and Tommasi, A. (2006) Slip systems and plastic shear anisotropy in Mg2SiO4 ringwoodite: insights from numerical modelling. European Journal of Mineralogy, 18, 149160.CrossRefGoogle Scholar
Carrez, P., Ferré, D. and Cordier, D. (2007 a) Implications for plastic flow in the deep mantle from modelling dislocations in MgSiO3 minerals. Nature, 446, 6870.CrossRefGoogle ScholarPubMed
Carrez, P., Ferré, D. and Cordier, D. (2007 b) Peierls- Nabarro model for dislocations in MgSiO3 postperovskite calculated at 120 GPa from first principles. Philosophical Magazine, 87, 32293247.CrossRefGoogle Scholar
Carrez, P., Walker, A.M., Metsue, A. and Cordier, D. (2008) Evidence from numerical modelling for 3D spreading of [001] screw dislocations in Mg2SiO4 forsterite. Philosophical Magazine, 88, 24772485.CrossRefGoogle Scholar
Carrez, P., Ferré, D. and Cordier, D. (2009 a) Peierls- Nabarro modelling of dislocations in MgO from ambient pressure to 100 GPa. Modelling and Simulation in Materials Science and Engineering, 17, art. num. 035010. doi:10.1088/0965-0393/17/3/ 035010CrossRefGoogle Scholar
Carrez, P., Ferré, D. and Cordier, D. (2009 b) Thermal activation of dislocation glide in MgO based on an Elastic-Interaction model of kink-pair nucleation. IOP Conference Series: Materials Science and Engineering, 3, art. num. 012011. doi:10.1088/ 1757-899X/3/012011CrossRefGoogle Scholar
Chen, J., Inoue, T., Weidner, D.J., Wu, Y. and Vaughan, M.T. (1998) Strength and water weakening of mantle minerals, olivine, wadsleyite and ringwoodite. Geophysical Research Letters, 25, 575578.CrossRefGoogle Scholar
Christian, J.W. and Vítek, V. (1970) Dislocations and stacking faults. Reports on Progress in Physics, 33, 307411.CrossRefGoogle Scholar
Clouet, E. (2009) Elastic energy of a straight dislocation and contribution from core tractions. Philosophical Magazine, 89, 15651584.CrossRefGoogle Scholar
Clouet, E. Ventelon, L. and Willaime, F. (2009) Dislocation core energies and core fields from first principles. Physical Review Letters, 102, art. num. 055502.CrossRefGoogle ScholarPubMed
Cordier, P. (2002) Dislocations and slip systems in mantle minerals. Pp. 137179 in: Plastic Deformation and Deformation Microstructure in Earth Materials (Karato, S.-I. and Wenk, H.-R., editors). Reviews in Mineralogy, 51. Mineralogical Society of America, Washington D.C. Google Scholar
Cordier, P., Barbe, F., Durinck, J., Tommasi, A. and Walker, A.M. (2005) Plastic deformation of minerals at high pressure: multiscale numerical modelling. Pp. 389415 in: Mineral Behaviour at Extreme Conditions (Miletich, R., editor). EMU Notes in Mineralogy, 7, Eötvö s University Press, Budapest.Google Scholar
Couret, A. and Caillard, D. (1989) Prismatic slip in beryllium I. The controlling mechanism at the peak temperature. Philosophical Magazine A, 59, 783800.CrossRefGoogle Scholar
Couvy, H., Frost, D.J., Heidelbach, F., Nyilas, K., Ungár, T., Mackwell, S. and Cordier, P. (2004) Shear deformation experiments of forsterite at 11 GPa – 1400°C in the multianvil apparatus. European Journal of Mineralogy, 16, 877889.CrossRefGoogle Scholar
Davis, K.J., Dove, P.M. and De Yoreo, J.J. (2000) The role of Mg2+ as an impurity in calcite growth. Science, 290, 11341137.CrossRefGoogle ScholarPubMed
Dehlinger, U. (1929) Zur Theorie der Rekristallisation reiner Metalle. Annalen der Physik, 393, 749793.CrossRefGoogle Scholar
de Koning, M., Antonelli, A., Buzant, M.Z., Kaxiras, E. and Justo, J.F. (1998) Finite-temperature molecular dynamics study of unstable stacking fault free energies in silicon. Physical Review B, 58, 1255512558.CrossRefGoogle Scholar
Denoual, C. (2004) Dynamic dislocation modeling by combining Peierls Nabarro and Galerkin methods. Physical Review B, 70, art. num. 024106.CrossRefGoogle Scholar
Denoual, C. (2007) Modeling dislocation by coupling Peierls-Nabarro and element-free Galerkin methods. Computer Methods in Applied Mechanics and Engineering, 196, 19151923.CrossRefGoogle Scholar
Dorn, J.E. and Rajnak, S. (1964) Nucleation of kink pairs and the Peierls mechanism of plastic deformation. Transactions of the Metallurgical Society of AIME, 230, 10521064.Google Scholar
Dumrul, S., Bazzana, S., Warzywoda, J., Biederman, R.R. and Sacco, A. (2002) Imaging of crystal growth-induced fine surface features in zeolite A by atomic force microscopy. Microporous and Mesoporous Materials, 54, 7988.CrossRefGoogle Scholar
Dupas, C., Doukhan, N., Doukhan, J.-C., Green, H.W.I. and Young, T.E. (1994) Analytical electron microscopy of a synthetic peridotite experimentally deformed in the β olivine stability field. Journal of Geophysical Research, 99, 1582115832.CrossRefGoogle Scholar
Dupas-Bruzek, C., Sharp, T.G., Rubie, D.C. and Durham, W.B. (1998) Mechanisms of transformation and deformation in Mg1.8Fe0.2SiO4 olivine and wadsleyite under non-hydrostatic stress. Physics of the Earth and Planetary Interiors, 108, 3348.CrossRefGoogle Scholar
Durinck, J., Legris, A. and Cordier, P. (2005 a) Influence of crystal chemistry on ideal plastic shear anisotropy in forsterite: First principle calculations. American Mineralogist, 90, 10721077.CrossRefGoogle Scholar
Durinck, J., Legris, A. and Cordier, P. (2005 b) Pressure sensitivity of olivine slip systems: first-principle calculations of generalised stacking faults. Physics and Chemistry of Minerals, 32, 646654.CrossRefGoogle Scholar
Durinck, J., Carrez, P. and Cordier, P. (2007) Application of the Peierls-Nabarro model to dislocations in forsterite. European Journal of Mineralogy, 19, 631639.CrossRefGoogle Scholar
Ewels, C.P., Wilson, N.T., Heggie, M.I., Jones, R. and Briddon, P.R. (2001) Graphitization at diamond dislocation cores. Journal of Physics: Condensed Matter, 13, 89658972.Google Scholar
Ferré, D., Carrez, P. and Cordier, P. (2007) First principles determination of dislocations properties of MgSiO3 perovskite at 30 GPa based on the Peierls-Nabarro model. Physics of the Earth and Planetary Interiors, 163, 283291.CrossRefGoogle Scholar
Ferré, D., Carrez, P. and Cordier, P. (2008) Modelling dislocation cores in SiTiO3 using the Peierls-Nabarro model. Physical Review B, 77, art. no. 014106.CrossRefGoogle Scholar
Ferré, D., Carrez, P. and Cordier, P. (2009 a) Dislocation modeling in calcium silicate perovskite based on the Peierls-Nabarro model. American Mineralogist, 94, 135142.CrossRefGoogle Scholar
Ferré, D., Carrez, P. and Cordier, P. (2009 b) Peierls dislocation modelling in perovskite (SaTiO3): comparison with tausonite (SrTiO3) and MgSiO3 perovskite. Physics and Chemistry of Minerals, 36, 233239.CrossRefGoogle Scholar
Frank, F.C. (1951) Crystal dislocations - Elementary concepts and definitions. Philosophical Magazine Series 7, 42, 809819.CrossRefGoogle Scholar
Frost, H.J. and Ashby, M.F. (1982) Deformation- Mechanism Maps: The Plasticity and Creep of Metals and Ceramics. Pergamon Press, Oxford, UK.Google Scholar
Gaboriaud, R.J. (2009) Dislocation core and pipe diffusion in Y2O3 . Journal of Physics D: Applied Physics, 42, art. num. 135410.CrossRefGoogle Scholar
Gale, J.D. and Rohl, A.L. (2003) The general utility lattice program (GULP). Molecular Simulation, 29, 291341.CrossRefGoogle Scholar
Gehlen, P.C., Hirth, J.P., Hoagland, R.G. and Kanninen, M.F. (1972) A new representation of the strain field associated with the cube-edge dislocation of a-iron. Journal of Applied Physics, 43, 39213933.CrossRefGoogle Scholar
Gumbsch, P., Taeri-Baghbadrani, S., Brunner, D., Sigle, W. and Rühle, M. (2001) Plasticity and an inverse brittle-to-ductile transition in strontium titanate. Physical Review Letters, 87, art. num. 085505 CrossRefGoogle Scholar
Hartford, J., von Sydow, B., Wahnström, G. and Lundqvist, B.I. (1998) Peierls barrier and stresses for edge dislocations in Pd and Al calculated from first principles. Physical Review B, 58, 24872496.CrossRefGoogle Scholar
Healy, D., Reddy, S.M., Timms, N.E., Gray, E.M. and Brovarone, A.V. (2009) Trench-parallel fast axes of seismic anisotropy due to fluid-filled cracks in subducting slabs. Earth and Planetary Science Letters, 283, 7586.CrossRefGoogle Scholar
Heggie, M.I., Jenkins, S., Ewels, C.P., Jemmer, P., Jones, R. and Briddon, P.R. (2000) Theory of dislocations in diamond and silicon and their interactions with hydrogen. Journal of Physics: Condensed Matter, 12, 1026310270.Google Scholar
Heggie, M.I., Ewels, C.P., Martsinovich, N., Scarle, S., Jones, R., Goss, J.P., Hourahine, B. and Briddon, P.R. (2002) Glide dislocations in diamond: first principles calculations of similarities with and differences from silicon and the effects of hydrogen. Journal of Physics: Condensed Matter, 14, 1268912696.Google Scholar
Hirose, K. (2006) Post-perovskite phase transition and its geophysical implications. Reviews of Geophysics, 44, RG3001.CrossRefGoogle Scholar
Hirth, J.P. (1972) Anisotropic elastic solutions for line force arrays. Scripta Metallurgica, 6, 535540.CrossRefGoogle Scholar
Hirth, J.P. and Lothe, J. (1984) Theory of Dislocations, 2nd edition. John Wiley and Sons, New York.Google Scholar
Hoagland, R.G., Hirth, J.P. and Gehlen, P.C. (1976) Atomic simulation of the dislocation core structure and Peierls stress in alkali halide. Philosophical Magazine, 34, 413439.CrossRefGoogle Scholar
Hull, D. and Bacon, D.J. (1984) Introduction to Dislocations. Pergamon Press, Oxford, UK.Google Scholar
Hunt, S.A., Weidner, D.J., Li, L., Wang, L., Walte, N.P., Brodholt, J.P. and Dobson, D.P. (2009) Weakening of calcium iridate during its transformation from perovskite to post-perovskite. Nature Geoscience, 2, 794797.CrossRefGoogle Scholar
Hÿtch, M.J., Snoeck, E. and Kilaas, R. (1998) Quantitative measurement of displacement and strain fields from HRTEM micrographs. Ultramicroscopy, 74, 131146.CrossRefGoogle Scholar
Hÿtch, M.J., Putaux, J.-L. and Pénisson, J.-M. (2003) Measurement of the displacement field of dislocations to 0.03 Å by electron microscopy. Nature, 423, 270273.CrossRefGoogle ScholarPubMed
Iitaka, T., Hirose, K., Kawamura, K. and Murakami, M. (2004) The elasticity of the MgSiO3 post-perovskite phase in the Earth's lowermost mantle. Nature, 430, 442445.CrossRefGoogle ScholarPubMed
Ismail-Beigi, S. and Arias, T.A. (2000) Ab initio study of screw dislocations in Mo and Ta: a new picture of plasticity in bcc transition metals. Physical Review Letters, 84, 14991502.CrossRefGoogle Scholar
Jia, C.L., Thust, A. and Urban, K. (2005) Atomic-scale analysis of the oxygen configuration at a SrTiO3 dislocation core. Physical Review Letters, 95, art. num. 225506.CrossRefGoogle Scholar
Johnson, C.L., Hÿtch, M.J., Buseck, P.R. (2004) Displacement and strain fields around a [100] dislocation in olivine measured to sub-angstrom accuracy. American Mineralogist, 89, 13741379.CrossRefGoogle Scholar
Joós, B., Ren, Q. and Duesbery, M.S. (1994) Peierls- Nabarro model of dislocations in silicon with generalized stacking-fault restoring forces. Physical Review B, 50, 58905898.CrossRefGoogle ScholarPubMed
Jung, H. and Karato, S.-I. (2001) Water-induced fabric transition in olivine. Science, 293, 14601463.CrossRefGoogle Scholar
Jung, H., Katayama, I., Jiang, Z., Hiraga, T. and Karato, S.-I. (2006) Effect of water and stress on the lattice preferred orientation in olivine. Tectonophysics, 421, 12.CrossRefGoogle Scholar
Jung, H., Mo, W. and Green, H.W. (2009) Upper mantle seismic anisotropy resulting from pressure-induced slip transition in olivine. Nature Geoscience, 2, 7377.CrossRefGoogle Scholar
Katayama, I. and Karato, S.-I. (2006) Effect of temperature on the B- to C-type olivine fabric transition and implications for flow pattern in subduction zones. Physics of the Earth and Planetary Interiors, 157, 3345.CrossRefGoogle Scholar
Katayama, I. and Karato, S.-I. (2008) Low temperature high stress deformation of olivine under water saturated conditions. Physics of the Earth and Planetary Interiors, 168, 125133.CrossRefGoogle Scholar
Katayama, I., Hirauchi, K., Michibayashi, K. and Ando, J. (2009) Trench-parallel anisotropy produced by serpentine deformation in the hydrated mantle wedge. Nature, 461, 11141117.CrossRefGoogle ScholarPubMed
Kaplan, T., Liu, F., Mostoller, M., Chisholm, M.F. and Milman, V. (2000) First-principles study of impurity segregation in edge dislocations in Si. Physical Review B, 61, 16741676.CrossRefGoogle Scholar
Kaxiras, E. and Duesbery, M.S. (1993) Free energies of generalized stacking faults in Si and implications for the brittle-ductile transition. Physical Review Letters, 70, 37523755.CrossRefGoogle Scholar
Kinsland, G.L. and Basset, W.A. (1977) Strength of MgO and NaCl polycrystals to confining pressures of 250 kbar at 25°C. Journal of Applied Physics, 48, 978986.CrossRefGoogle Scholar
Koizumi, H., Kirchner, H.O.K. and Suzuki, T. (1993) Kink pair nucleation and critical shear stress. Acta Metallurgica et Materialia, 41, 34833493.CrossRefGoogle Scholar
Kroupa, F. and Lejček, L. (1972) Splitting of dislocations in the Peierls-Nabarro model. Czechoslovak Journal of Physics B, 22, 813825.CrossRefGoogle Scholar
Lee, M.R. (2010) Transmission electron microscopy (TEM) of Earth and planetary materials: A review. Mineralogical Magazine, 74, 127.CrossRefGoogle Scholar
Legros, M., Dehm, G., Arzt, E. and Balk, T.J. (2008) Observation of giant diffusivity along dislocation cores. Science, 319, 16461649.CrossRefGoogle ScholarPubMed
Lejček, L. (1972) Peierls-Nabarro model of planar dislocation cores in BCC crystals. Czechoslovak Journal of Physics B, 22, 802812.CrossRefGoogle Scholar
Li., P., Karato, S.-I. and Wang, Z. (1996) Hightemperature creep in fine-grained polycrystalline CaTiO3, an analogue material of (Mg,Fe)SiO3 perovskite. Physics of the Earth and Planetary Interiors, 95, 1936.CrossRefGoogle Scholar
Li, J., Cai, W., Chang, J. and Yip, S. (2003) Atomistic measures of materials strength and deformation. Pp. 359387 in: Computational Mineral Science (Catlow, C.R.A. and Kotomin, E., editors). NATO Science Series III, 187, IOS Press, Amsterdam, The Netherlands.Google Scholar
Liu, F., Mostoller, M., Chisholm, M.F. and Kaplan, T. (1995) Electronic and elastic properties of edge dislocations in Si. Physical Review B, 51, 1719217195.CrossRefGoogle ScholarPubMed
Love, A.E.H. (1920) A Treatise on the Mathematical Theory of Elasticity, 3rd edition, Cambridge University Press, Cambridge, UK.Google Scholar
Lu, G. (2005) The Peierls-Nabarro Model of Dislocations: A venerable theory and its current development. Pp. 119 in: Handbook of Materials Modeling. Volume 1: Methods and Models (Yip, S., editor). Springer, Berlin.Google Scholar
Martsinovich, N., Heggie, M.I. and Ewels, C.P. (2003) First-principles calculations on the structure of hydrogen aggregates in silicon and diamond Journal of Physics: Condensed Matter, 15, S2815S2824.Google Scholar
Matsunaga, T. and Saka, H. (2000) Transmission electron microscopy of dislocations in SrTiO3 . Philosophical Magazine Letters, 80, 597604.CrossRefGoogle Scholar
Medvedeva, N.I., Mryasov, O.N., Gornostyrev, Y.N., Novikov, D.L. and Freeman, A.J. (1996) First-principles total-energy calculations for planar shear and cleavage decohesion processes in B2-ordered NiAl and FeAl. Physical Review B, 54, 1350613514.CrossRefGoogle ScholarPubMed
Merkel, S., Kubo, A., Miyagi, L., Speziale, S., Duffy, T.S., Mao, H.-K. and Wenk, H.-R. (2006) Plastic deformation of MgGeO3 post-perovskite at lower mantle pressures. Science, 311, 644646.CrossRefGoogle ScholarPubMed
Merkel, S., McNamara, A.K., Kubo, A., Speziale, S., Miyagi, L., Meng, Y., Duffy, T.S. and Wenk, H.-R. (2007) Deformation of (Mg,Fe)SiO3 post-perovskite and D″ anisotropy. Science, 316, 17291732.CrossRefGoogle ScholarPubMed
Metsue, A., Carrez, P., Mainprice, D. and Cordier, P. (2009) Numerical modelling of dislocations and deformation mechanisms in CaIrO3 and MgGeO3 post-perovskites - Comparison with MgSiO3 postperovskite. Physics of the Earth and Planetary Interiors, 174, 165173.CrossRefGoogle Scholar
Metsue, A., Carrez, P., Denoual, C. and Cordier, P. (2010) Plastic deformation of wadsleyite: IV Dislocation core modelling based on the Peierls- Nabarro-Galerkin model. Acta Materialia, 58, 14671478.CrossRefGoogle Scholar
Miranda, C.R. and Scandolo, S. (2005) Computational materials science meets geophysics: dislocations and slip planes in MgO. Computer Physics Communications, 169, 2427.CrossRefGoogle Scholar
Miyagi, L., Nishiyama, N., Wang, Y., Kubo, A., West, D.V., Cava, R.J., Duffy, T.S. and Wenk, H.-R. (2008) Deformation and texture development in CaIrO3 post-perovskite phase up to 6 GPa and 1300 K. Earth and Planetary Science Letters, 268, 515525.CrossRefGoogle Scholar
Miyagi, L., Merkel, S., Yagi, T., Sata, N., Ohishi, Y. and Wenk, H.-R. (2009) Diamond anvil cell deformation of CaSiO3 perovskite up to 49 GPa. Physics of the Earth and Planetary Interiors, 174, 159164.CrossRefGoogle Scholar
Miyajima, M. and Walte, N. (2009) Burgers vector determination in deformed perovskite and postperovskite of CaIrO3 using thickness fringes in weak-beam dark-field images. Ultramicroscopy, 109, 683692.CrossRefGoogle Scholar
Mookherjee, M., Stixrude, L. and Karki, B. (2008) Hydrous silicate melt at high pressure. Nature, 452, 983986.CrossRefGoogle ScholarPubMed
Mossenfelder, J.L., Connolly, J.A.D., Rubie, D.C. and Liu, M. (2000) Strength of (Mg,Fe)2SiO4 wadsleyite determined by relaxation of transformation stress. Physics of the Earth and Planetary Interiors, 120, 6378.CrossRefGoogle Scholar
Mryasov, O.N., Gornostyrev, Y.N. and Freeman, A.J. (1998) Generalized stacking-fault energetics and dislocation properties: compact versus spread unit-dislocation structures in TiAl and CuAu. Physical Review B, 58, 1192711932.CrossRefGoogle Scholar
Murakami, M., Hirose, K., Kawamura, K., Sata, N. and Ohishi, Y. (2004) Post-perovskite phase transition in MgSiO3 . Science, 304, 855858.CrossRefGoogle ScholarPubMed
Nabarro, F.R.N. (1947) Dislocations in a simple cubic lattice. Proceedings of the Physical Society of London, 59, 256272.CrossRefGoogle Scholar
Narayan, J. and Washburn, J. (1972) Self-climb of dislocation loops in magnesium oxide. Philosophical Magazine, 26, 11791190.CrossRefGoogle Scholar
Ngan, A.H.W. (1997) A generalized Peierls-Nabarro model for non-planar screw dislocation cores. Journal of the Mechanics and Physics of Solids, 45, 903921.CrossRefGoogle Scholar
Nishigaki, J., Kuroda, K. and Saka, H. (1991) Electron microscopy of dislocation structures in SrTiO3 deformed at high temperatures. Physica Status Solidi (a), 128, 319336.CrossRefGoogle Scholar
Nishihara, Y., Tinker, D., Kawazoe, T., Xu, Y., Jing, Z., Matsukage, K.N. and Karato, S.-I. (2008) Plastic deformation of wadsleyite and olivine at highpressure and high-temperature using a rotational Drickamer apparatus (RDA). Physics of the Earth and Planetary Interiors, 170, 156169.CrossRefGoogle Scholar
Niwa, K., Yagi, T., Ohgushi, K., Merkel, S., Miyajima, N. and Kikegawa, T. (2007) Lattice preferred orientation in CaIrO3 perovskite and post-perovskite formed by plastic deformation under pressure. Physics and Chemistry of Minerals, 34, 679686.CrossRefGoogle Scholar
Nocedal, J. (1980) Updating quasi-Newton matrices with limited storage. Mathematics of Computation, 25, 773782.CrossRefGoogle Scholar
Oganov, A.R. and Ono, S. (2004) Theoretical and experimental evidence for a post-perovskite phase of MgSiO3 in Earth's D″ layer. Nature, 430, 445448.CrossRefGoogle Scholar
Oganov, A.R., Martoňák, R., Laio, A., Raiteri, P. and Parrinello, M. (2005) Anisotropy of Earth's D″ layer and stacking faults in the MgSiO3 post-perovskite phase. Nature, 438, 11421144.CrossRefGoogle ScholarPubMed
Orowan, E. (1934) Zur Kristallplastizität I-III. Zeitschrift für Physik A Hadrons and Nuclei, 89, 605659.Google Scholar
Peierls, R. E. (1940) On the size of a dislocation. Proceedings of the Physical Society of London, 52, 3437.CrossRefGoogle Scholar
Pizzagalli, L., Godet, J. and Brochard, S. (2009) Glissile dislocations with transient cores in silicon. Physical Review Letters, 103, art. num. 065505.CrossRefGoogle ScholarPubMed
Poirier, J.-P. (1985) Creep of Crystals. High-temperature Deformation Processes in Metals, Ceramics and Minerals. Cambridge University Press, Cambridge, UK.CrossRefGoogle Scholar
Polanyi, M. (1934) Über eine Art Gitterstörung, die einen Kristall plastisch machen könnte. Zeitschrift für Physik A Hadrons and Nuclei, 89, 660664.Google Scholar
Prandtl, L. (1928) Hypothetical model for the kinetic theory of solid bodies. Zeitschrift für Angewandte Mathematik und Mechanik, 8, 85.CrossRefGoogle Scholar
Puls, M.P. (1980) Vacancy-dislocation interaction energies in MgO. Philosophical Magazine A, 41, 353368.CrossRefGoogle Scholar
Puls, M.P. (1983) Vacancy-dislocation interaction energies in MgO. A re-analysis. Philosophical Magazine A, 47, 497513.Google Scholar
Puls, M.P. and Norgett, M.J. (1976) Atomic calculation of the core structure and Peierls energy of an (a/2)[110] edge dislocation in MgO. Journal of Applied Physics, 47, 466477.CrossRefGoogle Scholar
Puls, M.P., Woo, C.H. and Norgett, M.J. (1977) Shellmodel calculations of interaction energies between point defects and dislocations in ionic crystals. Philosophical Magazine, 36, 14571472.CrossRefGoogle Scholar
Rabier, J. and Puls, M.P. (1989) On the core structures of edge dislocations in NaCl and MgO. Consequences for the core configurations of dislocation dipoles. Philosophical Magazine A, 59, 821842.Google Scholar
Rabier, J., Soullard, J. and Puls, M.P. (1990) Atomic calculations of point-defect interactions with an edge dislocation in NiO. Philosophical Magazine A, 61, 99108.CrossRefGoogle Scholar
Rao, S.I., Hernandez, C., Simmons, J.P., Parthasarathy, T.A. and Woodward, C. (1998) Green's function boundary conditions in two-dimensional and three-dimensional atomistic simulations of dislocations. Philosophical Magazine A, 77, 231256.CrossRefGoogle Scholar
Rao, S.I., Parthasarathy, T.A. and Woodward, C. (1999) Atomistic simulation of cross-slip processes in model fcc structures. Philosophical Magazine A, 79, 11671192.CrossRefGoogle Scholar
Raterron, P., Chen, J., Li., L., Weidner, D. and Cordier, P. (2007) Pressure-induced slip-system transition in forsterite: Single-crystal rheological properties at mantle pressure and temperature. American Mineralogist, 92, 14361445.CrossRefGoogle Scholar
Raterron, P., Amiguet, E., Chen, J., Li, L. and Cordier, P. (2009) Experimental deformation of olivine single crystals at mantle pressures and temperatures. Physics of the Earth and Planetary Interiors, 172, 7483.CrossRefGoogle Scholar
Reddy, S.M., Timms, N.E., Trimby, P., Kinny, P.D., Buchan, C. and Blake, K. (2006) Crystal-plastic deformation of zircon: A defect in the assumption of chemical robustness. Geology, 34, 257260.CrossRefGoogle Scholar
Russo, R.M. and Silver, P.G. (1994) Trench-parallel flow beneath the Nazca plate from seismic anisotropy. Science, 263, 11051111.CrossRefGoogle ScholarPubMed
Sakaguchi, I., Yurimota, H. and Sueno, S. (1992) Self-diffusion along dislocations in single-crystal MgO. Solid State Communications, 84, 889893.CrossRefGoogle Scholar
Saunders, V.R., Freyria-Fava, C., Dovesi, R. and Roetti, C. (1994) On the electrostatic potential in linear periodic polymers. Computer Physics Communications, 84, 156172.CrossRefGoogle Scholar
Schoeck, G. (1996) Dislocation emission from crack tips as a variational problem of the crack energy. Journal of the Mechanics and Physics of Solids, 44, 413437.CrossRefGoogle Scholar
Schoeck, G. (1997) The core structure of <001> dislocations in bcc metals. Philosophical Magazine Letters, 76, 1524.CrossRefGoogle Scholar
Schoeck, G. (1999 a) Peierls energy of dislocations: A critical assessment. Physical Review Letters, 82, 23102313.CrossRefGoogle Scholar
Schoeck, G. (1999 b) The Peierls energy revisited. Philosophical Magazine A, 79, 26292636.CrossRefGoogle Scholar
Schoeck, G. (2005) The Peierls model: Progress and limitations. Materials Science and Engineering A, 400-401, 717.CrossRefGoogle Scholar
Schoeck, G. and Krystian, M. (2005) The Peierls energy and kink energy in fcc metals. Philosophical Magazine, 85, 949966.CrossRefGoogle Scholar
Seeger, A. (1981) The kink picture of dislocation mobility and dislocation-point-defect interactions. Journal de Physique, 42, 201228.Google Scholar
Sharp, T.G., Bussod, G.Y.A. and Katsura, T. (1994) Microstructures in β-Mg1.8Fe0.2SiO4 experimentally deformed at transition-zone conditions. Physics of the Earth and Planetary Interiors, 86, 6983.CrossRefGoogle Scholar
Sinclair, J.E. (1971) Improved atomistic model of a bcc dislocation core. Journal of Applied Physics, 42, 53215329.CrossRefGoogle Scholar
Sinclair, J.E., Gehlen, P.C., Hoagland, R.G. and Hirth, J.P. (1978) Flexible boundary conditions and nonlinear geometric effects in atomic dislocation modeling. Journal of Applied Physics, 49, 38903897.CrossRefGoogle Scholar
Steeds, J.W., (1973) Introduction to Anisotropic Theory of Dislocations. Oxford University Press, Oxford, UK.Google Scholar
Steeds, J.W. and Willis, J.R. (1979) Dislocations in anisotropic media. Pp. 143165 in: Dislocations in Solids, The Elastic Theory, 1 (Nabarro, F.N.R., editor). North-Holland Publishing Company, Amsterdam, The Netherlands.Google Scholar
Stroth, A.N. (1958) Dislocations and cracks in anisotropic elasticity. Philosophical Magazine, 3, 625646.CrossRefGoogle Scholar
Suarez-Martinez, I., Savini, G., Haffenden, G., Campanera, J.-M. and Heggie, M.I. (2007) Dislocations of Burgers vector c/2 in graphite. Physica Status Solidi (c), 4, 29582962.CrossRefGoogle Scholar
Sun, Y. and Kaxiras, E. (1997) Slip energy barrier in aluminium and implications for ductile-brittle behaviour. Philosophical Magazine A, 75, 11171127.CrossRefGoogle Scholar
Sunagawa, I. and Tsukamoto, K. (1972) Growth spirals on NaCl and KCl crystals grown from solution phase. Journal of Crystal Growth, 15, 7378.CrossRefGoogle Scholar
Taylor, G.I. (1934) The mechanism of plastic deformation of crystals. Part I - Theoretical. Proceedings of the Royal Society of London, 145, 362387.Google Scholar
Thurel, E. and Cordier, P. (2003) Plastic deformation of wadsleyite: I. High-pressure deformation in compression. Physics and Chemistry of Minerals, 30, 256266.CrossRefGoogle Scholar
Thurel, E., Cordier, P., Frost, D. and Karato, S-I. (2003 a) Plastic deformation of wadsleyite: II. Highpressure deformation in shear. Physics and Chemistry of Minerals, 30, 267270.CrossRefGoogle Scholar
Thurel, E., Douin, J. and Cordier, P. (2003 b) Plastic deformation of wadsleyite: III. interpretation of dislocations and slip systems. Physics and Chemistry of Minerals, 30, 271279.CrossRefGoogle Scholar
Tsuchiya, T., Tsuchiya, J., Umemoto, K. and Wentzcovitch, R.M. (2004) Phase transition in MgSiO3-perovskite in the Earth's Lower Mantle. Earth and Planetary Science Letters, 224, 241248.CrossRefGoogle Scholar
Verma, A.K. and Karki, B.B. (2009) Ab initio investigation of native and protonic point defects in Mg2SiO4 polymorphs under high pressure. Earth and Planetary Science Letters, 285, 140149.CrossRefGoogle Scholar
Vítek, V. (1966) Thermally activated motion of screw dislocations in B.C.C. metals. physica status solidi (b), 18, 687701.CrossRefGoogle Scholar
Vítek, V. (1968) Intrinsic stacking faults in body-centred cubic crystals. Philosophical Magazine, 18, 773786.CrossRefGoogle Scholar
Vítek, V., Perrin, R.C. and Bowen, D.K. (1970) The core structure of (111) screw dislocations in b.c.c. crystals. Philosophical Magazine, 21, 10491073.CrossRefGoogle Scholar
Volterra, V. (1907) Sur l’équilibre des corps élastiques multiplement connexes. Annales Scientifiques de l’Ecole Normale Supérieure, 24, 401517.CrossRefGoogle Scholar
Walker, A.M. (2010) Simulation of screw dislocations in wadsleyite. Physics and Chemistry of Minerals, 37, 301310.CrossRefGoogle Scholar
Walker, A.M., Wright, K. and Slater, B. (2003) A computational study of oxygen diffusion in olivine. Physics and Chemistry of Minerals, 30, 536545.CrossRefGoogle Scholar
Walker, A.M., Slater, B., Gale, J.D. and Wright, K. (2004) Predicting the structure of screw dislocations in nanoporous materials. Nature Materials, 3, 715720.CrossRefGoogle ScholarPubMed
Walker, A.M., Gale, J.D., Slater, B. and Wright, K. (2005 a) Atomic scale modelling of the cores of dislocations in complex materials part 1: methodology. Physical Chemistry Chemical Physics, 7, 32273234.CrossRefGoogle ScholarPubMed
Walker, A.M., Gale, J.D., Slater, B. and Wright, K. (2005 b) Atomic scale modelling of the cores of dislocations in complex materials part 2: applications. Physical Chemistry Chemical Physics, 7, 32353242.CrossRefGoogle ScholarPubMed
Walker, A.M., Hermann, J., Berry, A.J. and O’Neill, H.St.C. (2007) Three water sites in upper mantle olivine and the role of titanium in the water weakening mechanism. Journal of Geophysical Research, 112, art. no. B05211CrossRefGoogle Scholar
Walker, A.M., Zhang, F., Wright, K. and Gale, J.D. (2009) Magnesium vacancy segregation and fast pipe diffusion for the 1/2<110>{110} edge dislocation in MgO. EOS Transactions of the AGU, 90, Fall meeting supplement, abstract MR23B-06.Google Scholar
Walte, N.P., Heidelbach, F., Miyajima, N., Frost, D.J., Rubie, D.C. and Dobson, D.P. (2009) Transformation textures in post-perovskite: Understanding mantle flow in the D″ layer of the Earth. Geophysical Research Letters, 36, L04302.CrossRefGoogle Scholar
Wang, Y., Durham, W.B., Getting, I. and Weidner, D.J. (2003) The deformation-DIA: a new apparatus for high-temperature triaxial deformation to pressures up to 15 GPa. Review of Scientific Instruments, 74, 3002-11.CrossRefGoogle Scholar
Watson, G.W., Kelsey, E.T., de Leeuw, N.H., Harris, D.J. and Parker, S.C. (1996) Atomistic simulation of dislocations, surfaces and interfaces in MgO. Journal of the Chemical Society, Faraday Transactions, 92, 433438.CrossRefGoogle Scholar
Watson, G.W., Kelsey, E.T. and Parker, S.C. (1999) Atomistic simulation of screw dislocations in rock salt structured materials. Philosophical Magazine A, 79, 527536.CrossRefGoogle Scholar
Watson, G.W., Oliver, P.M. and Parker, S.C. (2001) Atomistic simulation of crystal growth at the a<100> screw dislocation terminating at the {100} surface of MgO. Surface Science Letters, 474, L185L190.CrossRefGoogle Scholar
Wolf, D., Keblinski, P., Phillpot, S.R. and Eggebrecht, J. (1999) Exact method for the simulation of Coulombic systems by spherically truncated, pairwise r–1 summation. Journal of Chemical Physics, 110, 82548282.CrossRefGoogle Scholar
Woo, C.H. and Puls, M.P. (1976) An improved method of calculating the lattice friction stress using an atomistic model. Journal of Physics C: Solid State Physics, 9, L27L31.CrossRefGoogle Scholar
Woo, C.H. and Puls, M.P. (1977 a) Atomistic breathing shell model calculations of dislocation core configurations in ionic crystals. Philosophical Magazine, 35, 727756.CrossRefGoogle Scholar
Woo, C.H. and Puls, M.P. (1977 b) The Peierls mechanism in MgO. Philosophical Magazine, 35, 16411652.CrossRefGoogle Scholar
Woodward, C. (2005) First-principles simulations of dislocation cores. Materials Science and Engineering A, 400-401, 5967.CrossRefGoogle Scholar
Woodward, C. and Rao, S.I. (2002) Flexible ab initio boundary conditions: Simulating isolated dislocations in bcc Mo and Ta. Physical Research Letters, 88, art. num. 216402.CrossRefGoogle ScholarPubMed
Woodward, C., Trinkle, D.R., Hector, L. G. Jr., and Olmsted, D.L. (2008) Prediction of dislocation cores in aluminium from density functional theory. Physical Review Letters, 100, art. num. 045507.CrossRefGoogle ScholarPubMed
Wookey, J., Stackhouse, S., Kendall, J.M., Brodholt, J.P. and Price, G.D. (2005) Efficacy of the postperovskite phase as an explanation for lowermostmantle seismic properties. Nature, 438, 10041007.CrossRefGoogle Scholar
Wright, K., Price, G.D. and Poirier, J.P. (1992) High temperature creep of the perovskites CaTiO3 and NaNbO3 . Physics of the Earth and Planetary Interiors, 74, 922.CrossRefGoogle Scholar
Xu, G. and Argon, A.S. (2001) Energetics of homogeneous nucleation of dislocation loops under a simple shear stress in perfect crystals. Materials Science and Engineering A, 319-321, 144147.CrossRefGoogle Scholar
Yamazaki, D. and Karato, S.-I. (2001) High-pressure rotational deformation apparatus to 15 GPa. Review of Scientific Instruments, 72, 4207–11.CrossRefGoogle Scholar
Zhang, Z., Sigle, W. and Rühle, M. (2002 a) Atomic and electronic characterization of the a[100] dislocation core in SrTiO3 . Physical Review B, 66, art. num. 094108.CrossRefGoogle Scholar
Zhang, Z., Sigle, W., Kurtz, W. and Rühle, M. (2002 b) Electronic and atomic structure of a dissociated dislocation in SrTiO3 . Physical Review B, 66, art. num. 214112.CrossRefGoogle Scholar