Publication: Dislocations in cubic crystals described by discrete models
Loading...
Files
Full text at PDC
Publication Date
2007
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Citations
Exportar
Abstract
Discrete models of dislocations in cubic crystal lattices having one or two atoms per unit cell are proposed. These models have the standard linear anisotropic elasticity as their continuum limit and their main ingredients are the elastic stiffness constants of the material and a dimensionless periodic function that restores the translation invariance of the crystal and influences the dislocation size. For these models, conservative and damped equations of motion are proposed. In the latter case, the entropy production and thermodynamic forces are calculated and fluctuation terms obeying the fluctuation-dissipation theorem are added. Numerical simulations illustrate static perfect screw and 60 degrees dislocations for GaAs and Si.
Description
UCM subjects
Unesco subjects
Keywords
Citation
[1] H.J. Kim, Z.M. Zhao, Y.H. Xie, Three-stage nucleation and growth of Ge self-assembled quantum dots grown on partially relaxedSiGe buffer layers, Phys. Rev. B 68 (2003) 205312 (7pp.).
[2] Z.M. Zhao, O. Hul’ko, H.J. Kim, J. Liu, T. Sugahari, B. Shi, Y.H. Xie, Growth and characterization of InAs quantum dots onSi(0 0 1) surfaces, J. Cryst. Growth 271 (2004) 450–455.
[3] H.T. Grahn (Ed.), Semiconductor Superlattices: Growth and Electronic Properties, World Scientific, Singapore, 1995.
[4] D. Hull, D.J. Bacon, Introduction to Dislocations, fourth ed., Butterworth-Heinemann, Oxford, UK, 2001.
[5] J.W. Matthews, A.E. Blakeslee, Defects in epitaxial multilayers. I. Misfit dislocations, J. Cryst. Growth 27 (1974) 118–125.
[6] H. Brune, H. Ro¨ der, C. Boragno, K. Kern, Strain relief at hexagonal-close-packed interfaces, Phys. Rev. B 49 (1994) 2997–3000.
[7] C.B. Carter, R.Q. Hwang, Dislocations and the reconstruction of (1 1 1) fcc metal surfaces, Phys. Rev. B 51 (1995) 4730–4733.
[8] J.-S. Chen, S. Mehraeen, Variationally consistent multi-scale modeling and homogenization of stressed grain growth, Comput.Methods Appl. Mech. Eng. 193 (2004) 1825–1848.
[9] F.R.N. Nabarro, Theory of Crystal Dislocations, Oxford University Press, Oxford, UK, 1967.
[10] J.P. Hirth, J. Lothe, Theory of Dislocations, second ed., Wiley, New York, 1982.
[11] L.B. Freund, Dynamic Fracture Mechanics, Cambridge University Press, Cambridge, UK, 1982.
[12] P. Szuromi, D. Clery, (Eds.), Special Issue on Control and Use of Defects in Materials, Science, vol. 281, 1998, pp. 939.
[13] D.L. Holt, Dislocation cell formation in metals, J. Appl. Phys. 41 (1970) 3179–3201.
[14] J.M. Rickman, J. Vin˜ als, Modeling of dislocation structures in materials, Philos. Mag. A 75 (1997) 1251–1262.
[15] I. Groma, F.F. Csikor, M. Zaiser, Spatial correlations and higher-order gradient terms in a continuum description of dislocationdynamics, Acta Mater. 51 (2003) 1271–1281.
[16] P. Ha¨ hner, K. Bay, M. Zaiser, Fractal dislocation patterning during plastic deformation, Phys. Rev. Lett. 81 (1998) 24702473.
[17] A. Carpio, L.L. Bonilla, Discrete models of dislocations and their motion in cubic crystals, Phys. Rev. B 71 (2005) 134105 (10pp.).
[18] L.D. Landau, E.M. Lifshitz, Fluid Mechanics, Pergamon Press, London, 1959.
[19] W. van Saarloos, D. Bedeaux, P. Mazur, Non-linear hydrodynamic fluctuations around equilibrium, Physica A 110 (1982) 147–170.
[20] V. Romero-Rochı´n, J.M. Rubı´, Discretized integral hydrodynamics, Phys. Rev. E 58 (1998) 18431850.
[21] L.D. Landau, E.M. Lifshitz, Theory of Elasticity, third ed., Pergamon Press, London, 1986.
[22] A. Carpio, L.L. Bonilla, Edge dislocations in crystal structures considered as traveling waves of discrete models, Phys. Rev. Lett. 90(2003) 135502 (4pp.).
[23] D. Bedeaux, A.M. Albano, P. Mazur, Boundary conditions and nonequilibrium thermodynamics, Physica A 82 (1975) 438–462.
[24] G. Gomila, J.M. Rubı´, Fluctuations generated at semiconductor interfaces, Physica A 258 (1998) 17–31.
[25] H.T. Grahn, Introduction to Semiconductor Physics, World Scientific, Singapore, 1999.
[26] M.F. Gyure, C. Ratsch, B. Merriman, R.E. Caflisch, S. Osher, J.J. Zinck, D.D. Vvedensky, Level-set methods for the simulation ofepitaxial phenomena, Phys. Rev. E 58 (1998) R6927–R6930.
[27] M. Born, K. Huang, Dynamic Theory of Crystal Lattices, Oxford University Press, Oxford, UK, 1954.
[28] K. Hjort, J. So¨ derkvist, J.A. Schweitz, Gallium arsenide as a mechanical material, J. Micromech. Microeng. 4 (1994) 1–13.
[29] R.I. Cottam, G.A. Saunders, Elastic constants of GaAs from 2K to 320 K, J. Phys. C Solid State Phys. 6 (13) (1973) 2105–2118.
[30] S.P. Nikanorov, Yu.A. Burenkov, A.V. Stepanov, Elastic properties of silicon, Sov. Phys. Solid State 13 (10) (1971) 2516–2518 [Fiz.Tverd. Tela 13 (1972) 3001–3004].
[31] Yu.A. Burenkov, Yu.M. Burdukov, S.Yu. Davidov, S.P. Nikanorov, Temperature dependences of the elastic constants of galliumarsenide, Sov. Phys. Solid State 15 (6) (1973) 1175–1177 [Fiz. Tverd. Tela 13 (1973) 1757–1761].