Elastic constants from microscopic strain fluctuations

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 2, 2000, Pages 1072-1080

  Sengupta, Surajit ^a   Nielaba, Peter ^b   Rao, Madan ^c   Binder, K ^a  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

^b UNIVERSITY OF KONSTANZ   (Germany)

^c RAMAN RESEARCH INSTITUTE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; ELASTIC CONSTANTS; LATTICE CONSTANTS; MOLECULAR DYNAMICS; MONTE CARLO METHODS; STRAIN;

ATOMISTIC COMPUTER SIMULATION; CANONICAL ENSEMBLE; FINITE-SIZE SCALING THEORY; MOLECULAR DYNAMICS SIMULATIONS; NONZERO TEMPERATURE; SINGULAR POTENTIALS; STRAIN FLUCTUATIONS; THERMODYNAMIC LIMITS;

COMPUTER SIMULATION;

EID: 0000977288     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.1072     Document Type: Article

References (66)

1. Solids Far from Equilibrium, edited by C. Godréche (Cambridge University Press, Cambridge, 1992).
2. Z. Nishiyama, Martensitic Transformations (Academic, New York, 1979)
3. A. Roitburd, in Solid State Physics, edited by H. Ehrenreich, F. Seitz, and D. Turnbull (Academic Press, New York, 1958)
4. G. R. Barsh and J. A. Krumhansl, Phys. Rev. Lett. 37, 9328 (1974)
5. Phys. Rev. Lett.M. Rao and S. Sengupta, 78, 2168 (1997).
6. Solitons in Condensed Matter Physics, edited by A. Bishop and T. Schneider (Springer, Berlin, 1978)
7. Statistical Mechanics of Membranes and Surfaces, edited by D. Nelson and S. Weinberg (World Scientific, Singapore, 1989).
8. B. Lawn, Fracture in Brittle Solids, 2nd ed. (Cambridge University Press, Cambridge, England, 1975)
9. L. B. Freund, Dynamic Fracture Mechanics (Cambridge University Press, New York, 1990)
10. D. Holland and M. P. Marder, Phys. Rev. Lett. 81, 4029 (1998).
11. Physics of Sliding Friction, Vol. E311 of NATO Advanced Study Institute Series B: Physics, edited by B. N. J. Persson and E. Tosatti (Kluwer, Dordrecht, 1996)
12. G. He, M. H. Müser, and M. O. Robbins, Science 284, 1650 (1999).
13. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon Press, Oxford, 1990)
14. D. Frenkel and B. Smit, Understanding Molecular Simulations (Academic Press, San Diego, 1996).
15. P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, 1995).
16. L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 3rd ed. (Pergamon, Oxford, 1986).
17. A. D. Bruce and R. A. Cowley, Structural Phase Transitions (Taylor & Francis, London, 1981)
18. R. A. Cowley, Phys. Rev. B 13, 4877 (1976)
19. R. Folk, H. Iro, and F. Schwabl, Z. Phys. B: Condens. Matter 25, 69 (1976)
20. K. Binder, in Phase Transformations in Materials, edited by P. Haasen (VCH, Weinheim, 1991), p. 143;L. Delaye, ibid.
21. R. M. Lynden-Bell and K. H. Michel, Rev. Mod. Phys. 66, 721 (1994)
22. B. De Raedt, K. Binder, and K. H. Michel, J. Chem. Phys. 75, 2977 (1981).
23. B. I. Halperin and D. R. Nelson, Phys. Rev. Lett. 41, 121 (1978)
24. A. P. Young, Phys. Rev. B 19, 1855 (1979)
25. K. J. Strandburg, Rev. Mod. Phys. 60, 161 (1988)
26. H. Kleinert, Gauge Fields in Condensed Matter (World Scientific, Singapore, 1989).
27. D. R. Nelson and B. I. Halperin, Phys. Rev. B 19, 2457 (1979).
28. S. T. Chui, Phys. Rev. Lett. 48, 933 (1982)
29. S. T. ChuiPhys. Rev. B 28, 178 (1983).
30. M. Parrinello and A. Rahman, J. Chem. Phys. 76, 2662 (1982)
31. A. A. Gusev, M. M. Zehnder, and U. W. Suter, Phys. Rev. B 54, 1 (1996).
32. D. R. Squire, A. C. Holt, and W. G. Hoover, Physica (Utrecht) 42, 388 (1969).
33. D. Frenkel and A. J. C. Ladd, Phys. Rev. Lett. 59, 1169 (1987).
34. K. J. Runge and G. V. Chester, Phys. Rev. A 36, 4852 (1987).
35. K. W. Wojciechowski and A. C. Brańka, Phys. Lett. A 134, 314 (1988).
36. J. A. Barker and D. Henderson, Mol. Phys. 21, 187 (1971).
37. D. C. Wallace, in Solid State Physics (Ref. 2)
38. J. H. Weiner, Statistical Mechanics of Elasticity (Wiley, New York, 1983).
39. Application of the Monte Carlo Method in Statistical Physics, edited by K. Binder (Springer, Berlin, 1998).
40. K. Binder, Z. Phys. B: Condens. Matter 43, 119 (1981).
41. M. Rovere, D. W. Heermann, and K. Binder, Europhys. Lett. 6, 585 (1988)
42. M. RovereD. W. HeermannK. BinderJ. Phys.: Condens. Matter 2, 7009 (1990).
43. M. Rovere, P. Nielaba, and K. Binder, Z. Phys. B: Condens. Matter 90, 215 (1993).
44. F. L. Román, J. A. White, and S. Velasco, Europhys. Lett. 42, 371 (1998)
45. F. L. RománJ. A. WhiteS. VelascoJ. Chem. Phys. 107, 4635 (1997).
46. S. Sengupta, D. Marx, P. Nielaba, and K. Binder, Phys. Rev. E 49, 1468 (1994).
47. D. Marx, P. Nielaba, and K. Binder, Phys. Rev. Lett. 67, 3124 (1991).
48. J. L. Lebowitz, J. K. Percus, and L. Verlet, Phys. Rev. 153, 250 (1967)
49. K. W. Krathy, Phys. Rev. A 31, 945 (1985)
50. J. J. Salacuse, A. R. Denton, and P. A. Egelstaff, Phys. Rev. E 53, 2382 (1996).
51. C. Domb, in Phase Transition and Critical Phenomena (Academic Press, London, 1974), Vol. 3.
52. M. E. Fisher and R. J. Burford, Phys. Rev. 156, 583 (1967).
53. A. M. Ferrenberg, D. P. Landau, and K. Binder, J. Stat. Phys. 63, 867 (1991).
54. F. H. Stillinger and Z. W. Salzburg, J. Chem. Phys. 46, 3962 (1967).
55. The results presented in this paper for the perfect triangular solid in the hard disk system were obtained by imposing a “single cell occupancy” constraint, rejecting all Monte Carlo moves that take a particle out of its (hexagonal) Wigner-Seitz cell. This ensures that no defects are produced during the Monte Carlo runs though the effect of the constraint on elastic moduli for the densities considered is negligible. Below a density of (Formula presented) this constraint becomes increasingly relevant.
56. To eliminate the effects of finite size completely one has to use system sizes at least an order of magnitude larger than the correlation length. Our fits to Eq. (20) yield correlation lengths of about 2–3 lattice spacings, which implies that we would need a system of at least (Formula presented) particles taking care of periodic boundary conditions. This is much larger than the sizes used by Wojciechowski and Branka.
57. For general discussions on Cauchy relations see F. Seitz, Modern Theory of Solids (McGraw-Hill, New York, 1940)
58. M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Oxford University Press, Oxford, 1954).
59. For experimental temperature-dependent elastic constants of solid argon, see H. Meixner, P. Leiderer, P. Berberich, and E. Lüscher, Phys. Lett. 40A, 257 (1972).
60. V. N. Ryzhov and E. E. Tareyeva, Phys. Rev. B 51, 8789 (1995).
61. J. Q. Broughton, G. H. Gilmer, and J. D. Weeks, Phys. Rev. B 25, 4651 (1982).
62. K. Bagchi, H. C. Andersen, and W. Swope, Phys. Rev. E 53, 3794 (1996).
63. A. Zippelius, B. I. Halperin, and D. R. Nelson, Phys. Rev. B 22, 2514 (1980).
64. A. Jaster, e-print, cond-mat/9810274.
65. K. Zahn, R. Lenke, and G. Maret, Phys. Rev. Lett. 82, 2721 (1999).
66. Q.-H. Wei, C. Bechinger, D. Rudhardt, and P. Leiderer, Phys. Rev. Lett. 81, 2606 (1998).