DETERMINATION OF ELASTIC CONSTANTS BY MONTE CARLO SIMULATIONS
Wojciechowski Krzysztof W. #,$, Tretiakov Konstantin V. #
#Institute of Molecular Physics, Polish Academy of Sciences
Smoluchowskiego 17/19, 60-179 Poznan, Poland
$International Centre for Theoretical Physics, Trieste, Italy
e-mail: kww@man.poznan.pl
DOI: 10.12921/cmst.1996.01.01.25-28
OAI: oai:lib.psnc.pl:466
Abstract:
Simple computational method for studying elastic constants of solids is presented and applied to the case of a f.c.c. tethered crystal. It is shown that the system exhibits negative Poisson’s ratio in a range of isotropic tension (negative pressure).
References:
[1] M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Clarendon, Oxford, 1954).
[2] J. H. Weiner, Statistical Mechanics of Elasticity (Wiley, New York, 1983).
[3] D. R. Squire, A. C. Holt, and W. G. Hoover, Physica 42, 388 (1968).
[4] M. Parrinello and A. Rahman, J. Chem. Phys. 76, 2662 (1982).
[5] M. Parrinello and A. Rahman, J. Appl. Phys. 52, 7182 (1981).
[6] J. R. Ray and A. Rahman, J. Chem. Phys. 80, 4423 (1984).
[7] K. W. Wojciechowski, A. C. Brańka, and M. Parrinello, Molec. Phys. 53, 1541 (1984).
[8] Y. Kantor, M. Kardar, and D. R. Nelson, Phys. Rev. Lett. 57, 791 (1986); Y. Kantor, M. Kardar, and D. R. Nelson, Phys. Rev. A35, 3056 (1987).
[9] D. H. Boal, U. Seifert, and J. C. Schillcock, Phys. Rev. E48, 4274 (1993).
[10] K. W. Wojciechowski, Mol. Phys. Reports 10 (1995).
[11] R. F. Almgren, Journal of Elasticity 15, 427 (1985).
[12] R. Lakes, Science 235, 1038 (1987).
[13] B. D. Caddock and K. E. Evans, J. Phys. D22, 1877 (1989).
[14] G. W. Milton, J. Mech. Phys. Solids 40, 1105 (1992).
[15] K. W. Wojciechowski, Mol. Phys. 61 1247 (1987); K. W. Wojciechowski and A. C. Brańka, Phys. Rev. A40, 7222 (1989).
[16] R. J. Bathurst and L. Rothenburg, J. Appl. Mechanics. 55, 17 (1988); R. J. Bathurst and L. Rothenburg, Int. J. Eng. Sei. 26, 373 (1988).
[17] K. W. Wojciechowski, Phys. Lett. 137, 61 (1989).
[18] L. Rothenburg, A. A. Berlin, and R. J. Bathurst, Nature 354, 470 (1991).
[19] K. W. Wojciechowski and A. C. Brańka, Mol. Phys. Reports 6, 71 (1994) and references therein.
Simple computational method for studying elastic constants of solids is presented and applied to the case of a f.c.c. tethered crystal. It is shown that the system exhibits negative Poisson’s ratio in a range of isotropic tension (negative pressure).
[1] M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Clarendon, Oxford, 1954).
[2] J. H. Weiner, Statistical Mechanics of Elasticity (Wiley, New York, 1983).
[3] D. R. Squire, A. C. Holt, and W. G. Hoover, Physica 42, 388 (1968).
[4] M. Parrinello and A. Rahman, J. Chem. Phys. 76, 2662 (1982).
[5] M. Parrinello and A. Rahman, J. Appl. Phys. 52, 7182 (1981).
[6] J. R. Ray and A. Rahman, J. Chem. Phys. 80, 4423 (1984).
[7] K. W. Wojciechowski, A. C. Brańka, and M. Parrinello, Molec. Phys. 53, 1541 (1984).
[8] Y. Kantor, M. Kardar, and D. R. Nelson, Phys. Rev. Lett. 57, 791 (1986); Y. Kantor, M. Kardar, and D. R. Nelson, Phys. Rev. A35, 3056 (1987).
[9] D. H. Boal, U. Seifert, and J. C. Schillcock, Phys. Rev. E48, 4274 (1993).
[10] K. W. Wojciechowski, Mol. Phys. Reports 10 (1995).
[11] R. F. Almgren, Journal of Elasticity 15, 427 (1985).
[12] R. Lakes, Science 235, 1038 (1987).
[13] B. D. Caddock and K. E. Evans, J. Phys. D22, 1877 (1989).
[14] G. W. Milton, J. Mech. Phys. Solids 40, 1105 (1992).
[15] K. W. Wojciechowski, Mol. Phys. 61 1247 (1987); K. W. Wojciechowski and A. C. Brańka, Phys. Rev. A40, 7222 (1989).
[16] R. J. Bathurst and L. Rothenburg, J. Appl. Mechanics. 55, 17 (1988); R. J. Bathurst and L. Rothenburg, Int. J. Eng. Sei. 26, 373 (1988).
[17] K. W. Wojciechowski, Phys. Lett. 137, 61 (1989).
[18] L. Rothenburg, A. A. Berlin, and R. J. Bathurst, Nature 354, 470 (1991).
[19] K. W. Wojciechowski and A. C. Brańka, Mol. Phys. Reports 6, 71 (1994) and references therein.
