COMPUTER SIMULATIONS OF ELASTIC CONSTANTS WITHOUT CALCULATING DERIVATIVES OF THE INTERACTION POTENTIAL
Institute of Molecular Physics, Polish Academy of Sciences,
Smoluchowskiego 17/19, 60-179 Poznań, Poland
email: kww@man.poznan.pl
DOI: 10.12921/cmst.2002.08.02.77-83
OAI: oai:lib.psnc.pl:539
Abstract:
Two Monte Carlo methods of elastic constants determination which do not require using any derivatives of the interaction potential between the particles are described. The first method corresponds to the free energy differentiation with respect to deformation in the fixed box ensemble (NVT). The second method is based on the analysis of the box fluctuations in the constant pressure ensemble with variable box shape (NpT). Its additional advantage is that it does not require any knowledge of the reference state of the system prior to simulations.
References:
[1] M. Born, K. Huang, Dynamical Theoiy of Ciystal Lattices, Oxford University Press, Oxford, 1954.
[2] D. C. Wallace. Thermodynamics of Crystals, Wiley, New York, 1972.
[3] J. H. Weiner, Statistical Mechanics of Elasticity (Wiley, New York. 1983).
[4] L. D. Landau, E. M. Lifshits, A. M. Kosevich, I. P. Pitaevskii, Theoiy of Elasticity, Pergamon Press, London, 1986.
[5] D. R. Squire, A. C. Holt, W. G. Hoover, Physica (Amsterdam) 42, 388 (1968).
[6] W. G. Hoover, Z. W. Salsburg, J. Chem. Phys. 54, 2129 (1971).
[7] J. Q. Broughton, G. H. Gilmer, J. D. Weeks, Phys. Rev. B25, 4651 (1982).
[8] M. Parrinello, A. Rahman, J. Chem. Phys. 76, 2662 (1982).
[9] M. Sprik, R. W. Impey, M. L. Klein, Phys. Rev., B29, 4368 (1984).
[10] J. R. Ray, A. Rahman, J. Chem. Phys., 80, 4423 (1984).
[11] J. R. Ray, A. Rahman, J. Chem. Phys., 82, 4243 (1985).
[12] J. R.. Ray, M. C. Moody, A. Rahman, Phys. Rev., B32, 733 (1985).
[13] J. R. Ray, M. C. Moody, A. Rahman,- Phys. Rev., B33, 895 (1986).
[14] K. W. Wojciechowski, Molec, Phys., 61, 1247 (1987).
[15] D. Frenkel, A. J. C. Ladd, Phys. Rev! Lett., 59, 1169 (1987).
[16] K. J. Runge, G. V. Chester, Phys. Rev. A36, 4852 (1987).
[17] T. Çagin, J. R. Ray, Phys. Rev., B38, 7940 (1988).
[18] K. W. Wojciechowski, A. C. Branka, Phys. Lett., A134, 314 (1989).
[19] D. H. Boal, U. Seifert, J. C. Shillcock, Phys. Rev., E48, 4274 (1993).
[20] K. W. Wojciechowski, K. V. Tretiakov, Comput. Phys. Commun,. 121-122, 528 (1999).
[21 ] O. Farago, Y. Kantor, Phys. Rev., E61, 2478 (2000).
[22] S. Sengupta, P. Nielaba, M. Rao, K. Binder, Phys. Rev. E61, 1072 (2000).
[23] M. A. Bates, D. Frenkel, Phys. Rev., E61, 5223 (2000).
[24] Z. Zhou, J. Chem. Phys., 114, 8769 (2001).
[25] M. Bowick, A. Cacciuto, G. Thorleifsson, A. Travesset, Phys. Rev. Lett., 87, 148103 (2001).
[26] D. Frenkel, A. J. C. Ladd, J. Chem. Phys., 18, 3188 (1984).
[27] K. V. Tretiakov, K. W. Wojciechowski, Phys. Rev., E60, 7626 (1999).
[28] K. V. Tretiakov, K. W. Wojciechowski, J. Phys.: Cond. Matter, 14, 1261 (2002).
[29] K. W. Wojciechowski, K. V. Tretiakov, M. Kowalik, to be published.
[30] K. W. Wojciechowski, K. V. Tretiakov, A. C. Brańka, M. Kowalik, to be published.
[31] K. W. Wojciechowski, Mol. Phys. Rep., 10, 129 (1995).
[32] K. W. Wojciechowski, Simple and efficient method of elastic properties determination by computer simulation, in Proc. IX Workshop of the Polish Soc. Computer Simul., Koszalin 28-31.08.2002, in print (in Polish).
[33] K. W. Wojciechowski, K. V. Tretiakov, Comput. Meth. Sci. Technol., 8(2), 84-92 (2002).
Two Monte Carlo methods of elastic constants determination which do not require using any derivatives of the interaction potential between the particles are described. The first method corresponds to the free energy differentiation with respect to deformation in the fixed box ensemble (NVT). The second method is based on the analysis of the box fluctuations in the constant pressure ensemble with variable box shape (NpT). Its additional advantage is that it does not require any knowledge of the reference state of the system prior to simulations.
[1] M. Born, K. Huang, Dynamical Theoiy of Ciystal Lattices, Oxford University Press, Oxford, 1954.
[2] D. C. Wallace. Thermodynamics of Crystals, Wiley, New York, 1972.
[3] J. H. Weiner, Statistical Mechanics of Elasticity (Wiley, New York. 1983).
[4] L. D. Landau, E. M. Lifshits, A. M. Kosevich, I. P. Pitaevskii, Theoiy of Elasticity, Pergamon Press, London, 1986.
[5] D. R. Squire, A. C. Holt, W. G. Hoover, Physica (Amsterdam) 42, 388 (1968).
[6] W. G. Hoover, Z. W. Salsburg, J. Chem. Phys. 54, 2129 (1971).
[7] J. Q. Broughton, G. H. Gilmer, J. D. Weeks, Phys. Rev. B25, 4651 (1982).
[8] M. Parrinello, A. Rahman, J. Chem. Phys. 76, 2662 (1982).
[9] M. Sprik, R. W. Impey, M. L. Klein, Phys. Rev., B29, 4368 (1984).
[10] J. R. Ray, A. Rahman, J. Chem. Phys., 80, 4423 (1984).
[11] J. R. Ray, A. Rahman, J. Chem. Phys., 82, 4243 (1985).
[12] J. R.. Ray, M. C. Moody, A. Rahman, Phys. Rev., B32, 733 (1985).
[13] J. R. Ray, M. C. Moody, A. Rahman,- Phys. Rev., B33, 895 (1986).
[14] K. W. Wojciechowski, Molec, Phys., 61, 1247 (1987).
[15] D. Frenkel, A. J. C. Ladd, Phys. Rev! Lett., 59, 1169 (1987).
[16] K. J. Runge, G. V. Chester, Phys. Rev. A36, 4852 (1987).
[17] T. Çagin, J. R. Ray, Phys. Rev., B38, 7940 (1988).
[18] K. W. Wojciechowski, A. C. Branka, Phys. Lett., A134, 314 (1989).
[19] D. H. Boal, U. Seifert, J. C. Shillcock, Phys. Rev., E48, 4274 (1993).
[20] K. W. Wojciechowski, K. V. Tretiakov, Comput. Phys. Commun,. 121-122, 528 (1999).
[21 ] O. Farago, Y. Kantor, Phys. Rev., E61, 2478 (2000).
[22] S. Sengupta, P. Nielaba, M. Rao, K. Binder, Phys. Rev. E61, 1072 (2000).
[23] M. A. Bates, D. Frenkel, Phys. Rev., E61, 5223 (2000).
[24] Z. Zhou, J. Chem. Phys., 114, 8769 (2001).
[25] M. Bowick, A. Cacciuto, G. Thorleifsson, A. Travesset, Phys. Rev. Lett., 87, 148103 (2001).
[26] D. Frenkel, A. J. C. Ladd, J. Chem. Phys., 18, 3188 (1984).
[27] K. V. Tretiakov, K. W. Wojciechowski, Phys. Rev., E60, 7626 (1999).
[28] K. V. Tretiakov, K. W. Wojciechowski, J. Phys.: Cond. Matter, 14, 1261 (2002).
[29] K. W. Wojciechowski, K. V. Tretiakov, M. Kowalik, to be published.
[30] K. W. Wojciechowski, K. V. Tretiakov, A. C. Brańka, M. Kowalik, to be published.
[31] K. W. Wojciechowski, Mol. Phys. Rep., 10, 129 (1995).
[32] K. W. Wojciechowski, Simple and efficient method of elastic properties determination by computer simulation, in Proc. IX Workshop of the Polish Soc. Computer Simul., Koszalin 28-31.08.2002, in print (in Polish).
[33] K. W. Wojciechowski, K. V. Tretiakov, Comput. Meth. Sci. Technol., 8(2), 84-92 (2002).
