On Relative Stability of Selected Hard Tetramer Solids
Kowalik Mikołaj, Tretiakov Konstantin V., Wojciechowski Krzysztof W.
Institute of Molecular Physics, Polish Academy of Sciences
ul. Smoluchowskiego M. 17, PL-60-179 Poznań, Poland
e-mails: {kowalik/kvt/kww}@ifmpan.poznan.pl; kww@man.poznan.pl
Received:
Received: 29 October 2010; revised: 10 December 2010; accepted: 13 December 2010; published online: 17 December 2010
DOI: 10.12921/cmst.2010.16.02.141-146
OAI: oai:lib.psnc.pl:721
Abstract:
The Einstein crystal method was used to determine free energy differences between some crystalline structures of hard, homonuclear tetramers. The tetramers, each built of four identical hard spheres centered on vertices of a regular tetrahedron of sides equal to the sphere diameter, were arranged in such a way that the spheres formed the fcc lattice at close packing. Various sample sizes were studied and the results were extrapolated to the thermodynamic limit. It was found that the simplest structure of the tetramers, a simple cubic lattice of molecular mass centres with all the molecules having the same orientation, shows the highest free energy amongst the studied ones. The most stable structure of the studied ones was also found.
Key words:
Einstein crystal method, free energy, hard multispheres, molecular crystals, Monte Carlo method
References:
[1] B.J. Alder, T.E. Wainwright, J. Chem. Phys. 27, 1208 (1957).
[2] W.W. Wood, J.D. Jacobson, J. Chem. Phys. 27, 1207 (1957).
[3] H.C. Longuet-Higgins, B. Widom, Mol. Phys. 8, 549 (1964).
[4] A.D.J. Haymet, Science 236, 1076 (1987).
[5] J.A.C. Veerman, D. Frenkel, Phys. Rev. A 41, 3237 (1990).
[6] R. Blaak, D. Frenkel, B.M. Mulder, J. Chem. Phys. 110, 11652 (1999).
[7] D. Frenkel, B.M. Mulder, J.P. McTague, Phys. Rev. Lett. 52, 287 (1984).
[8] D. Frenkel, B.M. Mulder, Mol. Phys. 55, 1171 (1985).
[9] B.M. Mulder, D. Frenkel, Mol. Phys. 55, 1193 (1985).
[10] S.J. Singer, R. Mumaugh, J. Chem. Phys. 93, 1278 (1990).
[11] C. Vega, E.P.A. Paras, P.A. Monson, J. Chem. Phys. 96, 9060 (1992).
[12] C. Vega, E.P.A. Paras, P.A. Monson, J. Chem. Phys. 97, 8543 (1992).
[13] C. Vega, P.A. Monson, J. Chem. Phys. 107, 2696 (1997).
[14] W.N. Shen, P.A. Monson, J. Chem. Phys. 103, 9756 (1995).
[15] J.W. Schroer, P.A. Monson, J. Chem. Phys. 112, 8950 (2000).
[16] J.W. Schroer, P.A. Monson, J. Chem. Phys. 114, 4124 (2001).
[17] J. Largo, C. Vega, L.G. MacDowell, J.R. Solana, Mol. Phys. 100, 2397 (2002).
[18] M. Cao, P.A. Monson, J. Chem. Phys. 122, 05405 (2005).
[19] K. Huang, Statistical Mechanics (John Wiley & Sons, New York, 1963).
[20] L.V. Woodcock, Nature 385, 141 (1997).
[21] L.V. Woodcock, Nature 388, 236 (1997).
[22] R.J. Speedy, J. Phys.: Condens. Matter 10, 4387 (1998).
[23] K.V. Tretiakov, K.W. Wojciechowski, Phys. Rev. E 60, 7626 (1999).
[24] S.C. Mau, D.A. Huse, Phys. Rev. E 59, 4396 (1999).
[25] K.W. Wojciechowski, Mod. Phys. Lett. B 5, 1843 (1991).
[26] K.W. Wojciechowski, D. Frenkel, A.C. Brańka, Phys. Rev. Lett. 67, 3168 (1991).
[27] K.V. Tretiakov, K.W. Wojciechowski, J. Non-Cryst. Sol. 352, 4221 (2006).
[28] M. Kowalik, K.W. Wojciechowski, Phys. Stat. Solidi (b) 242, 626 (2005).
[29] D. Frenkel, A.J. Ladd, J. Chem. Phys. 81, 3188 (1984).
[30] D. Frenkel, B. Smit, Understanding molecular simulation (Academic Press, San Diego, 2002).
[31] E.G. Noya, C. Vega, J.P.K. Doye, A.A. Louis, J. Chem. Phys. 127, 054501 (2007).
[32] E.G. Noya, M.M. Conde, C. Vega, J. Chem. Phys. 129, 104704 (2008).
[33] E.G. Noya, C. Vega, J.P.K. Doye, A.A. Louis, J. Chem. Phys. 132, 234511 (2010).
[34] E. de Miguel, R.G. Marguta, E.M. del Río, J. Chem. Phys. 127, 154512 (2007).
[35] C. Vega, E. Sanz, J.L.F. Abascal, E.G. Noya, J. Phys.: Condens. Matter 20, 153101 (2008).
[36] J.M. Polson, E. Trizac, S. Pronk, D. Frenkel, J. Chem. Phys. 112, 5339 (2000).
[37] J. Chang, A.M. Lenhoff, S.I. Sandler, J. Chem. Phys. 120, 3003 (2004).
[38] C. Vega, P.A. Monson, J. Chem. Phys. 109, 9938 (1998).
[39] G. Navascués, E. Velasco, J. Chem. Phys. 132, 134106 (2010).
The Einstein crystal method was used to determine free energy differences between some crystalline structures of hard, homonuclear tetramers. The tetramers, each built of four identical hard spheres centered on vertices of a regular tetrahedron of sides equal to the sphere diameter, were arranged in such a way that the spheres formed the fcc lattice at close packing. Various sample sizes were studied and the results were extrapolated to the thermodynamic limit. It was found that the simplest structure of the tetramers, a simple cubic lattice of molecular mass centres with all the molecules having the same orientation, shows the highest free energy amongst the studied ones. The most stable structure of the studied ones was also found.
Key words:
Einstein crystal method, free energy, hard multispheres, molecular crystals, Monte Carlo method
References:
[1] B.J. Alder, T.E. Wainwright, J. Chem. Phys. 27, 1208 (1957).
[2] W.W. Wood, J.D. Jacobson, J. Chem. Phys. 27, 1207 (1957).
[3] H.C. Longuet-Higgins, B. Widom, Mol. Phys. 8, 549 (1964).
[4] A.D.J. Haymet, Science 236, 1076 (1987).
[5] J.A.C. Veerman, D. Frenkel, Phys. Rev. A 41, 3237 (1990).
[6] R. Blaak, D. Frenkel, B.M. Mulder, J. Chem. Phys. 110, 11652 (1999).
[7] D. Frenkel, B.M. Mulder, J.P. McTague, Phys. Rev. Lett. 52, 287 (1984).
[8] D. Frenkel, B.M. Mulder, Mol. Phys. 55, 1171 (1985).
[9] B.M. Mulder, D. Frenkel, Mol. Phys. 55, 1193 (1985).
[10] S.J. Singer, R. Mumaugh, J. Chem. Phys. 93, 1278 (1990).
[11] C. Vega, E.P.A. Paras, P.A. Monson, J. Chem. Phys. 96, 9060 (1992).
[12] C. Vega, E.P.A. Paras, P.A. Monson, J. Chem. Phys. 97, 8543 (1992).
[13] C. Vega, P.A. Monson, J. Chem. Phys. 107, 2696 (1997).
[14] W.N. Shen, P.A. Monson, J. Chem. Phys. 103, 9756 (1995).
[15] J.W. Schroer, P.A. Monson, J. Chem. Phys. 112, 8950 (2000).
[16] J.W. Schroer, P.A. Monson, J. Chem. Phys. 114, 4124 (2001).
[17] J. Largo, C. Vega, L.G. MacDowell, J.R. Solana, Mol. Phys. 100, 2397 (2002).
[18] M. Cao, P.A. Monson, J. Chem. Phys. 122, 05405 (2005).
[19] K. Huang, Statistical Mechanics (John Wiley & Sons, New York, 1963).
[20] L.V. Woodcock, Nature 385, 141 (1997).
[21] L.V. Woodcock, Nature 388, 236 (1997).
[22] R.J. Speedy, J. Phys.: Condens. Matter 10, 4387 (1998).
[23] K.V. Tretiakov, K.W. Wojciechowski, Phys. Rev. E 60, 7626 (1999).
[24] S.C. Mau, D.A. Huse, Phys. Rev. E 59, 4396 (1999).
[25] K.W. Wojciechowski, Mod. Phys. Lett. B 5, 1843 (1991).
[26] K.W. Wojciechowski, D. Frenkel, A.C. Brańka, Phys. Rev. Lett. 67, 3168 (1991).
[27] K.V. Tretiakov, K.W. Wojciechowski, J. Non-Cryst. Sol. 352, 4221 (2006).
[28] M. Kowalik, K.W. Wojciechowski, Phys. Stat. Solidi (b) 242, 626 (2005).
[29] D. Frenkel, A.J. Ladd, J. Chem. Phys. 81, 3188 (1984).
[30] D. Frenkel, B. Smit, Understanding molecular simulation (Academic Press, San Diego, 2002).
[31] E.G. Noya, C. Vega, J.P.K. Doye, A.A. Louis, J. Chem. Phys. 127, 054501 (2007).
[32] E.G. Noya, M.M. Conde, C. Vega, J. Chem. Phys. 129, 104704 (2008).
[33] E.G. Noya, C. Vega, J.P.K. Doye, A.A. Louis, J. Chem. Phys. 132, 234511 (2010).
[34] E. de Miguel, R.G. Marguta, E.M. del Río, J. Chem. Phys. 127, 154512 (2007).
[35] C. Vega, E. Sanz, J.L.F. Abascal, E.G. Noya, J. Phys.: Condens. Matter 20, 153101 (2008).
[36] J.M. Polson, E. Trizac, S. Pronk, D. Frenkel, J. Chem. Phys. 112, 5339 (2000).
[37] J. Chang, A.M. Lenhoff, S.I. Sandler, J. Chem. Phys. 120, 3003 (2004).
[38] C. Vega, P.A. Monson, J. Chem. Phys. 109, 9938 (1998).
[39] G. Navascués, E. Velasco, J. Chem. Phys. 132, 134106 (2010).
