Determination of Elastic Moduli of the r^(−12) Soft Disk Crystal by the Minimum Image Method
Tretiakov Konstantin V. 1,2*, Wojciechowski Krzysztof W. 1,2
1 Institute of Molecular Physics
Polish Academy of Sciences
M. Smoluchowskiego 17, 60-179 Poznań, Poland2 Uniwersytet Kaliski im. Prezydenta Stanisława Wojciechowskiego
Wydział Politechniczny, Katedra Informatyki
Nowy Świat 4, 62-800 Kalisz, Poland∗E-mail: tretiakov@ifmpan.poznan.pl
Received:
Received: 26 January 2024; revised: 14 February 2024; accepted: 15 February 2024; published online: 22 February 2024
DOI: 10.12921/cmst.2024.0000003
Abstract:
Elastic moduli of soft disk crystals close to the melting point have been evaluated by Monte Carlo simulations. The inverse-power potential has been used to model the interactions between particles. In calculations of the elastic moduli by the Parrinello-Rahman formalism, the long-range interactions between atoms have been taken into account using the minimum image method. The study shows that for systems consisting of around a hundred particles there are differences between the values of the elastic moduli obtained by the calculations using the minimum image method and those coming from the traditional approach. It has been found that the elastic moduli obtained by the simulations using the minimum image method even for as small as a hundred-particle systems are very close to these values at the thermodynamic limit N → ∞.
Key words:
elastic moduli, inverse-power potential, minimum image method, Monte Carlo simulation, soft disk crystal
References:
[1] J.P. Hansen, I.R. McDonald, Theory of Simple Liquids, Academic press, Amsterdam (2006).
[2] M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford (1987).
[3] A.J.C. Ladd, Monte-Carlo simulation of water, Mol. Phys. 33, 1039 (1977).
[4] A.J.C. Ladd, Long-range dipolar interactions in computer simulations of polar liquids, Mol. Phys. 36, 463 (1978).
[5] K.V. Tretiakov, K.W. Wojciechowski, Quick and accurate estimation of the elastic constants using the minimum image method, Comput. Phys. Commun. 189, 77–83 (2015).
[6] M. Parrinello, A. Rahman, Polymorphic transitions in single crystals: A new molecular dynamics method, J. Applied Physics 52, 7182 (1981).
[7] M. Parrinello, A. Rahman, Strain fluctuations and elastic constants, J. Chem. Phys. 76, 2662 (1982).
[8] K.V. Tretiakov, K.W. Wojciechowski, Elastic properties of the degenerate crystalline phase of two-dimensional hard dimers, J. Non-Cryst. Solids 352, 4221 (2006).
[9] K.W. Wojciechowski, K.V. Tretiakov, M. Kowalik, Elastic properties of dense solid phases of hard cyclic pentamers and heptamers in two dimensions, Phys. Rev. E 67, 036121 (2003).
[10] K.V. Tretiakov, K.W. Wojciechowski, Elastic properties of soft disk crystals, Rev. Adv. Mater. Sci. 14, 104 (2007).
[11] J.Q. Broughton, G.H. Gilmer, J.D. Weeks, Molecular-dynamics study of melting in two dimensions. Inverse-twelfth-power potential, Phys. Rev. B 25, 4651 (1982).
[12] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, Equation of State Calculations by Fast Computing Machines, J. Chem. Phys. 21, 1087–1092 (1953).
Elastic moduli of soft disk crystals close to the melting point have been evaluated by Monte Carlo simulations. The inverse-power potential has been used to model the interactions between particles. In calculations of the elastic moduli by the Parrinello-Rahman formalism, the long-range interactions between atoms have been taken into account using the minimum image method. The study shows that for systems consisting of around a hundred particles there are differences between the values of the elastic moduli obtained by the calculations using the minimum image method and those coming from the traditional approach. It has been found that the elastic moduli obtained by the simulations using the minimum image method even for as small as a hundred-particle systems are very close to these values at the thermodynamic limit N → ∞.
Key words:
elastic moduli, inverse-power potential, minimum image method, Monte Carlo simulation, soft disk crystal
References:
[1] J.P. Hansen, I.R. McDonald, Theory of Simple Liquids, Academic press, Amsterdam (2006).
[2] M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford (1987).
[3] A.J.C. Ladd, Monte-Carlo simulation of water, Mol. Phys. 33, 1039 (1977).
[4] A.J.C. Ladd, Long-range dipolar interactions in computer simulations of polar liquids, Mol. Phys. 36, 463 (1978).
[5] K.V. Tretiakov, K.W. Wojciechowski, Quick and accurate estimation of the elastic constants using the minimum image method, Comput. Phys. Commun. 189, 77–83 (2015).
[6] M. Parrinello, A. Rahman, Polymorphic transitions in single crystals: A new molecular dynamics method, J. Applied Physics 52, 7182 (1981).
[7] M. Parrinello, A. Rahman, Strain fluctuations and elastic constants, J. Chem. Phys. 76, 2662 (1982).
[8] K.V. Tretiakov, K.W. Wojciechowski, Elastic properties of the degenerate crystalline phase of two-dimensional hard dimers, J. Non-Cryst. Solids 352, 4221 (2006).
[9] K.W. Wojciechowski, K.V. Tretiakov, M. Kowalik, Elastic properties of dense solid phases of hard cyclic pentamers and heptamers in two dimensions, Phys. Rev. E 67, 036121 (2003).
[10] K.V. Tretiakov, K.W. Wojciechowski, Elastic properties of soft disk crystals, Rev. Adv. Mater. Sci. 14, 104 (2007).
[11] J.Q. Broughton, G.H. Gilmer, J.D. Weeks, Molecular-dynamics study of melting in two dimensions. Inverse-twelfth-power potential, Phys. Rev. B 25, 4651 (1982).
[12] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, Equation of State Calculations by Fast Computing Machines, J. Chem. Phys. 21, 1087–1092 (1953).
