PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Density Functional Formalism as a Description of the Elastic Behavior of a Hard-Sphere Crystal

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The density functional method of Jaric and Mohanty [Phys. Rev. B ´ 37, 4441 (1988)] for calculating the elastic moduli of crystalline solids is considered here from the perspective of some new findings. The very slow convergence of the reciprocal-lattice vector summations and presence of the three body term in the method’s computational scheme identified in [J. Chem. Phys. 118, 6594 (2003)] is confirmed and discussed. The sensitivity of the results to the scheme parameters, such as the width of the Gaussian density profiles and the Percus-Yevick approximation used for the direct correlation function is explored. The calculations are for a hard-sphere crystal but most conclusions can be applicable to model crystalline solids in general.
Twórcy
  • Institute of Molecular Physics Polish Academy of Sciences M. Smoluchowskiego 17, 60-179 Poznań, Poland
  • Institute of Molecular Physics Polish Academy of Sciences M. Smoluchowskiego 17, 60-179 Poznań, Poland
  • Royal Holloway, University of London Department of Physics Egham, Surrey TW20 0EX, United Kingdom
Bibliografia
  • [1] P. Hohenberg, W. Kohn, Inhomogeneous Electron Gas, Physical Review 136, B864 (1964).
  • [2] W. Kohn, L.J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Physical Review 140, A1133 (1965).
  • [3] W. Koch, M.C. Holthausen, A Chemist’s Guide to Density Functional Theory, Wiley (2001).
  • [4] N.D. Mermin, Thermal Properties of the Inhomogeneous Electron Gas, Physical Review 137, A1441 (1965).
  • [5] M. Baus, Statistical mechanical theories of freezing: An overview, Journal of Statistical Physics 48, 1129 (1987).
  • [6] B. Groh, B. Mulder, Hard-sphere solids near close packing: Testing theories for crystallization, Physical Review E 61, 3811 (2000).
  • [7] Y. Singh, Density-functional theory of freezing and properties of the ordered phase, Physics Reports 207, 351 (1991).
  • [8] R. McRae, A.D.J. Haymet, Freezing of polydisperse hard spheres, The Journal of Chemical Physics 88, 1114 (1988).
  • [9] T.V. Ramakrishnan, M. Yussouff, First-principles order-parameter theory of freezing, Physical Review B 19, 2775 (1979).
  • [10] N. Sushko, P. van der Schoot, M.A.J. Michels, Density-functional theory of the crystallization of hard polymeric chains, The Journal of Chemical Physics 115, 7744 (2001).
  • [11] J.-P. Hansen, I.R. McDonald, Theory of Simple Liquids; with Applications to Soft Matter, Elsevier LTD, Oxford (2013).
  • [12] P. Tarazona, A density functional theory of melting, Molecular Physics 52, 81 (1984).
  • [13] M. Baus, J.L. Colot, Density-Wave Theory of First-Order Freezing in Two Dimensions, Molecular Physics 55, 653 (1985).
  • [14] J.L. Colot, M. Baus, The freezing of hard spheres, Molecular Physics 56, 807 (1985).
  • [15] R.O. Jones, Density functional theory: its origins, rise to prominence, and future, Reviews of Modern Physics 87, 897 (2015).
  • [16] H. Löwen, Density functional theory of inhomogeneous classical fluids: recent developments and new perspectives, Journal of Physics: Condensed Matter 14, 11897 (2002).
  • [17] M. Yussouff, Generalized structural theory of freezing, Physical Review B 23, 5871 (1981).
  • [18] T.V. Ramakrishnan, Density-Wave Theory of First-Order Freezing in Two Dimensions, Physical Review Letters 48, 541 (1982).
  • [19] M.V. Jarić, U. Mohanty, “Martensitic” instability of an icosahedral quasicrystal, Physical Review Letters 58, 230 (1987).
  • [20] G.L. Jones, Elastic constants in density-functional theory, Molecular Physics 61, 455 (1987).
  • [21] M.V. Jarić, U. Mohanty, Density-functional theory of elastic moduli: Hard-sphere and Lennard-Jones crystals, Physical Review B 37, 4441 (1988).
  • [22] D. Frenkel, A.J.C. Ladd, Elastic constants of hard-sphere crystals, Physical Review Letters 59, 1169 (1987).
  • [23] M.V. Jarić, U. Mohanty, Jarić and Mohanty Reply, Physical Review Letters 59, 1170 (1987).
  • [24] B.B. Laird, J.D. McCoy, A.D.J. Haymet, Density functional theory of freezing: Analysis of crystal density, The Journal of Chemical Physics 87, 5449 (1987).
  • [25] N. Sushko, P. van der Schoot, M.A.J. Michels, Density functional theory for the elastic moduli of a model polymeric solid, The Journal of Chemical Physics 118, 6594 (2003); Erratum: The Journal of Chemical Physics 119, 639 (2003).
  • [26] D.C. Wallace, Thermodynamics of Crystals, Dover Publication (1998).
  • [27] M. Oettel, S. Görig, A. Härtel, H. Löwen, M. Radu, T. Schilling, Free energies, vacancy concentrations, and density distribution anisotropies in hard-sphere crystals: A combined density functional and simulation study, Physical Review E 82, 051404 (2010).
  • [28] D.A. Young, B.J. Alder, Studies in molecular dynamics. XIII. Singlet and pair distribution functions for hard-disk and hard-sphere solids, The Journal of Chemical Physics 60, 1254 (1974).
  • [29] K.W. Wojciechowski, K.V. Tretiakov, Elastic properties of the f.c.c. hard sphere crystal free of defects, Computational Methods in Science and Technology 8, 84 (2002).
  • [30] K.V. Tretiakov, K.W. Wojciechowski, Poisson’s ratio of the fcc hard sphere crystal at high densities, The Journal of Chemical Physics 123, 074509 (2005).
  • [31] S. Pieprzyk, M.N. Bannerman, A.C. Brańka, M. Chudak, D.M. Heyes, Thermodynamic and dynamical properties of the hard sphere system revisited by molecular dynamics simulation, Physical Chemistry Chemical Physics 21, 6886 (2019).
  • [32] S. Bravo Yuste, A. Santos, Radial distribution function for hard spheres, Physical Review A 43, 5418 (1991).
  • [33] C.F. Tejero, M. López de Haro, Direct correlation function of the hard-sphere fluid, Molecular Physics 105, 2999 (2007).
  • [34] H. van Beijeren, M.H. Ernst, The modified Enskog equation, Physica 68, 437 (1973).
  • [35] J.R. Dorfman, H. van Beijeren, T.R. Kirkpatrick, Contemporary Kinetic Theory of Matter, Cambridge University Press (2021).
  • [36] T.R. Kirkpatrick, S.P. Das, M.H. Ernst, J. Piasecki, Kinetic theory of transport in a hard sphere crystal, The Journal of Chemical Physics 92, 3768 (1990).
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-4374c9bb-c1e9-4cb2-8d7e-f54cde77bb52
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.