Hot Solid Properties From Liquid Structure Within Density Functional Theory

  • M. P. Tosi
Part of the Condensed Matter Theories book series (COMT, volume 8)


The idea that structural correlations in a liquid near freezing carry useful information on properties of its solid near melting is an old one. Early examples are the Kirkwood-Monroe theory of the liquid-solid transition1 and Faber’s treatment of the vacancy formation energy in hot close-packed metals,2 which were framed in terms of the liquid pair distribution function g(r) (or equivalently the liquid structure factor S(k)) and a pairwise potential of interaction between the particles. The underlying assumption of these theories is that the character of the interatomic forces should not be altered across the phase transition. The approximate notion of pair potentials is transcended in the functional cluster expansion of Lebowitz and Percus.3 This leads to a formal expression for the free energy of a classical system in an inhomo-geneous state as a function of its density profile n(r), involving the many-particle direct correlation functions of its homogeneous liquid. Their work preluded to the development of the density functional theoretical approach4, 5 (DFT), which focusses on the free energy functional F[n(r)] of the inhomogeneous system and aims at approximately evaluating it from a knowledge of thermodynamic and microscopic correlation-response functions of a corresponding homogeneous system.


Elastic Constant Phonon Frequency Liquid Structure Phonon Dispersion Curve Phonon Dispersion Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J.G. Kirkwood and E. Monroe, Statistical mechanics of fusion, J. Chem. Phys. 9:514 (1941).ADSCrossRefGoogle Scholar
  2. 2.
    T.C. Faber, “An Introduction to the Theory of Liquid Metals”, University Press, Cambridge (1972).Google Scholar
  3. 3.
    J.L. Lebowitz and J.K. Percus, Statistical thermodynamics of nonuniform fluids, J. Math. Phys. 4:116 (1963).MathSciNetADSMATHCrossRefGoogle Scholar
  4. 4.
    R. Evans, The nature of the liquid-vapour interface and other topics in the statistical mechanics of nonuniform classical fluids, Adv. Phys. 28:143 (1979).ADSCrossRefGoogle Scholar
  5. 5.
    S. Lundqvist and N.H. March, “Theory of the Inhomogeneous Electron Gas”, Plenum, New York (1983).Google Scholar
  6. 6.
    T.V. Ramakrishnan and M. Yussouff, First-principles order-parameter theory of freezing, Phys. Rev. B 19:2775 (1979).ADSCrossRefGoogle Scholar
  7. 7.
    A.D.J. Haymet and D.W. Oxtoby, A molecular theory for the solid-liquid interface, J. Chem. Phys. 74:2559 (1981).ADSCrossRefGoogle Scholar
  8. 8.
    N.H. March and M.P. Tosi, Liquid direct correlation function, singlet densities and the theory of freezing, Phys. Chem. Liquids 11:129 (1981).CrossRefGoogle Scholar
  9. 9.
    G. Senatore and G. Pastore, Density-functional theory of freezing for quantum systems: the Wigner crystallization, Phys. Rev. Lett. 64:303 (1990).ADSCrossRefGoogle Scholar
  10. 10.
    T.V. Ramakrishnan, Density wave theory of freezing and the solid, Pramana 22:365 (1984).ADSCrossRefGoogle Scholar
  11. 11.
    M. Rovere, G. Senatore and M.P. Tosi, Ordering transitions induced by Coulomb interactions, in: “Progress on Electron Properties of Solids”, E. Doni, R. Girlanda, G. Pastori Parravicini and A. Quattropani, eds., Kluwer, Dordrecht (1989).Google Scholar
  12. 12.
    M. Baus, The present status of the density-functional theory of the liquid-solid transition, J. Phys.: Condens. Matter 2:2111(1990).ADSCrossRefGoogle Scholar
  13. 13.
    M.P. Tosi, Freezing of Coulomb liquids, in: “Strongly Coupled Plasma Physics”, S. Ichimaru, ed., Yamada Science Foundation, Tokyo (1990).Google Scholar
  14. 14.
    Y. Singh, Density-functional theory of freezing and properties of the ordered phase, Phys. Rept. 207:351 (1991).ADSCrossRefGoogle Scholar
  15. 15.
    A.J.M. Yang, P.D. Fleming and J.H. Gibbs, Molecular theory of surface tension, J. Chem. Phys. 64:3732 (1976).ADSCrossRefGoogle Scholar
  16. 16.
    A.R. Denton and N.W. Ashcroft, Modified weighted-density-functional theory of nonuniform classical liquids, Phys. Rev. A 39:4701 (1989).ADSCrossRefGoogle Scholar
  17. 17.
    C.N. Likos and N.W. Ashcroft, Self consistent theory of freezing of the classical One Component Plasma, in press.Google Scholar
  18. 18.
    M. Born and K. Huang, “Dynamical Theory of Crystal Lattices”, University Press, Oxford (1954).MATHGoogle Scholar
  19. 19.
    R. A. Cowley, Anharmonic crystals, Rept. Progr. Phys. 31:123 (1968).ADSCrossRefGoogle Scholar
  20. 20.
    P.F. Choquard, “The Anharmonic Crystal”, Benjamin, New York (1967).Google Scholar
  21. 21.
    M. Ferconi and M.P. Tosi, Phonon dispersion curves in high-temperature solids from liquid structure factors, Europhys. Lett. 14:797 (1991).ADSCrossRefGoogle Scholar
  22. 22.
    M. Ferconi and M.P. Tosi, Density functional approach to phonon dispersion relations and elastic constants of high-temperature crystals, J. Phys.: Condens. Matter 3:9943 (1991).ADSCrossRefGoogle Scholar
  23. 23.
    M.C. Mahato, H.R. Krishnamurthy and T.V. Ramakrishnan, Phonon dispersion of crystalline solids from the density-functional theory of freezing, Phys. Rev. B 44:9944 (1991).ADSCrossRefGoogle Scholar
  24. 24.
    R.A. Cowley, A.D.B. Woods and G. Dolling, Crystal dynamics of potassium I: pseudopotential analysis of phonon dispersion curves at 9 K, Phys. Rev. 150:487 (1966).ADSCrossRefGoogle Scholar
  25. 25.
    W.J.L. Buyers and R.A. Cowley, Crystal dynamics of potassium II: the anharmonic effects, Phys. Rev. 180:755 (1969).ADSCrossRefGoogle Scholar
  26. 26.
    Z. Badirkhan, M. Rovere and M.P. Tosi, Freezing of liquid alkali metals as screened ionic plasmas, J. Phys.: Condens. Matter 3:1627 (1991).ADSCrossRefGoogle Scholar
  27. 27.
    D. Wolf, P.R. Okamoto, S. Yip, J.F. Lutsko and M. Kluge, Thermodynamic parallels between solid-state amorphization and melting, J. Mater. Res. 5:286 (1990).ADSCrossRefGoogle Scholar
  28. 28.
    M.D. Lipkin, S.A. Rice and U. Mohanty, The elastic constants of condensed matter: a direct-correlation function approach, J. Chem. Phys. 82:472 (1985).ADSCrossRefGoogle Scholar
  29. 29.
    G.L. Jones, Elastic constants in density-functional theory, Molec. Phys. 61:455 (1987).ADSCrossRefGoogle Scholar
  30. 30.
    M.V. Jaric and U. Mohanty, “Martensitic” instability of an icosahedral quasicrystal, Phys. Rev. Lett. 58:230 (1987).ADSCrossRefGoogle Scholar
  31. 31.
    E. Velasco and P. Tarazona, Elastic properties of a hard-sphere crystal, Phys. Rev. A 36:979 (1987).ADSCrossRefGoogle Scholar
  32. 32.
    M.V. Jaric and U. Mohanty, Density-functional theory of elastic moduli: hard-sphere and Lennard-Jones crystals, Phys. Rev. B 37:4441 (1988).ADSCrossRefGoogle Scholar
  33. 33.
    S. Gewurtz and B.P. Stoicheff, Elastic constants of argon single crystals determined by Brillouin scattering, Phys. Rev. B 10:3487 (1974).ADSCrossRefGoogle Scholar
  34. 34.
    M. P. Tosi and V. Tozzini, to be published.Google Scholar
  35. 35.
    L.L. Foldy and B. Segall, Anion-cation mirror symmetry in alkali halide ion dynamics, Phys. Rev. B 25:1260 (1982).ADSCrossRefGoogle Scholar
  36. 36.
    M.H. Dickens, M.T. Hutchings and J.B. Suck, Temperature variation of phonon frequency distribution in the fast ion conductor Lead Fluoride, Solid State Commun. 34:559 (1980).ADSCrossRefGoogle Scholar
  37. 37.
    M. Ferconi and G. Vignale, in the course of publication.Google Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • M. P. Tosi
    • 1
  1. 1.Scuola Normale SuperiorePisaItaly

Personalised recommendations