Hot Solid Properties From Liquid Structure Within Density Functional Theory
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.
KeywordsElastic Constant Phonon Frequency Liquid Structure Phonon Dispersion Curve Phonon Dispersion Relation
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