VIBRATIONAL AND ELASTIC PROPERTIES OF THE HOT SOLID RELATED TO THE STATIC AND DYNAMIC STRUCTURE OF THE LIQUID WITHIN DENSITY-FUNCTIONAL THEORY

Within the density functional formalism for inhomogeneous equilibrium states in the classical regime, differences between the thermodynamic potentials of solid at melting and of the liquid at freezing can be constructed from the static structure of the liquid. This approach has led to the density wave theory of liquid-solid coexistence and has more recently allowed treatment of structural deformations in hot crystals. We review the available calculations of renormalized phonon dispersion relations and elastic constants in monatomic classical crystals near melting from input involving the Ornstein-Zernike function of the liquid and the Lindemann parameter of the solid. An extension to multicomponent systems is presented, with specific focus on a canonical phonon dispersion relation for a symmetric model of alkali halides composed of isoelectronic ions. By recourse to recent developments of density functional theory for time-dependent problems it is further shown that phonons in the hot crystal can be related to both the static and the dynamic structure of the liquid, with relaxation times expressing phonon widths and governing interpolation between static and high frequency behaviours.