Density functional approach to phonon dispersion relations and elastic constants of high-temperature crystals

Abstract

The renormalized phonon frequencies of a monatomic classical crystal at melting are related to the direct correlation functions of its liquid at freezing by means of a functional expansion of the free energy of a suitably deformed crystal around the liquid phase. Expressions for the elastic constants follow by the 'long-waves' method and are compared with earlier results obtained by the homogeneous deformation method. The role of three-body correlations in the functional expansion is discussed, but the illustrative calculations that the authors present include only the Ornstein-Zernike two-body direct correlation function of the liquid, weighted by a Debye-Waller factor. The Ornstein-Zernike function can be obtained either directly from the measured liquid structure factor of by liquid structure theory in model systems. The authors calculations of phonon dispersion relations and elastic constants refer to the BCC metals sodium and potassium, to a Lennard-Jones model for FCC argon, and to the classical one-component plasma crystallized in the BCC and FCC structures. The theoretical results are compared with neutron inelastic scattering and elastic constants data on sodium, potassium and argon, as well as with computer simulation data on the crystallized plasma.