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 arerelated tothedirectcorrelationfunctionsofitsliquidatfreezing by meansofafunctional expansion of the free energy of a suitably deformed crystal around the liquid phase. Expressions for lhe elastic ~~~t a n t ~ follow by the 'long-waves' method and are compared with earlier results obtained by the homogeneous deformation method. The role of threebody correlations in the functional expansion is discussed, but the illustrative calculations that we present include only the Omstein-Zernike two-body direct correlation function of the Liquid, weighted by a Debye-Waller factor. The Orstein-Zemike function can be obtained eitherdirecllyfrom the measured liquidstructure factoror by liquid structure theory in modelsystems. Ourcalculationsofphonondispersion relations and elasticconstantsrefer to the BCC metals sodium and potassium, to a Lennard-Jones model for FCC argon, and to lheclassicalone-componentplasmacrystallizedintheBccandFCCstructures. The theoretical resultsare compared with neutron inelasticscatteringandelasticconstantsdataonsodium, potassium and argon, as well as with computer simulation data on the crystallized plasma.

Vibrational and Elastic Properties of the Wigner Electron Lattice Near Melting

“…We have also calculated the elastic constants of the Wigner crystal near melting both by the dynamic method of long waves (LW) [12] and by the method of static homogeneous deformations (HD) [20]. The latter method does not involve charge separation and hence allows one to separately evaluate the elastic constants cll and c12, rather than only the shear combination cll-c12.…”

Displacement field and elastic constants in nonideal crystals

“…Because we have a systematic way to discover the hydrodynamic fields and their equations, we can correct the work by Szamel and Ernst and achieve consistency with the phenomenological description, which these authors could not 10,11 . Our approach uses density functional theory (DFT), to describe the equilibrium correlations in a crystal, and thus superficially bears similarities to earlier works using approximate DFTs [12][13][14][15][16][17][18][19][20] . In contrast to these previous works, we use exact DFT relations to simplify our expressions, and do not approximate the free energy functional, nor start from parametrizations of density fluctuations 21 ; see Kirkpatrick et al 21 for a discussion of these approximate theories, and computer simulations 19,20,[22][23][24] for possible problems arising concerning the elastic constants 25 .…”

Classical dynamical density functional theory: from fundamentals to applications

“…While these approaches consider fluids, DFT is also useful for the description of waves in crystals. It allows to calculate the free energy change associated with a small deformation of a crystal, which then gives the phonon dispersion relation [1059][1060][1061][1062]. More recently, a combination of DFT and projection operator methods (see Section 5.3.1) was employed in Refs.…”