Crystal Instability and Premelting Phenomena

Abstract

On the -basis of the cell model, the atomic distribution in each cell in a solid system consisting of N atoms is discussed to investigate the solid-liquid transition. In the crystalline phase the atomic density is well localized around each lattice site and there is a periodic lattice· structure in the system as a whole. The cluster variation method in the second order approximation is applied to derivation of a set of self-consistent equations determining the effective single particle potential, by means of which the single-particle distribution in each cell is obtained. The effective potential is influenced by the long-range and short-range atomic correlations in the system.· One of the purposes of this paper is to discuss the premelting phenomena, as a primary investigation. The harmonic Einstein model, in which the short-range correlation is not taken into account, cannot lead to the uniform distribution as a solution of the self-consistent equations. The temperature dependence of the effective harmonic frequencies is investigated for a simple system in which the interaction potential consists of hard-core and attractive-well parts. Above a certain critical temperature, this harmonic potential disappears and. therefore the crystalline phase can no longer exist as a stable state. It is seen from the temperature dependence of the effective frequency that the specific heat increases more than linearly above a certain temperature and diverges as the inverse square root at. the threshold temperature slightly above the melting point. It is then concluded that the premelting occurs as a precursor of the crystal instability.