Prog. Theor. Phys. Vol. 52 No. 2 (1974) pp. 385-396
Crystal Instability and Premelting Phenomena
Department of Applied Physics, Nagoya University, Nagoya
(Received January 14, 1974)
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-liqud 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 veriation 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.
DOI : 10.1143/PTP.52.385
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Citing Article(s) :
Progress of Theoretical Physics Vol. 53 No. 3 (1975) pp. 889-891
Statistical-Mechanical Approach to Solid-Liquid Transition in Hard Disc System
Progress of Theoretical Physics Vol. 55 No. 4 (1976) pp. 1024-1037
On a Hard-Sphere Crystal