Theory of Melting Based on Lattice Instability

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Abstract
A lattice instability which may be related to melting is proposed as follows: The energy of thermal vibration cannot exceed a critical value, because of anharmonicity, and the lattice may be unstable above the temperature corresponding to this critical energy. The effect of anharmonicity arises from the effective increase in interatomic distances due to the lattice vibrations. This increase is called "vibrational elongation." The critical temperature of instability is written in terms of atomic volume, elastic constants, and the Grüneisen parameter under the assumption of a linear dispersion relation, and is shown to be in fairly good agreement with the observed melting point. The Lindemann formula and the empirical law that the product of thermal expansivity and melting point is approximately constant are examined on the basis of the present theory. The thermal expansion and the elastic properties predicted by the theory up to the melting point are qualitatively consistent with the observed values.

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