Diatomic model of a quantum crystal

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Abstract
The anharmonic zero-point vibrations of a crystal are studied using a two-atom model. It is shown that the amplitude of such vibrations cannot exceed a certain limiting value, which is a fraction of the interatomic distance. Compressing the crystal decreases and stretching increases the amplitude of the zero-point vibrations. It is found that the melting temperature of the crystal depends on the de Boer parameter, which is qualitatively close to the observed dependence. It is shown that the melting temperature satisfies Lindemann’s formula in the classical limit. There exists a critical value of the de Boer parameter for which the melting temperature vanishes. For values of the de Boer parameter less than but close to the critical value, melting is of a strongly quantum character.