Variation of the Amplitude of Thermal Vibration on the Fusion Curve

Abstract

A differential relation given previously, which is equivalent to the Debye-Waller identification of the Debye and Lindemann frequencies at fusion, is generalized to take into account variation along the fusion curve of the critical ratio of the root-mean-square amplitude of thermal vibration to the nearest-neighbor distance of the atoms in the solid at fusion. Thus extended, the theory yields an expression for the Grüneisen parameter of a solid at fusion in terms of fusion parameters and the rate of change of the critical ratio with respect to volume, which is valid for elements whose fusion curves have either normal or abnormal slopes. Values of derivatives of the critical ratio with respect to volume, temperature, and pressure at fusion are obtained for 16 elements. The results yield evaluations of the change in the critical ratio along the experimentally determined fusion curves for three alkali metals, and permit estimates in other cases. It is concluded that the assumption of a fixed Lindemann constant along the fusion curve of a particular element represents an excellent approximation, in general, for elements with normal fusion curves (for the case of classical excitation of the lattice vibrations). The same conclusion is obtained, within certain approximations, from the order-disorder theory of Lennard-Jones and Devonshire for the melting process, and the theory of Fisher for stability of the liquid phase.