Electrical conductivity, self-diffusion, and volume expansion of alkali halides at the melting point

Abstract

In an earlier paper, Heisenberg's uncertainty principle was invoked at the melting point T m of crystalline solids to provide fundamental justification for Lindemann's melting law and to compute diffusion coefficients of several alkali halides. The uncertainty principle defines breakdown of Debye zone boundary (ZB) phonons as valid collective excitations when phonon energies and line widths due to anharmonicity become comparable at T m. Upon breakdown, random, high-frequency single-particle motion or “partial decoupling” of crystal ions sets in. Lifetimes of these single-particle ZB motions are determined from the “minimum-uncertainty product” inequality by assuming that it becomes an equality at T m for ZB phonons. The present paper addresses improved formulation of that work and extended application to ionic electrical conductivities of 18 molten alkali halides at T m. It is shown that use of the Debye model produces an approximate lower bound to the mean free time, not the unconstrained direct estimate previouslu implied. This feature is generally reflected in results for ionic conductivities and alkali halide diffusion coefficients for which comparison experimental data were found. However, in spite of this lower-bound formulation and the simple nature of the computation, the results compare favorably with experiment. A model of random single-particle harmonic motion superimposed on the lower-frequency collective motion is proposed to account for volume expansion accompanying the partial decoupling for hard-sphere ions. Experimental comparisons for 15 alkali halides show the decoupling volume change to account largely for the total volume change of melting (in the hard-sphere approximation), yielding a closer agreement with experiment than recent calculations aimed explicitly at the total volume change.