Self-diffusion at the melting point: From H2 and N2 to liquid metals

Abstract

A nominal lower bound to the mean free diffusion time at the melting point Tm was obtained earlier which provided a factor-two type estimate for self-diffusion coefficients of the alkali halides, alkali metals, eight other metals, and Ar. The argument was based on the classical Uncertainty Principle applied to the solid crystal, whereby maximum-frequency phonons lose validity as collective excitations and degenerate into aperiodic, single-particle diffusive motion at the melting point. Because of the short time scale of this motion, the perfect-gas diffusion equation and true mass can be used to obtain the self-diffusion coefficient in the Debye approximation to the phonon spectrum. This result for the self-diffusion coefficient also yields the scale factor that determines the order of magnitude of liquid self-diffusion coefficients, which has long been an open question. The earlier theory is summarized and clarified, and the results extended to the more complex molecular liquids H2 and N2. It is also demonstrated that combining Lindemann's melting law with the perfect-gas diffusion equation estimate yields a well-known empirical expression for liquid-metal self-diffusion at Tm. Validity of the self-diffusion estimate over a melting temperature range from 14 to more than 1300 K and over a wide variety of crystals provides strong confirmation for the existence of the specialized diffusive motion at the melting point, as well as confirmation of a relation between the phonon spectrum of the solid crystal and diffusive motion in the melt.