Theory of Melting: Thermodynamic Basis of Lindemann's Law

Abstract

A melting equation closely resembling the differential form of Lindemann's melting law, which relates the melting point to the pressure in terms of the thermal Griineisen parameter and incompressibility, is derived from the Clausius-Clapeyron relation with the assumption that the MieGriineisen equation can be adapted directly to describe the pressure change associated with melting at constant volume. This assumption implies that melting is only a minor perturbation of the crystal structure, such that the atomic coordination is almost unaffected and that atomic bonds are merely stretched or compressed. It appears that 'normal' melting complies with this assumption reasonably closely but that departures from Lindemann's law occur when materials undergo major changes in coordination during melting. A particular merit of Lindemann's law is that it allows the extrapolation of melting points to the pressures of the Earth's deep interior. Extrapolation of data on the ironsulphur eutectic suggests a temperature of 4160 K at the boundary of the Earth's inner (solid) and outer (liquid) cores. Adiabatic extrapolation to the core-mantle boundary gives 2940 K at the base of the mantle.