A critical re-examination of the thermodynamic basis of Lindemann's melting law

Abstract

A version of Lindemann's melting law is derived from elementary thermodynamic principles in a manner that clearly exposes the assumptions and approximations. Corrections for the anharmonic departure from equipartition of the thermal energy of a solid, the breaking of atomic nearest-neighbour bonds in the melting process and the role of electron thermal energy all appear to be small. However, the derived formula d lnT M d lnρ M =2γ where ρ M and γ are the density and Grüneisen parameter of the solid phase at the melting point, T M, clearly gives too steep an increase in T M with pressure and indicates a fundamental deficiency in understanding of the melting process.