Liquid Structure at the Melting Temperature Related to Surface Energy and to Vacancy Formation Energy in the Hot Crystal

Abstract

Abstract A review is first given of the theoretical basis for the relation, valid near the triple point [sgrave]KT = l where [sgrave] is the liquid surface energy, KT is the bulk isothermal compressibility while l measures the thickness of the liquid-vapour interface. Attention is then focussed on the work of Alonso and March in which, for liquid metals, it is shown that l = α{STm (0)/kBTm } 1/2 where STm (0) is the long wavelength limit of the bulk liquid structure at the melting temperature Tm , while α is a constant so far determined only empirically. A modified free electron argument is then given to relate surface energy to vacancy formation energy, for simple metals like the alkalis. Again, the argument does not take account of ionic structure. Finally therefore, a pair potential theory of the vacancy formation energy, worked out in argon to avoid the complication of density dependent pair potentials in metals, is shown to relate vacancy formation energy Ev , now in the hot solid, to bulk liquid structure at the melting point.