The Lindemann hypothesis and the size dependence of melting temperatures. II

Abstract

The concept that melting occurs when the root-mean-square atomic vibrational amplitude is a particular fraction of the nearest–neighbour separation, and an expression for the effect of system size and geometry on the summed phonon spectrum, provide an explicit equation for size–dependent melting temperatures. Further, it is shown that for certain classes of solids the ratio of size–dependent to bulk melting temperatures can be described by one equation. For example, this approach holds for the four noble–gas solids Kr, Ar, Xe, Ne, yielding a size–dependent ' corresponding–states principle ' for this species. The results of these formal considerations are compared to those of two other theories for size–dependent melting temperatures: the thermodynamic treatment, and the Kosterlitz–Thouless–Feynman description of melting in two–dimensional solids. The first of these comparisons yields an equation for solid–liquid interfacial energies in terms of bulk properties; the second an equation for bulk melting temperatures.