On the nature of the excess heat capacity of mixing

Abstract

The excess vibrational entropy (ΔSvibex) of several silicate solid solutions are found to be linearly correlated with the differences in end-member volumes (ΔVi) and end-member bulk moduli (Δκi). If a substitution produces both, larger and elastically stiffer polyhedra, then the substituted ion will find itself in a strong enlarged structure. The frequency of its vibration is decreased because of the increase in bond lengths. Lowering of frequencies produces larger heat capacities, which give rise to positive excess vibrational entropies. If a substitution produces larger but elastically softer polyhedra, then increase and decrease of mean bond lengths may be similar in magnitude and their effect on the vibrational entropy tends to be compensated. The empirical relationship between ΔSvibex, ΔVi and Δκi, as described by ΔSvibex = (ΔVi + mΔκi)f, was calibrated on six silicate solid solutions (analbite–sanidine, pyrope–grossular, forsterite–fayalite, analbite–anorthite, anorthite–sanidine, CaTs–diopside) yielding m = 0.0246 and f = 2.926. It allows the prediction of ΔSvibex behaviour of a solid solution based on its volume and bulk moduli end-member data.