On the nature of the excess heat capacity of mixing

The excess vibrational entropy (ΔS vib ex ) of several silicate solid solutions are found to be linearly correlated with the differences in end-member volumes (ΔV i ) and end-member bulk moduli (Δκ i ). 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 ΔS vib ex , ΔV i and Δκ i , as described by ΔS vib ex = (ΔV i + mΔκ i )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 ΔS vib ex behaviour of a solid solution based on its volume and bulk moduli end-member data.