Free Energies of Vacancies and Rare-Gas Crystal Mixtures

The Gibbs-Bogolyubov variational principle is used to calculate the free energy of vacancy formation gᵥ(T) in solid Kr, Ne, and Cu and the interchange parameter w for dilute Ar-Kr mixtures. These calculations include vibrational properties and, since any temperature can be considered, all other thermal properties can be obtained. For the vacancy, the formation energy obtained in this way as hᵥ=gᵥ-(dgᵥdT)PT is essentially the same as expected from equivalent static-lattice calculations at $T=0$ ^∘{}K. Thus, the vibrational motion does not encourage further relaxation and there remains a large discrepancy between computed and observed hᵥ in solid Kr, although the entropies sᵥ compare well. The computed w's agree very well with the observed values of Fender and Halsey.