Free Energies of Vacancies and Rare-Gas Crystal Mixtures

The Gibbs-Bogolyubov variational principle is used to calculate the free energy of vacancy formation $g_v\mathrm{}\left(T\right)\mathrm{}$ 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 $h_v=g_v-{\left(\frac{d{g}_v}{\mathrm{dT}}\right)}_{P}T$ is essentially the same as expected from equivalent static-lattice calculations at $T=0\mathrm{}$ °K. Thus, the vibrational motion does not encourage further relaxation and there remains a large discrepancy between computed and observed $h_v$ in solid Kr, although the entropies $s_v$ compare well. The computed $w\text{'}\mathrm{s}$ agree very well with the observed values of Fender and Halsey.