Vacancy-Formation Entropy in Cubic Metals

Vacancy-formation entropies were computed for a number of face-centered-cubic solids from vibrational frequency distributions which were computed from pair potentials. The formation entropy is a monotonic function of the vacancy relaxation, computed from the same pair potential. It is shown that the relaxation of the nearest neighbors to the vacancy in fcc solids can be described by ${\delta }_1=-5.8\mathrm{}\times {10}^{15}{\left(\frac{K}{\alpha V}\right)}^2$, where ${\delta }_1$ is in percent, $K$ is the compressibility, $\alpha$ the linear thermal-expansion coefficient, and $V$ is the molar volume. The computed vacancy-formation entropies are described by $\Delta S=1.83+3.4\mathrm{}\times {10}^{15}{\left(\frac{K}{\alpha V}\right)}^2$ in units of $k$/vacancy. Similar relations are obtained for bcc metals. The experimental relations found for model solids are used to predict vacancy relaxations and formation entropies from experimental values of $K$, $\alpha$, and $V$. Vacancy relaxations are predicted to be less than 0.2% of the normal neighbor distance in most fcc metals and 2-5% in bcc metals. Vacancy-formation entropies are predicted to be 1.$8k-2.0k$ in most fcc metals and $2.2k-2.6k$ in bcc metals. The predictions for the entropy are in satisfactory agreement with experimental data, where reliable data exist.