Excess entropy for a vacancy in a crystal

The excess entropy for a single vacancy in any crystal with cyclic boundary conditions is given, within the small perturbation approximation, by ΔS/k/sub B/ = d/2, independent of crystal structure and particle interaction, dependent only on the dimensionality of the crystal, d. It is argued that the effect of free surface boundary conditions on ΔS, within an exact theory, for any localized defect (not only a vacancy), is negligible. Using the vacancy perturbation result for ΔS and Lawson's formula, a value for the vacancy formation volume is obtained only in terms of known measured parameters. If localized vibrational modes are present due to the vacancy, what effect these might have on ΔS, and, from this, what materials might be candidates for observing these localized modes are discussed. (U.S.)