The temperature dependence of the mono-vacancy concentration in metals was studied by using models for the perturbation of the atomic frequencies which was associated with vacancy formation. The effect of lattice thermal expansion was also considered. Calculations which were based upon the quasi-harmonic model for solids indicated that Arrhenius plots of the vacancy concentration as a function of the reciprocal temperature would exhibit a measurable curvature in the case of Al. Much smaller degrees of curvature were expected to be observed in such plots for Cu and Au.

R.B.McLellan, Y.C.Angel: Acta Metallurgica et Materialia, 1995, 43[10], 3721-5