Diffusion, Debye temperature and elastic constants of cubic metals

Recent experimental and theoretical work has led to a better understanding of the dependence of vacancy migration on the elastic properties of face-centred cubic (f.c.c.) and body-centred cubic (b.c.c.) metals. A unique picture is found for both crystal structures. The situation is less clear for the process of vacancy formation. It is the main aim of the present work to get reliable information on the behavior of this diffusion parameter. For this purpose former attempts relating the activation enthalpies of vacancy formation and self-diffusion to the Debye temperature are modified, that is by replacing the dependence on the Debye temperature by a dependence on the elastic constants. Three points become evident: A common behavior is not observed for the f.c.c. and b.c.c. structures; for the f.c.c. metals a well-defined law similar to that derived for the migration enthalpy is found; marked but correlated deviations occur for f.c.c. Rh and Ir and for b.c.c. Cr, Mo and W. The latter may be explained by anomalously high elastic constants of these transition metals. This effect, which has been recently dealt with in the literature. is eventually related to filling of the d-bands. B.c.c. alpha-Fe does not seem to fit into any picture. Lindemann's melting-point rule is discussed in the light of the above results.