Migration frequencies for complex diffusion paths

Possible migration paths are examined for complex crystal structures. Many migration paths consist of a variety of metastable intermediate states. During migration the diffusing atom may reside briefly at these intermediate locations. The expression for the overall jump frequency derived earlier by Condit (Mater. Sci. Res. 4, 284, 1969) and Condit et al. (Oxidat. Metals 8, 409, 1974) is expanded to include multiple jumps. This expression is interpreted to obtain very general rules about the activation energy for migration and the fraction of successful traverses of a complex pathway. The activation energy for migration is simply the difference between the highest saddle point energy and the normal site energy. The fraction of successful traverses of the diffusion path is I/N, where N is the number of saddle points in the path that have the same peak energy. This formalism applied equally for diffusion that requires several atoms to move; in this case, reaction coordinates are used instead of distance. Three examples of diffusion in compounds with complex diffusion paths are then examined in detail.