Theory of nucleation in solid state reactions

The theory of nucleation in solid state reactions is formulated in a general way and a solution to the problem of multi-step nucleation obtained. Two special cases of the general formulation are considered: the second of these corresponds to Bagdassarian's approximate model and some corrections to his treatment are pointed out. A new equation describing the kinetics of a solid state reaction, which involves multi-step nucleation followed by a constant and isotropic rate of growth, is derived. This equation is termed the generalized Avrami equation since it removes the restriction, in Avrami's treatment, of a single-step nucleation process. Erofeev's analysis of the problem is shown to be valid only in the limit of short times: the generalized Avrami equation reduces to Erofeev's equation in this limit.