Some new insights into the old Avrami’s equation

Abstract

Melvin Avrami published a series of interesting papers [M. Avrami, J. Chem. Phys. 7, 1103 (1939); 8, 212 (1940); 9, 177 (1941)] on the kinetics of phase change. Since this seminal work half a century ago, Avrami’s theory has found several applications in different physicochemical contexts, the electrochemical phase formation being one such application. In this paper we outline some random coverage problems which arise in the modeling of solid-state transformations at the electrode/electrolyte interface. After briefly reviewing the earlier developments in this area, we go on to show that a new and more general perspective could be provided to Avrami’s problem once we clothe it in the language of geometrical probability and nearest-neighbor statistics. We also show how some of these new insights could remove two of the major restrictions of Avrami’s theory, namely the assumption of a large-sized system and the uniformly random (i.e., Poissonian) distribution of active sites. In particular, we demonstrate the usefulness of Robbins’ theorem and derive a new result with its help, viz., an overlap formula for the Neyman–Scott cluster process. Some interesting connections are also established between order neighbor statistics and overlap formulas.