Five Decades of the Zener Equation

Abstract

The Zener equation was first reported by C. S. Smith in 1948 and since then it has become an integral part of any theory which deals with recovery, recrystallization and grain growth in particle-containing materials. Several modifications to the original equation have been made over the past five decades to improve its applicability to more realistic situations. This paper summarises these modifications and discusses which modifications are reasonable and justifiable based on the analytical models and experimental evidence reported in the literature. Several examples of the applications of the equation are provided to describe annealing phenomena in a wide variety of materials. The paper also examines the impact of the equation in the field of materials science and engineering and suggests a direction for its future development.