The kinetics of grain boundary nucleated reactions

Abstract Rate laws are derived for transformations in which the new phase nucleates on grain boundary surface, grain edges, or grain corners, and in which the new phase grows with constant radial velocity. Time-dependent and time-independent nucleation rates are treated. At high nucleation rates (relative to growth rates and grain sizes) the rate law assumes a form independent of the nucleation rate, and the half-time of the transformation becomes approximately 0.1 D G , where D is the grain diameter and G the radial growth velocity, independently of which sites are responsible for nucleation. At low nucleation rates the rate law approaches that given by randomly distributed nucleation sites. The conditions which determine which type of site will produce the most nuclei, and hence determine the form of the rate law, are discussed.