Transformation kinetics for nucleation on second-phase particles : analytical solution and computer simulation

An analytical solution, based on stochastic geometry concepts, is presented here for transformations in which nuclei are located on the interface between second-phase particles and the parent matrix. The analytical solution aims at the most common situation in which the particles are dispersed within the matrix with a particle volume fraction less than 0.1 so that particle/particle impingement is small. A computer simulation was carried out to compare with the analytical solution. This comparison revealed that in some circumstances the analytical solution may be valid for particle volume fractions well beyond 0.1 when there is a significant amount of impingement. The formalism is valid for particle stimulated nucleation during recrystallization as well as for phase transformations that nucleate on the interface of a previously extant phase and the parent matrix. Detailed determination of the bounds within which the analytical solution is valid is carried out with the help of computer simulation. The reasons for this extended validity of the analytical solution are discussed in depth.