Theory of phase transition kinetics with growth site impingement. I. Homogeneous nucleation

Abstract

Abstract The nonlinear integral equations governing phase transition kinetics with homogeneous nucleation and growth site impingement are developed and solved to the first order for the two‐dimensional case. It is shown that the fractional transformed area at time t is given approximately by a(t) = Kt 3 /(1 + Kt 3 ). The iteration method used to get the solution is applicable to certain other nonlinear differential and integral equations. It is shown that the theory predicts the total number of growth sites formed, and that the nucleation rate and growth constants can be deduced from this and the gross kinetic data. The extension of the method of three‐dimensional growth is indicated.