Modelling Some Recrystallization Processes with Random Growth Velocity of the Grains

Heterogeneous transformations (or reactions) may be defined as those transformations in which there is a sharp moving boundary between the transformed and untransformed region. Such transformations may be modelled by the so-called birth-and-growth processes. We focus here on the effect that a random velocity of the moving boundaries of the grains has in the overall kinetics. One example of a practical situation in which such a model may be useful is that of recrystallization; a recent review of 3-D experimental results on recrystallization kinetics concluded that there is compelling evidence that every grain has its own distinct growth rate. Motivated by this practical application we present general kinetics expressions for various situations of practical interest, in which a random distribution of growth velocities is assumed. Previously known results follow here as particular cases. Although the motivation was recrystallization, the expressions presented here may be applied to nucleation and growth reactions in general.