On modelling recrystallization processes with random growth velocities of the grains in Materials Science

Heterogeneous transformations (or reactions) may be defined as those transformations in which there is a sharp moving boundary between the transformed and untransformed region. In Materials Science such transformations are normally called nucleation and growth transformations, whereas birth-and-growth processes is the preferred denomination in Mathematics. Recently, the present authors in a series of papers have derived new analytical expressions for nucleation and growth transformations with the help of stochastic geometry methods. Those papers focused mainly on the role of nuclei location in space, described by point processes, on transformation kinetics. In this work we focus 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. Juul Jensen and Godiksen reviewed recent 3-d experimental results on recrystallization kinetics and concluded that there is compelling evidence that every grain has its own distinct growth rate. Motivated by this practical application we present here new general kinetics expressions for various situations of practical interest, in which a random distribution of growth velocities is assumed. In order to do this, we make use of tools from Stochastic Geometry and Geometric Measure Theory. Previously known results follow here as particular cases. Although the motivation for this paper was recrystallization the expressions derived here may be applied to nucleation and growth reactions in general.