Generalization of classical Hillert's grain growth and LSW theories to a wide family of kinetic evolution equations and stationary distribution functions

Coarsening of objects as grains or precipitates belongs to the most relevant processes during the heat treatment and high-temperature application of materials. Based on the appropriate models incorporating the relevant phenomena, the coarsening of objects can be described by evolution equations, which are reflected by stationary radius distribution functions. Such a distribution function for a distinct evolution equation has been derived e.g. in the frame of Lifshitz, Slyozov and Wagner (LSW) theory for the precipitate coarsening. The current evolution equations are in prevailing number of cases based on the mean field approach. A two-parametric family of evolution equations is proposed, which includes e.g. the LSW theory as a special case. The specific phenomena controlling the object evolution can be incorporated by using proper values of parameters used in the evolution equation. An effective procedure is presented how the corresponding stationary radius distribution function can be calculated for each evolution equation from the family. The distribution functions are demonstrated for several combinations of admissible parameters. Basic characteristics of their shapes are also evaluated.