Analysis of non-steady-state distribution functions for grain growth and coarsening

The description of non-steady-state grain growth or precipitate coarsening using object radius distribution functions with multiple time-dependent parameters (distribution concept) appears promising. The present paper deals with the simplest case of non-steady-state distribution functions with two parameters - the first one scaling the object radius, the second determining the shape of the distribution function. The main question concerns the physical basis behind the evolution of these two parameters. The principle of maximum dissipation has proven to be a suitable tool to derive the evolution equations. Semi-analytical solutions for the evolving parameters of arbitrary two-parameter distribution functions can be developed. As examples, Kirkaldy- Lind Weibull-type distribution functions are investigated. It is shown that the parameters of the Kirkaldy distribution function are not independent and, thus, the general non-steady-state analysis fails. For a Weibull-type distribution function, nearly exact and simple analytical expressions for both parameters are presented and discussed for the grain growth and coarsening cases.