Kinetic theory of microstructural evolution in nucleation and growth processes

Abstract

Macroscopic properties of materials are highly dependent on their microstructure. In materials obtained by a phase transformation the complete knowledge of microscopical parameters, such as mean radius and grain size distribution, is essential to tailor properties of technological interest, A kinetic theory is presented, based on the same assumptions as the Kolmogorov-Johnson, Mehl-Avrami (KJMA) formulation; that is to say, randomly distributed active nucleation sites that grow isotropically until collision gives rise to growth stop at the grain boundaries. The theory is an extension of KJMA because it evaluates probabilities of impingement between grains, giving actual grain size populations as a function of time. The formalism allows us to model arbitrary dependencies of the kinetic parameters (nucleation and growth rates) on macroscopic and/or microscopic variables, and on time. The theory has been tested against Monte Carlo simulations, showing that it is quantitatively exact in its predictions of the grain size populations. Specific dependencies on the kinetic parameters have been studied in order to understand the growth behavior of real materials. In particular, interface and diffusion controlled growth are studied, and differences in the final grain size distribution and related parameters are discussed.