Stochastic Effects in Microstructure

Abstract

We are currently studying microstructural responses to diffusion-limited coarsening in two-phase materials. A mathematical solution to late-stage multiparticle diffusion in finite systems is formulated with account taken of particle-particle interactions and their microstructural correlations, or "locales". The transition from finite system behavior to that for an infinite microstructure is established analytically. Large-scale simulations of late-stage phase coarsening dynamics show increased fluctuations with increasing volume fraction, Vv, of the mean flux entering or leaving particles of a given size class. Fluctuations about the mean flux were found to depend on the scaled particle size, R/<R>, where R is the radius of a particle and <R> is the radius of the dispersoid averaged over the population within the microstructure. Specifically, small (shrinking) particles tend to display weak fluctuations about their mean flux, whereas particles of average, or above average size, exhibit strong fluctuations. Remarkably, even in cases of microstructures with a relatively small volume fraction (Vv ~ 10-4), the particle size distribution is broader than that for the well-known Lifshitz-Slyozov limit predicted at zero volume fraction. The simulation results reported here provide some additional surprising insights into the effect of diffusion interactions and stochastic effects during evolution of a microstructure, as it approaches its thermodynamic end-state

Analytical estimation of distance–disorientation function of the material microstructure

“…The main idea is to reconstruct the full microstructure media from the n-point correlation statistics using different optimization and homogenization techniques. Various research studies of correlation between particle interactions with the length scale effect were studied and discussed in the experimental and modelling works of Glicksman et al [19] and Wang et al [20,21]. In their research, the authors presented the study of spatial and nearest-neighboor correlations in a polydispersed particle systems.…”