Phase Field Modelling of Precipitate Coarsening in Binary Alloys with Respect to Atomic Mobility of Solute in the Precipitate Phase

Abstract

In the current work, a phase field model is used to study the effect of atomic mobility inside the precipitate phase on coarsening behaviour in two-dimensional (2D) systems. In all the coarsening theories until now, the diffusivity inside the precipitate phase has not been explicitly considered which would imply that there is no chemical potential gradient inside the precipitate. The aim of this study is to assess the potential effect of diffusivity inside the precipitate on coarsening behaviour by examining systems with moderate volume fractions, i.e. $$f_{\mathrm{v}}=0.2$$ , $$f_{\mathrm{v}}=0.3$$ and variable atomic mobilities inside the precipitate phase. The atomic mobility inside the matrix is considered to be constant. The Cahn–Hilliard (C–H)-type nonlinear diffusion equation with variable mobility is numerically discretized and solved for a two-phase coarsening system, using a semi-implicit Fourier spectral method. Coarsening behaviour is studied and analysed by keeping in track, the variation of the number density of precipitates, their average size and size distribution with respect to time. The key observation is that, the atomic mobility inside the precipitate phase has a substantial effect on the coarsening kinetics of precipitates. The effect is more clearly observed when the atomic mobility inside the precipitate phase is greater than that of matrix.