Grain growth and microstructural evolution in a two-dimensional two-phase solid containing only quadrijunctions

Abstract

Recently, Cahn [l] performed a thermodynamic analysis for the stability of microstructures in a twodimensional two-phase solid in which the volume fractions are not conserved, i.e., they have the same composition, and hence long-range diffision and Ostwald ripening are not involved. In his theory, the microstructural stability was analyzed based on the energetic ratios of grain boundaries to the interphase boundary, i.e. 1~. = IJ../u_~ and R, = er+,/c+ where o,, and app are the grain boundary energies of the a and p phases, respectively, and oap is the interphase boundary energy. It is shown that for 0 s R = s 0, aaa trijunctions are stable; otherwise, they are unstable with respect to the nucleation of p grains. Similarly, p p p trijunctions are stable for 0 s R p s fi and are unstable with respect to the nucleation of a grains for R ,, > 0. a a p and a p p trijunctions are stable under the conditions of 0 ?: R, < 2 and 0 < R, < 2. More interestingly, he found that the quadrijunctions aPaP will become stable if the condition Ri + Ri -2 4 is satisfied [l]. Following Cahn’s work, Holm et al. performed Monte Carlo simulations on the same system, i.e., a two-phase solid in which the volume fractions are not conserved [2]. They showed that quadrijunctions can indeed be stable within a certain range of the values for R, and R, as predicted by Cahn’s thermodynamic analysis. More surprisingly, based on their simulations, they predicted that the grain growth in a system with only quadrijunctions may be frozen [2]. The main objective of this paper is to investigate the stability and evolution kinetics of quadrijunctions in a model two-dimensional two-phase solid in which the volume fractions are CONSERVED, using a continuum difuse-interface grain growth model, i.e., by numerically solving a set of coupled continuum time-dependent partial differential equations. We have applied this model to grain growth in single-phase systems [3-51 and to coupled grain growth and Ostwald ripening in two-phase solids [6]. It should be emphasized that most two-phase solids in real applications belong to the case of conserved volume fractions.