Triple-junction motion for an Allen-Cahn/Cahn-Hilliard system

Long time asymptotics are developed here for an Allen-Cahn/Cahn-Hilliard sy stem derived recently by Cahn and Novick-Cohen [J.W. Cahn, A. Novick-Cohen, J. Statist. Phys. 76 (1994) 877-909] as a diffuse interface model for simu ltaneous order-disorder and phase separation. Proximity to a deep quench li mit is assumed, and spatial scales are chosen to model Krzanowski instabili ties in which droplets of a minor disordered phase bounded by interphase bo undaries (LPBs) of high curvature coagulate along a slowly curved antiphase boundaries (APBs) separating two ordered variants. The limiting motion cou ples motion by mean curvature of the APBs with motion by minus the surface Laplacian of the IPBs on the same timescale. Quasi-static surface diffusion of the chemical potential occurs along APBs. The framework here yields bot h sharp interface and diffuse interface modeling of sintering of small grai ns and thermal grain boundary grooving in polycrystalline films. (C) 2000 E lsevier Science B.V. All rights reserved.