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

Long time asymptotics are developed here for an Allen–Cahn/Cahn–Hilliard system 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 simultaneous order–disorder and phase separation. Proximity to a deep quench limit is assumed, and spatial scales are chosen to model Krzanowski instabilities in which droplets of a minor disordered phase bounded by interphase boundaries (IPBs) of high curvature coagulate along a slowly curved antiphase boundaries (APBs) separating two ordered variants. The limiting motion couples 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 both sharp interface and diffuse interface modeling of sintering of small grains and thermal grain boundary grooving in polycrystalline films.