Triple Junction Motion for Allen-Cahn/Cahn-Hilliard Systems

Long time asymptotics are developed here for an Allen-Cahn/Cahn-Hilliard system derived recently by Cahn & Novick-Cohen [11] as a di use interface model for simultaneous orderdisorder 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 (IPB) of high curvature coagulate along a slowly curved antiphase boundaries (APB) 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 time scale. Quasi-static surface di usion of the chemical potential occurs along APBs. The framework outlined here should also be suitable for describing sintering of small grains and thermal grain boundary grooving in polycrystalline lms.