Spinodal decomposition in thin plates subjected to a temperature gradient

The spinodal decomposition of a regular-solution, binary alloy under thermal gradients is explored. The alloy is configured as an isotropic thin plate that is free to bend. A steady-state thermal gradient is imposed through the thickness of the plate. A non-linear, Cahn-Hilliard type equation accounting for both compositional and thermal stresses is solved numerically using a dual grid, finite differences method in order to follow the evolution of the microstructure. For sufficiently small thermal gradients in which the critical temperature is everywhere greater than the plate temperature, the initial decomposition forms alternating layers of the phases which coarsen at long-times by the rapid thickening of a single layer of a different phase from each of the two plate surfaces. For larger thermal gradients, spinodal decomposition initiates at the coldest surface and then sweeps across the plate with the phase composition being a strong function of position.