Creep motion of a solidification front in a two-dimensional binary alloy

The propagation of a solidification front in a two-dimensional binary alloy is studied by Monte Carlo simulations. A random atomic configuration is qu enched and the atoms that prefer to be in the liquid phase act as quenched pinning centers to the advancing solidification front. For a system with la rge kink formation energy epsilon and finite system width N, we show that t he liquidus and solidus lines in the equilibrium phase diagram correspond t o pinning-depinning transition lines, like in a one-dimensional system. In the one-phase region the front is depinned and propagates steadily, whereas in the two-phase region it is pinned and the velocity v decays as time t p asses with a power-law behavior v(t)similar to t(v-1), with v<1. For a mode rate epsilon or for a large width N, the pinning transition is smeared out and the front propagates steadily even in the two-phase region by thermal c reep. When the driving force H is small, the velocity v decays exponentiall y with epsilon and H-1. The size dependence is interpreted in terms of the height correlation. [S1063-651X(99)06601-5].