Curvature effects in rapid alloy solidification

The growth of a cylindrical or spherical crystal into its undercooled melt is a process whose description is complicated by the lack of a stationary regime. A simple approach to the problem, justified for low growth rates and widely used in the past for both pure substances and alloy solidification, is based on a quasistatic approximation which assumes an instantaneous adaptation of the diffusional field to the interface configuration. For alloy solidification, assuming isothermal conditions and local interface equilibrium, this simplified model predicts a diffusion controlled growth, with the radius of the crystal increasing asymptotically as proportional tot(1/2). However, as pointed out by recent investigations, thermal diffusion and nonequilibrium effects enter as essential ingredients in rapid alloy solidification. In the present paper we use the phase-field model to simulate the cylindrical and spherical growth of a solid germ into a supersaturated alloy melt. The problem is treated in its full time-dependent characteristics. accounting for nonequilibrium effects as well as for the rejection of both heat and solute away from the advancing front. We observe a complex behavior and a rich variety of dynamic regimes: in different regions of parameter space the growth rate is limited by diffusion (either thermal or chemical) or is kinetic controlled. Traversing the boundaries which limit these regions, the process undergoes sharp transitions which leave a trace in the solidified alloy. For realistic values of the Lewis number, thermal effects drive the process into a a diffusive regime, in which the rate limiting mechanism is the rejection of solute.