Analysis for the prediction of non-equilibrium phase formation in rapid conduction cooling

A new model for alloy solidification, stimulated by results from rapid liquisol quenching experiments, is proposed. The model incorporates kinetic processes into the liquid-solid interfacial conditions by introducing a kinetic delay time for solidification. The ratio of this kinetic delay time to the thermal diffusion time in a slab becomes a dimensionless parameter in determining the motion of the interface with time, and a perturbation analysis for very large values of the parameter is constructed. The problem for determining the progress of the interface for arbitrary values of the parameter and general boundary conditions is set up. In this case, a critical value of the parameter for a given set of experimental conditions is identified above which non-equilibrium phases are formed, and below which the equilibrium products are formed. Comparison of theoretical predictions with experimental results are made and found to be in agreement for several known cases.