A model for spontaneous grain refinement in alloy systems at low undercooling

An analysis of the stability of a dendrite against a small perturbation to the tip velocity is presented for alloy systems at low undercooling. We find that above a critical concentration, dendritic growth may become unstable below a critical undercooling, offering a potential explanation of spontaneous grain refinement in these systems. This accords well with a number of experimental studies of alloy systems at low undercooling. The model is illustrated with reference to the system Ni-Cu.