Grain refinement and the stability of dendrites growing into undercooled pure metals and alloys

We present an analysis of the stability of a dendrite against a small perturbation to the tip velocity. We find that dendritic growth in pure metals and alloys will become unstable above some upper critical undercooling Delta T-2*. In alloys above a critical concentration, dendritic growth may also become unstable below a lower critical undercooling, Delta T-1*. In the example systems studied, Ni-Cu and Ag-O, the location of these unstable regions shows remarkably close agreement with the onset: of spontaneous grain refinement. We obtain values of Delta T-2* for Mi and Ag of 195 K and 160 K, respectively, in good agreement with the observed values of 170 K and 133-153 K. (C) 1997 American Institute of Physics.