Stability and instability in crystal growth: Symmetric solutions of the Stefan problem

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Abstract
The stability is studied of the previously known solutions of the equations for the growth of a sphere, cylinder, or plate from the melt. These solutions are shown to be particular cases of a more general formulation, and to be stable against perturbations that retain the initial symmetry. The case of one-dimensional growth of a plate is shown to exhibit neutral stability only at the critical undercooling for which the latent heat of freezing is precisely equal to the amount required to raise the bulk material to the melting point. In conditions of large undercooling kinetic considerations determine the form of the asymptotically stable solutions.

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