Abstract
Three-dimensional steady-state solutions for nonplanar interface morphologies are computed numerically by using finite differences. A linear temperature field is assumed, corresponding to the case of equal thermal properties in the crystal and melt, with negligible latent heat release. The solute field in the melt and the unknown crystal-melt interface position are obtained self-consistently. For a model of an aluminum-chromium alloy with distribution coefficient greater than one, steady-state solutions corresponding to two-dimensional bands and three-dimensional hexagonal nodes are obtained, as well as solutions with rectangular interface planforms. The stability of the computed steady-state solutions is suggested by the behavior of the iterative scheme used in the calculation: successive iterates may be viewed as evolving in a time-like manner as determined by a set of governing equations that depend on an artificial time. Near the onset of instability the calculations predict hexagonal nodes, which is consistent with weakly nonlinear theory.
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