Morphological stability of a solid–liquid interface growing in a cylindrical mold

Abstract

The morphological stability of the planar interface of dilute alloys solidifying in a cylindrical mold is analyzed based on the perturbation model presented by Mullins and Sekerka under the assumption that the interface crosses the mold wall at right angles, to examine the effect of the inside diameter of the mold. When the interface grows in a mold of a larger inside diameter, the stability-instability criterion of the planar interface is coincident with the MS criterion. On the other hand, in a mold of a smaller diameter, the rippled interface is permitted to take a frequency of discrete values (the permitted frequency), and the planar interface grows stably under thermal conditions slightly exceeding the MS criterion. Also, there exists a minimum permitted frequency ωmin, and the critical inside diameter dc is derived from ωmin. When the alloy solidifies in a mold of an inside diameter less than dc, the interface grows stably under thermal conditions in which the MS model predicts unstable growth of the interface. Moreover, there is a lower limit dG in dc, and when the alloy solidifies in a mold of an inside diameter less than dG, the interface grows stably even at a zero temperature gradient in the liquid.