Cellular interface morphologies in directional solidification. The one-sided model

Abstract

Results of the shape and stability of finite-amplitude cellular interfaces arising in directional solidification are reported for a binary alloy described by a "one-sided" solidification model in which an imposed temperature gradient is unaffected by changes in interface shape. Asymptotic results valid for slightly deformed melt-solid interface shapes describe both smooth and sudden transitions to cellular interfaces in terms of supercritical and subcritical bifurcations with decreasing temperature gradient. Computer-implemented perturbation methods are combined with finite-element approximations of interface shape and concentration field to verify the asymptotic results for small-amplitude cells and extend the analysis to highly deformed interfaces. Numerical results predict that at large amplitudes, families of cellular interfaces which first evolved unstably toward increased temperature gradient reverse direction and regain stability. A discontinuous change in the stable interface morphology with an effective halving of its spatial wavelength is predicted to occur for highly deformed interfaces by secondary bifurcation between two neighboring shape familes and is related to the existence of second-order critical points for the onset of cellular forms.