Stability of a melting interface

Abstract

Comparison between experimental observations of a melting interface and a theoretical analysis of interface stability has been made. The theoretical analysis follows the method of Mullins and Sekerka but includes diffusion in the growing phase. The analysis, which is appropriate for melting where diffusion in the growing phase is rapid, predicts that a melting interface should be more stable than a freezing interface in the same material. Comparison of this analysis has been made with observation of the stability of a melting planar interface of transparent organic binary mixtures which have low entropies of fusion. Experimentally, ripples were observed at the interface under some conditions of melting. It was found that the wavelength of the ripples decreased with increasing melting rate and increasing solute concentration. The experimental data are in good agreement with the theoretical analysis both for the onset of instability, and the wavelength of the ripples. These experiments confirm that the onset of melting instability is predicted correctly by stability theory, and that it does not coincide with the onset of constitutional superheating. Calculations of the wavelength of the instability have also been made for the case of a freezing interface. The wavelength was found to be independent of concentration and to depend primarily on the diffusion layer width, D l / V, for normal growth conditions, in accord with observation.