A Stability Function for Explicit Evaluation of the Mullins-Sekerka Interface Stability Criterion

Abstract

A stability function 𝒮 for explicit evaluation of the Mullins-Sekerka interface stability criterion is introduced and tabulated. Their criterion is then written in terms of 𝒮 and compared with the constitutional supercooling criterion for interface stability. From these results, experimental data can be analyzed and a conclusive test of the stability theory can be made.

Supercooling at Melt Growth of Single and Mixed Fluorite Compounds: Criteria of Interface Stability

“…Besides, this theory provides a description of time evolution of the perturbed interface, following the alterations in thermal and concentration fields. It seams this theory should replace that of CMSc principle despite giving a much more complicated expression for perturbation IF L/S stability criterion (Sekerka, 1965). One may assess the reasonability of such replacement after writing the perturbation IF L/S stability criterion in a form usable for comparative analysis to inequality (5):…”

“…Indeed, the constitutional supercooling principle refers only to liquid phase, thus ignoring the latent heat of fusion and the heat flow throughout the growing crystal. Unlike it, the perturbation theory of interface stability has been developed being based upon the dynamics of the whole melt-crystal system (Mullins & Sekerka, 1963, 1964Sekerka, 1965, 1967, as cited in Sekerka, 1968. Besides, this theory provides a description of time evolution of the perturbed interface, following the alterations in thermal and concentration fields.…”

Micro-scale mass-transfer variations during electrodeposition

“…A great deal of work has been done, especially by Mullins and Sekerka [92,93], on the melt-crystal interface, which is partially analogous to electrodeposition (since a new solid phase is formed in response to a thermodynamic driving force). Instabilities occur at such interfaces, resulting in a sinusoidally-shaped boundary.…”

Studies on the development of mossy zinc electrodeposits from flowing alkaline electrolytes

“…The first rigorous stability analysis was performed by Mullins and Sekerka (33,34,35 Aogaki and co-workers (37,38) applied the principles advanced by Mullins and Sekerka to electrochemical processes with the goal of explaining why a crystal begins and why it continues to grow on a planar surface. Using the same perturbation methods, they found that under mass transport controlled conditions, electrodeposition processes are always unstable.…”