Liquid film migration as a broken symmetry due to an unbalanced anisotropy of surface tension

Abstract

A new quantitative phenomenological theory of asymmetric solidification or liquid film migration (LFM) is presented. This is designed to replace a currently popular phenomenology which is demonstrated to be faulty in two crucial aspects. Firstly, the planar quasi-steady state diffusion model contradicts the leading interface mass balance and must accordingly be replaced by a Boltzmann-type parabolic structure suggested in part by the definitive experiments of Kuo and Fournelle. Secondly, while a proposed coherency strain effect may be involved in the initial symmetry-breaking, it cannot as a necessary constant corollary of the usual diffusion model be fully sustained beyond the initiation stage. The configuration, as a consequence of the modern theory of layered films, is seen to be strongly unstable to formation of mobile misfit dislocations, especially as it lies near the melting point. It is demonstrated that a typical critical film thickness (∼1 μm) is very much less than the actual film thickness (∼the grain size). It is suggested that anisotropy of surface tension expressed as a decreased mobility of the frontal interface is the essential cause of asymmetry. The experimental record is salutary to the new mechanically relaxed structure. In particular, it is predicted that a time 1/2 dependency of the melting front motion which, allowing for a damping effect of developing curvature, is consistent with the observations of Kuo and Fournelle. Since the diffusion and interface reaction laws remain close to the linearity required by Onsager's irreversible thermodynamics, the global selection to the asymmetric parabolic state is seen to be a quantitative illustration of the integral principle of minimum dissipation as a thermokinetic imperative.