Abstract
Despite the structural and diffusional-kinetic differences between the solid and liquid phases, the fundamental kinetic processes occurring at a migrating solid–liquid interface are common to solidification and melting. In this work, a three-kinetic-process solute-drag and solute-trapping model, recently developed for rapid solidification within the framework of irreversible thermodynamics and linear kinetic laws, is extended to melting. Three coupled kinetic processes are considered: interface migration, diffusion on the solid (parent-phase) side of the interface, and diffusion on the liquid (product-phase) side. The solid-side diffusional flux, directed from the interface into the solid, causes the interfacial solid composition to deviate from the bulk solid composition and is governed by the interfacial diffusivity. The liquid-side diffusional flux supplies solute from the liquid toward the interface and is governed by the liquid diffusivity. A key feature of the formulation is that the solute-drag parameter is derived from the relative kinetics of these diffusional processes rather than prescribed independently. Molecular-dynamics-supported estimates of the ratio between the characteristic interfacial and liquid-side diffusive speeds indicate that solutal melting occurs close to the full-drag limit.
The model is applied to calculate kinetic melting phase diagrams for a hypothetical binary A–B ideal solid-solution system, an SCN–water system, a binary Al–Mg alloy, and a multicomponent Alnico alloy. For comparison with experimentally measured melting rates, the calculated kinetic phase diagram is coupled with analytical solutions of the diffusion equations in the bulk phases. The case studies show that the interface contact conditions can be described by a kinetic melting phase diagram. With increasing interface velocity, the kinetic solidus and liquidus approach each other while both shift toward higher temperatures. At the low interface velocities relevant to the Al–Mg and SCN–water experiments, local equilibrium remains a good approximation.
The model also provides a description of solutal melting. Bulk diffusion in the liquid transports solute toward the interface, while the difference in diffusion potential across the interface drives solute transport into the solid. This increases the solute concentration in the interfacial solid relative to that in the bulk solid. This solute enrichment causes liquidation of the interfacial solid, thereby lowering its diffusion potential and facilitating further solute transport toward the solid side. The resulting kinetic phase diagram can subsequently be used to provide boundary conditions for numerical models of melting kinetics. Future work will focus on determining interfacial diffusive-speed parameters for multicomponent alloys using molecular-dynamics simulations.