Phase-field model for isothermal phase transitions in binary alloys

TLDR

The paper introduces a phase‑field model for isothermal phase transitions between ideal binary‑alloy liquid and solid phases. The model derives governing equations for the phase field and composition, identifies three temporal stages—rapid interfacial genesis, diffusion‑controlled motion, and curvature‑driven Ostwald ripening—and relates the phase‑field parameters to material and growth properties. Asymptotic analysis confirms that the model reduces to classical sharp‑interface solidification when interfacial layers are thin, linking phase‑field parameters to material and growth properties, and numerical simulations illustrate its behavior.

Abstract

In this paper we present a phase-field model to describe isothermal phase transitions between ideal binary-alloy liquid and solid phases. Governing equations are developed for the temporal and spatial variation of the phase field, which identifies the local state or phase, and for the composition. An asymptotic analysis as the gradient energy coefficient of the phase field becomes small shows that our model recovers classical sharp-interface models of alloy solidification when the interfacial layers are thin, and we relate the parameters appearing in the phase-field model to material and growth parameters in real systems. We identify three stages of temporal evolution for the governing equations: the first corresponds to interfacial genesis, which occurs very rapidly; the second to interfacial motion controlled by diffusion and the local energy difference across the interface; the last takes place on a long time scale in which curvature effects are important, and corresponds to Ostwald ripening. We also present results of numerical calculations.