Planar Solidification from Undercooled Melt: An Approximation of a Dilute Binary Alloy for a Phase-field Model

TL;DR

This paper develops a phase-field model for planar solidification of a dilute binary alloy from an undercooled melt, deriving analytical solutions and asymptotic expansions for various growth regimes, and validating with numerical results.

Contribution

It introduces an approximation for dilute binary alloys in phase-field modeling, providing analytical solutions and asymptotic relations for different solidification velocities.

Findings

Derived equilibrium partition coefficient and liquidus slope from the model.

Obtained asymptotic expansions for solute and phase fields at high growth velocities.

Validated analytical results with numerical calculations.

Abstract

Planar solidification from an undercooled melt has been considered using the phase-field model. The solute and the phase fields have been found in the limit of small impurity concentration. These solutions in the limit of vanishing velocity of the interface motion give the equilibrium partition coefficient and the liquidus slope. Asymptotic expansions for the solute and for the phase fields, and the relation between the diffusive speed and the parameters of the phase field model have been found at high growth velocity. A comparison with numerical calculations is presented.