Phase-field model of alloy solidification far from chemical equilibrium at the solid-liquid interface

TL;DR

This paper advances a phase-field model for rapid alloy solidification, incorporating enhanced solute diffusivity to simulate microstructure development at realistic scales, and extends it to concentrated alloys with thermodynamic data.

Contribution

It introduces a robust variational formulation for the model, extends it to concentrated alloys using thermodynamic databases, and validates its effectiveness through 2D and 3D simulations.

Findings

The simplest variational formulation is most robust.

High-velocity phase diagram is independent of interface width.

Standard stability theory predicts critical velocities accurately.

Abstract

We further develop a recently introduced phase-field model of rapid alloy solidification [Ji et al., PRL 2023]. This model utilizes enhanced solute diffusivity within the spatially diffuse interface region to quantitatively capture solute trapping with a larger interface width, thereby making simulations on experimentally relevant length and time scales computationally feasible. The main developments presented here include testing the robustness of different variational formulations, extending the model to concentrated alloys by incorporating solid and liquid free energies from thermodynamic databases, as illustrated for hypoeutectic Al-Ag alloys with CALPHAD, extending convergence tests as a function of interface width to 3D, and carrying out simulations in both 2D and 3D to examine existing theories of microstructure development. Our results indicate that the simplest variational formulation that interpolates the bulk free-energy density between its solid and liquid forms is the most robust. Remarkably, for hypoeutectic Al-Ag alloys, this formulation yields a high-velocity nonequilibrium phase diagram that is independent of interface width, thereby demonstrating that the framework of enhanced solute diffusivity can be non-trivially extended to concentrated alloys. Other variational formulations have restricted ranges of materials or processing parameters that can be reliably modeled. We use 2D simulations to construct high-velocity microstructure selection maps for dilute Al-Cu alloys. Furthermore, 3D simulations demonstrate a good convergence similar to that observed in 2D as a function of interface width. Full 3D simulations reveal that the standard theory of absolute stability is a good predictor of the upper critical velocity beyond which steady-state growth becomes unstable, despite the different morphological manifestations of this instability in 2D and 3D.