Multi-phase-field analysis of short-range forces between diffuse interfaces

TL;DR

This paper analyzes short-range forces between diffuse interfaces in multi-phase-field models, deriving asymptotic forms, validating predictions, and proposing a new model capable of describing both attractive and repulsive forces, with applications to material stability.

Contribution

It introduces a new multi-phase-field formulation that captures both attractive and repulsive interface forces, validated by analytical and numerical methods, and explores effects of solute and stress.

Findings

Forces are always attractive in traditional models.

Numerical validation confirms asymptotic force predictions.

Solute addition causes bistability of interfacial states.

Abstract

We characterize both analytically and numerically short-range forces between spatially diffuse interfaces in multi-phase-field models of polycrystalline materials. During late-stage solidification, crystal-melt interfaces may attract or repel each other depending on the degree of misorientation between impinging grains, temperature, composition, and stress. To characterize this interaction, we map the multi-phase-field equations for stationary interfaces to a multi-dimensional classical mechanical scattering problem. From the solution of this problem, we derive asymptotic forms for short-range forces between interfaces for distances larger than the interface thickness. The results show that forces are always attractive for traditional models where each phase-field represents the phase fraction of a given grain. Those predictions are validated by numerical computations of forces for all distances. Based on insights from the scattering problem, we propose a new multi-phase-field formulation that can describe both attractive and repulsive forces in real systems. This model is then used to investigate the influence of solute addition and a uniaxial stress perpendicular to the interface. Solute addition leads to bistability of different interfacial equilibrium states, with the temperature range of bistability increasing with strength of partitioning. Stress in turn, is shown to be equivalent to a temperature change through a standard Clausius-Clapeyron relation. The implications of those results for understanding grain boundary premelting are discussed.