Phase-field modeling of the discontinuous precipitation reaction

TL;DR

This paper develops a multi-phase-field model to simulate discontinuous precipitation, revealing how diffusion coefficients influence structure and growth velocity, and challenging the local equilibrium assumption in existing theories.

Contribution

It introduces a novel multi-phase-field model that incorporates surface and volume diffusion for discontinuous precipitation, providing new insights into interface dynamics and stability.

Findings

Precipitation front structure depends on diffusion coefficients.

Steady-state solutions are limited by instabilities at certain spacings.

Local equilibrium assumption is invalid under typical conditions.

Abstract

A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that the structure and steady-state growth velocity of spatially periodic precipitation fronts strongly depend on the relative magnitudes of the diffusion coefficients. Steady-state solutions always exist for a range of interlamellar spacings that is limited by a fold singularity for low spacings, and by the onset of tip-splitting or oscillatory instabilities for large spacings. A detailed analysis of the simulation data reveals that the hypothesis of local equilibrium at interfaces, used in previous theories, is not valid for the typical conditions of discontinuous precipitation.