Formation of solid-state dendrites under the influence of coherency stresses: A diffuse interface approach

TL;DR

This study develops a phase-field model to simulate solid-state dendrite formation influenced by coherency stresses, revealing the absence of a unique tip shape and the linear increase of the selection constant over time.

Contribution

The paper introduces a grand-potential based phase-field model for precipitate growth under coherency stresses, highlighting differences from solidification dendrites.

Findings

Dendrite-like patterns form due to diffusive instabilities.

No unique dendrite tip shape is observed.

Selection constant increases linearly with time.

Abstract

In this paper, we have formulated a phase-field model based on the grand-potential functional for the simulation of precipitate growth in the presence of coherency stresses. In particular, we study the development of dendrite-like patterns arising out of diffusive instabilities during the growth of a precipitate in a supersaturated matrix. Here, we characterize the role of elastic energy anisotropy and its strength on the selection of a dendrite tip radius and velocity. We find that there is no selection of a unique tip shape as observed in the case of solidification, and the selection constant $\sigma^{*}=2d_0D/R_{tip}^{2}V_{tip}$ increases linearly with simulation time for all the simulation conditions (where $R_{tip}$ and $V_{tip}$ are the tip radius and velocity). Therefore, structures derived in solid-state in the presence of elastic anisotropy may only be referred to as dendrite-like.