Competition between Surface Energy and Elastic Anisotropies in the Growth of Coherent Solid State Dendrites

TL;DR

This paper introduces a phase field model incorporating elastic strain energy to study the competition between surface energy and elastic anisotropies in the growth of coherent solid state dendrites, revealing a transition in growth directions.

Contribution

It develops a new phase field model that includes elastic effects and analyzes morphological transitions in dendritic growth due to anisotropy competition.

Findings

Solid state dendrites switch growth directions based on anisotropy changes.

Elastic anisotropy can dominate surface energy effects in dendritic growth.

The model predicts growth morphology using curvature and strain corrections.

Abstract

A new phase field model of microstructural evolution is presented that includes the effects of elastic strain energy. The model's thin interface behavior is investigated by mapping it onto a recent model developed by Echebarria et al (Phys Rev E, 70:061604,2004). Exploiting this thin interface analysis the growth of solid state dendrites are simulated with diffuse interfaces and the phase field and mechanical equilibrium equations are solved in real space on an adaptive mesh. A morphological competition between surface energy anisotropy and elastic anisotropy is examined. Two dimensional simulations are reported that show that solid state dendritic structures undergo a transition from a surface dominated [10] growth direction to an elastically driven [11] growth direction by changes in the elastic anisotropy, the surface anisotropy and the supersaturation. Using the curvature and strain corrections to the equilibrium interfacial composition and linear stability theory for isotropic precipitates as calculated by Mullins and Sekerka, the dominant growth morphology is predicted.