Pattern formation during diffusion limited transformations in solids

TL;DR

This paper models diffusion-limited growth in solid-solid transformations, emphasizing elastic effects and interface kinetics, and predicts unique growth patterns and velocities through analytical and simulation methods.

Contribution

It introduces a comprehensive framework combining analytical, Green's function, and phase field methods to study elastic effects in diffusion-limited solid transformations.

Findings

Single finger growth with symmetry breaking at high driving forces

Twin structures can form during shear transformations

Predicted growth velocities can exceed those of dendritic growth

Abstract

We develop a description of diffusion limited growth in solid-solid transformations, which are strongly influenced by elastic effects. Density differences and structural transformations provoke stresses at interfaces, which affect the phase equilibrium conditions. We formulate equations for the interface kinetics similar to dendritic growth and study the growth of a stable phase from a metastable solid in both a channel geometry and in free space. We perform sharp interface calculations based on Green's function methods and phase field simulations, supplemented by analytical investigations. For pure dilatational transformations we find a single growing finger with symmetry breaking at higher driving forces, whereas for shear transformations the emergence of twin structures can be favorable. We predict the steady state shapes and propagation velocities, which can be higher than in conventional dendritic growth.