Theory of dendritic growth in the presence of lattice strain

TL;DR

This paper develops a theoretical framework to understand how lattice strain influences dendritic growth, revealing that elastic effects can alter interface conditions and pattern formation.

Contribution

It introduces a nonlinear integro-differential equation incorporating elastic effects into dendritic growth modeling, extending classical theories to include lattice strain.

Findings

Elastic effects can shift transition temperatures in dendritic growth.

Shear transitions induce dendritic patterns even with isotropic surface energy.

Elastic effects significantly influence pattern formation in solid-solid interfaces.

Abstract

Elastic effects due to lattice strain modify the local equilibrium condition at the solid-solid interface compared to the classical dendritic growth. Both, the thermal and the elastic fields are eliminated by the Green's function techniques and a closed nonlinear integro-differential equation for the evolution of the interface is derived. In the case of pure dilatation, the elastic effects lead only to a trivial shift of the transition temperature while in the case of shear transitions, dendritic patterns are found even for isotropic surface energy.