Theory of dendritic growth in the presence of lattice strain

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.