  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.
