Evolution of multivariant microstructures with anisotropic misfit: A phase field study

Abstract

We study, in two dimensions, the effect of misfit anisotropy on microstructural evolution during precipitation of an ordered β phase from a disordered α matrix; these phases have, respectively, 2- and 6-fold rotation symmetries. Thus, precipitation produces three orientational variants of β phase particles, and they have an anisotropic (and crystallographically equivalent) misfit strain with the matrix. The anisotropy in misfit is characterized using a parameter t = ϵ yy / ϵ xx , where ϵ xx and ϵ yy are the principal components of the misfit strain tensor. Our phase field simulations show that the morphology of β phase particles is significantly influenced by t, the level of misfit anisotropy. Particles are circular in systems with dilatational misfit ( t = 1), elongated along the direction of lower principal misfit when 0 < t < 1 and elongated along the invariant direction when −1 ⩽ t ⩽ 0. In the special case of a pure shear misfit strain ( t = −1), the microstructure exhibits star, wedge and checkerboard patterns; these microstructural features are in agreement with those in Ti–Al–Nb alloys.