Effect of elastic interaction on the formation of a complex multi-domain microstructural pattern during a coherent hexagonal to orthorhombic transformation

The effect of elastic interaction on the formation and dynamic evolution of multi-domain micro-structures during a hexagonal to orthorhombic transformation in the absence and presence of an externally applied strain field is investigated numerically using the phase field model. In particular, three cases are considered, which include a single variant, two variants, and all three variants of the orthorhombic phase produced by the transformation. In each case, the morphology and spatial distribution of the orientation variants are characterized. It is shown that nucleation and growth of a single variant produces thin plates of the orthorhombic domains with definite habit planes. In the case of two variants, the domains developed at the initial stages are also platelets of well-defined habit planes, which is similar to the case of a single variant. However, the impingement and intersection of the platelets of different variants results in the formation of twin boundaries and "zig-zag" patterns. The overlap regions of the "zig-zag" cross sections remain untransformed which agrees very well with experimental observations. If all three variants are present, the hexagonal to orthorhombic transformation results in a number of unique multi-domain structures such as the star patterns, compound star patterns, fan patterns, etc., which have been frequently observed experimentally in systems undergoing hexagonal to orthorhombic or similar transformations. It is found that if the boundary of the system is constrained, e.g. a grain embedded in a polycrystalline material, the transformation can go to completion only when all three variants are present. In the presence of external strain field, the coupling between the applied strain field and the stress-free transformation strain associated with the domain formation leads to selective growth of variants.