On the shape evolution of a two-dimensional coherent precipitate with a general misfit strain

For a coherent precipitate in two dimensions, any misfit strain, i.e. stress-free transformation strain is expressed with two principal terms of ε and η. Therefore, all the transformation problems can be divided into three cases, (a) a purely dilatational case with ε=η; (b) a tetragonal case of opposite signs with εη≤0; and (c) a tetragonal case of same signs with εη>0. For case (a) with purely dilatational misfit strain, if elastic anisotropy is uniform, a soft particle takes on a plate-like shape along an elastically soft direction. A hard particle, however, tends to take on a shape of high symmetry with edges parallel to elastically soft directions. A homogeneous particle tends to follow the hard particle case in the early stage of evolution, but eventually changes to the pattern of a soft particle. For case (b) with tetragonal misfit strain of opposite signs, there exists always a preferred orientation at an angle of tan−1(−η/ε)1/2 with respect to a principal direction. This is true whether the particle is soft or hard, i.e. regardless of inhomogeneity. The third case (c), a misfit strain of same signs with εη>0, represents a combination of the previous two. A hard particle of this case tends to change its morphology from a plump shape to a somewhat elongated one with its major axis parallel to the preferred orientation due to the tetragonal part of opposite signs. A soft particle becomes a plate lying along a direction between an elastically soft direction and the preferred orientation.