Shape of a rhombohedral coherent Ti₁₁Ni₁₄ precipitate in a cubic matrix and its growth and dissolution during constrained aging

The shape of a coherent rhombohedral precipitate in a cubic matrix and its growth and dissolution during strain-constrained aging were investigated using a time-dependent Ginzburg-Landau kinetic model by taking into account the coupling between the constraint (applied) strain and the local strain. The effect of boundary conditions, constraint strain or constraint stress, has been discussed. A particular example of Ti₁₁Ni₁₄ precipitate growth in a TiNi shape memory alloy was considered without any a priori assumption about the particle shape. It was demonstrated that a Ti₁₁Ni₁₄ precipitate grown from a supersaturated cubic TiNi matrix has a lens-like shape, with its normal parallel to the [111]_B2 orientation of the matrix, in agreement with experimental observations. Precipitate growth and dissolution under various strain-constraint conditions have been discussed.