Three-dimensional dynamic calculation of the equilibrium shape of a coherent tetragonal precipitate in Mg-partially stabilized cubic ZrO₂

The equilibrium shape of a tetragonal precipitate coherently embedded in a cubic matrix is examined in three dimensions by a computer simulation. Independent experimental data of Mg-partially stabilized ZrO₂ are used as the input parameters. The equilibrium shape is obtained by diffusional relaxation of an initially nonequilibrium spherical shape. The relaxation is described through a generalized field kinetic model which takes into account the transformation-induced elastic strain arising from a cubic → tetragonal crystal lattice rearrangement. Without any a priori constraint on the geometry of the particle, the equilibrium shape is shown to be a rotation disk formed by two cones with the common base. It is far from the ellipsoidal shape assumed in the conventional analytical calculations based on Eshelby's model.