The effect of strain energy on the morphology of a cubic crystalline precipitate in an amorphous matrix

The present work is concerned with the configuration of crystalline precipitates in an amorphous isotropic matrix. The shape and orientation of precipitates were determined by minimizing the elastic strain energy while neglecting surface energy effects. Based on Eshelby's approach, numerical calculations of the dependence of the strain energy on the shape of a cubic precipitate were performed for different combinations of the elastic constants of the matrix and of the precipitate, and for various crystallographic orientations of the precipitate. The results indicate that only disk- or sphere-shaped precipitates are associated with minimum strain energy. It was further shown that the parameters which determine the shape of the precipitate are the shear modulus of the matrix C₄₄, and the shear modulus of the crystal, C_{44, π/4}^*, measured in axes inclined by π/4 to the crystallographic axes. The minimum strain energy is associated with a thin plate-shaped precipitate, parallel to a 100 plane, when C₄₄ > C_{44, π/4}^* and the anisotropy factor A > 1, and parallel to a 111 plane, when C₄₄ > FC_{44, π/4}^* and A < 1 where F is the orientation factor depending also on A. In all other cases, a spherical precipitate is associated with minimum strain energy. Our results generalize a known criterion for isotropic systems. They are in agreement with the experimentally observed configuration of crystallization in a Fe-B metallic glass.