Criterion for predicting the morphology of crystalline cubic precipitates in a cubic matrix

Abstract

The present work is concerned with the configuration of precipitates having cubic crystal symmetry in a cubic matrix. The shape and orientation of the precipitates were determined by minimizing the elastic strain energy, while neglecting surface energy effects. Lee, Barnett, and Aaronson7 have shown that only spherical or plate-shaped precipitates are associated with minimum strain energy. Equating the exact expression for the energy of an infinite coherent plate-shaped precipitate with an approximation suggested for the energy of a spherical precipitate, a simple criterion is derived. The criterion enables the prediction of the shape and orientation of the precipitate associated with minimum strain energy, and allows identification of the basic elastic parameters which determine this configuration. When compared to exact numerical results, good agreement was obtained. The criterion predicts that the minimum strain energy is associated with a plate-shaped precipitate, parallel to its 100 planewhen HC ₄₄ >C* ₄₄/A* and the anisotropy factor of the precipitateA * > 1, and parallel to its {111} plane whenHC ₄₄ > F*(111)C*₄₄/A* andA* < 1. In all other cases, a spherical precipitate is associated with minimum strain energy.H is a parameter which depends on the anisotropy of the matrix.F * is an orientation factor which depends on the anisotropy of the precipitate.