Elastic strain energy due to misfit strains in a polyhedral precipitate composed of low-index planes

The dependence of precipitate shape on the elastic strain energy caused by anisotropy of the elastic moduli is discussed for polyhedral precipitates with purely dilatational misfit strains. By considering cubic structures for the precipitates and matrix phase, the elastic strain energy is calculated for the precipitate shapes of a {100} cube, a {110} rhombic-dodecahedron, a {111} octahedron, and the truncated shapes of all three polyhedra. The anisotropy of the elastic moduli of Cu is used for the numerical calculations. The polyhedral shapes of the {111} octahedron and {100} cube result in the highest and lowest values of the elastic strain energy per unit volume of precipitate. The calculated values of the elastic strain energy obtained for the truncated polyhedra are compared with values estimated using a geometrical method that considers the area changes of the {100}, {101} and {111} interfaces. (c) 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.