Equilibrium particle morphologies in elastically stressed coherent solids

We determine the three-dimensional equilibrium shapes of particles with a p urely dilatational misfit in an elastically anisotropic medium with cubic s ymmetry. We have identified a succession of cuboidal shapes with four-fold rotational symmetry that minimize the total energy of the system. In the pr ocess of determining these equilibrium morphologies, we have also developed a computationally efficient approach to determine the equilibrium shape wh ich is many orders of magnitude faster than a standard implementation of Ne wton's method. For small elastic stress a (100) cross-section of the three- dimensional equilibrium shape agrees well with the two-dimensional calculat ion. However, for larger values of the elastic stress, the agreement is not as good. Elastic-stress-induced configurational forces are identified as t he reason for the non-spherical equilibrium shapes. (C) 1999 Acta Metallurg ica Inc. Published by Elsevier, Science Ltd. All rights reserved.