Equilibrium particle morphologies in elastically stressed coherent solids

Abstract We determine the three-dimensional equilibrium shapes of particles with a purely dilatational misfit in an elastically anisotropic medium with cubic symmetry. We have identified a succession of cuboidal shapes with four-fold rotational symmetry that minimize the total energy of the system. In the process of determining these equilibrium morphologies, we have also developed a computationally efficient approach to determine the equilibrium shape which is many orders of magnitude faster than a standard implementation of Newton's method. For small elastic stress a (100) cross-section of the three-dimensional equilibrium shape agrees well with the two-dimensional calculation. However, for larger values of the elastic stress, the agreement is not as good. Elastic-stress-induced configurational forces are identified as the reason for the non-spherical equilibrium shapes.

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