A simple faceting model for the interfacial and cleavage energies of Σ3 grain boundaries in the complete boundary plane orientation space

Interfacial energies play a crucial role in the evolution of polycrystalline microstructures both in structural and functional materials. From a crystallographic perspective, the energy landscape depends both on the misorientation and the boundary-plane orientation of grain boundaries (GBs). Traditionally, however, GB structure-property relationships have been investigated primarily for interfaces with twist or tilt character and with an emphasis on the role of misorientation. In this article, we introduce an automated routine for simulating the minimum energy structures for general GBs. The important role of the boundary-plane orientation is elucidated by simulating 297 distinct Aluminum Sigma 3 GBs that adequately sample the fundamental zone of the plane orientation space. It is observed that while the energy varies significantly as a function of the boundary-plane orientation, the variation is also smooth and without cusps in the fundamental zone. In this article, a simple energy function, motivated by the two-dimensional faceting model for interface structures, is proposed for the free-surfaces and the Sigma 3 GBs in Aluminum. The energy function consists of only three fitting parameters and predicts the energy landscape surprisingly well. It is anticipated that this model may be extended to represent the energies of GBs corresponding to higher Sigma-misorientations. Finally, as an application of the faceting model for interfaces, the theoretical cleavage energies for Sigma 3 GBs in Aluminum have been computed. It has been observed that, contrary to conventional wisdom, the Sigma 3(111) twin boundary does not exhibit the highest cleavage energy and these results are expected to have consequences for grain boundary engineering. Published by Elsevier B.V.