Comparison of the Energies of Symmetrical and Asymmetrical Grain Boundaries

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Two simple geometrical criteria, based on Pauli’s principle, which were derived recently for the identification of low-energy symmetrical (“special”) grain boundaries are applied to assess whether or not asymmetrical configurations are expected to have, indeed, higher energies than symmetrical ones. The latter is postulated to be the case within the framework of the coincident-site-lattice (CSL) model. For a given lattice misorientation (i.e., CSL) this model assumes that the energetically most favorable grain-boundary plane is a densest CSL plane, i.e., the symmetrical grain-boundary configuration. In this article it is demonstrated, based essentially on Pauli’s principle, that this is not always the case. Two criteria are formulated which enable one to, at least qualitatively, predict in which cases an asymmetrical grain boundary is expected to show a lower energy than the corresponding symmetrical configurations with the same lattice misorientation.