Overview no. 61 On geometric criteria for low interfacial energy

A review of geometric criteria for low interfacial energy which have been proposed in the literature is given. These include, (i) low reciprocal volume density of coincidence sites; (ii) high planar density of coincidence sites, Γ; (iii) high Γ at constant interplanar spacing, d; (iv) large d; and (v) high density of locked-in rows of atoms. These criteria are then tested against available experimental results which include measurements of: (a) interfacial energy; (b) rotations of crystallites on flat crystal substrates; (c) boundary faceting; (d) boundary dissociation; and (e) observations of grain boundary dislocations. No support for the general usefulness of criteria (i), (ii), (iv) and (v) is found. In all cases, significant numbers of results violating these criteria are found or else it is demonstrated that their range of validity is undefined, and, hence, their predictive power is highly limited. Criterion (iii) is found to apply for a limited number of cases involving metal/metal or ionic/ionic interfaces but fails for metal/ionic interfaces. Further testing and consideration of this criterion seems called for. It is concluded that no general and useful criterion for low energy can be enshrined in a simple geometric framework. Any understanding of the variations of interfacial energy must take account of the atomic structure and the details of the bonding at the interface.