An expression derived for the average inverse-power potential energy of interaction, between a particle at a fixed distance above a half-crystal face and the half-crystal, was applied to calculation of the minimum energy spacing and interfacial energy between two perfect half-crystals placed together to form a so-called completely-misfitting grain boundary. The grain-boundary energies and spacings of various juxtaposed surfaces of face-centered cubic Ar at 0K were calculated, predicting energies of 41.7, 22.8 and 16.0mJ/m2 for (100)/(110), (100)/(111) and (111)/(111), respectively. The method appeared to be applicable to any system which obeyed the specified type of potential function when there was a continuous spontaneous generation of dislocations in two dimensions at the boundary. This seemed to be the case for high-angle twist or tilt boundaries.

The Grain Boundary Energy and Configuration of Inert Gas Crystals-II. H.H.Schmidt, G.Jura: Journal of Physics and Chemistry of Solids, 1960, 16[1-2], 67-70