Calculation of energy of low-angle grain boundaries

Various techniques for calculating the linear elastic energy of low-angle grain boundaries are reviewed. The dependence of both elastic and inelastic contributions on boundary-plane orientation ň and axis of rotation û is considered in detail. Particular attention is devoted to the treatment of the elastic contribution near the dislocation cores. The differences in elastic energy between the recent calculations of Rey and Saada (1977) and Bonnet (1981) with the classic calculation of Read and Shockley (1950) are explained by the differing treatments used by these authors for the region near the cores. The elastic energy for low-angle grain boundaries composed of three sets of parallel, equally spaced dislocations is calculated, within an easily understood convention for handling the region near the cores, for the first time. The dependence of the total energy, elastic plus core, on ň and û is given.