Dislocation models of grain boundaries was suggested by Bragg (1940) and Burgers (1940). The first quantitative study of these models was given by Read and Shockley (1950). They obtained a formula for the dependence of the grain boundary energy on the misorientation of the neighbouring grains, which became a cornerstone of the grain boundary theory. The Read–Shockley formula was based upon a proposition that the grain boundary energy was the sum of energies of the two sets of dislocations that come from the two neighbouring grains. This proposition was proved under an assumption on a quite special geometry of the slip planes. This paper aims to show that the assumption was not necessary and the proposition holds for arbitrary geometry of slip planes. Another goal of this paper was to provide all basic formulas of the theory: though the dislocation model of grain boundaries was considered in all treatises on dislocation theory, a complete analysis, including the relations for lattice rotations and displacements, had not been given. This analysis showed, in particular, that continuum theory did not yield the proper relations for the lattice misorientations, and these relations must be introduced by an independent ansatz.

On Dislocation Models of Grain Boundaries. V.L.Berdichevsky: Continuum Mechanics and Thermodynamics, 2011, 23[3], 185-209