On the Stresses and Energies associated with Inter-Crystalline Boundaries

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Abstract
Models, largely based on the assumptions introduced by Peierls and Nabarro in dealing with a single dislocation, are used in calculations on three types of intercrystalline boundaries, namely, (I) a boundary due to a difference of atomic spacing, (II) a twist boundary, and (III) a symmetrical tilt boundary. With these models the resolution of the boundary into a sequence of dislocations is a natural consequence of the analysis, which also yields the expressions for the stresses, atomic displacements and energies associated with the boundary, as functions of the angle of tilt, etc. By allowing the distance between dislocations to tend to infinity, these expressions reduce to the corresponding ones for single dislocations. The outstanding feature of the interfacial energy is that it increascs initially very rapidly with the angle of tilt, etc. An application of the results to the theory of oriented overgrowths, developed by Frank and the present author, is described. The validity of the assumptions and approximations involved and the advantages of the treatment as compared with those of other writers are discussed.

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