Grain Boundary Dislocations in Noncubic Crystals. 1. The Model
ARMY MATERIALS AND MECHANICS RESEARCH CENTER WATERTOWN MA
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A model is developed for the dislocation structure of grain boundaries in noncubic crystals. Important differences are noted between the grain boundary dislocation GBD description of boundaries in cubic and noncubic crystals. In both types of crystals the GBDs are present to preserve low-engery patterns characteristic of exact coincidence-site lattices CSLs. In cubic crystals exact three-dimensional CSLs can be found for rotations about any axis. In noncubic crystals, however, exact three-dimensional CSLs exist only in special circumstances in general, only near-coincidence site lattices near- CSLs can occur in three dimensions. When only near-coincidence is possible an additional component to the GRB array is necessary to compensate for the distortion implicit in near-coincidence. In twist boundaries this additional component alters the spacing of dislocations in the screw grid. Moreover, it is impossible to obtain a twist boundary free of GBDs. The minimum dislocation content occurs at misorientations at which exact coincidence exists in a single plane parallel to the twist axis, i.e., when an exact two-dimensional CSL exists, in which case a single set of screw GBDs parallel to the plane of exact coincidence is present. In tilt boundaries two dislocation arrays may be necessary an array of pattern-preserving dislocations and an array of misfit dislocations. The function of the former array is to preserve the low-engery coincidence pattern on either side of the GBD the function of the misfit array is again to compensate for the distortion inherent in near-coincidence.