We study the energetics and the structure of small-angle tilt grain boundaries (i.e., dislocation walls). By considering the elastic properties of groups of dislocations, we show that the structure of the Wulff plot is much richer than previously expected. Previous calculations found that the insertion of a single step costs a logarithmically divergent energy; we show that this step energy can be made finite if elastic screening is taken into account. Stepped structures lead to a whole series (i.e., a devil’s staircase) of commensurate boundary orientations. Also, a first-order phase boundary is found. We speculate on the interface structure to be expected in the region midway between two symmetric boundary orientations; our calculations are not capable of making a definitive prediction for this structure.

• Received 31 July 1987

DOI:https://doi.org/10.1103/PhysRevB.37.5242