Coincidence Lattice Model for the Structure and Energy of Grain Boundaries

摘要

It is proposed that, to a good approximation, the construction of a boundary can be described in terms of three basic steps: (1) a rigid body joining of two perfect crystals along the boundary plane (Step I); (2) a primary relaxation (Step II) consisting of relaxations in the boundary centered on O-Lattice elements which act to improve lattice matching in these regions; and (3) a possible secondary relaxation (Step III) which produces the final structure composed of patches of a low sigma boundary and secondary grain boundary dislocations. The energy after Step I is obtained by summing pairwise interactions across the boundary and is found to be relatively low for a number of low sigma boundaries and to approach a larger constant value for all large sigma boundaries. The energy decrease due to Step II varies monotonically with crystal misorientation according to a Read-Shockley function, and the energy decrease associated with Step III produces cusps in the energy versus misorientation curve at misorientations corresponding to low sigma boundaries. The model appears to be consistent with the present knowledge of boundary structure and energy, and its general applicability is discussed. (ERA citation 06:017747)