Coincidence lattice model for the structure and energy of grain boundaries

The Coincidence Site Lattice (CSL) model of grain boundaries is developed on a simple physical basis. We propose 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 0-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 ∑ 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 ∑ boundaries and to approach a larger constant value for all large ∑ 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 ∑ boundaries. The model appears to be consistent with our present knowledge of boundary structure and energy, and its general applicability is discussed.