A systematic analysis of good matching sites between two lattices

The geometrical matching/mismatching of lattices overlapped in 1, 2 and 3 dimensions have been analyzed systematically by variation of lattice misfit in a large range, far beyond the limits for semicoherent interfaces. In order to evaluate the degree of matching, the density of good matching site (GMS) between two lattices is calculated. The analysis shows that the GMS density remains approximately constant, irrespectively to the degree of lattice misfit. This constant, defined as the average GMS density, decreases exponentially with the increasing dimension of misfit. Typically, for δ = 15%, the average GMS densities are approximately 30%, 7%, and 1.4% for 1D, 2D, and 3D lattice misfits, respectively. The GMS density deviates significantly if a CSL of small Σ can be defined. The relationship between the GMS distribution and O-lattice is investigated. It indicates that an abrupt increase in the GMS density in an interface parallel to a principal O-lattice plane is equivalent to a reduction of dimension of misfit. This shows the agreement between the selections of principal O-lattice planes as candidates of the preferred interfaces and the condition that interfaces with high GMS density are preferred.