Structures in irrational singular interfaces

Abstract

We consider periodic good matching bands (which are centered at the O-lines) as the characteristic feature of the structures in irrational singular interfaces in the primary preferred state. This feature is shared by various structures described by different models for irrational singular interfaces, and it can be used to consolidate different descriptions. We have made a quantitative analysis on the distribution of good matching zones (GMZs) in a relationship with plane matching geometry. This analysis emphasizes that matching of one set of principal planes does not represent good lattice matching. Good lattice matching is possible only at the locations of 0-d intersections, where three sets of nonlinearly related Moire planes intersect. Matching of one or more sets of principal planes in an interface usually implies the possible presence of periodic GMZs in the interface. The analysis also explains why and in what condition a dislocation configuration can be described by the traces of Moire planes. The distribution of exact 0-d intersections can be determined based on the O-lattice theory. The approximate 0-d intersections can be used for determining a possible interfacial structure when periodic O-elements do not exist.