The physical basis for the Frank-Bilby equation is considered. Dual descriptions in terms of interface physics and mechanics are introduced. Natural (NDP), commensurate (COP) and rotated (RCDP) dichromatic patterns are introduced. Burgers vectors are defined by symmetry operations or circuits in the CDP and RCDP. Structures are described for misfit arrays, tilt arrays, twist arrays, disconnections and combinations of these defects. The concepts of partitioning of elastic distortions, array energies, node formation, and the lateral spreading of defects within interfaces are considered. Examples with analytical solutions, numerical solutions and iterative solutions are presented. We elucidate some principles that emerge from the solutions and present reasons why some results differ from other methods of analysis. (C) 2012 Elsevier Ltd. All rights reserved.