Classification of epitaxy in reciprocal and real space: rigid versus flexible lattices

Early investigations of epitaxy focused on inorganic adsorbates consisting of atoms or few-atom molecules, where commensurate registries are predominantly encountered. Expanding such studies to larger (organic) molecules has revealed hitherto unknown types of epitaxy with coherence between adlayer and substrate lattices in just one direction. Here we review recent contributions to the fundamental understanding and modeling of epitaxy. By sorting the ideas brought forward in the literature and amending some basic algebraic considerations a universal scheme for the classification of lattice epitaxy is presented. Ultimately, the occurrence of the different types of epitaxy is made plausible by easy-to-grasp energetic arguments.