Models for the treatment of crystalline solids and surfaces

Crystalline solids and surfaces have become a subject of growing interest. The difficulty of a comprehensive description of a variety of phenomena by a single method has led to the development of many models. These models can be classified as nonperiodic and periodic models. The former include free clusters, saturated clusters, and embedded clusters. The latter two models serve to remove the boundary effects of the free clusters. No perfect avoidance of such effects can be achieved in this way. The cyclic cluster model overcomes this difficulty in a natural way. It is periodic with a finite periodicity. An embedding can take into account a long-range effect in ionic crystals. Previous periodic approaches relied on the large unit cell model, which is related to the supercell approach. For perfect crystals the conventional unit cell approach is a well-known standard. However, its disadvantage is the unphysical periodicity of defects, which is avoided in the cyclic cluster model. The present article presents a description of these models together with selective applications to solid-state systems and surfaces.