Supercell symmetrical

The substitution of divalent cations for Mg2+ ions in MgO has been extensively studied within the ionic model (Mackrodt and Stewart, 1979). Recently these systems have been the subject of a series of systematic studies within the LCAO-HF formalism in which the highly symmetric nature of the system is exploited to lower computational costs and to simplify the geometrical relaxation (Freyria-Fava et al., 1993 Dovesi and Orlando, 1994 Orlando et al., 1994a). These studies contain the only published attempt to demonstrate the convergence of the supercell method for the treatment of defects within a QM formalism in ionic systems. The defect formation energy ( D) of, e.g., substitution of Ca for Mg ions in MgO may be referenced to the energies of the isolated ions ( Mg2< and ca2+)> i.e. 

FIGURE 11.2 Number of configurations (K) in a model of a binary alloy with BCC structure using a 2x2x2 supercell, compared with the number of symmetrically inequivalent configurations. 

Matrices of the Symmetrical Supercell Transformations of 14 Three-dimensional Bravais Lattices... 

Reciprocal Matrices of the Symmetric Supercell Transformations of the Three Cubic Bravais Lattices... 

The supercell of the complex is defined as the smallest translationally symmetric subunit of the complex. 

---