Optimum distance model of relaxation around substitutional defects

Abstract

The relaxation patterns around isovalent substituent atoms in the NaCl, CsCl, ZnS, CaF₂, Li₂O, and ReO₃ structure types have been calculated. Such models (1) emphasize geometric structural criteria and are thus conceptually simple, (2) are computationally straightforward though perhaps computer-time consuming for large, low symmetry cases, and (3) agree reasonably well with more complex calculations, such as energy minimization methods. On the basis of such optimum interatomic distance models, atomic displacements resulting from an isovalent substitution: (1) depend strongly on the structural connectivity (structural type) involved, (2) are decidedly greater for atoms with radius vectors parallel to the substituent's bonds and least for atoms with radius vectors oriented between such bonds, (3) decrease in magnitude approximately inversely proportional to the square of the distance to the substituent, regardless of direction, and (4) are mostly, but not strictly, radial. The simplest relationship to structural type is the dependence on the coordination of the substituent's ligands — the greater the coordination number of the atoms bonded to the substituting atom, the less compliant the structure.