Analysis of unit cell dimensions in terms of frameworks and elemental atomic diameters

Abstract

Structural description in terms of frameworks – three-dimensional periodic arrangements of points which are occupied by atoms – is used as the basis of analysing the cell dimensions of phases with the MgCu₂ structure (cubic) in terms of the elemental diameters of the component atoms. The MgCu₂ structure is described in terms of interpenetrating homogeneous D and T′ frameworks or the heterogeneous [D + T′] framework. The relative influences of the atoms occupying these three frameworks on the cell dimensions of different groups of phases that show distinct dimensional behaviour are determined. The self-coordination of atoms on the T′ framework is six. Some interesting observations are made on whether the basic diameters of atoms on this framework might correspond to a coordination number of six rather than twelve which is the overall coordination number of the atoms on the framework (T′).