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

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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′).