Dimensional analysis of the crustal structures of intermetallic phases

Abstract

A method of analysing the unit-cell dimensions of crystal structures of binary intermetallic phases is described, that avoids the usual difficulties that result from uncertainty about the appropriate sizes of the atoms, because of their coordination numbers and valencies in the structures considered. Linear equations are obtained that relate the cell dimensions to the atomic diameters for coordination number 12, and sometimes to the valency. These equations permit the explicit identification of the atomic arrays that control the cell dimensions and, therefrom, new quantitative information not previously available, can be derived: for example, (i) the reason for remarkably constant axial ratios of phases of certain uniaxial crystal structures, (ii) the significance of variable or fixed atomic coordinates in relation to structural dimensions, (iii) the fact that, frequently, different atomic arrays control the cell dimensions of phases containing rare-earth atoms, and phases with the same crystal structure that do not contain rare-earth atoms, (iv) the extent to which a system of atomic diameters determined from elemental structures, may be applicable to alloy phases formed by the atoms, and (v) inferences concerning electronic interactions in true interstitial phases.