Dimensional analysis of phases with the A15 β-W structure

Abstract

It is found that the method of dimensional analysis of binary metallic phases M x N y , recently developed by the author, can be applied successfully to a tetrahedrally close-packed structure, e.g. the A15 or β-W type MN 3, Linear equations are developed for the cell edge a in terms of D M and D N , the atomic diameters for coordination number (CN) 12 of the atoms, and of such valency effects as are apparent; these reproduce the observed a values of 63 phases to within an average of a fraction of a per cent. Differences are found between those phases which have transition metal M components and those which do not. In the former it is the M-N contacts in the icosahedron of N atoms surrounding M that control a, whereas in the latter it is the contacts in the CN 14 polyhedron of four M and ten N atoms surrounding the N atoms that together control a. A pseudo-valency effect occurs for the N atoms in phases with transition metal M components. This appears to result in part from valency considerations and in part from geometrical constraints related to the two close N-N contacts. In this paper we compare phases with the A15 structure, rare earth dihydrides with the fluorite structure and rare earth nitrides with the rock salt structure, in each of which two or more sets of atomic contacts act simultaneously to control the cell dimension. A lemma is provided for such cases to indicate how the individual expected cell edge dependences on D M or D N are to be combined to give the overall expected dependence.