Dimensional analysis of phases with the A15 structure: Further considerations

Abstract

A previous study of the cell dimensions of MN 3 phases with the A15 structure as a function of the atomic diameters D M and D N for CN 12 is continued. It is now shown that, when several contacts from an atom to its M and N neighbours act together to control the cell dimension a, the dependence of a on D M cannot be independent of D N and vice versa. This leads to new non-linear equations for the dependence of a on D M and D N that reproduce the observed a values of the stoichiometric phases to about the limit of their accuracy, from CN 12 atomic diameters alone. The observations now suggest that the cell dimensions of the transition metal-transition metal (T-T) phases are controlled by all contacts in both coordination polyhedra acting together rather than by the 12-4 M-N contacts alone. Also discussed are the size of the tin atom in phases with the A15 structure, the valency effect of the N atoms in T-T but not in non-transition metal-transition metal (B-T) phases and the relative atomic volumes in T-T and B-T phases. Finally, the dimensional behaviours of T-T and B-T phases with the A15 and CsCl structures are compared and found to be completely analogous, so the particular properties of phases with the A15 structure cannot be attributed to their two very close N-N contacts.