Lattice-parameter relationships in transition-metal laves phases

Abstract

The application of the Pauling equation for atomic radii, r(1)− r( n)=0.3 log n, to transition-metal AB 2 Laves phases (where Zr, Hf, and Ti constitute the “A” atoms) yields the same apparent valencies of “A” and “B” from crystallographic data, irrespective of whether the cubic or hexagonal allotropic modifications are considered. This enables the lattice parameters of one allotropic form to be calculated from the parameters of the other form to within about 0.2% of experimental values. The lattice parameters of Zr, Hf, and Ti Laves phases have been calculated for hitherto undiscovered allotropes where parameters of the other form are available. It is suggested that the observed smooth variation across the Periodic Table of the apparent valency for both A and B atoms might be attributed to varying amounts of electron transfer from B atoms to A atoms, or to a smooth change in the single-bond radii with increasing d-orbital contributions.