Electrons per atom ratio determination and Hume-Rothery electron concentration rule for P-based polar compounds studied by FLAPW-fourier calculations.

The extent to which reliable electrons per atom ratio, e/a, are determined and the validity of the Hume-Rothery stabilization mechanism are ensured upon increasing ionicity are studied by applying first-principles full potential linearized augmented plane wave (FLAPW)-Fourier band calculations to as many as 59 binary compounds formed by adding elements from periods 2-6 to phosphorus in group 15 of the Periodic Table. Van Arkel-Ketelaar triangle maps were constructed both by using the Allen electronegativity data and by using an energy difference between the center-of-gravity energies of FLAPW-derived s and p partial densities of states (DOSs) for the equiatomic compounds studied. The determination of e/a and the test of the interference condition, both of which play a key role in the Hume-Rothery stabilization mechanism, were reliably made for all intermetallic compounds, as long as the ionicity is less than 50%.