Theoretical modification of Hume Rothery condition of phase stability in a good agreement with experimental data

We presented in this paper a theoretical modification of Hume Rothery condition of phase stability in good agreement with experimental data. This modification is derived directly from the quantum conditions on the free electron Fermi gas inside the crystal. The new condition relates both the volume of Fermi sphere VF and volume of Brillouin zone VB by the valence electron concentration VEC as ; for tetragonal and hexagonal systems and as; for cubic systems.