Theory of the crystal structures of transition metals

The structure trend that is observed across the transition metal series as the number of valence electrons N increases 3 to 11 is explained quantitatively. The difference in the total one-electron band structure energy between the close-packed structures face-centred cubic and hexagonal close-packed is shown to determine completely which structure is favoured, whereas an additional hard-core repulsive contribution is necessary when comparing the body-centred cubic and close-packed structures at the noble metal end of the series. The calculations were performed assuming a model transition metal characterized by only the two d-resonance parameters epsilon d and Gamma , from which the densities of states for the three structures were obtained using energy levels calculated by the hybrid nearly- free-electron tight-binding scheme of Pettifor.