Heat of formation and band structure of binary and ternary metal hydrides

The heat of formation, ΔH, of metal hydrides is empirically found to be linearly related to a characteristic energy ΔE of the electronic band structure of the host metal. Independently of the position of the host metal in the Periodic Table (simple metals, noble metals, transition metals, actinides, and rare earths) we found ΔH=α ΔE+β, with ΔE=E_F-E_s, α=29.62 kJ/eV mol H, and β=-135 kJ/mol H (E_F is the Fermi energy and E_s is the center of the lowest band of the host metal; ΔH is expressed in kJ/mol H and ΔE in eV). Assuming that this relation also holds for ternary metal hydrides we used the (simple) tight-binding coherent-potential-approximation model of Cyrot and Cyrot-Lackmann to evaluate the characteristic energy ΔE of A_yAB_yB alloys where A and B are both nonsimple metals. The values of ΔH derived from the calculated ΔE are in good agreement with existing experimental data on the heat of formation of ternary metal hydrides.