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

The heat of formation, $\Delta H$, of metal hydrides is empirically found to be linearly related to a characteristic energy $\Delta E$ 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 $\Delta H=\alpha \Delta E+\beta$, with $\Delta E=E_F-E_s$, $\alpha =29.62\mathrm{}$ kJ/eV mol H, and $\beta =-135\mathrm{}$ kJ/mol H ($E_F$ is the Fermi energy and $E_s$ is the center of the lowest band of the host metal; $\Delta H$ is expressed in kJ/mol H and $\Delta E$ 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 $\Delta E$ of $A_{y_A}{B}_{y_B}$ alloys where $A$ and $B$ are both nonsimple metals. The values of $\Delta H$ derived from the calculated $\Delta E$ are in good agreement with existing experimental data on the heat of formation of ternary metal hydrides.