Empirical models, metal hydrides

In order to meet the requirements of a practical application, a metal hydride must first satisfy the thermodynamic requirements operation temperature and hydrogen pressure. As the entropy term of Eq. (1.11) is effectively the same for all compounds, this means that the heat of formation (AH) is the principal parameter of a given alloy for hydrogen storage applications. Unfortunately, first principles calculations of AH for ternary alloys are still lacking [47]. However, semi-empirical models can be applied for some systems and give useful physical insight on the hydride formation. 

The volume expansion accompanying hydrogen uptake In metals and alloys has recently been calculated55 using a semi-empirical model which relates the heat of formation, AH, of a metal hydride to the difference of the Fermi energy, Fp and the center, Fg, of the s band of the host metal.56 The remarkable constancy of AV was shown to be in agreement with the model and due mainly to the volume dependence of the width, W, of the electronic bands.55... 

The number of electrons available for empirical evaluation of metal-metal bonding has been taken as the Pauling metallic valence less the number of H ions per metal. In this connection the valence numbers of Borelius (6) give somewhat better correlations—e.g., in differentiating Pd from Ag (valences 7 and 1, respectively). Heats of formation calculated from the lattice energies by the Born-Haber cycle are not yet sufficiently accurate to be useful numerically, but they provide an interesting rationalization of the formation of many hydrides. This is the principal reason for considering such a naive model. 

A direct application of the semi-empirical band structure model of Griessen and Driessen (eq. 34) is to predict standard enthalpies of hydride formation of metals which absorb only negligible amounts of hydrogen under normal conditions. Driessen et al. and Hemmes et al. ) predicted on the basis of this model that formation of hydrides of Be, Cu, Ru, Ag, Cd, In,... 

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