Isotope effect for the solution of hydrogen in metals: application to Pd/H(D)

Abstract

The isotope effect for the solution of hydrogen in metals cannot be described over the whole temperature range by the usually employed model of localized oscillators. Consideration is given to the transition from localized harmonic oscillator behaviour at the lowest temperatures to that of a three-dimensional translator at the highest temperatures. Application of this new model to the Pd/H(D) system reveals that the experimental isotope solubility ratio data do not agree with the theoretical expectations. At low temperatures the isotope data are in disagreement with the Einstein characteristic temperature, θ_H= 795 K, determined by inelastic neutron scattering, if θ_D=θ_H/√2 is assumed. The isotopic solubility ratio data are also contrary to expectations at higher temperatures. The discrepancies are removed if it is assumed that θ_D=θ_H/1.53, a choice which is not unrealistic in view of recent interpretations of the inverse isotope effect observed for the super-conductive transition temperatures of Pd/H(D) alloys.