A Review of the Statistical Theory of the Phase-Change Behavior of Hydrogen in Metals

Abstract

Theoretical treatments of the phase-change behavior of hydrogen in metals based on the lattice-gas model of statistical mechanics are reviewed. Early model calculations assumed that hydrogen in metals could be treated as a lattice-gas model in which the hydrogen-hydrogen interactions were either attractive (as in the Lacher model) or repulsive (as in the blocking models). Models based on attractive interactions predicted phase separations between the disordered phases α and α’ but did not predict the correct saturation behavior while models based on repulsive interactions predicted the correct saturation behavior but could not predict phase transitions. In the mid 1970’s work by Hall and Stell showed that both attractions and repulsions between hydrogen atoms were necessary to obtain the ordered ß phase as well as the phases α and α’. Work by Horner and Wagner, showed that the elastically-based hydrogen-metal interaction is mathematically equivalent to an effective hydrogen-hydrogen interaction and that this effective interaction can be calculated in terms of experimentally measurable quantities. Recently, Futran, Coats, Hall and Welch have developed a model for hydrogen in niobium based on the Horner-Wagner work which predicts the α, α’ and β phases. The model has been extended to apply to the case where hydrogen is absorbed in niobium-vanadium alloys.