The data for the solubility of hydrogen in nickel in equilibrium with H2-gas at atmospheric pressure have been analyzed in terms of a model which considers H–vacancy interactions. This model has been shown to be compatible with both the thermodynamic and kinetic data for Ni–H system.

The solubility of hydrogen in equilibrium with H2-gas at atmospheric pressure exhibits a temperature variation, in the BCC phase range, which is incompatible with the simple quasi-regular statistics expected for a dilute interstitial solid solution. This behavior has been analyzed in term of a statistical model that includes the interactions between interstitial H-atoms and lattice vacancies. Good agreement is found between the model and the experimental data.

The thermodynamics of metal–hydrogen solid solutions have been studied using a Fermi–Dirac distribution function in order to describe the formation of H–vacancy clusters. The H–vacancy interaction energies for clusters (decorated vacancies) containing up to six H-atoms have been taken from effective medium calculations. The solute metals Pd, Ni, Fe, Mo and Nb have been considered. The calculations enable the relative fractions of clusters of a given order to be calculated as a function of H-concentration and temperature. A mathematical model for the simultaneous diffusion of H-atoms, vacancies and H–VAC clusters has been developed. The numerical evaluation of the basic kinetic equations is based upon finite difference methods. Kinetic calculations have been made based upon Ni–H solutions as a model system.

The effect of equilibrium vacancy formation on the solubility of hydrogen in metals has been derived. The treatment is based on a Fermi–Dirac distribution function so that problems which arise at low temperatures in Maxwell–Boltzmann formulations are obviated. Using input data for Ni, the effect of vacancy formation on the validity of Sieverts' law is calculated and the (pT)-region in which the thermodynamic functions of the solute (H) atoms can be easily extracted from measured solubility has been mapped.

One of the most common methods used to measure the diffusivity D of hydrogen in solids is to determine the outgassing kinetics of H-charged bodies. The simple outgassing rate laws depend for their strict validy upon the assumption that the as-charged H-profile in the sample is uniform, and that this profile is not perturbed in the heat-up phase before the outgassing pressure is recorded. These experimental conditions are difficult to fulfill, especially at temperatures where D is large. It is shown by "computer experiments" that the validy of D-values extracted from outgassing kinetics is not sensibly affected even when deviations from these boundary conditions are large.

The thermodynamic properties of AI-H solid solutions containing lattice vacancies have been discussed using an approach in which the grand canonical ensemble is used to elucidate the behavior of the Al-VAC-H system in Fermi-Dirac statistics. Calculations have been presented and compared for specific models in which H-atoms act both as a simple interstitial species and forms either decorated vacancies or substitutional defects.Vacancy concentrations concomitant to different levels of hydrogenization are calculated and approximate penetration curves for the ingress of vacancies from the metal surface are presented. (C) 2002 Published by Elsevier Science Ltd.

Finite difference methods have been used to calculate penetration profiles for the transient diffusion of interstitial (H) atoms from a surface of constant solute concentrations into solid films. The solid contains trapping sites which modify the transient diffusion behavior. Dislocation-related sites of fixed concentration and vacancy-related sites, whose concentration is dependent on temperature, have been considered. Numerical evaluations using input parameters for the Al–H system have been carried out.

The thermodynamic properties of aluminum–hydrogen solid solutions containing lattice vacancies have been calculated using a canonical ensemble approach and a Fermi–Dirac distribution to describe the distribution of H atoms between vacancy-generated sites and ‘normal’ interstitial sites. The equilibrium vacancy concentration has been calculated as a function of temperature and hydrogen concentration.

The solubility of hydrogen in FeAl in equilibrium with gas as a constant pressure was measured in the temperature range 513–1301K. The solubility data have been analyzed in terms of a statistical model in which the interstitial atoms are distributed through the three distinct sites in the B2 lattice.

A statistical mechanical calculation of the thermodynamic properties of Ni–H solid solutions, based upon the concept of H-atoms possessing translational mobility over path lengths of several lattice parameters, has been shown to be compatible with the observed solubility behavior, but not compatible with the well-established linear Arrhenius behavior of the H-diffusivity above 300K.

In the hydrogenation of metals under high fugacity conditions (such as electrolytic charging), non-steady state diffusion produces concentration–distance profiles which may not be calculated by assuming simple diffusion behavior. Such profiles have been calculated using finite difference methods by considering specific models for the concentration-perturbation of the appropriate jump activation barriers. The results show that much greater H concentrations are produced for a given penetration distance than would be expected by assuming fickian diffusion.

The hydrogenation of metals, often a rapid process, may lead to the production of high vacancy concentrations in the solid when equilibrium is reached. The achievement of equilibrium in this “upquenching” process depends, at least in part, upon the migration of vacancies from the surface into the interior of the solid. Because individual vacancy jump frequencies may depend on position within the vacancy density gradient, particularly when the solid is under an applied stress, analytical solutions of Fick's second law are not appropriate. A finite difference method has been developed to treat such vacancy diffusion problems and applied to vacancy migration in nickel.

Statistical mechanical calculations have been carried out in order to determine the vacancy concentration C-1v in bulk nickel crystals containing dissolved hydrogen. As expected the C-1v concentrations are enhanced with respect to the H-free crystal due to the formation of H-vacancy clusters, Corresponding calculations on the {111} surface have shown that the presence of H-atoms also results in an enhancement of the surface vacancy concentrations.The energy level spectra for the H-decorated bulk and surface vacancy calculations were taken from effective medium calculations. (C) 1999 Elsevier Science Ltd. All rights reserved.

Measurements of the dependence of the creep strain of polycrystalline Pd wires in the temperature range 736–1200K at differing stress levels have been carried out both in inert gas (Ar) and H2 atmospheres. The effect of the presence of H atoms in the Pd samples is to enhance the creep rate by approximately six times. The activation energy deduced from the creep data is consistent with a Coble mechanism in which the grain boundary diffusion of lattice atoms is the predominant mode of deformation.

A four-point constant-current technique was used to determine the change in resistivity with time at 298 K for Pd-wires which had been annealed for 20 h at 1000 K in both argon and hydrogen atmospheres. A large resistivity decrement was discovered in the H2-annealed wires which was not obtained in the case of the Ar-annealed specimens. The resistivity decrement has been related to recrystallization effects concomitant with the production of H-induced vacancies in the Pd-lattice.

Measurements of the H-solubility of stoichiometric NiAl in the temperature range 670–1373K have been carried out at a constant H2 gas pressure of 1.01×105Pa. The data obtained are not consistent with simple mixing statistics where the H-atoms occupy unique interstitial sites in the B2 cubic NiAl lattice. The thermodynamic behavior is consistent with a model in which H-atoms may occupy both tetrahedral and octahedral sites and the relative site occupancy depends on the temperature.

Statistical mechanical techniques have been used to calculate the effects of interactions between H-atoms and vacancies in Pd. Using a spectrum of H-vacancy binding energies generated by effective medium calculations, it has been shown that the creation of H-induced vacancies can lead to drastic increases in the diffusivity of the lattice atom, but that the effects reflected in the thermodynamic functions of the H-atoms will be less than the experimentally detectable limits.

The thermodynamic properties of interstitial solute atoms in a substitutional binary solvent matrix have been derived in terms of the cell model for such solutions. The results pertain to low temperatures where the solute distribution is governed by Fermi-Dirac statistics rather than the Boltzmann distribution usually employed in the high-temperature limit. The thermodynamic functions, calculated by numerical methods, exhibit singularities concomitant to the successive occupation of cells of a given energy level. The relevance of the results to the thermodynamics and kinetics of highly mobile interstitial atoms is discussed.

The dependence of the diffusivity D of interstitial atoms in a particle density gradient has been calculated as a function of interstitial atom concentration and temperature. The method of calculation is a combination of Absolute Rate Theory and cumulant expansion techniques. The presence of a gradient results in “skewing” effects which cause D to increase with interstitial atom concentration more rapidly than is found for the diffusivity D measured with interstitial tracers in the absence of a density gradient.

A short survey of previous calculations of the thermodynamic and kinetic properties of metal-interstitial solutions considering vacancy-interstitial interactions has been given. The effects of vacancy-interstitial interactions on the determination of vacancy concentrations in metals and on the observation of dislocation loops in austenite have been discussed. Suggestions are proposed for future work related to the influence of abundant vacancies induced by interstitial solute on the mechanical behavior of solids.