Solubility and diffusivity of hydrogen in complex materials

Abstract

A general model based on Statistical Mechanics and Random Walk is presented which allows to desribe the behavior of hydrogen in disordered systems, i.e. metallic glasses, amorphous silicon, nanocrystalline metals, deformed metals, disordered metallic solutions, and metallic multi layers. The various systems are specified by a lattice with an appropriate site energy disorder and a distribution of site transitions rates. Lattice sites are filled according to Fermi–Dirac Statistics because double occupancy is excluded. Thus the model is applicable to adsorption on heterogeneous surfaces or solutions of small particles in oxide glasses and polymers. With a given distribution of site energies a relationship between chemical potential (Fermi energy) of hydrogen and its concentration can be derived and compared with experimental results. It is a unique feature of hydrogen that its chemical potential and its diffusion coefficient can be determined rather easily by electrochemical techniques or by measuring partial pressures at moderate temperatures around 300 K. With increasing H-content the sites are usually filled from lower to higher energies. As a consequence Henry's Law is not fulfilled and the diffusion coefficient increases because at high concentrations low energy sites are saturated and additional H-atoms have to perform their random walk through sites of low occupancy or small time of residence, respectively. Some results for metallic glasses, nanocrystalline metals, deformed metals, and metallic multi layers are presented and compared with the model. Thus information on the interaction between defects (dislocations, grain boundries, distorted tetrahedral sites in glasses) and hydrogen are obtained. For extended defects the diffusion is strongly anisotropic, i.e. it differs in a Pd/Nb-multi layer by a factor of 105 for diffusion in plane and out of plane.