Diffusion of hydrogen and other interstitials in disordered and amorphous materials

There is a large variety of technological important disordered materials where interstitial diffusion plays an important role, i.e. hydrogen in metallic materials containing structural defects or being amorphous, small molecules in polymers, hydrogen and interstitial diffusers in amorphous semiconductors and alkali ions in oxidic glasses. Interstitial chemical diffusion in these materials is more or less strongly dependent on solute concentration, where this dependence is due to site energy disorder giving rise to saturation of low energy sites and deviations from Henry's Law leading to a thermodynamic factor which depends on interstitial concentration. Knowing the thermodynamic factor and calculating the tracer diffusion coefficient D* from experimental data it will be shown that D* of hydrogen in deformed, nanocrystalline and amorphous metals and of small molecules (CO2, CH4, Acetone) in glassy polymers (various polycarbonates and Kapton) are proportional to the activity coefficient gamma of the interstitial solute. This rather general relationship has been derived before by assuming site energy disorder and activated hopping of the interstitial over constant saddle point energies. However, it will be shown by a new approach that the same proportionality between D* and gamma can be derived as well for the uncorrelated walk of a single solute atom belonging to a Fermi lattice gas without referring to the nature of the transition from one site to the adjacent one. The approach is similar to the one electron approximation describing the behaviour of electrons in reciprocal space despite the fact that a Fermi gas in real space is considered. The relation D*proportional to gamma arises from ergodicity because the time of residence of a solute particle in a site which affects D* is equivalent to the thermal occupancy of this site which affects gamma. Hydrogen in metals as well as small molecules in polymers offer the advantage that both quantities D and gamma can be determined rather easily. Alkali ions in oxidic glasses are different in comparison with the materials mentioned before because the strong Coulomb interaction between mobile cations and fixed anions causes the site energy distribution to depend on concentration. In addition the density of oxygen atoms within the network decreases with increasing alkali content. If one assumes that both site energy disorder and network modification change the mobility of cations, the well-known mixed alkali effect can be explained quantitatively.