D. Richter’s research while affiliated with Forschungszentrum Jülich and other places

The jump rate of a particle in quantum diffusion is theoretically expected to be proportional to the square of the tunnel splitting (or tunnel matrix element). This basic relationship is exemplified in neutron spectroscopic experiments on the tunnelling of trapped-H interstitials in Nb.

Hydrogen diffusion was studied by quasielastic neutron scattering in the system alpha -NbH0.004 with 0.7 at.% nitrogen impurities, for temperatures between 180 and 373K. From comparing the spectra at small and at large scattering vectors, the trapping of the hydrogen in the vicinity of a dissolved nitrogen atom was studied. Typical trapping times are several hundred times larger than the mean rest time of a hydrogen atom on an undisturbed interstitial site.

The diffusion of hydrogen in FeTiHx (0.65<or=x<or=1.03) was studied as a function of temperature in the range 633<or=T<or=759K by means of quasielastic neutron scattering. The diffusion constant was found to obey an Arrhenius law D=D0 exp-EA/kT with D0=(7.2+or-3.6)*10-4 cm2 s-1 and EA=500+or-50 meV. The results are discussed together with recent NMR studies of hydrogen diffusion in FeTiHx.

Neutron scattering experiments have been performed in order to measure the position of the optic phonon modes in hydrogenated and deuterated alpha phase Ti and Zr. The weak anharmonic effects are discussed with respect to the superconducting properties of these materials, especially the observed inverse isotope effect in Zr-(H, D). It is shown that the superconducting behaviour of both Ti-(H, D) and Zr-(H, D) cannot simply be correlated with the position of the optic phonon modes.

High-resolution quasi-elastic neutron scattering has been used to study the hydrogen diffusion in the multi-component Laves phase hydride Ti0.8Zr0.2CrMnH3, one of the most promising hydrogen storage materials for technical applications. The data analysis is complicated by multiple scattering which, even with only moderately scattering samples, leads to a fictitious line broadening at small momentum transfers and considerably hinders the determination of diffusion coefficients. An evaluation procedure is presented which allows for the necessary multiple scattering corrections independent of details of the single diffusive steps. In the temperature range of the study, 230-360K, the hydrogen self-diffusion coefficient in Ti0.8Zr0.2CrMnH3 obeys the Arrhenius law: D=(3+or-1)*10-4 cm2 s-1 exp(-(220+or-20) meV/kBI). This comparatively fast hydrogen diffusion is not the rate determining step in the absorption and desorption kinetics.

In order to clarify the discrepancy between the Gaussian distribution of H-site energies suggested from different macroscopic measurements and the evidence for two energetically well separated types of H sites obtained from a microscopic H diffusion study by means of quasi-elastic neutron scattering, the authors have measured neutron vibrational spectra of hydrogen in amorphous Pd85Si15Hx, 0.13<or=x<or=8.23. At concentrations below 1% the spectra exhibit distinct features that indicate the occupation of distorted Pd6 octahedra, along with a range of tetrahedral sites. These observations are consistent with a bimodal distribution of H-site energies in this glassy metal hydride.

Nb100−xVxHy is a random b.c.c. alloy system with an H sublattice disordered with respect to site energies. Previous incoherent inelastic neutron scattering (IINS) studies ascertained both octahedral (o) and tetrahedral (t) site occupation by H for x = 50, 10 and 50. On the basis of spectroscopic and statistical arguments, the low-temperature H vibrational peaks in the Nb-rich, low-H-concentration Nb95V5H1 alloy were assigned to Nb4V2 o sites and NbV3 t sites. To probe the regime of lower H concentration and the effects of D substitution, further IINS spectra were measured for Nb95V5Hy (y = 0.5 and 0.8) and Nb95V5D2.7. As the H concentration was decreased, the spectra at 4 K indicated an increasingly predominant 38 meV peak, which was assigned to the doubly degenerate H vibrations in the Nb4 plane of the Nb4V2 o site. A portion of the board feature centered at approximately 200 meV was assigned to the much stiffer H vibration polarized along the V-V apical axis. The Nb95V5D2.7 results located the analogous soft D vibration at 29 meV, yielding an H/D vibrational energy ratio of 1.31. To our knowledge, this is the only known case of spectroscopically confirmed o-site occupation by H in a b.c.c. metal (alloy) lattice. Moreover, the soft modes yield the lowest observed vibrational energy for H in a metal hydride.

The diffusion of positive muons was studied in the normal and superconducting states of aluminum. Large differences were observed, indicating that the diffusion mechanism depends sensitively on the interaction between the muon and the conduction electrons. The samples were high-purity aluminum doped with controlled amounts of lithium. The lithium impurities act as traps for the muons, leading to a loss of muon polarization. However, the time and temperature dependencies of the muon depolarization function G(t) could not be satisfactorily explained using a simple diffusion limited trapping model. In particular, in the superconducting state the measured G(t) requires a more complex model for a reasonable fit. These data can be described, in a first approximation, with two fractions, one corresponding to muons stopped in the defect potential created by the doping element and the other representing muons which diffuse freely without being trapped. In this model, which supports a microscopic theory by Kagan and Prokof'ev taking into account static as well as dynamic effects on the tunneling of positive particles in a conducting medium, a large fraction of the muons is practically immobile below 0.3 K in doped samples. The data can also be fitted by assuming that the spatial distribution of doping elements leads to a distribution in trapping times and that the fraction of diffusing muons is described by a so-called stretched exponential time dependence. The relative merits of these two types of interpretation are discussed.