Van Vleck second moments and hydrogen diffusion in YH2.1--measurements and simulations

Proton magnetic resonance absorption spectra of yttrium dihydride (YH(2+x)), with x = 0.10, were recorded in the temperature ranges 4.2-310 K at 36.01 MHz and 150-400 K at 299.8 MHz. The evidence of proton self-diffusion follows from the changes of linewidth with temperature. The second moment of the resonance lines was determined from the experimental spectra and was compared with values calculated from the crystallographic data. The averaging effect of diffusion on the second moment was taken into account through Monte Carlo simulations of the diffusion process. The simulation was performed in a block of unit cells 5 x 5 x 5 with periodic boundary conditions. They compensated the effect of finite dimensions of the block. The calculated temperature dependence of the proton second moment values was fitted to the experimental ones. The fitting parameters were: the attempt frequency v0 and the activation energy Ea for hydrogen diffusion, assuming Arrhenius behavior of the jump frequencies vc = v0 exp(-Ea/k(B)T). In these preliminary studies, the Monte Carlo simulations were performed for tetrahedral-octahedral exchanges while direct tetrahedral-tetrahedral jumps were neglected for simplicity. Three models of hydrogen diffusion, differing in the maximum jump lengths allowed for a given model, were considered. These lengths were taken as the distances from the hydrogen attempting to jump to the first (1NN), second (2NN), and third (3NN) nearest neighbor position able to accept the jumping atom. Assuming the same attempt frequency v0 = 6.0 x 10(12)s(-1) for all three models, the activation energies giving the best fit to experimental data were 0.5, 0.54, and 0.55 eV for 1NN, 2NN, and 3NN models, respectively.