Diffusion of hydrogen in niobium in the presence of trapping impurities studied by neutron spectroscopy

The diffusion of hydrogen in niobium with interstitial impurities was investigated by highresolution neutron spectroscopy for the system NbNₓHy with x=0.4 and 0.7 at.% and y=0.4 and 0.3 at.%, respectively. The neutron spectrum at larger scattering vector →Q consists of two parts: a narrow line centered at energy transfer ω=0 (width 0.1-3 {μ}eV) which is caused which is caused by hydrogen trapped on nitrogen atoms, and a broad component in the spectrum from hydrogen atoms which diffuse in the more or less undisturbed regions of the lattice. At small →Q, the spectral width is directly related to the self-diffusion constant. The experimental spectra, measured as a function of temperature and scattering vector, were interpreted by two theoretical models: (i) a two-state random-walk model (RWM) where the hydrogen alternates between a trapped state and a state of undisturbed diffusion. The RWM is characterized by the mean escape rate from the trap 1τ₀, and the capture rate on the traps 1τ₁; and (ii) an elastic-continuum model: the nitrogen-hydrogen interaction is treated in terms of the elastic strain field produced by the interstitial nitrogen and hydrogen atoms, and in terms of a short-range hard-core repulsion. This model uses the elastic parameters of the niobium and the interstitial nitrogen and hydrogen atoms. The hard-core radius r₀ is the only disposable parameter of the model. The RWM should hold as long as 2π→Q is larger than the linear dimensions of the trapping region. Model (i) yields a very good and consistent description of the measured spectra as a function of the concentration x, the temperature and the scattering vector. The resulting parameters τ₀ and τ₁ have the predicted behavior. In particular, τ₀ is independent of x, and τ₁^-1 is proportional to xD(T) where D is the self-diffusion constant in pure niobium. The trapping times are about two orders of magnitude larger than the mean rest time in pure niobium. Using a hard-core radius of r₀2.3 {}, model (ii) describes very well the experimental spectra at small and large →Q values.