Lattice-distortion-mediated local jumps of hydrogen in niobium from diffuse neutron scattering

We reconsider the mobility of hydrogen in bcc metals, in particular H and D in Nb, and its influence on the coherent and incoherent quasielastic neutron and x-ray scattering. An approach to describe time-dependent lattice distortions around highly mobile protons is presented, using the frequency-dependent Green’s function of the host lattice so that effects of the so-called quasielastic effects and resonances with host lattice phonons are included. We discuss within this formalism how noncubic components of the long-ranged displacement field can fade away in the presence of a high defect mobility and we demonstrate by a detailed calculation that the experimentally observed disappearance of the coherent quasielastic diffuse (x-ray and neutron) scattering in ${\mathrm{NbH}}_{\mathit{x}}$ (${\mathrm{NbD}}_{\mathit{x}}$) from these Fourier components of the displacement field points to an unusual, hitherto neglected rapid local diffusion process between adjacent tetrahedral sites with a short-time constant of ${\mathrm{\tau }}_{\mathrm{loc}}$≃${10}^{\mathrm{-}13}$–${10}^{\mathrm{-}14}$ s. The consequences of such a diffusion mechanism on the incoherent quasielastic neutron scattering are discussed in detail. We show that the elastic incoherent structure factor of the interstitial proton exhibits, in addition to the usual Debye-Waller factor behavior, distinct oscillations as a function of the neutron momentum transfer.