The Debye-Waller factor and the diffusion process for hydrogen in Nb, Ta, and V single crystals investigated by neutron spectroscopy

Abstract

Quasielastic scattering of slow neutrons on hydrogen diffusing in theα-phase of NbH0.02, TaH0.13 and VH0.07 single crystals was investigated in a wide range of temperatures and scattering vectorsQ (0.5≦Q≦2.5 A−1). The incoherent scattering lawS d (Q,ω) for four different diffusion models was consistently compared with the measured lineshapes. At elevated temperatures one had to introduce correlated jumps to describe the experimental data, whereas at room temperature a model with jumps between adjacent sites is sufficient. The integrated quasielastic intensityI(Q) obtained from the fit ofS d (Q,ω) with the measured spectra follows an isotropic Debye-Waller factor with mean square amplitudes 〈u2〉=0.02–0.04 A2 for H in Ta (20°C–500°C), and 〈u2〉=0.03–0.04 A2 for H in Nb (20°C–300°C). For H in V,I(Q) obtained from the analysis of the quasielastic scattering deviates from a normal Debye-Waller factor behaviour. This effect is assumed to be due to the flight process between the interstitial sites. On the other hand, a normal Debye-Waller factor was obtained from theQ-dependence of the inelastic scattering of the band modes, with values of 〈u2〉=0.02–0.04 A2 (135°C–500°C). The observed values of 〈u2〉 were compared with theoretical calculations.