X-ray measurement of the static Debye–Waller factor of NbH_x

Integrated X-ray Bragg intensities from Nb single crystals have been measured as a function of H concentration and scattering vector along high-symmetry directions. The observed attenuation can be described in terms of a static Debye–Waller factor (DWF) due to the static displacements of the Nb lattice atoms around the dissolved H. The crystals were loaded with H in situ on the X-ray diffractometer. The static DWF was determined from the ratio of the intensities from a crystal with and without H. Corrections are necessary for several magnitudes which change with the lattice-parameter change and the change of the thermal displacements upon the uptake of H. The measured static DWF is proportional to the H concentration c(H/Nb) for c≤0.30 and the square of the scattering vector K² for small K, as expected from theory. From analysis of the static DWF the static displacements of the Nb atoms closest to the H impurity u₁ = 0.1 Å were determined.