The static Debye-Waller factor of defect-induced lattice displacements

The attenuation of Bragg scattering intensities due to static displacements is discussed for interstitially dissolved point-defects. It is shown that in the single defect approximation the static Debye-Waller factor (DWF) exp (–2L) decreases linearly with the defect concentrationc and quadratically with the scattering-vectorK (for smallK andc). From a model calculation of the displacements around H in Nb the static DWF is shown to be primarily due to the displacements closest to the impurity. Therefore the measurement of the static DWF can be used as a method to determine these displacements. From X-ray measurements of the integrated Bragg intensities of NbH _x single crystals we obtained the displacements of the four nearest neighbours around a tetrahedral interstitial site to beu ₁=0.1Å. This is in good agreement with the results of our model calculation.