Comparison of x-ray and neutron diffuse scattering intensities in niobium

Abstract

It is not clear whether or not the x-ray diffuse intensity scattered by crystals outside the Bragg spots can be entirely explained by considering thermal vibrations. Striking discrepancies are found in some cases, when x-ray data are compared with phonon dispersion relations determined via inelastic neutron scattering. A careful analysis is carried out for niobium, which exhibits anomalies (humps) in the elastic neutron diffuse scattering intensity. These anomalies are not found in the x-ray diffuse scattering, which can be very accurately accounted for by considering incoherent (Compton) scattering plus first- and higher-order phonon scattering. The latter was calculated using dispersion relations obtained by neutron inelastic scattering. It seems unlikely that hydrogen may be responsible for the extra scattering observed with neutrons. No explanation is found for this discrepancy between x-ray and neutron results.