The evaluation of thermal diffuse scattering of neutrons for a one-velocity model

The nature of the scattering surfaces for thermal diffuse scattering (TDS) and the contribution of TDS to the intensity measured during a scan through a Bragg reflexion are considered for a model in which all phonons are assumed to have the same velocity in the crystal. For neutrons which are faster than this sound velocity the contribution is independent of the neutron velocity and can be calculated using the formulae derived for X-ray scattering. However, for neutrons which are slower than the sound velocity the contribution is a function of the neutron velocity and will be less than that given by the X-ray formulae. The behaviour of the TDS contribution as a function of the neutron velocity is considered for a type scan for which an analytical evaluation is possible and these considerations are extended to the conventional ω and θ−2θ types of scan. It is concluded that there is no discontinuity in the TDS contribution when the velocity of the neutrons is the same as that of the phonons, but that evaluation of a reliable correction is difficult for slower-than-sound neutrons for the conventional types of scan. These conclusions will also apply for a more realistic case for which the phonon velocities are not all identical.