Intensity correction factors for neutron powder diffraction measurements

The derivation of the conventional Lorentz factor for a powder diffraction measurement is made assuming a rectangular acceptance function for the detector aperture and by assuming that the curvature of the diffraction cone can be ignored within this aperture. Neither of these assumptions is valid for neutron diffraction measurements, particularly at low scattering angles, and corrections are therefore derived and evaluated for the case of a Gaussian acceptance function. Similar corrections are also derived and evaluated for detectors which have been displaced out of the scattering plane perpendicular to their axis of rotation.