THE 3-DIMENSIONAL RESOLUTION FUNCTION FOR SMALL-ANGLE SCATTERING AND LAUE GEOMETRIES

An analytical calculation of the three-dimensional resolution function for a small-angle neutron scattering setup has been performed by application of a combination of phase-space analysis and Gaussian approximations for the neutron distribution as well as for the transmission functions of the different apertures. Small-angle approximations for the scattering angles have not been used and the results can be applied to other scattering geometries of the same type. The results are compared with Monte Carlo simulations and good agreement is found. To apply the method for analysing single-crystal diffraction data, a finite mosaic spread of the crystal and finite correlation widths of the Bragg reflections have been introduced in the cross section. The measured intensity (scattering function) is the cross section convoluted with the resolution function. The mosaicity and the finite correlation widths were described by Gaussian distribution functions and the convolutions were done analytically. The model cross section smeared by the resolution function has been applied to the analysis of single-crystal data of the long-range magnetic order in MnSi.