Validity of the Darwin and Ewald reflectivity functions in the range of the far wings: Neutron diffraction study

Using the neutron time-of-flight (TOF) technique, we have examined the reason for the dramatic departure of experimental results from the Darwin and Ewald reflectivity functions in the far wings. The scattering from Si(111) single- and triple-bounce crystals set up at the Bragg angle θB=24.4° was dispersed in time-of-flight in the wavelength range 0.3<λ<3.0Å. The experiment reveals admixture of the single-scattered Bragg peaks and thermal diffuse scattering (TDS) originating at λ<0.6Å in the spectrum registered from a triple-bounce crystal. Our study explains the discrepancy between the theory and the experimental results reported in many neutron studies and proves the validity of the Darwin and Ewald theories in the far wings.