Aiming for the theoretical limit of sensitivity of Bonse-Hart USANS instruments

Abstract

The basis of the Double-Crystal Diffractometer (DCD), used for ultra-small angle neutron scattering (USANS), is that the reflectivity function is very near 1.0 for |y| < 1, where y = (θ - θB)/ δΘD, falls off rapidly for |y| >1, eventually decreasing as y −2. In the Bonse-Hart multi-bounce crystal the reflectivity function R(y) transforms into Rm(y) and in the wings, for large |y|, theoretically decreases as y−2m after m consecutive Bragg reflections inside the channel-cut crystal. Here θ and θB are respectively the diffraction angle and the Bragg angle (for given wavelength) and δΘD is the width of the Darwin plateau. However, the experimental reflectivity Rmexp(y) obtained for m = 3 exceeds the theoretical prediction by over two orders of magnitude in the range of the far wings, which creates limitations for USANS studies of weakly scattering objects.We used the pulsed-source neutron time-of-flight (TOF) technique to study this discrepancy in more detail. Two identical Si(111) crystals, a slab-shaped single-bounce and a channel-cut triple-bounce, were measured at the nominal Bragg angle θB = 24.4o in the TOF powder diffractometer GPPD at IPNS, in the range 0.2 < λ < 4.0 Å of the first seven Bragg reflections from Si(111) family. Cadmium shielding protected the detectors from view of the first-bounce crystal. The experimental data obtained from the single-bounce crystal shows thermal diffuse (phonon) scattering (TDS) filling the region between the Bragg reflections, and exhibiting the symmetry of the reciprocal lattice. With appropriate shielding installed, the triple-bounce Bragg reflections, in contrast, are TDS-free in the range 0.6 < λ < 3.0 Å; however, the intensity of TDS grows in the range λ < 0.5 Å, reaching the level of TDS registered for the single-bounce reflections (777) and (888). The growth of TDS correlates with the increase of the Cd transmission T(λ) in the range 0.2 < λ < 0.5 Å, which in the vicinity of (888) reflection is T(λ) ≈ 0.9. Therefore, the Cd shielding of the triple-bounce crystal becomes ineffective and the parasitic single-bounce back-face reflection and TDS, blocked for 0.5 < λ < 3.0 Å, reappear for λ< 0.5 Å.It is practically impossible to separate this parasitic scattering from the triple-bounce reflection at steady state neutron beam lines except by the use of highly curved neutron guides. However, the TOF-USANS instrument, which is currently under construction at SNS, allows separation of the orders of Bragg reflections and the residual TDS in time-of-flight and thus the discovered parasitic effect cannot compromise its sensitivity. Thus, we expect to approach the theoretical limit of sensitivity for the SNS TOF-USANS instrument.