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

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 - θ_B)/ δΘ_D, 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 R^m(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 δΘ_D is the width of the Darwin plateau. However, the experimental reflectivity R^m_exp(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.