Section 2.6.2.1.1. Wavelength

In the case of SANS – as in that of X-rays from synchrotron sources – the wavelength dependence of the momentum transfer Q, , where is half the scattering angle and λ is the wavelength, has to be taken into account explicitly. Q corresponds to k, h, and used by other authors.

SANS offers an optimal choice of the wavelength: with sufficiently large wavelengths, for example, first-order Bragg scattering (and therefore the contribution of multiple Bragg scattering to small-angle scattering) can be suppressed: The Bragg condition written as cannot hold for , where is the largest atomic distance in a crystalline sample. For the usually small scattering angles in SANS, even quite small λ will not produce first-order peaks.

The neutrons produced by the fuel element of a reactor or by a pulsed source are moderated by the (heavy) water surrounding the core. Normally, the neutrons leave the reactor with a thermal velocity distribution. Cold sources, small vessels filled with liquid deuterium in the reactor tank, permit the neutron velocity distribution to be slowed down (`cold' neutrons) and lead to neutron wavelengths (range 0.4 to 2 nm) which are more useful for SANS.

At reactors, a narrow wavelength band is usually selected for SANS either by an artificial-multilayer monochromator or – more frequently, owing to the slow speed of cold neutrons – by a velocity selector. This is a rotating drum with a large number (about 100) of helical slots at its circumference, situated at the entrance of the neutron guides used for collimation. Only neutrons of the suitable velocity are able to pass through this drum. The wavelength resolution Δλ/λ of velocity selectors is usually between 5 and 40% (full width at half-maximum, FWHM); 10 and 20% are frequently used values.

Alternatively, time-of-flight (TOF) SANS cameras have been developed on pulsed neutron sources (e.g. Hjelm, 1988). These use short bunches (about 100 µs long) of neutrons with a `white' wavelength spectrum produced by a pulsed high-energy proton beam impinging on a target with a repetition rate of the order of 10 ms. The wavelength and, consequently, the Q value of a scattered neutron is determined by its flight time, if the scattering is assumed to be quasi-elastic. The dynamic Q range of TOF SANS instruments is rather large, especially in the high-Q limit, owing to the large number of rapid neutrons in the pulse. The low-Q limit is determined by the pulse-repetition rate of the source because of frame overlap with the following pulse. It can be decreased, if necessary with choppers turning in phase with the pulse production and selecting only every nth pulse. This disadvantage does not exist for reactor-based TOF SANS cameras, where the pulse-repetition rate can be optimally adapted to the chosen maximal and minimal wavelength. A principal problem for TOF SANS exists in the `upscattering' of cold neutrons, i.e. their gain in energy, by ¹H-rich samples: The background scattering may not arrive simultaneously with the elastic signal, and may thus not be attributed to the correct Q value (Hjelm, 1988).