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Understanding inelastically scattered neutrons from water on a time-of-flight small-angle neutron scattering (SANS) instrument

It is generally assumed by most of the small-angle neutron scattering (SANS) user community that a neutrons energy is unchanged during SANS measurements. Here, the scattering from water, specifically light water, was measured on the EQ-SANS instrument, a time-of-flight SANS instrument located at the Spallation Neutron Source of Oak Ridge National Laboratory. A significant inelastic process was observed in the TOF spectra of neutrons scattered from water. Analysis of the TOF spectra from the sample showed that the scattered neutrons have energies consistent with room-temperature thermal energies (~20 meV) regardless of the incident neutron energy. With the aid of Monte Carlo particle transport simulations, we conclude that the thermalization process within the sample results in faster neutrons that arrive at the detector earlier than expected based on the incident neutron energies. This thermalization process impacts the measured SANS intensities in a manner that will ultimately be sample- and temperature-dependent, necessitating careful processing of the raw data into the SANS cross-section.


Introduction
Small-angle neutron scattering (SANS) is a powerful tool for investigating the structure of materials at the nanoscale that is applicable to materials of interest to condensed matter physics, the materials sciences, chemistry, and the biosciences. SANS measurements are performed using instruments installed at both steady-state and time-of-flight (TOF) pulsed neutron sources. The basic physical design of the instruments at the two types of sources are essentially the same, but the scattered intensity as a function of momentum transfer (q) is collected using a wide band of neutron wavelengths at a pulsed source, while SANS instruments at steady state sources use a nearly monochromatic band of neutron wavelengths. In both cases, the q-range, statistics, and the resolution can be varied by the selection of a combination of wavelength band, sample to detector distance, and instrument optics. In general, TOF-SANS instruments have the advantage of capturing a larger q-range in a single instrument setting compared to steady-state SANS instruments, which generally have the ability to probe smaller values of q as a result of a higher time-averaged flux of the long wavelength neutrons that are better suited to low-q measurements.
SANS data are typically analyzed assuming that the absolute cross-section produced by the data reduction process results strictly from elastic scattering [1]. However, several scattering processes take place when a neutron interacts with a sample, including absorption, incoherent scattering and inelastic scattering. Of these effects, inelastic scattering is generally assumed to be negligible in SANS experiments. However, this assumption is often inaccurate in the case of samples containing a large amount of hydrogen, which constitutes many samples studied by SANS as a result of the ability to substitute deuterium for hydrogen and dramatically alter the scattering from a sample. Water, organic solvents and polymeric materials, all of which contain a great deal of hydrogen, produce strong isotropic scattering that results from the large incoherent scattering cross section of hydrogen. Additionally, inelastic-incoherent effects resulting from hydrogen comprise a significant portion of the sample-dependent background.
These effects are known and methods have been developed to account for these processes when using water as a secondary calibration standard [1][2]. These inelastic scattering processes can also impact data correction operations, including background subtraction and sample transmission corrections, or when using hydrogenous materials as calibration standards [2][3][4].
Here, we present experimental data from the EQ-SANS at the Spallation Neutron Source of Oak Ridge National Laboratory [5], a TOF-SANS, that demonstrates how a considerable fraction of the scattered neutrons undergo a significant energy change after interacting with a water sample.
Through the use of advanced Monte Carlo simulations on the interaction of neutrons with a water sample, it is found that the scattering processes lead to a thermalization of the scattered neutrons.

Time-of-Flight SANS
Small-angle neutron scattering (SANS) measurements were performed at the EQ-SANS instrument at the Spallation Neutron Source (SNS) located at Oak Ridge National Laboratory (ORNL) using 60 Hz operation. A sample-to-detector distance of 4 m was used with various wavelength bands collectively covering the q range of 0.004 Å −1 < q < 0.3 Å −1 , where q = (4π/λ) sin(θ/2) is the magnitude of the scattering vector, and θ is the scattering angle. The instrument was configured to provide a 1 Å-wide incident bandwidth by appropriately setting the phases of the four disk choppers [5]. Data on the EQ-SANS instrument are collected and saved in 'event mode' where the time-of-flight to the detector and the detector pixel position is recorded for each detected neutron. The SNS source operates at 60 Hz, providing a 16,667 µs measurement time window at the detector. Data processing was accomplished with the MantidPlot software package (http://www.mantidproject.org). The light water sample, consisting of deionized water from a Barnstead water purification system, was loaded into a standard 1 mm path length amorphous quartz cell (Hellma USA). Graphite foil, which produces little incoherent scattering, served as a reference elastic scattering sample.

Simulation methods
Simulations of the scattering of neutrons by a thin light water sample were performed with the Monte Carlo particle transport code MCNPX version 2.6.0 [6]. In addition to describing the transport of a multitude of particle types with energies ranging from 10 -5 eV to 100 GeV through complex three-dimensional structures, the MCNPX code can simulate neutron scattering in condensed matter by utilizing so-called material-specific scattering kernels and includes that of light water [7]. For this study, the scattering kernels for light water were prepared from ENDF/B-VII evaluation files [7] into ACE-formatted scattering kernels in the energy-probability table format that can be read by the software. The scattering formalism based on the energyprobability table format is better-suited for simulating scattering of mono-directional neutron beams compared to the discrete-energy table format.
The interaction of mono-directional neutron beams having 1 Å wide wavelength bands between 4 and 11 Å with a 1 mm thick water sample were simulated. The simulated, scattered neutrons were collected in a square detector of 1 m 2 area positioned 4 meters away from the 6 sample to match the configuration of the EQ-SANS instrument employed. The neutron spectra were accumulated into energy bands ranging from 10 -5 eV to 1 eV that were divided into 20 bins per decade of energy. The 30 mm diameter area around the incident beam direction corresponding to the transmitted beam was not included in the analysis. The number of scattering events that the neutron experienced in the sample was retained for use in the simulation analysis.

Results
In Figure 1, the transmitted empty beam spectrum of a 4-5Å wavelength band measured at the EQ-SANS detector is shown within the 16,667 µs neutron pulse period, termed a 'frame', and multiple frames are shown to more easily visualize the data as it is collected during an experiment. It is important to note that the time shown in these plots is not the absolute travel time of the neutron from the sample to detector, but rather the relative arrival time in relation to the burst of neutrons from the target. At 4m sample to detector distance of EQ-SANS, approximately 4-7 Å neutrons arrive at the detector within the second frame (16,667 µs < T TOF < 33,334 µs) after they are produced in the target and 8-11 Å neutrons arrive within the third frame (33,334 µs < T TOF < 50,001 µs) in terms of the flight time from the source (T TOF ). The flux at EQ-SANS peaks near 2.5 Å and decreases almost monotonically with increasing wavelength [5], giving rise to the spectral shape. The slope between 1000 and 5000 µs shows this behaviour. The   (water + quartz cell) (green), the quartz cell only (blue) and the empty beam spectrum (red). The empty beam spectrum was scaled for ready comparison with the scattering spectrum of the water.
c) The TOF spectrum from water at the detector with different scattering angles. Each spectrum has been normalized to 1 for clear comparison.
To verify that the observed change in the scattered neutron spectrum results from neutrons experiencing a change in energy, measurements of graphite foil were performed. The scattering from graphite foil is purely elastic and the material is regularly used as an instrument resolution standard for neutron spin-echo (NSE) instruments [10], because it does not exhibit any dynamics under the spatial and energy ranges of NSE. To maximize the effect of any energy change experienced by a scattered neutron, neutrons with long wavelength (12 Å), and thus relatively low energy (ca. 0.57 meV) were used with the full wavelength band possible for this configuration of the EQ-SANS (3.5 Å). Here, the time axis represents the detector arrival time within the third frame and the start of the wavelength band is located at approximate 5000 µs.  Figure 3. In all cases, neutrons can be seen at to the left of the incident neutron TOF spectrum (i.e. apparently before the pulse starts) regardless of the incident neutron's energy.
The TOF spectral shapes of these early-arriving neutrons differs from the incident neutron spectrum, and so the energy difference cannot be defined precisely. However, the beginning of each wavelength band is at the peak of the intensity profiles of incident neutrons, so it can be assumed that neutrons arriving between t min and t max , as defined in Figure 3 Therefore, we speculate that these neutrons which form the peak of early arriving neutron in the TOF spectra are neutrons that have been thermalized as a result of scattering by water, causing them to arrive at the detector earlier than the incident neutrons. The thermalization process is governed by the temperature of water, so it is expected that the energy of a thermalized neutron would be independent of the incoming neutron energy and the change in energy would be greater for longer wavelength (lower energy) neutrons, as observed. The portion of neutrons being accelerated through interaction with the sample increases with increasing wavelength (Figures   3a-c). In the case of 10-11 Å neutrons (Figure 3c), nearly 60 % of the scattered neutrons are thermalized.

Conclusions
Changes in the neutron spectra resulting from scattering by water as measured on a TOF-SANS instrument have been investigated. Unlike the generally-accepted idea that a neutron's energy remains unchanged during small-angle scattering measurements, the results demonstrate that significant inelastic processes take place as a result of scattering by water that manifest in changes in the TOF spectra from that of the incident neutron spectra. TOF analysis showed that the scattered neutrons have energies consistent with room temperature thermal energies (~20 meV) regardless of the incident neutron's energy. With the aid of MCNPX simulations, it is clear that thermalization is responsible for the faster neutrons produced by scattering in the sample.
The faster neutrons manifest in a TOF-SANS measurement as neutrons arrive at the detector earlier than expected based on the incident neutron spectrum. The influence of thermalization by water is more significant for longer wavelength incident neutrons and the simulation shows that initial neutron energy spectrum has been mostly lost after two scattering events in the sample.
In TOF-SANS, the wavelength assigned to a neutron, and thus the q-value calculated, depends on the time-of-arrival of neutrons at the detector. Therefore, any neutrons that are inelastically scattered in the sample complicate the wavelength-dependent normalization that takes place during data reduction. The thermalization of neutron energies primarily results from incoherent scattering and multiply scattered neutrons are almost entirely thermalized. This suggests that avoiding multiple scattering is even more critical in TOF-SANS experiments in order to minimize the thermalization effect. These observations also suggest that careful background subtraction and sample preparation are very critical for performing successful TOF-SANS experiments. The effect can be reduced by performing measurements at shorter wavelengths and by performing very careful background subtraction rather than relying on a flat incoherent scattering background, as is generally applicable to SANS data collected at steadystate sources.