Investigation of neutron scattering in the Multi-Blade detector with Geant4 simulations
Gabor Galgoczi, Kalliopi Kanaki, Francesco Piscitelli, Thomas Kittelmann, Dezso Varga, Richard Hall-Wilton
PPrepared for submission to JINST
Investigation of neutron scattering in the Multi-Bladedetector with Geant4 simulations
G. Galgóczi a , b K. Kanaki c , F. Piscitelli c T. Kittelmann c D. Varga b R. Hall-Wilton c , d a Eötvös Loránd University, 1053 Budapest, Egyetem tér 1-3., Hungary b Hungarian Academy of Sciences, Wigner Research Centre for Physics, 1525 Budapest 114., Hungary c European Spallation Source ESS ERIC, SE-221 00 Lund, Sweden d Mid-Sweden University, SE-851 70 Sundsvall, Sweden
E-mail:
Abstract: The European Spallation Source (ESS) is the world’s next generation spallation-basedneutron source. The research conducted at ESS will yield in the discovery and development ofnew materials including the fields of manufacturing, pharmaceuticals, aerospace, engines, plastics,energy, telecommunications, transportation, information technology and biotechnology. The spal-lation source will deliver an unprecedented neutron flux. In particular, the reflectometers selectedfor construction, ESTIA and FREIA, have to fulfill challenging requirements. Local incident peakrate can reach 10 Hz/mm . For new science to be addressed, the spatial resolution is aimed tobe less than 1 mm with a desired scattering of 10 − (peak-to-tail ratio). The latter requirement isapproximately two orders of magnitude better than the current state-of-the-art detectors. The mainaim of this work is to quantify the cumulative contribution of various detector components to thescattering of neutrons and to prove that the respective effect is within the requirements set for theMulti-Blade detector by the ESS reflectometers. To this end, different sets of geometry and beamparameters are investigated, with primary focus on the cathode coating and the detector windowthickness.Keywords: Boron-10, Geant4 simulations, neutron scattering, thermal neutron detection Corresponding author. a r X i v : . [ phy s i c s . i n s - d e t ] N ov ontents The ESS ERIC [1], currently under construction in Lund, Sweden, aspires to become the mostpowerful pulsed neutron source in the world. With its long pulse of 2.86 ms and a brilliance higherthan 10 n/cm /s/sr/Å, it can deliver unprecedented flux on the sample and revolutionise the wayneutron experiments are conducted [2, 3]. The produced neutrons are destined to serve a varietyof instruments for reflectometry, diffraction, spectrometry and imaging purposes. According to thecurrent schedule the first neutrons will hit the target in 2019, with the user programme starting in2023.Reflectometry is an experimental technique present at every neutron source. Hence, two ofthe first instruments approved for construction at ESS are reflectometers. The one, with a verticalscattering plane, is called the Fast Reflectometer for Extended Interfacial Analysis (FREIA) [4–6]and the horizontal one is ESTIA [7–9]. The former one will be optimised for magnetic samples andin-situ or in-operando studies. The latter reflectometer is designed to achieve the best performancefor liquid/liquid or liquid/gas interfaces. With a sample flux of 10 -10 n/s/cm and a high samplereflectivity ( ∼ [7–9]. This value exceeds the rate capability of current neutron detector technologies(including He-based detectors) by approximately two orders of magnitude. Additionally, thelimit set for neutron scattering inside the detector is lower than what the current state-of-the-art– 1 –etectors are capable of [10]. These are the two biggest challenges for the detector design aimed atreflectometry for ESS.In the past He-based neutron detectors played a key role for thermal and cold neutron de-tection [11]. Due to the limitations of these detectors in scientific performance and the shortageof He [12, 13], the focus of the neutron detector community has shifted to alternative, higher-performing solutions, such as B C-based detectors [14–20], scintillators [21–28] or LiF-basedsolid state silicon detectors [29–31]. Additionally, it is already proven that B C-based detectorsare capable of outperforming He detectors in terms of spurious scattering of neutrons [10, 32].Several studies demonstrate the performance of this detector type and its suitability for neutronscattering experiments [32–35].The detector design developed and adopted for the ESS reflectometers is the Multi-Bladedetector [32–37]. It has been extensively characterised and validated at various neutron facilitiesand with various types of samples. To get a deeper understanding of the scattering patterns thedetector geometry causes and to support the choice of materials and component dimensions, adetailed Geant4 [38–40] detector model is implemented. The main aim of this simulation effort isto prove that the Multi-Blade detector meets the requirements set by ESS, particularly the scatteringof 10 − (see p.9, figure 9.1 in [8]).In the following sections the Multi-Blade detector is introduced. The details of the Geant4implementation are presented, as well as the figure of merit used in the subsequent analysis.Fractional scattering is defined and sources of background caused by misplaced detection events areidentified and studied as a function of neutron wavelength. The results are discussed with respectto the instrument requirements. The Multi-Blade detector is a novel neutron detector currently being designed at ESS (see figure 1a).Its development was initiated at Institute Laue-Langevin (ILL) [35, 37, 41, 42]. It consists of a setof successive Multi-Wire Proportional Chambers [43], with B C-coated cathodes and Ar/CO (80/20 by volume) as a gas counter mixture. In addition to the anode wires, each chamber isequipped with a strip readout. The strips are perpendicular to the wire direction, in order to achievetwo-dimensional spatial resolution.The detector consists of cassettes as building units. Each one has a boron carbide ( B C)converter layer that is on a titanium substrate called a “blade”. On the other side of the blade a kaptonlayer and 32 copper strips are located for charge readout. Between the blades 32 wires are stretchedat a 4 mm pitch. The blades are tilted in a way that the incoming neutron beam hits the converterlayer with an incident angle of 5 ◦ , as shown in figure 1b. Therefore the thickness of the converteris viewed by the neutrons as being effectively about 11 times larger [32, 44]. Several cassettesare assembled together forming a fan-like arrangement to achieve the area coverage required forreflectometry. – 2 – a) (b) Figure 1 : (a) A prototype of the Multi-Blade detector [33]. (b) Geant4 geometry model being hit by a red neutronbeam through the detector entrance window. The vessel is absent from both figures to allow a clear view of the geometry. It is exactly this fan-like geometry that is the core of the current simulation study. The detectorgeometry and data analysis are implemented in a framework based on Geant4 developed by theESS Detector Group [45, 46]. The detector geometry consists of ten 130 mm ×
140 mm × B C by 98% on one side and a kapton and copper layer onthe other, with thicknesses of 30 µ m and 40 µ m respectively. The copper layer is not segmentedin strips, unlike the real prototype, as the distance between the strips is 0.1-0.2 mm and the effectof spurious scattering in this part of the detector is negligible compared to other materials. Thetungsten wires are also included in the model. The Ar/CO mixture has a ratio of 80/20 by volumeand a pressure of 1.1 bar. The gas vessel surrounds the entire detector structure. It consists ofenriched B C acting as a total absorber, in order to prevent scattered neutrons from entering theactive volume again. On the beam entrance side an aluminium window allows the neutrons to reachthe converter (see figure 1b).All materials are selected from the Geant4 database of NIST materials, except for Ti, Al, Cuand W. The latter are described with the use of the NCrystal library [46, 47], as their crystallinestructure is important for the correct treatment of their interaction with thermal neutrons. Thephysics list used is QGSP_BIC_HP and the Geant4 version is 10.00.p03.Last, but not least, the neutron generator is a mono-energetic pencil beam, impinging theconverter layer at a 5 ◦ angle in the centre of the middle blade, as in figure 1b. The generator param-eters, albeit simple, condense the characteristics of typical neutron distributions from reflectometrysamples that are important for this study. All results are produced with 1 million events.– 3 – .3 Implementation of the detection process in the simulation In boron-based neutron detectors the secondary charged particles ( α and Li ions) are createdafter the B nucleus captures a neutron. The cross section of this process is 3835 b for neutronswith a wavelength of 1.8 Å (p. 15, [11]). The position where the neutron is absorbed is calledthe conversion point. Therefore the neutrons are detected indirectly. The ion products cross theconverter and enter the gas volume with a remaining energy. The maximum distance the Li and α ions can travel in the specific counting gas is 3 mm and 6 mm respectively at atmospheric pressureand room temperature conditions.In order to describe the physical phenomena behind the detection of neutrons in the Multi-Blade detector, an approximation is used. The geometrical center of the tracks of the chargedparticles created by ionisation in the gas of the detector is defined as the hit position (see figure 2).Furthermore, the fact that the readout of the hits is done by wires and strips has to be taken intoaccount. For example, in the direction perpendicular to the blades surface, the coordinate of the hitis measured by the wires. Therefore the position of the triggered wire is read out, not the actualposition of the centre of the charge cloud. In order to emulate this effect, the hits are projected tothe plane of the boron surface, a transformation that brings the simulation treatment closer to theexperimental process. Figure 2 : Distance between conversion and hit position as approximated in a simulation for 12 Å neutrons. The twopeaks reflect the maximum path of Li and α ions respectively, but are halved in this representation (1.5 mm and 3 mm)as a result of the hit definition. The bands around the lines represent the statistical uncertainties. The simulation results produced with the ESS simulation framework have been previously validatedin [48]. An additional validation of the current model is performed in terms of detection efficiency.The results are compared to analytical calculations [37] and experimental measurements performedat the ATHOS instrument of the BNC facility [32] in Hungary and CRISP [33, 36] at ISIS, UK. Theobserved agreement is within the error bars for most of the neutron wavelengths. The uncertaintiesof the experimental points depend on the statistics of each measurement and systematic effects on– 4 – F r a c t i o n a l e ffi c i e n c y Measurement at ATHOSMeasurement at CRISPGeant4 simulationTheoretical calculation
Figure 3 : Fractional detection efficiency of the Multi-Blade detector as a function of neutron wavelength, obtainedfrom theoretical calculations [37, 49], measurements [32, 33] and Geant4 simulation (this work). the experimental data are not accounted for in the simulation. In addition, the efficiency estimate ofthe simulation is affected to a small extent by the fact that the detector gas volume is not segmentedin the simulation. The detection threshold of 120 keV on the energy deposition is applied perevent for the entire gas volume and not per wire, as in the experimental data. However, due to thelocalised nature of the energy deposition the approximation does not compromise the simulationfor the purposes of this work.
The Multi-Blade is a position sensitive detector, intended to operate in Time-of-Flight (TOF) mode.This means that the energy of the incident neutron is indirectly derived from a time and a 3Dposition measurement. Two factors can impact the precision of the neutron position reconstruction;the detector spatial resolution (short-scale effect) and scattering (long-scale effect), with differentimpact to the distribution of the detection coordinates. Figure 4 demonstrates these scenarios. Infigure 4a a neutron, which is absorbed in the first converter layer it meets, leads to a secondaryparticle releasing its energy in the counting gas (the other particle gets stopped inside the cathodesubstrate and is therefore lost). The spatial resolution of the detector determined by the anode wirepitch and the strip width locally smears the experimental detection point in the data reconstructionprocess. Figures 4b and 4c depict long-range effects stemming from neutron scattering either withinthe detector itself or in the entrance window respectively. Such events lead to the miscalculation ofthe distance between sample and detection point, and eventually to a wrongly derived value for theincident neutron energy and scattering vector.In order to quantify the impact of the misplaced detected neutrons, an nonphysical technicalGeant4 particle, called “geantino”, is utilised. This particle is generated along with each primaryneutron with the same initial parameters (see figure 4c). Geantinoes do not interact with matter,– 5 – a)(b) (c)
Figure 4 : (a) Difference between conversion and detection point. (b) A neutron traversing the first converter layer(solid green) can scatter in the blade material and finally get converted away from the first crossing point (dashed green).This leads to the miscalculation of the distance between sample and detection point (dashed blue). (c) Similarly for ascattered neutron on the detector window. The latter is 1 ◦ inclined with respect to the vertical axis. The projection of thedetection point on the converter layer is not displayed here for view simplification. therefore their tracks are straight lines. The point where a primary neutron would be detected inan ideal measurement is defined by the intersection of the respective geantino track with the firstconverter layer it traverses. This position is then compared against the respective neutron detectioncoordinates. The definition of this condition is motivated by the detector design; the actual thicknessof the converter is at least 7.5 µ m [32, 33] to ensure that, aside from a high detection efficiency,almost all neutrons convert in the first boron layer they encounter, thus reducing the scatteringcaused by the cathode material.The utilisation of geantinoes allows for this study to be realised for arbitrary generators andgeometries. However, in the current one, due to the fact that primary neutrons start from (0,0,0)and form a pencil beam on the Z axis, the geantino “detection” coordinates are also 0 in X and Y.This means that the actual neutron hit coordinates are sufficient for the visualisation of scatteringeffects in this particular case (X hit − X geantino = X hit , Y hit − Y geantino = Y hit ). These hit coordinatesare the ones projected on the converter layer as explained at the end of subsection 2.3.The contributors to the scattering effects studied in this work are the converter layer and theentrance window of the detector, both looked at as a function of neutron wavelength. The material(Ti) and thickness of the blade (2 mm) have been dictated by engineering needs and the coatingprocess and are fixed for all simulations of this work.A visualisation of the scattered hits projected on the detector window appear in figure 5. Theprojection is necessary as the window is not vertical but has a 1 ◦ angle with respect to the Y-axis.– 6 –t is also the standard way of experimentally visualising the dataThe primary neutrons hit the centre of the distribution in figure 5a. The simulation is run forthe extreme case of 1 Å for the neutron wavelength and 1 cm for the window thickness, in order tomaximise the scattering effects. The entries away from the centre make up the scattering events.The asymmetry of the distribution reflects the asymmetry in the registration of the detection eventsdue to the orientation of the blades with respect to the incident beam. The latter effect is betterdemonstrable in the projection of figure 5c. Both figures 5b and 5c depict the short-scale effectattributed to the detector resolution, manifesting itself as the Gaussian smearing around 0. Theextended tails on either side of the distribution represent the long-scale scattering events. In thecase of figure 5c the tails are “modulated” by the succession of the blades in the Y-direction, inaddition to the window effects. Such structures are absent in the X-direction because of the detectorsymmetry along the wire length.A detected neutron is considered misplaced, if the detection occurs outside the 4 σ ( ∼ × FWHM)of the Gaussian fit of the spatial hit distributions (see figures 5b and 5c), i.e. 3.87 mm in the directionparallel to the wires (X-direction) and 0.267 mm in the Y-direction. The σ X and σ Y of the two fitsindicate minimal impact of scattering on resolution (e.g. FWHM detectorY =0.55 mm and FWHM f itY ≈ × FWHM detectorY ). The fraction of scattered neutrons is estimated by summing up all hits thatfulfil the above condition and dividing this sum with the total number of detected neutrons, as inthe equation below
Fraction = N scattered neutrons (| x | ≥ . mm and | y | ≥ . mm ) N all neutrons (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) detected . (3.1)This is the figure of merit used in the following subsections, in contrast to the instrument approach,which evaluates the peak-to-tail ratio. The current approach yields higher values of fractionalscattering but is important for the detector evaluation.– 7 – −
20 0 20 40X position [mm] − − Y p o s i t i o n [ mm ] − − − − − (a) -40 -20 0 20 40X position [mm]10 − − − − − − N o r m a li s e d c o un t s (b) -40 -20 0 20 40Y position [mm]10 − − − − − − N o r m a li s e d c o un t s (c) Figure 5 : (a) Two-dimensional distribution of hit coordinates, projected on the detector window surface. X (b)and Y (c) projections of distribution (a) in red. The figures are produced with 1 Å neutron wavelength and a windowthickness of 1 cm. All distributions are normalised to 1. A Gauss fit of the central bins (in blue) gives σ X =0.968 mm(FWHM f itX =2.27 mm) and σ Y =0.0667 mm (FWHM f itY =0.157 mm). Recently acquired experimental data allow for a comparison with the simulation results. Themeasurements [33, 36] were performed at the CRISP neutron reflectometer at the ISIS neutronand muon source [50]. The Geant4 model matches the geometrical choices of the respectivedemonstrator, i.e. the window thickness is 2 mm and the converter layer is 4.4 µ m thick in thisparticular demonstrator. The neutron wavelength in the simulation is set to 1 Å and the beam ispencil-like, while the experimental beam profile was approximately 3 mm ×
60 mm. The simulationsimplification serves the purpose of providing a clearer picture of the scattering topology and isjustified by the detector symmetry along the X-axis.The basis of the comparison is the Y position of the detection events, as in figure 5c and is– 8 –hown in figure 6. The experimental data correspond to a wavelength range of 0.5-2.5 Å, achievedvia the application of a TOF slice (red distribution of figure 10 in [33]). The simulated coordinatesare smeared with a Gaussian of σ =0.42 mm (ca. 2 × FWHM) [33, 36]. Only six cassettes wereexperimentally read-out, therefore only six “peaks” appear in the blue distribution of figure 6.In addition, three wires from the end of each cassette do not contribute to the measurement andhave also been accounted for in the simulation by excluding the respective Y histogram bins. Thedistributions are normalised to their integral. -40 -20 0 20 40 60Y position [mm]10 − − − − − N o r m a li s e d c o un t s MeasurementGeant4 simulation
Figure 6 : Comparison of Y-position of detected neutrons in measurements taken at CRISP [33] and the results of thesimulation (this work).
The Geant4 simulation is able of reproducing the shapes, widths and features of the experimentaldata. The systematic effects are out of scope of the current work. The shape agreement indicatesthat the simulation reproduces the location of the scattered events and gives confidence that thetopology of scattering is understood in a manner sufficient for the purposes of this study. Thefraction of scattered neutrons in the simulation is 3.5%. The same fraction estimated from theexperimental data amounts to 3.1%.
In [32, 33] it is argued that an increase of the converter thickness can respectively increase the fractionof absorbed neutrons, if set to a value higher than 4.4 µ m (figure 11 of [33]). The motivation is toprevent as many neutrons from reaching the titanium blade behind the coating, which is the primarycontributor to scattering. The detection efficiency anyway saturates at thicknesses above 3 µ m [32].At the same time, an upper value limit needs to be determined, as it is not cost-effective, nor goodthin-film deposition practice, to arbitrarily increase the boron carbide thickness.For the study of the converter thickness the material of the detector window is set to vacuum.Various thicknesses are selected, ranging from typical to extreme. The results are summarised intable 1 and figure 7a, listing the figure of merit defined with equation 3.1.The table and figure values represent the scattering which is intrinsic to the detector and isprimarily attributed to the blade material. Minor contributions come from the counting gas, the– 9 – able 1 : Fraction of scattered neutrons in %, as defined in equation 3.1, for various converter thicknesses and neutronwavelengths. λ [Å] c. thickness [ µ m] 0.1 1 5 7.5 10 201 22.250 17.310 4.310 1.840 0.831 0.0742.5 8.570 5.080 0.265 0.067 0.034 0.02212 0.460 0.098 0.045 0.040 0.038 0.037converter and the wires. Figure 7b depicts the distribution of the hit Y position for various converterthicknesses. Clearly, the thicker the coating, the higher the probability is that all neutrons convert µ m]10 − − − − F r a c t i o n o f s c a tt e r e dn e u tr o n s (a) -40 -20 0 20 40 Y position [mm] − − − − − − − N o r m a li s e d c o un t s µ m1 µ m5 µ m7.5 µ m10 µ m20 µ m (b) Figure 7 : (a) Fraction of scattered neutrons as defined in equation 3.1 as a function of converter thickness for variousneutron wavelengths. (b) Y position of hits for various converter thicknesses for a neutron wavelength of 1 Å. Theentrance window material is set to vacuum. and stop in the first layer - regardless of being detected, thus minimising scattering effects insidethe detector. Adopting a thickness between 5 µ m and 10 µ m can reduce the fractional scattering by1-2 orders of magnitude. The trend in figure 7a demonstrates that for wavelengths above 2.5 Å and4 Å which are the lowest limit for FREIA and ESTIA respectively, a cost-effective choice ofconverter thickness would be of the order of 7-8 µ m, for the fraction of scattered neutrons to staybelow 10 − . Following the same methodology, the next parameter to be studied is the thickness of the Al detectorwindow. This item is an integral component of the detector, separates the counting gas from thedetector environment and assures its operation in vacuum or atmospheric conditions. Similarstudies have been performed with other detector types [48]. The values selected represent typicalthicknesses used in neutron instruments, in addition to extreme values. The converter thicknessfor this series of simulations is now fixed at 7.5 µ m. The results are summarised in table 2 andfigures 8 and 9. Looking at figure 8, the scattering effects become more significant for lower– 10 –eutron wavelengths. The result is consistent with the trend of the scattering (see appendix A), incombination with the absorption cross sections of the materials involved for the specific geometry.It is interesting to note that a different, e.g. larger detector geometry, would not only scatterdifferently but also register these events differently. Especially for wavelengths below the Braggcut-off value of Al and Ti (see figure 10), it is possible to imagine a scenario where the Al windowscatters in such a way that although the fraction of scattered neutrons is higher, the scattering anglesare such that the neutrons are diverted away from the detector active volume. That is why it isessential to study the impact of the window in combination with the detector response. Scatteringis only an issue if it is detected.The Multi-Blade detector is intended to operate both in vacuum and a normal pressure at-mosphere. Given the engineering considerations based on these atmospheric conditions and thefact that the final detector installed at the ESS reflectometers will have a window with a size of500 mm ×
250 mm, engineering studies show that the window thickness can safely remain below5 mm for vacuum operation. Recent developments in the ESTIA design promote a neutron flightvessel of a 1 bar Ar/ He mixture, in which case the Multi-Blade detector can be operated with a thinfoil (ca. 25-100 µ m) instead of a window. In summary, for the wavelengths of interest, the fractionof scattered neutrons at the presence of the window is within acceptable limits. Table 2 : Fraction of scattered neutrons in %, as defined in equation 3.1, as a function of window thickness and neutronwavelength for a converter thickness of 7.5 µ m. λ [Å] window thickness [mm] 0 0.1 1 5 101 1.840 1.870 1.970 2.480 3.0602.5 0.063 0.069 0.098 0.238 0.3984 0.030 0.030 0.039 0.088 0.1876 0.030 0.031 0.036 0.054 0.07512 0.041 0.041 0.046 0.073 0.103The impact of the detector window is also demonstrable in figure 9. In figure 9a the lowerpeaks on either side of the centre are at least 4 orders of magnitude below the peak containingthe non-scattered events, especially for the values of interest above 2.5 Å. This value satisfies theinstrument requirement, the way it is defined as a peak-to-tail ratio. As expected, the fractionalscattering decreases as neutrons get colder. – 11 – − − − F r a c t i o n o f s c a tt e r e dn e u tr o n s Figure 8 : Fraction of scattered neutrons as defined in equation 3.1 as a function of window thickness for variouswavelengths and a converter thickness of 7.5 µ m. -40 -20 0 20 40 Y position [mm] − − − − − − − N o r m a li s e d c o un t s (a) -40 -20 0 20 40 Y position [mm] − − − − − − − N o r m a li s e d c o un t s (b) Figure 9 : (a) Y position of hits for various neutron wavelengths and no detector window for converter thickness of7.5 µ m. (b) Same distribution for 1 Å with varying window thicknesses. A detailed Geant4 model of the Multi-Blade detector is implemented, in order to identify andquantify scattering effects. To this end, a parameter scan is performed focusing mainly on theeffects related to the converter thickness and the detector window. The substrate material andthickness have been experimentally optimised and therefore the engineering values are used in thesimulation. Various neutron wavelengths of relevance for ESS reflectometry are used.A comparison of the simulation with experimental results obtained at the CRISP reflectometerconfirms our understanding of the detection and scattering topology within the detector. It is shownthat the degradation in spatial resolution due to scattering is smaller than the detector resolution. Theresult of the converter thickness study supports the design choice to increase this value to 7.5 µ m,– 12 –ith a 2 orders of magnitude gain in terms of scattering suppression. As for the detector window, itsimpact is within the instrument requirements for the values that result from the engineering studies,in particular for detector operation in vacuum.Last but not least, this study selects the amount of fractional scattering as a figure of merit. Itfollows a cumulative approach in contrast to the instrument one, in the sense that the backgroundis integrated over the entire tail length of the coordinate distributions, while the instrument re-quirements are expressed more as a peak-to-tail ratio. This implies that the cumulative approachpresented here leads to an overestimate of the scattering effects by at least half an order of magnitude.For neutron wavelengths above 2.5 Å, the peak-to-tail ratio is higher than 4 orders of magnitude,which means that the current implementation of the MultiBlade detector more than satisfies theESS reflectometry needs. Acknowledgments
The authors acknowledge the support from the EU Horizon2020 BrightnESS grant 676548 [51].This work was supported by the ÚNKP-17-2 new national excellence program of the HungarianMinistry of Human Capacities. The authors would like to thank ISIS, Didcot, UK and BNC,Budapest, Hungary for the beam time they made available. Computing resources were providedby the DMSC Computing Centre [52]. Gábor Galgóczi would like to thank Balázs Újvári for thefruitful discussions they had.
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56] NCrystal data library, [Online] Available: https://github.com/mctools/ncrystal/wiki/Data-library
A NCrystal cross sections
For the correct treatment of the interaction of thermal and cold neutrons with several single crystals,poly-crystalline materials and powders, the NCrystal library [46, 47] is used in this work. Thetreatment includes both coherent elastic (Bragg) diffraction and various models for the inelasticscattering. The library is publicly available for use under a highly liberal open source license(Apache 2.0) and already interfaces with several Monte Carlo packages, e.g. McStas [53, 54],ANTS2 [55] and Geant4. Its flexible interface though allows for easy integration with otherpackages.Two application examples that are used in this work are Ti and Al, presented in figure 10. Thereproduction of the respective scattering cross sections would not be possible without NCrystal. Thelibrary has been validated against available experimental data. A collection of existing crystallinestructures supported by NCrystal can be found in [56].A visual demonstration of the various types of scattering in the detector blade and windowappears in figure 11a. Coherent elastic scattering takes place when the neutron wavelength is belowthe Bragg cut-off value of the materials it is transported in (4.67 Å for Al and 5.14 Å for Ti). Whatthe figure presents for a neutron wavelength of 2.5 Å is the difference between the polar angle of aneutron at its conversion point - calculated from its momentum vectors - and the initial polar anglewith which it is generated: δ Θ = Θ conversion − Θ initial . (A.1)The red distribution contains only the contributions from gas and converter, as the blade and windowmaterials are set to vacuum. No Bragg scattering takes place with these conditions, as the remainingmaterials are not crystalline. Once the blade material is set to Ti, structures from the Debye-Scherrer Neutron wavelength [˚A] C r o sss ec t i o n [ b a r n ] BraggBkgdAbsorptionTotal (a)
Neutron wavelength [˚A] . . . . . . C r o sss ec t i o n [ b a r n ] BraggBkgdAbsorptionTotal (b)
Figure 10 : (a) Total scattering and absorption cross sections of Ti and (b) Al vs. neutron wavelength. “Bkgd” refersto coherent inelastic, elastic incoherent and inelastic incoherent processes. – 16 –ones become apparent (in green). Similarly, the Bragg scattering from the Al window appears inthe remaining two distributions (yellow, blue).By selecting “background” neutrons, as defined in the denominator of equation 3.1, andswitching off Bragg scattering in the simulation, it is estimated that about 30% of the neutronsscatter coherently elastically for 2.5 Å and a 2 mm Al window (see figure 11b). δ Θ = Θ conversion - Θ initial − − − − − − N o r m a li s e d c o un t s Ti blades with Al window (0.5mm)Ti blades no windowVacuum blades with Al window (0.5mm)Vacuum blades no window (a) δ Θ = Θ conversion - Θ initial N u m b e r o f s c a tt e r e dn e u tr o n s Bragg scattering onBragg scattering off (b)
Figure 11 : (a) Difference between the conversion polar angle and the primary polar angle forneutrons for a neutron wavelength of 2.5 Å. Coherent elastic scattering on the Al detector windowand the Ti blades is responsible for the structures appearing around 50 ◦ , 80 ◦ and 150 ◦◦