- Email: [email protected]
Energy-selective neutron imaging by exploiting wavelength gradients of double crystal monochromators—Simulations and experiments
Nuclear Inst. and Methods in Physics Research, A 943 (2019) 162477
Contents lists available at ScienceDirect
Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima
Energy-selective neutron imaging by exploiting wavelength gradients of double crystal monochromators—Simulations and experiments A.M. Al-Falahat a,b,c ,∗, N. Kardjilov a , T.V. Khanh a,c , H. Markötter a,c , M. Boin a , R. Woracek f , F. Salvemini d , F. Grazzi e , A. Hilger a,c , S.S. Alrwashdeh b , J. Banhart a,c , I. Manke a a
Helmholtz-Zentrum Berlin für Materialien und Energie (HZB), Hahn-Meitner-Platz 1, 14109 Berlin, Germany Mutah University, P.O Box 7, Al-Karak 61710, Jordan c Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany d ACNS, ANSTO, Lucas Heights, NSW, Australia e Museo di Storia Naturale, Sezione di Etnologia e Antropologia, of Università di Firenze, Firenze, Italy f European Spallation Source ERIC, P.O. Box 176, 22100 Lund, Sweden b
ARTICLE
INFO
Keywords: Neutron imaging Energy-selective neutron radiography Double-crystal monochromator A Monte Carlo simulation Wavelength gradient
ABSTRACT The potential of wavelength resolved neutron transmission experiments is well known. This paper is focused on the performance of the double crystal monochromator which is widely used at steady state neutron sources and compares simulation results based on neutron ray tracing with experimental results in order to provide a better understanding of the device. The influences of crystal mosacities on the neutron beam is reported for the utilised setup and the resulting wavelength gradients along one direction are determined. For the neutron imaging geometry applied, a wavelength gradient of about 0.005 Å/cm at the sample position was found. Moreover, a new neutron radiography technique for Bragg edge mapping in imaging experiments utilising a neutron wavelength gradient at the sample position was developed and is reported. Experiments and simulations are found to be in good agreement.
1. Introduction Neutron imaging is used for direct and non-destructive investigations of objects in science and technology [1,2]. Recently, new neutron imaging methods have being developed that connect real-space with reciprocal-space approaches [3–6] and allow for investigations of microstructures in bulk materials [7,8] on length scales down to 20 μm by employing high-resolution detector systems [9–13]. The combination of such high spatial resolution with the new imaging methods enables one to directly visualise magnetic structures [14–16], stress and strain fields, textures, heterogeneous microstructures [17–21], distributions of liquids and material phases etc. [22–29]. A step towards nanometresensitivity can be made with the help of imaging methods that connect the real with the reciprocal space such as grating interferometry [30– 34] and Bragg edge mapping [3,35–39] in propagation geometry. In this case, one can resolve collective nm scale lattice spacing, over many atoms with a spatial resolution of 350 μm. For polycrystalline materials, the wavelength-dependent neutron attenuation coefficient exhibits discontinuities whenever the conditions for Bragg scattering are no longer fulfilled upon increasing wavelengths — the so-called Bragg edges [40]. The positions of the Bragg cut-offs are related to the corresponding 𝑑hkl spacings of the crystals. Shifts of ∗
the Bragg edges [41–43] can be used to detect the presence of residual stresses in metallic samples. The height of the Bragg edge can be related to the presence of texture [19,36,44], while the shape of the edge depends on grain size [45]. A review of diffraction contrast in imaging is given in Woracek et al. [46]. In order to access the Bragg edge information, monochromatic neutron beams are used in imaging experiments [47,48]. Two main techniques are known and applied for beam monochromatisation at steady state neutron sources as shown in Fig. 1a–b: Double-crystal monochromators (DCM) and velocity selectors (VS) [49]. Spallation sources are best suited to exploit the time-of-flight (TOF) technique [50]. The first installation and application of a double-crystal monochromator setup for neutron imaging was reported by Treimer et al. in 2006 [51]. In the here presented work an almost identical setup was used with some improved mechanical stability. A comparison between different monochromatization techniques utilised at steady state sources is presented in Fig. 1c. The wavelengthdependent transmission of an iron sample measured using a velocity selector and a double-crystal monochromator, the latter utilising two different crystal mosaicities (degree of crystallite misalignment), as well as the theoretically tabulated data are included in the same figure [53].
Corresponding author at: Helmholtz-Zentrum Berlin für Materialien und Energie (HZB), Hahn-Meitner-Platz 1, 14109 Berlin, Germany. E-mail address: [email protected] (A.M. Al-Falahat).
https://doi.org/10.1016/j.nima.2019.162477 Received 8 February 2019; Received in revised form 28 June 2019; Accepted 29 July 2019 Available online 1 August 2019 0168-9002/© 2019 Elsevier B.V. All rights reserved.
A.M. Al-Falahat, N. Kardjilov, T.V. Khanh et al.
Nuclear Inst. and Methods in Physics Research, A 943 (2019) 162477
Fig. 2. (a) Schematic view of neutron beam path to imaging instrument CONRAD2 [60]; (b) Drawing of the double-crystal monochromator setup at CONRAD-2 as well as the wavelength distribution behind it.
of and behind the curved guide are straight guide sections (𝑚 = 2). The role of the final straight section is to homogenise the beam intensity over the guides’ cross section. All guide sections have a constant cross section of height × width = 12 × 3 cm2 . At the end of the guide, a double-crystal monochromator was installed in combination with a pinhole set [60]. This configuration allows for remotely switching between monochromatic and polychromatic neutron beams. A flight path of L = 12 m is available downstream of the final straight guide section. This distance is necessary in order to make full use of the pinhole configuration, where a certain L/D ratio can be realised by using apertures with different diameter D at the beginning of the flight path. For apertures with typical diameters of 1 cm to 3 cm, the calculated L/D ratios are between 1200 and 400, respectively. The double-crystal monochromator arrangement was simulated using the McStas standard component ‘Monochromator_flat’, which simulates an infinitely thin single crystal with a single scattering vector, 𝑄0 = 2𝜋∕𝑑𝑚 perpendicular to its surface. A typical use for this component is to simulate a simple monochromator or analyser. The physical model used here is based on the ‘Monochromator_flat’ component where a rectangular piece of material is composed of a large number of small micro-crystallites the orientation of which deviates from the nominal crystal orientation so that the probability of a given microcrystal orientation is proportional to a Gaussian in the angle between the given and the nominal orientation. The width of the Gaussian is given by the mosaic spread (𝜂), of the crystal (given in units of arc minutes). 𝜂 is assumed to be large compared to the inherent Bragg width of the scattering vector (often a few arc seconds). The mosaicity gives rise to a Gaussian reflectivity profile of width similar to – but not equal – the intrinsic mosaicity. In this component, and in real experiments, the mosaicity given is that of the reflectivity signal [61].
Fig. 1. Different techniques for neutron monochromatisation at steady state sources: (a) double-crystal monochromator (commonly employing pyrolytic graphite); (b) neutron velocity selector; (c) wavelength dependence of the linear attenuation coefficient of iron (bcc crystal structure) as measured using a velocity selector (blue) and two doublecrystal monochromators containing crystals of different mosaicities, 3.5◦ (red) and 0.8◦ (green) [49]. Tabulated data are given in black by the nxsPlotter tool [52,53]. Source: Figure c is partially taken from ref. [54] with permission by Elsevier.
Double-crystal monochromators have been recently installed and operated successfully at various imaging facilities [37,55–58]. Monte Carlo simulations based on the computer code ‘McStas’ [3,59] have here been performed to strengthen the understanding of the behaviour and the principle of a double-crystal monochromator device. The simulation results are presented together with experiments that allow us to verify the simulations. Additionally, a new approach to exploit the behaviour is presented and named ‘wavelength-gradient translation imaging (WGTI)’. 2. Monte Carlo simulations The Monte Carlo neutron beam simulations were based on the layout of the CONRAD-2 imaging instrument [60], which contains a curved guide section of 15 m length and a bending radius R of 750 m. This curvature is sufficient to keep fast neutrons and 𝛾 photons from the cold source of the reactor away from the experimental endstation. The curved guide has different wall coatings (m = 2.5 for the inner wall and m = 3.0 for the outer, top and bottom walls) that provide the best result in terms of transported beam intensity and homogeneity. In front 2
A.M. Al-Falahat, N. Kardjilov, T.V. Khanh et al.
Nuclear Inst. and Methods in Physics Research, A 943 (2019) 162477
Fig. 3. The wavelength distribution at the detector x and y position for 𝜆 = 4 Å obtained by using a ‘LambdaYPSD_monitor component’ of McStas. (a) Y-Position; (b) X-Position; (c) Intensity profile through the Y-position graph at Y-Position=0.
as an input parameter from which the Bragg angle 𝜃 can be calculated using Bragg’s law: ( ) 𝜆 𝜃 = arcsin , (3.1) 2𝑑002
The intensity and wavelength distributions as well as the horizontal and the vertical divergence can be monitored in a detector plane using the appropriate McStas monitor component. Such monitor components can be sensitive to any neutron property such as flight direction or energy as seen for example in the divergence/position sensitive monitor (‘PSD-monitor’). Such PSD-monitors were defined at 10 m distance from the monochromator at the detector position where the simulated neutrons were spatially detected over a plane of 30 cm × 40 cm (width × height) with a resolution of 1 × 1 mm2 while tracking their energies as well. For a comparison of the wavelength distribution at different positions in the detector plane as shown in Fig. 2a, five ‘L-monitor components’ from the McStas library are placed at Z = 10 m distance from the monochromator. Three regions of interest (P4, P1, P5) are chosen along the 𝑋-axis (horizontally) and are centred at the points with coordinates: (−10, 0), (0, 0), and (10, 0). Each monitor has an area of 1 cm × 1 cm (height × width). The others two monitors (P3, P2) are lined up along the 𝑌 -axis (vertically) at (0, 10) and (0, −10) and have the same size of 1 cm × 1 cm (height × width). Moreover, for the purpose of signal analysis, a component ‘LambdaYPSD monitor’ was used to count neutrons and store their wavelength and their Y position at the detector area. Similar to any other McStas monitor components, the LambdaYPSD monitor captures every neutron arriving at the component. The monitor geometry is simplified to a plane area where the neutron position parameters (x, y) and the wavelength will be recorded [62]. In this way it was possible to examine wavelength gradients in the detector plane caused by the double-monochromator device along both horizontal and vertical directions.
The monochromator plates are parallel and neutrons of corresponding wavelength 𝜆 will undergo a double reflection. The advantage of this arrangement is that the direction of the extracted monochromatic beam is parallel to the initial neutron beam. For setting a defined wavelength, the two plates are rotated to the corresponding angle 𝜃 and the bottom plate is moved horizontally along the neutron beam direction to a position Z determined by ( ◦ ) 𝑍 = ℎ tan 90 − 2𝜃 , (3.2) where h refers to the vertical distance between the plates and Z to the linear translation on the 𝑍-axis of the lower plate respectively, Fig. 2b. The HOPG crystals have a certain mosaicity, which allows for selecting a broader wavelength band around the corresponding wavelength fulfilling the Bragg reflection condition for the set scattering angle 𝜃. By ray-tracing the neutron beam through the double-crystal device, one can expect a spectral divergence depending on the direction of the neutrons flight paths through double reflection as shown in Fig. 2b. The mosaicity of the crystallites will allow smaller scattering angles for the longer wavelengths and larger angles for the shorter wavelengths. Considering the configuration shown in Fig. 2b the wavelength gradient is expected to be along a vertical line, with longer wavelengths on the bottom and shorter wavelengths on the top. In order to study this effect McStas simulations using the described model above were performed. For our experimental investigations we have chosen to focus on the (110) Bragg edge of a steel sample and the (111) edge of a Bronze sample.
3. Double-crystal monochromator
4. Results and discussion
The double-crystal monochromator at the CONRAD-2 instrument consists of two parallel plates, dimensions 6 × 5 cm2 (length × width), of highly oriented pyrolytic graphite HOPG (002) single crystals aligned one above the other with a fixed vertical distance of h = 7.4 cm [3]. In order to gain more intensity no pinhole was used in case of imaging with monochromatic beams. In this case the size of the source D in the L/D collimation ratio was defined as the used guide cross section illuminating the first crystal (30 mm x 30 mm) resulting in 𝐿∕𝐷 = 330 for a distance L of 10 m. The basic idea and concept is described in Treimer et al. [51]. The crystal lattice spacing is given by 𝑑002 = 3.348 Å. As shown in Fig. 2b the orientation and positioning of the monochromator crystal plates is performed by selecting a desired neutron wavelength 𝜆
The simulation performed here is equivalent to an open beam measurement, i.e. there is no sample in the beam to be transmitted. The calculated intensity distribution as a function of neutron wavelength for varying vertical positions on the McStas LambdaYPSD_ monitor for the monochromator set to 4 Å is shown in Fig. 3a. A slope of the neutron wavelength distribution (i.e. gradient of wavelength) along the (vertical) 𝑌 -axis is clearly visible. The analogous horizontal distribution along the 𝑋-axis is shown in Fig. 3b Contrary to the vertical position, the neutron wavelength along the horizontal 𝑋-axis remains the same, i.e. no change in neutron wavelength over the width of the 3
A.M. Al-Falahat, N. Kardjilov, T.V. Khanh et al.
Nuclear Inst. and Methods in Physics Research, A 943 (2019) 162477
Fig. 4. Images in first row – (a), (b) and (c) – show the intensity captured by the PSD-monitor of cross section (50 cm × 30 cm) for three different mosaicities 0.8, 2.0 and 3.0. Second and third rows display wavelength-resolved intensities captured by the five L-monitors. P3, P1, P2 are arranged vertically ((d), (e), (f), bottom to top), P4, P1, P5 horizontally ((g), (h), (j), left to right). The symbols 𝑥c and w represent the centre and the FWHM of a Gaussian fitting respectively. Monochromator set to 4 Å. Table 1 The peak positions and the wave resolutions of the middle region (P1) at a different mosaicities. Scatter bar reflects values given by the software McStas and the Gaussian fit software Origin.
detector occurs. The second order monochromator reflection, which also satisfies the Bragg condition, leads to neutron intensity distribution around 2 Å which can be seen in the graph as well (white arrows). This has to be taken into account also for the experimental setup. For an estimation of the wavelength distribution at different positions on the detector plane, the wavelength monitors were used in two positions (X and Y position) with 10 cm distance between them, see Fig. 4a. The neutron spectra for different mosaicities of the crystals (0.8, 2.0 and 3.0) were measured in boxes of 1 cm × 1 cm in order to estimate the wavelength gradient in the horizontal and vertical directions as described above. The results for the horizontal direction (P4, P1 and P5) and for the vertical direction (P3, P1 and P2) are shown in Fig. 4. In addition, the intensity distribution over the detector plane is shown.
Mosaicity
Peak position (xc ) (P1) (Å)
(𝛥𝜆∕𝜆) (%)
Area under the curve (P1)
0.8◦ 2◦ 3◦
3.9996(4) 3.9980(21) 3.9957(44)
1.36 3.20 4.70
7040.4 8081.5 8070.8
The values for the wavelength resolution taken from Fig. 4 (𝑥c and w, represent the centre and the FWHM of Gaussian fitting respectively) are summarised in Table 1. The following statements can be derived from these results: 4
A.M. Al-Falahat, N. Kardjilov, T.V. Khanh et al.
Nuclear Inst. and Methods in Physics Research, A 943 (2019) 162477
Fig. 5. (a) Radiographic image of steel plate divided into 23 ROIs with dimensions of 1 cm height × 25 cm width from the lower to the upper edge along the Y-direction. (b) Colour map of the wavelength distribution along the Y-direction in the steel plate. (c) Bragg edge positions for three different Y-positions (corresponding to P2, P1, P3 in the simulations) (d) Derivative and Gaussian fit of the Bragg edge transmission profiles for the same three Y-positions. The symbols 𝑥c and w represent the centre and the FWHM of the Gaussian fitting, respectively.
– The wavelength resolution (𝛥𝜆∕𝜆) gets worse with increasing crystal mosaicity, following a linear trend for the used range, see Table 1.
the parameters used in the Monte Carlo simulations and mosaicity of 0.8◦ was used to select different neutron wavelengths. A wavelength scan from 3.6 Å to 4.5 Å in steps of 0.02 Å was performed with an exposure time of three times 30 s per step (taking a median of three images) resulting in 80 min per wavelength scan. For each step the transmission through the mild steel plate was measured by the position sensitive detector. A transmission map was obtained by normalising the images of the sample by the open beam images, thus correcting for the beam inhomogeneity. As a result, a wavelength-dependent neutron transmission through the steel plate can be plotted for each point/pixel of the detector. The analysis of the images was accomplished by using ImageJ [66], where the height of the plate was divided into rectangular regions of interest (ROI) of 1 cm height and 25 cm width, as shown in Fig. 5a, In addition, the wavelength distribution in the steel plate along the Ydirection is clearly displayed in the colour map as shown in Fig. 5b. The wavelength-dependent transmission showing the Bragg edge for bcc steel can be plotted for each ROI in the vertical direction as shown in Fig. 5c for three ROIs (#2, #12 and # 22). In order to investigate the wavelength variation, a ROI#12 is selected to be the middle of the field of view and ROI #2 as well as ROI#22 are at 10 cm distance below and above the middle region as shown in Fig. 5a. The transmission was calculated by using the values from all pixels in the ROI. Due to the large number of pixels (2.105 ) the standard deviation was approximately 2% which explains the smooth curves presented in Fig. 5. The position of the Bragg edge was determined by nonlinear leastsquares fitting. The centre of the Gaussian represents the location of the Bragg edge and corresponds to a Bragg peak shift as shown in Fig. 5d. This shift is a result of the wavelength gradient produced by the doublecrystal monochromator. The obtained Gaussian fitting parameters are shown in Fig. 5d and allow us to compare the experimental data with the Monte Carlo simulation results. Such a comparison is presented in Table 2. An agreement between experimental and simulated data better than 1% for the absolute wavelength values was obtained, which proves
– For a double crystal reflection the angular dispersion of the neutrons in the scattering plane is not depending on the mosaic which can be explained by analysis of scattering vector (k-space) diagram [63]. However, the components out of the plane will depend on the mosaic spread. As a consequence the beam size increases asymmetrically with the increase of crystal mosaicity (Fig. 4a–c). The increase in our case is in the horizontal direction (parallel to the rotation axis of the monochromator crystals) only. The beam spread in vertical direction is defined by the divergence of ◦ the initial beam which is 0.2 / Å resulting in 0.8◦ for a neutron wavelength of 4 Å. For a distance of 10 m between the monochromator and the detector one can calculate the vertical beam extension as 2 ∗ 10 m ∗ tan (0.8◦ ) = 28 cm which agrees well with the result shown in the beam plots in Fig. 4. – The wavelength gradient is constant for a certain beam divergence and crystal configuration does not depend on the mosaicity in the case where the mosaicities are larger than the beam divergence. These conclusions can be explained by analytical description of the double reflection from monochromators using the k-space diagram which is a subject of forthcoming paper being in preparation [63]. 4.1. Comparison with experimental results In order to verify the results from the Monte Carlo simulations a test experiment was performed at the CONRAD-2 instrument [64,65]. For this purpose, a mild steel (body-centred cubic (bcc) crystal structure) plate of dimensions 30 cm × 30 cm × 1 cm (B × H × T) was used to cover the detector. A double-crystal monochromator with 5
A.M. Al-Falahat, N. Kardjilov, T.V. Khanh et al.
Nuclear Inst. and Methods in Physics Research, A 943 (2019) 162477
Fig. 6. (a) Radiograph of a bronze coin (fcc crystal structure) and steel screws (bcc crystal structure) holding the coin. White boxes denote 5 mm-high regions, in which transmission values were averaged. (b, c) Comparison of the Bragg edges measured for bronze and steel by (b) standard scanning and by (c) wavelength gradient translation imaging. The red box corresponds to the wavelength range in (c). Table 2 Comparison of the wavelength shift obtained from the simulation and from the experiment. Mosaicity = 0.8◦ ± 0.2◦ . Position
Upper ROI#22 Middle ROI#12 Bottom ROI#2
𝜆centre (Å)
profile will be obtained. The advantage compared to the traditional wavelength scanning method is an increased wavelength stability due to the missing uncertainty coming from the mechanical fine-positioning system of the monochromator orientation for each step of a scan. An example for such an investigation is presented in Fig. 6, where a Roman coin made of bronze (face-centred cubic (fcc) crystal structure) was fixed by steel screws (bcc crystal structure) and visualised using the two energy-selective methods. For the standard wavelength scan using the double-crystal monochromator a step of 0.01 Å was conducted within 6 h (105 s per step). For wavelength gradient imaging, the double-crystal monochromator was set to 3.95 Å, 4.05 Å and 4.15 Å, where for each setting a stepwise shift of the sample over 20 cm with a step of 5 mm was performed resulting in total measuring time of 3.5 h (105 s per step). The wavelength regions covered by the three measurements are marked with different background colours in Fig. 6c. In the transmission curves from the WGTI measurements intensity drops of less than 1% can be observed. They can be explained by the intensity variations produced from the guide system where the joints between the guide segments (non-reflecting areas) are projected optically on the detector as dark stripes where slight spectral inhomogeneities are expected. If we consider the measured wavelength shift of 0.05 Å/10 cm this means that the wavelength resolution per step of 5 mm would be
Wavelength shift (Å)
Experiment
Simulation
Experiment
Simulation
4.047 4.000 3.946
4.053 3.999 3.945
0.047 0 0.053
0.053 0 0.054
the reliability of the simulations. In addition one can conclude that the wavelength shift over 10 cm distance in the vertical direction is approximately 0.05 Å. 5. Wavelength-gradient translation imaging (WGTI) While seemingly an undesired effect, the wavelength gradient obtained can be used for imaging purposes in order to measure the Bragg edges of different materials without performing a scan with the doublecrystal monochromator. For this it is necessary to select a wavelength in the middle of the Bragg edge. When the sample is translated through the wavelength gradient (e.g. from top to bottom) a narrow Bragg edge 6
A.M. Al-Falahat, N. Kardjilov, T.V. Khanh et al.
Nuclear Inst. and Methods in Physics Research, A 943 (2019) 162477
0.0025 Å without considering the wavelength broadening due to the mosaicity of the crystals. The correspondence of the Bragg edge profiles measured by the two methods shows that wavelength gradient translation imaging can be used for collecting data with excellent sampling resolution and supports a reliable fitting procedure providing the position and the amplitude of the Bragg edge. The sample scan through the wavelength gradient provides much more points for the curve of the Bragg-edge so that the step between 2 points is much smaller than the step in the monochromator scanning technique where limitations related to the mechanical reproducibility of the positions of the crystals introduce additional wavelength uncertainty. In addition the WGTI method can be used for precise wavelength scans at facilities with static DCM device where the position of the monochromator crystals is fixed.
[11] S.H. Williams, A. Hilger, N. Kardjilov, I. Manke, M. Strobl, P.A. Douissard, T. Martin, H. Riesemeier, J. Banhart, Detection system for microimaging with neutrons, J. Instrum. 7 (2012) P02014. [12] E.H. Lehmann, G. Frei, G. Kuhne, P. Boillat, The micro-setup for neutron imaging: A major step forward to improve the spatial resolution, Nucl. Instrum. Methods Phys. Res. A 576 (2007) 389–396. [13] M.A. Hickner, N.P. Siegel, K.S. Chen, D.S. Hussey, D.L. Jacobson, M. Arif, In situ high-resolution neutron radiography of cross-sectional liquid water profiles in proton exchange membrane fuel cells, J. Electrochem. Soc. 155 (2008) B427–B434. [14] A. Hilger, I. Manke, N. Kardjilov, M. Osenberg, H. Markötter, J. Banhart, Tensorial neutron tomography of three-dimensional magnetic vector fields in bulk materials, Nature Commun. 9 (2018) 4023. [15] W. Treimer, Radiography and tomography with polarized neutrons, J. Magn. Magn. Mater. 350 (2014) 188–198. [16] I. Manke, H. Markotter, C. Totzke, N. Kardjilov, R. Grothausmann, M. Dawson, C. Hartnig, S. Haas, D. Thomas, A. Hoell, C. Genzel, J. Banhart, Investigation of energy-relevant materials with synchrotron X-rays and neutrons, Adv. Energy Mater. 13 (2011) 712–729. [17] M.G. Makowska, M. Strobl, E.M. Lauridsen, S. Kabra, W. Kockelmann, A. Tremsin, H.L. Frandsen, L. Theil Kuhn, In situ time-of-flight neutron imaging of NiO–YSZ anode support reduction under influence of stress, J. Appl. Crystallogr. 49 (2016). [18] J. Santisteban, M. Vicente-Alvarez, P. Vizcaino, A. Banchik, S. Vogel, A. Tremsin, J. Vallerga, J. McPhate, E. Lehmann, W. Kockelmann, Texture imaging of zirconium based components by total neutron cross-section experiments, J. Nucl. Mater. 425 (2012) 218–227. [19] J.R. Santisteban, L. Edwards, V. Stelmukh, Characterization of textured materials by TOF transmission, Physica B 385–386 (I) (2006) 636–638. [20] M.G. Makowska, M. Strobl, E.M. Lauridsen, H.L. Frandsen, A. Tremsin, T. Shinohara, L.T. Kuhn, Phase transition mapping by means of neutron imaging in SOFC anode supports during reduction under applied stress, ECS Trans. 68 (2015) 1103–1114. [21] N. Kardjilov, A. Hilger, I. Manke, M. Strobl, W. Treimer, J. Banhart, Industrial applications at the new cold neutron radiography and tomography facility of the HMI, Nucl. Instrum. Methods Phys. Res. A 542 (2005) 16–21. [22] A. Schröder, K. Wippermann, J. Mergel, W. Lehnert, D. Stolten, T. Sanders, T. Baumhöfer, D.U. Sauer, I. Manke, N. Kardjilov, A. Hilger, J. Schloesser, J. Banhart, C. Hartnig, Combined local current distribution measurements and high resolution neutron radiography of operating Direct Methanol Fuel Cells, Electrochem. Commun. 11 (2009) 1606–1609. [23] M.A. Hickner, N.P. Siegel, K.S. Chen, D.N. McBrayer, D.S. Hussey, D.L. Jacobson, M. Arif, Real-time imaging of liquid water in an operating proton exchange membrane fuel cell, J. Electrochem. Soc. 153 (2006) A902–A908. [24] C. Totzke, I. Manke, A. Hilger, G. Choinka, N. Kardjilov, T. Arlt, H. Markotter, A. Schroder, K. Wippermann, D. Stolten, C. Hartnig, P. Kruger, R. Kuhn, J. Banhart, Large area high resolution neutron imaging detector for fuel cell research, J. Power Sources 196 (2011) 4631–4637. [25] S.S. Alrwashdeh, I. Manke, H. Markötter, J. Haußmann, N. Kardjilov, A. Hilger, M.J. Kermani, M. Klages, A.M. Al-Falahat, J. Scholta, J. Banhart, Neutron radiographic in operando investigation of water transport in polymer electrolyte membrane fuel cells with channel barriers, Energy Convers. Manage. 148 (2017) 604–610. [26] J. Kaetzel, H. Markoetter, T. Arlt, M. Klages, J. Haussmann, M. Messerschmidt, N. Kardjilov, J. Scholta, J. Banhart, I. Manke, Effect of ageing of gas diffusion layers on the water distribution in flow field channels of polymer electrolyte membrane fuel cells, J. Power Sources 301 (2016) 386–391. [27] A. Schröder, K. Wippermann, W. Lehnert, D. Stolten, T. Sanders, T. Baumhöfer, N. Kardjilov, A. Hilger, J. Banhart, I. Manke, The influence of gas diffusion layer wettability on direct methanol fuel cell performance: A combined local current distribution and high resolution neutron radiography study, J. Power Sources 195 (2010) 4765–4771. [28] L. Gondek, N.B. Selvaraj, J. Czub, H. Figiel, D. Chapelle, N. Kardjilov, A. Hilger, I. Manke, Imaging of an operating LaNi4.8Al0.2-based hydrogen storage container, Int. J. Hydrogen Energy 36 (2011) 9751–9757. [29] A. Lange, A. Kupsch, M.P. Hentschel, I. Manke, N. Kardjilov, T. Arlt, R. Grothausmann, Reconstruction of limited CT data of fuel cell components using DIRECTT, J. Power Sources 196 (2010) 5293–5298. [30] F. Pfeiffer, T. Weitkamp, O. Bunk, C. David, Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources, Nat. Phys. 2 (2006) 258. [31] C. David, J. Bruder, T. Rohbeck, C. Grunzweig, C. Kottler, A. Diaz, O. Bunk, F. Pfeiffer, Fabrication of diffraction gratings for hard X-ray phase contrast imaging, Microelectron. Eng. 84 (2007) 1172–1177. [32] S.W. Lee, K.Y. Kim, O.Y. Kwon, N. Kardjlov, M. Dawson, A. Hilger, I. Manke, Observation of magnetic domains in insulation-coated electrical steels by neutron dark-field imaging, Appl. Phys. Express 3 (2010) 106602. [33] A. Hilger, N. Kardjilov, T. Kandemir, I. Manke, J. Banhart, D. Penumadu, A. Manescu, M. Strobl, Revealing microstructural inhomogeneities with dark-field neutron imaging, J. Appl. Phys. 107 (2010) 036101. [34] M. Strobl, B. Betz, R.P. Harti, A. Hilger, N. Kardjilov, I. Manke, C. Gruenzweig, Wavelength-dispersive dark-field contrast: micrometre structure resolution in neutron imaging with gratings, J. Appl. Crystallogr. 49 (2016) 569–573.
6. Conclusions The double-crystal monochromator is a very important device for energy-selective imaging at continuous neutron sources. The simulations and analytical calculations presented herein help to understand its functionality and to optimise its parameters. The influence of crystal mosaicity on the beam size and intensity at the sample position was studied. The wavelength gradient caused by crystal mosaicity was simulated and measured and good agreement obtained. A new method for wavelength-gradient translation imaging (WGTI) using a translation scan through the wavelength gradient was proposed and tested. Such wavelength-gradient imaging provides better sampling (∼200 times more points on the plot) of Bragg edge measurements, and can be used to determinate its position and shape by using a fitting function. In addition the new technique allows for wavelength scans at monochromator devices with fixed crystals. Acknowledgement The authors would like to thank Dr. David Jacobson (NIST) for his help in understanding the principle of double-crystal monochromator by applying k-space diagram representation in case of double crystal reflection [63]. References [1] J. Banhart, Advanced Tomographic Methods in Materials Research and Engineering, first ed., Oxford University Press, Oxford, UK, 2008. [2] N. Kardjilov, I. Manke, R. Woracek, A. Hilger, J. Banhart, Advances in neutron imaging, Mater. Today 21 (2018) 652–672. [3] M. Boin, R.C. Wimpory, A. Hilger, N. Kardjilov, S.Y. Zhang, M. Strobl, Monte Carlo Simulations for the analysis of texture and strain measured with Bragg edge neutron transmission, J. Phys. Conf. Ser. 340 (2012) 012022. [4] C. Grunzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, R. Schafer, S. Pofahl, H.M.R. Ronnow, F. Pfeiffer, Bulk magnetic domain structures visualized by neutron dark-field imaging, Appl. Phys. Lett. 93 (2008) 112504. [5] M. Strobl, General solution for quantitative dark-field contrast imaging with grating interferometers, Sci. Rep. 4 (2014). [6] N. Kardjilov, A. Hilger, I. Manke, M. Strobl, M. Dawson, J. Banhart, New trends in neutron imaging, Nucl. Instrum. Methods Phys. Res. A 605 (2009) 13–15. [7] J. Banhart, A. Borbely, K. Dzieciol, F. Garcia-Moreno, I. Manke, N. Kardjilov, A.R. Kaysser-Pyzalla, M. Strobl, W. Treimer, X-ray and neutron imaging Complementary techniques for materials science and engineering, Int. J. Mater. Res. 101 (2010) 1069–1079. [8] C. Grunzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, J. Kohlbrecher, R. Schafer, P. Lejcek, H.M.R. Ronnow, F. Pfeiffer, Neutron decoherence imaging for visualizing bulk magnetic domain structures, Phys. Rev. Lett. 101 (2008). [9] N. Kardjilov, I. Manke, A. Hilger, S. Williams, M. Strobl, R. Woracek, M. Boin, E. Lehmann, D. Penumadu, J. Banhart, Neutron Bragg-edge mapping of weld seams, Int. J. Mater. Res. 103 (2012) 151–154. [10] P. Trtik, J. Hovind, C. Grünzweig, A. Bollhalder, V. Thominet, C. David, A. Kaestner, E.H. Lehmann, Improving the spatial resolution of neutron imaging at Paul Scherrer Institut–The Neutron Microscope Project, Physics Procedia 69 (2015) 169–176. 7
A.M. Al-Falahat, N. Kardjilov, T.V. Khanh et al.
Nuclear Inst. and Methods in Physics Research, A 943 (2019) 162477 [50] M. Strobl, Future prospects of imaging at spallation neutron sources, Nucl. Instrum. Methods Phys. Res. A 604 (2009) 646–652. [51] W. Treimer, M. Strobl, N. Kardjilov, A. Hilger, I. Manke, Wavelength tunable device for neutron radiography and tomography, Appl. Phys. Lett. 89 (2006). [52] Experimental Nuclear Reaction Data (EXFOR), 2018, 2018. [53] M. Boin, NXS: a program library for neutron cross section calculations, J. Appl. Crystallogr. 45 (2012) 603–607. [54] N. Kardjilov, S. Baechler, M. Bastürk, M. Dierick, J. Jolie, E. Lehmann, T. Materna, B. Schillinger, P. Vontobel, New features in cold neutron radiography and tomography Part II: applied energy-selective neutron radiography and tomography, Nucl. Instrum. Methods Phys. Res. A 501 (2003) 536–546. [55] H.G. Esser, A. Carminati, P. Vontobel, E.H. Lehmann, S.E. Oswald, Neutron radiography and tomography of water distribution in the root zone, J. Plant Nutr. Soil Sci. 173 (2010) 757–764. [56] D.S. Hussey, C. Brocker, J.C. Cook, D.L. Jacobson, T.R. Gentile, W.C. Chen, E. Baltic, D.V. Baxter, J. Doskow, M. Arif, A new cold neutron imaging instrument at NIST, Physics Procedia 69 (2015) 48–54. [57] M. Schulz, P. Boeni, E. Calzada, M. Muehlbauer, B. Schillinger, Energy-dependent neutron imaging with a double crystal monochromator at the ANTARES facility at FRM II, Nucl. Instrum. Methods Phys. Res. A 605 (2009) 33–35. [58] N. Kardjilov, A. Hilger, I. Manke, M. Strobl, M. Dawson, S. Williams, J. Banhart, Neutron tomography instrument CONRAD at HZB, Nucl. Instrum. Methods Phys. Res. A 651 (2011) 47–52. [59] K. Nielsen, K. Lefmann, Monte Carlo simulations of neutron-scattering instruments using McStas, Physica B 283 (2000) 426–432. [60] N. Kardjilov, A. Hilger, I. Manke, R. Woracek, J. Banhart, CONRAD-2: the new neutron imaging instrument at the Helmholtz-Zentrum Berlin, J. Appl. Crystallogr. 49 (2016) 195–202. [61] K. Lefmann, K. Nielsen, McStas, a general software package for neutron ray-tracing simulations, Neutron News 10 (1999) 20–23. [62] M. Boin, Developments Towards the Tomographic Imaging of Local Crystallographic Structures, (Ph.D. thesis), Open University, 2010. [63] D. Jacobson, Analytical Description of Double-Crystal Monochromator for Neutron Imaging Applications, 2019. [64] N. Kardjilov, A. Hilger, I. Manke, CONRAD-2: Cold neutron tomography and radiography at BER II (V7), J. Large-Scale Res. Facil. 2 (2016) A98. [65] N. Kardjilov, M. Dawson, A. Hilger, I. Manke, M. Strobl, D. Penumadu, K.H. Kim, F. Garcia-Moreno, J. Banhart, A highly adaptive detector system for high resolution neutron imaging, Nucl. Instrum. Methods Phys. Res. A 651 (2011) 95–99. [66] C.A. Schneider, W.S. Rasband, K.W. Eliceiri, NIH Image to ImageJ: 25 years of image analysis, Nature Methods 9 (2012) 671–675.
[35] R. Woracek, D. Penumadu, N. Kardjilov, A. Hilger, M. Boin, J. Banhart, I. Manke, 3D Mapping of crystallographic phase distribution using energy-selective neutron tomography, Adv. Mater. 26 (2014) 4069–4073. [36] J.R. Santisteban, M.A. Vicente-Alvarez, P. Vizcaino, A.D. Banchik, S.C. Vogel, A.S. Tremsin, J.V. Vallerga, J.B. McPhate, E. Lehmann, W. Kockelmann, Texture imaging of zirconium based components by total neutron cross-section experiments, J. Nucl. Mater. (2011). [37] E. Dabah, B. Pfretzschner, T. Schaupp, N. Kardjilov, I. Manke, M. Boin, R. Woracek, A. Griesche, Time-resolved Bragg-edge neutron radiography for observing martensitic phase transformation from austenitized super martensitic steel, J. Mater. Sci. (2016) 1–7. [38] R. Woracek, D. Penumadu, N. Kardjilov, A. Hilger, M. Strobl, R.C. Wimpory, I. Manke, J. Banhart, Neutron Bragg-edge-imaging for strain mapping under in situ tensile loading, J. Appl. Phys. 109 (2011) 093506. [39] K. Iwase, H. Sato, S. Harjo, T. Kamiyama, T. Ito, S. Takata, K. Aizawa, Y. Kiyanagi, In situ lattice strain mapping during tensile loading using the neutron transmission and diffraction methods, J. Appl. Crystallogr. 45 (2012) 113–118. [40] W. Kockelmann, G. Frei, E.H. Lehmann, P. Vontobel, J.R. Santisteban, Energyselective neutron transmission imaging at a pulsed source, Nucl. Instrum. Methods Phys. Res. A 578 (2007) 421–434. [41] V. Wagner, Z. Kouril, P. Lukas, P. Mikula, J. Saroun, P. Strunz, M. Vrana, Residual Strain/Stress Analysis By Means of Energy-Dispersive Neutron Transmission Diffraction (EDNTD), 1997, pp. 168–171. [42] J.R. Santisteban, L. Edwards, M.E. Fitzpatrick, A. Steuwer, P.J. Withers, M.R. Daymond, M.W. Johnson, N. Rhodes, E.M. Schooneveld, Strain imaging by Bragg edge neutron transmission, Nucl. Instrum. Methods A 481 (2002) 765–768. [43] H.J. Kirkwood, S.Y. Zhang, A.S. Tremsin, A.M. Korsunsky, N. Baimpas, B. Abbey, Neutron strain tomography using the radon transform, Mater. Today: Proc. 2 (2015) S414–S423. [44] T. Sun, A.S. Tremsin, M.J. Roy, M. Hofmann, P.B. Prangnell, P.J. Withers, Investigation of residual stress distribution and texture evolution in aa7050 stationary shoulder friction stir welded joints, Mater. Sci. Eng. A 712 (2018) 531–538. [45] K. Oikawa, Y.H. Su, Y. Tomota, T. Kawasaki, T. Shinohara, T. Kai, K. Hiroi, S.Y. Zhang, J.D. Parker, H. Sato, Y. Kiyanagi, A comparative study of the crystallite size and the dislocation density of bent steel plates using bragg-edge transmission imaging, TOF neutron diffraction and EBSD, Physics Procedia 88 (2017) 34–41. [46] R. Woracek, J. Santisteban, A. Fedrigo, M. Strobl, Diffraction in neutron imaging-A review, Nucl. Instrum. Methods A 878 (2018) 141–158. [47] W. Treimer, A. Hilger, M. Strobl, Slit and phase grating diffraction with a double crystal diffractometer, Physica B 385–86 (2006) 1388–1391. [48] W. Treimer, S.O. Seidel, O. Ebrahimi, Neutron tomography using a crystal monochromator, Nucl. Instrum. Methods A 621 (2010) 502–505. [49] N. Kardjilov, Further Developments and Applications of Radiography and Tomography with Thermal and Cold Neutrons, (Ph.D. thesis), Universität München, 2003.
8
Contents lists available at ScienceDirect
Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima
Energy-selective neutron imaging by exploiting wavelength gradients of double crystal monochromators—Simulations and experiments A.M. Al-Falahat a,b,c ,∗, N. Kardjilov a , T.V. Khanh a,c , H. Markötter a,c , M. Boin a , R. Woracek f , F. Salvemini d , F. Grazzi e , A. Hilger a,c , S.S. Alrwashdeh b , J. Banhart a,c , I. Manke a a
Helmholtz-Zentrum Berlin für Materialien und Energie (HZB), Hahn-Meitner-Platz 1, 14109 Berlin, Germany Mutah University, P.O Box 7, Al-Karak 61710, Jordan c Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany d ACNS, ANSTO, Lucas Heights, NSW, Australia e Museo di Storia Naturale, Sezione di Etnologia e Antropologia, of Università di Firenze, Firenze, Italy f European Spallation Source ERIC, P.O. Box 176, 22100 Lund, Sweden b
ARTICLE
INFO
Keywords: Neutron imaging Energy-selective neutron radiography Double-crystal monochromator A Monte Carlo simulation Wavelength gradient
ABSTRACT The potential of wavelength resolved neutron transmission experiments is well known. This paper is focused on the performance of the double crystal monochromator which is widely used at steady state neutron sources and compares simulation results based on neutron ray tracing with experimental results in order to provide a better understanding of the device. The influences of crystal mosacities on the neutron beam is reported for the utilised setup and the resulting wavelength gradients along one direction are determined. For the neutron imaging geometry applied, a wavelength gradient of about 0.005 Å/cm at the sample position was found. Moreover, a new neutron radiography technique for Bragg edge mapping in imaging experiments utilising a neutron wavelength gradient at the sample position was developed and is reported. Experiments and simulations are found to be in good agreement.
1. Introduction Neutron imaging is used for direct and non-destructive investigations of objects in science and technology [1,2]. Recently, new neutron imaging methods have being developed that connect real-space with reciprocal-space approaches [3–6] and allow for investigations of microstructures in bulk materials [7,8] on length scales down to 20 μm by employing high-resolution detector systems [9–13]. The combination of such high spatial resolution with the new imaging methods enables one to directly visualise magnetic structures [14–16], stress and strain fields, textures, heterogeneous microstructures [17–21], distributions of liquids and material phases etc. [22–29]. A step towards nanometresensitivity can be made with the help of imaging methods that connect the real with the reciprocal space such as grating interferometry [30– 34] and Bragg edge mapping [3,35–39] in propagation geometry. In this case, one can resolve collective nm scale lattice spacing, over many atoms with a spatial resolution of 350 μm. For polycrystalline materials, the wavelength-dependent neutron attenuation coefficient exhibits discontinuities whenever the conditions for Bragg scattering are no longer fulfilled upon increasing wavelengths — the so-called Bragg edges [40]. The positions of the Bragg cut-offs are related to the corresponding 𝑑hkl spacings of the crystals. Shifts of ∗
the Bragg edges [41–43] can be used to detect the presence of residual stresses in metallic samples. The height of the Bragg edge can be related to the presence of texture [19,36,44], while the shape of the edge depends on grain size [45]. A review of diffraction contrast in imaging is given in Woracek et al. [46]. In order to access the Bragg edge information, monochromatic neutron beams are used in imaging experiments [47,48]. Two main techniques are known and applied for beam monochromatisation at steady state neutron sources as shown in Fig. 1a–b: Double-crystal monochromators (DCM) and velocity selectors (VS) [49]. Spallation sources are best suited to exploit the time-of-flight (TOF) technique [50]. The first installation and application of a double-crystal monochromator setup for neutron imaging was reported by Treimer et al. in 2006 [51]. In the here presented work an almost identical setup was used with some improved mechanical stability. A comparison between different monochromatization techniques utilised at steady state sources is presented in Fig. 1c. The wavelengthdependent transmission of an iron sample measured using a velocity selector and a double-crystal monochromator, the latter utilising two different crystal mosaicities (degree of crystallite misalignment), as well as the theoretically tabulated data are included in the same figure [53].
Corresponding author at: Helmholtz-Zentrum Berlin für Materialien und Energie (HZB), Hahn-Meitner-Platz 1, 14109 Berlin, Germany. E-mail address: [email protected] (A.M. Al-Falahat).
https://doi.org/10.1016/j.nima.2019.162477 Received 8 February 2019; Received in revised form 28 June 2019; Accepted 29 July 2019 Available online 1 August 2019 0168-9002/© 2019 Elsevier B.V. All rights reserved.
A.M. Al-Falahat, N. Kardjilov, T.V. Khanh et al.
Nuclear Inst. and Methods in Physics Research, A 943 (2019) 162477
Fig. 2. (a) Schematic view of neutron beam path to imaging instrument CONRAD2 [60]; (b) Drawing of the double-crystal monochromator setup at CONRAD-2 as well as the wavelength distribution behind it.
of and behind the curved guide are straight guide sections (𝑚 = 2). The role of the final straight section is to homogenise the beam intensity over the guides’ cross section. All guide sections have a constant cross section of height × width = 12 × 3 cm2 . At the end of the guide, a double-crystal monochromator was installed in combination with a pinhole set [60]. This configuration allows for remotely switching between monochromatic and polychromatic neutron beams. A flight path of L = 12 m is available downstream of the final straight guide section. This distance is necessary in order to make full use of the pinhole configuration, where a certain L/D ratio can be realised by using apertures with different diameter D at the beginning of the flight path. For apertures with typical diameters of 1 cm to 3 cm, the calculated L/D ratios are between 1200 and 400, respectively. The double-crystal monochromator arrangement was simulated using the McStas standard component ‘Monochromator_flat’, which simulates an infinitely thin single crystal with a single scattering vector, 𝑄0 = 2𝜋∕𝑑𝑚 perpendicular to its surface. A typical use for this component is to simulate a simple monochromator or analyser. The physical model used here is based on the ‘Monochromator_flat’ component where a rectangular piece of material is composed of a large number of small micro-crystallites the orientation of which deviates from the nominal crystal orientation so that the probability of a given microcrystal orientation is proportional to a Gaussian in the angle between the given and the nominal orientation. The width of the Gaussian is given by the mosaic spread (𝜂), of the crystal (given in units of arc minutes). 𝜂 is assumed to be large compared to the inherent Bragg width of the scattering vector (often a few arc seconds). The mosaicity gives rise to a Gaussian reflectivity profile of width similar to – but not equal – the intrinsic mosaicity. In this component, and in real experiments, the mosaicity given is that of the reflectivity signal [61].
Fig. 1. Different techniques for neutron monochromatisation at steady state sources: (a) double-crystal monochromator (commonly employing pyrolytic graphite); (b) neutron velocity selector; (c) wavelength dependence of the linear attenuation coefficient of iron (bcc crystal structure) as measured using a velocity selector (blue) and two doublecrystal monochromators containing crystals of different mosaicities, 3.5◦ (red) and 0.8◦ (green) [49]. Tabulated data are given in black by the nxsPlotter tool [52,53]. Source: Figure c is partially taken from ref. [54] with permission by Elsevier.
Double-crystal monochromators have been recently installed and operated successfully at various imaging facilities [37,55–58]. Monte Carlo simulations based on the computer code ‘McStas’ [3,59] have here been performed to strengthen the understanding of the behaviour and the principle of a double-crystal monochromator device. The simulation results are presented together with experiments that allow us to verify the simulations. Additionally, a new approach to exploit the behaviour is presented and named ‘wavelength-gradient translation imaging (WGTI)’. 2. Monte Carlo simulations The Monte Carlo neutron beam simulations were based on the layout of the CONRAD-2 imaging instrument [60], which contains a curved guide section of 15 m length and a bending radius R of 750 m. This curvature is sufficient to keep fast neutrons and 𝛾 photons from the cold source of the reactor away from the experimental endstation. The curved guide has different wall coatings (m = 2.5 for the inner wall and m = 3.0 for the outer, top and bottom walls) that provide the best result in terms of transported beam intensity and homogeneity. In front 2
A.M. Al-Falahat, N. Kardjilov, T.V. Khanh et al.
Nuclear Inst. and Methods in Physics Research, A 943 (2019) 162477
Fig. 3. The wavelength distribution at the detector x and y position for 𝜆 = 4 Å obtained by using a ‘LambdaYPSD_monitor component’ of McStas. (a) Y-Position; (b) X-Position; (c) Intensity profile through the Y-position graph at Y-Position=0.
as an input parameter from which the Bragg angle 𝜃 can be calculated using Bragg’s law: ( ) 𝜆 𝜃 = arcsin , (3.1) 2𝑑002
The intensity and wavelength distributions as well as the horizontal and the vertical divergence can be monitored in a detector plane using the appropriate McStas monitor component. Such monitor components can be sensitive to any neutron property such as flight direction or energy as seen for example in the divergence/position sensitive monitor (‘PSD-monitor’). Such PSD-monitors were defined at 10 m distance from the monochromator at the detector position where the simulated neutrons were spatially detected over a plane of 30 cm × 40 cm (width × height) with a resolution of 1 × 1 mm2 while tracking their energies as well. For a comparison of the wavelength distribution at different positions in the detector plane as shown in Fig. 2a, five ‘L-monitor components’ from the McStas library are placed at Z = 10 m distance from the monochromator. Three regions of interest (P4, P1, P5) are chosen along the 𝑋-axis (horizontally) and are centred at the points with coordinates: (−10, 0), (0, 0), and (10, 0). Each monitor has an area of 1 cm × 1 cm (height × width). The others two monitors (P3, P2) are lined up along the 𝑌 -axis (vertically) at (0, 10) and (0, −10) and have the same size of 1 cm × 1 cm (height × width). Moreover, for the purpose of signal analysis, a component ‘LambdaYPSD monitor’ was used to count neutrons and store their wavelength and their Y position at the detector area. Similar to any other McStas monitor components, the LambdaYPSD monitor captures every neutron arriving at the component. The monitor geometry is simplified to a plane area where the neutron position parameters (x, y) and the wavelength will be recorded [62]. In this way it was possible to examine wavelength gradients in the detector plane caused by the double-monochromator device along both horizontal and vertical directions.
The monochromator plates are parallel and neutrons of corresponding wavelength 𝜆 will undergo a double reflection. The advantage of this arrangement is that the direction of the extracted monochromatic beam is parallel to the initial neutron beam. For setting a defined wavelength, the two plates are rotated to the corresponding angle 𝜃 and the bottom plate is moved horizontally along the neutron beam direction to a position Z determined by ( ◦ ) 𝑍 = ℎ tan 90 − 2𝜃 , (3.2) where h refers to the vertical distance between the plates and Z to the linear translation on the 𝑍-axis of the lower plate respectively, Fig. 2b. The HOPG crystals have a certain mosaicity, which allows for selecting a broader wavelength band around the corresponding wavelength fulfilling the Bragg reflection condition for the set scattering angle 𝜃. By ray-tracing the neutron beam through the double-crystal device, one can expect a spectral divergence depending on the direction of the neutrons flight paths through double reflection as shown in Fig. 2b. The mosaicity of the crystallites will allow smaller scattering angles for the longer wavelengths and larger angles for the shorter wavelengths. Considering the configuration shown in Fig. 2b the wavelength gradient is expected to be along a vertical line, with longer wavelengths on the bottom and shorter wavelengths on the top. In order to study this effect McStas simulations using the described model above were performed. For our experimental investigations we have chosen to focus on the (110) Bragg edge of a steel sample and the (111) edge of a Bronze sample.
3. Double-crystal monochromator
4. Results and discussion
The double-crystal monochromator at the CONRAD-2 instrument consists of two parallel plates, dimensions 6 × 5 cm2 (length × width), of highly oriented pyrolytic graphite HOPG (002) single crystals aligned one above the other with a fixed vertical distance of h = 7.4 cm [3]. In order to gain more intensity no pinhole was used in case of imaging with monochromatic beams. In this case the size of the source D in the L/D collimation ratio was defined as the used guide cross section illuminating the first crystal (30 mm x 30 mm) resulting in 𝐿∕𝐷 = 330 for a distance L of 10 m. The basic idea and concept is described in Treimer et al. [51]. The crystal lattice spacing is given by 𝑑002 = 3.348 Å. As shown in Fig. 2b the orientation and positioning of the monochromator crystal plates is performed by selecting a desired neutron wavelength 𝜆
The simulation performed here is equivalent to an open beam measurement, i.e. there is no sample in the beam to be transmitted. The calculated intensity distribution as a function of neutron wavelength for varying vertical positions on the McStas LambdaYPSD_ monitor for the monochromator set to 4 Å is shown in Fig. 3a. A slope of the neutron wavelength distribution (i.e. gradient of wavelength) along the (vertical) 𝑌 -axis is clearly visible. The analogous horizontal distribution along the 𝑋-axis is shown in Fig. 3b Contrary to the vertical position, the neutron wavelength along the horizontal 𝑋-axis remains the same, i.e. no change in neutron wavelength over the width of the 3
A.M. Al-Falahat, N. Kardjilov, T.V. Khanh et al.
Nuclear Inst. and Methods in Physics Research, A 943 (2019) 162477
Fig. 4. Images in first row – (a), (b) and (c) – show the intensity captured by the PSD-monitor of cross section (50 cm × 30 cm) for three different mosaicities 0.8, 2.0 and 3.0. Second and third rows display wavelength-resolved intensities captured by the five L-monitors. P3, P1, P2 are arranged vertically ((d), (e), (f), bottom to top), P4, P1, P5 horizontally ((g), (h), (j), left to right). The symbols 𝑥c and w represent the centre and the FWHM of a Gaussian fitting respectively. Monochromator set to 4 Å. Table 1 The peak positions and the wave resolutions of the middle region (P1) at a different mosaicities. Scatter bar reflects values given by the software McStas and the Gaussian fit software Origin.
detector occurs. The second order monochromator reflection, which also satisfies the Bragg condition, leads to neutron intensity distribution around 2 Å which can be seen in the graph as well (white arrows). This has to be taken into account also for the experimental setup. For an estimation of the wavelength distribution at different positions on the detector plane, the wavelength monitors were used in two positions (X and Y position) with 10 cm distance between them, see Fig. 4a. The neutron spectra for different mosaicities of the crystals (0.8, 2.0 and 3.0) were measured in boxes of 1 cm × 1 cm in order to estimate the wavelength gradient in the horizontal and vertical directions as described above. The results for the horizontal direction (P4, P1 and P5) and for the vertical direction (P3, P1 and P2) are shown in Fig. 4. In addition, the intensity distribution over the detector plane is shown.
Mosaicity
Peak position (xc ) (P1) (Å)
(𝛥𝜆∕𝜆) (%)
Area under the curve (P1)
0.8◦ 2◦ 3◦
3.9996(4) 3.9980(21) 3.9957(44)
1.36 3.20 4.70
7040.4 8081.5 8070.8
The values for the wavelength resolution taken from Fig. 4 (𝑥c and w, represent the centre and the FWHM of Gaussian fitting respectively) are summarised in Table 1. The following statements can be derived from these results: 4
A.M. Al-Falahat, N. Kardjilov, T.V. Khanh et al.
Nuclear Inst. and Methods in Physics Research, A 943 (2019) 162477
Fig. 5. (a) Radiographic image of steel plate divided into 23 ROIs with dimensions of 1 cm height × 25 cm width from the lower to the upper edge along the Y-direction. (b) Colour map of the wavelength distribution along the Y-direction in the steel plate. (c) Bragg edge positions for three different Y-positions (corresponding to P2, P1, P3 in the simulations) (d) Derivative and Gaussian fit of the Bragg edge transmission profiles for the same three Y-positions. The symbols 𝑥c and w represent the centre and the FWHM of the Gaussian fitting, respectively.
– The wavelength resolution (𝛥𝜆∕𝜆) gets worse with increasing crystal mosaicity, following a linear trend for the used range, see Table 1.
the parameters used in the Monte Carlo simulations and mosaicity of 0.8◦ was used to select different neutron wavelengths. A wavelength scan from 3.6 Å to 4.5 Å in steps of 0.02 Å was performed with an exposure time of three times 30 s per step (taking a median of three images) resulting in 80 min per wavelength scan. For each step the transmission through the mild steel plate was measured by the position sensitive detector. A transmission map was obtained by normalising the images of the sample by the open beam images, thus correcting for the beam inhomogeneity. As a result, a wavelength-dependent neutron transmission through the steel plate can be plotted for each point/pixel of the detector. The analysis of the images was accomplished by using ImageJ [66], where the height of the plate was divided into rectangular regions of interest (ROI) of 1 cm height and 25 cm width, as shown in Fig. 5a, In addition, the wavelength distribution in the steel plate along the Ydirection is clearly displayed in the colour map as shown in Fig. 5b. The wavelength-dependent transmission showing the Bragg edge for bcc steel can be plotted for each ROI in the vertical direction as shown in Fig. 5c for three ROIs (#2, #12 and # 22). In order to investigate the wavelength variation, a ROI#12 is selected to be the middle of the field of view and ROI #2 as well as ROI#22 are at 10 cm distance below and above the middle region as shown in Fig. 5a. The transmission was calculated by using the values from all pixels in the ROI. Due to the large number of pixels (2.105 ) the standard deviation was approximately 2% which explains the smooth curves presented in Fig. 5. The position of the Bragg edge was determined by nonlinear leastsquares fitting. The centre of the Gaussian represents the location of the Bragg edge and corresponds to a Bragg peak shift as shown in Fig. 5d. This shift is a result of the wavelength gradient produced by the doublecrystal monochromator. The obtained Gaussian fitting parameters are shown in Fig. 5d and allow us to compare the experimental data with the Monte Carlo simulation results. Such a comparison is presented in Table 2. An agreement between experimental and simulated data better than 1% for the absolute wavelength values was obtained, which proves
– For a double crystal reflection the angular dispersion of the neutrons in the scattering plane is not depending on the mosaic which can be explained by analysis of scattering vector (k-space) diagram [63]. However, the components out of the plane will depend on the mosaic spread. As a consequence the beam size increases asymmetrically with the increase of crystal mosaicity (Fig. 4a–c). The increase in our case is in the horizontal direction (parallel to the rotation axis of the monochromator crystals) only. The beam spread in vertical direction is defined by the divergence of ◦ the initial beam which is 0.2 / Å resulting in 0.8◦ for a neutron wavelength of 4 Å. For a distance of 10 m between the monochromator and the detector one can calculate the vertical beam extension as 2 ∗ 10 m ∗ tan (0.8◦ ) = 28 cm which agrees well with the result shown in the beam plots in Fig. 4. – The wavelength gradient is constant for a certain beam divergence and crystal configuration does not depend on the mosaicity in the case where the mosaicities are larger than the beam divergence. These conclusions can be explained by analytical description of the double reflection from monochromators using the k-space diagram which is a subject of forthcoming paper being in preparation [63]. 4.1. Comparison with experimental results In order to verify the results from the Monte Carlo simulations a test experiment was performed at the CONRAD-2 instrument [64,65]. For this purpose, a mild steel (body-centred cubic (bcc) crystal structure) plate of dimensions 30 cm × 30 cm × 1 cm (B × H × T) was used to cover the detector. A double-crystal monochromator with 5
A.M. Al-Falahat, N. Kardjilov, T.V. Khanh et al.
Nuclear Inst. and Methods in Physics Research, A 943 (2019) 162477
Fig. 6. (a) Radiograph of a bronze coin (fcc crystal structure) and steel screws (bcc crystal structure) holding the coin. White boxes denote 5 mm-high regions, in which transmission values were averaged. (b, c) Comparison of the Bragg edges measured for bronze and steel by (b) standard scanning and by (c) wavelength gradient translation imaging. The red box corresponds to the wavelength range in (c). Table 2 Comparison of the wavelength shift obtained from the simulation and from the experiment. Mosaicity = 0.8◦ ± 0.2◦ . Position
Upper ROI#22 Middle ROI#12 Bottom ROI#2
𝜆centre (Å)
profile will be obtained. The advantage compared to the traditional wavelength scanning method is an increased wavelength stability due to the missing uncertainty coming from the mechanical fine-positioning system of the monochromator orientation for each step of a scan. An example for such an investigation is presented in Fig. 6, where a Roman coin made of bronze (face-centred cubic (fcc) crystal structure) was fixed by steel screws (bcc crystal structure) and visualised using the two energy-selective methods. For the standard wavelength scan using the double-crystal monochromator a step of 0.01 Å was conducted within 6 h (105 s per step). For wavelength gradient imaging, the double-crystal monochromator was set to 3.95 Å, 4.05 Å and 4.15 Å, where for each setting a stepwise shift of the sample over 20 cm with a step of 5 mm was performed resulting in total measuring time of 3.5 h (105 s per step). The wavelength regions covered by the three measurements are marked with different background colours in Fig. 6c. In the transmission curves from the WGTI measurements intensity drops of less than 1% can be observed. They can be explained by the intensity variations produced from the guide system where the joints between the guide segments (non-reflecting areas) are projected optically on the detector as dark stripes where slight spectral inhomogeneities are expected. If we consider the measured wavelength shift of 0.05 Å/10 cm this means that the wavelength resolution per step of 5 mm would be
Wavelength shift (Å)
Experiment
Simulation
Experiment
Simulation
4.047 4.000 3.946
4.053 3.999 3.945
0.047 0 0.053
0.053 0 0.054
the reliability of the simulations. In addition one can conclude that the wavelength shift over 10 cm distance in the vertical direction is approximately 0.05 Å. 5. Wavelength-gradient translation imaging (WGTI) While seemingly an undesired effect, the wavelength gradient obtained can be used for imaging purposes in order to measure the Bragg edges of different materials without performing a scan with the doublecrystal monochromator. For this it is necessary to select a wavelength in the middle of the Bragg edge. When the sample is translated through the wavelength gradient (e.g. from top to bottom) a narrow Bragg edge 6
A.M. Al-Falahat, N. Kardjilov, T.V. Khanh et al.
Nuclear Inst. and Methods in Physics Research, A 943 (2019) 162477
0.0025 Å without considering the wavelength broadening due to the mosaicity of the crystals. The correspondence of the Bragg edge profiles measured by the two methods shows that wavelength gradient translation imaging can be used for collecting data with excellent sampling resolution and supports a reliable fitting procedure providing the position and the amplitude of the Bragg edge. The sample scan through the wavelength gradient provides much more points for the curve of the Bragg-edge so that the step between 2 points is much smaller than the step in the monochromator scanning technique where limitations related to the mechanical reproducibility of the positions of the crystals introduce additional wavelength uncertainty. In addition the WGTI method can be used for precise wavelength scans at facilities with static DCM device where the position of the monochromator crystals is fixed.
[11] S.H. Williams, A. Hilger, N. Kardjilov, I. Manke, M. Strobl, P.A. Douissard, T. Martin, H. Riesemeier, J. Banhart, Detection system for microimaging with neutrons, J. Instrum. 7 (2012) P02014. [12] E.H. Lehmann, G. Frei, G. Kuhne, P. Boillat, The micro-setup for neutron imaging: A major step forward to improve the spatial resolution, Nucl. Instrum. Methods Phys. Res. A 576 (2007) 389–396. [13] M.A. Hickner, N.P. Siegel, K.S. Chen, D.S. Hussey, D.L. Jacobson, M. Arif, In situ high-resolution neutron radiography of cross-sectional liquid water profiles in proton exchange membrane fuel cells, J. Electrochem. Soc. 155 (2008) B427–B434. [14] A. Hilger, I. Manke, N. Kardjilov, M. Osenberg, H. Markötter, J. Banhart, Tensorial neutron tomography of three-dimensional magnetic vector fields in bulk materials, Nature Commun. 9 (2018) 4023. [15] W. Treimer, Radiography and tomography with polarized neutrons, J. Magn. Magn. Mater. 350 (2014) 188–198. [16] I. Manke, H. Markotter, C. Totzke, N. Kardjilov, R. Grothausmann, M. Dawson, C. Hartnig, S. Haas, D. Thomas, A. Hoell, C. Genzel, J. Banhart, Investigation of energy-relevant materials with synchrotron X-rays and neutrons, Adv. Energy Mater. 13 (2011) 712–729. [17] M.G. Makowska, M. Strobl, E.M. Lauridsen, S. Kabra, W. Kockelmann, A. Tremsin, H.L. Frandsen, L. Theil Kuhn, In situ time-of-flight neutron imaging of NiO–YSZ anode support reduction under influence of stress, J. Appl. Crystallogr. 49 (2016). [18] J. Santisteban, M. Vicente-Alvarez, P. Vizcaino, A. Banchik, S. Vogel, A. Tremsin, J. Vallerga, J. McPhate, E. Lehmann, W. Kockelmann, Texture imaging of zirconium based components by total neutron cross-section experiments, J. Nucl. Mater. 425 (2012) 218–227. [19] J.R. Santisteban, L. Edwards, V. Stelmukh, Characterization of textured materials by TOF transmission, Physica B 385–386 (I) (2006) 636–638. [20] M.G. Makowska, M. Strobl, E.M. Lauridsen, H.L. Frandsen, A. Tremsin, T. Shinohara, L.T. Kuhn, Phase transition mapping by means of neutron imaging in SOFC anode supports during reduction under applied stress, ECS Trans. 68 (2015) 1103–1114. [21] N. Kardjilov, A. Hilger, I. Manke, M. Strobl, W. Treimer, J. Banhart, Industrial applications at the new cold neutron radiography and tomography facility of the HMI, Nucl. Instrum. Methods Phys. Res. A 542 (2005) 16–21. [22] A. Schröder, K. Wippermann, J. Mergel, W. Lehnert, D. Stolten, T. Sanders, T. Baumhöfer, D.U. Sauer, I. Manke, N. Kardjilov, A. Hilger, J. Schloesser, J. Banhart, C. Hartnig, Combined local current distribution measurements and high resolution neutron radiography of operating Direct Methanol Fuel Cells, Electrochem. Commun. 11 (2009) 1606–1609. [23] M.A. Hickner, N.P. Siegel, K.S. Chen, D.N. McBrayer, D.S. Hussey, D.L. Jacobson, M. Arif, Real-time imaging of liquid water in an operating proton exchange membrane fuel cell, J. Electrochem. Soc. 153 (2006) A902–A908. [24] C. Totzke, I. Manke, A. Hilger, G. Choinka, N. Kardjilov, T. Arlt, H. Markotter, A. Schroder, K. Wippermann, D. Stolten, C. Hartnig, P. Kruger, R. Kuhn, J. Banhart, Large area high resolution neutron imaging detector for fuel cell research, J. Power Sources 196 (2011) 4631–4637. [25] S.S. Alrwashdeh, I. Manke, H. Markötter, J. Haußmann, N. Kardjilov, A. Hilger, M.J. Kermani, M. Klages, A.M. Al-Falahat, J. Scholta, J. Banhart, Neutron radiographic in operando investigation of water transport in polymer electrolyte membrane fuel cells with channel barriers, Energy Convers. Manage. 148 (2017) 604–610. [26] J. Kaetzel, H. Markoetter, T. Arlt, M. Klages, J. Haussmann, M. Messerschmidt, N. Kardjilov, J. Scholta, J. Banhart, I. Manke, Effect of ageing of gas diffusion layers on the water distribution in flow field channels of polymer electrolyte membrane fuel cells, J. Power Sources 301 (2016) 386–391. [27] A. Schröder, K. Wippermann, W. Lehnert, D. Stolten, T. Sanders, T. Baumhöfer, N. Kardjilov, A. Hilger, J. Banhart, I. Manke, The influence of gas diffusion layer wettability on direct methanol fuel cell performance: A combined local current distribution and high resolution neutron radiography study, J. Power Sources 195 (2010) 4765–4771. [28] L. Gondek, N.B. Selvaraj, J. Czub, H. Figiel, D. Chapelle, N. Kardjilov, A. Hilger, I. Manke, Imaging of an operating LaNi4.8Al0.2-based hydrogen storage container, Int. J. Hydrogen Energy 36 (2011) 9751–9757. [29] A. Lange, A. Kupsch, M.P. Hentschel, I. Manke, N. Kardjilov, T. Arlt, R. Grothausmann, Reconstruction of limited CT data of fuel cell components using DIRECTT, J. Power Sources 196 (2010) 5293–5298. [30] F. Pfeiffer, T. Weitkamp, O. Bunk, C. David, Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources, Nat. Phys. 2 (2006) 258. [31] C. David, J. Bruder, T. Rohbeck, C. Grunzweig, C. Kottler, A. Diaz, O. Bunk, F. Pfeiffer, Fabrication of diffraction gratings for hard X-ray phase contrast imaging, Microelectron. Eng. 84 (2007) 1172–1177. [32] S.W. Lee, K.Y. Kim, O.Y. Kwon, N. Kardjlov, M. Dawson, A. Hilger, I. Manke, Observation of magnetic domains in insulation-coated electrical steels by neutron dark-field imaging, Appl. Phys. Express 3 (2010) 106602. [33] A. Hilger, N. Kardjilov, T. Kandemir, I. Manke, J. Banhart, D. Penumadu, A. Manescu, M. Strobl, Revealing microstructural inhomogeneities with dark-field neutron imaging, J. Appl. Phys. 107 (2010) 036101. [34] M. Strobl, B. Betz, R.P. Harti, A. Hilger, N. Kardjilov, I. Manke, C. Gruenzweig, Wavelength-dispersive dark-field contrast: micrometre structure resolution in neutron imaging with gratings, J. Appl. Crystallogr. 49 (2016) 569–573.
6. Conclusions The double-crystal monochromator is a very important device for energy-selective imaging at continuous neutron sources. The simulations and analytical calculations presented herein help to understand its functionality and to optimise its parameters. The influence of crystal mosaicity on the beam size and intensity at the sample position was studied. The wavelength gradient caused by crystal mosaicity was simulated and measured and good agreement obtained. A new method for wavelength-gradient translation imaging (WGTI) using a translation scan through the wavelength gradient was proposed and tested. Such wavelength-gradient imaging provides better sampling (∼200 times more points on the plot) of Bragg edge measurements, and can be used to determinate its position and shape by using a fitting function. In addition the new technique allows for wavelength scans at monochromator devices with fixed crystals. Acknowledgement The authors would like to thank Dr. David Jacobson (NIST) for his help in understanding the principle of double-crystal monochromator by applying k-space diagram representation in case of double crystal reflection [63]. References [1] J. Banhart, Advanced Tomographic Methods in Materials Research and Engineering, first ed., Oxford University Press, Oxford, UK, 2008. [2] N. Kardjilov, I. Manke, R. Woracek, A. Hilger, J. Banhart, Advances in neutron imaging, Mater. Today 21 (2018) 652–672. [3] M. Boin, R.C. Wimpory, A. Hilger, N. Kardjilov, S.Y. Zhang, M. Strobl, Monte Carlo Simulations for the analysis of texture and strain measured with Bragg edge neutron transmission, J. Phys. Conf. Ser. 340 (2012) 012022. [4] C. Grunzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, R. Schafer, S. Pofahl, H.M.R. Ronnow, F. Pfeiffer, Bulk magnetic domain structures visualized by neutron dark-field imaging, Appl. Phys. Lett. 93 (2008) 112504. [5] M. Strobl, General solution for quantitative dark-field contrast imaging with grating interferometers, Sci. Rep. 4 (2014). [6] N. Kardjilov, A. Hilger, I. Manke, M. Strobl, M. Dawson, J. Banhart, New trends in neutron imaging, Nucl. Instrum. Methods Phys. Res. A 605 (2009) 13–15. [7] J. Banhart, A. Borbely, K. Dzieciol, F. Garcia-Moreno, I. Manke, N. Kardjilov, A.R. Kaysser-Pyzalla, M. Strobl, W. Treimer, X-ray and neutron imaging Complementary techniques for materials science and engineering, Int. J. Mater. Res. 101 (2010) 1069–1079. [8] C. Grunzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, J. Kohlbrecher, R. Schafer, P. Lejcek, H.M.R. Ronnow, F. Pfeiffer, Neutron decoherence imaging for visualizing bulk magnetic domain structures, Phys. Rev. Lett. 101 (2008). [9] N. Kardjilov, I. Manke, A. Hilger, S. Williams, M. Strobl, R. Woracek, M. Boin, E. Lehmann, D. Penumadu, J. Banhart, Neutron Bragg-edge mapping of weld seams, Int. J. Mater. Res. 103 (2012) 151–154. [10] P. Trtik, J. Hovind, C. Grünzweig, A. Bollhalder, V. Thominet, C. David, A. Kaestner, E.H. Lehmann, Improving the spatial resolution of neutron imaging at Paul Scherrer Institut–The Neutron Microscope Project, Physics Procedia 69 (2015) 169–176. 7
A.M. Al-Falahat, N. Kardjilov, T.V. Khanh et al.
Nuclear Inst. and Methods in Physics Research, A 943 (2019) 162477 [50] M. Strobl, Future prospects of imaging at spallation neutron sources, Nucl. Instrum. Methods Phys. Res. A 604 (2009) 646–652. [51] W. Treimer, M. Strobl, N. Kardjilov, A. Hilger, I. Manke, Wavelength tunable device for neutron radiography and tomography, Appl. Phys. Lett. 89 (2006). [52] Experimental Nuclear Reaction Data (EXFOR), 2018, 2018. [53] M. Boin, NXS: a program library for neutron cross section calculations, J. Appl. Crystallogr. 45 (2012) 603–607. [54] N. Kardjilov, S. Baechler, M. Bastürk, M. Dierick, J. Jolie, E. Lehmann, T. Materna, B. Schillinger, P. Vontobel, New features in cold neutron radiography and tomography Part II: applied energy-selective neutron radiography and tomography, Nucl. Instrum. Methods Phys. Res. A 501 (2003) 536–546. [55] H.G. Esser, A. Carminati, P. Vontobel, E.H. Lehmann, S.E. Oswald, Neutron radiography and tomography of water distribution in the root zone, J. Plant Nutr. Soil Sci. 173 (2010) 757–764. [56] D.S. Hussey, C. Brocker, J.C. Cook, D.L. Jacobson, T.R. Gentile, W.C. Chen, E. Baltic, D.V. Baxter, J. Doskow, M. Arif, A new cold neutron imaging instrument at NIST, Physics Procedia 69 (2015) 48–54. [57] M. Schulz, P. Boeni, E. Calzada, M. Muehlbauer, B. Schillinger, Energy-dependent neutron imaging with a double crystal monochromator at the ANTARES facility at FRM II, Nucl. Instrum. Methods Phys. Res. A 605 (2009) 33–35. [58] N. Kardjilov, A. Hilger, I. Manke, M. Strobl, M. Dawson, S. Williams, J. Banhart, Neutron tomography instrument CONRAD at HZB, Nucl. Instrum. Methods Phys. Res. A 651 (2011) 47–52. [59] K. Nielsen, K. Lefmann, Monte Carlo simulations of neutron-scattering instruments using McStas, Physica B 283 (2000) 426–432. [60] N. Kardjilov, A. Hilger, I. Manke, R. Woracek, J. Banhart, CONRAD-2: the new neutron imaging instrument at the Helmholtz-Zentrum Berlin, J. Appl. Crystallogr. 49 (2016) 195–202. [61] K. Lefmann, K. Nielsen, McStas, a general software package for neutron ray-tracing simulations, Neutron News 10 (1999) 20–23. [62] M. Boin, Developments Towards the Tomographic Imaging of Local Crystallographic Structures, (Ph.D. thesis), Open University, 2010. [63] D. Jacobson, Analytical Description of Double-Crystal Monochromator for Neutron Imaging Applications, 2019. [64] N. Kardjilov, A. Hilger, I. Manke, CONRAD-2: Cold neutron tomography and radiography at BER II (V7), J. Large-Scale Res. Facil. 2 (2016) A98. [65] N. Kardjilov, M. Dawson, A. Hilger, I. Manke, M. Strobl, D. Penumadu, K.H. Kim, F. Garcia-Moreno, J. Banhart, A highly adaptive detector system for high resolution neutron imaging, Nucl. Instrum. Methods Phys. Res. A 651 (2011) 95–99. [66] C.A. Schneider, W.S. Rasband, K.W. Eliceiri, NIH Image to ImageJ: 25 years of image analysis, Nature Methods 9 (2012) 671–675.
[35] R. Woracek, D. Penumadu, N. Kardjilov, A. Hilger, M. Boin, J. Banhart, I. Manke, 3D Mapping of crystallographic phase distribution using energy-selective neutron tomography, Adv. Mater. 26 (2014) 4069–4073. [36] J.R. Santisteban, M.A. Vicente-Alvarez, P. Vizcaino, A.D. Banchik, S.C. Vogel, A.S. Tremsin, J.V. Vallerga, J.B. McPhate, E. Lehmann, W. Kockelmann, Texture imaging of zirconium based components by total neutron cross-section experiments, J. Nucl. Mater. (2011). [37] E. Dabah, B. Pfretzschner, T. Schaupp, N. Kardjilov, I. Manke, M. Boin, R. Woracek, A. Griesche, Time-resolved Bragg-edge neutron radiography for observing martensitic phase transformation from austenitized super martensitic steel, J. Mater. Sci. (2016) 1–7. [38] R. Woracek, D. Penumadu, N. Kardjilov, A. Hilger, M. Strobl, R.C. Wimpory, I. Manke, J. Banhart, Neutron Bragg-edge-imaging for strain mapping under in situ tensile loading, J. Appl. Phys. 109 (2011) 093506. [39] K. Iwase, H. Sato, S. Harjo, T. Kamiyama, T. Ito, S. Takata, K. Aizawa, Y. Kiyanagi, In situ lattice strain mapping during tensile loading using the neutron transmission and diffraction methods, J. Appl. Crystallogr. 45 (2012) 113–118. [40] W. Kockelmann, G. Frei, E.H. Lehmann, P. Vontobel, J.R. Santisteban, Energyselective neutron transmission imaging at a pulsed source, Nucl. Instrum. Methods Phys. Res. A 578 (2007) 421–434. [41] V. Wagner, Z. Kouril, P. Lukas, P. Mikula, J. Saroun, P. Strunz, M. Vrana, Residual Strain/Stress Analysis By Means of Energy-Dispersive Neutron Transmission Diffraction (EDNTD), 1997, pp. 168–171. [42] J.R. Santisteban, L. Edwards, M.E. Fitzpatrick, A. Steuwer, P.J. Withers, M.R. Daymond, M.W. Johnson, N. Rhodes, E.M. Schooneveld, Strain imaging by Bragg edge neutron transmission, Nucl. Instrum. Methods A 481 (2002) 765–768. [43] H.J. Kirkwood, S.Y. Zhang, A.S. Tremsin, A.M. Korsunsky, N. Baimpas, B. Abbey, Neutron strain tomography using the radon transform, Mater. Today: Proc. 2 (2015) S414–S423. [44] T. Sun, A.S. Tremsin, M.J. Roy, M. Hofmann, P.B. Prangnell, P.J. Withers, Investigation of residual stress distribution and texture evolution in aa7050 stationary shoulder friction stir welded joints, Mater. Sci. Eng. A 712 (2018) 531–538. [45] K. Oikawa, Y.H. Su, Y. Tomota, T. Kawasaki, T. Shinohara, T. Kai, K. Hiroi, S.Y. Zhang, J.D. Parker, H. Sato, Y. Kiyanagi, A comparative study of the crystallite size and the dislocation density of bent steel plates using bragg-edge transmission imaging, TOF neutron diffraction and EBSD, Physics Procedia 88 (2017) 34–41. [46] R. Woracek, J. Santisteban, A. Fedrigo, M. Strobl, Diffraction in neutron imaging-A review, Nucl. Instrum. Methods A 878 (2018) 141–158. [47] W. Treimer, A. Hilger, M. Strobl, Slit and phase grating diffraction with a double crystal diffractometer, Physica B 385–86 (2006) 1388–1391. [48] W. Treimer, S.O. Seidel, O. Ebrahimi, Neutron tomography using a crystal monochromator, Nucl. Instrum. Methods A 621 (2010) 502–505. [49] N. Kardjilov, Further Developments and Applications of Radiography and Tomography with Thermal and Cold Neutrons, (Ph.D. thesis), Universität München, 2003.
8