On possible exploitation of fully asymmetric diffraction geometry of bent perfect crystals for neutron monochromators in diffraction instruments

Abstract

This paper summarizes recent results of an exhaustive experimental study on possible uses of bent perfect crystal (BPC) slabs of Si employed in the fully asymmetric diffraction (FAD) geometry. In all cases the FAD-BPC slab is employed as the second crystal of the dispersive double-crystal setting in combination with another BPC slab. The FAD geometry was tested in the output beam expansion (OBE) as well as in the output beam compression (OBC) diffraction orientations. A comparison of dispersive parallel $(+ n, - m)$ and antiparallel $(+ n, + m)$ settings was carried out with the FAD-BPC slab in the OBE orientation. High-resolution properties of the dispersive double-crystal settings are demonstrated by several experimental results, e.g. edge refraction or powder diffraction. Due to the given experimental conditions, for FAD geometry studies, we used Si(311) crystal planes having 29.5° with respect to the main surface of the crystal slab.

Keywords

Neutron diffraction Bragg diffraction optics bent perfect crystal

1. Introduction

First publications on the diffraction properties of bent perfect crystal (BPC) slabs in the FAD geometry appeared in the nineteen eighties with the suggestion to use them mainly for one crystal neutron monochromators [5–7,9,11]. Special attention was paid to reflectivity properties of the FAD-BPC slabs [3,9]. However, practical exploitation of them for neutron scattering instrumentation can be found mainly in the next decade, namely, in the case of high-resolution SANS diffractometers [2,4,10,23,24], where the nondispersive $(+ n, - n)$ setting was used. Since that time until recently, when we have focused on the studies of dispersive $(+ n, - m)$ and $(+ n, + n)$ settings [12–20], practically no further neutron diffraction studies have appeared. Though that a design of focusing $(+ n, + m)$ setting employing mosaic crystals appeared in the nineties [21,22], however, there was a lack of experimental results showing the properties of dispersive double-crystal settings employing BPC slabs, namely, with the second BPC slab in the FAD geometry. Figure 1 shows a variety of performances of the double-crystal Si(220) + Si(311) settings in combination with the BPC Si(111)-premonochromator which were tested with the aim of their possible exploitation. The use of the premonochromator is given by the fact that we had at our disposal a three axis neutron optics instrument with the fixed installation of the first BPC slab usually serving as a crystal monochromator. As the second and third axes were free, they were used for the tests of the double-crystal settings. The Si(111)-premonochromator is set for a rather small Bragg angle (15°) and the neutron beam of the wavelength of $λ = 0.162$ nm extracted from the polychromatic beam has quite a large $Δ λ$ spread [1]. Together with the fact that no Soller collimators were used on the neutron beam path, we considered that the employment of the premonochromator had a negligible influence on the resolution properties of the double-crystal setting situated on the second and third axis of the instrument.

Fig. 1.

Schematic sketch of the experimental arrangements (a) and (b) as used for the studies of the properties of the double-crystal settings Si(220) + Si(311) with the Si(311) slab in the FAD-OBE and FAD-OBC diffraction geometry, respectively. SC – scintillation camera was at 50 cm and IP (Imaging plate) with the pixel dimension of 50 μm × 50 μm was at 40 cm from the FAD crystal.

Finally, the dispersive double-crystal Si(111) + Si(311) setting was used, where the former Si(111) premonochromator played an active role (as the first crystal) of the dispersive setting and made possible to free the third axis for installation of samples. Dimensions of all BPC Si slabs were: 200 × 40 × 4 mm (length × width × thickness). For cylindrical bending of the crystal slabs we used four-point bending devices [8].

2. Experimental

(+ n, - m)

arrangement with the convex curvature of the FAD-OBE crystal with respect to the detection unit (case I from Fig. 1(a))

First, some properties of the FAD geometry (case I) related to the behaviour of the peak intensity and FWHM of the output diffraction profiles for different curvatures of the FAD crystal were studied. The obtained results are shown in the Fig. 2. It can be seen that in all cases of fixed curvatures on the bent Si(220) crystal slab, FWHM of the double diffracted beam profile decreases with the increase of the curvature of the FAD crystal. As the corresponding peak intensity of the profiles does not change considerably, it means that the change of FWHM is not given directly by focusing in real space but by the overlapping of the phase space elements of individual crystals as well as by the increase of the crystal effective mosaicity with the curvature [9]. However, it should be noted that thanks to the dispersive arrangement of the Si(220) + Si(311) setting, one can expect a highly monochromatized and highly collimated beam outgoing from the FAD crystal. In the case of small curvatures, the width of the output beam is relatively large and can be used for neutron imaging (see example in Figs 3 and 4). On the other hand, for the large curvature of the FAD crystal, the output beam is concentrated to a small width and can possibly be used for scattering experiments.

Fig. 2.

Peak intensity and FWHM of the diffraction profile dependences on the FAD crystal curvature for fixed curvatures of the Si(220) slab as registered by the scintillation camera: (a) 0.11 m⁻¹, (b) 0.083 m⁻¹, (c) 0.056 m⁻¹ and (d) 0.028 m⁻¹.

Fig. 3.

Refraction images of hypodermic needle and two office staples: $R_{1} = 36$ m, $R_{2} = 36$ m, IP 40 cm from the sample.

Fig. 4.

Holes in the Cd absorber vertically situated in front of the FAD crystal (a) and the image of them for $R_{1} = 36$ m (b) and $R_{2} = 9$ m. IP was at the distance of 10 cm from the FAD crystal. The numbers on the x and y axes mean the pixel (50 μm × 50 μm) numbers.

Fig. 5.

Peak intensity and FWHM of the diffraction profile dependences on the FAD crystal curvature for fixed curvatures of the Si(220) crystal as registered by the scintillation camera: (a) 0.11 m⁻¹ and (b) 0.028 m⁻¹.

Fig. 6.

Summarized maximum peak intensity and minimum FWHM dependences on the curvature of the Si(220) slab.

Fig. 7.

Intensity profiles related to the refraction on the edges of the 10 × 10 mm² α-Fe rod for $R_{1} = R_{2} = 36$ m and IP at 40 cm.

Fig. 8.

Photo of the small piece of the supermirror – (a), supermirror reflections as imaged by IP at the distance of 40 cm – (b) and 3d-representation of the reflections – (c).

3. Experimental

(+ n, - m)

arrangement with the concave curvature of the FAD-OBE crystal with respect to the detection unit (case II from Fig. 1(a))

By rotating the FAD-crystal slab by 180° around the vertical axis, we could test the second curvature mode, the concave curvature with respect to the detection unit. The obtained related results for two radii of curvature $R_{1}$ of the Si(220) crystal are shown in Fig. 5. The dependences for other values of $R_{1}$ had a similar behaviour. Then, the maximum peak intensity and minimum FWHM for several curvatures of the Si(220) slab can be summarized as shown in Fig. 6. Contrary to the case I, the maximum peak intensity and the minimum FWHM of the beam profile were observed in the vicinity of the maximum used curvature of the FAD crystal slab. High collimation of the output beam is demonstrated in the following figures. Figure 7 shows the image of the refraction effects on the edges of an α-Fe rod and Fig. 8 shows the results obtained on a piece of supermirror slab when rocking it in the vicinity of the position roughly parallel to the output beam from the FAD crystal.

Fig. 9.

The dependences of the peak intensity and FWHM of the diffraction profile on the FAD crystal curvature as registered by the scintillation camera for fixed curvatures of the Si(220) crystal: (a) 0.11 m⁻¹, (b) 0.083 m⁻¹, (c) 0.056 m⁻¹ and (d) 0.028 m⁻¹.

Fig. 10.

Intensity profiles related to the refraction on two edges of the 10 × 10 mm² α-Fe rod (compare with Fig. 7).

4. Experimental antiparallel

(+ n, + m)

setting with the convex curvature of the FAD-OBE crystal with respect to the detection unit (case III from Fig. 1(a))

In this case, we used the opposite antiparallel diffraction geometry of the FAD crystal slab with respect to the Si(220) crystal (see Fig. 1(a), case III). Figure 9 shows the basic parameters of the output beam as a function of the curvature of the FAD-BPC slab for several curvatures of the Si(220)-BPC slab. Again, it can be seen from Fig. 9 that depending on the curvature of the FAD-BPC slab one can obtain either a wide beam, of about 20 mm, usable for some imaging experiments (see Fig. 10), or a narrow one, of about 5 mm, for some other diffraction experiments.

Fig. 11.

Examples of the profiles of the beam coming from the bent Si(220) crystal for radii of curvature of 9 m, 12 m and 18 m – (a) and FWHM and the peak intensity of the beam profiles related to the neighbour figure (a) measured at the place just before the FAD-BPC slab – (b).

5. Experimental

(+ n, - m)

arrangement with the convex curvature of the FAD-OBC crystal with respect to the Si(220) crystal (case I from Fig. 1(b))

By using this experimental performance, first, the profile of the beam coming from the Si(220) crystal and incident on the FAD crystal was measured for several curvatures. The obtained results are shown in Fig. 11. Then, as the curvature of both BPC Si(220) and Si(311) slabs were changeable, properties of the profiles of the output beam from the FAD crystal slab as registered by the scintillation camera were studied for different combinations of the crystal curvatures $1 / R_{1}$ and $1 / R_{2}$ . Examples of the obtained results are shown in Fig. 12. From the obtained results the following properties could be derived: FWHM of the profile of the compressed beam going out of the FAD crystal is slightly larger than 3 mm and determined by the thickness (4 mm) of the FAD slab. It is practically independent from its curvature and slightly dependent on the curvature of the Si(220) slab. However, the peak intensity of the profile strongly depends on the curvature of both Si(220) and FAD-Si(311) slabs. Finally, even though no effect of real space focusing was expected, a test was carried out for some chosen curvatures of the Si(220) and FAD-Si(311) crystal slabs (see one of the tests in Fig. 13). As expected, no special focusing on the beam diffracted by the FAD crystal takes place. However, it can be seen from the obtained results that the OBC geometry can provide a narrow and powerful monochromatic beam for high-resolution diffraction experiments on samples of small dimensions as will be demonstrated in Section 7.

Fig. 12.

Examples of the output beam diffraction profiles as registered by SC for $R_{1} = 9$ m and several values of $R_{2}$ – (a), peak intensity and FWHM of the diffraction profile dependences on the FAD crystal curvature for fixed curvatures $R_{1} = 9$ m – (b) and $R_{1} = 36$ m – (c) of the BPC Si(220) slab.

Fig. 13.

Peak intensity and FWHM of diffraction profiles taken at different distances of the camera from the FAD crystal for $R_{1} = 9$ m and $R_{2} = 9$ m.

Fig. 14.

Peak intensity and FWHM of the diffraction profile dependences on the FAD crystal curvature for different radii of curvatures of the Si(220) one: $R_{1} = 9$ m – (a), $R_{1} = 18$ m – (b) and $R_{1} = 36$ m – (c).

Fig. 15.

Peak intensity and FWHM of diffraction profiles taken at different distances of the camera from the FAD crystal for $R_{1} = 18$ m and $R_{2} = 9$ m.

6. Experimental

(+ n, - m)

arrangement with the concave curvature of the FAD-OBC crystal with respect to the Si(220) crystal (case II from Fig. 1(b))

In this case, the FAD-BPC slab was rotated by 180° about the vertical axis making a concave curvature with respect to the bent Si(220) slab. As the mode of the curvature of Si(220) slab and the FAD-Si(311) is the same, the double-crystal setting is less dispersive in comparison with the former case. Similarly to the case I, the properties of the beam profile as registered by the scintillation camera were studied for different combinations of the individual curvatures. The obtained results are shown in the following Fig. 14. Comparison of these figures with the related ones of the previous section reveals a big difference in the properties of both dispersive settings due to the employment of the FAD-BPC slab with the opposite mode of the curvature. As the case II is less dispersive, the peak intensity of the double-diffracted profiles is much higher and their FWHM depends on the curvatures of individual crystal slabs; for $R_{1} = 9$ m FWHM does not practically change while for smaller curvatures of the Si(220) slab (i.e. larger radii), it changes significantly. It means that the output beam becomes more divergent. As shown in the next Fig. 15, this statement was confirmed by the focusing test. For larger radius curvature $R_{1}$ , the dispersity is weaker and also the FWHM behaviour with respect to the distance of the camera from the FAD crystal is different and strongly depends on the mutual ratio of the curvatures (or radii of curvatures) of the Si(220) and FAD-(311) slabs.

7. Dispersive $(+ n, - m)$ DBC monochromator Si(111) + Si(311)

Finally, we tested the dispersive $(+ n, - m)$ DBC setting without the so called premonochromator (see Fig. 16) when in fact the former premonochromator was used as the first crystal of the DBC setting. In such a case, the third axis of the diffractometer was free for the installation of some samples. The width of the slit was changeable and the height of the slit was 20 mm and remained unchanged during the experiment. First, the FAD crystal slab was used in the OBC diffraction geometry in order to test the DBC setting for a possible exploitation in powder diffractometry. A polycrystalline standard sample was placed at a distance of 50 cm from the FAD crystal and the image plate was situated also at a distance of 50 cm from the sample. Then, the second crystal was used in the OBE diffraction geometry for testing the spatial resolution of the output monochromatic beam. In this case, it is necessary to point out that the double-crystal setting could not be fully optimized because of a fixed curvature of the Si(111) crystal. Furthermore, due to the given experimental conditions, the distance between the bent crystals was rather large (1.7 m).

Fig. 16.

The DBC setting with the FAD-geometry of the second Si(311) crystal in OBC as well as OBE orientations.

Fig. 17.

Double crystal rocking curves of the FAD crystal for three different widths of the incident beam: 10 mm – (a), 20 mm – (b), 35 mm – (c) and different radii of curvature of the second crystal slab.

7.1. DBC Si(111) + FAD-Si(311) setting with the second OBC geometry

First, double-crystal rocking curves were measured in order to document the effect of the width of the beam (by changing the width of the incident slit) incident on the second FAD-crystal on the luminosity of the obtained output double diffracted beam. Figure 17 shows the rocking curves obtained by rotating the second FAD crystal, in the vicinity of the Bragg condition, with respect to the first one for three widths of the incident beam. It is evident that the larger the width of the incident beam used, the higher the intensity of the double reflected beam (measured by the peak intensity of the rocking curves) can be obtained. Therefore, in the next step, the intensity of the double diffracted beam as well as FWHM of its profile for peak position on the rocking curve ( $Δ ω = 0$ °) as a function of the FAD-crystal curvature $1 / R_{2}$ were measured by means of the scintillation camera at the distance of 50 cm from the second crystal. The following Fig. 18 shows the obtained parameters of the imaged profiles. Favourite beam property can be seen from Fig. 18 when for the largest curvature of the crystal, a minimum FWHM (slightly less than the crystal thickness) and simultaneously a maximum peak intensity of the profiles are obtained. After the preparation of the monochromatic beam by the double diffraction process, its resolution properties were tested on the standard α-Fe(211) polycrystalline pin of the diameter of 2 mm. The tests were carried out in both so called parallel and antiparallel diffraction geometries (see Fig. 16) and for two widths of the incident beam. Figure 19 shows examples of the powder diffraction profiles displayed by IP. It reveals a high-resolution property for both geometries. The estimation provides the value of FWHM( $Δ d$ /d) of about 3 × 10⁻³ for the case of the Fig. 19(a) and 9 × 10⁻³ for the case of the Fig. 19(d). Figure 20 summarizes the results of FWHM for different curvatures of the FAD slab and for the incident beam-slit width of 35 mm.

Fig. 18.

Properties of the double diffracted beam as a function of the crystal curvature imaged by the scintillation camera for different widths of the beam incident on the second crystal.

Fig. 19.

Examples of the diffraction profiles from the α-Fe(211) polycrystalline pin for two widths of the incident beam slit.

Fig. 20.

FWHMs of the beam profiles from the standard polycrystalline pin for different curvatures of the FAD slab and the incident beam slit width of 35 mm.

7.2. DBC Si(111) + FAD-Si(311) setting with the second OBE geometry

In this case, the FAD geometry (see insert in Fig. 16) provides a wide monochromatic beam. The incident beam is passing along the longest edge of the Si crystal and on the way, neutrons meet a large range of incident Bragg angles determined by the length of the crystal slab as well as its curvature. An example of the expansion of the monochromatic beam is demonstrated in Fig. 21 for the radius of curvature of the FAD-crystal $R_{2} = 12$ m. The opposite FAD geometry providing a wide beam can be exploited, e.g. for imaging. A high parallelism of the double diffracted beam which is characteristic for dispersive double-crystal settings, could be very favourable in this case. The following figures document this property on the imaging of edge refraction profiles. Figure 22 demonstrates the difference of the edge refraction effects obtained on Si and Fe samples and Fig. 23 shows the edge effects obtained on steel comb.

Fig. 21.

Image of the diffracted beam from the FAD-crystal in the OBE geometry for $R_{2} = 12$ m.

Fig. 22.

Refraction on edges of rectangular α-Fe (1 × 1 cm²) and Si (1 × 0.5 cm²) samples.

Fig. 23.

Photo of the steel comb with 4.5 × 4.5 mm² teeth – (a) and the image of the refraction effects on the edges of the individual teeth – (b).

Fig. 24.

Related peak reflectivity vs crystal curvature as calculated for symmetric diffraction geometry of Si(111), Si(220) and Si(311) crystals as well as for the FAD diffraction geometry of the Si(311) one.

8. Summary

Some diffraction properties of the FAD geometry of the BPC Si(311) slab employed in the double-crystal settings with respect to the BPC Si(220) and Si(111) slabs were tested. Monochromatic beam provided by such a double-crystal setting is highly collimated and one can work with open beams without any Soller collimator, which is documented by several attached edge refraction images. In the case of OBC-geometry of the FAD-BPC slab, the width of the monochromatic output beam is narrow and practically determined by the thickness of the FAD crystal. Due to the mutual dispersive setting of the BPC slabs, the double diffracted beam has also a narrow $Δ λ$ /λ spread of the order of 10⁻³ or less. The reflection probabilities (often called as the peak reflectivities) of the Si(111), Si(220) and FAD-Si(311) BPC crystals calculated according to formulae introduced in ref. [3,9] and [18] are for the used curvatures larger than 0.5 and 0.9, respectively (see Fig. 24) and the integrated reflectivity of the double-crystal setting corresponds to the overlapping areas of the individual phase space elements of the BPC Si(220) and FAD-BPC Si(311) or BPC-Si(111) and FAD-BPC Si(311) slabs. Of course, the individual diffraction performances can be practically exploited for high-resolution powder diffraction, namely, at high-flux neutron sources.

Footnotes

Acknowledgements

Measurements were carried out at the CANAM infrastructure of the NPI CAS Řež supported through MŠMT project No. LM2015056. The presented results were also supported in the frame of LM2015074 infrastructural MŠMT project “Experimental nuclear reactors LVR-15 and LR-0”. Bragg diffraction optics investigations are in the Czech Republic supported by the ESS project LM2010011: “Contribution to Partnership in Large Research Infrastructure of Pan European Importance”. We thank Ms. B. Michalcová from NPI ASCR for a significant help in the measurements and basic elaboration of the data.

References

G.E.

Bacon , Neutron Diffraction, Clarendon Press, Oxford, 1975, p. 67 and p. 95.

Hempel ,

Eichhorn ,

Reichel and

Boede , Nucl. Instrum. Methods in Phys. Res. A 381 (1996), 466–471. doi:10.1016/S0168-9002(96)00757-7.

Kulda , A novel approach to dynamical neutron diffraction by a deformed crystal, Acta Cryst. A 40 (1984), 120–126. doi:10.1107/S0108767384000271.

Kulda and

Mikula , A medium resolution double crystal diffractometer for SANS studies, J. Appl. Cryst. 16 (1983), 498–504. doi:10.1107/S0021889883010894.

Mikula ,

Chalupa ,

Kulda ,

Vrána ,

Sedláková and

R.T.

Michalec , An experimental test of a double-crystal monochromator for thermal neutrons based on two bent silicon crystals, J. Appl. Cryst. 18 (1985), 135–140. doi:10.1107/S0021889885009980.

Mikula ,

Krüger ,

Scherm and

Wagner , An elastically bent silicon crystal as a thermal neutron monochromator, J. Appl. Cryst. 23 (1990), 105–110. doi:10.1107/S0021889889012975.

Mikula ,

Kulda ,

Horalík ,

Chalupa and

Lukáš , The spatial condensation of the neutron beam by an asymmetric diffraction in thermal-neutron monochromatization, J. Appl. Cryst. 19 (1986), 324–330. doi:10.1107/S0021889886089288.

Mikula ,

Kulda ,

Lukáš ,

Vrána ,

Ono and

Sawano , Instrumentation components of focusing diffraction used in NPI, ILL, KURRI and PTB, Physica B 276–278 (2000), 174–176. doi:10.1016/S0921-4526(99)01250-8.

Mikula ,

Kulda ,

Vrána and

Chalupa , A proposal of a highly efficient double crystal monochromator for thermal neutrons, J. Appl. Cryst. 17 (1984), 189–195. doi:10.1107/S0021889884011274.

10.

Mikula ,

Lukáš and

Eichhorn , New version of a medium resolution double-crystal diffractometer for the study of a small angle neutron scattering (SANS), J. Appl. Cryst. 21 (1988), 33–37. doi:10.1107/S0021889887008653.

11.

Mikula ,

Lukáš and

R.T.

Michalec , An experimental test of a bent Si crystal as a thermal-neutron monochromator, J. Appl. Cryst. 20 (1987), 428–430. doi:10.1107/S0021889887086345.

12.

Mikula ,

Šaroun ,

Stammers and

Em , High resolution dispersive double bent crystal monochromators Si(111) + Si(311) and Si(111) + Si(400) with a strongly asymmetric diffraction geometry of the analyser for powder diffractometry, Powder Diffraction 34(S1) (2019), S18–S22. doi:10.1017/S0885715619000137.

13.

Mikula and

Vrána , New type of versatile diffractometer with a double-crystal (DC) monochromator system, Powder Diffraction 30(S1) (2015), S41–S46. doi:10.1017/S0885715614001201.

14.

Mikula ,

Vrána and

Korytár , Observation of edge refraction on a conventional neutron diffractometer employing dispersive double-crystal monochromator, Physics Procedia 69 (2015), 320–326. doi:10.1016/j.phpro.2015.07.045.

15.

Mikula ,

Vrána and

Korytár , On the edge refraction contrast imaging on a conventional neutron diffractometer employing dispersive double-reflection crystal monochromator, Journal of Physics: Conference Series 746 (2016), 012028.

16.

Mikula ,

Vrána ,

Pilch ,

B.S.

Seong ,

Woo and

Em , Neutron diffraction studies of double crystal

(+ n, - m)

setting containing a fully asymmetric diffraction geometry (FAD) of a bent perfect crystal (BPC) with the output beam expansion (OBE), J. Appl. Cryst. 47 (2014), 599–605. doi:10.1107/S1600576714001964.

17.

Mikula ,

Vrána ,

Šaroun and

Em , Neutron diffraction studies of a double crystal

(+ n, - m)

setting containing a fully asymmetric diffraction geometry (FAD) of a bent perfect crystal (BPC), Powder Diffraction 32(S1) (2017), S13–S18. doi:10.1017/S0885715616000725.

18.

Mikula ,

Vrána ,

Šaroun ,

Em and

Čapek , Neutron diffraction studies of fully asymmetric diffraction geometry (FAD) of a bent perfect crystal (BPC) with the output beam compression, Acta Physica Polonica A 130 (2016), 1114–1117. doi:10.12693/APhysPolA.130.1114.

19.

Mikula ,

Vrána ,

Šaroun ,

B.S.

Seong and

Woo , Double bent crystal monochromator for high resolution neutron powder diffraction, Powder Diffraction 28(S2) (2013), S351–S359. doi:10.1017/S0885715613000912.

20.

Mikula ,

Vrána ,

Šaroun ,

Woo ,

Em ,

Čapek and

Korytár , Comparison of double crystal

(+ n, - m)

and

(+ n, + m)

settings containing a fully asymmetric diffraction (FAD) of a bent perfect crystal (BPC) with the output beam expansion (OBE), Journal of Physics: Conference Series 746 (2016), 012029.

21.

Popovici and

W.B.

Yelon , Design of microfocusing bent-crystal double monochromators, Nucl. Instrum. Methods in Phys. Res. A 338 (1994), 132–135. doi:10.1016/0168-9002(94)90173-2.

22.

Popovici and

W.B.

Yelon , Focusing monochromators for neutron diffraction, Journal of Neutron Research 3(1) (1995), 1–25. doi:10.1080/10238169508200187.

23.

Šaroun ,

Lukáš ,

Mikula and

Alefeld , J. Appl. Cryst. 27 (1994), 80–88. doi:10.1107/S0021889893006831.

24.

Strunz ,

Šaroun ,

Mikula ,

Lukáš and

Eichhorn , Double bent crystal SANS setting and its applications, J. Appl. Cryst. 30 (1997), 844–848. doi:10.1107/S0021889897001271.

On possible exploitation of fully asymmetric diffraction geometry of bent perfect crystals for neutron monochromators in diffraction instruments

Abstract

Keywords

1. Introduction

7. Dispersive ( + n , − m ) DBC monochromator Si(111) + Si(311)

Footnotes

Acknowledgements

References

7. Dispersive $(+ n, - m)$ DBC monochromator Si(111) + Si(311)