High-Resolution Neutron Diffraction Monochromators for Neutron Diffractometry

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1 High-Resolution Neutron Diffraction Monochromators for Neutron Diffractometry Pavol Mikula, Nuclear Physics Institute ASCR Řež near Prague, Czech Republic NMI3-Meeting, Barcelona, 21

2 Motivation Backscattering setting can be easily realized for a rather small take-off angle of the monochromator. Monochromatic beam is highly collimated. λ -spread depends on the effective mosaicity of both reflections participating on the double dif-fraction process ( λ /λ is about 1-3 or less). No Soller collimators are required. If necessary, beam can be defined by slits. Therefore Further studies of multiple reflections (MR) in bent perfect crystals To identify strong MR effects for possible applications in high resolution diffractometry To construct testing multipurpose diffractometer employing MR monochromator Testing of new ideas and diffractometer arrangements, where MRmonochromators or MR-analyzers are employed MC simulations of MR-effects which have not been carried out

3 Neutron optics testing bench Fixed take off angle of the premonochromator λ =.1629 nm ± λ White beam White beam Si(111) premonochromator Si(111) premonochromator MR-monochromator MR-monochromator PSD, IP Sample or an analyzer PSD, IP MR-monochromators - Si(222), Si(2) or Ge(222), Ge(2) set for diffraction in symmetric or asymmetric transmission/reflection geometry

4 Multiple-reflection (MR) monochromator Basic reflection (h,k,l ) (forbidden) Bent perfec t crystal k (h 2,k 2,l 2) Secondary reflection g 1 = g 2 + g 3 (h 3,k 3,l 3) Tertiary reflec tion r 1 = r r 2 3 k+ g2+ g3 k + g 1 Relation for scattering vectors Double reflection realized on (h 2,k 2,l 2 ) and (h 3,k 3,l 3 ) in a bent perfect or mosaic single crystal can simulate a forbidden primary reflection (or strengthen a week one) corresponding to (h 1,k 1,l 1 ). Due to the bending the double reflection reflectivity can be substantially increased that such a monochromator crystal can provide a good intensity of highly monochromatic and highly collimated beam for a further use.

5 Search for multiple reflections in a single crystal Momentum space representation of a multiple reflection process τ m τ Relation for scattering vectors Y τ p = τ m + τ m In the search of strong multiple reflection effects two methods are usually used: a. The method of azimuthal rotation of the crystal lattice around the scattering vector of the primary reflection for a fixed wavelength. b. The method of θ 2θ D scan in the white beam for a fixed azimuthal angle.

6 Search for strong multiple-reflection effects Guide tube Incident beam Bent perfect crystal 2θ For the experimental search of strong multiple reflection effects we used three Si slabs of different cut. [11] [111] [112] [111] Point detector [11] [1] Experimental arrangement with symmetric transmission geometry of the bent perfect Si crystal as used for an identification of umweg-reflections by θ 2θ scanning. Thanks to symmetric transmission geometry, crystal deformation has no influence on the reflectivity related to the basic primary reflection and its higher orders. This is not valid for mosaic crystals.

7 Search for strong multiple-reflection effects 1 Umw 222 Flat crystal Background R=6 m, t = 3 mm Intensity / 2 sec 1 λ =.238 nm 1 Main face of the slab parallel to (112) θ - angle / deg θ 2θ scan taken with the Si crystal slab set for 222 forbidden reflection in symmetric transmission geometry.

8 Multiple reflection monochromator Intensity / 6 sec nm Umw 222 Flat crystal Background R=1 m, t = 5 mm Main face of the slab parallel to (11) θ - angle / deg θ 2θ scan taken with the Si(222) crystal slab set for diffraction in symmetric transmission geometry; if we use Ge(222) slab the corresponding wavelength is.1629 nm.

9 Search for strong multiple-reflection effects 1 λ =.2166 nm λ =.1336 nm Umw 2 Background R = 9 m, t = 4 mm Intensity / 6 s 1 1 Main face of the slab parallel to (11) θ - angle / deg θ 2θ scan taken with the Si crystal slab set for 2 forbidden reflection in symmetric transmission geometry

10 Test of the beam divergence at λ=.2348 nm Intensity / rel. units L SD =.3 m L SD = 1.5 m L SD = 2 m 2 mm slit, R A = 15 m Intensity / rel. units mm slit 1 mm slit L SD = 2 m R A = 26 m Horizontal coordinate / mm Horizontal coordinate / mm FWHM is in this case determined by the spatial resolution of the PSD Images of the obtained beam profiles (intensity distribution on the horizontal scale) taken by 1d-PSD. L SD the distance between the bent crystal and the PSD.

11 Examples of the α-fe powder diffraction profiles taken with the Si(222) mutiple-reflection monochromator λ =.1565 nm Relative intensity Fe(11) FWHM = 7.13 (7) / ' Fe(2) FWHM = 6.43(13) / ' Fe(211) FWHM = 6.35(9) / ' Fe(22) FWHM = 5.9(16) / ' 2 45, 45,5 46, 66, 66,5 83,5 84, 19,5 11, 11,5 2θ S / deg The obtained FWHM is determined by the width of the sample (Φ=2 mm) and the spatial resolution of the PSD (1.5 mm) No Soller collimators!!!

12 Experimental test with a multiphase steel sample The high-resolution diffraction performance we used for investigation of Fe-reflections in an induction hardened S45C rod (Φ=2 mm) having different phase composition at different distances from the rod axis. For determination of gauge volume we used 2 mm input and output slits in the incident as well as diffracted beam, respectively. Relative intensity S45C steel Exp.data Fit Gauss 1 Gauss 2 Gauss 3 λ =.1565 nm Relative intensity S45C steel Exp. data Fit Gauss 1 Gauss 2 λ =.1565 nm θ / deg Induction-hardened S45C steel diffraction profile taken at 2 mm under the surface with the fitted profiles corresponding to the perlitic, ferritic and martensitic phases θ / deg Induction-hardened S45C steel diffraction profile taken at 4 mm under the surface with the fitted profiles corresponding to the ferritic and martensitic phases.

13 Experimental high-resolution neutron radiography tests In addition to a possibility of using a highly collimated beam for conventional absorption radiography with a imaging plate at a rather large distance from the sample, highly collimated neutrons obtained by means of dispersive multiple reflection monochromator can be considered as plane waves and permit to design a completely new technique of phase contrast neutron radiography experiments at a distance much smaller in comparison with the conventional pin-hole geometry. The folloving preliminary tests on office staples at λ =.238 nm have been carried out with the imaging plate situated at the distance of 7 cm from the sample.

14 First neutron radiography tests Office staples Screw λ =.238 nm Iint - Iav Y / mm Y / mm X / mm X / mm X / mm

15 Radiography tests at λ =.165 nm I Int - I av I Int / relative (1) (2) (3) (4) (5) Neutron radiography of the office staple (1), Cu-wire (2), hair (3), needle- grouting point (4), graphite black lead (5). X-Y: Pixel numbers, spatial resolution 5 µm 1 pixel. (1) (2) (3) (4) (5) X / mm Intensity data integrated in the Y-direction I Int - I av (1) (2) (3) (4) (5) X / mm Office staple X / mm Intensity distribution in the vicinity of the image of the chosen samples

16 New investigations Intensity / 6 sec Crystal thickness 5 mm Bending radius1 m Main face (11) 5 6 Multiple reflections accompanying the (111) reflection Flat crystal Background 7 8 (a) Intensity / 6 sec Multiple reflections accompanying the (111) reflection Crystal thickness 3 mm Bending radius R = 6 m Main face (112) (b) θ - angle θ - angle Enlarged parts of the θ-2θ scans where strong multiple reflections accompanying the allowed 111 reflection were observed P. Mikula, M. Vrána, J. Šaroun, B.S. Seong, V. Em and M.K. Moon, Multiple neutron Bragg reflections in single crystals should not be considered negligible, In the Proc. of Int. Workshop on Neutron Optics NOP21, Alpe d'huez near Grenoble, France, 17-19th of March 21, submitted to NIM.

17 Peak N. 1a 1a 1a 1a 1a 1a 2a 2a 3a 3a 4a 4a 4a 4a 5a 5a 6a 6a 7a 7a 7a 7a 8a 8a Primary, secondary and tertiary reflections 111/315/44 111/153/44 111/311/ /44/ /44/ /242/ /224/ /135/ /355/ /444/ /313/44 111/44/ /133/22 111/22/ /353/ /444/ /511/62 111/62/ /133/ /151/4 111/4/ /224/ /153/ /422/513 Wavelength /Å Bragg angle /deg Peak N. 1b 1b 2b 2b 3b 3b 3b 3b 3b 3b 4b 4b 4b 4b 5b 6b 7b 7b Primary, secondary and tertiary reflections 111/135/ /315/ /533/ /353/ /117/26 111/117/26 111/317/ /137/ /246/ /426/ /311/4 111/131/4 111/331/44 111/22/ /242/ /335/ /224/ /224/133 Wavelength /Å Bragg angle /deg Calculated parameters related to the peaks accompanying 111 reflections for two different cuts of the slab

18 Monte Carlo simulations of parasitic and multiple Bragg reflections 12 sample flux [1 7 s -1 cm -2 ] IN2, 1999 measured values simulation with MR simulation without MR Comparison of measured in 1999 and simulated monochromatic flux at IN2. Experimental data from J. Saroun, J. Kulda, A. Wildes, A. Hiess, Physica B (2) wavelength [A] A new ray-tracing code has been developed, which permits quantitative predictions of the intensities of parasitic and multiple reflections (Umweganregung) in elasticaly bent perfect crystals including Good agreement with experimental data Part of the next RESTRAX release - available for instrument development: prediction of monochromatic flux, filterig properties, new monochromator and analyzers...

19 Comparison with experiment - Umweganregung Intensity [1 3 / 6s] (5) experimental MC simulation peak (5) = = = = θ [deg] Measurement: POLDI, GKSS Geesthacht, MC simulation: RESTRAX ver J. Šaroun, P. Mikula, J. Kulda, Monte Carlo simulations of parasitic and multiple reflections in elastically bent perfect single-crystals, In the Proc. of Int. Workshop on Neutron Optics NOP21, Alpe d'huez near Grenoble, France, 17-19th of March 21, submitted to NIM.

Application: Multianalyzer systems in transmission arrangement Simulated setup - SIMRES source (sample) 5 x 2 mm 2, isotropic, uniform spectrum distance=15 cm crystals 2 x 2 mm, 1 x 1 mm sandwich

20 Application: Multianalyzer systems in transmission arrangement Simulated setup - SIMRES source (sample) 5 x 2 mm 2, isotropic, uniform spectrum distance=15 cm crystals 2 x 2 mm, 1 x 1 mm sandwich monochromatic focusing to the source mutual angle θ =1.5 o ~ channel of a flatcone multianalyzer intensity [rel. units] segment 2 segments 3 segments wavelength [Å] Transmitted spectrum after the 3rd crystal

Search and testing some strong multiple-reflection effects 26 25 (3-1 -1)+(3-1 3) (3 1-1)+(3 1 3) Bragg angle θ / deg 24 23 22 21 (5 1 1) (5-1 1) 2 (1 1-1)+(1 1 3) (1-1 1)+(1-1 3) -6-4 -2 2 4 6

21 Search and testing some strong multiple-reflection effects (3-1 -1)+(3-1 3) (3 1-1)+(3 1 3) Bragg angle θ / deg (5 1 1) (5-1 1) 2 (1 1-1)+(1 1 3) (1-1 1)+(1-1 3) Azimuthal angle φ / deg (x1) I / 1 s θ = -. o θ = -.15 o θ = -.3 o Azimuthal angle Φ / deg θ = ο θ =.15 ο θ =.3 ο Imaging by PSD detector Calculated Azimuth-Bragg angle dependences and the experimental results for the crystal Si(2) slabs with the main face parallel to (1). λ =.222 nm.

22 Search for strong multiple-reflection effects: Azimuthal rotation of the crystal slab for a fixed neutron wavelength Bragg angle θ / deg (-3-1 3) (-1-3 3) (-3 1 3) (1-3 3) Ge(222) (-3 1 5) (-3-1 5) (-1-3 5) (1-3 5) (-1 3 3) (1 3 3) (3 1 3) (3-1 3) Azimuthal angle φ / deg (x1) I / 1 s θ = o θ =.1 o θ =.15 o θ =.21 o θ =.27 o Azimuthal angle φ / deg Azimuth-Bragg angle relationship for multiple reflection occurrences related to the 222 reflection in diamond structure. Φ = o corresponds to the position of the crystal slab with the main face parallel to the 112 planes and perpendicular to the scattering plane. θ =3.8 o is the mean Bragg angle for Ge(222) reflection at the fixed wavelength of λ=.1657 nm. Intensity versus azimuthal angle dependence for Ge(222) bent crystal slab of the thickness of 4 mm and having the main face parallel to the (112) plane for different θ from the mean Bragg angle of θ =3.8 o. Asymmetric transmission geometry, R=9 m.

23 Set of 7 office staples, λ =.165 nm Relative intensity (normalized) Relative intensity (normalized) L = 36 cm Distance / mm L = 96 cm Distance / mm Relative intensity (normalized) Relative intensity (normalized) L = 66 cm Distance / mm L = 13 cm Distance / mm Dependence on the distance of the IP from the sample

$235 nm 35 Relative intensity 3 25 2 15 1 5-5 -1-15 1 2 3 4-2 94 96 98 1 12 14 16 18 11 112 114 116 Distance / mm Properties: Visibility of the refraction effects depends on the$

24 4 types of office staples, λ =.235 nm 35 Relative intensity Distance / mm Properties: Visibility of the refraction effects depends on the curvature of the MR monochromator Refraction effects can be observed at the distance of 3 cm from the sample IP at the distance of 5 cm from the sample

25 hair hair thread hyp. needle b. lead Cu wire o. staple hyp. needle office staples Distance / mm λ =.165 nm Relative intensity (normalized)

26 Preparations of the search of MR on the neutron optics testing bench Bragg angle θ / deg Bragg angle θ / deg (-1 3-3) (-2 2 4) (-2 6 ) (-5 3 1) Si(111) (1 5 1) (-4 ) (-1 5 3) Ge(111) (-4 2-2) (-3 5-3) (-4 4 4) ( 6 2) (-5 1-1) (-4 6 2) (-5 5-1) (-3 1-3)+(-2-2) ( 4 4)+(1 3 3) 12 (-6 2 ) (-1 7 1) (-5 5 3)+(-6 4 2) (-3 7-1)+(-4 6-2) (-6 4-2) (-3 7 3) (-5 7 1)+(-6 6 2) 11 (-2 6 4) (-5 1 3) ( 6-2) (-5 3-3) Azimuthal angle φ / deg (x1) 34 (-1 5-1) (-3 3 3) Si(222) 31 (-3 5 3) (-3 5-1) Ge(222) 3 (-3 1-1)+(1 5 3) 29 (1 1-1) (1 1 3) (-3 1 3) (1 5-1) Azimuthal angle φ / deg (x1) Bragg angle θ / deg Bragg angle θ / deg (2-2 4) (-2 2 4) (-1-3 5) (-3-1 5) (1-3 1) (1 1 5) (-3 1 1) Si(111) (-2 6) ( -2 6) Ge(111) (-3-3 5) (-3 1 5)+(-4 4) (1-3 5)+( -4 4) (-4-2 2) (-2-2 )+(-3-3 1) (-2-4 2) (-4-2 6)+(-3-1 7) (-2-4 6)+(-1-3 7) (-1 1 7) (1-1 7) (-3-5 3) (-5-3 3) (-1 3 5) (3-1 5) Azimuthal angle φ / deg (x1) (-3-1 3) (-1-3 3) Si(222) (-3 1 3) (1-3 3) (-3-1 5) Ge(222) (-1-3 5) (1-3 5) (-3 1 5) (-1 3 3) (1 3 3) (3 1 3) (3-1 3) Azimuthal angle φ / deg (x1) Calculated Azimuth-Bragg angle dependences for the crystal slabs with the main face parallel to (22) and (112) planes, respectively.

27 Plans Further studies will be carried out on Si(2) - forbidden, Si(4) allowed, Si(24) forbidden, Si(424) forbidden. Three axis arrangements in combination with PSD will be tested High resolution radiography studies High resolution powder diffraction studies Studies of mosaic distribution of mosaic single crystals Reflectivity studies of single crystals etc.

28 Sandwich type two crystal dispersive monochromator (continuation) (hkl) 2 (hkl) 1 Ψ 2 Ψ 1 Properties: Rather small take-off angle A large Bragg angle (at least) of one reflection Good peak reflectivity of the bent perfect crystals Obtained neutron current corresponds to intersection of two corresponding phase-space elements Possible combinations of bent perfect crystal slabs: Si(h 1 k 1 l 1 ) + Si (h 2 k 2 l 2 ), Si(h 1 k 1 l 1 ) + Ge(h 2 k 2 l 2 ). Depending on the cut of the individual crystal slabs many convenient reflection combinations can be found.

29 Choice of the crystals and reflections For the preliminary test we used the following combination: The first Si slab had the main face parallel to the planes (1-1) and the longest edge parallel to the vector [111]. The second Si slab had the main face parallel the planes (11-1) and the longest edge parallel to the vector [112]. Si(22) (Ψ 22 = o ) + Si(331) (Ψ 331 =-22. o ), θ 22 =31.39 o θ 331 =53.39 o λ=.2 nm Si(22) (Ψ 22 = o ) + Si(4-4) (Ψ 44 = o ), θ 22 =25.99 o θ 44 =61.22 o λ=.168 nm Si(22) (Ψ 22 = o ) + Si(331) (Ψ 331 = o ), θ 22 =4.45 o θ 331 =88.98 o λ=.249 nm Si(311) (Ψ 311 =31.48 o ) + Si(333) (Ψ 333 = o ), θ 311 = o θ 333 =67.67 o λ=.193 nm Si(311) (Ψ 311 = o ) + Si(331) (Ψ 331 = o ), θ 311 =39.3 o θ 331 =56.35 o λ=.27 nm Si(111) (Ψ 111 = o ) + Si(11-1) (Ψ 11-1 =-29.5 o ), θ 111 =75.25 o λ=.66 nm Si(111) (Ψ 111 = o ) + Si(11-1) (Ψ 11-1 =-29.5 o ), θ 111 =14.75 o λ=.16 nm

30 Experimental test with the premonochromator Bent Si(111) premonochromator Ψ 1 (hkl) 2 (hkl) 1 Ψ 2

31 Experimental test with the premonochromator Si(111) (Ψ 111 = o ) + Si(11-1) (Ψ 11-1 =-29.5 o ) θ 111 =75.13 o λ=.66 nm For the test, λ=.22 nm and 3rd order reflection was used Bent Si(111) premonochromator (hkl) 1 Peak intensity / relative units Si(333) + Si(33-3) λ =.22 nm R = 12.5 m - (hkl) 2 Ψ 2 1 Take-off angle 2θ S =59 o Rocking angle ω / min of arc Rocking curve of the sandwich with respect to the premonochromator

32 Experimental test with the premonochromator Measurements with higher orders Si( ) (Ψ 333 = ο ) + Si( ) (Ψ 33 3 = 29.5 ο Si( ) (Ψ 444 = ο ) + Si( ) (Ψ 44 4 = 29.5 ο Counts / 6 s Si(333) + Si(33-3) λ =.22 nm R= 12.5 m Counts / 6 s Si(444) + Si(44-4) λ =.1515 nm R = 12.5 m Channel number Channel number Diffraction profiles as seen by 1d-PSD at the optimum position of the sandwich with respect to the premonochromator

33 Experimental test with the premonochromator Si(22) (Ψ 22 = o ) + Si(4-4) (Ψ 4-4 = o ) θ 22 =25.99 o θ 44 =61.22 o λ=.168 nm Si(22) (Ψ 22 = o ) + Si(33-1) (Ψ 33-1 = o ) θ 22 =4.45 o θ 33-1 =88.98 o λ=.249 nm Take-off angles 2θ S =7.46 o 2θ S =97.6 o Counts / 2 s Si(22) + Si(4-4) λ =.1683 nm R = 15 m R = 33 m Counts / 6 s Si(22) + Si(33-1) λ =.249 nm R = 15 m R = 33 m Channel number Channel number Diffraction profiles as seen by 1d-PSD at the optimum position of the sandwich with respect to the premonochromator

Pavol Mikula al. Nuclear Physics Institute, Řež. Czech Republic

Pavol Mikula al. Nuclear Physics Institute, 2 68 Řež Czech Republic Kuala Lumpur, July 2-4, 29, 2nd RCM of the IAEA F1-RC-156.1 on Improved production and utilization of short pulsed, cold neutrons at