1. Gizo Bokuchava Frank Laboratory of Neutron Physics Joint Institute for Nuclear Research STI 2011, J UNE 6-9, D UBNA

2. Diffraction experiment for measuring of internal stresses inside material or component incident neutron beam diaphragm sample By two detectors at  90  one can measure stresses in both Q 1 and Q 2 directions simultaneously gauge volume Peak shift for steel sample (E=200 Gpa) at stress value of 20 MPa and 200 MPa Peak shift under applied load  a/a 0 = (d – d 0 )/d 0 - peak shift (macro-stress) Bragg law: 2d exp sin  = d = t μs /(505.556 L m sin  ) (TOF-method)  a/a 0 = (d – d 0 )/d 0 - peak shift (macro-stress) Bragg law: 2d exp sin  = d = t μs /(505.556 L m sin  ) (TOF-method)

3. Diffraction peak broadening effects Resolution function (standard Al 2 O 3 sample) and peak broadening effect due to crystallite size (dispersive Ni). Peak broadening due to microstrain. Estimated microstrain value: e=0.012±0.004 (Sample 1) e=0.010  0.004 (Sample 2) W 2 = W 0 2 + C 1 d 2 + C 2 d 4 – diffraction peak width C 1 = 2 – variance of d (microstrain) C 2 ~ 1/ 2 – crystallite size W 0 – instrument resolution function W 2 = W 0 2 + C 1 d 2 + C 2 d 4 – diffraction peak width C 1 = 2 – variance of d (microstrain) C 2 ~ 1/ 2 – crystallite size W 0 – instrument resolution function

4. IBR-2 Spectrometers IBR-2 pulsed reactor Courtesy of J.Emelina

5. High-resolution Fourier diffractometry for long pulse neutron source IBR-2 is a long-pulse neutron source. Δt≈300 μs, R ≈ 0.01 (L=25 m, d=2 Å) IBR-2 is a long-pulse neutron source. Δt≈300 μs, R ≈ 0.01 (L=25 m, d=2 Å) Objective: R ≤ 0.001 (L=25 m, d=2 Å) F-chopper parameters (FSD): N=1024 V max =6000 rpm Ω max =100 KHz Δt 0 ≈10 μs F-chopper parameters (FSD): N=1024 V max =6000 rpm Ω max =100 KHz Δt 0 ≈10 μs Fast Fourier chopper

6. Fourier chopper Slit width 0.7 mm Rotor Stator Transmission function Binary signals 1. P.Hiismaki, Introduction of RTOF-method Neutron Inelastic Scattering, IAEA, Vienna, 1972, 803 2. The first realization of RTOF Fourier-method R.Heinonen, P.Hiismaki, A.Piirto et al, New Methods and Techniques in Neutron Diffraction, Report RCN-234, Petten, 1975, 347 Schematic diagram of the Fourier diffractometer

7. Resolution of a TOF - diffractometer R(t, θ) = Δd/d = [(Δt 0 /t) 2 + (Δθ/tgθ) 2 +  2 +d 2 / 2 ] 1/2, t ~L·d·sinθ, R→0 ifΔt 0 →0 or L→∞ and Δθ→0 or θ→π/2 FSD diffractometer, IBR-2 (RUSSIA) R(t) ≈ ∫ g(ω)cos(ωt)dω, ΔR=Δt 0 ≈ 1/Ω m =(Nω m ) -1 =(1024·100 kHz) -1 ≈10 μs For Δt 0 ≈10 μs and L≈6.5 m: time component Δt 0 /t ≈ 2.5·10 -3 for d=1 Å and 2  =90 

8. R(t) ≈ ∫ g(ω)cos(ωt)dω is Fourier transformation of g(ω). Resolution function (peak shape) 0 ΩmΩm g(ω) is frequency distribution (frequency window) Frequency window FSD: Blackman window g(u)=1 + p·cosπu + q·cos2πu where p=1.03, q=0.08, u=ω/ω max

9. Simulation: RTOF data acquisition

10. FSD – Fourier Stress Diffractometer at the IBR-2 pulsed reactor (JINR, Dubna)

11. 90º-detector Neutron guide Sample position FSD diffractometer Backscattering detector Current status of the detector system : Three modules of ZnS(Ag) +90° (left) detector are installed on FSD. The similar three modules are installed on -90° (right) detector.

12. FSD detector system: combined geometrical and electronic focusing Right bank of 90º-detector consists of 7 ZnS(Ag) based modules. Flexible the scintillation screen allows each element of the detector to approximate the time focusing surface of the scattered neutrons with a necessary accuracy. At the same time, the electronics provides the adding up of signals from separate detector elements on a single TOF- scale. This combination leads to a sharp increase of the solid angle of the detector system and as a results, to an increase of its luminosity preserving high resolution  d/d  4  10 -3. Courtesy of Valery Kudryashov Interior arrangement of the single detector module

13. FSD detector system: combined geometrical and electronic focusing RTOF spectra focusing Scale coefficients for each detector element: k i = L i  sin(  i ) / L 0  sin(  0 ), where L is flight path,  is scattering angle for i-th and base detectors, correspondingly. E.S. Kuzmin, A.M. Balagurov, G.D. Bokuchava et al., J. of Neutron Research, Vol. 10, Number 1 (2002) 31-41

14. Radial collimator Multisectional radial collimator Multisectional radial collimator system: 7° and 10° modules are installed Single modules of the collimator Gauge volume = 2 mm, Number of slits = 160, Length = 600 mm, Focus distance = 350 mm

15. Measured spatial resolution function for radial collimator (FHWM  2 mm) Gauge volume definition: neutron intensity distribution map for radial collimator. Incident beam width ~10 mm Sample surface scan with radial collimator Residual stress study by neutron diffraction within bulk sample using radial collimators

16. FSD resolution function measured on  -Fe powder at maximal Fourier chopper speed V max =6000 rpm Part of neutron diffraction pattern from the  -Fe standard sample measured on FSD in high- resolution mode by BS - (top) and 90  (bottom) detectors. Experimental points, profile calculated by the Rietveld method and difference curve are shown. Measured spectra and resolution function

17. Effective neutron pulse width dependence versus maximal Fourier chopper speed Diffraction peak shape dependence versus maximal Fourier chopper speed Diffraction peak shape and pulse width

18. FSD operation parameters Neutron guidemirror, Ni-covered Beam cross-section at exit10  75 mm 2 Moderator – sample distance28.14 m Chopper – sample distance5.55 m Fourier - chopper (disk)high-strength Al based alloy outer diameter540 mm slit width0.7 mm number of slits1024 max. rotation speed6000 rpm max. modulation frequency100 kHz Thermal neutron pulse width: low-resolution mode320  s high-resolution mode9.8  s Neutron detectors: Backscattering (2  = 141 , 6 Li)2.3  10 -3 ASTRA (2  = ±90 , ZnS)4.0  10 -3 Wavelength interval0.9 ÷ 8 Å Flux at sample position: without Fourier chopper1.8  10 6 n/cm 2 /sec with Fourier chopper3.7  10 5 n/cm 2 /sec

19. 5 – axis HUBER goniometer ,  -axis, x,y,z-table Sample environment Investigated sample installed on “Huber” goniometer.

20. Sample environment Mirror furnace Two standard halogen lamps (output power of 1 kW) with a common focus at sample position provide a working temperature range up to 1000  C (can be upgraded up to 2000  C) and temperature stability of  0.2  C. The design of the furnace allows one to use wide range of neutron scattering angles: in the scattering plane -  360 , in the vertical plane -  22 .

21. Stress rig ”TIRAtest” (F max =60 kN) Sample environment

22. New stress rig LM-20 for FSD diffractometer (produced in NPI, Řež, Czech Republic) Force range - ±20 kN, temperature range - up to 800 ºС Mechanical testing machine LM-20 during test experiments in FLNP JINR. Steel sample with mechanical extensiometer Typical samples Sample heating by direct current

23. New SONIX+ instrument control system developed by Kirilov A.S., Murashkevich S.M., Petukhova Т.B., Yudin V.E. (SONIX - SOftware for Neutron Instruments on X11 base) New SONIX+ instrument control system developed by Kirilov A.S., Murashkevich S.M., Petukhova Т.B., Yudin V.E. (SONIX - SOftware for Neutron Instruments on X11 base) Sonix+ advantages: -GUI user friendly interface -flexible Python-based script language -simple data visualization -low cost Sonix+ advantages: -GUI user friendly interface -flexible Python-based script language -simple data visualization -low cost

24. Four point bending device with test sample. Scan points are shown in blue Lattice strain vs X coordinate Four point bend experiment x Sample

25. E, GPa67.2169.9568.7968.51 22 1.971.780.030.01 Experimental values of Young‘s modulus for D16 Al alloy (russ. grading) Mean value = 68.62  0.82 GPa for D16 alloy Elastic lattice strain versus applied load. Sample Nr.4 undergoes plastic deformation Elastic lattice strain versus sample deformation in elastic region (up to  ~0.004)

26. Further development -Additional elements for detector system; - 2 nd radial collimator; - Sample environment improvement.

27. Conclusions - the obtained results show that the RTOF neutron diffraction method can be used for residual stress studies in various industrial components and new advanced materials; - the achieved parameters of the FSD (high resolution, wide d hkl - range, high contrast of Fourier chopper, appropriate neutron intensity spectral distribution) allows one to study residual stresses with required accuracy. - further expansion of the solid angle of the detector system (preserving a high resolution level  d/d  2.3÷4  10 -3 ) will lead to a sharp increase of experiment effectiveness.

28. Thank you for attention!