Calculation dependence of shift and size of the sample for X-ray diffraction and SANS Supervisor Dr A. I. Kuklin Rafał Idczak University of Wrocław JINR Summer Student Practicies 2010, Dubna

The goal of the project at JINR Dubna summer practice 1 – recalculation of angles in XPD method 2 – determination of nanodiamonds lattice parameters 3 – determination of nanodiamonds size of domains 4 – estimation of influence of sample size on resolution in SANS 5 – comparison between the SANS spectrometers with and without TOF method

Recalculation angles in XPD

Recalculation for Al 2 O 3

Number of peak α + β2α

Recalculation for nanodiamonds Number of peakα + β2α

Nanodiamonds size of domains Scherrer equation K – shape factor (K = 1) F – FWHM θ – Bragg angle (2θ = 2α) λ – wavelength (λ = Å) τ – mean size of domains Number of peak FWHMθτ [Å]

Estimation of influence of sample size on resolution in SANS for ,   0 d = 5 – 20 mm L = 2 – 12 m = 0.7 – 10 Å

Q resolution for λ = 0.7 Å

Q resolution for λ = 5 Å

Q resolution for λ = 10 Å

YuMO - Frank Laboratory of Neutron Physics, Joint Institute of Nuclear Physics, Dubna, Russia. 1, 2, 3 – pulse reactor parts 4, 6 – collimators 5 – vacuum tube 7 – thermostate 8 – table for sample 10, 11 – Vn standards – detectors

D11 – Institute Laue-Langevin, Grenoble, France Main differences between YuMO and D11 1 – D11 has got 1 PSD detector, YuMO has got 2 detectors 2 – YuMO has got Vanadium standard before detectors 3 – YuMO hasn’t got neutron guide (vacuum tube)

Comparison of the main feature of SANS spectrometers with and without TOF YuMOD11 With TOF ↓ Wavelength resolution (1%) Without TOF ↓ Wavelength r esolution (5-10%) Pulsed reactor source ↓ Power of the flux 2 MW Continuous reactor source ↓ Power of the flux 50 MW Two detectors system ↓ Better dynamic Q rate (Q max /Q min ) Power of the flux + neutron guide + collimation ↓ Better Q-range and background Vanadium standards before detectors ↓ Calibration during measurements Additional calibration measurements needed

Conclusions 1 – It was shown that continuous and pulsed sources have both advantages and disadvantages in characteristics of main features 2 – We obtained the mean size of domains for nanodiamonds sample is 50.5(2.7) Å. 3 – We calculated that resolution dependence of size d of the measured sample in SANS experiment is also dependent of L and. d ↑ Q res ↓ L ↑ Q res ↑ λ ↑ Q res ↑

Special thanks to: Dr A. I. Kuklin (FLNP, JINR, Dubna) Dr S. Z. Pakuliak (BLTP JINR, Dubna) Dr W. Chmielowski (JINR, Dubna) Dr hab. R. Zawodny (UAM, Poznań)

Thank you for attention