Calculation dependence of shift and size of the sample for X-ray diffraction and SANS

SupervisorDr A. I. Kuklin

Rafał IdczakUniversity 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

cos

cos

sintan

L

L

2cos

tan

cossin

L

Recalculation for Al2O3

Recalculation for Al2O3

Number of peak α + β 2α

1 34.433 35.1462 37.020 37.7713 42.513 43.347

2costan

cossin

L

019.0L

Recalculation for nanodiamonds

Number of peak α + β 2α

1 43.017 43.897

2 74.208 75.909

3 90.059 92.331

Nanodiamonds size of domains

cos

FK

Scherrer equation

K – shape factor (K = 1)F – FWHMθ – Bragg angle (2θ = 2α)λ – wavelength (λ = 1.5405 Å)τ – mean size of domains

Number of peak FWHM θ τ [Å]

1 1.9828 21.729 47.919

2 2.3381 37.529 47.608

3 2.2535 45.598 55.978

Estimation of influence of sample size on resolution in SANS

L

d tantan

Ld

tan

tan

for , 0

d = 5 – 20 mm

L = 2 – 12 m

= 0.7 – 10 Å

12

sin4

2sin

4

Ld

Qres

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 parts4, 6 – collimators5 – vacuum tube7 – thermostate8 – table for sample10, 11 – Vn standards12 - 14 – detectors

D11 – Institute Laue-Langevin, Grenoble, France

Main differences between YuMO and D11

1 – D11 has got 1 PSD detector, YuMO has got 2 detectors2 – YuMO has got Vanadium standard before detectors3 – YuMO hasn’t got neutron guide (vacuum tube)

Comparison of the main feature of SANS spectrometers with and without TOF

YuMO D11With TOF

↓Wavelength resolution (1%)

Without TOF↓

Wavelength resolution (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 (Qmax/Qmin)

Power of the flux + neutron guide + collimation

↓Better Q-range and background

Vanadium standards before detectors↓

Calibration during measurements

Additional calibration measurements needed

Conclusions1 – 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 ↑ Qres ↓

L ↑ Qres ↑

λ ↑ Qres ↑

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