The Resolution of Small Angle Neutron Scattering (SANS): Theory and the Experimental

1. The Resolution of Small Angle Neutron Scattering (SANS):Theory and the Experimental Authors: E. L. Maweza (University of Fort Hare in SA) A. KUKLIN (Supervisor: JINR in Dubna)

2. Table of Contents • Introduction • Theory and Literature Review • Experimental Setup • Description of the Equipment • Sample Characterization • Experimental Procedure • Results and discussion • Conclusion • Acknowledgements

3. Introduction • The choice of Small Angle Neutron Scattering (SANS) as a technique to investigate the structure of materials was based at its efficiency in determining their structural properties at length range 10 to 1000 Å. • The SANS experiments require a wide range of momentum transfer (Q range) to determine reliable structural properties of materials. • Frank’s Laboratory for Neutron Physics currently uses a modernized two-detector (“old” and “new”) system in order to increase the Q-range of the instrument.

4. Theory and Literature Review • The intensity of the scattered neutron beam is given by • P(Q) : Periodicity function – Form factor. • Definition: , where • S() : Inter-particle function - Structure Factor. • Definition: and Figure: 1: Schematic representation of a scattering experiment.

5. Bragg’s equation for crystallite periodicity and size • Bragg’s Equation is given by • Combining the Bragg’s equation with momentum transfer we obtain the periodicity of the crystal. • The size of the crystallite is given by the DeBye’s equation. • The wavelength of the neutrons is given by

6. Experimental Setup 1. The two-reflector system. 2. The reactor with the moderator. 3. The chopper. 4,5. The first collimator. 6,7. Vacuum cube. 8. The second collimator. 9,11. Table for the sample holder , sample holder 10. The water bath thermostat 12,14. Vanadium Standards 13. First detector 15,16. Second detector 17. The direct neutron beam detector Figure 2: The two detector YuMO spectrometer http://flnp.jinr.ru/135/

7. Description of the Equipment • The YuMO two-detector system uses 8 homemade ring wire detectors with central holes: • Old detector : 200 mm central hole. • New detector : 80 mm central hole. • SANS experiments are carried out in two stages. • The study of the sample in the beam without vanadium standards. • The sample with both vanadium standards in the beam.

8. Sample Characterization • The sample for this project is Silver Behenate powder (“AgBE”). • Chemical Formula: • Made up of small plate-like crystals • Surface dimensions: (0.2-2.0 µm) and thickness ≤ 1000 Å • The long-period spacing obtained from literature is given by 58.378 Å.

9. Experimental Procedure • The primary aim is to obtain periodicity and the size of the AgBE crystallite. • Origin data analysis program was used to treat the results obtained from the SANS program. • The data obtained and analyzed covers the neutron scattering observed by detectors from the 2nd to the 7th ring. • The peaks occur where the diffraction of the AgBE crystals take place.

10. Results and Discussion Figure 3: Illustration of the periodicity of AgBE by Lorentz Approximation.

11. Periodicity by Gaussian Approximation Figure 4: Illustration of the periodicity of AgBE by Gaussian Approximation.

12. Periodicity by Lorentz Approximation Figure 5: Illustration of the periodicity of AgBE by Lorentz Approximation.

13. The size of the AgBE crystal Figure 6: Illustration of the size of AgBE crystallite.

14. Analysis • Periodicity values that are in agreement with values obtained by other authors were expected for AgBE because it has been adopted as calibration standard. • The considerable deviation that was observed is attributed to systematic errors like: • Time of delay must be calculated more precisely • (not by “vision” as we did.) • Asymmetry of the peaks (as shown in figure 3). • The size of the crystallite clearly becomes constant for bigger rings showing better resolution.

15. Conclusion • The characteristic parameters of AgBE were obtained. • The periodicity ≤ 58 Å • The size of crystallite was about 7300 Å. . • It was shown, that time of delay obtained from raw spectra must be corrected. • In this case we have good agreement with another authors. • The AgBE is suitable as calibration sample.

16. Conclusion • Standard procedure of SAS program gives us the Gaussian resolution value. • Both the Gaussian and Lorentz distribution is suitable for low resolution of SANS method. • For averaging data using Gaussian distribution one should be careful.

17. References • Teixeira, J. (1992) “ Introduction to Small Angle Neutron Scattering Applied to Colloidal Science”. Structure and Dynamics of Strongly Interacting Colloids and Supramolecular Aggregates in Solution. Kluwer Academic Publishers. • Cser, L.(1976)”Investigation of Biological Macromolecular Systems With Pulsed Neutron Source- A Review”. Brookhaven. Symp. Biol. (27) VII3 – VII29. • Keiderling, U., Gilles, R., Wiedernmann, A., (1999) “Application of Silver Behenate Powder for the Wavelength Calibration of a SANS instrument- a comprehensive study of experimental setup variations and data processing techniques”. J. Appl. Cryst., 32., 456 – 463. • A. J.Kuklin, A. KH. Islamov, V. I., Gordelly (2005), Two-Detector System for Small-Angle Neutron Scattering Instrument. Neutron News. V. 16, 16 -18pp

18. Acknowledgements • JINR SA Representation (Dr. Jacobs and Prof. Lekala) • YuMO Team • Raul Erhan • Oleksandr Ivankov • Dmitry Soloviov • Andrey Rogachev • Yury Kovalev

19. Helpful definitions