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)

Table of Contents1. Introduction2. Theory and Literature Review3. Experimental Setup4. Description of the Equipment5. Sample Characterization 6. Experimental Procedure7. Results and discussion8. Conclusion9. Acknowledgements

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.

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

QSQPQI

2QFQP dVeQF rQi

lumeParticleVo

.0

,

exp RRQiQS

Q2k

1k

1k2k

2sin

4),(

Q

Figure: 1: Schematic representation of a scattering experiment.

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

2sin2

dn

nQ

d2

L

t85.3

)2/cos(

w

kD

Experimental Setup

Figure 2: The two detector YuMO spectrometerhttp://flnp.jinr.ru/135/

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 detector15,16. Second

detector17. The direct neutron

beam detector

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.

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.

COOAgCHCH 2023

001d

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.

Results and Discussion

0.0 0.1 0.2 0.3 0.4 0.5 0.6

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Inte

nsity, cm

-1

Q, (Å-1)

Gauss fit of BelOr4sm_B Gauss fit of BelOr4sm_B

Figure 3: Illustration of the periodicity of AgBE by Lorentz Approximation.

Periodicity by Gaussian Approximation

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

2 3 4 5 6 750

51

52

53

54

55

56

57

58

59

60

Literature Values Gaussian Approximation: Peak 1 Gaussian Approximation: Peak 2

Perio

dic

ity, (Å

)

Ring No.

Periodicity by Lorentz Approximation

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

2 3 4 5 6 750

52

54

56

58

60

Theoritical Values Lorentz Approximation: Peak 1 Lorentz Approximation: Peak 2

Perio

dic

ity, (Å

)

Ring No.

The size of the AgBE crystal

2 3 4 5 6 70

1000

2000

3000

4000

5000

6000

7000

8000

DGi1A DLi1B

Avera

ge S

ize o

f C

ryst

al, Å

Ring No.

Figure 6: Illustration of the size of AgBE crystallite.

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.

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.

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.

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

Acknowledgements

1. JINR SA Representation (Dr. Jacobs and Prof. Lekala)

2. YuMO Teami. Raul Erhan ii. Oleksandr Ivankoviii. Dmitry Solovioviv. Andrey Rogachev v. Yury Kovalev

Helpful definitionsidealresolution www

tCons

wresolutiontan

)2/cos(

w

kD