Transcript Slide 1

Resolution function for small angle
neutron scattering
Khaled Gad
Mostafa ashshoush
supervisor
Dr.Alexander Kuklin
Neutron sources
Since the early days of neutron scattering, there has
been an insatiable demand for higher neutron fluxes.
Neutron sources are based on various processes that
liberate excess neutrons in neutron rich nuclei such as Be,
W, U, Ta or Pb. Presently, the highest fluxes available are
around a few 1015 n/cm2 sec. Even though various neutron
sources exist, only a few are actually useful for scattering
purposes. These are:
1- continuous reactors
2- spallation sources
3- some other neutron sources.
1-Continuous reactors
Most of nuclear reactors is continuous fission mode reactor which neutrons are
one of the fission products, the intensities of the neutron at the sample and the detector
are as in the following fig
Spallation
• High energy incoming particle
(typically protons)
• Heavy metal target (Ta, W, U)
• Neutron cascade
• >10 neutrons per incident proton
• low power load per outgoing neutron
(~ 55 MeV)
Fragmentation
• 2.5 neutrons per event
•1 neutron consumed in
sustaining
reaction
• 0.5 absorbed
• high power load per
neutron
(~ 180
MeV)
Universitatea din Bucuresti, Facultatea de Fizica, Septembrie 2008
IBR-2 Pulst Fast Reactor
REGATA
Advantage of neutron scattering
1- Neutrons interact through short-range nuclear interactions.
They are very penetrating and do not heat up (i.e., destroy)
samples.
2- Neutron wavelengths are comparable to atomic sizes and
inter-distance spacing.
3- Neutron energies are comparable to normal mode
energies in materials (for example phonons, diffusive
modes). Neutrons are good probes to investigate the
dynamics of solid state and liquid materials.
Disadvantage of neutron scattering
1- Neutron sources are very expensive to build and to
maintain.
2- Neutron sources are characterized by relatively low fluxes
compared to x-ray sources (synchrotrons) and have limited use
in investigations of rapid time dependent processes.
3- Relatively large amounts of samples are needed: typically 1
mm-thickness and 1 cm diameter samples are needed for
SANS measurements. This is a difficulty when using expensive
deuterated samples or precious (hard to make) biology
specimens.
Sizes of interest = “large scale structures” = 1 – 300 nm or more
•Mesoporous structures
•Biological structures (membranes, vesicles, proteins in solution)
•Polymers
•Colloids and surfactants
•Magnetic films and nanoparticles
•Voids and Precipitates
EQUIPMENT
Reactor parameters:
•Mean power 2 MW,
in pulse 1500 MW
•Pulse frequency of
5 Hz
YuMO Spectrometer: 1 – reflectors;
2 – chopper; 4,6 – collimator;
8 – sample table; 11,12 – detectors;
14 – direct beam detector
Spectrometer
parameters:
•Wavelength 0.5 A to
8A
•Size range of
object 500 A – 10 A
•Size of beam on
sample 8 – 22 mm2
•Detectors of 3He
(home made)
•Detector for direct
beam of 6Li (home
made)
IBR – 2 Reactor
Sizes of interest = “large scale structures” = 1 – 300 nm or more
SANS Approach
 
sin  
2
Q  4
kS
QS
ki

S1
S1
≈
2θ
2 S2
Δθ
3m – 16m
1m – 15m
SSD
≈
SDD
Optimized for ~ ½ - ¾ inch diameter sample
SANS PRINCIPLE


A typical sans result is a graphic of the Scattering
Intensity function of a wavevector Q
Q is defined as
 
sin  
2
Q  4
• where

•Q = wavevector
•Theta = scattering angle
•Lambda = Wavelength of
incident beam
•The scattering intensity is defined as:
I (Q)  P(Q)S (Q)
•Where
•I(Q) = scattering intensity
•Phi = density of particles in volume
•P(Q) = form factor
•S(Q) = structure factor
J. Texeira, Introduction to Small Angle Neutron
Scattering Applied to Colloidal Science, Kluwer
Academic Publishers, Netherlands, 1992
FORM AND STRUCTURE FACTORS
FORM FACTOR
 Concerns each particle and is related to its nuclear
density
 Usually defined as:
P(Q) | F (Q)2 |

volume of particle
(   0 )eiQr dV
Rho is the density of scattering length of the sample
It can be calculated using a simple formula (given
here for heavy water):
D O( 
2

S (Q)   e
Where F(Q) is defined as:
F (Q)  


STRUCTURE FACTOR

Is related to the spatial distribution of the centres of mass

Is usually defined as
D2O / M ) N A (bD  2bO )
Where b is the scattering length of deuterium
respectively oxygen

iQ ( R  R  )

Where R is the position vector of a particle inside the
compound
CONTRAST VARIATION METHODS
•Contrast variation is used when the
sample being studied is made up of a
series of compounds with close scattering
lengths
•One of the most important advantages of
SANS spectroscopy is the ability to change
contrast by isotope substitution
•The most common form of substitution is
changing hydrogen compounds with
deuterium ones
•Another interesting situation appears
when a mixture of normal and deuterated
solvents are obtained in colloidal
suspensions in such a way that the
background scattering length of the
solvent is “erased”. This is called contrast
matching
•We can take as an example a sample
containing three compounds and, using
contrast matching, we can erase the
contrast between two parts allowing us to
analyze the third compound
THE SANS INSTRUMENTAL
RESOLUTION
 Instrumental smearing affects SANS data. In order to
analyze smeared SANS data, either desmearing of the
data or smearing of the fitting model function is
required
THE RESOLUTION FUNCTION
1. THE RESOLUTION FUNCTION
Instrumental smearing is represented by the following 1D convolution smearing integral (suitable for radially
averaged data):
the 1D resolution function is defined as a Gaussian function:
σQ is the Q standard deviation.
2. VARIANCE OF THE Q RESOLUTION
In order to express σQ, differentiate Q on both sides:
Take the square:
VARIANCE OF THE Q RESOLUTION
SANS resolution has three contributions
Geometry part
Wave part
Gravity part
Conclusion
SANS is a powerful method for condensed matter investigation for objects of sizes
between 1 nm to 100 nm – therefore it can be considered a nanoscale procedure
The IBR – 2 reactor at the JINR is adequate for SANS machine
Several
applications for SANS exist in the fields of Biology, Chemistry, Polymers,
Ferrofluids, etc.
The resolution of the device depends and the quality of the information depend on
considering the errors due to wavelength ,finite width of the detector cell ,finite time
of the detector and collimation system .
AKNOWLEDGEMENTS
The authors would like to acknowledge the following:
 Kuklin Aleksandr
 Ahmed Islamov
 Balasoiu Maria
 Raul Erhan
All of the above from the YuMO Group, Condensed Matter Department
We would also like to extend our regards to the organizer of this Practice and all
members of the JINR involved with this project.
Thank you for attention!