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Small Angle X-ray Scattering(SAXS)
Outline
1. SAXS overview
2. SAXS Experiment1. X-Ray source
2. Beam path instrument
3. Detector
3. SAXS Theory1. Basic principle
2. Importance of small angle
3. Interpretation
SAXS Overview
• elastic scattering
• x-ray wavelength0.01 - 0.2 nm
• detection angle0 - 10˚
• distance probenanometers to micrometers
O..Glatter, O. Kratky. “Small Angle X-Ray Scattering”Academic Press, 1982.
SAXS Overview
John A. Pople. “Everything You Ever want To Know About SAXS But Were Afraid To ASK”(http://www-ssrl.slac.stanford.edu/conferences/workshops/scatter2006/talks/pople_saxs_workshop_060522.pdf)
SAXS Experiment : X-ray source
• X-ray is high energy electromagnetic wave(25 keV per photon @ 0.05 nm wavelength)
• Conventional X-ray source : X-ray tube
“X-ray tube” @ wikipedia(http://en.wikipedia.org/wiki/X-ray_tube)
SAXS Experiment : X-ray source
• X-ray is high energy electromagnetic wave(25 keV per photon @ 0.05 nm wavelength)
• Conventional X-ray source : X-ray tube
“X-ray tube” @ wikipedia(http://en.wikipedia.org/wiki/X-ray_tube)
SAXS Experiment : X-ray source : Synchrotron
Synchrotron light source
• high intensity
• high collimation(small divergence)
• wide wavelength tunability
SPring-8, Hyogo prefecture, Japan
SAXS Experiment : X-ray source : Synchrotron
Synchrotron light source
• high intensity
• high collimation(small divergence)
• wide wavelength tunability
“How do synchrotron work?”www.diamond.ac.uk
SAXS Experiment : X-ray source : Synchrotron
D. Atterwood, “Synchrotron Radiation” Berkley University lecture presentation
SAXS Experiment : X-ray source : Synchrotron
Insertion devices
“Undulator” @ wikipedia(http://en.wikipedia.org/wiki/Undulator)
cm
eBK
e
u
2
undulator
K 1
wiggler
K 1
SAXS Experiment : X-ray source : Synchrotron
Insertion devices
cm
eBK
e
u
2
undulator
K 1
wiggler
K 1
D. Atterwood, “Synchrotron Radiation” Berkley University lecture presentation
SAXS Experiment : X-ray source : Synchrotron
Emitted photon energy
bending magnet & wiggler
undulator
mBeEc 2/3 2
)()(6650.0)( 2 TBGeVEkeVE cc
2222 )2/(12/ Ku
222
2
)2/(1)(
)(9496.0)(
Kcm
GeVEkeVE
u
e
SAXS Experiment : Beam path instrument
Optical system (monochromator, collimator)
D. Atterwood, “Synchrotron Radiation” Berkley University lecture presentation
SAXS Experiment : X-ray detector
sequential mode vs parallel mode
sequential
parallel
O..Glatter, O. Kratky. “Small Angle X-Ray Scattering” Academic Press, 1982.
SAXS Experiment : X-ray detector
• gas-filled radiation detector
• scintillators
• semiconductor detectors
• photographic plate
• novel detectors (CCD, solid state)
SAXS Theory : Basic Principle
Radiation Visible light X-rays Neutrons
TypeElectromagnetic wave
Electromagnetic wave
Particle/Wave
Wavelength 400-700 nm 0.01-0.2 nm* 0.01-2.0 nm*
Distance probed >0.01 μm nm to μm nm to μm
Scattered by variations of
refractive index electron densitynuclear scattering properties
* the wavelengths which used in scattering technique, not the entire region of radiation
SAXS Theory : Basic Principle
Scattering cross section of X-rays and neutrons
J. M. Carpenter “Introduction to Theory of Neutron Scattering” Presentation at Argonne National Laboratory, 2006
SAXS Theory : Basic Principle
light scattering
2θ
scattering vector (Q)
Incident beam transmitted beam (k)
scattered beam (k’)
detector
kkQ
'
sin4Q
SAXS Theory : Importance of small angle
from Bragg’s law, distance probed is inversely proportional to Q
Qd
2
sin2
sin4
Q;
high Q : intra-particle, atomic level data
low Q : inter-particle, colloidal level data
since wavelength > 0.2 nm tend to absorbed strongly, small angle is needed for colloidal system
SAXS Theory : Importance of small angle
WAXS vs SAXS• theoretically same experiment
with different condition• experimentally have some
difference in instrument design
WAXS
SAXS
John A. Pople. “Everything You Ever want To Know About SAXS But Were Afraid To ASK”
SAXS Theory : Interpretation
Extracting data from scattering
Q
I(Q)
Q
I(Φ)
Φ
SAXS Theory : Interpretation : Size of Particles
Scattering pattern for dispersed colloid system
2
3
cossin3
QR
QRQRQRQP
QPVNQI PPMP22
ρP ρM
for spherical particle,
SAXS Theory : Interpretation : Size of Particles
Scattering pattern for dispersed colloid system
2
3
cossin3
QR
QRQRQRQP
QPVNQI PPMP22
for spherical particle,
T. Cosgrove “Colloid science : Principle, methods and applications” Blackwell Publishing, 2005
SAXS Theory : Interpretation : Polydispersity
polydispersity gives multiple R value, promote smearing
2
3
cossin3
QR
QRQRQRQP
T. Cosgrove “Colloid science : Principle, methods and applications” Blackwell Publishing, 2005
SAXS Theory : Interpretation : Shapes
Guinier’s law : approximation for Q < 1/RG
aRG
5
3
3/exp 2222GPP RQVNQI
VG dVr
VR 2
//
1;
2
rRG
12
IRG
T. Cosgrove “Colloid science : Principle, methods and applications” Blackwell Publishing, 2005
SAXS Theory : Interpretation : Surface area
Porod law : approximation at high Q
422 SQQI QDAQI s ln6ln ;
2Rarea 2sD
3Rarea 3sDT. Cosgrove “Colloid science : Principle, methods and applications”
Blackwell Publishing, 2005
References
1. O.Glatter; O. Kratky “Small Angle X-Ray Scattering” Academic Press, 1982.
2. L. Feigin; G. Taylor “Structure Analysis by Small Angle X-ray and Neutron Scattering” Plenum Press, 1987.
3. D. Attwood “Synchrotron Radiation for Materials Science Applications” lecture presentation (available at http://ast.coe.berkeley.edu/srms/)
4. J. Pople “Everthing You Ever Wanted to Know About SAXS But Were Afraid to Ask” SSRL workshop(available at http://www.camd.lsu.edu/Workshops/JohnPople.pdf)
5. T. Cosgrove “Colloid science : Principle, methods and applications” Blackwell Publishing, 2005
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