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