1. Materials Characterization Lab
www.mri.psu.edu/mcl
SMALL ANGLE XRAY SCATTERING (SAXS)
AUGUST 10, 2005
Mark S. Angelone
msa3@psu.edu

2. Materials Characterization Lab
www.mri.psu.edu/mcl
Summer Characterization Open Houses
Technique Time Date Location
Thermal analysis (TGA, DTA, DSC) 9:45 AM June 8 250 MRL Bldg.
Transmission Electron Microscopy (TEM/STEM) 9:45 AM June 15 114 MRI Bldg
Scanning electron microscopy (SEM) 9:45 AM June 22 541 Deike Bldg.
Analytical SEM 11:00 AM June 22 541 Deike Bldg.
X-ray Diffraction (XRD) 9:45 AM June 29 250 MRL Bldg.
Dielectric Characterization (25 min lecture only) 9:45 AM July 6 250 MRL bldg.
High temperature sintering lab (20 min lecture only) 10:15 AM July 6 250 MRL Bldg.
Focused Ion Beam (FIB) 9:45 AM July 13 114 MRI Bldg
TEM sample preparation 11:00 AM July 13 114 MRI Bldg
Orientation imaging microscopy (OIM/EBSD) 9:45 AM July 20 250 MRL Bldg.
Chemical analysis (ICP, ICP-MS) 9:45 AM July 27 541 Deike Bldg.
Atomic Force Microscopy (AFM) 9:45 AM August 3 114 MRI Bldg
Small angle x-ray scattering (SAXS) 9:45 AM August 10 541 Deike Bldg.
Particle Characterization 9:45 AM August 17 250 MRL
X-ray photoelectron spectroscopy (XPS/ESCA) 9:45 AM August 24 114 MRI Bldg
Auger Electron Spectroscopy (AES) 11:00 AM August 24 114 MRI Bldg
NOTE LOCATIONS: The MRI Bldg is in the Innovation Park near the Penn Stater Hotel; MRL Bldg. is on Hastings Road.
More information: www.mri.psu.edu/mcl

3. Materials Characterization Lab
www.mri.psu.edu/mcl
Materials Characterization Lab Locations
MRI Bldg:
XPS/ESCA, FIB
SIMS, TEM, HR-
TEM, FE-Auger,
MRL Bldg:
Hosler Bldg:
AFM, XRD
SEM, XRD, OIM, DTA,
SEM,AFM,ESEM, FE-
DSC, TGA, FTIR, Penn Stater
SEM, EPMA, ICP,
Hotel
Raman, AFM, Powder,
E&ES Bldg: ICP-MS,BET, SAXS
dielectric, prep, shop,
SEM
IC, UV-Vis
Route 322
Steidle Bldg:
Atherton Street
Nanoindenter
(322 Business)
I-99
Park Ave.
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Community
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Shortlidg
Hospital
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Burrowes Road
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Pollock Road
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North
Hastin
Deike Bldg: gs Ro
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College Ave.

4. Materials Characterization Lab
www.mri.psu.edu/mcl
MCL SERVICES
• Facilities/Instruments
• User Training
• Operators/Analyst for hire
• 24/7
• Online bookings
• User fees
• website/contacts to get started

5. Materials Characterization Lab
www.mri.psu.edu/mcl
200 mesh
400 mesh

6. Materials Characterization Lab
www.mri.psu.edu/mcl
Scattering ‘Live’ Demo
Real Space Reciprocal Space
d1
d2 = d1/2
Smaller d yields larger SD
Scattered Beam (1st order)
θ
SOURCE Direct Beam - - - - - - -
θ SD
Scattered Beam (1st order)
Smaller
TAN θ = For
Sample/Detector D
SD/D Larger d

7. Materials Characterization Lab
www.mri.psu.edu/mcl
Bragg Scattering (WAXS-XRD)
ηλ = 2 d sin θ
λ = Cu Kα = 1.5401 Å
q =(4π/λ) sin θ = 2 π/d
d 2θ
10Å (0.001 Micron) 8.84º 0.628 A-1
0.126 A-1
50Å 1.17 º
0.063 A-1
100Å 0.88 º
0.021 A-1
300Å 0.29 º
0.010 A-1
600Å 0.15 º
0.006 A-1
1000Å 0.09 º
Atomic Structures
WAXS (Cu Ka, 2-160 2θ) Sub Angstrom - 10Å
Nano/ Colloidal
(PSU)
Laboratory SAXS 10Å - 1000Å
Structures
Synchrotron SAXS/SANS 10Å – several 1000Å

8. Materials Characterization Lab
www.mri.psu.edu/mcl
What kinds of materials?
Compiled by Earle Ryba

9. Materials Characterization Lab
www.mri.psu.edu/mcl
What kinds of materials?

10. Materials Characterization Lab
www.mri.psu.edu/mcl
What kinds of materials?

11. Materials Characterization Lab
www.mri.psu.edu/mcl
Examples from literature
Polymer dendrimers
dilute solns in CH3OH to get dendrite sizes
dilute so dendrimers don’t correlate
Alkanediols
solns in water to study clustering
heavy water improves contrast (sans)
Water-based polymer latexes
use anionic surfactant to suspend in water
Macromolecular foams
wafers cut & immersed in toluene to get swelling
banded matls are translated in situ
Microemulsions
oils in water to get droplet size

12. Materials Characterization Lab
www.mri.psu.edu/mcl
Examples from literature
CVD SiGe films
µ-thin films stacked to get Ge heterogeneity
Nanotubes
use surfactant in water & sonicate; place in quartz cells
to study nanotube aggregation
Powders
thin-walled capillaries
Polymers
study crystallization processes in situ in hot cell

13. Materials Characterization Lab
www.mri.psu.edu/mcl
Examples from literature
Thin films on glass substrates
as is, but requires grazing incidence
Random crystalline block copolymers
rheology study in situ in rotating parallel disk cell
to get crystal alignment and grain rotations
Splat-cooled glass
in situ annealing study to follow pptn of PbTe
nano-crystals

14. Materials Characterization Lab
www.mri.psu.edu/mcl
Examples from literature
Blown polymer films
special cell for in situ studies
Liq. Crystals
special magnetic cell for molecule rotation
Ionomers
cell w/ kapton windows
Hi pressure studies
diamond windows

15. Materials Characterization Lab
www.mri.psu.edu/mcl
Mouse bone

16. Materials Characterization Lab
www.mri.psu.edu/mcl
Reciprocal Space Reciprocal Space
Real Space Real Space
I(q)
⏐A⏐
Γ (r)
⏐A⏐2
ρ (r) I.F.T.
F.T. 1/r (q)
q r
r
1/r (q)
Not Possible By Direct Calc
Calc – Scattering Theory – F.T.
Calc – Auto Correlation Function of ρ (r)
Large r
Correlation function, radial
Large r Amplitude/Phase
distribution
Observed scattering
Particulate shapes Spectra of scattering
intensity-
Phase mix from individual scatters
Small r
Noise/truncation
Large period structures (continuous/discrete)
Pair (Radial) distribution: Short
effects
range atomic ordering
Small r
(amorphous materials)
Atomic positions
•Crystals
Large r (SAXS) Diffuse scatter Patterson function: Interatomic
•amorphous
Small r (WAXS) Diffraction dominates vectors (crystals)
for xtals, diffuse scatter for liquids,
amorphous solids

17. Materials Characterization Lab
www.mri.psu.edu/mcl
Analytical Interpretation
Model ρ(r) → calculate I(q) → fit to observed I(q)
Or
Model ρ(r) → calculate Γ(r) → fit to F.T. of observed I(q)
(models cast in parameters of size, shape, dispersity, thermo mixing
energy, etc.)

18. Materials Characterization Lab
www.mri.psu.edu/mcl
Common SAXS Models
DILTUE PARTICULATE SYSTEM
•Mono or poly dispersed
•No interparticle scattering effects
SAXS Interpretation yields
•Size/dispersity for known shapes
•Rg for unknown shapes
•Can incorporate dense packing effects into model

19. Materials Characterization Lab
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Dilute Particulate models

20. Materials Characterization Lab
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Dilute Particulate models

21. Materials Characterization Lab
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Dilute Particulate Models

22. Materials Characterization Lab
www.mri.psu.edu/mcl
Common SAXS Models
Non Particulate 2 Phase System
•2 intermixed phases without host or matrix
SAXS Interpretation yields
•Phase volume fraction, domain size,
•information on interphase boundary
(sharp or diffuse)

23. Materials Characterization Lab
www.mri.psu.edu/mcl
Common SAXS Models
Periodic Systems
•Lamellar stacks, ordered copolymers, biologic
Periodic and ordered structures
WAXS methods apply but with emphasis on
deviations from ordered structures

24. Materials Characterization Lab
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25. Materials Characterization Lab
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Photoresist grating

26. Materials Characterization Lab
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Common SAXS Models
Soluble Blend System
•Single disordered phase dissolved molecularly with
density inhomogeneity
(miscible polymers, block copolymers, polymer solns)
SAXS Interpretation yields
•Solution properties
(could be treated as dilute system but blend model formulated
for more direct treatment of thermodynamic properties
rather than size and shape)

27. Materials Characterization Lab
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TWO IMPORTANT GENERAL MODEL RESULTS
(some interpretation without models)
•GUINIER LAW
•POROD LAW

28. Materials Characterization Lab
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GUINIER LAW
•Even for unknown, irregular or ‘non-describable shapes; scattering has
predictable form at low q

29. Materials Characterization Lab
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GUINIER LAW
Valid for
•q << 1/Rg
•Dilute system
•Isotropic (random particle orientation)
•Solvent scattering subtracted

30. Materials Characterization Lab
www.mri.psu.edu/mcl
POROD LAW
•Predictable relationship between I(q) and total interface area
in 2 phase systems at high q
•Can obtain total interface area for absolute intensities or specific
surface area (S/V) for relative measure of
scattered intensity
•Deviations from Porod Law indicate and give information on
diffuse interphase boundaries
•

31. Materials Characterization Lab
www.mri.psu.edu/mcl
INSTRUMENTS FOR SAXS
•KRATKY CAMERA
•PINHOLE CAMERA
•LABORATORY SOURCES
•SYNCHROTRON SOURCES

32. Materials Characterization Lab
www.mri.psu.edu/mcl
KRATKY CAMERA

33. Materials Characterization Lab
www.mri.psu.edu/mcl
INSTRUMENTS FOR SAXS
•Scattering in transmission mode
•1-2mm ideal thickness for polymers/organics
•Source is critical
•Monochromatic
•Intense
•Collimated
•Small cross section (pinhole)

34. Materials Characterization Lab
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BEAM CONDITIONING

35. Materials Characterization Lab
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MOLMET (PSU) SAXS

36. Materials Characterization Lab
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37. Materials Characterization Lab
www.mri.psu.edu/mcl
INSTRUMENTS FOR SAXS
•Scattering in transmission mode
•1-2mm ideal thickness for polymers/organics
•Source is critical
•Monochromatic
•Intense
•Collimated
•Small cross section (pinhole)
•Evacuated beam path
•Sample holders
•Detectors
•Film, plates, PSD, Area

38. Materials Characterization Lab
www.mri.psu.edu/mcl
Sample holders

39. Materials Characterization Lab
www.mri.psu.edu/mcl
Multi-wire Area Detector

40. Materials Characterization Lab
www.mri.psu.edu/mcl
EXAMPLES

41. Materials Characterization Lab
www.mri.psu.edu/mcl
Silver Behenate Standard
r
Calibrates center and q on 58.37 A d-space

42. Materials Characterization Lab
www.mri.psu.edu/mcl
Polyelectrolytes in Solution
SAXS of 60PMVP-I in NMF
500 60PMVP-I/EG
Correlation length, ξ ( Angstrom)
3500 concentration:
I(q), normalized intensity, (A.U.)
60PMVP-I/NMF
2.5 mg/ml
3000 5.0mg/ml
10.0mg/ml
20.0 mg/ml
2500
100 Slope = -0.4 2000
1500
1000
0.00 0.02 0.04 0.06 0.08 0.10
0.01 0.1 1
-1
q, (Angstrom )
Concentration, c (M)
Shichen Dou; PSU Colby group

43. Materials Characterization Lab
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Core-Shell latex spheres

44. Materials Characterization Lab
www.mri.psu.edu/mcl
Supercritical Fluid Treatment of Polymers
Poly(aryl ether ether ketone) PEEK
high performance thermoplastic with high
impact strength, tensile yield strength and
thermal and chemical resistance
Group studied methyl substituted PEEK annealed in air
and supercritical CO2 to control crystallization
and reduce processing costs.
unpublished Queen’s University, Ontario

45. Materials Characterization Lab
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46. Materials Characterization Lab
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47. Materials Characterization Lab
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Pt particle size in carbon-supported Pt electrocatalysts
for fuel cell applications
Random pore model;
three supports
Stevens, et al, CARBON 41 (2003)

48. Materials Characterization Lab
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Pt particle size in carbon-supported Pt electrocatalysts
for fuel cell applications
SAXS: Pt loadings by mass/ 2 supports
Stevens, et al, CARBON 41 (2003)

49. Materials Characterization Lab
www.mri.psu.edu/mcl
Pt particle size in carbon-supported Pt electrocatalysts
for fuel cell applications
Pt Size Distribution: Pt loadings by mass/ 2 supports
Stevens, et al, CARBON 41 (2003)

50. Materials Characterization Lab
www.mri.psu.edu/mcl
Pt particle size in carbon-supported Pt electrocatalysts
for fuel cell applications
•This study used moderately small angle so that size
agreed with WAXS/Scherrer but SAXS best at smaller size
•Generally, WAXS/Scherrer not effective in large sizes (no line
broadening, xtal domain vs. grain domain, no distribution info)
•TEM/SEM: specific areas vs. average important to catalyst
properties
Stevens, et al, CARBON 41 (2003)

51. Materials Characterization Lab
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Deformation Stage SAXS
unstressed stressed
Toughened Polystyrene

52. Materials Characterization Lab
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Come see the PSU MCL Molmet SAXS Room 6/7 Hosler