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



SMALL ANGLE XRAY SCATTERING (SAXS)

         AUGUST 10, 2005




         Mark S. Angelone
          msa3@psu.edu
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
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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                                                                              Ave.                                                                              0
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                                                                 Park            0
                                                                                                                         Beaver
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                                                                 0
                                                                                                                         Stadium
                                                                 0
                                              0
                                              0
                                                                                                                                                         Centre
                0
                0




                                                                                                                              Porter Road
                                                                                                                                                        Community
                                                                                                Univ
                                                                 Shortlidg




                                                                                                                                                         Hospital
                    0
                    0
                        Burrowes Road




                                                                                                     ersi
                                                                                                          ty D
                                                                          e




                                                  Pollock Road
                                                                     Road




                                                                                                              rive




                                                                                                                                                                            North
                                                                                       Hastin
                                           Deike Bldg:                                       gs Ro
                                                                                                  ad


                                                  College Ave.
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
Materials Characterization Lab
          www.mri.psu.edu/mcl




200 mesh




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




What kinds of materials?




                           Compiled by Earle Ryba
Materials Characterization Lab
                               www.mri.psu.edu/mcl



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




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




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



Dilute Particulate models
Materials Characterization Lab
                                www.mri.psu.edu/mcl



Dilute Particulate models
Materials Characterization Lab
                                www.mri.psu.edu/mcl


Dilute Particulate Models
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)
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
Materials Characterization Lab
    www.mri.psu.edu/mcl
Materials Characterization Lab
                          www.mri.psu.edu/mcl




Photoresist grating
Materials Characterization Lab
                                                      www.mri.psu.edu/mcl




                 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)
Materials Characterization Lab
                                     www.mri.psu.edu/mcl




TWO IMPORTANT GENERAL MODEL RESULTS
    (some interpretation without models)


             •GUINIER LAW

              •POROD LAW
Materials Characterization Lab
                                                         www.mri.psu.edu/mcl


                           GUINIER LAW

•Even for unknown, irregular or ‘non-describable shapes; scattering has
                       predictable form at low q
Materials Characterization Lab
                                            www.mri.psu.edu/mcl



               GUINIER LAW

Valid for


                 •q << 1/Rg

               •Dilute system

   •Isotropic (random particle orientation)

       •Solvent scattering subtracted
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
                                  •
Materials Characterization Lab
                              www.mri.psu.edu/mcl



   INSTRUMENTS FOR SAXS


•KRATKY CAMERA


•PINHOLE CAMERA

       •LABORATORY SOURCES

       •SYNCHROTRON SOURCES
Materials Characterization Lab
                    www.mri.psu.edu/mcl




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


BEAM CONDITIONING
Materials Characterization Lab
                        www.mri.psu.edu/mcl


MOLMET (PSU) SAXS
Materials Characterization Lab
    www.mri.psu.edu/mcl
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
Materials Characterization Lab
                     www.mri.psu.edu/mcl


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


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




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


                       Silver Behenate Standard



                                             r




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




Core-Shell latex spheres
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
Materials Characterization Lab
    www.mri.psu.edu/mcl
Materials Characterization Lab
    www.mri.psu.edu/mcl
Materials Characterization Lab
                                                     www.mri.psu.edu/mcl



   Pt particle size in carbon-supported Pt electrocatalysts
                    for fuel cell applications

Random pore model;
  three supports




                                 Stevens, et al, CARBON 41 (2003)
Materials Characterization Lab
                                                       www.mri.psu.edu/mcl



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)
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)
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)
Materials Characterization Lab
                                               www.mri.psu.edu/mcl



      Deformation Stage SAXS




unstressed                           stressed

             Toughened Polystyrene
Materials Characterization Lab
                                            www.mri.psu.edu/mcl



Come see the PSU MCL Molmet SAXS Room 6/7 Hosler

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Saxs 2005

  • 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. 0 0 0 0 0 0 0 Ave. 0 0 0 0 0 Park 0 Beaver 0 0 Stadium 0 0 0 Centre 0 0 Porter Road Community Univ Shortlidg Hospital 0 0 Burrowes Road ersi ty D e Pollock Road Road rive North Hastin Deike Bldg: gs Ro ad 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 www.mri.psu.edu/mcl Dilute Particulate models
  • 20. Materials Characterization Lab www.mri.psu.edu/mcl Dilute Particulate models
  • 21. Materials Characterization Lab www.mri.psu.edu/mcl 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 www.mri.psu.edu/mcl
  • 25. Materials Characterization Lab www.mri.psu.edu/mcl Photoresist grating
  • 26. Materials Characterization Lab www.mri.psu.edu/mcl 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 www.mri.psu.edu/mcl TWO IMPORTANT GENERAL MODEL RESULTS (some interpretation without models) •GUINIER LAW •POROD LAW
  • 28. Materials Characterization Lab www.mri.psu.edu/mcl GUINIER LAW •Even for unknown, irregular or ‘non-describable shapes; scattering has predictable form at low q
  • 29. Materials Characterization Lab www.mri.psu.edu/mcl 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 www.mri.psu.edu/mcl BEAM CONDITIONING
  • 35. Materials Characterization Lab www.mri.psu.edu/mcl MOLMET (PSU) SAXS
  • 36. Materials Characterization Lab www.mri.psu.edu/mcl
  • 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 www.mri.psu.edu/mcl 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 www.mri.psu.edu/mcl
  • 46. Materials Characterization Lab www.mri.psu.edu/mcl
  • 47. Materials Characterization Lab www.mri.psu.edu/mcl 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 www.mri.psu.edu/mcl 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 www.mri.psu.edu/mcl Deformation Stage SAXS unstressed stressed Toughened Polystyrene
  • 52. Materials Characterization Lab www.mri.psu.edu/mcl Come see the PSU MCL Molmet SAXS Room 6/7 Hosler