Saxs 2005

Materials Characterization Labwww.mri.psu.edu/mcl

SMALL ANGLE XRAY SCATTERING (SAXS)

AUGUST 10, 2005

Mark S. [email protected]


250 MRLAugust 179:45 AMParticle Characterization

114 MRI BldgAugust 249:45 AMX-ray photoelectron spectroscopy (XPS/ESCA)

114 MRI BldgAugust 2411:00 AMAuger Electron Spectroscopy (AES)

541 Deike Bldg.July 279:45 AMChemical analysis (ICP, ICP-MS)

541 Deike Bldg.August 109:45 AMSmall angle x-ray scattering (SAXS)

114 MRI Bldg August 39:45 AMAtomic Force Microscopy (AFM)

250 MRL Bldg.July 209:45 AMOrientation imaging microscopy (OIM/EBSD)

114 MRI BldgJuly 1311:00 AMTEM sample preparation

114 MRI BldgJuly 139:45 AMFocused Ion Beam (FIB)

250 MRL Bldg.July 610:15 AMHigh temperature sintering lab (20 min lecture only)

250 MRL bldg.July 69:45 AMDielectric Characterization (25 min lecture only)

250 MRL Bldg.June 299:45 AMX-ray Diffraction (XRD)

541 Deike Bldg.June 2211:00 AMAnalytical SEM

541 Deike Bldg.June 229:45 AMScanning electron microscopy (SEM)

114 MRI BldgJune 159:45 AMTransmission Electron Microscopy (TEM/STEM)

250 MRL Bldg.June 89:45 AMThermal analysis (TGA, DTA, DSC)

LocationDateTimeTechnique

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

Summer Characterization Open HousesSummer Characterization Open Houses


BeaverStadium

Park Ave.

Park Ave.

Porter RoadPollock Road

University Drive

College Ave.

Shortlidge Road North

Bur ro w

es Ro ad

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Centre Community

Hospital

E&ES Bldg:SEM

Hosler Bldg:SEM,AFM,ESEM, FE-SEM, EPMA, ICP, ICP-MS,BET, SAXS

MRI Bldg:XPS/ESCA, FIB SIMS, TEM, HR-TEM, FE-Auger, AFM, XRD

Atherton Street

(322 Business)

MRL Bldg:SEM, XRD, OIM, DTA, DSC, TGA, FTIR, Raman, AFM, Powder, dielectric, prep, shop, IC, UV-Vis

Hastings Road

Penn Stater Hotel

00

Materials Characterization Lab Locations

Route 322

I-99 00

Steidle Bldg:Nanoindenter

Deike Bldg:


• Facilities/Instruments• User Training• Operators/Analyst for hire• 24/7• Online bookings• User fees• website/contacts to get started

MCL SERVICES


200 mesh

400 mesh


Scattering ‘Live’ DemoReal Space Reciprocal Space

d1

d2 = d1/2

SOURCE

Scattered Beam (1st order)

Direct Beam - - - - - - -

Scattered Beam (1st order)SD

TAN θ = SD/D

SmallerFor

Larger dSample/Detector D

θ

θ

Smaller d yields larger SD


ηλ = 2 d sin θ

Bragg Scattering (WAXS-XRD)

λ = Cu Kα = 1.5401 Å

q =(4π/λ) sin θ = 2 π/dd 2θ

10Å (0.001 Micron)

50Å

100Å

300Å

600Å

1000Å

8.84º

1.17 º

0.88 º

0.29 º

0.15 º

0.09 º

0.628 A-1

0.126 A-1

0.063 A-1

0.021 A-1

0.010 A-1

0.006 A-1

WAXS (Cu Ka, 2-160 2θ)Laboratory SAXSSynchrotron SAXS/SANS

Sub Angstrom - 10Å10Å - 1000Å10Å – several 1000Å

Atomic StructuresNano/ Colloidal

Structures(PSU)


What kinds of materials?

Compiled by Earle Ryba






Examples from literature

Polymer dendrimersdilute solns in CH3OH to get dendrite sizes

dilute so dendrimers don’t correlate

Alkanediolssolns in water to study clustering

heavy water improves contrast (sans)

Water-based polymer latexesuse anionic surfactant to suspend in water

Macromolecular foamswafers cut & immersed in toluene to get swelling

banded matls are translated in situ

Microemulsionsoils in water to get droplet size



CVD SiGe filmsµ-thin films stacked to get Ge heterogeneity

Nanotubesuse surfactant in water & sonicate; place in quartz cellsto study nanotube aggregation

Powders thin-walled capillaries

Polymersstudy crystallization processes in situ in hot cell



Thin films on glass substratesas is, but requires grazing incidence

Random crystalline block copolymersrheology study in situ in rotating parallel disk cellto get crystal alignment and grain rotations

Splat-cooled glassin situ annealing study to follow pptn of PbTenano-crystals



Blown polymer filmsspecial cell for in situ studies

Liq. Crystalsspecial magnetic cell for molecule rotation

Ionomerscell w/ kapton windows

Hi pressure studiesdiamond windows


Mouse bone


Real Space

ρ (r)

r

F.T.

Reciprocal Space

⏐A⏐

1/r (q)

⏐A⏐2

Γ (r)

q

I.F.T.

1/r (q)

r

Reciprocal SpaceReal Space

I(q)

Not Possible By Direct CalcCalc – Scattering Theory – F.T.

Calc – Auto Correlation Function of ρ (r)

Large rParticulate shapesPhase mixLarge period structures

Small rAtomic positions

•Crystals•amorphous

Amplitude/PhaseSpectra of scatteringfrom individual scatters(continuous/discrete)

Large rCorrelation function, radial distribution

Small rPair (Radial) distribution: Short range atomic ordering (amorphous materials)

Patterson function: Interatomicvectors (crystals)

Large r (SAXS) Diffuse scatterSmall r (WAXS) Diffraction dominatesfor xtals, diffuse scatter for liquids, amorphous solids

Observed scattering intensity-Noise/truncation effects


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 mixingenergy, etc.)


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


Dilute Particulate models


Dilute Particulate models


Dilute Particulate Models


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)


Common SAXS Models

Periodic Systems

•Lamellar stacks, ordered copolymers, biologicPeriodic and ordered structures

WAXS methods apply but with emphasis on deviations from ordered structures



Photoresist grating


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 formulatedfor more direct treatment of thermodynamic properties

rather than size and shape)


TWO IMPORTANT GENERAL MODEL RESULTS(some interpretation without models)

•GUINIER LAW

•POROD LAW


GUINIER LAW

•Even for unknown, irregular or ‘non-describable shapes; scattering has predictable form at low q


GUINIER LAW

Valid for

•q << 1/Rg

•Dilute system

•Isotropic (random particle orientation)

•Solvent scattering subtracted


POROD LAW

•Predictable relationship between I(q) and total interface areain 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 ondiffuse interphase boundaries

•


INSTRUMENTS FOR SAXS

•KRATKY CAMERA

•PINHOLE CAMERA

•LABORATORY SOURCES

•SYNCHROTRON SOURCES


KRATKY CAMERA



•Scattering in transmission mode

•Source is critical

•1-2mm ideal thickness for polymers/organics

•Monochromatic•Intense•Collimated•Small cross section (pinhole)


BEAM CONDITIONING


MOLMET (PSU) SAXS




•Scattering in transmission mode

•Source is critical

•Evacuated beam path

•Sample holders

•Detectors

•1-2mm ideal thickness for polymers/organics

•Monochromatic•Intense•Collimated•Small cross section (pinhole)

•Film, plates, PSD, Area


Sample holders


Multi-wire Area Detector


EXAMPLES


r

Calibrates center and q on 58.37 A d-space

Silver Behenate Standard


SAXS of 60PMVP-I in NMF

0.00 0.02 0.04 0.06 0.08 0.10

1000

1500

2000

2500

3000

3500

I(q),

norm

aliz

ed in

tens

ity, (

A.U

.)

q, (Angstrom-1)

2.5 mg/ml 5.0mg/ml 10.0mg/ml 20.0 mg/ml

60PMVP-I/EGconcentration:

0.01 0.1 1

100

Cor

rela

tion

leng

th, ξ

( A

ngst

rom

)

Concentration, c (M)

Slope = -0.4

50060PMVP-I/NMF

Polyelectrolytes in Solution

Shichen Dou; PSU Colby group


Core-Shell latex spheres


Supercritical Fluid Treatment of PolymersPoly(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




Pt particle size in carbon-supported Pt electrocatalystsfor fuel cell applications

Random pore model;three supports

Stevens, et al, CARBON 41 (2003)




SAXS: Pt loadings by mass/ 2 supports




Pt Size Distribution: Pt loadings by mass/ 2 supports




•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


Deformation Stage SAXS

Toughened Polystyrene

unstressed stressed


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

Saxs 2005

Business

mrl bldg

dielectric characterization

edumclwhat kinds of

northhastindeike bldg

steidle bldg

ees bldg

hosler bldg

mri bldg note locations