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![Page 1: A Big-Angle View of Small-Angle Measurements: SAXS · PDF fileA Big-Angle View of Small-Angle Measurements: SAXS Techniques. Welcome Brian Jones. Sr. Applications Scientist. Bruker](https://reader036.vdocuments.net/reader036/viewer/2022070606/5a78c55e7f8b9a273b8e9a5f/html5/thumbnails/1.jpg)
A Big-Angle View of Small-Angle
Measurements: SAXS Techniques
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Welcome
Brian JonesSr. Applications ScientistBruker AXS Inc.
Kurt ErlacherSr. Applications ScientistBruker AXS GmbH
A Tour of the Nano-Cosmos•
Introduction to SAXS•
1D SAXS Instruments•
1D SAXS Application Examples
•
2D Method -
NanoSTAR•
2D Simultaneous SAXS/WAXS
•
NanoSTAR –
Typical Applications
•
Summary•
Q & A
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IntroductionIntroduction to SAXSto SAXS
Brian Jones
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The
SAXS
Experiment
SAXSscattering at particles orelectron density changesscattering angles: 0 - 4°
XRDdiffraction at crystal latticediffraction angles: 4 - 170°
incidentX-ray beam
d
d
sinθ
= λ
/ 2d
Large θ small dSmall θ large d
d 10 – 100nm
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Nanostructural
Parameters Obtained from SAXS
Mean size, size distribution
Shape (spheric, cylindric, platelet, cubic ...)
Orientation, degree of orientation
Mean distance between particles
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Scattering Vector q
λθπ /sin4≡q
2θ
ki
ksq
d = 2π
/ qFor isotropic systems (fluids, glasses,
polycrystals):→ no direction dependence of the scattered
radiation
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Example SAXS Scattering Curve log –
log
Scale
HDPE
q [Å-1]
0.001 0.01 0.1 10.001
0.01
0.1
1
10
100
HDPE: 600 s
0.14° 1.4°2θ
0.014°
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Transmission SAXS
IsI0Liquid dispersions, gels, powders, sheets, etc.
X-rays are incident normal to the surface of the sample and transmission is sufficient to provide suitable SAXS scattering intensity.
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Grazing Incidence Small-Angle X-Ray Scattering (GI-SAXS)
GI
–
Incident angle close to the critical angle (0.1 to 1 degree)SAXS
-
length scale, beam definition by multiple slits, and (usually) an area detector.
Nanoscale particles embedded in a matrix subsurface, supported on a substrate or buried in a thin layer on a substrate.
Examples:Semiconductor quantum dots/islandsPorous films on substrates Condensed powderNanoparticles embedded in polymers
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1D SAXS Instruments1D SAXS Instruments
Brian Jones
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SAXS Breakdown by Instrument Type
Point collimation
Line collimation
NanoSTAR
D8 GADDS
D8 Advance
D8 Discover
Transmission SAXS
GI-SAXS
Transmission SAXS
GI-SAXS
Transmission SAXS
GI-SAXS
Transmission SAXS
GI-SAXS
1D
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Bruker AXS Instruments 1D SAXS
D8 Advance D8 Discover
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1D SAXS Line Collimation Goals
Monochromatic X-rays
High intensity beam
Well collimated beam
Axial divergence minimal
Beam width is narrow and adjustable for high-flux / high-resolution trade-off.
Background to either side of direct beam is very low
(optional) Can scan over the direct beam to determine sample transmission.
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1D SAXS Line Collimation Goals
Monochromatic X-raysGobel
Mirror High intensity beamGobel
MirrorWell collimated beamGobel
Mirror + aperture slitsAxial divergence minimalSoller
slitsBeam width is narrow and adjustable for high-flux / high-resolution trade-off2 incident beam slits and 2 diffracted beam slits of various sizesBackground to either side of direct beam is very low4 aperture slit system with narrow apertures and optional knife edge(optional) Can scan over the direct beam to determine sample transmissionRotary absorber
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Gobel
Mirror –
Monochromatic, High Intensity, Collimated
Parabolic, laterally graded, multilayer mirror
Captures a large solid angle of divergent radiation and converts to collimated, monochromatic beam
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Soller
Slits Reduce Axial Divergence
Many closely spaced metal foil pieces stacked parallel to one another.
Controls the angular acceptance angle along the axial direction.
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D8 SAXS Transmission Configuration
slit1 slit2 slit4
detectorGobel mirror soller1
slit3
and/or knife edge
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Hardware Configuration
GobelMirror
RotaryAbsorber
Slit1Slit2Slit3Slit4
Soller1
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Measurement diameter = 500mm – 600mmCu tube (40kv, 40mA)60mm 3rd generation Gobel mirror0.2 mm mirror exit slitRotary Absorber (RA)0.1 mm slit after RA0.1 deg anti-scatter slit1.5 degree Soller slit0.1 mm detector slitScintillation counter
D8 Advance/Discover Typical Experimental Setup
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Please use your mouse to answer the question on your screen:
What types of samples do you analyze? (Check all that apply):
liquidpowdergel sheetfiberthin filmsolid/bulk
Audience Poll
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SAXS Transmission Sample Holders
Holder for sheets, powders, gels, etc.
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SAXS Transmission Sample Holders
Liquids, powders, deposited in capillary tube
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D8 Advance Goniometer Head-Mount Stage
Entire stage can be quickly removed and replaced
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D8 Advance Goniometer Base Stage Sample Holder Attached
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D8 Advance Primary Beamstop
and Knife Edge
Mounts to primary beam track.
Beamstop behind the sample.
Knife edge in front of sample.
Compatible with many D8 Advance transmission sample holders
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D8 Advance Primary Beamstop
and Knife Edge
Knife edge used to reduce parasitic scatter
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D8 Advance Primary Beamstop
and Knife Edge
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D8 Discover
Vertical Horizontal
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D8 Discover Centric Eulerian
Cradle
Mounted on diffractometer permanently
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D8 Discover -
Capillary Spinner for Eulerian
Cradle Stage
Beamstop and knife edge are adjustable or can be completely removed from beam path.
Goniometer head base will accommodate numerous sample holders.
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D8 Discover –
Capillary Spinner Mounted to Eulerian
Cradle
Drawing of capillary spinner mounted to Eulerian cradle on a horizontal system
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D8 Discover –
Capillary Spinner Mounted to Eulerian
Cradle
Only knife edge is mounted
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D8 Discover –
Capillary Spinner Mounted to Eulerian
Cradle
Knife edge and capillary holder are mounted to the capillary spinner for the Eulerian cradle
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1D SAXS 1D SAXS ––Application Application ExamplesExamples
Brian Jones
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Example 1: Glassy Carbon
Glassy Carbon is a porous material often used as a standard in SAXS. The pore size and shape have been previously determined with high accuracy.
Ellipsoid pore shapeOuter radius ~ 20-23 Ab/a (aspect ratio) = 0.3
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File: MES=0.2, RA=0.1, GC, AS=0.1 deg, double soller, DetS=0.1.rawFile: MES=0.2, RA=0.1, AS=0.1 deg, double soller, DetS=0.1.raw
Log
(Cps
)
10
100
1000
1e4
1e5
1e6
1e7
2-Theta - Scale-2 -1 0 1 2 3 4 5
Example 1: Glassy Carbon 1D SAXS Scattering Curve
Glassy carbon
Empty beam
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Example 1: Glassy Carbon Analysis with DiffracPlus
Nanofit
Least-squares data analysis program for small angle scattering data by direct modeling
Supports basic geometric models and polymer models, polydispersity, and concentration effects
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Example 1: Glassy Carbon Direct Modeling with Nanofit
The graph shows the experimental data (blue) and the fit (red)
The measured scattering profile can be nicely described by using a model for ellipsoids
Previously determined Pore dimensions:
•
Outer radius:r = 20-23 Å
•
Aspect Ratio:b/a = 0.3
Results of D8 SAXS fit:•
Outer radius:r = 19.7Å
•
Aspect Ratio:b/a = 0.303
Good Agreement!
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Example 1: Glassy Carbon
Lower limit of fit q = 0.0106 A-1
d = 2π/q ~ 60 nm
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File: MES=0.1, RA=none, KE3,GC, AS=0.1 deg, 1.5 soller, DetS=0.1.rawFile: MES=0.1, RA=none, KE3, AS=0.1 deg, 1.5 soller, DetS=0.1 background.raw
Log
(Cps
)
1
2
10
3456
100
1000
1e4
1e5
2-Theta - Scale0.1 1 2
Example 1: Glassy Carbon Using Knife Edge
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File: MES=0.1, RA=none, KE3,GC, AS=0.1 deg, 1.5 soller, DetS=0.1.raw
Log
(Cps
)
1
2
10
3456
100
1000
1e4
1e5
2e5
2-Theta - Scale0.1 1 2
Example 1: Glassy Carbon Improved Resolution with Knife Edge
Meaningful SAXS data as low as q = 0.0085 Å-1
d ~ 75nm
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Example 2: NIST Reference Standard Au Nanoparticles in Liquid Suspension
*https://srmors.nist.gov/view_detail.cfm?srm=8011
Mean particle size
Particle size distribution
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Log (
Counts
)
0.2 1 2
Example 2: NIST SRM 8011 Au Nanoparticles
–1D SAXS Scattering Curve
Scaled direct beam scattering
NIST SRM 8011 scattering
2θ
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Example 2: NIST SRM 8011 Au Direct Modeling with Nanofit
Background corrected SAXS (blue) and fitted SAXS (red)
Fitting results:
Mean sphere radius = 45.54 Å
Size distribution modeled by a Gaussian distribution with sigma = 3.65 Å
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Example 2: NIST SRM 8011 Au Nanoparticles –
Comparison
Results from D8 Advance SAXSmodeled with Nanofit
Mean particle size = 9.108 nm
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Example 3: Nano-Metallic Particles Deposited on Carbon Black Substrate
For SAXS measurements, sample was deposited
between 2 pieces of adhesive tape.
For comparison, this sample was run on the 2D
Bruker AXS dedicated SAXS instrument, the NanoSTAR
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Example 3: Metallic Nanoparticles 1D SAXS Scattering Curve from NanoSTAR
q (A-1)
0.01 0.1
Log
(Inte
nsity
)
1e-3
1e-2
1e-1
1e+0
1e+1
1e+2
1e+3
1e+4
1e+5
q vs Sample 1 q vs tape only
Azimuthally averaged intensity vs. scattering vector q and the scattering intensity of the holder that is used for correction
where 2θ is the scattering angle and λ is the used wavelength
θλπ sin4
=q
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Example 3: Metallic Nanoparticles 1D SAXS Scattering Curve from D8 Advance
File: just tape.raw - Type: Detector ScanFile: sample 1 in tape.raw - Type: Detector Scan
Log
(Cps
)
100
1000
1e4
1e5
1e6
1e7
2-Theta - Scale-2 -1 0 1 2
Detector scan: 2θ
= -2 to 3°
Step size = 0.02°
Count time = 2.3 seconds/step
Powder in tapeTape only (background)
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Example 3: Metallic Nanoparticles 1D SAXS Scattering Comparison
q (A-1)
0.01 0.1
Log
(Inte
nsity
)
1e-3
1e-2
1e-1
1e+0
1e+1
1e+2
1e+3
1e+4
1e+5Comparison of background-corrected SAXS scattering shown on a double-log scale
Intensity is given in arbitrary units and the profiles are separated by a scaling factor
Note the similarity of the scattering profiles
Nanostar UD8 Advance
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q (A-1)
0.01 0.1Lo
g (In
tens
ity)
0.1
1
10
100
1000
Example 3: Metallic Nanoparticles Analysis -
Comparison
Scattering profiles after Carbon black is removed
q (A-1)
0.01 0.1
Log
(Inte
nsity
)
1e+0
1e+1
1e+2
1e+3
1e+4
1e+5
D8 Advance NanoSTAR
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This profile is fitted assuming a model for spherical structures.
The best fit is obtained using size polydispersity(Schultz).
Fit results:•
Radius: 32.4 Å•
σ
of Schultz size distribution: 11.9Å.
Example 3: Metallic Nanoparticles Direct Modeling with Nanofit
-
NanoSTAR
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Example 3: Metallic Nanoparticles Direct Modeling with Nanofit
–
D8 Advance
This profile is fitted assuming a model for spherical structures
The best fit is obtained using size polydispersity(Schultz)
Fit results:•
Radius: 32.2 Å•
σ
of Schultz size distribution: 9.7Å.
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Example 3: Metallic Nanoparticles Nanofit
Comparison
Fit results (NanoSTAR):•
Radius: 32.4 Å•
σ
of Schultz size distribution: 11.9Å
Fit results (D8 Discover):•
Radius: 32.2 Å•
σ
of Schultz size distribution: 9.7Å
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GI-SAXS Examples GI-SAXS Geometry Configuration
Grazing incidence angle near the critical angle is set to make the configuration surface sensitive.
Detector on secondary diffracted beam track is scanned along qy
Scattering geometry combining SAXS condition with conditions diffuse x-ray reflectivity
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GM0,120,12
Ultra GID geometry
Replace Beam Compressor withSoller slit for GI-SAXS configuration
GI-SAXS Geometry Modify Ultra GID Configuration
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GI-SAXS Example 1 -
Au Nanoparticles Embedded a Polymer Matrix
Fit result: 80 Å diameter spherical nanoparticles
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GI-SAXS Example 2 –
Quantum Dot Film
Operations: Import
File: GISAXS3.raw - Type: Detector Scan
Log (
Counts
)
1
10
100
1000
1e4
1e5
1e6
2-Theta - Scale
-5 -4 -3 -2 -1 0 1 2 3 4 5
Parallel beam0.2 mm slit after mirror0.12 degree thin film attachment (incident)0.12 degree thin film (diffracted beam)Secondary Detector Scan•
Incident angle = 0.5 deg.
•
2θ
= -5 to 5 degrees•
0.024 degree stepsize
•
0.4 s / step•
Total scan time < 3 minutes
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GI-SAXS Example 2 –
Quantum Dot Film
45.2(10) Å
89.41(49) Å
Peaks are fit with TOPAS and positions are given in d-spacing
1st and 2nd
order peaks are visible
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Summary 1D SAXS with D8 Advance/Discover
1D SAXS capability integrated into multipurpose instruments, D8 Advance and D8 Discover
Sample stages for investigating liquids, powders, gels, sheets, fibers, thin-films, etc.
Configuration can be easily modified to obtain maximum resolution or maximum intensity to accommodate the sample
Powerful GI-SAXS capability using a modification of the Ultra GID configuration
Dedicated software, Nanofit, for direct modelling of SAXS scattering resulting in a detailed analysis of particle shapes, sizes, size distributions, and concentration effects
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2D 2D MethodMethod -- NanoSTARNanoSTAR
Kurt Erlacher
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Please use your mouse to answer the question on your screen:
What method do you need to analyze preferred-orientation samples?
1D SAXS2D SAXSNot sure
Audience Poll
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NanoSTAR
Motorized reference sample
holder
Collimation systems for high flux, high resolution or Nanography
MultipleX-ray
sources available
D8 based electronics
Sample can be investigated
under vacuum or atmospheric
condition
simple alignment concept
Integrated radiation safety
Automatic XY sample stage
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IμS
-
Incoatec Microfocus Source The Brightest Sealed Tube X-ray Source
no moving parts, very long lifetime without maintenanceextremely stableno water-cooling requiredeasy to replacelow cost of ownership -comparable to common sealed tubes significantly more intense than previous microfocus source designsoperation power 30 W2D parallel beam Montel mirror in an evacuated housing
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Turbo X-Ray Source TXS
Implementation of advanced technologies
Direct drive anodeCeramic feed through for cathode powder supplyAlignment-free filament mountingNew shutter and safety concept, similar to sealed tube D8
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Arrangement •
two identical mirrors in a side-by-side
configuration
Benefits:•
more compact•
easy alignment•
symmetrical divergence spectrum
Montel mirror: two identical mirrors in a side-by-side configuration (W/C coating, deposit by magnetron sputtering)
Optics Montel Multilayer Mirror
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Variable Source to Sample DistancePin hole alignment better than 10µm, even
under vacuum conditionsIntegration of primary beam path into the
radiation safety systemEasy exchange of pin holes for configuring high
resolution set up (larger structures)
Easy reconfiguration to scanning SAXS 2 pin hole collimation by removing the beam path tubes and pin hole pedestal and sliding the X-ray source along the track
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Pinhole Collimation
Distances between pinholes:
1st pinhole -
2nd pinhole -
3rd pinhole –
sample -
detector:
925 mm –
482 mm –
35 mm -
variable
Diameter of first / second / third pinhole:SAXS configuration: 0.75 / 0.4 / 1.0 [mm]HRSAXS configuration: 0.5 / 0.15 / 0.5 [mm]
Available beamstop diameters: 2.0 - 4.2 mm
SAXS configuration provides approximately 10 times higher flux
Typical experimental q-range with e.g. 105 cm sample to detector distance:SAXS configuration: 0.009 Å-1 to 0.21 Å-1 (700 Å to 30 Å) HRSAXS configuration: <0.005 Å-1 to 0.22 Å-1 (>1250 Å to 30 Å)
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Nanography Scanning-SAXS
X-ray Nanography is the non-destructive investigation of nm structures of mm sized samples with µm resolution
SAXS pattern outside the crack
SAXS pattern at the beginning of the crack
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HI-STAR 2D Multi-Wire Detector
Multi wire gas filled proportional counterReal time data collection and displayHigh sensitivity and low backgroundDynamic range > 106
Energy resolution <20%>80% single photon sensitivity for Cu-radiation
The beamstop is made of low fluorescence material to ensure minimum backgroundMounted with Kapton strings for full 360 access to scattered photonsAlignment accuracy better than 10µm
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VÅNTEC-2000 2D Mikro-GapTM
X-Ray
Detector
High Spatial Resolutionunrivalled data accuracy in precision and accuracyHigh Local and Global Count RateHigh Dynamic RangeRadiation HardInert Counting Gasno maintenance requiredLarge active areaconveniently increases qmax
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Data
Evaluation with DIFFRACplus NanoFit
NanoFit is an interactive graphic-based, non-linear, least-squares data analysis program for small angle X-ray scattering (SAXS) data by direct modeling.
The displayed data (blue dots) are the calculated scattering data for a model of Polydisperse Spherical Block Copolymer Micelles with a smooth interface and a Hard Sphere Structure Factor with statistical noise added.The red line is the fitted scattering profile using the same model.
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DIFFRACplus NanoFit
Set of several built-in nano particle modelsBasic geometrical models (spherical, ellipsoidal, cylindrical). Selected polymer models (flexible and semi-flexible chains, Gaussian star, spherical block copolymer micelle)Polydispersity (Gaussian or Schultz size distribution)Concentration effects (Hard-Sphere or RPA structure factor)
Automatic FittingDifferent refinement methods for automatic evaluation:
Levenberg-MarquardtSimplex
Online display of intermediate results and changes of the chi² cost function.Selectable fit region.
Graphical evaluation of one-dimensional data setsDisplay and comparison of measured and simulated data. Simple, interactive evaluation of SAXS measurements:Easy interactive adjustment of all available model parameters.Wide selection of commonly used axis scaling.
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2D 2D SimultaneousSimultaneous SAXS/WAXSSAXS/WAXS
Kurt Erlacher
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Simultaneous SAXS/WAXS Experimental Setup
Turbo X-ray Source, focal spot = 0.1 mm x 1 mm
Cu-Kα 50 kV / 24mA, from point focus (0.1 mm x 0.1 mm)
Montel-P multilayer optics
Diameter of first / second / third pinhole = 750 mm / 400 mm / 1000 mm
Diameter of beamstop: 4.3 mm
SAXS:
sample – detector distance: 1063.5 mm
Bruker AXS HI-STAR position sensitive area detector
WAXS:
sample – detector distance: 51.8 mm
FUJIFILM FLA-7000 Imaging Plate reader system
Software: SAXS for WindowsTM NT
SigmaPlotTM
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Simultaneous SAXS/WAXS
FUJI FLA-7000 IP WAXS DETECTORImage Plate detector system for recoding WAXS (wide angle x-ray scattering)About 20 x 25 cm large IP is mounted into the NanoSTAR sample chamberRead-out of the signal is executed off-line using a FLA-7000 scanner (Fuji)Obtained SAXS/WAXS data are read by Bruker AXS 2D software for further data evaluation
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Simultaneous SAXS/WAXS Samples
Reference Materials: Silver Behenate
Corundum (NBS SRM 674)
Ordered Mesoporous silica: Meso-SiO2 1)
Samples were measured at room temperature
SAXS and WAXS signals were collected simultaneously!
1) samples were kindly provided by M.-O. Coppens, Delft University of Technology, and Rensselaer Polytechnic Institute, Troy NY
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System Calibration Silver Behenate
(AgBh)
AgBh is ideal because itcan be used as a calibrant for both, theSAXS (top) as well as theWAXS (bottom) signalhttp://srs.dl.ac.uk/NCD/station82/silver_behenate.htmlDebye-Scherrer rings are used for determination of:
exact sample-detector distance
center position of primary beam
Measurement time was 120s.
2 Theta [deg]0 20 40 60
1e+4
q [Å-1]0 1 2 3 4 5
Mea
sure
d in
tens
ity I(
q)
1e+4
1e+5
1e+6
1e+7
q [Å-1]0.00 0.05 0.10 0.15 0.20 0.25
Mea
sure
d in
tens
ity I(
q)
1e+0
1e+1
1e+2
1e+3
1e+4
1e+5
1e+6
2 Theta [deg]0.0 0.5 1.0 1.5 2.0 2.5 3.0
1e+0
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NBS SRM 674 α-Al2O3
α-Al2O3 is a good standard for the WAXS region only (and was used as a cross reference)Notice the sharp peak profileMeasurement time was 300sIncident beam was attenuated by a factor of 10
2 Theta [deg.]
0 10 20 30 40 50 60 70
Mea
sure
d in
tens
ity I(
q)
2e+6
4e+6
6e+6
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MESO-SiO2 2D SAXS / WAXS Pattern
Individual SAXS (left) and WAXS (right) pattern that were measured simultaneouslyMeasurement time was 318 s
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MESO-SiO2
Individual SAXS (left) and WAXS (right) profiles that were measured simultaneouslyMeasurement time was 318 s
q [Å-1]0 1 2 3 4
Mea
sure
d in
tens
ity I(
q)1e+4
1e+5
1e+6
1e+7
2 Theta [deg]0 20 40 60
1e+4
2 Theta [deg]0.0 0.5 1.0 1.5 2.0 2.5 3.0
1e+0q [Å-1]
0.00 0.05 0.10 0.15 0.20
Mea
sure
d in
tens
ity I(
q)
1e+0
1e+1
1e+2
1e+3
1e+4
1e+5
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MESO-SiO2 Combined SAXS/WAXS Profile
SAXS/WAXS profiles that were measured simultaneouslyIntensities are plotted vs. reciprocal lattice vector q (left) and vs. scattering angle 2 Theta (right)Measurement time was 318 s
q [Å-1]0 1 2 3 4
Mea
sure
d in
tens
ity I(
q)
1e-2
1e-1
1e+0
1e+1
1e+2
1e+3
1e+4
1e+5
2 Theta [deg]
0 20 40 60 80
Mea
sure
d in
tens
ity I(
q)
1e-2
1e-1
1e+0
1e+1
1e+2
1e+3
1e+4
1e+5
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Summary SAXS/WAXS
Simultaneous SAXS/WAXS experiments were performed on the standards Silver Behenate, α-Al2O3 as well as on the mesoporoussilica samples MESO-SiO2All samples show distinct scattering characteristic in the wide angle regimeIn order get a fully continuous profile from the SAXS towards the WAXS region it is possible to asymmetrically align the Image Plate for WAXS experimentsIn addition the sample to Image Plate position can be varied such that the max. 2 Theta angle is either around 50°, 70° (current data) or 82°
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NanoSTAR UNanoSTAR U TypicalTypical ApplicationsApplications
Kurt Erlacher
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Typical Applications
Gold NanoparticlesSize dependence on preparation temperature
Biological MacromolecuesDimension of viruses and its monodispersityConformation state
Block Copolymer MicellesShape and dimension of micellesRadial excess electron density profile
Liquid CrystalsMicrodomain structure like lamellar, cylinder or hexagonal array
HDPELamellar thickness
NanographyDistribution of mineral particles in trabecular bone
SuperalloysSize of precipitates as a function of temperature treatment
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Application Gold Nano-Particles
HAuCl4.3H2O aq Oct4N+Br-
toluene
Oct4N+AuCl4-toluene HBr aq
NaBH4 aq
Water with excess NaBH4
MPC's
n-C12H25SH
Applying the desired temperature
Work-up
Preparation according Schiffrin Procedure1) for series 1 and 8
Modified procedure to avoid water in the synthesis for an extended temperature range
All samples were prepared with the same relative amount of of gold/thiol (4:1) and gold/NaBH4 (1:10)
1) Brust, M.; Walker, M.; Bethell, D.; Schiffrin, D.J.;Whyman, R. J. Chem. Commun. (1994) 801- 802
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SAXS Profiles and Results
SAXS
q [Å-1]
0.01 0.1
dσ/d
Ω [c
m-1
]
0.0001
0.001
0.01
0.1
11.1a 1.1c1.2b1.3a 1.3c1.4b
Size Distribution
R [Å]
0 10 20 30 40 50
D(R
)
0.0
0.2
0.4
0.6
0.8
1.01.1a 1.1c1.2b1.3a1.3c1.4b
( ) ( )( )
2
3cos-sin 3),( ⎟⎟
⎠
⎞⎜⎜⎝
⎛=
qRqRqRqRRqP
)sin(4 θλπ
=q
∫∝ P(q,R) dRRVRDI(q) 2)()(
SAXS
q [Å-1]
0.01 0.1
dσ/d
Ω [c
m-1
]
0.0001
0.001
0.01
0.1
11.1a 1.1c1.2b1.3a 1.3c1.4bFit
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Results
T / oC
-40 -20 0 20 40 60 80 100
Rg
/ nm
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
The Radius of Gyration Rg can be calculated from the particle size distribution D(R) by
6
82
53
MMRg = ∫= dRRRDM n
n )(with
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Comparison with TEM
T = -17.0°C
T = 31.5°C
T = 81.4°C
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Conclusion
A clear relation between the average size of the colloids and their preparation temperature is observed
The size of the colloids is not only controlled by the gold to thiol ratio but also by the temperature
By means of a non aqueous approach it is possible to expand the temperature interval in which the gold colloids are prepared
A trend towards a similar temperature dependence was found
Jørgen M. Jørgensen, Kurt Erlacher, Jan S. Pedersen, and Kurt V. Gothelf. Langmuir 2005, 21, 10320-10323
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Application
TBSV Tomato Bushy Stunt Virus
Brunt, A.A., Crabtree, K., Dallwitz, M.J., Gibbs, A.J., Watson, L. and Zurcher, E.J. (eds.) (1996 onwards). `Plant Viruses Online: Descriptions and Lists from the VIDE Database. Version: 20th August 1996.' URL http://biology.anu.edu.au/Groups/MES/vide/
Physical and biochemical properties
Particle morphologyVirions isometric; 30 nm in diameter.
Physical propertiesOne sedimenting component in purified preparations; sedimentation coefficient 135 S. Density 1.36 g cm-3 in CsCl (unfixed).
Biochemical propertiesGenome consists of RNA; single-stranded. Total genome size 4.7 kb. Genome unipartite; largest (or only) genome part 4.7 kb.
Features of proteinsVirion protein(s) one; Mr 37000; coat protein.
CytopathologyVirions found in cytoplasm, in nuclei, and in mitochondria
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SAXS Data 2D Pattern of TBSV 20 mg/mL
The sample shows an isotropic scattering behavior
Measurement time is 5400 s
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Experimental Data and Fit
Background corrected data of the azimuthally averaged scattering intensities of the TBSV sample.
The red line gives the fit of the Fourier Transform of the pair distance distribution function p(r) to the experimental data.
TBSV 18.9 mg/mL
q [Å-1]
0.0 0.1 0.2 0.3
dσ/d
Ω [c
m-1
]
0.0001
0.001
0.01
0.1
1
10
100
ExperimentFit
TBSV 20mg/mL
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TBSV Compact Pair Distance Distribution Function p(r)
The shape of the p(r) functions indicates spherical particles
Rg = 123.1 ± 0.1 Å
I(0) = 121.2 ± 0.4 cm-1
Dmax = 320 Å
Note that the error bars of the p(r)-function are smaller than the thickness of the drawn red line
The data were fitted using a program written by Jan Skov Pedersen
TBSV 18,9 mg/mL
r [Å]
0 50 100 150 200 250 300
p(r)
0.00
0.01
0.02
0.03
0.04
0.05
0.06
TBSV 20mg/mL
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TBSV Compact Experiment and Fit
Background corrected data of the azimuthally averaged scattering intensities of the TBSV sample.
Measurement time was 5400s.
The red line gives the fit of the Fourier Transform of the pair distance distribution function p(r) to the experimental data.
TBSV 0.91 mg/mL
q [Å-1]
0.0 0.1 0.2 0.3
dσ/d
Ω [c
m-1
]
0.0001
0.001
0.01
0.1
1
10
ExperimentFit
TBSV 0.91 mg/mL
q [Å-1]
0.0 0.1 0.2 0.3
dσ/d
Ω [c
m-1
]
0.0001
0.001
0.01
0.1
1
10
ExperimentFit
TBSV 1mg/mL
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TBSV Compact Pair Distance Distribution Function p(r)
The shape of the p(r) functions indicates spherical particles
Rg = 120.7 ± 0.3 Å
I(0) = 4.77 ± 0.03 cm-1
Dmax = 320 Å
The data were fitted using a program written by Jan Skov Pedersen
TBSV 0,91 mg/mL
r [Å]
0 50 100 150 200 250 300
p(r)
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
TBSV 1mg/mL
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TBSV Compact Experiment and Fit
TBSV 18.9 mg/mL
q [Å-1]
0.00 0.02 0.04 0.06 0.08 0.10
dσ/d
Ω [c
m-1
]
0.2
0.4
0.6
0.8
1.0
ExperimentFit
TBSV 18.9 mg/mL
q [Å-1]
0.00 0.02 0.04 0.06 0.08 0.10
dσ/d
Ω [c
m-1
]
0.2
0.4
0.6
0.8
1.0
ExperimentFit Linear plots of the
low-q-range of the TBSV samples
Intensity ratio between first peak and the previous minimum is around 10 for the high concentration sample
TBSV 0.91 mg/mL
q [Å-1]
0.00 0.02 0.04 0.06 0.08 0.10
dσ/d
Ω [c
m-1
]
0.01
0.02
0.03
0.04
0.05
ExperimentFit
TBSV 0.91 mg/mL
q [Å-1]
0.00 0.02 0.04 0.06 0.08 0.10
dσ/d
Ω [c
m-1
]
0.01
0.02
0.03
0.04
0.05
ExperimentFit
TBSV 1mg/mL
TBSV 20mg/mL
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Application
Lysozyme
Lysozyme in aqueous solution
The red lines give the fit of the Fourier Transform of the pair distance distribution function p(r) to the experimental data
The sample was measured in an quartz capillary at T=4°C
Measurement time was 5400s for both, the sample and the solvent
q [Å-1]
0.0 0.1 0.2 0.3 0.4
dσ/d
Ω [c
m-1
]
0.0001
0.001
0.01
0.1
6.6 mg/mL2.63 mg/mLFit 6.6 mg/mL Fit 2.6 mg/mL Pair Distance Distribution Function
r [Å]
0 10 20 30 40 50
p(r)
0.00000
0.00005
0.00010
0.00015
0.00020
0.00025
6.6 mg/mL2.6 mg/mL
Resultant pair distance distribution function p(r) normalized by the concentration.
6.6 mg/mL:Rg = 14.8 ± 0.1 ÅI(0) = 0.060 ± 0.004 cm-1Dmax = 45 Å
2.6 mg/mL:Rg = 14.3 ± 0.2 ÅI(0) = 0.024 ± 0.003 cm-1Dmax = 42 Å
Vizualization of hen egg white lysozyme as provided by the Protein Data Bank (PDB 2LYZ).
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Application
Urate
OxidaseVizualization of UNCOMPLEXED URATE OXIDASE FROM ASPERGILLUS FLAVUS provided by the Protein Data Bank (PDB 1R56).
The concentration is about 1.7wt%.
The red lines give the fit of the Fourier Transform of the pair distance distribution function p(r) to the experimental data.
The sample was measured in an quartz capillary at T=4°C
Measurement time was 5400s for both, the sample and the solvent.
Resultant pair distance distribution function p(r) normalized by the concentration.
Rg = 31.28 ± 0.03 ÅR= 40.4 ÅI(0) = 1.230 ± 0.003 cm-1Dmax = 82 Å
q [Å-1]
0.0 0.1 0.2 0.3
dσ/d
Ω [c
m-1
]
0.001
0.01
0.1
1
10
ExperimentFit
Pair Distance Distribution Function
r [Å]
0 20 40 60 80
p(r)
0.0000
0.0005
0.0010
0.0015
0.0020
0.002517.0 mg/mL
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Urate
Oxidase: DIFFRACplus
NanoFit
The experimental data can be described very well with a model for spherical particles with a smooth interface and a Hard Sphere structure factorThe obtained particle size is 40.0 Å with a moderate Gaussian size distribution (σ of 2.5Å)
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Application Brij
700 in Water
Concentration is 1wt%.
Measurement time was 7200s.
Fit using advanced model with compact core and highly solvated corona of PEO
Excess electron density distribution
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Application Liquid Crystal
Liquid crystal sample is a mixture of Pluronic P84 (41wt%), water (33 wt%) and p-xylene (26 wt%)
The 2D pattern show a weak anisotropy. The anistotropy was maybe caused by slightly squeezing the gel-like sample within the Paste Sample holder.
Measurement time from left to right was
1min. 5min.
10min.
Images show 2D pattern of the scattering intensity
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Background Corrected Data
Background corrected scattering intensity of the sample.
4 Peaks are identified:
d [Å] q[Å-1]
127.9 0.0491
63.9 0.0982
42.6 0.1475
31.7 0.198
Peak positions (1:2:3:4) indicatelamellar microstructure!q [Å-1]
0.05 0.10 0.15 0.20 0.25
Inte
rnsi
ty I(
q) [a
.u.]
0.1
1
10
100
1000
Sample A
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Application Liquid Crystal II
Polymer (34EO) content 60%
Measurement time was 20 min
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SAXS Profile
Azimuthalyaveraged scattering intensity
Transmission of the sample was 0.2894
Peak positions (1:√3:2) indicate hexagonal microstructure
q [Å-1]
0.01 0.1
Mea
sure
d in
tens
ity I(
q) [a
.u.]
0.1
1
10
100
1000
q=0.1351Å-1
q=0.0683Å-1
q=0.1181Å-1
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Application HDPE Using the High Resolution Setup
diameter of first / second / third pinhole = 500 mm / 150 mm / 500 mm
diameter of beamstop: 2.0 mm
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High Resolution SAXS Data High Density Polyethylene
Azimuthally averaged scattering intensity of the HDPE sample (background corrected)
Intensities are given in absolute units
Measurement time was 600s
HDPE
q [Å-1]
0.001 0.01 0.1 1
I(q) [
cm-1
]
0.001
0.01
0.1
1
10
100
HDPE: 600 s
2D SAXS pattern
q<0.004Å-1
d=2π/q>1500Å
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Application X-ray Nanography Investigation of a Bone Section
corticalis
spongiosa
~ mm
1.5 nm
67 nm
thickness of calcium-
phosphate platelets:
2-4 nm
collagen- mineral
fibrecomposite
nanostructuremicrostructuremacrostructure
~ cm
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Application Nanography Investigation of a Bone Section
orientation distribution map of mineral crystals
in human bone
x
y
specimen
Detector
X-ray beam
x
y
SAXSNanography
0,1 nm-11 mm
P. Fratzl, H.F. et. Al.J. Appl. Cryst. 30, 765-769 (1997)
GC
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Nanography Two
Scales
in One
X-ray scattering(nm-range)
DetectorDiameter ofX-ray beam(μm-range)
Specimen
X-ray Nanography is the non-destructive investigation of nm structures of mm sized samples with µm resolution
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Application Superalloys Precipitates
in Inconel 718
Ni Cr Fe Nb Mo Al Ti Mn Si Cwt % 52,67 18,37 18,06 6,00 2,91 1,00 0,45 0,21 0,29 0,04at % 51,79 20,39 18,66 3,73 1,75 2,14 0,54 0,22 0,60 0,19
Temperature treatment2h homogenized at 960°C (Serie A)
at 1060°C (Serie B)annealed at 720°C for(30, 60, 120, 240, 480 and 960) min
sample preparation for SAXS
Precipitates: Ni3M-Type: Ni3(Nb, Al, Ti)
γ‘, fcc(γ‘‘, bcc)
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Inconel Data
Treatment
q [Å-1]0.01 0.1
Inte
nsity
[a.u
.]
0.1
1
10
1000 h 0.5 h1 h2 h4 h8 h16 h
q [Å-1]
0.01 0.1
Inte
nsity
[a.u
.]
0.1
1
10
100
1000 0 h0.5 h1 h2 h4 h8 h16 h
Background correction
ττ
ln−
−= bgraw
c
III
q-4
Subtraction of „large“ particles4−−= aqII c
annealing time [min.]0 200 400 600 800 1000 1200
a [Å
-4]
0
5e-7
1e-6
2e-6
2e-6
2e-6
3e-6
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Inconel Scaling
Behavior
q/αm(t) [Å-1]0.01 0.1 1
I / β
m(t)
0.001
0.01
0.1
1
100 h0.5 h1 h2 h4 h8 h16 h
))(/()(),( tqGttqI mm αβ=
2 main parameters
0
50100
150
200
250300
350
0 200 400 600 800 1000Annealing time [min.]
2 π/ α
q max
[Å]
Serie BSerie A
D=2π/(q αm (t))max
Mean particle distance
01020304050607080
0 500 1000
Annealing time [min.]
Rg
[Å]
Serie BSerie A
Radius of Gyration
ReqI g
m
q
m
S2
2
31
)( ⎟⎟⎠
⎞⎜⎜⎝
⎛−
= αλβ
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Comparison SAXS / SANS
SAXS Co-NanoSTAR
Co- Kα (λ = 1.79 Å) 35 kV / 34 mA
cross coupled Göbel mirrors
two pinhole system (100 μm, 300 μm)
sample to detector distance: 64 cm
100 m 40 m 40 m
64 cm
64 c
m
2D-multidetector(resolution 1cm )2
64 cm
Uraniumfuel element
neutron guides
monochromator(mechanical
velocity selector)
ω
cold source evacuated detector tube
sampleI = 10 n/(cm s)max
7 2
SANS D11 facility at the Institute Laue- Langevin (ILL), Grenoble, France
λ = 8 Å
Δλ/λ = 9%
Sample to detector distance: 1.1 m and 4.0 m
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Inconel SANS Data
SANS
q / Å-10,01 0,1
Inte
nsity
[cm
-1]
0,1
1
10 0 h0.5 h1 h2 h4 h8 h16 h
q-4 at q<0.02Å„large“ particles
2 main parameters
radius of gyration
0
10
20
30
40
50
60
0 5 10 15 20
annealing time [h]
Rg
[Å]
SANSSAXS
mean particle distance
0
50
100
150
200
250
300
0 5 10 15 20
annealing time [h]
2 π/q
max
[Å]
SANSSAXS
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Inconel TEM Dark
Field
Micrographs
500 Å
[001] [100]
[100]
disc like shape
128
222 hdRg +=
radius of gyration
0
10
20
30
40
50
60
0 5 10 15 20
annealing time [h]
Rg
[Å]
SANSSAXSTEM
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Summary 2D SAXS with NanoSTAR
Nearly synchrotron like performance on weakly scattering systemsFast and automated measurements on virtually any application (analysis of polymers, biological materials, fibres, metals, nanopowders, complex fluids, proteins, etc)Analysis of sizes, size distributions, shapes and orientation distributionsEfficient solution for scientists as well as researchers requiring fully automated measurementsAll in one instrument
nanostructure analysis by means of Small Angle X-ray Scattering (SAXS)nanostructure mapping with scanning SAXS / X-ray Nanographymolecular structure determination by Wide Angle X-ray Scattering (WAXS)
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SAXS SAXS –– TheThe BigBig--AngleAngle ViewView
Brian Jones
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