instrumentation for small-angle x-ray and neutron ... · j. skov pedersen (2002). `instrumentation...
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Jan Skov Pedersen
Preliminary version
Instrumentation for Small-Angle X-ray and Neutron Scattering and
Instrumental Smearing Effects
Jan Skov Pedersen, Department of Chemistry,
and iNANO Interdicsiplinary NanoScience CenterUniversity of Aarhus, Denmark
Limited to most common instruments……
Jan Skov Pedersen
Preliminary version
Outline
• Instrumental Smearing• SAXS Instrumentation• SANS Instrumentation
Keywords:Long-slitPin-holeFocussing…
Litterature
J. SKOV PEDERSEN, (1995). `Instrumentation for Small-angle Scattering'. In: `Modern Aspects of Small-angle Scattering'. Ed.: H. Brumberger (Kluwer Academic Press). 57-91
J. SKOV PEDERSEN (2002). `Instrumentation for Small-Angle X-Ray and Neutron Scattering and Instrumental Smearing Effects.' In ' Neutrons, X-Rays and Light. Scattering Methods Applied to Soft CondensedMatter'. Eds.: T. Zemb and P. Lindner (Elsevier). 127-144.
Jan Skov Pedersen
Preliminary version
Schematic setup for small-angle scattering
SourceMonochromator
Wavelength λ
2θλθπ /sin4≡qC. Glinka
Jan Skov Pedersen
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Flux and resolution
Well-defined wavelength and well-collimated beam
⇒ low flux
⇒ relax resolution,
usually wavelength or collimationor one of the directions of collimation (out-of-plane or focusing)
Often not an issue for synchrotron radiation due to extreme flux!
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Preliminary version
Increase flux:
Focussing at detector
• Relax instrumental resolutionLong-slit geometry (x-rays)Increase wavelength spread
• Focus beamMainly used for x-rays
λθπ /sin4≡q
Does not lead to smearing for SAXS from non-crystalline samples
Jan Skov Pedersen
Preliminary version
Long-slit geometry
λθπ /sin4≡q
2θ
SourceSample Detector
Jan Skov Pedersen
Preliminary version
Long-slit geometry
λθπ /sin4≡q
2θ
SourceSample Detector
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Distributions of q
(a) long-slit geometry (b) pinhole geometry.
Constant q contours
Distributions of q:
Jan Skov Pedersen
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Rotating anode
X-ray sources I
• Laboratory- Sealed tube- Rotating anode (distribute heat)- Micro source (reduce heat,
increase peak intensity)• Isotropic emission !• Characteristic lines !• Source size: 10µm to 1 mm
Sealed tube
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X-ray sources II• Synchrotron
-Bending magnet-Wiggler (series of magnet, incoherent addition of rays) I∝ N-Undulator (series of magnet, coherent addition of rays) I∝ N2
• Collimated emission !• Continuous spectrum (except Undulator)!• beam size: 10µm to 1 mm
Als-Nielsen and MacMorrow:
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SAXS principle beamstopsample
Guard pinhole/slit or anti-scatter pinhole/slit
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Kratky block camera (Long slit)
q range to 0.003 1/Å1/ÅSealedSealed tube 10tube 1077--10108 8 phph/s/sNonNon--orientedoriented samplesample
-- oror perfectlyperfectly orientedoriented
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Data from block copolymer micelles
1% (w/w) P-85 solution at 50 C:
Smeared data
Ideal data
Otto Glatter, Gunther Scherf, Karin Schillen and Wyn Brown,Macromolecules 1994, 27, 6046-6054
Characterization of a Poly(ethy1ene oxide)-Poly(propy1ene oxide)Triblock Copolymer (E027-PO39-EO27) in Aqueous Solution
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Long-slit geometry: Smearing
2θ
Source Detector
q||
λθπ /sin4≡q
q⊥
Sample
w||(q||) wλ (qλ)
λq||
w⊥ (q⊥ )
q⊥
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Preliminary version
Long-slit smearing
)(qddΩσ
is ideal is ideal crosscross sectionsection
Note: 3 numerical integrations !!!
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Preliminary version
SAXSess cameraImproved Kratky camera:
Rotating anode + Göbel mirrors: 1010 ph/s !(monochromatic beam)
Short acquisition times/deadtime effects
Image plate detector with less than 0.1 mm resolution
(’photographic’ linear detector)
Note: Also wide-angle option and pseudo-pinhole geometry
A. Bergmann, D. Orthaber, G. Scherf and O. GlatterAppl. Cryst. (2000). 33, 869-875 Improvement of SAXS measurements on Kratky slit systems by Göbel mirrors and imaging-plate detectors
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Preliminary version
Göbel mirrors
Si-W multi-layers on a parabolic substrate
Lattice spacing of multilayer varies with position,so that divergent beam comes out parallel !
Length about 5 cm, Bragg angle a few degrees
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Preliminary version
Bonse-Hart camera = Ultra SAXS
Two multiple bounce perfect crystals⇒ Good collimation in scattering plane of crystal
’long-slit’ smearing in perpendicular direction• Large beam size (3 x 3 mm2)• q down to 10-4 1/Å• Rotating anode: 106 ph/s• Sequential data collection• Always subtract two very large signals to obtain scattering from sample
•Zemb et al.: Göbel mirrors gives factor of 10 increase in flux•Synchrotrons allows double Bonse-Hart geometry with pinhole smearing
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Perfect crystal
Extinction gives effectively a finite number of layers contributingto the diffraction
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Perfect crystal: Darwin curveWidth at 1 Å is about 0.1 mrad
Als-Nielsen and MacMorrow:
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Bonse and Hart, 1965
Single bounce R(θ) = (θ-θo)2
m-bounce R(θ) = (θ-θo)2m
-but limitations due to thermal diffuse scattering and imperfections
- note also influence of absorption
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Simple pin-hole camera
•Lower flux, but use 2D detector•In general: qmin=0.01-0.005 1/Å at lab sources
qmin=0.001 1/Å at synchrotron sources•Can be used for any sample!
Oak Ridge 10 m camera:sample beamstop
Graphite monochromator
2D detector
sample 1x1 mm2; 106 ph/s6kW rot. anode
Graphite: Mosaic crystal: Broad roacking curve
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Huxley-Holmes SAXS
Detector
EMBL Hamburg, bending magnet 1012 photons/s/100mARotating anode: 107 ph/s
•Mirror: 1m !•Source-monochr.: 20 m•Monochr.-detector: 10 m•Sample size 5 x 2 mm2
Franks-type set-up: Two mirrors + filter at conv. source
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Pinhole PinholeSample
0.4 x 0.4 mm, 2 kW 0.1 mmØ 0.3 mmØ 2.5mm
Beamstop DetectorSource Göbel mirrors
150mm 40 – 400 mm 150mm 640 cm
Developed by P. Fraztl,Bruker AXS and Anton Paar
Nanostar ori short
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NanoSTAR for solution scattering
The Small Angle X-rayScattering (SAXS)setup consists of:
• A rotating anode• Göbel mirrors• A three pin-hole
collimation• An integrated
vacuum• A 2D-gas detector
High fluxLow background
•Standard: 0.01 to 0.35 1/Åwith 2 x 107 ph/s
•Beamsize 1 mm diamterAarhus SAXS
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New NanoSTAR
Close window
Jan Skov Pedersen
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SAXS data from Aarhus NanoSTAR
•Sodium dodecyl sulphate (SDS) micelles•1wt% in water. •2 hrs acquisition time
SDS 1wt%
q [Å-1]
0.1 0.2 0.3
I(q) [
cm-1
]
0.001
0.01
0.1
DataFit
∆ρ(r) for SDS micelle model
r [Å]
0 10 20 30 40 50
∆ρ(r)
[a.u
.]
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
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Neutron sources• Steady-state fission reactors
- cold sources for long wavelength neutrons
• Spallation sources (accellerators based)- Moderators(time of flight technique!!)
Institute Laue-langevin, Grenoble
ISIS, UK:
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Steady-state SANS
Broad band monochromator: mechanical velocity selector
Typically 10 – 20 % (FWHM) wavelength spread
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Low q – high q 0.001 – 0.5 1/Åλ = 3 – 30 Å
Long wavelengthlow q
Short wavelengthhigh q
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Risø SANS: now at the PSI
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Smearing contributions
<λ>∆λ/<λ> <2θ>
Nominal q: <q> = 4πsin <θ>/<λ>
Jan Skov Pedersen
Preliminary version
Smearing contributions
2θ
<2θ>
λ
<λ>∆λ/<λ>
Nominal q: <q> = 4πsin <θ>/<λ>Actual q: q = 4πsin θ/λ
Jan Skov Pedersen
Preliminary version
SANS resolution function I
Derivative with respect to λ:
Derivative with respect to θ:
Assume independent distributions described by Gassians:
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SANS resolution function IIThe various contributions can be measured, simulated or calculated
Pedersen, Posselt and Mortensen (1990). J. Applied Cryst. 32, 321
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Preliminary version
Collimation and detector contributions
- Includes also detector smearing
ILL D11: (Timmins, Svergun)Direct beam (attenuated): Azmuthally averagedSource: 5.0 x 3.0 cm2
Sample: 1.0 x 0.7 cm2
Source-sample: 5 mSample-detector: 3 m
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Analysis with smearing2
322
)()]cos()[sin(3)(
−∆=
Ω qRqRqRqRVq
dd ρσ
q [Å-1]
0.000 0.005 0.010 0.015 0.020 0.025 0.030
I(q)
10-1
100
101
102
103
104
105
SANS from Latex spheresSmeared fitIdeal fit
Data from Wiggnal et al.
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Preliminary version
TOF SANS LOQ at ISIS, UK
Advantage:Everything recorded at one settingMain problem:Low flux at low q
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Preliminary version
Neutron Bonse-Hart set-up
Low fluxLarge sample (cm2)q = 2x10-5-3x10-3 1/Å
Agamalian, M., Wignall, G.D. and Triolo, R. (1997). J. Appl. Cryst., 30, 345–352.
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Preliminary version
SummarySAXS: Kratky camera
Bonse-hart setup
Simple pinhole cameraHuxley Holmes cameraFranks setupNanoSTAR with Göbel mirros+ many others
SANS: Steady state pinhole cameraTime-of Flight pinhole cameraBonse-Hart setup+ more
Instrumental smearing: - is routinely included in state-of-the-artdata analysis
Long-slit geometry
Long-slit geometry