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

Preliminary version

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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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

Jan Skov Pedersen

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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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Long-slit smearing

)(qddΩσ

is ideal is ideal crosscross sectionsection

Note: 3 numerical integrations !!!

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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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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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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

Jan Skov Pedersen

Preliminary version

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

Jan Skov Pedersen

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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

Jan Skov Pedersen

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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

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SANS resolution function I

Derivative with respect to λ:

Derivative with respect to θ:

Assume independent distributions described by Gassians:

Jan Skov Pedersen

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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

Jan Skov Pedersen

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

Jan Skov Pedersen

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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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TOF SANS LOQ at ISIS, UK

Advantage:Everything recorded at one settingMain problem:Low flux at low q

Jan Skov Pedersen

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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.

Jan Skov Pedersen

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