Small Angle Neutron Scattering in Different Fields of Research. Henrich Frielinghaus
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1 Small Angle Neutron Scattering in Different Fields of Research Henrich Frielinghaus Jülich Centre for Neutron Science Forschungszentrum Jülich GmbH Lichtenbergstrasse Garching (München) h.frielinghaus@fz-juelich.de
2 Locations
3 Instruments Apply for beam-time: KWS-1, -2 SPHERES MARIA DNS TOPAS ORNL: NSE ILL: IN12-TAS (TREFF) NOSPEC NSE KWS-3 POLI, HEIDI
4 Material Science Physics Scattering Theory Scattering Models Concepts Soft Matter Research Chemistry Biology Materials (Polymers ) Model Systems Concepts Cytology Model Systems Concepts
5 Neutron Sources: (a) Reactors 235 U absobs thermal neutron. Decay to medium heavy nuclei fast neutrons. Moderation needed (1n). Surplus of 1.5 neutrons. (b) Spallation Sources High energy protons hit a heavy nucleus (Hg ). Excitation leads to evaporation of 20-25n with 1 to 100MeV. Decay of nucleus. The spallation source is pulsed. Peak intensity very high (good for instruments: TOF). The medium flux compares well to reactors (not so well for SANS, NSE )
6 New reactor Old reactor
7 Reactors Reactor Period Flux [cm -2 s -1 ] FRM-1 Munich ~1.0e13 FRJ-2 Jülich e14 HFR Grenoble e15 FRM-2 Munich e15 Spallation Sources SNS Oak Ridge, USA J-PARC Tokai, Japan ESS Sweden
8 Neutron Particle Properties m n kg radioactive particle with τ ± 1.8s n p + + e - + ν practically stable, since v ~1000m/s and length ~100m. Spin ½ particle with µ n µ N (µ N is the nuclear magneton) The kinetic energy is non-relativistic (Newton, de Broglie ). Units are: 1 mev J Å (de Broglie wavelength) m/s (E hν) Hz (used less frequently) (E k B T) K
9 Neutron Particle Properties λ n h m v n n h 2m n E n De Broglie wavelength with m n mass v n velocity E n energy ½ m n v n 2 Hot: ~2000K Thermal: ambient T Cold: ~30K (liquid hydrogen / deuterium)
10 Velocity distribution in a thermal source φ( v) ~ v 3 exp v k T B
11 Comparison neutron photon (x-ray) particle: X-rays transversal wave neutron particle wave Mass m phot 0 m n (10) kg Charge 0 0 Spin 1 ½ Magnetic moment 0 µ n (45) µ N Typical energy 10 kev 25 mev Wavelength λ x ch/e 1.24 Å λ n h /(2m n E n ) ½ 1.81 Å Velocity c m/s v n (2E n /m n ) ½ 2187 m/s Both kinds of radiation used to study materials (soft matter, liquids, ) No charge, but strong interaction of photon with electrons. Magnetic moment allows neutrons to study magnetic structures. Energy given here: λ 1Å. (for SANS λ 6 to 15Å) For this wavelength, the large neutron mass leads to small energies. Relative changes of this energy are easily detectable. These energy changes are suitable for soft-matter research. For x-rays one needs larger efforts to detect changes of the energy.
12 Triple Axis Spectrometer: slits Θ slits detector source 123 monochromator sample analyzer 123 preparation analysis r k i 2π r 2π r p mv h h k r f Ei 1 mv 2 2 E f
13 Triple Axis Spectrometer: slits Θ slits detector source 123 monochromator sample analyzer 123 preparation analysis r k i Ei 2π r 2π r p mv h h 1 mv 2 2 r r r Q k f k i E E f E i k r f E f Intensity
14 Bragg s Scattering Law: Θ For preparing/analyzing the beam: d nλ 2d sin Θ retardation k 2π λ πn d sin Θ ``Selective Mirror
15 Bragg s Scattering Law: Θ As a sample: d nλ 2d sin Θ k 2π λ πn d sin Θ k r i Q r k r f r Q Q r k f r k 2 k sin Θ i 2πn d reciprocal space!!
16 Bragg s Scattering Law: (different planes) d All possible Q of constructive interference form also a lattice. (reciprocal lattice)
17 The priciples of neutron scattering (Born Approximation ) dσ dω Flux of scattered neutrons in Ω Flux of incoming neutrons dσ dω 1 V dσ dω Only 10% of neutrons are scattered (coherently). single scattering event The nuclei appear as pointlike particles (nuclear physics Fermi pseudo potential)
18 The priciples of neutron scattering (Born Approximation ) A j b j rr exp( iqr ) j pointlike particles 3 r rr A d r ρ( )exp( iqr ) continuous density dσ dω A 2 intensity Isotopes: different b H D exchange
19 The priciples of neutron scattering (Born Approximation ) n randomly distributed nuclear spins b 2 ( b b ) new coherent scattering length incoherent cross section structure of a pointlike particle
20 Problems of x-ray scattering A 3 r rr d r ( )exp( iqr ) r r f ( Q) s( Q) ρ structure factor of ideal pointlike particles s(q) formfactor of single atoms f(q) At larger angles intensity reduced. What model of electron distribution???
21 Comparison: neutron and x-ray scattering Neutrons Pointlike particles (easy modelling) Hydrogen-nucleus easily detectable Non-systematic scattering length Isotope labelling Each atom can be highlighted Spin density directly detectable (µ n ) Energy transfers comparable to kinetic energy. Penetration: thick samples 1-5mm, and even more (10cm) Non-destructive X-rays Formfactor of atom Hydrogen electron cloud distorted Scattering length ~ Z Resonances prepare certain nuclei Heavier atoms scatter more ( res.) (magnetic dichroism) (huge effort) Thin samples ( mm) Chemical modifications
22 Small Angle Neutron Scattering (SANS)
23 Small Angle Neutron Scattering (SANS)
24 Small Angle Neutron Scattering (SANS) δ δ k1 k 0 Q P(QR) 10 0 k k 2π / λ form factor of sphere with radius R 0 1 Q 4π sin( δ /2) λ elastic Q R Remark on vectors: r Q now Q
25 Q-range of Small Angle Scattering Techniques According to D 2π/Q one can explore particles of size: Probe Wave Length Length Scale Light ~ 6000 Å µm Neutron 2 15 Å 10Å 20µm Three different SANS instruments allow to measure a particle size in a range of four orders of magnitude: Pin - Hole SANS 0.2Å -1 < Q < 10-3 Å -1 Focusing SANS Å -1 < Q < 10-4 Å -1 Double Crystal Diffractometer 10-3 Å -1 < Q < Å -1
26 SANS geometry k 0 k1 2π / λ Q 4π sin( Θ/2) λ - Monochromator - Position Sensitive Detector
27 Velocity selector λ*f [10 3? s] λf f [f]1/s Dornier Selector theory λ 2127 / f Theor Intensität [a.u.] f16000 rpm <λ>8.01å λ/λ0.2 λ7.94å f [10 4 min -1 ] λ [Å]
28 Position sensitive detector Example of sample with oriented anisotropic particles : Isoprene rubber stretched
29 Gas detector 2D-lattice of wires: He + n H + H MeV Resolution ~1cm Time per count ~10µs
30 Scintillation detector Ce activated 6 Li glass Li + n He + H MeV One neutron gives about 4000 photons of 0.4µm wave length
31 Neutron Spin Echo (NSE) Spectrometer Small energies detectable (soft matter) Signal in time domain
32 Summary: r r r Q k f k i A 3 r rr d r ρ( )exp( iqr ) E E f E i dσ dω A 2 Pin - Hole SANS 0.2Å -1 < Q < 10-3 Å -1 Focusing SANS Å -1 < Q < 10-4 Å -1 Double Crystal Diffractometer 10-3 Å -1 < Q < Å -1 Length scale given by: D 2π/Q
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