Small Angle Neutron Scattering in Different Fields of Research Henrich Frielinghaus Jülich Centre for Neutron Science Forschungszentrum Jülich GmbH Lichtenbergstrasse 1 85747 Garching (München) h.frielinghaus@fz-juelich.de
Locations
Instruments Apply for beam-time: www.jcns.info!!! KWS-1, -2 SPHERES MARIA DNS TOPAS ORNL: NSE ILL: IN12-TAS (TREFF) NOSPEC NSE KWS-3 POLI, HEIDI
Material Science Physics Scattering Theory Scattering Models Concepts Soft Matter Research Chemistry Biology Materials (Polymers ) Model Systems Concepts Cytology Model Systems Concepts
Neutron Sources: (a) Reactors 235 U absobs thermal neutron. Decay to medium heavy nuclei + 2.5 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 )
New reactor Old reactor
Reactors Reactor Period Flux [cm -2 s -1 ] FRM-1 Munich 1950-1960 ~1.0e13 FRJ-2 Jülich 1960-1970 2.0e14 HFR Grenoble 1970-1980 1.5e15 FRM-2 Munich 1990-2000 0.8e15 Spallation Sources SNS Oak Ridge, USA J-PARC Tokai, Japan ESS Sweden
Neutron Particle Properties m n 1.675 10-27 kg radioactive particle with τ 889.1 ± 1.8s n p + + e - + ν practically stable, since v ~1000m/s and length ~100m. Spin ½ particle with µ n -1.913 µ N (µ N is the nuclear magneton) The kinetic energy is non-relativistic (Newton, de Broglie ). Units are: 1 mev 1.602 10-22 J 9.044 Å (de Broglie wavelength) 437.4 m/s (E hν) 0.2418 10 12 Hz (used less frequently) (E k B T) 11.60 K
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)
Velocity distribution in a thermal source φ( v) ~ v 3 exp 1 2 2 v k T B
Comparison neutron photon (x-ray) particle: X-rays transversal wave neutron particle wave Mass m phot 0 m n 1.6749286(10) 10 27 kg Charge 0 0 Spin 1 ½ Magnetic moment 0 µ n 1.91304275(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 3.00 10 8 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.
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
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
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
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!!
Bragg s Scattering Law: (different planes) d All possible Q of constructive interference form also a lattice. (reciprocal lattice)
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)
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
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
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???
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 (0.1 0.5mm) Chemical modifications
Small Angle Neutron Scattering (SANS)
Small Angle Neutron Scattering (SANS)
Small Angle Neutron Scattering (SANS) δ δ k1 k 0 Q P(QR) 10 0 k k 2π / λ 10-1 10-2 10-3 10-4 10-5 form factor of sphere with radius R 0 1 Q 4π sin( δ /2) λ elastic 10-6 10-7 0 5 10 15 20 25 Q R Remark on vectors: r Q now Q
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 0.5 20µm 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 5 10-3 Å -1 < Q < 10-4 Å -1 Double Crystal Diffractometer 10-3 Å -1 < Q < 2 10-5 Å -1
SANS geometry k 0 k1 2π / λ Q 4π sin( Θ/2) λ - Monochromator - Position Sensitive Detector
Velocity selector λ*f [10 3? s] 3.0 2.5 2.0 1.5 1.0 0.5 λf2011+0.456f [f]1/s Dornier Selector theory λ 2127 / f Theor Intensität [a.u.] 3000 2500 2000 1500 1000 f16000 rpm <λ>8.01å λ/λ0.2 λ7.94å 0.0 0.00 0.50 1.00 1.50 2.00 2.50 f [10 4 min -1 ] 500 0 5 10 15 λ [Å]
Position sensitive detector Example of sample with oriented anisotropic particles : Isoprene rubber stretched
Gas detector 2D-lattice of wires: He + n H + H +0.77 MeV 3 3 1 Resolution ~1cm Time per count ~10µs
Scintillation detector Ce activated 6 Li glass Li + n He + H + 4.79MeV 6 4 3 One neutron gives about 4000 photons of 0.4µm wave length
Neutron Spin Echo (NSE) Spectrometer Small energies detectable (soft matter) Signal in time domain
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 5 10-3 Å -1 < Q < 10-4 Å -1 Double Crystal Diffractometer 10-3 Å -1 < Q < 2 10-5 Å -1 Length scale given by: D 2π/Q