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Introduction to Neutron Spin Echo Spectroscopy

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Introduction to Neutron Spin Echo Spectroscopy 6/15/12 Introduction to Neutron Spin Echo Spectroscopy Antonio Faraone NIST Center for Neutron research & Dept. of Material Science and Engineering, U. of Maryland Methods and Applicaons of SANS, NR, and NSE NCNR, June 18th – 23rd, 2012 Outline • History • Dynamic Neutron Scattering (Recap) • The principles of Neutron Spin Echo • Instrumental Setup of Neutron Spin Echo • Conclusion 1 6/15/12 The beginning F. Mezei, Z. Physik. 255, 146 (1972). NSE Today in the World SPAN MUSES RESEDA NG5-NSE IN11 J-NSE IN15 (SNS-NSE) iNSE + NSE option for triple-axis spectrometers! + developing ones! 2 6/15/12 What does a NSE Spectrometer Look Like? IN-11 @ ILL The first IN-11c @ ILL; Wide Detector Option 3 6/15/12 IN-15 @ ILL MUSES, Resonance Spin Echo @ LLB 4 6/15/12 NSE @ NCNR NSE @ SNS 5 6/15/12 NSE Publications 60 total number of Papers Spectrometer polymer 50 glass membrane SolidStatePhysics 40 Further improvement and development of P. G. de Gennes the NSE technique! Nobel Prize in Physics 1991 30 The technique papers Number ofPapers Number 20 discovery of the principle are still increasing by F. Mezei in 1972 10 polymer dynamics researches by D. Richter in 1980’s 0 1975 1980 1985 1990 1995 2000 2005 Year publication record; searched using web of science: keyword=neutron spin echo! 6 6/15/12 Static and Dynamic Scattering Sample ki, Ei θ ki Probe: photons (visible light, X-rays), kf Q neutrons, electrons, … kf, Ef Momentum Exchanged: Q=ki-kf Energy Exchanged: E=Ei-Ef Detector dσ d 2σ StaticScattering: ≈ S(Q) Dynamic Scattering: ≈ S(Q, E) dΩ dΩdE Static and Dynamic Scattering S(Q) = FTS {exp[−iQ(ri −r j )] } Fourier Transform of the Space Correlation Function S(Q, E) = FTT {exp[−iQ(r(t) −r(0))] }= FTT {I(Q,t)}= FTST {G(r,t)} Fourier Transform of the Space-Time Correlation Function I(Q,t) Intermediate Scattering Function (ISF) G(r,t) van Hove Correlation Function 7 6/15/12 S(Q,E) Inelastic Scattering Q=x.xx Å-1 excitation: neutrons Instrumental exchange energy with an Resolution oscillatory motion which has a finite energy transfer Quasielastic Ex: phonon, magnon, ... Inelastic Broadening Scattering Quasielastic Scattering relaxation: neutrons exchange energy with random motion which makes another new Thermally Activated Motions equilibrium state (no typical Takes Place in the System. finite energy transfer exists) Ex.: rotation, vibration, diffusion… Energy and Time Domain NSE works in the TIME domain NSE measures the Normalized Intermediate Scattering Function: I(Q,t)/I(Q,0) 1.0 0.8 0.6 FT! 0.4 I(q,t)/I(q,0) 0.2 0.0 0 20 40 60 80 100 120 t 1.0 0.8 0.6 FT! 0.4 I(q,t)/I(q,0) 0.2 0.0 0 20 40 60 80 100 120 t NSE Deals Almost Exclusively with Quasielastic Scattering 8 6/15/12 Dynamic Neutron Scattering NSE is the neutron scattering techniques that gives acces to the largest length- scales and longest time scales 9 6/15/12 The Idea of Neutron Spin Echo NSE Breaks the Relationship between Intensity & Resolution • Traditional Instruments – define both incident & scattered wavevectors in order to define E and Q accurately • Traditional Instruments – use collimators, monochromators, choppers etc to define both ki and kf • NSE – measure the difference between appropriate components of ki and kf (original use: measure ki – kf i.e. energy change) • NSE – use the neutron’s spin polarization to encode the difference between components of ki and kf • NSE – can use large beam divergence &/or poor monochromatization to increase signal intensity, while maintaining very good resolution Neutron Precession ω B Neutron Properties L -27 • Mass, mn = 1.675×10 kg • Spin, S = 1/2 [in units of h/(2π)] • Gyromagnetic ratio =g /[h/(2 )] = γ nµn π S 1.832×108 s-1T-1 (29.164 MHz T-1) In a Magnetic Field N • The neutron experiences a torque from a magnetic field B perpendicular to its spin N = S × B direction. • Precession with the Larmor frequency: ωL = γB 10 6/15/12 Scattering Event: Single Neutron • elastic scattering • inelastic scattering sample B B S Bdl 1 1 γΔv mλ γΔv ∫ ⎛ ⎞ Bdl Bdl Bdl ϕ = γ Δϕ = γ ⎜ − ⎟ = 2 = v ⎝ v v' ⎠∫ v ∫ h v ∫ 1 γBmλ γmλ NT (λ)= dl = Bdl = 7370× J[T ⋅m]×λ[Å] 2π ∫ h 2πh ∫ J field integral. At NCNR: J = 0.5 T.m J = Bdl max ∫ NT (λ=8Å) ≈ 3×105 Scattering Event: Neutron Beam B B0 1 Analyzer S f(λ) Again: Elastic scattering The measured quantity is the Polarization, i.e. the spin component along x: Px=〈cosϕ(λ)〉: B0dl B1dl ϕ = γ ∫ −γ ∫ Echo Condition: J = J v v 0 1 f (λ ) Note: P =1 ϕ = 0 x The requirement that ϕ=0 can be in some cases released. This treatment is valid for the most common case of Quasi-Elastic Scattering 11 6/15/12 Scattering Event: Neutron Beam B B0 1 Analyzer S f(λ) Again: Quasi-Elastic scattering The measured quantity is the Polarization, i.e. the spin component along x: Px=〈cosϕ(λ)〉: B dl B dl ∫ 0 ∫ 1 m m ϕ = γ −γ Series Expansion in δλ and δJ ϕ ≈ γ J0δλ +γ (J0 − J1 )λ v(λ) v(λ)+δv h h h2 ⎡ 1 1 ⎤ h2 δλ phase E ω = Δ = ⎢ 2 − 2 ⎥ ≈ 3 2 3 2m ⎣λ (λ +δλ) ⎦ m λ m λ m ϕ = γ 2 J0ω +γ (J0 − J1 )λ ω 2πh h δλ = mλ3 2πh 0 at the echo condition The Basic Equations of NSE ⎡ m2λ3 m ⎤ P = cos ϕ = f λ S Q,ω cos γ J ω +γ J − J λ dλdω x ( ) ∫∫ ( ) ( ) ⎢ 2 0 ( 0 1 ) ⎥ ⎣ 2πh h ⎦ Even Function ⎡ m ⎤ ⎡ m2λ3 ⎤ P = cos ϕ = f λ cos γ J − J λ dλ × S Q,ω cos γ J ω dω x ( ) ∫ ( ) ⎢ ( 0 1 ) ⎥ ∫ ( ) ⎢ 2 0 ⎥ ⎣ h ⎦ ⎣ 2πh ⎦ 2 FT of the wavelength FT of the Dynamicm 3 Structure Fourier time t = γ J0λ distribution 2Factorπh2 P J phi ,Q,t P J phi S Q, cos t d P J phi I Q,t x (Δ )= s (Δ )∫ ( ω) [ω ] ω = s (Δ ) ( ) NSE measures the Fourier Transform of the Dynamic Structure Factor 12 6/15/12 NSE principles: summary • Neutron Spin Echo Instruments are “machinery” which measure the Fourier transform of the Dynamic Structure Factor, S(Q,ω), i.e. the (normalized) Intermediate Scattering Function (ISF), I(Q,t)/I(Q,0). • The neutrons’ velocity is encoded into their spin state. - The neutron beam goes through two equals homogeneous magnetic field paths before and after the sample. - Within the magnetic fields each neutrons’ spin performs a precession at a speed determined by the field intensity. - If the scattering event does not change the neutrons’ speed (elastic scattering), the initial polarization of the beam is recovered. • The polarization of the scattered neutron beam is proportional to the ISF at a specific value of t determined by the strength of the precession field (and by the incident neutron wavelength). NSE Effect Elastic Scattering QuasiElastic Scattering 13 6/15/12 NSE: Instrumental Setup Neutron Velocity Selector Phase coil Analyzer Mezei Cavity, Sample Transmission Polarizer Area Detector 2nd π/2 flipper π flipper, phase Stop of the Precession inversion 1st π/2 flipper Start of the Precession 1st and 2nd main precession coils 14 6/15/12 Polarization Analysis Neutron Velocity Selector Phase coil Analyzer Mezei Cavity, Sample Transmission Polarizer Area Detector 2nd π/2 flipper π flipper, phase Stop of the Precession inversion 1st π/2 flipper Start of the Precession 1st and 2nd main precession coils SF Polarization Analysis Neutron Velocity Selector Phase coil Analyzer Mezei Cavity, Sample Transmission Polarizer Area Detector 2nd π/2 flipper π flipper, phase Stop of the Precession inversion 1st π/2 flipper Start of the Precession 1st and 2nd main precession coils NSF 15 6/15/12 Nuclear Scattering Event and Neutron Moment non-flip coherent 1/3 non-flip + 2/3 flip incoherent Nuclear Scattering Polarization Analysis If no magnetic scattering is present and the sample is isotropic, the three polarization directions, xyz, are equivalent: 3 N incoh = SF 2 1 N coh = NSF − SF 2 16 6/15/12 Structure Factor The Structure Factor, S(Q), is the most relevant information for the preparation and, later, interpretation of a NSE experiment. SANS Liquid Correlation Peaks Incoherent Nanoscale Atoms Object NSE: Coherent vs Incoherent NSE is known for the investigation of the coherent dynamics. Incoherent scattering intensity is reduced to -1/3 in NSE. The best achievable flipping ratio is 0.5. However, the main limitation to the study of incoherent scattering by NSE is the Q coverage of the instrument. Recent advancements in NSE instrumentation aim to overcome this limitation (IN-11C, the WASP project). 17 6/15/12 NSE: Coherent vs Incoherent NSE is known for the investigation of the coherent dynamics. Incoherent scattering intensity is reduced to -1/3 in NSE. The best achievable flipping ratio is 0.5. However, the main limitation to the study of incoherent scattering by NSE is the Q coverage of the instrument. Most important is to avoid Q areas where coherent and incoherent intensity cancel each other. The Intermediate Scattering Function NSE measures the time decay of the structures defining S(Q): I(Q,t) exp{− iQ[ri (t)− rj (0)]} = I(Q,0) exp{− iQ[ri (0)− rj (0)]} 18 6/15/12 Types of Dynamics Diffusion Rota5on Atomic/molecular Dynamics Shape Fluctua5on Self H dynamics At length scales larger than the macromolecular size: Diffusion.
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