Introduction to Echo

Laura R. Stingaciu NScD - Large Scale Structures, Oak Ridge National Laboratory

Piotr A. Zolnierczuk Jülich Centre for Neutron Science, Forschungszentrum Jülich 1. Basic Principles of NSE 2. NSE and variations 3. The NSE @ SNS 4. Science Examples 5. Summary and References Neutron in a Nutshell

➢ Measures very small velocity changes by using neutron spin precession in magnetic field

➢ Broad Δ흀/흀 and high resolution

➢ Intermediate Function: I(Q,휏)

➢ Counting intensive and large samples

➢ Complementary to SANS/SAXS Neutron and X-Ray Instruments Landscape

NSE can study:

• Coherent Dynamics • Diffusion • Shape fluctuations • Polymer dynamics • Glassy systems

• Incoherent Dynamics •

• Magnetic Dynamics • Spin Glasses NSE : From an Idea to a Instrument

1972 → 1978 Basic Principles of Inelastic

Neutron scattering kinematics 1 Δ퐸 = ℏ휔 = 푚푣2 − 푚푣2 2 𝑖 푓 푄 = 푘𝑖 − 푘푓

푄

푘푓 Dynamic Structure Factor 푑2휎 휎 푘 = 푓 푁 푆 푄, 휔 푑Ω푑퐸 4휋 푘 푖 푘𝑖

2휋 푘 = 휆 ℎ λ = (Louis de Broglie, 1924) 푚푣 Larmor Precession (I)

Bloch Equation 푑휇Ԧ = 훾휇Ԧ × 퐵 푑푡 B Larmor Frequency μ 휔퐿 = 훾퐵

Neutron Gyromagnetic Ratio n |훾/2휋| ≈ 30 MHz/T Larmor Precession (II)

s Accumulated phase 1 휑 = 휔 푡 = 훾퐵푙 B 퐿 푣 or 푚 휑 = 훾 퐽휆 ℎ for example: λ = 8Å, 퐵푙 = 0.5 Tm → 휑/2휋 ≅ 3 × 104 [nr. of turns]

Notes: 퐽 ≝ 퐵푙 or more precisely 퐽 ≝ ׬ 퐵 ∙ 푑푙 HAHN Echo Neutron Spin Echo (I) Neutron Spin Echo (II) Neutron Spin Echo (inelastic) Neutron Spin Manipulation Mezei Flippers

휋-flipper 휋/2-flipper Correction Coils

r

x

• Problem: • 퐽 = 퐵푙 the same for all trajectories • Solenoid field 퐵 푟 ~푟2

• Solution: • correction coils Neutron Spin Echo Signal

Fourier NSE Signal: 퐼~ cos 휙 = cos 휔휏 time 휏 ≅ 0.186 퐽 휆3 [ns] J = Tm, [휆]=Å 퐼 ~ 퐼 푄 ± න 푆 푄, 휔 cos(휔휏) 푑휔 U = Up

Fourier transform (Real part)

B ~ 퐼(푄) B=Average A=Amplitude A ~ 퐼 푄, 휏 = ℱ[푆 푄, 휔 ]

퐼 푄, 휏 2 A = D = Down 퐼(푄, 0) U − D Coherent/Incoherent Scattering in NSE 1 퐼up = 퐼coh + 퐼inc coherent 3

no-flip incoherent + 1/3 no-flip 2/3 flip

2 퐼down = 퐼inc 1 3 퐼 = 퐼 푓 (휏) − 퐼 푓 (휏) echo coh coh 3 inc inc Energy and Time Domain (QENS/INS ↔ NSE)

QENS: Dynamic Structure Factor NSE: Intermediate Scattering Function S(Q,⍵) I(Q,휏)

퐼퐷(푄, 휔) = 푆(푄, 휔) ∗ 푅(푄, 휔) 퐼퐷(푄, 휏) = 퐼(푄, 휏) 푅(푄, 휏) To get S(Q,⍵) we have to To get I(Q,휏) we just de-convolute instrument divide out instrument resolution resolution NSE Data Reduction

1. Resolution • symmetry phase (echo) • get 푅 푄, 휏; pixel 2. Sample: 퐼푟푎푤(푄, 휏; pixel) 3. Background: • 퐼푏푔푟 푄, 휏; pixel • correction → 퐼푠𝑖푔 푄, 휏; pixel I 푄,휏 퐼 푄, 휏; pixel = sig 4. Compute 푅 푄,휏 Some NSE Theme Variations Resonance and SANS Spin Echo

NRSE SESANS Neutron Resonance Spin Echo Spin Echo SANS

RF field instead of solenoid Spin Echo encoded SANS

• more compact design. • tilted magnetic field • shorter Fourier times • angle encoded in spin precession Paramagnetic NSE

sample is the 휋-flipper

3M/4

M/2

M/4 Wide Angle Neutron Spin Echo

• Large angular coverage • Higher Q (up to 3Å-1) NSE Spectrometers in the World

MUSES ` J-NSE, RESEDA, MIRA VIN-ROSE SNS-NSE NG-A NSE iNSE NSE’s around the World

IN11C @ ILL IN15 @ ILL

J-NSE @ FRM II RESEDA @ FRM II All NSE Spectrometers Classic “IN11-Type” • IN11 - Institute Laue-Langevin, Grenoble, France • IN15 - Institute Laue-Langevin, Grenoble, France • J-NSE – JCNS hosted by FRM-II, Garching, Germany • NG-A NSE – NIST, Gaithersburg, USA • BL-15 SNS-NSE – FZJ & ORNL, Oak Ridge, USA • C2-3-1 iNSE, ISSP JRR-3M, Tokai, Japan

Other • MUSES [NRSE] – Laboratoire Léon Brillouin, Saclay, France • RESEDA [NRSE] – FRM-II, Garching, Germany • MIRA [TAS+MIEZE] – FRM-II, Garching, Germany • FLEXX [TAS+NRSE] – HZB, Berlin, Germany • Larmor [SE+SANS] – ISIS, Didcot, UK • SESANS [SE+SANS] – TU Delft, Holland • C2-3-1 iNSE, ISSP JRR-3M, Tokai, Japan SNS-NSE: NSE Spectrometer at SNS SNS-NSE is an IN11-Type NSE

SC coils, main actively precession shielded

field integral J = 0.56 Tm

cold-coupled moderator hydrogen

neutron guide Ni coated h x b 4 x 8 cm2 wavelength system of 4 selection choppers 2Å < λ < 14Å wavelength BW 3.6Å – frame 2.4Å max. 29/42/56/79° scattering conf. angle dependent)

sample size 30 x 30 mm2

3 rotatable analyzer supermirrors moderator - sample distance: 30x30 cm2 3He DENEX detector mu metal shielding, → 18 m, 21 m, 24 m, 27 m → 32x32 pixels shielding factor 137 TFS: - sample - detector distance: TOF up to 99 channels (typical 42) → echo phase temperature 80+375C → 4 m → dl ~ 0.07Å for @ 42 TOF stability range Cryo: 5K to 650K SNS-NSE Instrument Layout Instrument Cave & Magnetic Shielding

Choppers & Polarizers

Phase Stability Δϕ << 1° SNS-NSE Science Examples SDS Micelles J. Hayter, J. Penfold, J. Chem. Soc., Faraday Trans. 1, 1981,77, 1851-1863

퐼 푄, 푡 2 = 푒−퐷eff 푄 푄 푡 퐼(푄, 0)

퐷eff = 퐷0퐻 푄 /푆 푄 푘푇 퐷 = Stokes-Einstein 0 6휋휂푅 Reptation Model (de Gennes/Doi/Edwards) A. Wischnewski et al., Phys. Rev. Lett. 90 (2003), 058301

Coherent scattering, labeled chain

Melt of long chain linear PEP

푆 푄, 휏 = 1 − 퐹(푄) 푆푙표푐 + F Q 푆푒푠푐 푆(푄, 0) Aspirin modulates the dynamical behavior of membranes V. K. Sharma et al., Phys. Chem. Chem. Phys. 2017

Zilman-Granek Model

퐼 푄, 푡 푘 푇 1/2 푘 푇 = exp −(Γ 푡 2/3) Γ = 0.025 훾 퐵 퐵 푄3 퐼(푄, 0) Bend Bend 푘 휅 휂 Mechanical Properties of Nanoscopic Lipid Domains J. Nickels et al., J. Am. Chem. Soc., 2015, 137 (50)

푆 푞, 휏 푘 푇 1/2 푘 푇 = exp −(Γ 푞 휏 2/3) Γ 푞 = 0.0058 퐵 퐵 푞3 푆(푞, 0) 휅 휂 Fast antibody domain motion L.R. Stingaciu et al. Scientific Reports 2016 Example of Paramagnetic NSE Summary • NSE • high resolution • complementary to SANS/SAXS • measures the intermediate scattering function I(Q,휏)

• SNS-NSE (BL-15) • the first NSE at a Spallation Source • the first one with superconducting coils • the only one with magnetic shielding • available in user program – write and submit proposals! • see http://neutrons.ornl.gov/nse Suggested Literature

1. R. Pynn, Neutron Scattering, Neutron Spin Echo http://www.iub.edu/~neutron/notes/20061204_Pynn.pdf 2. F. Mezei, Z. Physik (1972) 255: 146. 3. F. Mezei (Ed.): Neutron Spin-Echo, Lecture Notes in 128, Springer, 1980. 4. F. Mezei, C. Pappas, T. Gutberlet (Eds.): Neutron Spin-Echo Spectroscopy, Lecture Notes in Physics 601, Springer, 2003. 5. D. Richter, M. Monkenbusch, A. Arbe, J. Colmenero, Neutron Spin Echo in Polymer Systems, Adv. in Polymer Science 174, Springer, 2005 6. M. Monkenbusch, D. Richter, High Resolution Neutron Spectroscopy http://doi.org/10.1016/j.crhy.2007.10.001 7. C.Pappas, G. Ehlers, F. Mezei, Neutron Spin Echo and Magnetism in Neutron Scattering from Magnetic Materials, ed. T. Chatterji, Spinger 2006 8. B.Farago, Basics of Neutron Spin-Echo, ILL Neutron Data Booklet, https://www.ill.eu/fileadmin/users_files/documents/links/documentation/NeutronDat aBooklet.pdf 9. G.L. Squires, Introduction to the Theory of Thermal Neutron Scattering, Cambridge Univ. Press, 3rd edition (2012) Δ흀/흀0 up to ~50% Echo Signals

Time-of-Flight and NSE why we don’t measure 4 points

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