What Can Be Done Using NEUTRON SPIN ECHO

What can be done using NEUTRON SPIN ECHO

Michihiro Nagao

NIST Center for Neutron Research & Indiana University published papers using NSE

60 total number of Papers Spectrometer polymer 50 glass membrane SolidStatePhysics 40 Further improvement and development of P. G. de Gennes the NSE technique! 30 Nobel Prize in Physics 1991

Number of Papers 20 Still increasing the discovery of the principle technique papers by F. Mezei in 1972

10 polymer dynamics researches by D. Richter in 1980’s

0 1975 1980 1985 1990 1995 2000 2005 Year searched using web of science: keyword=neutron spin echo how to choose a spectrometer

1. length scale diffraction? small-angle? structure research & method

neutron energy [meV] ~100 ~1 ~0.01 thermal neutron cold neutron

DNA

protein viruses

crystalline, micelles magnetic polymers, gels strucutre

zeolites micro-porus polymer phase separated vesicles structure neutron diffraction small-angle neutron scattering x-ray diffraction ultra small-angle neutron scattering small-angle x-ray scattering ultra small-angle x-ray scattering elecron microscope optical microscope 10-10 10-9 10-8 10-7 10-6 10-5 size [m] how to choose a spectrometer

1. length scale diffraction? small-angle? 2. energy scale neV? meV? dynamics research & method d [Å] 105 104 103 102 101 100 10-1 10-2 100 10-6 Raman TOFhydrogen 10-1 modes molecular 10-5 -2 vibrations 10 spin lattice 10-4 waves vibrations -3 10 heavy 10-3 Fermions NSE -4 Brillouin critical molecular 10 10-2 t [ns] scattering rotations -5 10 diffusion -1 E [eV] 10 tunneling -6 spectroscopyBS 10 100 polymers 10-7 biological systems 101 NSE: highest energy glasses 10-8 2 resolution among other 10 -9 10 neutron spectrometers 103 DLS XPCS 10-10 10-4 10-3 10-2 10-1 100 101 102 q [Å-1 ] dynamics research & method d [Å] 105 104 103 102 101 100 10-1 10-2 100 10-6 Raman TOF -1 10 10-5 -2 side chain motion 10 10-4 -3 10 local motion 10-3 -4 Brillouin NSE

10 -2 t [ns] segment motion 10 10-5 -1

E [eV] 10

-6 BS 10 100 -7 10 101 -8 10 collective diffusion motion 102 10-9 3 reptation motion 10 DLS XPCS 10-10 10-4 10-3 10-2 10-1 100 101 102 q [Å-1 ] how to choose a spectrometer

1. length scale diffraction? small-angle? 2. energy scale neV? meV? 3. dynamics excitation? relaxation? inelastic vs quasi-elastic scattering

10 10 elastic scattering elastic scattering 8 8

6 6

4 4 Intensity Intensity quasi-elastic scattering 2 inelastic scattering 2

0 0 -10 -5 0 5 10 -10 -5 0 5 10 [a.u.] [a.u.] excitation: neutrons exchange relaxation: neutrons exchange energy with an oscillation energy to make another new motion which has a finite equilibrium state (no typical energy transfer finite energy transfer exists)

mean energy of neutrons are the phonon, magnon, ... same before and after the scattering NSE works in time domain: S(q,ω) vs I(q,t)

intermediate scattering function is the fourier transform of dynamic structure factor excitation I(q,t) shows an oscillating function

10 1

4 Intensity Intensity

0 0 -10 -5 0 5 10 0 5 10 [a.u.] t [a.u.] NSE works in time domain: S(q,ω) vs I(q,t)

intermediate scattering function is the fourier transform of dynamic structure factor relaxation I(q,t) shows a decaying function

10 1

4 Intensity Intensity

0 0 -10 -5 0 5 10 0 5 10 [a.u.] t [a.u.]

NSE is the best suited to see relaxation dynamics how to choose a spectrometer

1. length scale diffraction? small-angle? 2. energy scale neV? meV? 3. dynamics excitation? relaxation? 4. intensity coherent dynamics? incoherent dynamics? Scattering Intensity

Scattering Angle [˚] -3 -2 -1 0 10 10 10 10 10 10 Reptation motion Colldective Diffusion Coherent 8 Incoherent

] Segment motion

-1 6 Local motion Side chain motion 4

I(q) [cm coherent scattering incoherent 2

0 -4 -3 -2 -1 0 10 10 10 10 10 -1 NSE q [Å ] BS DCS larger scale objects: slower dynamics coherent dynamics incoherent dynamics at high q problems to observe incoherent dynamics ... 1: limitation of the detection area 2: spin flip scattering Spin ﬂip scattering

non-flip coherent

1/3 non-flip + 2/3 flip incoherent we loose 1/3 of signals when we measure incoherent dynamics

flip magnetic settings of NSE spectrometer for coherent nucleus scattering and magnetic scattering experiments are different summary: usage of NSE 1. length scale We can cover q-range from 0.02 to 1.8 Å-1 . However, the detection area is limited and normally high-q experiment takes longer time. 2. energy scale We can cover energy range from several neV to sub meV (time range from ps to hundreds of ns). Highest energy resolution among inelastic/quasi elastic neutron scattering spectrometers. 3. dynamics Suited to observe relaxation dynamics. 4. intensity Coherent core scattering at low q is the best measured by NSE so far. Incoherent dynamics and magnetic scattering can also be measured. large length scale (>1nm), small energy scale (neV), coherent dynamics, relaxation, ... some keywords today

Neutron Spin Polarization & Precession

Neutron Spin Echo & Echo Signal

Fourier Time how NSE achieves highest energy resolution Coherent, Incoherent & Magnetic Scattering

Intermediate Scattering Function we use I(q,t) and S(q,t) as the same meaning

Relaxation, Diffusion, Thermal Fluctuation,... THANK YOU FOR YOUR ATTENTION!