by

Roger Pynn

Lectures 11: Neutron Spin Echo

The Goal of Neutron Spin Echo is to Break the Inverse Relationship between Intensity & Resolution

• Traditional – define both incident & scattered wavevectors in order to define E and Q accurately

• Traditional – use collimators, monochromators, choppers etc to define both ki and kf

• NSE – measure as a function of 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

The Principles of NSE are Very Simple

• If a spin rotates anticlockwise & then clockwise by the same amount it comes back to the same orientation– Need to reverse the direction of the applied field– Independent of neutron speed provided the speed is constant

• The same effect can be obtained by reversing the precession angle at the mid-point and continuing the precession in the same sense– Use a π rotation

• If the neutron’s velocity, v, is changed by the sample, its spin will not come back to the same orientation– The difference will be a measure of the change in the neutron’s speed or

energy

In NSE*, Neutron Spins Precess Before and After Scattering & a Polarization Echo is Obtained if Scattering is Elastic

Initially, neutronsare polarizedalong z

Rotate spins intox-y precession plane

Allow spins toprecess around z: slower neutrons precess further overa fixed path-length

Rotate spins through π aboutx axis

Elastic ScatteringEvent

Allow spins to precessaround z: all spins are in the same direction at the echo point if ΔE = 0

Rotate spinsto z andmeasurepolarization

SF

SFπ/2

π

π/2

)cos( , 21 φφ −=PonPolarizatiFinal

yxz

* F. Mezei, Z. Physik, 255 (1972) 145

For Quasi-elastic Scattering, the Echo Polarization depends on Energy Transfer

• If the neutron changes energy when it scatters, the precession phases before & after scattering, φ1 & φ2, will be different:

• To lowest order, the difference between φ1 & φ2 depends only on ω (I.e. v1 – v2) & not on v1 & v2 separately

• The measured polarization, <P>, is the average of cos(φ1 - φ2) over all transmitted neutrons I.e.

2

32

3221

21

22

21

211

)(21 using

hBdm

mvBdv

vBd

vvBd

vmvvvm

πωλγωγδγγφφ

δω

=≈≈⎟⎟⎠

⎞⎜⎜⎝

⎛−=−

≈−=

h

h

∫∫∫∫ −

=ωλωλ

ωλφφωλ

ddQSI

ddQSIP

),()(

)cos(),()( 21r

r

Neutron Polarization at the Echo Point is a Measure of the Intermediate Scattering Function

• I(Q,t) is called the intermediate scattering function– Time Fourier transform of S(Q,ω) or the Q Fourier transform of G(r,t), the two

particle correlation function

• NSE probes the sample dynamics as a function of time rather thanas a function of ω

• The spin echo time, τ, is the “correlation time”

32

2

21

2 time"echospin " thewhere

) )cos(),(),()(

)cos(),()(

λπ

γτ

ωωτωωλωλ

ωλφφωλ

hmBd

,τQI(dQSddQSI

ddQSIP

=

=≈−

= ∫∫∫∫∫ rr

r

r

1861.01400.61120.41

τ(ns)

λ (nm)

Bd(T.m)

What does a NSE Spectrometer Look Like?IN11 at ILL was the First

Neutron Polarization is Measured using an Asymmetric Scan around the Echo Point

0 1 2 3 4 5 6 70

500

1000

1500

2000

Neu

tron

coun

ts (

per 5

0 se

c)

Current in coil 30 1 2 3 4 5 6 7

0

500

1000

1500

2000

Neu

tron

coun

ts (

per 5

0 se

c)

Bd2 (Arbitrary Units)

The echo amplitude decreases when (Bd)1 differs from (Bd)2because the incident neutron beam is not monochromatic. For elastic scattering:

{ } λλγλ dBdBdhmIP .)()(cos)(~ 21∫ ⎥⎦

⎤⎢⎣⎡ −

Echo Point

Because the echo point is the same for all neutron wavelengths,we can use a broad wavelength band and enhance the signal intensity

Field-Integral Inhomogeneities cause τ to vary over the Neutron Beam: They can be Corrected

• Solenoids (used as main precession fields) have fields that vary as r2

away from the axis of symmetry because of end effects (div B = 0)

• According to Ampere’s law, a current distribution that varies as r 2 can correct the field-integral inhomog-eneities for parallel paths

• Similar devices can be usedto correct the integral alongdivergent paths

Fresnel correction coil for IN15

B

solenoid

0 .001 0 .01 0 .1 1 10 100Q (Å-1)

Ene

rgy

Tran

sfer

(meV

)

Ne utro ns in Co nde ns e d Matte r Re s e arc h

S pa lla tio n - Ch opp er ILL - w ithou t s p in -ec ho ILL - w ith s p in -e ch o

Crystal Fields

Spin Waves

Neutron Induced

ExcitationsHydrogen Modes

Molecu lar Vibrations

Lattice Vibrations

and Anharmonicity

Aggregate Motion

Polymers and

Biological Systems

Critical Scattering

Diffusive Modes

Slower Motions

Resolved

Molecular Reorientation

Tunneling Spectroscopy

Surface Effects?

[Larger Objects Resolved]

Proteins in Solution Viruses

Micelles PolymersMetallurgical

SystemsColloids

Membranes Proteins

C rystal and Magnetic

StructuresAmorphous

Systems

Accurate Liquid StructuresP recision Crystallography

Anharmonicity

1

100

10000

0.01

10-4

10-6

Momentum DistributionsElastic Scattering

Electron- phonon

Interactions

Itinerant Magnets

Molecular Motions

Coherent Modes in Glasses

and Liquids

SPSS - Chopper Spectrometer

Neutron Spin Echo has significantly extended the (Q,E) range to which neutron scattering can be applied

Neutron Spin Echo study of Deformations of Spherical Droplets*

* Courtesy of B. Farago

• Within a coil, the neutron is subjected to a steady, strong field, B0, and a weak rf field B1cos(ωt) with a frequency ω = ω0 = γ B0

– Typically, B0 ~ 100 G and B1 ~ 1 G

• In a frame rotating with frequency ω0, the neutron spin sees a constant field of magnitude B1

• The length of the coil region is chosen so that the neutron spin precessesaround B1 thru an angle π.

• The neutron precession phase is:

The Principle of Neutron Resonant Spin Echo

B1(t)

B0

vdentryneutron

entryRF

entryneutron

entryRF

exitRF

exitneutron

/2

)(

0ωφφ

φφφφ

+−=

−+=entryB1

entryS

rotatedS π

exitB1

exitS

�

����� �� ���� ��������

���� ��� ���� �� ������ ���� ���� �

� �� ��� �

�� ��� � �� � ��

���� ���� � ���

� �� � �� � �����

�

��� ���� � ���

�� ��� � �� � ������

�

���� �� �����

�

� �� ���� �� �����

�

�� ��� � �� � ��

����� ��

���

� ���� � �� �����

�

� �� � �� � �����

��

���� ��

���

� ���� � �� �����

�

�� ��� � �� � ������

��

����� ��� ������

�

�����

��

�

NRSE spectrometer

B=0

tA tA’ t tB

+ + + +d lAB

B= B=0

tC tC’ t tD

+ + + +

B=0Sample

A B C D

B0 B0nB0B0

d d dlCD

Echo occurs for elastic scattering when lAB + d = lCD + d

Neutron Spin Phases in an NRSE Spectrometer*

* Courtesy of S. Longeville

H = 0

Just as for traditional NSE, if the scattering is elastic, all neutron spins arrive at the analyzer with unchanged polarization, regardless of neutron velocity. If the neutron velocity changes, the neutron beam is depolarized

The Measured Polarization for NRSE is given by an Expression Similar to that for Classical NSE

• Assume that v’ = v + δv with δv small and expand to lowest order, giving:

• Note the additional factor of 2 in the echo time compared with classical NSE (a factor of 4 is obtained with “bootstrap” rf coils)

• The echo is obtained by varying the distance, l, between rf coils

• In NRSE, we measure neutron velocity using fixed “clocks” (the rf coils) whereas in NSE each neutron “carries its own clock” whose (Larmor) rate is set by the local magnetic field

32

2

0 2)(2 time"echospin " thewhere

),()(

)cos(),()(

λπ

γτ

ωλωλ

ωλωτωλ

hmdlB

ddQSI

ddQSIP

NRSE

NRSE

+=

=∫∫

∫∫r

r

An NRSE Triple Axis Spectrometer at HMI:Note the Tilted Coils

Measuring Line Shapes for Inelastic Scattering

• Spin echo polarization is the FT of scattering within the spectrometertransmission function

• An echo is obtained when

• Normally the lines of constant spin-echo phase have no gradient in Q,ωspace because the phase dependsonly on

• The phase lines can be tilted by using“tilted” precession magnets

ω

Q

ω

Q

22

221

1

2

2

1

1

1 0)()(

kN

kN

kBd

kBd

dkd

=⇒=⎥⎦

⎤⎢⎣

⎡−

k

By “Tilting” the Precession-Field Region, Spin Precession Can Be Used to Code a Specific Component of the Neutron Wavevector

If a neutron passes through arectangular field region at anangle, its total precession phase will depend only on k⊥.

⊥k

d

χ

B

kk//

⊥

===

=

kKBddBt

B

L

L

χγωφ

γω

sinvStop precession here

Start precession herewith K = 0.291 (Gauss.cm.Å)-1

“Phonon Focusing”• For a single incident neutron wavevector, kI, neutrons are

scattered to kF by a phonon of frequency ωo and to kf by neighboring phonons lying on the “scattering surface”.– The topology of the scattering surface is related to that of the phonon dispersion

surface and it is locally flat

• Provided the edges of the NSE precession field region are parallel to the scattering surface, all neutrons with scatteringwavevectors on the scattering surface will have equal spin-echo phase

Q0

kIkF kf

scattering surface

Precession field region

kf⊥

“Tilted Fields”

• Phonon focusing using tilted fields is available at ILL and in Japan (JAERI)….however,

• The technique is more easily implemented using the NRSE method and is installed as an option on a 3-axis spectrometers at HMI and at Munich

• Tilted fields can also be used can also be used for elastic scattering and may be used in future to:– Increase the length scale accessible to SANS– Separate diffuse scattering from specular scattering in reflectometry– Measure in-plane order in thin films– Improve Q resolution for diffraction

An NRSE Triple Axis Spectrometer at HMI:Note the Tilted Coils

Nanoscience & Biology Need Structural Probes for 1-100 nm

10 nm holes in PMMA

CdSe nanoparticlesPeptide-amphiphile nanofiber

Actin

1μ

Si colloidal crystal

10μ2μ

Thin copolymer filmsStructures over many lengthscales in self-assembly of ZnS and cloned viruses

“Tilted” Fields for Diffraction: SANS

• Any unscattered neutron (θ=0) experiences the same precession angles (φ1 and φ2) before and after scattering, whatever its angle of incidence

• Precession angles are different for scattered neutrons

π/2 π/2π

⎥⎥⎦

⎤

⎢⎢⎣

⎡=

⎥⎥⎦

⎤

⎢⎢⎣

⎡≈−⇒

+==

∫ QkKBdQSdQP

kKBd

kKBd

kKBd

χχ

θχχφφ

θχφ

χφ

22

22121

sincoscos).(.

sincoscos)cos(

)sin( and

sin

χ θχ

B B

Polarization proportional toFourier Transform of S(Q)

φ1 φ2

d

Spin Echo Length, 2)sin/(cos χχ kKBdr =

NSE Angle Coding Illustrated for SANS• Make the number of spin precessions depend on the neutron’s direction

of travel instead of (only) its speed…..

π/2 π/2π

precession field precession field

θ0 θ0

d

ζθπ

θλδθδθθπ

θλφφ

δθθπλ

δθθγωφ

γω

QQBdKBdK

BdKdBt

B

L

L

=≈−≈−

+=

+==

=

20

02

120

20

21

101011

)sin2(cos)(

sin2cos

)sin(2)sin(v

∫∫∞

∞−

∞

∞−

= dQQSdQQQSPP )(/)cos()(/ 0 ζ

δθ1δθ2

+BO -BO

spinanalyser

spinpolarizer

1st spin-echoarm

2nd spin-echoarm

DIFFERENT PATH LENGTHS FOR THE DIFFERENT TRAJECTORIES !

P =

1The Classical Picture of Spin Precession

sampleposition

Viewgraphsequence byA. Vorobiev

+BO -BO

spinanalyser

spinpolarizer

DEPOLARIZEDBEAM !

ALL SPINSARE PARALLEL:

FULL POLARIZATION

0

1

0.5 Pi

0

1

0.5

ALL SPINSARE PARALLEL AGAIN:

POLARIZATIONIS BACK

0

1

0.5 Pf

Spin Echo Scattering Angle Measurement (SESAME)No Sample in Beam

Pi = Pf‘SPIN-ECHO’

sampleposition

+BO -BO

spinanalyser

spinpolarizer

FULL POLARIZATION

0

1

0.5 Pi

DEPOLARIZATION !0

1

0.5 Pf

Spin Echo Scattering Angle Measurement (SESAME)Scattering by the Sample

Pi > Pf

+BO -BO

spinanalyser

spinpolarizer

FULL POLARIZATION

0

1

0.5 Pi

DEPOLARIZATION !0

1

0.5 Pfthe same depolarization

Pi > Pfindependently ofinitial trajectory

Spin Echo Scattering Angle Measurement (SESAME)Scattering of a Divergent Beam

FULL POLARIZATION

0

1

0.5 Pi

0 100 200 300 400 5000,0

0,2

0,4

0,6

0,8

1,0

δ~cotΘ [nm]

Pf

Pi

Θ

0

1

0.5 Pf

Spin-echo angular encoding:the experiment

How Large is the Spin Echo Length for SANS?

7,5001065,000

3,5002065,000

1,5002045,000

1,0002043,000

r(Angstroms)

χ(degrees)

λ(Angstroms)

Bd/sinχ(Gauss.cm)

It is relatively straightforward to probe length scales of ~ 1 micron

HMI Experiments:2002 - 2004 1

1

2

3

4

5

2

1. π/22. Precession film3. Sample4. π5. Iron plate

High Angular Resolution using SESAME

1

2

31

4

5

21

2

31

4

5

2

0 50 100 150 2000.90

0.92

0.94

0.96

0.98

1.00

P/P

0

Spin Echo Length (nanometers)

240 250 260 270 280 290 300 310 320 330

0

500

1000

1500

2000

2500

off02 on02 offminuson

inte

nsity

channel

omega = 0.2 degrees

Thin, magnetized Ni0.8Fe0.2 films on silicon wafers (labelled 1, 2 & 4) are the principal physical components used for this new method.

High angular resolution is obtained using Neutron Spin Echo.

A 200 nm correlation distance was achieved for SANS

Specular neutron reflection (blue) was separated from diffuse reflection with high fidelity. Black and red data include diffuse scattering

Patterson function for PS spheres(measurement & theory)

240 250 260 270 280 290 300 310 320 330-200

0

200

400

600

800

Inte

nsity

PSD Channel

Diffuse Specular

theta = 0.4 degrees

Conclusion:NSE Provides a Way to Separate Resolution from

Monochromatization & Beam Divergence

• The method currently provides the best energy resolution for inelastic neutron scattering (~ neV)– Both classical NSE and NRSE achieve similar energy resolution– NRSE is more easily adapted to “phonon focusing” I.e. measuring the energy

line-widths of phonon excitations

• The method is likely to be used in future to improve (Q) resolution for elastic scattering– Extend size range for SANS (SESANS)– May allow 100 – 1000 x gain in measurement speed for some SANS exps– Separate specular and diffuse scattering in reflectometry– Measure in-plane ordering in thin films (SERGIS)

SESAME Apparatus on ASTERIX30 μ Permalloy films on Si

Mezei flipper (π)

V-coils (π/2)

Sample

Eqpt with guide fieldplates in place

FerriteMagnets

Hz

x

Hy

Iflip

time

Mezei π-flipper

y

z

V-coil

Hguide

Implementation of polychromatic flipper componentsImplementation of polychromatic flipper components

Obtaining a Spin Echo

Measure flip ratioas a function of flipper position

With π flipper set to echo position, incline 1st

Py film, then measure flip ratio as a function of 2nd film angle

4 5 6 7 8 9 10-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

Calculated result allows SEL to be related to lamda

Measurement of Dilute 96 nm-diameter Polystyrene Spheres in 3:1 D2O/H2O

• SESAME measures the (Q) Fourier transform of S(Q)

• For hard spheres G(z) can be calculated exactly (black lines in figures)

• In our measurement, slits cut off the scattered intensity, so we had to include this effect in the calculated Fourier transform (black dots)

• The SEL range corresponds to 4 Å < λ < 8.5 Å

0 200 400 600 800 10000.5

0.6

0.7

0.8

0.9

1.0

red line -- smoothed datablack line -- theory - no resolutionlarge black dots -- theory including resolution

P/P

0

Spin Echo Length (Angstroms)

Single Foil; 96 nm diamter PS spheres in D2O/H20 3/1

)0()(

0

2

2

PP

0)G(z ;)0(

)cos(),(

4)(

GZG

zzyS

zy

e

tG

ZQd

QQddQdQ

SZG

−

∞

∞−

∞

∞−

=

=∞→=

Ω= ∫∫

σ

σπλ

0 500 1000 1500 20000.5

0.6

0.7

0.8

0.9

1.0

red line -- smoothed datablack line -- theory - no resolutionlarge black dots -- theory including resolution

P/P

0

xsi (Angstroms)

Double Foil; 96 nm diamter PS spheres in D2O/H20 3/1

Conclusions from Precession Film Experiments• SESAME can be implemented using thin magnetic films at

either CW or pulsed neutron sources– Particularly good for pulsed source because spin echo length is scanned by λ– Spin echo lengths up to ~ 250 nm are not hard to achieve using cold

neutrons– Precession fields are large (~ 1 T) so only thin films are needed– Precession field boundaries are well-defined

• The method has several limitations;– 30 μ – 100 μ Permalloy films are not readily available– Film thickness homogeneity is a limitation (5 - 10% by electro-deposition)– Small film inclinations are needed for large spin echo lengths => large films

for reasonable neutron beam size– Film transmission losses increase as spin echo length goes up

Glass Slab:n = n0; dn/dλ = - |d|

Glass Slabwith anomalous dispersion;

n = n0; dn/dλ = |d|

The spatial separation, z, of the red and blue rays depends on:(a) dn/dλ; (b) the glass thickness; (c) the inclination of the slab

z

An Optical Analogy

A Better Method?

• A better method is to use separated π flippers– Implemented at Delft using thin Py films as flippers– Implemented on EVA using NRSE

• NRSE is clumsy to pulsed sources– Try triangular cross section solenoids

+ - - + + - - +

π/2 π/2π200 mm

L = 200-500 mm

neutron

Stay tuned …..

Cutting the slab into prisms allows the spatial separation of red andblue rays to be controlled by the separation of the prisms

d

Adding prisms with the opposite dispersion increases the separation ofthe red and blue rays

Increasing the Spin Echo Length

We Can Clearly Do This With Neutrons

• We can add and subtract rectangular field regions without affecting the dispersion of spin states

• This leaves us with a “slab” with twice the magnetic field• We can make the slab as thick as we like by choosing the

separation of the prisms along the beam line

++─

─

We Can Do the Same Thing With Neutrons

• Prepare neutrons in a mixture of eigenstates | > + | >• The two, correlated spin states of a neutron can be separated

in space by a magnetic field with inclined boundaries• When the states are recombined, they provide information

about correlations between scattering events that are separated by the spin echo length, z

+ vemagnetic field

─ vemagnetic field

z

sample

x

z

yαi

αf

ϕ

qx = (2π/λ)( cosαf - cosαi )qy = (2π/λ) sinϕ

Geometry at grazing incidence

αf Resolve with PSD

ϕ Resolve with Spin Echo

tight collimation

coarse collimation

Θ

αi αf = αi

αf = -αi

TOP VIEW

SIDE VIEW

Y

XZ

Z

XY

+B -B

+ B - Bincident

incident specular

specular

direct

direct

THE SAME POLARIZATION IN DIRECT AND SPECULAR BEAMS

Grazing incident geometry

A comparative study of P. Müller-Buschbaum et al., Physica B283,53 (2000)

AFM picture of drops of d-polystyrene/polyparamethylstyreneon silicon

Zoomed AFM picture

Model of scattering length densities as seenby X-rays(GISAXS)

Model of scatteringlength densities asseen by neutrons

(GISANS)

Dewetting of polymer-blend films from Silicon

a) scattering geometry. The incident beam (I) impinges on the sample surface at a shallow angle αi; transmitted (T), specular (S) and diffuse (Y) intensities are simultaneously recorded by PSD.

b) Image taken by 2-dimensional PSD during real experiment. The size of the incoming beam at the sample position was 30×2 mm2.

Diffraction figure in transmission and reflection geometry

GISANS from copolymer dropletsD22(ILL), 8 hours

sinϑf + sinϑisinϑI + sinϑf cosϕ

qz

cosϑf sinϕsinϑf sinϕqy

cosϑf cosϕ - cosϑicosϑf - cosϑiqx

Transmission Reflection

P. Müller-Buschbaum et al.J. Phys.: Cond. Mat. 17 (2005) S363–S386

SFM:Λ ~ h2

pancake-type droplets

0 100 200 300 4000,4

0,6

0,8

1,0

1,2

LSE, nm

GISANS:no internal regular phase separation

GIS

AXS

RPPexp

SERGIS

SERGIS results: PpMS(polyparamethylstryrene):dPS

BLEND 3:2

P. Müller-Buschbaum et al.J. Phys.: Cond. Mat. 17 (2005) S363–S386

SFM:Λ ~ h1

‘spherical’ droplets

LSE, nm

RPPexp

SERGIS

GISANS:regular phase

separation-100 0 100 200 300 400

0,0

0,2

0,4

0,6

0,8

1,0

1,2

SERGIS results: Diblock Copolymerpoly(styren-block-paramethylstryrene) P (S-b-

pMS)

-600 -400 -200 0 200 400 6000.0

0.2

0.4

0.6

0.8

1.0

high

t, ar

b. u

n.

y, nm

0 50 100 150 200 250 300 350 400-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.01.2

pola

rizat

ion

y, nm

L=15 nm d=490 nm

EXPERIMENTAL DATA AND CALCULATED CORRELATION FUNCTIONS

BLEND SAMPLE DIBLOCK COPOLYMER

-600 -400 -200 0 200 400 6000.0

0.2

0.4

0.6

0.8

1.0

high

t, ar

b. u

n.

y, nm

lDB=65 nmd=580 nm

0 50 100 150 200 250 300 350 400-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.01.2

pola

rizat

ion

y, nm

Measuring Correlations in Space & Time

• Use space and time resolving NSE simultaneously• Large (~ 1 T.m) solenoidal field: τ = 186 B0.L. λ3 ns (λ in nm)• Triangular solenoids (~ 0.01 T): r = 147,000 B.d cot θ. λ2 nm• At a reactor source, we could set r and τ independently• At a pulsed source we could keep B λ2 constant by varying B

with time after a pulse: TOF then maps out τ

• This would be a completely different way of measuring structural correlations using scattering – (r,τ) instead of (Q,ω)

-+ -+π/2 π/2π

+-+-

solenoid solenoid

dL

B0 B0

B

θ

Preliminary Tests have been Carried Out

• Tests by Mezei, Farago and Falus on IN 15 at ILL– Did not use triangular coils but current-carrying aluminum plates,

perpendicular to the neutron beam, just inside main precession solenoids

• The length scale accessible on IN15 could be increased by a factor of 10 while keeping the usual dynamical range in time.

• The resolution function was a product: P1(r)P2(τ)– Could scan τ from 5% to 100% of maximum value without depolarization

independent of current in the sheets

solenoidπ/2 π π/2

Aluminum plate sample

Spin Echo Polarization versus r: P1(r)

• The relatively rapid decrease of P1(r) with r is not yet understood

0 10 20 30 400.0

0.2

0.4

0.6

0.8

1.0

250 500 750 1000

N

orm

aliz

ed N

SE s

igna

l P(r

)

Current in field tilt sheets [A]

Fourier distance r [Å]

Stay tuned…….

Summary of NSE

• Field boundaries perpendicular to the neutron beam code neutron’s speed (not it’s trajectory)– Correlation time (up to ~ 300 ns on IN15) scales as λ3

• Field boundaries inclined to neutron beam code neutron’s trajectory – Correlation length (also called the spin echo length) scales as λ2

– Up to 5 microns correlation length has been achieved (Delft)

• Neither method requires highly collimated or monochromatic neutron beams– NSE is suitable for long correlation times or large length scales typical of soft

materials such as complex fluid films

Collaborators

Experiments at HMI, BerlinMike Fitzsimmons, LANLHelmut Fritzsche, Chalk RiverMarita Gierlings, HMIJanos Major, MPI, Stuttgart

Experiments at LANSCEMike Fitzsimmons, LANLGian Felcher, ANL

Triangular solenoidsMike Fitzsimmons, LANLMark Leuschner, IndianaPaul Stonaha, IndianaAdam Washington, IndianaHaiyang Yan, IndianaHal Lee, SNS