NCNR, NISTGaithersburg, MD 20899

E-mail:afaraone@nist.gov

Internet:http://www.ncnr.nist.gov/

Neutron Spin Echo Spectroscopy(NSE)

A. Faraone, D.P. Bossev, S.R. Kline, L. Kneller

Why we need a magnetic field?

• In Neutron spin echo the precessing neutron spin is employed as a kind of “individual” clock for each neutron. Thus, the velocity (energy) change of the neutrons can be measured directly in a single step.

• NSE technique allows the use of neutron beam wavelength spread ∆λ/λ = 5 – 20%, and therefore reasonably intense.

• Goal: δδδδE=10-5–10-2 meV (very small!!!) • We need low energy neutrons. Cold

neutrons: λ = 5 – 12 Å, E = 0.5 – 3.3 meV.• A “classical” inelastic technique works in two steps: preparation of the incoming monochromatic beam and analysis of the scattered beam.

Neutron Flux along NG5 guide to NSE

Neutrons in magnetic fields: Precession

Mass, mn = 1.675×10-27 kg

Spin, S = 1/2 [in units of h/(2π)]

Gyromagnetic ratio γ = µn/[S×h/(2π)] =

1.832×108 s-1T-1 (29.164 MHz T-1)

• The neutron will experience a torque from a magnetic field B perpendicular to its spin direction.

• Precession with the Larmor frequency:ωL = γB

• The precession rate is predetermined by the strength of the field only.

BωωωωL

S

LSBSdtdS ωγ ×=×=

BSN ×=

N

Spin echo effect

-1.0

-0.5

0.0

0.5

1.0

l0 l1

A B C

P

Px

z

x

y

V

� ��

���

�==

=

=

dvvlH

vfP

vlH

ll

Lx

L

0

0

10

cos)(cosγϕ

γϕ

S

B B

Monochromatic beam

vL

Bγϕ =

• elastic scattering • inelastic scattering

( ) [ ] [ ]ÅmTJdlBh

mdl

hBm

N NN λλγµλπγµπ

λ ×⋅×=== �� 737024

21

22

J field integral. At NCNR: Jmax = 0.5 T.mN (λ=8Å) ~ 3×105

S

B Bsample

# ofcycles 0 2Nπ+ϕ 2Nπ+ϕ

2Nπ+ϕ-(2Nπ+ϕ)

-(2Nπ+ϕ)±∆ϕ0

± ∆ϕ

2'11

vvBL

vvBL

∆=�

��

−=∆ γγϕ

5101 −≈≈∆Nv

v !�= BdlJ

Polychromatic beam

.)(

)(then );(

00

00

00

0000

λδλ

λλ

λδλλϕ

λλλλ

NNN

NNNN

∆+∆+=∆

=≡

Energychange

Asymmetry betweencoil field integrals

Neglect 2nd order termsfor small asymmetries

or quasielastic scattering

[ ]

sorder term 2nd2cosN2cos

/)(N2cos

00

00

000

+��

���

∆��

���

=

=∆+

λλπ

λδλπ

λλδλπ

N

N

The measured quantity is the spin component along z: cos(∆ϕ(λ)):

Neglected

S

B Bsample

# ofcycles 0 2N(λ)π+ϕ(λ) ±∆ϕ(λ)

02N(λ)π+ϕ(λ)

f(λ)λ>λ0

λ<λ0

λ0

The Principles of NSE

• 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 � rotation

• If the neutron’s velocity 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’sspeed or energy.

NSE Spectrometer schematic

�

1 2 34 5 7 98 10

6

S

B B

8. �/2 flipper(stops Larmor precession)

4. First main solenoid(phase and correction coils)

7. Second main solenoid(phase and correction coils)

3. �/2 flipper(starts Larmor precession)

10. Area detector(20×20 cm2)

6. Sample2. Polarizer(Polarizing supermirrors)

9. Polarization analyzer(radial array of polarizing supermirrors)

5. � flipper(Provides phase inversion)

1. Velocity selector(selects neutron with certain �0)

z

x

y

Spin flippers

ππππ/2 flipperPrecession

BωωωωL

Sn

Sini

B

Send

ππππ flipper

Sini

B

Send

Intensity at the detector

0

2000

4000

6000

8000

1 104

1.2 104

-4 -2 0 2 4

1nsec_8A_19990609.dat1 cm apertures before solmain1 and after solmain2

solphase1 = 1.1296 A

Cou

nts/

35se

c

Phase Current (solphase2) (A)

y = m1*exp(-(m0-m2)*(m0-m2)/...13.7085159m1

9.1772e-050.56644m2 0.00429611.238m3 3.552e-050.23287m4

2.66367229.4m5 NA2539.1Chisq

( ) ��

���

��∞

∞−

ωλωω dtS )(cos),(Q

At small N0 vary ∆N0:- Period gives λ0- Envelope gives f(λ)

( ) λωλωωλλπλ ddtSNfP

��

�

�

��

�

�

��

���

∆= ��

∞

∞−

∞

)(cos),(2cos)(0 0

0 Q

where t ≡N0mλ3

hλ0

since δλ =mλ3

2πhω

For wavelength distribution, f(λ), with mean wavelength, λ0:

��

���

��

���

∆

00

00 N2cos2cos

λδλπ

λλπ N

For a single wavelength:

λλλπλ dNfP

t

�∞

��

���

∆=

=

0 002cos)(

0at

Intermediate Scattering Function I(Q,t)

Measuring I(Q,t)

0

500

1000

1500

2000

2500

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-0.4 -0.2 0 0.2 0.4 0.6

10% SDS in D2O Q=0.13899Å– 1 t=1ns

10× ∆By

− ∆Bx

–10× ∆Bz

Cou

nts/

60s

Change in field near π -flipper (µ T

)

Solphase2 (A)

EchoPoint

A

NON

NOFF

InstrumentalBackgroundSignal before resolution correction is

2ANON − NOFF

• The difference between theflipper ON and flipper OFF data gives I(Q,0)

• The echo is fit to a gaussian-damped cosine.

How to deal with the resolution?

),(),(

),(

),(),(),(

tRtJ

tI

tRtItJ

QQQ

QQQ

=

⋅=

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25

Signal Q=0.13899Å–1

Q=0.13899Å–1 Res

I(0.13899Å–1, t )

I(Q,t)

/I(Q

,0)

t (ns)

( ) λωλωωλλπλ ddtSNfP �

�

���

���

���

∆= ��

∞

∞−

∞

)(cos),(2cos)(0 0

0 Q

( )

λλλ

λωλωω

dtIfP

N

tIdtS

))(,()(

,0 point, echo At the

))(,()(cos),(

0

0

Q

QQ

�

�

∞

∞

∞−

=

=∆

=��

���

�

In the time domain the resolutionis simply divided

Inhomogeneities in the magnetic field may further reduce the polarization. Since they are not correlated with S(Q,�) or f(�), their effect may be divided out by measuring the polarization from a purely elastic scatterer.

The main application of NSE is to measure the intermediate coherent scattering function Icoh(Q,t), the coherent density fluctuations that correspond to some SANSintensity pattern.• Diffusion• Internal dynamics (shape fluctuations)• …

Example: Diffusion of Surfactant Molecules

Hydrophobic tail Hydrophilic head

AOT

AOT micelles in n-decane (C10D22)

Inverse spherical micelle

C10D22

Translationaldiffusion

~ 25 AOT

( )( ) [ ]tQDExpQI

tQIeff

2

0,, −=

ExperimentShape fluctuations in AOT/D2O/C6D14 inverse microemulsion droplet

D2O

C10D22

AOT

Translationaldiffusion

Shapefluctuations

Shapefluctuations

( )( ) ( )[ ]tQQDExpQI

tQIeff

2

0,, −=

( )( )[ ] ( )[ ]2

2022

002

22022

54

5

)()(

aQRfQRjQ

aQRfD

QDDQD

tr

deftreff

++

=+=

π

λ

4 5 6 7 8 90.1

2

Q

I(Q) Deff(Q)

Dtr

Ddef

( ) ( ) ( )[ ]0300202 45 QRjQRQRjQRf +=

Experiment( )

( )[ ] ( )���

��� +

+=2

2022

002

22022

54

5)(

aQRfQRjQ

aQRfDQD treff

π

λ

���

�

���

� ++=η

ηηηλπ 3

32'23481 3

022R

p

Tkk B

Goal: Bending modulus of elasticity

λ2 – the damping frequency – frequency of deformation<|a|2> – mean square displacement of the 2-nd harmonic – amplitude of deformationp2 – size polydispersity, measurable by SANS or DLS� is the bulk viscosity of deuterated n-hexane�’ is the bulk viscosity of deuterated water