Post on 27-Jul-2020
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
�
�
∞
∞
∞−
=
=∆
=��
���
�
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