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Introduction to Neutron Spin Echo Spectroscopy
NIST Center for Neutron research &
Antonio Faraone
NIST Center for Neutron research &
Dept. of Material Science and Engineering, U. of Maryland
Outline• Dynamic Neutron Scattering and NSE
– Coherent and Incoherent Dynamics
• The principles of Neutron Spin Echo (NSE)
• NSE Spectrometers Around the World
• NSE Exercise• NSE Exercise– Collective Dynamics of Microemulsion Droplet.
• NSE History
• Conclusion
Static and Dynamic Scatteringki, Ei
kf, Ef
Sample
Probe: photons (visible light, X-rays),neutrons, electrons, …
θ
Momentum Exchanged: Q=ki-kf
Q
ki
kf
Detector
Momentum Exchanged: Q=ki-kf
Energy Exchanged E=Ei-Ef
StaticScattering: )(QSd
d≈
Ω
σDynamic Scattering: ),(
2
EQSdEd
d≈
Ω
σ
))]0()((exp[),( rtrQiFTEQS −−= )](exp[)( ji rrQiFTQS −−=
Fourier Transform of the SpaceCorrelation Function
Fourier Transform of the Space-TimeCorrelation Function
Nuclear InteractionNeutrons are scattered by the nuclei.
Scattering power varies “randomly” from isotope to isotope.
The scattering also depends on nuclear spin state of the atom.
•If the scattered neutron waves from the different nuclei
Magnetic Scattering.
•If the scattered neutron waves from the different nuclei
have definite relative phases, they do interfere
Coherent Scattering
•If the scattered neutron waves from the different nuclei
have RANDOM relative phases, they don’t interfere
Incoherent Scattering
Scattering functionsS(Q,Ε) = Sinc(Q,Ε) + Scoh(Q,Ε)
S (Q,E) is the time and space Fourier transform of the SELF
Scoh(Q,E) is the time and space Fourier transform of the PAIR
correlation function
( )[ ] )0()(exp),( jicoh rtriQFTEQS −−=
Sinc(Q,E) is the time and space Fourier transform of the SELF
correlation function
( )[ ] )0()(exp),( iiinc rtriQFTEQS −−=
Hydrogen has a very high
Incoherent Scattering
Cross-Section
coherent
non-flip
Scattering Event andNeutron Moment
incoherent
1/3 non-flip 2/3 flip+
2/3 of the polarization signal is lost during the incoherent scattering event
Coherent Scattering
• Static Scattering– Diffraction
– Reflectometry
– SANS
• Inelastic/Quasielastic Scattering– Collective dynamics
• Phonons
• Shape Fluctuations
• Long Range coupled Domain Motions
• …
Incoherent Scattering
• Inelastic/Quasielastic Scattering– Single Particle Dynamics
• Diffusion
• Rotation• Rotation
• Vibrations
Neutron Scattering Techniques
NSE is the neutron scattering techniquesNSE is the neutron scattering techniquesthat gives acces to the largest length-
scales and longest time scales
What Does NSE Study?• Coherent Dynamics
Density Fluctuations corresponding to some SANS pattern
– Diffusion
– Shape Fluctuations (Internal Dynamics)
– Polymer Dynamics
– Glassy Systems
• Incoherent Dynamics• Incoherent Dynamics
Self-Dynamics (mostly of Hydrogen atoms)
• Magnetic Dynamics
Spin Glasses
Reptation motion Colldective DiffusionSegment motion
Local motionSide chain motion
coherent scattering incoherent
Dynamic Processes: Time and Length ScalesThe Dynamics Landscape of Polymers
NSEBS
DCSlarger scale objects: slower dynamics
coherent dynamics at low q and at q corresponding to relevant length scalesincoherent dynamics at high q
• Uncertainties in the neutron wavelength & direction of travelimply that Q and E can only be defined with a certain precision
• When the box-like resolution volumes in the figure are convolved,the overall resolution is Gaussian(central limit theorem) and has an
Instrumental Resolution
(central limit theorem) and has anelliptical shape in (Q,E) space
• The total signal in a scattering experiment is proportional to the phase space volume within the elliptical resolution volume
The better the resolution, the smaller the resolution volume and the lower the count rate
Neutron Spin Echo Breaks 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
The Idea of Neutron Spin Echo
• 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
Neutrons in magnetic fields:Precession
Neutron Properties
• 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)
BωωωωL
S
In a Magnetic Field
• The neutron experiences a torque from a
magnetic field B perpendicular to its spin
direction.
• Precession with the Larmor frequency:
• The precession rate is predetermined by the
strength of the field only. LSBSdt
dSωγ ×=×=
BSN ×=
N
BL γω =
1.0
Spin Echo effect
l0 l1A B C
Px
x
y
zVn
S
B B
NSE measures the polarization: Px=⟨cosϕ⟩
l0=l1
-1.0
-0.5
0.0
0.5
Px
v
lBd∫= γϕ ∫
∫
== dv
v
BdlvfPx
γϕ cos)(cos
1cos)(cos =
+== ∫ ∫∫ dvvBdlBdlvfP
C
B
B
A
Cx γϕ ∫ ∫
== λγλλϕ dBdl
h
mFPx cos)(cos
Px is the Fourier transform of the wavelength distribution
Scattering Event: Single Neutron• elastic scattering
S
sampleB B
• inelastic scattering
( ) [ ] [ ]ÅmTJdlBh
mdl
h
BmN λ
π
λγλγ
πλ ×⋅×=== ∫∫ 7370
221
v
Bdl∫= γϕ ∫∫∫
∆=
∆=
−=∆ Bdl
v
v
h
mBdl
v
vBdl
vv
γλγγϕ
2'11
J field integral. At NCNR: Jmax = 0.5 T.mN (λ=8Å) ≈ 3×105∫= BdlJ
Scattering Event: Neutron Beam
Again:
S
f(λ)
B0B1 Analyzer
Again:The measured quantity is the Polarization, i.e.the spin component along x: Px=⟨cosϕ(λ)⟩:
Elastic scattering
( )λ
γγϕ
fv
dlB
v
dlB ∫∫−=
10Echo Condition: 10 JJ =
0=ϕ1=xPNote:
The requirement that ϕ=0 can be in some casesreleased. This treatment is valid for the mostcommon case of Quasi-Elastic Scattering
Scattering Event: Neutron Beam
Again:
S
f(λ)
B0B1 Analyzer
Again:The measured quantity is the Polarization, i.e.the spin component along x: Px=⟨cosϕ(λ)⟩:
Quasi-Elastic scattering
( ) ( ) vv
dlB
v
dlB
δλγ
λγϕ
+−=
∫∫ 10
( )
3
3
2
22
2
2
112
λπ
ωδλ
λ
δλ
δλλλω
mh
m
h
m
hE
=
≈
+−=∆=h
( )λγδλγϕ 100 JJh
mJ
h
m−+≈
( )λγωπ
λγϕ 1002
32
2JJ
h
mJ
h
m−+=
Series Expansion in δλ and δJ
0 at the echo condition
( ) ( ) ( ) ( )∫∫
×
−== ωω
π
λγωλλγλϕ dJ
h
mQSdJJ
h
mfPx 02
32
10 2cos,coscos
The Basic Equations of NSE( ) ( ) ( ) ( )∫∫
−+== ωλλγω
π
λγωλϕ ddJJ
h
mJ
h
mQSfPx 1002
32
2cos,cos
Even Function
FT of the wavelength FT of the Dynamic Structure2FT of the wavelengthdistribution
FT of the Dynamic StructureFactor
302
2
2λ
πγ J
h
mt =Fourier time
( ) ( )( ) [ ]
( )∫∫
∆=∆ωω
ωωω
dQS
dtQSJPtQJP ii ph
sph
x,
cos,,,
NSE measures the Fourier Transform of the Dynamic Structure Factor
How NSE works: summary• 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• 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 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.
NSE EffectElastic Scattering QuasiElastic Scattering
What does a NSE Spectrometer Look Like?
IN-11 @ ILLThe firstThe first
IN-11c @ ILL; Wide Detector Option
IN-15 @ ILL
NSE @ NCNR
NSE @ SNS
Surfactant molecules
A surfactant (“Surface Active Agent”) is soluble both in
•Oils and water do not mix! Why?
Water is a polar liquid, ε = 81;
Oils are non polar, ε ~ 2
Hydrophobic tailCH3-CH2-CH2- …CF3-CF2-CF2- …
Hydrophilic headSO3
-Na+
NH3+Cl-
-(OCH2CH2)n-
A surfactant (“Surface Active Agent”) is soluble both in
water and in organic liquids (oils)
Spherical micelles
When surfactants are dissolved in water they:- reduce the surface tension because they are adsorbed on the surfaces - form variety of aggregates – micelles, lamellae, bicelles, vesicles, etc
Cylindrical micelles Lamellae Vesicles
Surfactant aggregates in water
H2O
H2O
Vesicles
Ås
nm
Wormlike micelles canbe as long as fewmicrons
Surfactants are everywhereSurfactants are very useful to:
• Reduce the interfacial tension
• Solubilize oils in water
• Stabilize liquid films and foams
• Modify the interparticle interactions
• Stabilize dispersion• Stabilize dispersion
• Modify the contact angle and wetting
• …
Surfactants in our daily life:
• Cosmetics – moisturizers, lotions, healthcare products, soap, …
• Food – mayonnaise, margarine, ice cream, milk, …
• Industry – lubricants, stabilizers, emulsifiers, detergents, …
• Medicine – drugs, bio applications, …
• Agriculture – aerosols, fertilizers, …
Surfactants are everywhere II
• Agriculture – aerosols, fertilizers, …
• …
Micelles and MicroemulsionsOils and water do not mix?!? The surfactants help them mix.
Microemulsion dropletoil
Solubilized organicmolecules (oil)
H2O
Micelle
H2O
When surfactants are dissolved in oils they form “inverse” micelles, …Inverse microemulsion droplet
H2O
4-50 nm
H2OInverse micelle
oil oil
Microemulsion Properties
• Thermodynamically stable, isotropic, and optically transparent solutions
• The diameters range between 2 and 50 nm
decane
water
AOT/water/decane
Properties of the surfactant film
Properties of the surfactant
film change with:
• Molecular structure
Surfactant film Properties of the surfactant film:
• Interfacial tension
• Lateral elasticity
• Spontaneous curvature• Molecular structure• Additives• Ionic strength• Co-surfactant• Temperature, pressure etc.
• Spontaneous curvature
• Bending elasticity
• Saddle splay elasticity
∫
+
−++= dS
RR
k
RRR
kE
s 2121
2112
γHelfrich Free Energy
An Example: Microemulsion
• Light Scattering• Small Angle Scattering (Neutrons: SANS; x-rays: SAXS)
– Large length scales (10 Å-1000 Å)– ‘Low resolution diffraction technique’
Structure
SANS:
The intensity is the FT of the contrast distribution.
Contrast: Difference in Scattering Length Density
Contrast Matching Technique
∑=i
cohiA
w
bNM
dρ
Microemulsion:How to study them
Microemulsions move in solution because of thermal energy.– Diffusion– Shape fluctuations
Experimental techniques:
Dynamics
Experimental techniques:• Dynamic Light Scattering• Nuclear magnetic resonance• Neutron Spin-Echo (NSE)
NSE: T scale from ≈0.01 to 100 ns, L scale from ≈1 to 100 Å
ExperimentalShape fluctuations in AOT/water/hexane microemulsion
AOT
Inverse Microemulsion droplet
•Translational Diffusion
•Shape FluctuationsAOT
D2O
C6D14
σS (barn) bcoh (fm) bincoh (fm)
H 82.03 -3.741 25.274
D 2.05 6.671 4.04
4
6
1
2
4
6
10
I/cm
-1
AOT micelles AOT/D2O/C10D22
SANS dataAOT micellesAOT microemulsion
AOT/D2O/C6D14
Vol. fraction 0.078
Avg. radius (Å) ~ 30
polydispersity ~ 0.2
SLD (×10-6 Å-2)
n-hexane -0.67
H2O -0.56
d-hexane 6.14
D2O 6.35
AOT 0.10
0.1
2
2 3 4 5 6 7 8 90.1
2 3 4
Q/Å-1
Data Analysis: DiffusionFick Law, Diffusion Equation
[ ]tDQtQI 2exp),( −=
( )tQIDt
tQI,
),( 2∇−=∂
∂
φφ 2∇−=
∂
∂D
t
NSE measures coherent dynamics.
• The diffusion coefficient measured is the collective diffusioncoefficient.
• At finite concentration inter-particle interaction make the measured(effective) diffusion coefficient be Φ and Q dependent: Dc(Φ,Q).
• In the limit of infinite dilution the diffusion coefficient coincide with theself diffusion coefficient.
Data Analysis: Shape Fluctuations
∫∫ +
−+=
2121
12112 RR
dSkRRR
dSk
Es
bend
Expansion of r in spherical harmonics with amplitude a:
I(Q) Deff(Q)
( ) ( )
ΩΥ+=Ω ∑
mllmlmarr
,0 1
Frequency of oscillations of a droplet:
( )ηη
ηφ
πηλ
32'2324
4
334 0
30
2+
−−= f
k
Tk
k
k
R
R
R
k B
s4 5 6 7 8 9
0.12
Q
Dtr
Ddef
Data Analysis III
Translational Diffusion( )( )
[ ]tDQQI
tQI 2exp0,,
−=
( )( )
( )[ ]tQQDQI
tQIeff
2exp0,,
−=AOT/D2O/C6D14 MicroemulsionTranslational Diffusion + shape fluctuations
( ) ( )QDDQD deftreff +=
( )
( )[ ] ( )
+
+=2
2022
002
22022
54
5)(
aQRfQRjQ
aQRfDQD treff
π
λ
The two dynamical processes are statistically independent.
( ) ( ) ( )[ ]20300202 45 QRjQRQRjQRf −=
The bending modulus, k( )
( )[ ] ( )
+
+=2
2022
002
22022
54
5)(
aQRfQRjQ
aQRfDQD treff
π
λ
++=
η
ηηηλ
π 332'23
481 3
022R
p
Tkk B
ηπ 348 2p
λ2 – the damping frequency – frequency of deformation
<|a|2> – mean square displacement of the 2-nd harmonic – amplitude of deformation
p2 – size polydispersity, measurable by SANS or DLS
η and η’ are the solvent and core viscosities
Results
[ ] 2
2022
002
2
2022
)(5)(4
)(5)(
aQRfQRjQ
aQRfDQD treff
++=
π
λ
The beginning
F. Mezei, Z. Physik. 255, 146 (1972).
NG5-NSE
(SNS-NSE)
MUSESIN11
IN15J-NSERESEDASPAN
iNSE
NSE Today in the World
+ NSE option for triple-axis spectrometers+ developing ones
60
50
40
30
Num
ber of Pap
ers
total number of Papers Spectrometer polymer glass membrane SolidStatePhysics
P. G. de GennesNobel Prize in Physics 1991
Further improvement and development of the NSE technique!
NSE Publications
30
20
10
0
Num
ber of Pap
ers
2005200019951990198519801975
Yearpublication record; searched using web of science: keyword=neutron spin echo
discovery of the principleby F. Mezei in 1972
Nobel Prize in Physics 1991
polymer dynamics researchesby D. Richter in 1980’s
Still increasing the technique papers
15
20
25
30
35
proposals and BTR
NG5-NSE proposals
Instrumentation
SmallMolecules
ComplexFluids
Magetism
Polymer
Bio
Biomodel bio-membraneprotein motion
Polymersegment dynamicshydro gelspolymer complex
NG5 NSE proposal statistics
0
5
10
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Cycle Call
Magnetismfrustrated magnetsspin glass
Complex Fluidsmicroemulsionssurfactant membranescluster dynamics
Molecular Liquidsconfined waterionic liquids
1999.4 2010.5
Take Home Messages• NSE gives you access to dynamics in the ps to ns
time range (covering four orders of magnitude in time)
• NSE Resolution is independent of the beam resolution
• NSE data is measured as S(Q,t), i.e. in the time • NSE data is measured as S(Q,t), i.e. in the time domain (the resolution can be simply divided out)
Caveat
Spin Echo is neutron intensive.
A successful experiment is due in large part to the sampleselection (quality, amount, etc.). Make sure you:
• choose and characterize your sample well
• take advantage of the isotopic substitution technique
Further ReadingsF. Mezei (ed.): Neutron Spin-Echo, Lecture Notes in Physics,128, Springer, Heidelberg, 1980
F. Mezei, C. Pappas, T. Gutberlet (Eds.): Neutron Spin-EchoSpectroscopy (2nd workshop), Lecture Notes in Physics, 601,Springer, Heidelberg, 2003.Springer, Heidelberg, 2003.
D. Richter, M. Monkenbusch, A. Arbe, and J. Colmenero,“Neutron spin echo in polymer systems” Adv. in polym. Sci, 174,1 (2005).