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TRANSCRIPT
1
● Short remarks on elastic scattering methods
● Triple axis spectrometer
● Time-of-flight spectrometer
● Backscattering spectrometer
● Neutron spin echo spectrometer
Neutron Scattering Part 2: Techniques
Reiner Zorn
Jülich Centre for Neutron Science Forschungszentrum Jülich
2
Elastic Neutron Scattering
a.k.a. Neutron Diffraction
3
Elastic scattering methods
10-4
10-3
10-2
0.1
1
10
180°
10°
1°
6‘
36“
100 nm
1 Å
1 nm
10 nm
1 µm
10 µm
Size l
][Å2 1−π
≈l
Q!!
2θ
Q =4π
λsinθ[λ =8Å]
Powder, single crystal diffractometer
Small angle scattering (SANS)
Ultra-small angle scattering (uSANS)
4
Laue camera
● Advantage:
● high information content (2D)
● Disadvantage:
● single crystal necessary
in general not for polymers, except proteins (biopolymers)
‘white’ beam
sample: crystal
Each spot contains a single wavelength λhkl under an angle θhkl/2 corresponding to a lattice plane by
( )2sin 2
hkl
hkl
hkl
dλ
=θ
5
Debye-Scherrer camera
● Advantage:
● macroscopically isotropic sample sufficient (necessary)
powders, polycrystals, liquids amorphous polymers…
● Disadvantage:
● lower information content (1D)
monochromatic beam
isotropic sample
Each ring corresponds to a lattice spacing by
( )2sin 2hkl
hkl
dλ
=θ
6
Neutron Small Angle Scattering (SANS) selector diaphragms sample detector
SANS:
• Velocity selector: 250 … 900 m/s ↔ 4.5 … 15 Å
• 20 m length, 2 cm diaphragms → min. 3 arc minutes
• Q = 10–3 … 0.2 Å–1
• l = 3 … 600 nm
7
Ultra-SANS:
• 11 m length, 2 mm apertures → min. 36 arc seconds
• Mirror optics enables to keep intensity (alternative: lenses)
• Q = 10–4 … 2 · 10–3 Å–1
• l = 0.3 … 6 µm
Ultra-small-angle scattering
8
Inelastic Neutron Scattering
a.k.a. Neutron Scattering Spectroscopy,
Dynamic Neutron Scattering, Quasielastic Neutron Scattering …
9 Space
1 Å 1 nm 10 nm 100 nm 1 µm
Tim
e
1 fs
1 ps
1 ns
1 µs
1 ms
1 s
1000 s D
yna
mic L
igh
t Sca
tterin
g
Raman
Brillouin
Ph
oto
n C
orre
latio
n
X-ray PCS
Inel. X-ray Sc.
NSE
BS TOF
3ax
TOF 3ax
BS
Inelastic Scattering Methods
Dynamics of polymers, glasses, microemulsions...
10
Triple-axis spectrometer
General construction scheme of neutron scattering spectrometers:
Primary spectrometer: selection of incident wavelength and direction
E and k
──── sample ────
Secondary spectrometer: detection of outgoing wavelength and direction
E' and k'
Q = k '− k
!ω = E '− E
Axis 1: Monochromator
Crystal
Axis 3: Analyzer Crystal
Detector
Axis 2: Sample
„White“ neutron beam from reactor
2θ ′k
k
E'
E
Collimator
Collimator
11
Triple-axis spectrometer
Axis 1
Axis 2
Axis 3
TASP, PSI, Villigen, Switzerland
3ax-principle requires motion of axis 3 in two dimensions: hovering airpads on ‚Tanzboden‘ floor.
12
Characteristics of triple-axis spectrometers
Flexibility:
● Full control of Q and ω within limits of wavelengths from source (using different monochromator crystals)
● Adjustable resolution (different collimators), tradeoff resolution-intensity possible
Disadvantage:
● Only one (Q,ω) point is measured at a time.
● Long registration time for complete spectra (hours-days)
● Better suited if only peaks have to be found (phonons, magnons)
13
Time-of-Flight Spectrometer
Q
t
,
,flight
ω
θ
!
⇓
Monochromator Crystal
„White“ neutron beam from reactor
Chopper
Detector Bank
14
Time-of-Flight Spectrometer
Q
t
,
,flight
ω
θ
!
⇓
Monochromator Crystal
Chopper
Detector Bank
„White“ neutron beam from reactor
IN6, IN5, ILL, Grenoble, France
15
Qmax [≈
-1]
1 10
ΔE
[m
eV
]
10-6
10-5
10-4
10-3
10-2
10-1
100
101
Specifications of TOF Instruments
IN6: cold neutrons, crystal monochromator
IN5, NEAT, TOFTOF: cold neutrons, chopper monochromator
IRIS: cold neutrons,spallation source, inverse geometry
IN4: hot neutrons, crystal monochromator
ps
ns
µs
t = ! / ΔE
Qmax [Å−1]
16
Backscattering Spectrometer
„White“ neutron beam from reactor
Monochromator Crystal Deflector
Crystal
Detector Bank
Analyser Crystals
Sample
2θ [∞]
0 60 120 180
λ [≈
]
0
2
4
6
Bragg condition λ = 2d sin θ :
→ optimal wavelength selection at 2θ = 180° (backscattering)
λ [Å
]
2θ [°]
17
Backscattering Spectrometer „White“ neutron
beam from reactor
Monochromator Crystal Deflector
Crystal
Detector Bank
Analyser Crystals
Doppler motion
Sample
2θ [∞]
0 60 120 180λ [≈
]0
2
4
6
IN10, ILL, Grenoble, France
λ [Å−
1]
2θ [°]
18
Qmax [≈
-1]
1 10
ΔE
[m
eV
]
10-6
10-5
10-4
10-3
10-2
10-1
100
101
Specifications of BS Instruments
Si-11
1 S
i-3
11
Ca
F2-4
22
ps
ns
µs
IN16, PI: (Si-111) Doppler, range 15 meV, best resolution 0.2 meV (polished)
SPHERES: phase space transformer
IN10B: (Si-111) thermal, range 120 meV
IN13: (CaF2-422) hot neutrons, thermal
Qmax [Å−1]
19
The Resolution-Intensity Dilemma
Δ!ω = ΔE2+ Δ ′E
2
E'
E
Conventional inelastic experiment:
E'
E
Δ!ω
Energy difference selection:
... needs identification of neutrons!
Intensity ∝ Δ!ω2 !
20
Neutron Spin
Is there any information the neutron carries with itself? — Yes: Spin Direction
Lecture 7: Larmor precession in constant field:
Gauss
srot/2900
Nn
L↔
µ=ω Bg
!
21
Neutron Spin
... used as individual stop-watch
Is there any information the neutron carries with itself? — Yes: Spin Direction
Lecture 7: Larmor precession in constant field:
Gauss
srot/2900
Nn
L↔
µ=ω Bg
!
22
Neutron Spin Echo Velocity Selector (10-20%)
Detector
π Flipper
π/2 Flipper π/2 Flipper
B Coil B' Coil
Analyzer Polarizer
Sample
23
Velocity Selector (10-20%) Detector
π Flipper
π/2 Flipper π/2 Flipper
B Coil B' Coil
Analyzer Polarizer
Sample
Neutron Spin Echo
Spin development, elastic:
E1
E0
24
Velocity Selector (10-20%) Detector
π Flipper
π/2 Flipper π/2 Flipper
B Coil B' Coil
Analyzer Polarizer
Sample
Spin development, elastic:
Neutron Spin Echo
E1
E0
25
Velocity Selector (10-20%) Detector
π Flipper
π/2 Flipper π/2 Flipper
B Coil B' Coil
Analyzer Polarizer
Sample
Spin development, elastic:
Neutron Spin Echo
E1
E0
26
Velocity Selector (10-20%) Detector
π Flipper
π/2 Flipper π/2 Flipper
B Coil B' Coil
Analyzer Polarizer
Sample
Spin development, elastic:
Neutron Spin Echo
E1
E0
27
Velocity Selector (10-20%) Detector
π Flipper
π/2 Flipper π/2 Flipper
B Coil B' Coil
Analyzer Polarizer
Sample
Neutron Spin Echo
Spin development, inelastic:
E1
E0
energy gain
energy loss
28
Neutron Spin Echo Theory
ωλµ
≈λ−λ⎟⎠
⎞⎜⎝
⎛ µπ=φΔ
!!"!!#$)(
)(2
NSE
3
3
nNn
if2
nNn
Bt
h
BlmgBl
h
mg
Precession angle mismatch:
⇒ Loss of polarization:
φΔ= cosP
... averaged over all scattered neutrons:
)0,(
),(
d),(
d)cos(),(),( NSE
NSE
NSEQI
tQI
QS
tQStQP =
ωω
ωωω=
∫
∫∞
∞−
∞
∞−
Neutron Spin Echo measures directly the normalized intermediate scattering function!
sensitivity proportional to λ3
time parameter proportional to B and current
29
NSE is not good for non-quasielastic scattering!
Distribution of wavelengths → ( )( )0
3
, ( ,0)P I Q t I Qλ
λ
λ=
Δλ = 20% means Δt = 54% ! For quasielastic scattering:
... but still the result looks ok! In addition compensation :
( )( ) ( ) ( )( ) ( )0
0
0
0
0
2 332
, exp expfor diffusion I Q t D Q t DQ tλ λ λ
λ λ λ
λ λ
λλ
λ= − = −
S(Q,ω) I(Q,t) blue: true red: measured
P(B)
But for non-quasielastic scattering: (even for Δλ = 10% only!)
S(Q,ω) I(Q,t) P(B)
30
J-NSE in Munich
● Standard set-up enhanced by multidetector: simultaneous observation of (narrow) Q range
● Highly efficient correction coils
● Time limit: 350 ns B coil
π/2 flipper
π flipper
sample
B´ coil
π/2 flipper
analyser
detector N
eu
tro
n d
ire
ctio
n
31
Qmax [≈
-1]
1 10
ΔE
[m
eV
]
10-6
10-5
10-4
10-3
10-2
10-1
100
101
Specifications of NSE Instruments = !
/tm
ax ps
ns
µs
Special features:
J-NSE: optimized correction coils
IN15: focusing mirror
SPAN: multidetector
NSE@SNS: pulsed beam at spallation source
Qmax [Å−1]
32
INS: summary of methods
TOF
ΔE > 10 µeV t < 0.2 ns
+ high efficiency ≈ 2h / Q-set of spectra
+ simultaneously accessible Q range
– resolution often not sufficient
BS
ΔE > 1 µeV
t < 2 ns
+ simultaneously accessible Q range
+ better than NSE for excitations
– low efficiency ≈ 12h / Q-set of spectra
– Doppler: short !ω range ( ±30 µeV)
NSE
ΔE > 2 neV t < 1 µs
+ measures I(Q,t) directly
– low efficiency ≈ 6h / single-Q spectrum
– (except few) only single Q vector
– less efficient for incoherent scattering
3AX
ΔE > 100 µeV t < 20 ps
+ flexibility of Q, ω
setting and resolution
– low efficiency hours / single-Q spectrum
– resolution often not sufficient