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