I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 11T H E E U R O P E A N N E U T R O N S O U R C E
I N S T I T U T L A U E L A N G E V I N
Neutron Optics
P. CourtoisService for Neutron Optics
EIROforum School on Instrumentation 13-17 May 2019
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 2
The neutron
Why we need neutron optics
Basic concepts & Optical components
Reflection Mirrors & Super-Mirrors
Diffraction Mosaic crystals
Filters Crystals, polycrystalline materials
Polarization Super-Mirrors, crystals, 3He spin filters
Some examples of applications at I.L.L.
Neutron OpticsNeutron Optics are key components for neutron instrumentation
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 3
Particle Mass m = 1.675 10-27 Kg → Kinetic Energy E = ½ m v2 ~ meV
No Charge Spin = 1/2 Magnetic moment m = -1.913 mN
Beta life time 886 s
neutrons E (meV) l (Å)
Hot 900 - 80 0.3 - 1
Thermal 80 - 5 1 - 4
cold 5 - 0.03 4 - 50
Wave Wavelength l = h/mv Wave vector k = 2p/l
Moment p = ћk Energy E = ћ2k2/2m
E(meV) = 81.81 / l2 (Å)
Neutrons have wave-like properties…
The Neutron
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 4
Interaction with the individual nuclei via short range forces
Coherent scattering : depends on the direction of scattering vector Q = ki-kf
→ Coherent scattering length bcoh (~10-12 cm)
→ Diffraction, reflection, refraction …
Incoherent scattering : uniform scattering→ Incoherent scattering length binc (~10-12 cm)
→ Background , beam attenuation
Coherent scattering
atomnki
kf
Neutron Scattering
Incoherent scattering
natom
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 5
Interaction with the individual nuclei via short range forces Neutron capture
Absorption cross section : sabs (~10-24 cm2)
Activation of materials - Emission of gamma rays
→ Radioprotection - shielding
Neutron Absorption
neutron capture
Atom*n
g
59Co
60Co*
n
g
E = 1.17 MeVg
E = 1.33 MeV
60Ni
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 6
Interaction with unpaired electrons via a dipole interaction Magnetic scattering
Magnetic scattering length p ≈ 0.269 mat (10-12 cm/mB)
p ≈ bcoh (e.g. mat (Fe)= 2.2mB , p = 0.59 10-12cm, bcoh = 0.94 10-12 cm )
→ study of magnetic structures, production of polarized neutron beams
Magnetic scattering
atomn
e-
Magnetic Scattering
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 7
Element bcoh (10-12 cm) binc (10-12 cm) sabs (10-24 cm2)
H -3.74 25.2 0.33
D 6.67 4.04 0.0005
BGdCd
- -767
488902520
C 6.64 ~ 0 0.0035
Ni 10.3 0.64 4.49
Si 4.14 0.015 0.17
Cu 7.72 0.20 3.78
Background
Neutron absorber
Optics !
Moderator
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 8
Neutron sources are large compared to sample size ( 100 cm2 vs 1 cm2)
Neutrons sources are weak (max neutron flux on sample is 1010 neutrons/cm2/s, while x-ray fluxcan be 1020 photons/cm2/s)
Neutron beams are divergent (beam divergence in the range of 0.2° to 1°)
Neutron beams are ”polychromatic” (wide energy range, e.g. thermal range: 5-80 meV)
Neutron beams are not polarized
Basic Properties of neutron beamsNeutrons are extracted by beam tubes from the reactor core and transported by neutron guides to the experimental area
a= 2 qcSampleS ~1 cm2Neutron source
(guide, beam tube)
Beam size S ~ 100 cm2Divergent beam
flux ~ 1010 n /cm2/sReactor core
flux ~ 1015 n /cm2/s
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 9
What do we need to perform neutron scattering experiments ?
We need to transport neutrons to the experimental area (guides)
Mirror & Super-Mirror : Flux, divergence, neutrons with wavelengths in the right range
We need to determine incident and scattered neutron directions
Collimator : Angular resolution
We need to select out unwanted neutrons - Filter
We need to determine incident and scattered wavelengths (Energies)
Crystal Monochromator : Wavelength resolution (Energy resolution)
We need also to polarize neutron beams
Crystal/ Super-Mirror/ 3He spin filter : Orientation of the neutron spin
Instrument Performances are then determined by Neutron Optics !
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 10
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 11
Neutron MirrorsReflection/Refraction at Surfaces
plq coh
c
Nb=
incident reflected
refracted
Nbcoh = Scattering Length DensityN = atoms/cm3
bcoh = coherent scattering length
for natural Ni: qc(°) = 0.1 x l (Å)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
l = 5 Å
refle
ctiv
ity
q [°]
qc
Ni mirror
θ
MaterialNb
(x 1038 /m2)qc (mrad)
58Nickel 13.31 2.03
Nickel 9.41 1.7
Iron 8.2 1.62
Copper 6.7 1.39
Silicon 2.08 0.81
Aluminium 2.08 0.81
Total reflection for q < qc
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 12
Periodic MultilayersReflection/Refraction at Surfaces
Total reflection for q < qc
+
additional Bragg peak at qB ≈ l / 2d
Rµ 4N 2d4 N1b1 - N2b2( )
2
π 2n4
Total reflection
Bragg peak
Total reflection
qc
Neutron Reflectivity
Wavelength band
qB l 2d
Dl
l=
2d2 N1b1-N2b2
π
d
θ
substrate (glass, Si…)
Nbcoh = Scattering Length Density
N : number of bilayers
n : order of the reflection
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 13
Super-Mirrors
substrate (glass, Si…)
d3
d2
d1
θ
Sequence of bi-layers of variable thicknesses d
Total reflection for q < qc + additional Bragg peaks
m =qc
SM
qc
Ni
G=qc
sm
qcNi
æ
èçç
ö
ø÷÷
2
µm2
0.00 0.25 0.50 0.75 1.00 1.250.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.5 1.0 1.5 2.0 2.5
m - value
l = 5 Å
refle
ctiv
ity
q [°]
regime ofsupermirror
regime oftotal
reflection
How to increase angular acceptance of mirrors
→ significant increase in critical angle (qc = l 2dmin)
m Super-Mirror
Gain in neutron flux
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 14
Ni/Ti Super-MirrorsProperties
Neutron Reflectivity R (N1b1-N2b2)2 High contrast → high reflectivity !
• Ni Nb = 9.40 (10-6Å-2)
• Ti Nb = -1.95 (10-6Å-2)
Reflectivity profiles of Ni/Ti super-mirrors for 4 ≤m ≤ 7(sources : www.swissneutronics.ch)
m=4
Performances
R > 80% for m = 4 Ni/Ti
Gain factor / Ni mirror = 16 (2D)
but transmission T Rn !!
eg : for a 100 m long guide , at least ten
reflections → Transmission < 10% ...
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 15
Ni/Ti Super-Mirrors Deposition : Reactive DC Magnetron Sputtering
Sputtering machine (ILL) - Production 0.8 m2 / day
Production m= 4 : 1600 layers ! Substrate : 0.5 cm thick Si wafers or 0.2 cm thick Glass/Si/Sapphire
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 16
1614/05/2019
Neutron Guide
m=2 Ni/Ti Super-Mirrors
Length > 50 m
Section ~ 20 x 10 cm2
4 reflective internal surfaces
Curvature R ~ 1-10 km
A neutron guide can transport neutrons over a long distance with “no loss”
Ni/Ti Super-Mirrors
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 17
Bragg MirrorsLarge wavelength band Monochromator
(Laue diffractometer for Protein crystallography)
guide
to produce a « monochromatic » beam at 3.5 Å with a bandwidth Dll = 20%
Q
Stacked Multilayer monochromator Beam width = 20 mm qB = 1.25 ° -> d0 = 80 Å Dll = 20 % -> graded d-spacing 74-90 Å Beam size >> Sample size (1 mm)
-> Focusing device (fan geometry)
•mirror length = 25 mm • thickness 0.5 mm• 40 mirrors Ni/Ti• Si substrate
(low attenuation factor)
monochromatorsample
L mono-sample = 2135 mm
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 18
Bragg Mirrors
guide
Q
monochromator
sample
monochromator
neutrons
direct beam
reflected beam l0 ≈ 3.5 Å
Dll ≈ 20%
Reflectivity ≈ 75%
TOF spectra on LADI
Large wavelength band Monochromator
(Laue diffractometer for Protein crystallography)
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 19
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 20
Use of single crystals to select a given wavelength band according to the Bragg’s Law
2 dhkl sinqB = nl0d= distance of the lattice (hkl) planes qB = Bragg angle
Determining the wavelength (Energy)Crystal Monochromator
polychromatic beam
monochromatic beam
l0
crystal
If a ~b , the resolution and intensity are said to be optimised
Mosaic Crystal, i.e. crystal with defects such as dislocations,must be used to match the divergence a of primary beam which is typically 0.2°- 0.8°
The relative bandwidth Dll is given for Gaussian distributions by Dll = (a 2 + b 2)1/2cotqB
a : divergence of the primary beamb : full width at half maximum of the neutron “rocking curve” or neutron mosaic spread
n/s
b q
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 21
A mosaic crystal consists of a distribution W(q) of small crystallites (perfect crystals) making small angles relative to the nominal plane. W(q) is usually taken to be a Gaussian distribution.
Defect free crystal = perfect crystal (Silicon) Crystal with defects such as dislocations = mosaic crystal
)2/exp(2
1)( 22
pq D=w
The mosaic crystalPerfect crystal vs Mosaic crystal
Perfect crystalDarwin width < 0.001°
w
Mosaic crystal width > 0.05 °
q
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 22
Mosaic Crystal
The reflection range of mosaic crystals is of the order of 0.3 °even more....
Mosaic crystals can reflect efficiently neutrons from the source of divergence a, if b a.
High intensity and reasonable resolution
Suitable for neutron beams !
fwhm < 10-4°
Dll =a cotqB ; flux → 0 !
Perfect crystal
<hkl> aa
Dll = (a 2 + b 2)1/2cotqB
Mosaic crystal
fwhm > 0.1 °
a+2bb
a
Perfect crystal
The reflection range of perfect crystals is in the order of 0.001°.
Perfect crystals do not reflect efficiently neutrons from the source of divergence a.
Very high resolution but no intensity
Not suitable for neutron beams !
Perfect crystal vs mosaic crystal
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 23
Mosaic CrystalsGood Materials should have
High neutron reflectivity R scattering power Q
Large structure factor Fhkl
High coherent scattering length bcoh (Fhkl bcoh) Small unit cell Volume V : Cubic, Diamond d-spacing optimized for a given wavelength (d ~ l )
Low incoherent scattering length → low background
Low absorption cross sections → small attenuation
Availability of large single crystals with suitable width and uniform mosaic block distribution !
I0 IR
crystal
R(l) = I0(l) / IR(l)
Bql /sin2/V)e(F=Q 32-W
hkl
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 24
Common mosaic crystals for neutron monochromators
Crystal orientationCrystal Mosaic
NeutronEnergy
Application Supplier
HOPG (C)d002= 3.35
ÅHOPG(002) 0.5°- 3°
ColdThermal
High fluxPanasonic, Optigraph, Momentive
Cu d111= 2.08
Å
(111)(220)
(200)…0.01° - 3°
Hot Thermal
Highresolutionor high flux
I.L.L. (or ?)
Sid111= 3.13
Å
(111)(113)…
Perfect Cold
ThermalHigh
resolutionmany !
Ged111= 3.26
Å
(111)(113)…
< 0.4°Cold
ThermalHigh
resolutionI.L.L.(or ?)
HeuslerCu2MnAl
(111) 0.2 – 0.6 °Hot
ThermalPolarized neutrons
I.L.L.
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 25
Crystal MonochromatorHighly Oriented Pyrolitic Graphite (HOPG)
Hexagonal unit cell - a = 2.461 Å; c= 6.707 Å ; space group P63mc
Structure FactorF00l = 4 bC l = 2N
F002 = 4 x 6.64 10-12 cm
Large Graphite single crystals not available
Production of mosaic HOPG crystals micro-crystallites oriented along the c axis random distribution in the (a,b) planes
Suppliers : Panasonic, Momentive, Optigraph
Only (0 0 2l) Reflections available HOPG(002) mosaic FWHM > 0.4°
Suitable for neutron applications !
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 26
Diamond structure ; space group Fd3m ; aSi = 5.43 Å and aGe = 5.65Å
Structure Factors Fhkl = 0 h,k,l mixed even or oddFhkl = 0 h,k,l all even and h+k+l=4n+2Fhkl = 8 b h,k,l, all even and h+k+l=4nFhkl = 4√2 b h,k,l all odd
Large perfect crystals available from industry
For h,k,l “all odd” reflections: Fhkl ≠ 0 and F2h,2k,2l = 0
→ No reflection of the second harmonic→ No l/2 contamination
but the mosaic distribution (FWHM) of a perfect crystal is too narrow for neutron applications !!
Crystal MonochromatorSi and Ge perfect crystals
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 27
Face-centred cubic structure aCu = 3.615Å; space group Fm3m
Structure Factors Fhkl = 0 h,k,l mixed even or oddFhkl = 4 bCu h,k,l all even or all odd
Fhkl = 4 x 7.72 10-12 cm
Crystal Growth at ILL Bridgman Technique large crystals of high quality
but the mosaic distribution (FWHM) of the as-grown crystal is too narrow for neutron applications !!
m = 8 kg-4 -2 0 2 4
Refle
ctiv
ity (a
rb.u
nits
)
diffraction angle (minutes)
as-grown Cu crystal
fwhm ~ 30 arc sec
Crystal MonochromatorCu mosaic crystal
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 28
crystal
Anvil
Heating element
FWHM=0.15°
FWHM=0.45°FWHM=1°
Mosaic Crystals Control of the mosaic distribution by plastic deformation (I.L.L.)
FWHM=0.4°Perfect crystal
Ge111
Cu200
Peak reflectivity at l = 3.4 ÅRexp = 50-55% (FWHM=0.4°)
Rexp ≈ 70 % of Rth
Peak reflectivity at l = 1.1 ÅRexp = 40-45% (FWHM=0.3°)
Rexp ≈ 80-90 % of Rth
T = 800 °C
P = 1 MPa
as-growncrystal
Cu200 P,T
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 29
Mosaic CrystalsBent perfect Silicon crystals (I.L.L.)
Effective mosaic d (rad) d = cot(qB) t / Rt = total crystal thicknessR = radius of curvatureqB = Bragg angle
<hkl>R
qB
Perfect Si crystal
neutrons
Stack of thin wafers to allow bending wafer thickness = 1 mm 10 wafers to get t = 10 mm (or more) Curvature : flat to RH ≈ 2 m
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 30
Monochromators
HOPGD19
• Large effective area to cover the direct beam
Assembly of mosaic crystals
• FWHM ~ beam divergence 0.2 < FWHM < 0.6 °
• Crystal size ~ Sample size (1 to 10 cm2)
• Crystals fixed onto specific mechanics
• 10B4C is used to reduce background and activation
• Orientation accuracy ± 0.03°
• Vertical Focusing
• Horizontal Focusing (Triple axis spectrometers)
crystal
AlB4C
crystal + support
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 31
Focusing devicesDivergent beamflux ~ 1010 n /cm2/s
a= 2 qcSampleS ~1 cm2
Neutron source (guide, beam tube)
Beam size S ~100 cm2
lost neutrons !
Focusing devices are used to increase the neutron flux at the sample position. However, theincrease of neutron flux implies a degradation of the angular resolution. (Liouville’s theorem!)
H1H2H1 a1 = H2 a2Divergence a1
a2
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 32
Focusing DevicesPrinciples
Vertical Focusing
Image size ~ crystal size (height) Gain in flux compression factor Increase of vertical angular divergence Rv l
Horizontal Focusing
Horizontal focusing affects Q resolution Rh 1/l
Sample
1
Rv
=1
2sinq
1
L1
+1
L2
æ
èç
ö
ø÷
1
RH
=sinq
2
1
L1
+1
L2
æ
èç
ö
ø÷
Rv
Source
Sample
L2
L1
θ
L2
L1Source
Sample
RHθ
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 33
Focusing DevicesMonochromators for neutron Diffractometers
Production of a fixed neutron wavelength at a given take-off angle
Ge (335) - l = 1.6 Åcrystal mosaic = 0.2 °
High Resolution
D2B
D20
Ge (111)- l = 3.15 Åcrystal mosaic = 0.4 °
High Resolution
D20
Ge monochromator is well suited
for high resolution neutron diffractometers
D20 (high intensity difffratometer with variableresolution) - D2B & D1B (powder diffractometers)
Large dimensions Heigth 300 mm
Width 50-120 mm
no l/2 contamination (odd reflections)
Fixed vertical focusing Rv = 2 LMS sinqB
D20 : Rv = 3200 mmD2B : Rv = 4600 mm
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 34
D20
Single crystal diffractometerHOPG (002) - l = 2.4 Åcrystal mosaic = 0.5 °
High Flux
D19
Single crystal diffractometerCu(200) - l = 1.2 Å
crystal mosaic = 0.2 °High Resolution
D10
HOPG monochromator
• Provides high neutron flux (thermal & coldneutrons)
l/2 contamination (002 reflections)
Use of HOPG Filter !
Fixed vertical focusingCu monochromator
provides high neutron flux or high resolution(hot & thermal neutrons)
l/2 contamination
use of HOPG Filter !
thermal neutron guide cut-off
Focusing DevicesMonochromators for neutron Diffractometers
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 35Auteur - Date
Optimization of instrument performances for a wide energy range
Variable horizontal and vertical curvature
Focusing monochromator is used in combination with focusing guide (virtual source)
Focusing DevicesMonochromators for Triple Axis Spectrometers
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 36
D20
HOPG(002) monochromatorcrystal mosaic = 0.5 °
cold neutrons
Cu(200) monochromatorcrystal mosaic = 0.3 °
High Flux – Thermal neutrons
Si(113) monochromatorbent perfect crystals
Hot neutrons
Thales IN8C IN1
Focusing DevicesMonochromators for Triple Axis Spectrometers
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 37
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 38
Neutron Filtersm super-mirrors can be used to select out unwanted neutrons
Neutron long wavelength cut-off filter
qm super-mirror
White beam
Transmittedl <lC
Ni
c
cmq
ql =
reflectedl >lC
sample
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 39
m Super-Mirrors Long wavelength cut-off filter (SANS instrument)
White beamTransmitted
l <lC
reflected l >lC
Q = 2.2
lc = 20 Å
to select out unwanted neutrons of wavelengths > lc
m=1.1 SM NiV/Ti on 0.5 cm thick Si substrate mounted at an angle q in a neutron guide
Borofloat glass m=0.65
0.84 m
Ni
c
cmq
ql =
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 40
to select out unwanted neutrons of wavelengths > lc
m=1.1 SM NiV/Ti on 0.5 cm thick Si substrate mounted at an angle q in a neutron guide
m Super-Mirrors Long wavelength cut-off filter (SANS instrument)
White beamTransmitted
l <lC
reflected l >lC
Q = 2.2lc = 20 Å
Q = 1.32
lc = 12 Å
Borofloat glass m=0.65
0.84 m
Transmittedl <lC
Ni
c
cmq
ql =
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 41
m Super-Mirrors Long wavelength cut-off filter (SANS instrument)
White beamTransmitted
l <lC
reflected l >lC
Q = 2.2lc = 20 Å
Q = 1.32
lc = 12 Å
Borofloat glass m=0.65
0.84 m
Transmittedl <lC
to select out unwanted neutrons of wavelengths > lc
m=1.1 SM NiV/Ti on 0.5 cm thick Si substrate mounted at an angle q in a neutron guide
Ni
c
cmq
ql =
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 42
m Super-Mirrors Long wavelength cut-off filters at I.L.L. (SANS instrument)
Neutron Flux at the sample position on D33
C. D. Dewhurst et al. , J. Appl. Cryst. (2016). 49, 1-14
no filter
lc = 20 Å
lc = 12 Å
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 43
Neutron Filterspolycrystalline Be & Saphirre crystal
θ
Polycrystalline Beryllium at 77Kis used to select out neutrons of l< 4 Å
(Cut-off at l = 2dBe max )
Perfect Saphirre crystal is used to select out fast neutrons of l < 0.5 Å
Reduction of background
T ~ 5%
T ~ 80%
n l > lcut
l < lcut
Cut-off
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 44
Neutron FiltersHOPG crystal
θ
l= 1.2 Å
l= 2.4 Å
Wavelength l (Å)
tran
smis
sio
n
l0 2
HOPG crystal (Highly Oriented PyroliticGraphite) is commonly used for eliminatinghigher-order contamination of amonochromated neutron beam
PG filter has strong attenuation at 1.2 Å butpasses 2.4 Å
• T > 80 % at 2.4 Å
• T < 1% at 1.2 Å
l= 0.8 Å
l0 = 2.4 Ål0 = 2.4 Å+ l0 2 = 1.2 Å
HOPG filter , 4 cm thick
HOPG filter
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 45
Production of Polarized neutron beams
at I.L.L.
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 46
Magnetic Field B (quantization axis) → sneutron= ± ½
Polarization of the neutron beam +
+
+
=
NN
NNP
B Principal methods
Fe/Si and Co/Ti super-mirrors (reflection, transmission)
Heusler Cu2MnAl crystal (diffraction)
3He3 spin filters (absorption by polarized 3He nuclei)
polarizer
P =1
N+ neutrons with >N- neutrons with >
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 47
Refraction index
for a magnetic layer π
pbNλn
2
)(1
2 =
Magnetic contribution
Reflectivity R of a bilayer system
> : R+ [N1b1-N2(b2+p2)]2
> : R- [N1b1-N2(b2-p2)]2
Polarization N1b1= N2(b2±p2)
→ Reflection / Transmissionof one spin state 1: non magnetic layer
2: ferromagnetic layer
q
>
>
> + >
B
Q
1
2
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 48
Co/Ti Super-Mirrors
> : N(b+p)Co = 6.55;
> : N(b-p)Co = -2.00 ≈ Nb Ti = -1.95
m= 3.2 Super-Mirrors
but Activation of Cobalt ! (lifetime 5 Years)
can be used only for polarization analysis
Fe/Si Super-mirrors
> : N(b+p)Fe = 13.04;
> : N(b-p)Fe = 3.08 ≈ Nb Si = 2.08
m = 4 super-Mirrors
→ Polarizer in reflection / Transmission geometry
Spin up Fe/Siq
>
>
P = 94%
R+
R-
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 49
Polarizing Fe/Si Super-Mirrors
to produce a polarized cold neutron beam
S bender Polarizer for neutron reflectometer
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 3
0 0.5 1 1.5 2 2.5 3 3.5 4
Re
fle
ctiv
ity
Omega
m=q / qc(Ni)
m = 3.8 Fe/SiR+ > 80%
R+
R-
P
m=3.8 Fe/Si SMson 0.2 cm thick Si substrate
Neutrons propagate into Si Spin > transmitted Stack of 60 blades(l 50 mm; h 160 mm; w 10 mm)
Pneutrons > 95% (5.5 Å) T ~ 40% of good neutrons
200 mm
Si channel
B
Polarizing supermirrors
>
neutrons
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 50
Polarizing Co/Ti Super-MirrorsAnalyzer for wide angle spin echo spectrometer (WASP)
Co/Ti m= 2.8
Teta (°)
R+
R-
P
C bender - optimized for l = [4 -12 Å]
Neutrons propagate into air
Curvature R = 7m to avoid direct line of sight : at least on reflection !
Double sided mirrors (h 141 x w 254 mm2)
C bender
substrate
absorbing layer
Co/Ti SM
0.2 cm thickBorated glass
substrate
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 51
Bragg reflection
from a ferromagnetic crystal
> : I+ [FN(Q) + FM(Q)]2
> : I- [FN(Q) - FM(Q)]2
FN(Q) nuclear structure factor
FM(Q) magnetic structure factor
Polarization FN(Q) = ± FM(Q)
>
BUnpolarized
White beam
Polarized
Monochromatic beam
Q
Crystal planes
M
>
>
>
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 52
Single crystal
• (111) reflection F111N = - F111M
• mosaic 0.2° < fwhm < 0.6°
• Reflectivity R experimental ≈ Rtheoretical
• Polarization P > 92 % 0
10
20
30
40
50
-0.4 -0.2 0 0.2 0.4
— calculated — experimental
Re
fle
ctiv
ity
(%)
Rocking angle (degree)
● Mn
● Cu
●AlCubic structure L21
Structures Factors(111)
Nuclear: F111N = 4 (bMn-bAl ) (F111N = -2.8 10-12 cm)
Magnetic: F111M= 4 pMn
(F111M = 2.78 10-12
cm)
Heusler Cu2MnAl single crystal
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 53
Neutron Filters – Polarized Neutrons3He spin filters
B
3He spin filter cell
P
For fully polarized gaseous 3He (PHe = 1), one spin state goes through the filter withzero absorption. The other spin state is almost fully absorbed since σ = 6000 barns→ polarized neutron beam
Absorption cross section of 3Helium nuclei If the nuclear spin of He and the neutron spin are parallel, sa ≈ 0 If the nuclear spin of He and the neutron spin are anti-parallel, sa ≈ 6000 barns
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 54
Neutron Filters – Polarized Neutrons3He spin filters
Polarization of 3He is time dependant : P(t) = exp(-t/T1)
]b[
750]h[
PTd =
h 400200 wT
Tm[h] =P[b]
7000
¶B /¶r[cm]
B
æ
èç
ö
ø÷
-2
1
T1
=1
Td
+1
Tw
+1
Tm
Tw : Relaxation due to interaction with paramagnetic impurities
Tm : Relaxation due to field gradients
Td : Dipolar relaxation among 3He nuclear spins
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
He-3
Fit
Hours
Heliu
m-3
Pola
risation
T1 = 96 hrs
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 55
The total relaxation time T1 must be in the order of 100 hours to perform high quality neutron experiments
High quality 3He spin filters (Polarization, Tw)
Homogeneous magnetic field
Production of polarized gas 3He !
Neutron Filters – Polarized Neutrons3He spin filters
¶B /¶r
B
æ
èç
ö
ø÷ <10-3cm-1
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 56Auteur - Date
Production of 3He spin filters at I.L.L.Metastability Exchange Optical Pumping (MEOP)
3He filling station at I.L.L.
polarization of 3He nuclei
I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N 57Auteur - Date
Production of 3He spin filters at I.L.L.Metastability Exchange Optical Pumping (MEOP)
Production rate > 1 bar-litre/h , Final pressure up to 4 bar, Polarization of 3He ≈ 80 %
58T H E E U R O P E A N N E U T R O N S O U R C E
Conclusion
Neutron Optics define beam properties
- Direction, Divergence, Wavelength, Energy, Polarization
- Angular Resolution, Wavelength resolution, Energy resolution
Vertical focusing devices allow the optimization of the neutron flux at the sample position
Double variable focusing devices allow the optimization of instrument performances for a wide energy range
Since the power of the source is low, neutron optical components must be of high quality and properly designed
Neutron Optics obey to Liouville’s Theorem : It costs flux to increase resolution and
it costs resolution to increase flux
The optimization of instrument performances is always
a compromise between flux and resolution
59T H E E U R O P E A N N E U T R O N S O U R C E
Thank You for your attention