The neutron-neutron scattering length - Institute for Nuclear Theory
Neutron scattering & disordered materials
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Transcript of Neutron scattering & disordered materials
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Neutron scattering &
disordered materials
Miguel A. GonzálezInstitut Laue Langevin (Grenoble, FRANCE)
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Why neutrons?
• Neutrons:
– Low intensity • ILL is for neutrons what a 6V bicycle lamp is for photons
– Expensive sources required (reactors, spallation sources).
– Serious drawbacks: difficult to guide, focus, or detect.
– Not direct access (no laboratory facilities).
• We need really good reasons… and the properties of the neutron will give them all
…
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Basic properties of the neutron
• Subatomic particle (nucleon)• Charge: zero• Mass
– 1.0087 a.m.u. (1.675·10-27 kg) • Spin of 1/2 h• Magnetic moment
– µn = –1.9132 nuclear magneton = –9.65·10–27 J/T
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Neutron as a probe
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Neutron as a probe
* Wavelength and energies well suited to explore interatomic distances and typical excitations in condensed matter (phonons, magnons, vibrational modes, ...)
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Neutron as a probe
* Wavelength and energies well suited to explore interatomic distances and typical excitations in condensed matter (phonons, magnons, vibrational modes, ...)* Weak absorption: penetrates bulk of large samples & containers
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Atomic number
10 80 90403020 60 7050
Pen
etra
tion
dee
p (
m)
10-2
1
10-4
10-6
0
Neutron as a probe
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Neutron as a probe
* Wavelength and energies well suited to explore interatomic distances and typical excitations in condensed matter (phonons, magnons, vibrational modes, ...)* Weak absorption: penetrates bulk of large samples & containers* Scattered (mainly) by nuclei:
1. Constant scattering length: Intensity at high scattering angles!
2. Arbitrarily changing with Z Light atoms beside heavy ones (H-O, Li-Mn, O-U) are visible Discriminating neighbours (O-N)
3. Arbitrarily changing with A: Isotopic exchange
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Neutron as a probe
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And very important ...
Direct probe of the dynamic structure factor (or scattering law), which contains everything we want to know about the properties of the sample (both structure and dynamics)!
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What do we measure?
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Coherent and incoherent scattering
coherent
incoherent
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• Information in both space and time
H/D substitution and polymer dynamics
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The case of hydrogen
4b2 = 4b2 + 4(b2b2) total = coh + inc
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Dynamic structure factor
intermediate scattering function, I(Q,t)
DIRECT RELATION: Measured quantity Physical information d2/dd S(Q, )
S(Q,) is a correlation function related only to the properties of the scattering system.
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More correlation functions
Van Hove time-dependent pair correlation function (1954)
S(Q,) is the Fourier transform in space and time of the density-density correlation function G(r,t):
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Relations S(Q,), I(Q,t), G(r,t)
FT in time FT in space
S(Q, ) I(Q,t) G(r,t)[energy]1 [] [volume]1
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• Large Q-range
• High stability
• High flux
• Very low background
• Simpler corrections
D4C (ILL)
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Liquid Ar @ 85KJ.L. Yarnell et al. (1973) PRA 7, 2130
TTkS B)0(
Q
Qp
FSDP
Limiting values Normalisation
P
d
Fourier Transformation
1)( QS
First Sharp Diffraction Peak
3.8 Å
Monoatomic system
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What can we see with QENS & INS
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Self intermediate scattering function
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Kinds of instruments used
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(Q,) explored in a step-by-step manner:
1. ki selected by Bragg reflection in a crystal monochromator (A1, A2)
2. Orientation of kf controlled by sample orientation (A3, A4)
3. kf selected by Bragg reflection in a crystal monochromator (A5, A6)
Three-Axis Spectrometer (TAS)
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Crystal-TOF spectrometer
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Kinematical range
ki
kf Q
2
2mki
2 kf2
Q (ki kf )
Q ki2 kf
2 2kikf cos
Cold neutron spectrometer
Hot neutron spectrometer
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SUMMARY
- Neutron Scattering can provide unique information about the structure (isotopic substitution) and dynamics (simultaneous measurement of Q and ) of (disordered) matter.
- Excellent complementary information to that provided by other techniques: dielectric spectroscopy, X-rays, NMR, ...
And many possibilities to use neutrons around the world ...
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ILL Grenoble
Isis
Dubna
Orphée
St PetersburgHMI Berlin
KFKI Budapest
FZ Jülich
PSI Zurich
FRM-II
Delft
ŘezPrague
Kjeller
DemokritisAthens
Swierk
GKSS
Thank youand
welcome!