Transcript No Slide Title

Neutron scattering
&
disordered materials
Miguel A. González
Institut Laue Langevin (Grenoble, FRANCE)
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 …
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
Neutron as a probe
Neutron as a probe
* Wavelength and energies well suited to explore interatomic
distances and typical excitations in condensed matter (phonons,
magnons, vibrational modes, ...)
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
Neutron as a probe
Penetration deep (m)
1
10-2
10-4
10-6
0
10
20
30
40
Atomic number
50
60
70
80
90
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
Neutron as a probe
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)!
What do we measure?

2
d 2
k'
2
(2, )  N
b S d (Q, )  b Ss (Q, )
dd
k

Coherent and incoherent scattering
coherent
incoherent
H/D substitution and polymer dynamics
• Information in both space and time
The case of hydrogen
4b2 = 4b2 + 4(b2b2)
total = coh + inc
Dynamic structure factor
S(Q,) is a correlation function related only to the
properties of the scattering system.
intermediate scattering function, I(Q,t)
DIRECT RELATION: Measured quantity
d2/dd
Physical information
S(Q, )
More correlation functions
S(Q,) is the Fourier transform in space and time of the
density-density correlation function G(r,t):
Van Hove time-dependent pair correlation function (1954)
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
D4C (ILL)
• Large Q-range
• High stability
• High flux
• Very low background
• Simpler corrections
Monoatomic system
FSDP
3
First Sharp Diffraction Peak
Liquid Ar @ 85K
J.L. Yarnell et al. (1973) PRA 7, 2130
2
S (Q   )  1
S(Q)
DQ
Fourier Transformation
1
3
Qp
0
2
4
6
8
10
3.8 Å
12
2
-1
Q/Å
S (0)   k BT T
P
g(r)
0
1
d
Limiting values  Normalisation
0
0
5
10
15
r/Å
20
25
What can we see with QENS & INS
Self intermediate scattering function
Kinds of instruments used
Three-Axis Spectrometer (TAS)
(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)
Crystal-TOF spectrometer
Kinematical range
kf
Q

k i2  k f2 



2m
Q  (ki  kf ) 
ki
Cold neutron
spectrometer

2


Q
k i2  k f2  2k i k f cos
Hot neutron
spectrometer
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 ...
St Petersburg
HMI Berlin
Dubna
FZ Jülich
GKSS Kjeller
Delft
Isis
Orphée
Swierk
ILL Grenoble
Thank you
and
welcome!
Řez
Prague
FRM-II
PSI Zurich
KFKI Budapest
Demokritis
Athens