Neutron scattering &

disordered materials

Miguel A. GonzálezInstitut 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

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

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?

Coherent and incoherent scattering

coherent

incoherent

• Information in both space and time

H/D substitution and polymer dynamics

The case of hydrogen

4b2 = 4b2 + 4(b2b2) total = coh + inc

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.

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):

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

• Large Q-range

• High stability

• High flux

• Very low background

• Simpler corrections

D4C (ILL)

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

What can we see with QENS & INS

Self intermediate scattering function

Kinds of instruments used

(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)

Crystal-TOF spectrometer

Kinematical range

ki

kf Q

2

2mki

2 kf2

Q (ki kf )

Q ki2 kf

2 2kikf cos

Cold neutron spectrometer

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 ...

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!