Neutron scattering disordered materials Miguel A González

Neutron scattering & disordered materials Miguel A. González Institut Laue Langevin (Grenoble, FRANCE)

Why neutrons? • Neutrons: – Low intensity • ILL is for neutrons what a 6 V 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?

Coherent and incoherent scattering coherent incoherent

H/D substitution and polymer dynamics • Information in both space and time

The case of hydrogen 4 b 2 = 4 b 2 + 4 ( 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 d 2 /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

D 4 C (ILL) • Large Q-range • High stability • High flux • Very low background • Simpler corrections

Monoatomic system FSDP First Sharp Diffraction Peak Liquid Ar @ 85 K J. L. Yarnell et al. (1973) PRA 7, 2130 DQ Fourier Transformation Qp 3. 8 Å P d Limiting values Normalisation

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 (A 1, A 2) 2. Orientation of kf controlled by sample orientation (A 3, A 4) 3. kf selected by Bragg reflection in a crystal monochromator (A 5, A 6)

Crystal-TOF spectrometer

Kinematical range kf Q ki 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. . .

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