Speaker: Xiangshi Yin

Instructor: Elbio Dagotto

Time: Mar. 4th 2010

(Solid State II project)

Outline

History Neutron Scattering Mechanism Neutron sources ORNL neutron facilities

History In 1932, neutron was first discovered by J.

Chadwick In 1936, W. Elsasser proposed the idea of

neutron scattering by crystalline materials In 1936, F. Bloch predicted the feasibility of

neutron scattering by magnetic moment in condensed materials

In 1940s and 1950s, high flux neutron reactor sources were built in U. S. and Canada(Chalk River’s NRX reactor, ORNL’s graphite reactor)

E. Wollan and C. Shull did a lot of pioneering work in modern neutron diffraction between 1948 and 1955

In 1956, B. Brockhouse built the first triple-axis spectrometer in Chalk River Laboratory

……

(1) The existence of ferromagnetic state in Fe3O4 (2) E. Wollan and W. Koehler determined the magnetic structure in La1-xCaxMnO3

1994, the Nobel Prize

Bertram N. Brockhouse Clifford G. Shull

……

Why Neutrons?

Advantages

Disadvantages

No chargeAlmost no electric dipole momentSpin-1/2Short range nuclear force(10-15m)λthermal ~10-10m

Penetrate deepDetect the lattice structureDetect the magnetic structure

Properties

Weakly scatteredLow intensity (104 neutrons/mm2·s)

Signal-limited technique!

1018 photons/mm2·s at synchrotron

source

It’s unique!

Neutron Scattering

Nuclear scattering Magnetic scattering

Inelastic scatteringElastic scattering

Neutron diffraction

Small angle neutron scattering

Surface reflection

Q: Scattering Vector2θ: Scattering Angle

Neutron

Sample

Scattering

I(Q, E)

Single CrystalPolycrystalline Powders

Fast neutrons: >1 eV, 0.1 MeV or 1 MeV (Depending on the definition)Slow neutrons: ≤0.4 eV. Epithermal : 0.025 eV ~ 1 eV. Hot neutrons : ~0.2 eV. Thermal neutrons: ~0.025 eV. Cold neutrons: 5x10-5 eV ~0.025 eV. Very cold neutrons: 3x10-7 eV ~5x10-5 eV. Ultra cold neutrons: ~3x10-7 eV. Continuum region neutrons: 0.01 MeV ~25 MeV. Resonance region neutrons:1 eV ~0.01 MeV. Low energy region neutrons: <1 eV

Coherent scattering

Incoherent scattering

Elastic Inelastic

Equilibriumm lattice structure

Phonons

Elastic Inelastic

Unwanted background

Atomic diffusion

Q: How do we distinguish nuclear scattering from magnetic scattering?

Difference between magnetic and nuclear scattering They normally occur at different wave

vectors Magnetic scattering is temperature

dependent while nuclear scattering is not

Using polarized neutrons we could get spin flipping for magnetic scattering

Neutron

Sample

Scattering

I(Q, E)

Coherent scattering

Incoherent scattering

Elastic Inelastic

Equilibriumm lattice structure

Phonons

Elastic Inelastic

Unwanted background

Atomic diffusion

Q: How do we distinguish magnetic scattering and

nuclear scattering?

Q: How do we measure

Q?

How to measure wave vector?Reactor source Pulsed source

Monochromator

(Powder diffraction)

Triple-axis spectrometer

(Inelastic scattering)

Time of flight technique

A triple-axis spectrometer built at the Institute Laue Langevin in Grenoble,

France

Powder diffractionBragg’s Law:2dSinθ = nλ

Qd

SinQ

2

4

In practice, crystallographers generally have to resort to modeling the structure of crystals, shifting atoms around until they find an arrangement that accurately predicts the measured Bragg intensities

In reality, atoms has thermal energy and oscillate about their lattice. Since an atom can contribute to the constructive interference of Bragg scattering only when it is located exactly at its official position at a lattice site, this scattering becomes weaker the more the atoms vibrate and the less time they spend at their official positions.

Inelastic scattering

When a neutron is scattered by a crystalline solid, it can absorb or emit an amount of energy equal to a quantum of phonon energy hν

In most solids ν is a few terahertz (THz), corresponding to phonon energies of a few meV (~4.18 meV). Because the thermal neutrons used for neutron scattering also have energies in the meV range, scattering by a phonon causes an appreciable fractional change in the neutron energy, allowing accurate measurement of phonon frequencies

The constant-Q scan(invented by B. Brockhouse).

Phonons

Phys. Rev. Lett. 102, 217001(2009)

CaFe2As2

Spin waves

Phys. Rev. B64, 224429 (2001)

Neutron sources

Research reactors Spallation sources

Research reactors

A kind of nuclear reactors but simpler than power reactors

Mechanism: The “chain reaction”

MeVnKrBaU

UUn

17738936

14456

23692

23692

23592

Spallation sources Spallation is a process in which

fragments of materials (spall) are ejected from a body due to impact or stress

The bullet: high energy species, such as proton(1 to 2 GeV)

The target: heavy metal, such as Mercury and Tantulum

20 to 30 neutrons are generated per impact

ORNL neutron facilities

HFIR(High Flux Isotope Reactor) SNS(Spallation Neutron Source)

HFIR

The highest flux reactor-based source of neutrons for condensed matter research in the United States

Fuel: Uranium-235 Reflector: Beryllium Moderator: Water

HFIR beam tubes and experiment locations

SNSNegatively charged hydrogen

Linear accelerator

foil

strip off electronsP

Accumulating ring

Proton pulsesHeavy metal

target(Mercury)

High energy neutron pulses

Moderator(Water)

Cold and thermal

neutrons

Summary

Neutron is a powerful probe to study complex materials

We can get information of both the lattice structure and magnetic structure

Two general neutron source: reactor and spallation source

References [1] J. Chadwick, Nature (London) 129 312 (1932) [2] W. M. Elsasser, C. R. Acad. Sci. Paris 202 1029 (1936) [3] H. Halban and P. Preiswerk, C. R. Acad. Sci. Paris 203 73 (1936) [4] D. P. Mitchell and P. N. Powers, Phys. Rev. 50 486 (1936) [5] F. Bloch, Phys. Rev. 50 259 (1936) [6] B. N. Brockhouse, Nobel Lecture, December 8, 1994 [7] URL http://en.wikipedia.org/wiki/Neutron_temperature [8] URL http://en.wikipedia.org/wiki/Neutron_diffraction [9] Tapan Chatterji, Neutron Scattering from Magnetic Materials URL http:// www.sciencedirect.com/science/book/9780444510501 [10]URL http://neutrons.ornl.gov [11]URL http://www.khwarzimic.org/takveen/seaborg.pdf [12] J. R. Alonso “The spallation neutron source project” Proceeding of the 1999 particle accelerator conference, New York, 1999 [13]URL http://irfu.cea.fr/en/Phocea/Vie_des_labos/Ast/ast_visu.php?id_ast=2215 [14] V.F. Sears, Methods of Experimental Physics, vol. 23, eds. K. Sköld and D.L. Price, Part A, Academic Press, London (1986) [15] D.L. Price and K. Sköld, in: Methods of Experimental Physics, vol. 23, Part A, p.1, Academic Press, London (1987) [16] R. Mittal, L. Pintschovius, D. Lamago, R. Heid, K-P. Bohnen, D. Reznik, S. L. Chaplot, Y. Su, N. Kumar, S. K. Dhar, A. Thamizhavel and Th. Brueckel Phys. Rev. Lett. 102, 217001(2009) [17] P. Dai, J. A. Fernandez-Baca, E. W. Plummer, Y. Tomioka and Y. Tokura Phys. Rev. B64, 224429 (2001)