1. Speaker: Xiangshi Yin Instructor: Elbio Dagotto Time: Mar. 4 th 2010 (Solid State II project)

2. Outline  History  Neutron Scattering Mechanism  Neutron sources  ORNL neutron facilities

3. 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)

4.  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 Fe 3 O 4 (2) E. Wollan and W. Koehler determined the magnetic structure in La 1-x Ca x MnO 3

5.  1994, the Nobel Prize Bertram N. BrockhouseClifford G. Shull

6.  ……

7. Why Neutrons? Advantages Disadvantages  No charge  Almost no electric dipole moment  Spin-1/2  Short range nuclear force(10 -15 m)  λ thermal ~10 -10 m  Penetrate deep  Detect the lattice structure  Detect the magnetic structure Properties  Weakly scattered  Low intensity (10 4 neutrons/mm 2 ·s) Signal-limited technique! 10 18 photons/mm 2 ·s at synchrotron source It’s unique!

8. Neutron Scattering Nuclear scatteringMagnetic scattering Inelastic scatteringElastic scattering Neutron diffraction Small angle neutron scattering Surface reflection Q: Scattering Vector 2θ: Scattering Angle

9. Neutron Sample Scattering I(Q, E)  Single Crystal  Polycrystalline 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 ElasticInelastic Equilibriumm lattice structure Phonons ElasticInelastic Unwanted background Atomic diffusion Q: How do we distinguish nuclear scattering from magnetic scattering?

10. 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

11. Neutron Sample Scattering I(Q, E) Coherent scattering Incoherent scattering ElasticInelastic Equilibriumm lattice structure Phonons ElasticInelastic Unwanted background Atomic diffusion Q: How do we distinguish magnetic scattering and nuclear scattering? Q: How do we measure Q?

12. How to measure wave vector? Reactor sourcePulsed 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

13. Powder diffraction Bragg’s Law: 2dSinθ = nλ

14.  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.

15. 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

16. Phys. Rev. Lett. 102, 217001(2009) CaFe 2 As 2

17. Spin waves Phys. Rev. B64, 224429 (2001)

18. Neutron sources  Research reactors  Spallation sources

19. Research reactors  A kind of nuclear reactors but simpler than power reactors  Mechanism: The “chain reaction” 

21. 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

23. ORNL neutron facilities  HFIR(High Flux Isotope Reactor)  SNS(Spallation Neutron Source)

24. HFIR  The highest flux reactor-based source of neutrons for condensed matter research in the United States  Fuel: Uranium-235  Reflector: Beryllium  Moderator: Water

25. HFIR beam tubes and experiment locations

26. SNS Negatively charged hydrogen Linear accelerator foil strip off electrons P Accumulating ring Proton pulses Heavy metal target (Mercury) High energy neutron pulses Moderator (Water) Cold and thermal neutrons

28. 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

29. 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_temperaturehttp://en.wikipedia.org/wiki/Neutron_temperature  [8] URL http://en.wikipedia.org/wiki/Neutron_diffractionhttp://en.wikipedia.org/wiki/Neutron_diffraction  [9] Tapan Chatterji, Neutron Scattering from Magnetic Materials URL http:// www.sciencedirect.com/science/book/9780444510501www.sciencedirect.com/science/book/9780444510501  [10]URL http://neutrons.ornl.govhttp://neutrons.ornl.gov  [11]URL http://www.khwarzimic.org/takveen/seaborg.pdfhttp://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=2215http://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)