Neutron scattering. Niina Jalarvo. SMN/FERMiO, Department of Chemistry, University of Oslo Gaustadalleen 21 NO-0349 Oslo, Norway UNIVERSITY OF OSLO

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1 Neutron scattering Niina Jalarvo SMN/FERMiO, Department of Chemistry, University of Oslo Gaustadalleen 21 NO-0349 Oslo, Norway UNIVERSITY OF OSLO

2 NEUTRON what is it? Neutrons are particles found in the atomic nuclei Mass No elecric charge! Spin m = 1675, 10 h s = 2 Lifetime about 20 min 24 g As all quantum particles, also neutrons, can exhibit wave phenomena. Due to the de Broglie relation 2 λ = v π = k h r p

3 Why Neutrons? Neutrons interact directly with the nuclei of the atoms strong but very short ranged nuclear interaction no electrostatic interaction (overall interaction is weak) => neutrons easily penetrate sample materials Most of other techniques for diffraction or inelastic scattering are based on interaction with the electron cloud surrounding each atom. difficulties to observe light elements in diffraction selection rules of observable modes for scattering

4 Why Neutrons? Neutron scattering is a very powerful tool to probe microscopic dynamical and geometrical properties of condensed matter. Especially dynamical processes of species containing hydrogen and structural properties of materials containing light elements, e.g. hydrogen (deuterium) or oxygen Nobel Prize in Physics was given to Brockhouse, for the development of neutron spectroscopy and to Shull, for the development of the neutron diffraction technique

5 Producing neutrons A neutron scattering measurement requires a neutron source (e.g. a nuclear reactor or spallation source). Research reactors in Europe: IFE, Kjeller, Norway ILL, Grenoble, France BENSC, Berlin, Germany FRM II, Munich, Germany LLB, Saclay, France Spallation Sources in Europe: ISIS, Oxfordshire, U.K. PSI, Zurich, Switzerland ESS,???,

6 Obtaining the desired wavelengths

7 Wavelength ~ Å s comparable to interatomic and intermolecular distances Energy ~ mev s comparable to the time scale of many motions in materials => vibrations, librations, reorientations, diffusion, and relaxational processes can be observed Problems: too low flux of neutrons long measuring times needed large amount of sample needed (normally hundreds or thousands of mg)

8 Interactions The neutron-nucleus interaction is described by a scattering cross section The scattering cross section varies randomly from isotope to isotope Cross section (σ) - Area related to the probability that a neutron will interact with a nucleus in a particular way (e.g. scattering or absorption) For systems containing a reasonable proportion of H atoms, scattering from H tends to dominate For a single nucleus σ cm 2 (unit barn) Relative total scattering cross sections for few isotopes

9 Structure and Dynamics Not all nuclei in a sample consisting of only one element or even only isotope necessarily scatter identically => RANDOMNESS If the scattered neutron waves from the different nuclei have RANDOM relative phases, they don t interfere => INCOHERENT SCATTERING If the scattered neutron waves from the different nuclei have definite relative phases, they can interfere => COHERENT SCATTERING DYNAMICS STRUCTURE

10 Structure and Dynamics Different atoms and isotopes have different coherent and incoherent scattering cross sections Element σ coh (barns) σ inc (barns) Hydrogen (H) Deuterium (D) Carbon (C) Oxygen (O) Deuterated sample for coherent Bragg diffraction to obtain structure Protonated to observe both single particle motion (quasielastic) and to weight the inelastic scattering spectrum in favor of hydrogen (vibrations) Deuteration can help to assign dynamics of particular groups

11 Scattering Kinematics The collision of two objects can be described in terms of momentum conservation and, in some cases, energy conservation. Neutron scattering events are described by means of energy and momentum transfer. r hq = hω = r r hk 1 hk 0 E1 E 0 hω = hω hω ELASTIC scattering INELASTIC scattering QUASIELASTIC scattering

12 If you want to study the structure of your hydrated oxide by neutrons a) Would you use elastic or inelastic neutron scattering? b) Would you prefer to deuterate your sample or not? Why? c) Which wavelength would you choose? Why?

13 Dynamics and Neutron Scattering The dynamics of a system reflect the interatomic and intermolecular interactions which are responsible for the properties of materials Neutron Scattering is an excellent way to study dynamics Measure the number of scattered neutrons as a function of Q and ω => S(Q,ω) (the scattering function) depends ONLY on the sample

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15 FANS DCS Backscattering Spin Echo Itinerant Magnets Spin Waves Heavy Fermions Critical Scattering Hydrogen Modes Molecular Vibrations Lattice Vibrations Molecular Rotations Diffusion Tunneling Polymers and Spectroscopy Biological Systems Relaxations in Glasses

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20 References and literature G. H. Lander: The Neutron - an introduction (lecture on Web) D. Neumann: Dynamics and Neutron Scattering (lecture on Web) G. L. Squires: Introduction to the Theory of Thermal Neutron Scattering, S. W. Lovesey: Theory of Neutron Scattering from Condensed Matter