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Neutron Sectroscopy

Neutron Sectroscopy. Neutron Scattering in Condensed Matter Physics https://doi.org/10.1142/4870 , 2009 Albert Furrer ( ETH Zurich & PSI Villigen , Switzerland ).

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Neutron Sectroscopy

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  1. Neutron Sectroscopy Neutron Scattering in Condensed Matter Physics https://doi.org/10.1142/4870, 2009 Albert Furrer (ETH Zurich & PSI Villigen, Switzerland)

  2. Neutron scattering is a powerful, non-destructive probe for the investigation of structure and dynamics in matter in a broad space and time domain • ranging from magnetic devices to semiconductors, composites to biomaterials and polymers it delivers direct information in both space and time (0.01 – 10 nm, 10-15 – 10-6 s, respectively),

  3. Neutrons have the dual properties of both particles and waves. • As particles they have a velocity and kinetic energy and as a wave they possess the wavelength, frequency and the wave vector: p=mV=hk=h/λ, Ekin= mV2/2=hf. • During the scattering event, the direction of the neutron wave vector and its velocity can be changed by interacting with the microscopic structure and microscopic motion of the studied objects, respectively. • Thus, analysis of these changes allows us to draw conclusions about the atomic motion and atomic structure. • Spin interactions

  4. Why Neutrons? • Neutrons have No Charge! • Highly penetrating • Nondestructive • Can be used in extremes • Neutrons have a Magnetic Moment! • Magnetic structure • Fluctuations • Magnetic materials • Neutrons have Spin! • Polarized beams • Atomic orientation • Coherent and incoherent scattering • The Energies of neutrons are similar to the energies of elementary excitations! • Molecular Vibrations and Lattice modes • Magnetic excitations • The Wavelengths of neutrons are similar to atomic spacing! • Sensitive to structure • Gathers information from 10-10 to 10-7 m • Crystal structures and atomic spacings • Neutrons probe Nuclei! • Light atom sensitive • Sensitive to isotopic substitution

  5. Neutron sources

  6. Crystal diffraction spectrometers and interferometers 1) Determination of neutron energy 2) Determination of crystal structure Usage of diffraction: Usage of crystal bend for measured energy change neutron diffractometer of NPI CAS Monochromators utilizing reflection Mechanical monochromators rotated absorption discs – properly placed holes very accurate measurement of energy of low energy neutrons

  7. COMPARATIVE PROPERTIES OF X-RAY AND NEUTRON SCATTERING Property X-Rays Neutrons Wavelength Characteristic line spectra such as Cu K= 1.54 Å Continuous wavelength band, or single  = 1.1  0.05 Å separated out from Maxwell spectrum by crystal monochromator or chopper Energy for  = 1 Å 1018 h 1013 h (same order as energy of elementary excitations) Nature of scattering by atoms Electronic Form factor dependence on [sin]/ Linear increase of scattering amplitude with atomic number, calculable from known electronic configurations Nuclear, Isotropic, no angular dependent factor Irregular variation with atomic number. Dependent on nuclear structure and only determined empirically by experiment Magnetic Scattering Very weak additional scattering ( 10-5) Additional scattering by atoms with magnetic moments (same magnitude as nuclear scattering) Amplitude of scattering falls off with increasing [sin ]/ Absorption coefficient Very large, true absorption much larger than scattering abs  102 - 103 increases with atomic number Absorption usually very small (exceptions Gd, Cd, B …) and less than scattering abs  10-1 Method of Detection Solid State Detector, Image Plate Proportional 3He counter

  8. Three axes spectrometers A three axes spectrometer (TAS) is defined by the three independent axes of the instrument: monochromator (1st axis), sample (2nd axis) and analyser (3rd axis).

  9. Time-of-flight spectrometers In a time-of-flight instrument the energy of the neutron is determined by the ‘time-of-flight’ the neutrons need to travel a well-defined distance. A monoenergetic neutron pulse collides with the sample. During the scattering process, the neutron may exchange energy with the sample.

  10. Backscattering spectrometers Backscattering spectrometers achieve an energy resolution below 1 μeV by using filtering incoming and scattered neutrons through Bragg reflection under 180°. This gives access to molecular processes on a nanosecond scale.

  11. Spin-echo spectrometers The neutron spin-echo spectrometer uses the precession of the neutron spin in a magnetic field as a very precise stop-watch to detect tiny energy exchanges with the sample. When the polarized neutron beam (i.e. all magnetic moments point in one direction) enters the magnetic field, the spins start to rotate around the field direction. After the scattering at the sample, the neutrons pass through the exact opposite magnetic field. If elastic scattering takes place, the original polarization is recovered. Small energy losses and gains result in a reduced polarization that yields rather indirect information about sample dynamics on a nanosecond scale.

  12. What does it mean to “detect” a neutron? • Need to produce some sort of measurable quantitative (countable) electrical signal • Can’t directly “detect” slow neutrons • Need to use nuclear reactions to “convert” neutrons into charged particles • Then we can use one of the many types of charged particle detectors • Gas proportional counters and ionization chambers • Scintillation detectors • Semiconductor detectors

  13. Medipix-2 Neutron detectors and spectrometers Detectors of slow neutrons (thermal, epithermal, resonance) Detectors of fast neutrons Detectors of relativistic and ultrarelativistic neutrons Detection of neutrons – by means of nuclear reactions where energy is transformed to charged particles or such particles are created Consequence: 1) Complicated reactions → strong dependency of efficiency on energy 2) Small efficiency → necessity of large volumes 3) Only part of energy is loosed → complicated energy determination → common usage of TOF Usage of neutronography Bonner spheres

  14. Used reactions: neutron + nucleus → reflected nucleus proton deuteron triton alpha particle fission products Very strong dependency of cross section on energy Compound detectors: 1) Convertor – creation of charged particles 2) Detector of charged particles Complicated structures of convertor and detector ITEP CTU Requierements on material of convertor and detector: 1) Large cross section of used reaction 2) High released energy (for detection of low energy neutrons) or high conversion of kinetic energy 3) Possibility of discrimination between photons and neutrons 4) Price of material production as cheap as possible A) Neutron counters – proportional counters, convertor is directly atworking gas or as admixture, eventually as part of walls B) Scintillators – organic (reflected proton and carbon), dopey by convertor liquid (NE213) or plastic (NE102A)

  15. n + 3He 3H + 1H + 0.764 MeV • n + 6Li 4He + 3H + 4.79 MeV • n + 10B 7Li* + 4He7Li + 4He + 0.48 MeV  +2.3 MeV (93%)7Li + 4He +2.8 MeV ( 7%) • n + 155Gd  Gd* -ray spectrum  conversion electron spectrum • n + 157Gd  Gd* -ray spectrum  conversion electron spectrum • n + 235U  fission fragments + ~160 MeV • n + 239Pu  fission fragments + ~160 MeV

  16. Gas Detectors Proportional Mode ~25,000 ions and electrons produced per neutron (~410-15 coulomb) Ionization Mode Proportional Mode

  17. Material Density of 6Li atoms (cm-3) Scintillation efficiency Photon wavelength (nm) Photons per neutron Scintillation Detectors Some Common Scintillators for Neutron Detectors 0.45 % 395 nm ~7,000 Li glass (Ce) 1.751022 2.8 % 470 ~51,000 LiI (Eu) 1.831022 9.2 % ~160,000 ZnS (Ag) - LiF 1.181022 450

  18. Semiconductor Detectors Detectors based on 6Li reactions All fibers

  19. Properties of neutron • Mass of the neutron • Mn = 1.675 x 10-27 Kg • Mp (mass of a Proton) = 1.673 x 10-27 Kg • Me (mass of an Electron) = 9.109 × 10-31 Kg • Electric Charge • Charge of a Neutron = 0 • Charge of Proton = 1.602 x 10-19C • Charge of Electron = -1.602 x 10-19 C • Spin angular momentum (Spin) • Spin of a Neutron = ½ • Spin of a Proton = ½ • Spin of an Electron = ½ • Magnetic dipole moment: • n = 9.6623640×10−27J.T-1 (-1.913 N) • p = 14.106067 × 10−27 J⋅T−1 • e = −9284.764 × 10−27 J⋅T−1 (Joule/Tesla) • What is the origin of magnetic dipole moment of neutron? • The non-zero magnetic moment of the neutron indicates that it is not an elementary particle.

  20. General Properties of the Neutron • The kinetic energy of a 1.8 Å neutron is equivalent to T = 293K (warm coffee!), so it is called a thermal neutron. • The relationships between wavelength (Å) and the energy (meV), and the speed (m/s, mi/hr) of the neutron are: e.g. the 1.8 Å neutron has E = 25.3 meV and v = 2200 m/s = 4900 mi/hr • The wavelength if of the same order as the atomic separation so interference occurs between waves scattered by neighboring atoms (diffraction). • Also, the energy is of same order as that of lattice vibrations (phonons) or magnetic excitations (magnons) and thus creation of annihilation of a lattice wave produces a measurable shift in neutron energy (inelastic scattering).

  21. https://webapps.frm2.tum.de/intranet/neutroncalc/ Brockhouse is the first person to develop slow neutron spectroscopy to study the excitations of atoms in condensed matter. The energy of thermal neutron is comparable to the quantum energy or phonon in a normal mode of vibration of a crystal

  22. Scattering Factors f • For x-rays the magntude of f is proportional to Z • For neutrons nuclear factors determine f, thus no regular with Z (different isotopes can have different f s) Shaded (negative) -->  phase change Life time of neutron: A free neutron is unstable and undergoes radioactive decay. It decay spontaneously into a proton, an electron and a electron anti-neutrino. The life time of a neutron is 886±1 sec Interaction mechanism: Neutrons interact with atomic nuclei via very short range (~fm) and it is characterized by a scattering length b. Total scattering cross-section is  =4b2

  23. Neutrons are more sensitive to light elements • Isotopic sensitivity • Contract variation to difference complex molecular structure

  24. Interaction of neutron with matter • Neutrons are neutral particle hence can pass large distance through matter. • Energy change and momentum transfer occur from • Nucleus • Crystal excitations (eg. Phonons) • Unpaired electrons via dipole scattering • Magnetic structure and excitations • Diffusion (atomic or molecular) Nuclear scattering Magnetic dipole scattering

  25. Total cross-section Let us consider scattering by a single nucleus. An incident plane wave of neutrons travelling In the x-direction Where is the wavenumber. The probability of finding a neutron in a volume dV is ( =1). The flux of neutrons incident normally on unit area per second is The scattered wave by an isolated atom is in the form b is known as scattering length of the nucleus. The minus sign indicate that the value of b is positive

  26. Total cross-section The scattered flux If is velocity = (b2/r2)v, and the number of neutrons scattered per second is flux  area: Divide I0/If Which is the effective area of the nucleus viewed by the neutron. This unit used for cross section is barns. 1 barn = 10-28 m2 . The unit used for scattering length is fermis, 1 fermi = 10-15 m.

  27. Differential cross-section The differential scattering cross section (SI unit: m2 sr-1) is the number of neutrons scattered per unit time into a solid angle d divided by the flux of the incident neutrons This cross section measured by using a neutron diffractometer. The scattered intensity as a function of the wave-vector transfer kf – ki In the figure the solid angle d subtended by the detector at the sample is ds/r2. Where ds is the area. The number of neutron scattered per second into this solid angle is flux  area or and this is equal to , for a spherical wave = b2/r2 and so , unit is barns/steradian

  28. Double differential cross-section The double differential cross section relates to those experiments where a change of neutron energy on scattering is measured. It is defined as Has the dimension of area per unit energy. The incident flux I0 is . Then the cross section of N atoms called “scattering law” or “dynamic structure factor”,

  29. Inelastic neutron scattering In a inelastic neutron scattering process the energy Ef = of the scattered neutron is not equal to the energy Ei = of the incident neutron energy. The energy transferred to the neutron from the sample is In the inelastic neutron scattering , the magnitude of the momentum transfer is no longer determined by solely by the scattering angle but depends also on the energy exchange If ki = kf and (1-cos 2 = 2sin2

  30. Source: Peter M. Gehring (NIST, USA)

  31. Coherent and incoherent scattering Coherent Incoherent

  32. Applications of Neutron Spectroscopy

  33. Elastic magnetic scattering or magnetic diffraction leads to the determination of the magnetic structure of crystal (the arrangement of the magnetic moments of atoms on the crystalline lattice). • Inelastic magnetic scattering yields information on the magnetic excitation in the sample. For example, spin wave, in which there are oscillations in the orientation of successive spins on the crystal lattice. The spin waves are quantized energy units called magnons

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