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X-rays – more bits and pieces
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  1. X-rays – more bits and pieces Learning Outcomes By the end of this section you should: • be aware of Compton scattering • understand how Moseley’s law relates wavelength to atomic number • understand the uses and implementation of the filter and monochromator within an X-ray instrument • be aware of the uses of synchrotron (X-ray) radiation and some of its uses

  2. Classical vs quantum • In the classical treatment, X-rays interact with electrons in an atom, causing them to oscillate with the X-ray beam. • The electron then acts as a source of an electric field with the same frequency •  Electrons scatter X-rays with no frequency shift

  3. Compton Scattering • Some radiation is also scattered, resulting in a loss of energy [and hence, E=h, shorter frequency and, c= , longer wavelength]. • The change in frequency/wavelength depends on the angle of scattering. This effect is known as Compton scattering • It is a quantum effect - remember classically there should be no frequency shift. Arthur Compton 1892-1962

  4. Implications? Calculate the maximum wavelength shift predicted from the Compton scattering equation. = 4.85 x 10-12m = 0.05Å

  5. Moseley’s Law 1913 Henry Moseley 1887-1915 C ~ 0.75 Rc  ~ 1 for K  ~ 7.4 for L

  6. Periodic Table Moseley corrected anomalies: 27Co 58.93 28Ni 58.71 29Cu 63.54 18Ar 39.95 19K 39.10 20Ca 40.08 52Te 127.6 53I 126.9 54Xe 131.3 Also identified a gap at Z=43 (Tc) Coster & von Hevesy predicted  for new element - Hf

  7. Absorption • X-ray photons absorbed when E is slightly greater than that required to cause a transition - i.e. wavelength slightly shorter than K

  8. Absorption So, as well as characteristic emission spectra, elements have characteristic absorption wavelengths e.g. copper

  9. Absorption - example Element At. No. K K Kedge Ni 28 1.66 1.50 1.49 Cu 29 1.54 1.39 1.38 Zn 30 1.44 1.30 1.29 • Ni does not absorb its own lines • Ni absorbs CuK - useful • Ni absorbs Zn K and Kstrongly

  10. Uses of absorption We want to choose an element which absorbs K [and high energy/low  white radiation] but transmits K e.g. Ni K absorption edge = 1.45 Å As a general rule use an element whose Z is one or two less than that of the emitting atom

  11. Monochromator Choose a crystal (quartz, germanium etc.) with a strong reflection from one set of lattice planes, then orient the crystal at the Bragg angle for K1  = 1.540 Å = 2dhklsin

  12. Example A monochromator is made using the (111) planes of germanium, which is cubic, a = 5.66 Å. Calculate the angle at which it must be oriented to give CuK1 radiation (1.540 Å) d=3.27Å =2d sin = 13.62°

  13. Synchrotron X-rays When charged particles are accelerated in an external magnetic field (according to Lorentz force), they will emit radiation (and lose energy) Theory proposed initially by Ivanenko and Pomeranchuk, 1944. First observed in 1947. (Physics Today article)

  14. Synchrotron X-rays Acceleration in a circle… • Electrons are kept in a narrow path by magnets • Emit e.m. radiation ahead • Large spectral range • Very focussed and intense X-rays produced (GeV) (also applications in particle, medical physics amongst other things)

  15. Schematic • electron gun (2) linear accelerator (3) booster synchrotron (4) storage ring (5) beamlines (6) experiment stations. (From: Australian Synchrotron, Illustrator: Michael Payne)

  16. APS Argonne

  17. Inside the synchrotron • Electrons emitted from cathode ~1100° C. • Accelerated by high-voltage alternating electric fields in linac. Accelerates the electrons to 450 MeV - relativistic LINAC: linear accelerator

  18. Inside the synchrotron Bending magnet • Electrons injected into booster synchrotron (a ring of electromagnets); accelerated to 7 GeV

  19. Inside the synchrotron • 7 GeV electrons injected into the 1 km storage ring • Circle of > 1,000 electromagnets etc. Storage ring

  20. ESRF, Grenoble

  21. ESRF, Grenoble

  22. Daresbury SRS, UK • Will close in December 2008

  23. Diamond, Oxfordshire - schematic

  24. Photos courtesy Diamond Light Source Ltd. February 2004 Sept 2004 Diamond, Oxon April 2004 July 2006

  25. Photo courtesy Diamond Light Source Ltd. Diamond + ISIS, Oxon

  26. Synchrotron vs lab data • Much higher count rates  signal to noise better • Wavelengths are variable. • Incident beam is usually monochromatic and parallel. • Very sharp peaks (smaller instrumental contribution) – FWHM can be 10 times narrower – better resolution

  27. Comparison Ru0.95Sn0.05Sr2GdCu2O8 A. C. Mclaughlinet al. J. Mat Chem (2000) Lab X-ray  = 1.54056 Å Synchrotron (ESRF)  = 0.325104 Å

  28. Synchrotron Diffraction - Uses • High resolution X-ray powder diffraction • “Resonant” X-ray powder diffraction (can select wavelength) • Analysis of strain (see later) • Sample environment (as with neutrons) • Surface XRD • Diffraction on very small single crystals (0.0001 mm3) A-amylose crystals, ESRF highlights, 2006

  29. Photoelectron ejected with energy equal to that of the incoming photon minus the binding energy. Characteristic of element. The ejected photoelectron then interacts with the surrounding atoms Back to absorption • X-ray absorption - generally in the range 2 – 100 keV

  30. x Io I Absorption - equations Beer’s law for X-rays  Also written as function of m (mass of element) and A (area of beam) m is the mass absorption coefficient

  31. Absorption energies • Energies of K edges  Z2 • Elements with Z>18 have either a K or L edge between 3 and 35 keV

  32. Interference effects The ejected photoelectron then interacts with the surrounding atoms This gives information on the local environment round a particular element within the crystal structure

  33. Interference effects

  34. XAS X-ray Absorption spectroscopy complements diffraction • Diffraction gives you information on average 3d structure of crystalline solids • XAS gives you localised environment in solids (including glasses), liquids, gases. Info on bonds, coordination, valence.

  35. XANES EXAFS Thin wafer of Silicon XANES/EXAFS • X-ray Absorption – near edge structure • Extended X-ray Absorption – Fine Structure

  36. More detail Copper compound

  37. Processed + FT Intensity vs R (radius from central atom)

  38. Summary • The interaction of X-rays with matter produces a small wavelength shift (Compton scattering) • The wavelength of X-rays varies as a function of atomic number - Moseley’s law • Filters can be used to eliminate K radiation; monochromators are used to select K1 radiation. • Synchrotrons can produce high intensity beams of X-rays suitable for structural studies • Absorption can be exploited to give localised information on elements within a crystal structure.