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X-rays – more bits and pieces Learning Outcomes By the end of this section you should: be aware of Compton scattering understand how Moseleys law relates.

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Presentation on theme: "X-rays – more bits and pieces Learning Outcomes By the end of this section you should: be aware of Compton scattering understand how Moseleys law relates."— Presentation transcript:

1 X-rays – more bits and pieces Learning Outcomes By the end of this section you should: be aware of Compton scattering understand how Moseleys 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 -12 m= 0.05Å

5 Moseleys Law 1913 C ~ 0.75 Rc ~ 1 for K ~ 7.4 for L Henry Moseley 1887-1915


7 Periodic Table Moseley corrected anomalies: 27 Co58.93 28 Ni58.71 29 Cu63.54 18 Ar39.95 19 K39.10 20 Ca40.08 52 Te127.6 53 I126.9 54 Xe131.3 Also identified a gap at Z=43 (Tc) Coster & von Hevesy predicted for new element - Hf

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

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

10 Absorption - example ElementAt. No.K K K edge Ni281.661.501.49 Cu291.541.391.38 Zn301.441.301.29 Ni does not absorb its own lines Ni absorbs CuK - useful Ni absorbs Zn K and K strongly

11 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

12 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 = 2d hkl sin

13 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°

14 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)Physics Today

15 Synchrotron X-rays Acceleration in a circle…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)

16 Schematic (1) electron gun(2) linear accelerator (3) booster synchrotron (4) storage ring (5) beamlines (6) experiment stations. (From: Australian Synchrotron, Illustrator: Michael Payne)

17 APS Argonne

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

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

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

21 ESRF, Grenoble


23 Daresbury SRS, UK Will close in December 2008

24 Diamond, Oxfordshire - schematic

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

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

27 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

28 Comparison Ru 0.95 Sn 0.05 Sr 2 GdCu 2 O 8 A. C. Mclaughlin et al. J. Mat Chem (2000) Synchrotron (ESRF) = 0.325104 Å Lab X-ray = 1.54056 Å

29 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 mm 3 ) A-amylose crystals, ESRF highlights, 2006highlights

30 Back to absorption X-ray absorption - generally in the range 2 – 100 keV 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

31 Absorption - equations Beers law for X-rays Also written as function of m (mass of element) and A (area of beam) m is the mass absorption coefficient IIoIo x

32 Absorption energies Energies of K edges Z 2 Elements with Z>18 have either a K or L edge between 3 and 35 keV

33 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

34 Interference effects

35 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.

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

37 More detail Copper compound

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

39 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 - Moseleys 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.

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