# X-rays – more bits and pieces

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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 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

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

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

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

Moseley’s Law 1913 C ~ 0.75 Rc  ~ 1 for K  ~ 7.4 for L Henry Moseley
C ~ 0.75 Rc  ~ 1 for K  ~ 7.4 for L

Periodic Table Moseley corrected anomalies:
27Co Ni Cu 63.54 18Ar K Ca 40.08 52Te I Xe 131.3 Also identified a gap at Z=43 (Tc) Coster & von Hevesy predicted  for new element - Hf

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

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

Absorption - example Element At. No. K K Kedge Ni 28 1.66 1.50 1.49
Cu Zn Ni does not absorb its own lines Ni absorbs CuK - useful Ni absorbs Zn K and K strongly

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

Monochromator  = 1.540 Å = 2dhklsin
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  = Å = 2dhklsin

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°

Synchrotron X-rays When charged particles are accelerated in an external magnetic field (according to Lorentz force), they will emit radiation (and lose energy) stationary charge produces an electric field while moving charge produces a magnetic field. It turns out that accelerated charge produces electromagnetic radiation. Theory proposed initially by Ivanenko and Pomeranchuk, First observed in (Physics Today article)

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)

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

APS Argonne

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

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

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

ESRF, Grenoble

ESRF, Grenoble

Daresbury SRS, UK Will close in December 2008

Diamond, Oxfordshire - schematic

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

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

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

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

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 ( mm3) A-amylose crystals, ESRF highlights, 2006

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

Absorption - equations
x 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

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

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

Interference effects

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.

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

More detail Copper compound

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

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.