x-rays – more bits and pieces
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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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
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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
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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.
)cos1(cm
h
e
Arthur Compton
1892-1962
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Implications?
Calculate the maximum wavelength shift predicted from the Compton scattering equation.
)cos1(cm
h
e
cm
h2
e
831
34
1031011.9
10626.62
= 4.85 x 10-12 m = 0.05Å
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Moseley’s Law
1913 2)Z(C
C ~ 0.75 Rc
~ 1 for K
~ 7.4 for L
Henry Moseley
1887-1915
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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
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Absorption
• X-ray photons absorbed when E is slightly greater than that required to cause a transition
- i.e. wavelength slightly shorter than K
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Absorption
So, as well as characteristic emission spectra, elements have characteristic absorption wavelengths
e.g. copper
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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
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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
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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 K1
= 1.540 Å = 2dhklsin
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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 CuK1 radiation (1.540 Å)
22
222
2 )66.5(
3
a
lkh
d
1
)27.32(
540.1sin
d2sin 11
d=3.27Å
=2d sin
= 13.62°
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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)
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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)
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Schematic
(1) electron gun (2) linear accelerator (3) booster synchrotron (4) storage ring (5) beamlines (6) experiment stations.
(From: Australian Synchrotron, Illustrator: Michael Payne)
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APS Argonne
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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
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Inside the synchrotron
Bending magnet
• Electrons injected into booster synchrotron (a ring of electromagnets); accelerated to 7 GeV
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Inside the synchrotron
• 7 GeV electrons injected into the 1 km storage ring• Circle of > 1,000 electromagnets etc.
Storage ring
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ESRF, Grenoble
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ESRF, Grenoble
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Daresbury SRS, UK
• Will close in December 2008
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Diamond, Oxfordshire - schematic
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Diamond, Oxon
February 2004
April 2004
Sept 2004
July 2006
Photos courtesy Diamond Light Source Ltd.
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Diamond + ISIS, OxonPhoto courtesy Diamond Light Source Ltd.
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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
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Comparison
Ru0.95Sn0.05Sr2GdCu2O8
A. C. Mclaughlin et al. J. Mat Chem (2000)
Synchrotron (ESRF)
= 0.325104 Å
Lab X-ray
= 1.54056 Å
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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
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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
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Absorption - equations
Beer’s law for X-rays
)xexp(I
Im
0
Also written as function of m (mass of element) and A (area
of beam)
m is the mass absorption coefficient
IIo
x
3
4
AE
Zm
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Absorption energies
• Energies of K edges Z2
• Elements with Z>18 have either a K or L edge between 3 and 35 keV
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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
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Interference effects
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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.
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XANES/EXAFS
• X-ray Absorption – near edge structure• Extended X-ray Absorption – Fine Structure
Thin wafer of Silicon
XANES
EXAFS
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More detail
Copper compound
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Processed + FT
Intensity vs R (radius from central atom)
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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 K1 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.