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X-ray Crystallography
GLY 4200
Fall, 2014
Discovery of X-rays
• Wilhelm Conrad Roentgen discovered x-radiation in 1895
• In 1912, Friedrich, Knipping, and von Laue demonstrated diffraction of x-radiation passing through a crystal
• The wavelength of x-radiation ranges from 10-6 to 10-1 nm
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Einstein Equation
• E = hυ = hc/λ
• where E = energy h = Planck's constant υ = frequency c = speed of light λ = wavelength.
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Conversion to Kinetic Energy
• If all the kinetic energy of an electron is converted to X-ray quanta, we can rewrite the equation as: eV = hc/λ
• Replacing constants gives: λ(nm) = 1.24/kV Where kV = kilovolts
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White Radiation
• Effect of excitation potential on minimum wavelength
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X-ray Tube
• X-ray tube schematic diagram
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Electron Shells
• Electron infall from outer to inner shells
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Copper X-ray
Spectrum
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Copper Energy Levels
• Energy-level diagram for electron transitions in Cu
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Copper X-ray
Spectrum
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Absorption Edge
• Absorption edge of Ni in relation to the emission spectrum of Cu
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Scattering
• Scattering of X-rays by a row of equally spaced, identical atoms
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Reflection
• Condition for reflection
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Path Difference
• Path difference = 2d sin θ
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Bragg Equation
• nλ = 2d sin θ
• where n is an integer d is the distance between successive parallel planes
(the "interplanar" spacing) θ = glancing angle of incidence
• This is the condition for successful reinforcement of waves reflected off different layers
W.H. and W.L. Bragg
• Derived by English physicists Sir William Henry Bragg and his son Sir William Lawrence Bragg
• Shared Nobel Prize in Physics, 1915
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Diffracted X-ray Cones
• Diffraction cones from a row of atoms
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Cone Intersection
• Diffraction cones from three noncoplanar rows of scattering atoms, intersecting in a common line
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Figure 12
• Arrangement for a powder photograph
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Powder Pattern
• Diagram showing the formation of lines from a powder
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Laue Method
• a) Obtaining a Laue photograph with a stationary crystal• b) Laue photograph of vesuvianite, taken along the A4 axis. Axial directions a1 and
a2 were inked onto the photograph after development.
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Laue Film
• Laue photograph, mineral unknown
• Named for its developer German physicist Max von Laue, who won the Nobel Prize in Physics in 1914 for the discovery of diffraction of X-rays by crystals
Weissenberg Rotation Method
• Austrian physicist Karl Weissenberg developed a rotating-crystal method which also translated the film, allowing unambigious index of each refraction
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Precession Camera
• Buerger precession camera
Martin Julian Buerger• American Crystallographer who
developed the precession camera
• Crystal and the film move
• Film shows an undistorted replica of the corresponding reciprocal lattice plane
• Each diffraction may be indexed
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Precession Film of Wavellite
• A precession photograph is quickly indexed since it shows very clearly the symmetry content of the reciprocal lattice
• Indeed the distance between the spots on the film is simply the reciprocal lattice distance between two nodes, scaled by the X-ray wavelength and the camera radius
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Four Circle Diffractometer
• A crystal is randomly set on the goniometric mount
• Computer will measure and calculate the exact value that each of four angles has in order to observe the reflections of a specific set of planes (hkl)
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Mounting Methods for Powders
• Placed in fine capillary tube of 0.2mm bore• Coated on a fine glass fiber - the fiber is
dipped in a liquid such as alcohol and then rolled in the powder
• Mixed with gum arabic and rolled between slips of glass into a fine spindle or a tiny ball, no more then 0.3 mm in diameter
• Sprinkled on a piece of tape mounted over a hole drilled in a circular piece of metal
Powder Diffractometer (XRD)
• Powders can also be analyzed utilizing an automatic powder diffractometer, which uses a detector crystal instead of film
• The machine is programed to rotate through a range of θ values, collecting the θ and intensity value on each line
• The θ is converted to interplanar spacing values using the Bragg equation
• The intensity data is recalulated, with the value of the most intense line being set to 100, and the other values adjusted accordingly
• The d and I (intensity) data are then stored electronically and analyzed by comparison with the PDF file.
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Advantages of Powder Method
• 1. It is fast, with an analysis being completed in two hours or less
• 2. It requires very small sample amounts, which is especially important in cases where the material is rare
• 3. Sample preparation times are usually small• 4. The cost of each analysis is low, although there
is an initial investment in the X-ray equipment and associated computer
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Use of XRD
• The most widespread use of powder diffraction is in the identification and characterization of crystalline solids, each of which produces a distinctive diffraction pattern
• Both the positions (corresponding to lattice spacings) and the relative intensity of the lines in a diffraction pattern are indicative of a particular phase and material, providing a "fingerprint" for comparison
• A multi-phase mixture, e.g. a soil sample, will show more than one pattern superposed, allowing for determination of the relative concentrations of phases in the mixture.
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Analysis by Database Comparison
• J.D. Hanawalt, an analytical chemist who worked for Dow Chemical in the 1930s, was the first to realize the analytical potential of creating a database, initially called the Hanawalt Index
• Identification is performed by comparison of the diffraction pattern to a known standard or to a database such as the International Centre for Diffraction Data's Powder Diffraction File (PDF) or the Cambridge Structural Database (CSD)
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Reitveld Refinement Method• Allows structural information to be extracted from powder data,
rather than the much more labor intensive single-crystal methods• This becomes especially important for minerals whose habit is
typically a fine powder, rather than discrete single crystals• These type of minerals include the clays, some zeolites, manganese
and iron oxides and hydroxides• The Rietveld method does require some prior knowledge of the actual
crystal structure, which is used as a starting model in the refinement• For example, if the mineral is known to be a clay, the structures of a
common clay mineral, such as kaolinite or montmorillionite, can be tried
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ET Remote Sensing Using XRD
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X-ray Fluorescence
• X-ray fluorescence (XRF) is the emission of characteristic "secondary" (or fluorescent) X-rays from a material that has been excited by bombarding with high-energy X-rays or gamma rays
• The phenomenon is widely used for elemental analysis and chemical analysis
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Physics of X-ray Fluorescence, 1
• When materials are exposed to X-rays, ionization of their component atoms may take place
• X-rays can be energetic enough to expel tightly held electrons from the inner orbitals of the atom
• Electron removal makes the electronic structure of the atom unstable, and electrons in higher orbitals "fall" into the lower orbital to fill the hole left behind
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Physics of X-ray Fluorescence, 2
• In falling, energy is released in the form of a photon, the energy of which is equal to the energy difference of the two orbitals involved
• The material emits radiation, which has energy characteristic of the atoms present
• The term fluorescence is applied to phenomena in which the absorption of radiation of a specific energy results in the re-emission of radiation of a different energy (generally lower)
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Application of X-ray Fluorescence
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Exam Date and Time Lecture Final Examination
Friday, December 5, 2014 from 7:45 a.m. to 10:15 a.m.
Do not be late, or you will join the Hall of Shame, and ……
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This May Be Your Future
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