X-ray Crystallography

X-ray Crystallography
GLY 4200
Fall, 2014
1
Discovery of X-rays
• Wilhelm Conrad Roentgen discovered xradiation 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
2
Einstein Equation
• E = hυ = hc/λ
• where





E = energy
h = Planck's constant
υ = frequency
c = speed of light
λ = wavelength.
3
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
4
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 Xrays 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
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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
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after development.
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
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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
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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
25
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 Xray 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
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planes (hkl)
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
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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)
32
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
33
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
35
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
36
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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