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
5
X-ray Tube
• X-ray tube schematic diagram
6
Electron
Shells
• Electron infall
from outer to
inner shells
7
Copper
X-ray
Spectrum
8
Copper
Energy
Levels
• Energy-level
diagram for
electron
transitions in
Cu
9
Copper
X-ray
Spectrum
10
Absorption
Edge
• Absorption
edge of Ni in
relation to the
emission
spectrum of Cu
11
Scattering
• Scattering of Xrays by a row of
equally spaced,
identical atoms
12
Reflection
• Condition for reflection
13
Path Difference
• Path difference = 2d sin θ
14
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
15
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
16
Diffracted
X-ray Cones
• Diffraction
cones from
a row of
atoms
17
Cone
Intersection
• Diffraction cones
from three
noncoplanar rows
of scattering
atoms,
intersecting in a
common line
18
Figure 12
• Arrangement for a powder photograph
19
Powder Pattern
• Diagram showing
the formation of
lines from a
powder
20
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
21
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
22
Weissenberg Rotation Method
• Austrian physicist Karl
Weissenberg developed a
rotating-crystal method
which also translated the
film, allowing unambigious
index of each refraction
23
Precession Camera
• Buerger precession camera
24
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
26
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
27
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
28
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.
29
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
30
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.
31
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
34
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)
37
Application of X-ray Fluorescence
38
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 ……
39
This May Be Your Future
40