HW 10 X-Ray Powder Diffraction (unknown)
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Name _______________________________
Identification of an unknown Mineral from a X-ray powder diffractometer spacing
See theory of xray generation below.
X-ray Generation and Powder Diffraction
5.1 X-ray Generation
Fig. 5.1 X-ray tube
Illustrated above is a cross section through an X-ray tube showing the filament, target, and X-ray windows.
There is a large DC potential between the filament (cathode) and the target (anode) of approximately 40,000
volts. The electrons stream off the filament and hit the target with energies equal to their charge (1e) times the
potential (40KV) or 4.0 x 104 eV (electron volts). (One electron volt equals 1.602 x 10-19 joules.)
Energy level diagram for Cu
These energetic electrons strike the target, which is a pure metal such as copper or molybdenum, and re move
inner (K) shell electrons. When this happens, other electrons from higher level shells drop into the vacant K1
shell and in so doing emit a photon (X-ray) whose wavelength (energy) is characteristic of the metal target
material. In order to remove the inner shell electron, the incoming electron must have an en ergy greater than
the difference in energy between the inner (K) shell electron and a free electron in the con duction band of the
target metal. This energy differ ence is referred to as the absorption edge energy.
The various energy levels of electrons in the target metal atoms are illustrated in Figure 5.2. The energies of the
photons can be computed form the wavelengths by e = h nu = hc/lambda where h is Planck's constant (6.6 x 1034
joule-sec) c is the speed of light (3 x 108 m/sec), and Lambda is the wavelength (typically in Ångstroms, 1Å =
10-10 m).
Fig 5.3. A typical spectrum of emitted X-rays from an X-ray tube is illustrated in Figure 5.3 in which intensity
is plotted versus wavelength.
X-ray Diffraction
In X-ray diffraction, we utilize the elastic scattering of X-rays by the electrons of the atoms in a crystal. Elastic
scattering is scattering in which the wavelength of the X-ray does not change, only the direction changes.
Because a crystal is a periodic array of atoms with a repeat distance on the order of a few Ångstroms, it acts like
a diffraction grating for photons of approximately the same wavelength as the repeat distance.
As mentioned at the beginning of the section on crystal chemistry, crystals are capable of scattering X-rays in
coherent patterns because X-rays have a wavelength which is within one order of magnitude of the lattice
spacing. This also is true of other types of radiation (e.g. electrons and neutrons).
BC = d sin q
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Figure 5.4. X-ray diffraction geometry. The path-length difference between rays scattered from adjacent lattice
planes must be an integral number of wave-lengths.
Bragg diffraction occurs when a grating (crystal) scatters radiation "in phase". This happens when the exit beam
is retarded by an integral number of wavelengths. This is satisfied when
nlambda = 2d sin q
This is known as the Bragg Equation and is used to compute the scattering angle, theta, for a given lattice
spacing, d, and X-ray wavelength lambda.
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This comes from Klein’s Minerals and Rocks Ch 22. Look at preceding 2 chapters for theory. In a
powder mount finely ground mineral dust is sprinkled randomly on a Vaseline smeared slide.
The crystals fall randomly. The diffractometer motor scans through ~180° less a bit so the X ray
beam doesn’t burn out the detector. Pick the most intense peaks = the most common d spacings in
the miieral lattice. Measure their 2 theta position and intensity relative to you highest peak. Solve
the bragg equation for d spacings one at a time using Cu K alpha radiation Lambda = 1.5405
sometimes (at approptiate 2 theta) the alpha 1 and alpha 2 wavelengths disperse and can be both
used for more precision in measurements. Measure 2 theta, divide by 2, take sin, multiply by 2,
divide this into lambda = d. Repeat for next peak 2 theta. Tabulate your d values, arrange them
most intense first, second most etc. Compare to d spacings tabulated for known minerals. Identify
your unknown mineral.
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