XRD

The smooth curves in Figure 1 corresponding to voltages of 20kV or less represent polychromatic, continuous, or white radiation, since it is made up of rays of many wavelengths (similar to white light). White radiation is also called Bremsstrahlung, German for "braking radiation" because it is caused by electron deceleration.

Bragg's Law

Figure 2 below illustrates interference (constructive) between waves scattering from two adjacent rows of atoms in a crystal. The net effect of scattering from a single row is equivalent to partial reflection from a mirror imagined to be aligned with the row. Thus, the angle of "reflection" equals the angle of incidence for each row. Interference then occurs between the beams reflecting off different rows of atoms in the crystal.

When X-rays are scattered from a crystal lattice, peaks of scattered intensity are observed which correspond to the following conditions:

1. The angle of incidence = angle of scattering.
2. The path length difference is equal to an integer number of wavelengths.

By finding the wavelengths () that allow the X-rays diffracting from the lower crystal plane to cover the distance from CB to BD and still be in constructive interference with the upper X-rays, Bragg's Law can be upheld. In equation form this is:

The condition for maximum intensity contained in Bragg's law above allow us to calculate details about the crystal structure, or if the crystal structure is known, to determine the wavelength of the X-rays incident upon the crystal.

During X-ray diffraction, we measure the angle (θ) by the angle between the arms of the diffractometer as they move. The "n" appears because of the periodicity of the wave and can be any positive integer. We are trying to find the spacing between the lattice planes, d, so the only variable left that we need to control in order to use the Bragg equation is the wavelength (λ) of the X-rays. That variable is controlled by the target that we use to create the beam. The following table lists some of the common X-ray wavelengths produced using different targets.
In our laboratory we commonly use Copper or Molybdenum targets, but other available targets include: Chromium, Iron, Cobalt, and Tungsten.

The different wavelengths produced by each target given in the table are present because each represents a different interest to a person analyzing X-ray diffraction data. (Eg. Someone who is focusing on the copper K_α1 peak will need to know where that peak should be. It will also be necessary to be able to eliminate the irrelevant peaks. In this case, the K_α2 and the K_β peaks.)

Our equipment

With our Brucker-AXS D8 Advance 2 axes diffractometer (fig. 3) we can provide θ,2θ-scans (fig. 4), rocking curves, etc. From the measured scans peak positions and intensities can be obtained as well as widths and FWHMs, phases can be identified, indexed and compared with the ICDD PDF data base, etc. With help of Rietveld analysis crystal structures can be identified. These way phase analysis, crystallography analysis, thin film characterization, powder characterisation, texture and residual stress investigations, etc. can be performed.

Figure 4: Example of 2θ-scans with peak index and different phases