Powder diffraction is most commonly applied for phase analysis and structure determination of polycrystalline samples. Powder samples are exposed to a beam of monochromatic x-rays to generate an x-ray diffraction pattern. This pattern is a unique fingerprint of the material and gives structural information about the material. These patterns can be compared to known patterns in databases such as the ICDD PDF 4+ to identify the exact material. Applications range from determining the composition of ore from a mine to quality control of pharmaceuticals.
X-ray diffraction can be used to measure the residual stress in a material by determining the distance between crystallographic planes (d-spacings). When the material is in tension, the d-spacing increases, and when under compression, the d-spacing decreases.
The d-spacings are calculated using Bragg's Law: nλ = 2dsinθ.
If a monochromatic (λ) x-ray beam impinges upon a crystalline sample, then constructive interference will occur at an angle θ. By measuring the angle θ with an x-ray detector, we can calculate the d-spacing, which can then be converted into a strain value. Finally, stress is determined using Hooke's law (stress = strain x elastic modulus). The non-destructive and very accurate nature of the x-ray diffraction technique has made residual stress characterization a useful tool for process optimization, design improvements, and failure analysis in metals and ceramics.
Laue diffraction is most commonly used to quantify the orientation of single-crystal materials. It can also be used to assess a crystal’s perfection and disorder. The Laue technique works by exposing a crystal to a collimated beam of polychromatic x-rays and collecting the diffracted image onto a 2D x-ray detector. The image is made up of a number of spots in a pattern that correspond to the orientation and structure of the crystal. One advantage of the Laue method is that it is fast and non-destructive. A common industrial application is checking the orientation of single-crystal turbine blades for use in gas turbine engines.