X-ray diffraction

What is X-ray diffraction used for?

X-ray diffraction (XRD) is used to determine the properties of the crystallographic structure (i.e. crystal structure) of crystalline materials. Crystal structure means the order of the particles (atoms, ions, or molecules) in a crystalline matter, where they are arranged into regular arrays of repeating unit cells.

Sodium chloride (table salt) and diamond are examples of crystalline matter. The components of crystalline solid structures are usually crystal planes, i.e. atoms that have settled as planes on top of each other at certain distances, specific to that certain structure. These distances can be measured with XRD. 

How does XRD work?

XRD is based on a phenomenon called diffraction. In diffraction, a regular array of scatterers produces a regular array of spherical waves of radiation when they interact with radiation. This is called elastic scattering. In almost all directions, the produced waves cancel each other out, which is called destructive interference. However, in a few specific directions, the waves add and amplify each other, which is called constructive interference. These specific directions appear as bright spots called reflections on the formed diffraction pattern.

Diffraction can be applied to the atomic level of different materials when X-rays are used as electromagnetic radiation to produce the diffraction pattern. In XRD, the X-rays scatter from the atoms in the crystal structure primarily because they interact with the electrons in the atoms. The diffraction pattern produced by the diffracted X-rays is different for every substance because of the unique order of the atoms or molecules in them.

The intensities and scattering angles of the X-rays diffracted from the material are measured with an X-ray analyzer. The final result of the measurement is a diffractogram, which is a plot that has the X-ray intensity on the y-axis and the angle between the incident and the diffracted X-ray beam on the x-axis. When the angles where the constructive interference happens and the reflections occur are measured and the wavelength of the used X-rays (λ) is known, the distances between the crystal planes or atoms in the material (d) can be calculated using the mathematical formula of Bragg’s law.

Information obtained through X-ray diffraction

Various types of information can be obtained using XRD analysis. Because every crystalline matter produces its own kind of diffraction pattern and thus diffractogram, different materials can be identified by comparing the obtained diffractogram with commonly used reference databases containing known crystal structures of different materials.

It is also possible to determine the relative amounts of components in a material that consists of several different phases or substances. The lattice parameters of particles in a crystalline structure can be determined with XRD, as it is possible to measure the dimensions, shapes, and geometries of the particles in the material. 

Rietveld refinement can be used to accurately quantify the components within a sample by fitting a theoretical model of known crystal structures to the XRD pattern of the sample. This allows for a more precise estimation of the amount of each phase present.

Additionally, the crystallite size and strain can be measured with XRD, because the width of the bright spots in the diffraction pattern depends on the crystallite size of the matter and microstrain in the sample. Single crystals can also be investigated to determine the three-dimensional structure of their molecules with the help of single-crystal diffraction (SCD). This analysis requires a single crystal from the sample which can be produced by varying conditions like solvent or evaporation rate.

Non-ambient XRD

X-ray diffraction measurements can be done under ambient or non-ambient conditions. In non-ambient XRD (NA-XRD), the sample is analyzed under different conditions which can be created by adjusting environmental parameters such as temperature, pressure, relative humidity, gas environment, mechanical load, as well as electrical and magnetic fields. 

The altering of the parameters in NA-XRD results in changes in the material and its structures and these changes can be examined as they happen. For example, structural changes during operation, heat treatment, calcination, and sintering, as well as hydration and dehydration processes can be studied with this method. 

High-temperature XRD (HT-XRD) is one of the most commonly used NA-XRD methods to understand phase transitions, track decompositions, and understand how the material responds to high temperatures. Some instruments allow temperature-programmed experiments, where the temperature is gradually increased while collecting XRD data, revealing how the material's structure evolves with heat.

Samples

For diffraction to occur, X-rays have to scatter from a regular array of particles that have a long-range order in the material. This is why the samples have to be solid crystalline materials with a regular crystal structure. Amorphous materials can also be examined with XRD but only a limited amount of information is obtained from them.

It is possible to pretreat the samples before analysis by grinding them into powder. This improves the quality of the measurement by increasing the diffraction intensity of the X-rays. 

For thin film characterization, the closely related GIXRD method is a better match. Another option for investigating crystal structures is EBSD analysis.