Source: Faisal Alamgir, School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA
X-ray diffraction (XRD) is a technique used in materials science for determining the atomic and molecular structure of a material. This is done by irradiating a sample of the material with incident X-rays and then measuring the intensities and scattering angles of the X-rays that are scattered by the material. The intensity of the scattered X-rays are plotted as a function of the scattering angle, and the structure of the material is determined from the analysis of the location, in angle, and the intensities of scattered intensity peaks. Beyond being able to measure the average positions of the atoms in the crystal, information on how the actual structure deviates from the ideal one, resulting for example from internal stress or from defects, can be determined.
The diffraction of the X-rays, that is central to the XRD method, is a subset of the general X-ray scattering phenomena. XRD, which is generally used to mean can wide-angle X-ray diffraction (WAXD), falls under several methods that use the elastically scattered X-ray waves. Other elastic scattering based X-ray techniques include small angle X-ray scattering (SAXS), where the X-rays are incident on the sample over the small angular range of 0.1-100 typically). SAXS measures structural correlations of the scale of several nanometers or larger (such as crystal superstructures), and X-ray reflectivity that measures the thickness, roughness, and density of thin films. WAXD covers an angular range beyond 100.
The following procedure applies to a specific XRD instrument and its associated software, and there may be some variations when other instruments are used.
X-Ray diffraction is a technique used to determine the atomic and molecular structure of materials. Solids have a crystalline structure, which corresponds to a microscopic arrangement of atoms that is repeated periodically. By staking planes, a 3-D structure of specific symmetry can be formed.
These structural arrangements result in a specific packing geometry that dictates the physical and chemical properties of the material. Such as magnetization, thermal conductivity, or malleability. Reflecting x-rays off of materials can reveal the inner details of their structure.
This video will illustrate the general principles of x-ray diffraction on a material and how this phenomenon is used in the laboratory to determine the structure and chemical composition of materials.
To begin, let's have a closer look at a crystal. It is formed of atomic lattices disposed in planes periodically separated by a distance dhkl of a few angstroms. H, k, l are Miller indices, a set of three integers the constitute a notation system for identifying directions and planes within crystals. The smallest repeating structure in a crystal is called the unit cell. Different angles, alpha, beta, gamma, and lengths a, b, c, of a unit cell forming the lattice will give rise to different symmetries. There are seven crystal systems. Cubic, tetragonal, orthorhombic, rhombohedral, monoclinic, triclinic, and hexagonal.
The relationship between the unit cell parameters and the Miller indices can be calculated for each crystal class. Electromagnetic of wavelength lambda can have similar dimensions with the differences between planes within the crystal's lattice. These correspond to wavelengths in the x-ray spectral range. When x-ray light waves irradiate a crystal at an incident angle theta, they propagate through the crystal and encounter lattice points from which they defract. Bragg's Law relates these parameters where n is an integer that represents the harmonic order of the diffraction. For a given lambda, only specific angles theta give rise to diffraction. This is the unique signature of a crystalline structure.
In an experiment, the sample is rotated and the detector that collects the scattered x-rays records peaks in intensity when reaching these characteristic angles. One can then extract the lattice spacing DHKL for each angle satisfying the Bragg's Law. Using multiple diffracted peak positions corresponding to several distinct DHKL values, the parameters of the unit cell can be solved uniquely.
Two main factors contribute to the relative intensity of the peaks. First, there are the non-structural contributions, which include the ability of the material to absorb x-ray light, and the geometry of the XRD experiment. These can be taken into account in the post-processing of the experimental data. Second, and most importantly, the structural contribution of the material is carried to the relative intensities of XRD. Each diffraction peak is in fact the sum of all the scattered amplitudes from multiple ray paths diffracted by all the unique atoms in a unit cell. If scattered lights are in phase, there is constructed interference. While if they are out of phase, there is destructed interference. These interferences directly affect the amplitude of the XRD peaks, representing the HKL planes of the crystal.
We will now see how these principles apply in an actual x-ray diffraction experiment.
Before starting, carefully inspect the XRD instrument and assess its status and safety. XRD users must be trained in basic radiation safety before having access to the instrument. Then proceed with sample preparation. In this experiment, we use a nickel powder sample in the form of a pressed pellet.
It is important that the sample is not thin and it should be at least three times thicker than the attenuation length of the x-rays. Note that the following procedure applies to a specific XRD instrument and its associated software and there may be some variations when other instruments are used.
Load the sample in the sample spinner stage and lock the sample into position, making sure the irradiated side of the sample is parallel to the sample stage. Use a mask to adjust the x-ray beam size of the instrument according to the sample diameter. At the smallest incident angle, the beam must have a footprint smaller than the sample width.
Now it is time to choose the acquisition parameters. First, select the angle range for the XRD scan. Typically, the range goes from 15 to 90 degrees. Then, select the degree step size as well as the integration time at each angle scanned.
Next, proceed to the data acquisition. After the scan, a graph of the intensity as a function of the angle to theta is obtained. From this initial scan, select specific peaks and determine peak positions.
Repeat the acquisition and focus this time on a narrower scan range around specific peaks. Using a smaller step size in angle to obtain higher resolution data. Once the data acquisition is finished, data can be analyzed to identify the structure of the material.
Using the instrument software and database library, each peak of the spectrum is identified and associated to a specific symmetry of crystal arrangement. In this particular case of the nickel powder sample, the spectrum shows a first peak corresponding to a one one one symmetry.
The second peak is associated to a two zero zero symmetry and so on. Then the software determines that this specific combination of symmetries corresponds to a face centered cubic structure and it identifies that the sample is a nickel powder.
X-ray diffraction is a standard method for determining the presence or absence of crystallographic order in materials. It is often used to obtain a variety of other structural information regarding internal stress and defects in a crystal, or multiple crystallographic phases in composite materials. XRD technique is also used in biology to determine the structure and spatial orientation of biological macromolecules such as proteins and nucleic acids.
In particular, this is how the double helix structure of DNA has been discovered, leading to the Nobel Prize in Physiology or Medicine in 1962. The study of the geochemistry of minerals either for mining purposes or even for planetary exploration also makes use of XRD technique. Think of the Rover Curiosity on Mars that has amongst its ten scientific instruments an XRD detector to analyze the composition of the martian soil.
You've just watched Jove's introduction to x-ray diffraction. You should now understand the crystalline structure of a solid and the principles of x-ray diffraction. You should also know how the XRD technique is used in the laboratory to obtain the structure and chemical composition of materials.
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