Crystals are something we come across every day. From the salt on your table to the ice in your cup, from your phone screen to the crystals sold for good luck, it’s unlikely that you can make it through the day without encountering at least a crystal or two. When all’s said and done though, what makes crystal structures so different and special from any other materials, and how do we know all that we do about them?
Just like crystals are part of our everyday life, the study of crystal structure is an integral part of physics and chemistry in identifying the chemical composition of a structure. This however cannot be done by observation alone and instead a technique called x-ray diffraction is used. Crystals are solids that are made up of building blocks such as atoms or molecules. These building blocks come together in a repeating pattern with an ordered arrangement to form a crystal. It is because of this long range order that crystalline solids can be studied using x-ray diffraction. This is due to the fact that the uniform spacing between the atoms and molecules in a crystal have a similar size to the wavelength of the x-rays that are used in x-ray diffraction. Solids that are not crystalline (amorphous solids) cannot be studied using x-ray diffraction as they do not have this uniform spacing.
To understand x-ray diffraction, we must first understand how the periodicity (repetitiveness) of a crystalline solid can be described. Each of the repeating building blocks or motifs in a crystal are called lattice points and as they repeat in the same pattern, i.e. are periodic, they can come together to form something called a lattice, which is used to describe the periodicity of the crystal. Crystals can be viewed as structures made up of “unit cells” which are the smallest group of atoms or molecules that when used with the lattice, make up the entire crystal structure.
The unit cell of a crystal can come in many different shapes and forms such as cubic and tetragonal and within those crystal systems, there are four different arrangement atoms can take, primitive, body centred and end-face centred. In order to define the lattice, the locations of the atoms on the unit cell, the symmetry of the crystal structure and the lattice parameters must be known. The lattice parameters are the lengths of each side of the unit cell and they are related to Miller indices and Miller planes. Miller planes are the set of parallel planes that exist on the axes of unit cells, and can be described by a set of three numbers called the Miller indices of the crystal.
Bragg’s Law, the Principle Used in X-Ray Diffraction (1)
This is where x-ray diffraction comes in, as the Miller indices can be found from the results of this technique. In x-ray diffraction, the x-rays are emitted and passed through a crystal. When this happens, the planes of the crystal reflect some of the x-rays at a scattering angle of theta. This angle theta corresponds to a Miller index. This relationship can be found using Bragg’s law as shown in the image above. X-ray diffraction provides an x-ray diffraction pattern of these different values of theta and so give the different Miller indices of the crystal. These can be used to find the unit cell parameters of the crystal, and give the type of unit cell that the crystal has. This pattern can also be compared to a database of diffraction patterns of known substances to identify the likely chemical composition of the crystalline solid or powder that is being analysed by x-ray diffraction.
With that we see how x-ray diffraction can be used to find out the lattice parameters of the unit cell of a crystal and from this its crystal structure, and can also be used to obtain the chemical composition of an unknown crystalline substance and thus is an incredibly important tool in the study of crystal structures.
(1) Image credit: X-Ray Diffraction, Veqter: https://www.veqter.co.uk/residual-stress-measurement/x-ray-diffraction
