# Crystallography

A crystal of strontium titanate seen up close: the bright spots show rows of strontium atoms, and the darker spots show rows of titanium and oxygen atoms.
Octahedral and tetrahedral spaces (called interstitial sites) in a face-centered cubic (FCC) structure. These are the small gaps between atoms where other atoms can fit.
Kikuchi lines seen in an electron backscatter pattern of single-crystal silicon. The image was taken using a strong electron beam at 20,000 volts.
**Crystallography** is the science of studying how atoms are arranged in solid materials that form crystals. Crystals are special because their atoms are packed in a repeating pattern. This technique helps scientists look at the exact 3D structure of these materials, all the way down to the atomic level. Crystallography is very important in many areas of science, including chemistry, physics, geology, biology, and materials science. It helps researchers understand how atoms stick together, how materials are built, and how these structures affect a material’s properties like how strong it is, how it reacts, or how it works in the body. The most common method used in crystallography is called X-ray crystallography. It has been around for a long time and has helped make many important discoveries. There are also other methods like neutron diffraction and electron crystallography, which are used for special types of materials or situations.

At its core, crystallography works by shining a beam of radiation, usually X-rays, at a crystal. When the X-rays hit the crystal, they scatter or diffract in different directions. How the beam scatters depends on how the atoms are arranged inside the crystal. This scattered pattern, called a diffraction pattern, is recorded and then studied using math and computers. From this, scientists can figure out exactly where the atoms are inside the crystal. Because crystals have a regular and repeating structure, crystallography can show very detailed information like how long bonds are between atoms, what angles they form, and how molecules are shaped. This method is so precise that it can show details smaller than an atom’s width, making it one of the most powerful tools for studying how materials and molecules are built.

In chemistry and materials science, crystallography is used to study all kinds of materials. These include metals, minerals, ceramics, semiconductors, plastics (polymers), and other man-made compounds. It helps scientists understand how these materials are built and how they might behave in different situations. Crystallography is especially useful when creating new materials, like catalysts that speed up chemical reactions, superconductors that carry electricity with no resistance, and nanomaterials, which are built on a super tiny scale. In biology, crystallography has helped scientists discover the structures of important molecules like proteins, enzymes, DNA and RNA, and even viruses. One of the most famous discoveries in science, the double helix shape of DNA, was made possible by crystallography. In 1953, James Watson and Francis Crick built their DNA model using X-ray diffraction images taken by Rosalind Franklin and Maurice Wilkins.

Crystallography is also very important in medicine, especially in pharmaceutical research. Scientists use it to study the shapes of drug molecules and the targets they bind to, like proteins or enzymes in the body. Knowing the exact structure helps them design better and more effective medicines. This technique helps researchers understand how a drug works, how it interacts with other molecules, and how to make it work even better. This is called structure-based drug design, and it has helped create many important medicines. Crystallography is also used in other fields. In forensic science, it helps identify unknown materials found at crime scenes. In art conservation, it helps protect and study old paintings and artifacts. In geology, it helps scientists study rocks and minerals. Even in space science, crystallography is used to understand materials found on other planets by looking at their crystal structures.

Crystallography has grown a lot over time, thanks to new tools and technology. One big improvement is single-crystal diffraction, which studies crystals made of just one piece. Another is powder diffraction, which works with tiny particles instead of one big crystal. Scientists also use powerful light sources called synchrotrons to get even better images of crystals. A newer method called cryo-electron microscopy (cryo-EM) is now being used to study biological samples that do not form crystals, like some proteins. This method freezes the samples and uses electrons to take very detailed pictures. Better computers, detectors, and automated machines that grow crystals have made crystallography much faster and easier. These tools help scientists around the world study materials more quickly than ever before. Crystallography is such an important science that many Nobel Prizes have been awarded for discoveries in this field.

## X-ray diffraction

Crystal structure is now found by analysis of the diffraction patterns of a sample targeted by a beam of some type.

The technique was jointly invented by Sir William Bragg (1862–1942) and his son Sir Lawrence Bragg (1890–1971), who jointly won the Nobel Prize in Physics for 1915. Lawrence Bragg was the youngest to become a Nobel Laureate. He was the Director of the Cavendish Laboratory, Cambridge University, when the discovery of the structure of DNA was made by James D. Watson and Francis Crick in February 1953.

X-rays are most commonly used, but for some purposes electrons or neutrons are used. Because of the different forms of interaction, the three types of radiation are suitable for different crystallographic studies.

### Technique

Some materials studied using crystallography, proteins for example, do not always occur naturally as crystals. Normally such molecules are placed in solution and allowed to crystallize over days, weeks, or months.

Once a crystal is obtained, data can be collected using a beam of radiation. Although X-ray equipment is commonplace, crystallography often uses special synchrotron light sources to make X-rays. They produce purer and more complete patterns. Synchrotron sources also have a much higher intensity of X-ray beams, so data collection takes a fraction of the time normally necessary at weaker sources.

Producing an image from a diffraction pattern requires sophisticated mathematics.

The mathematical methods for the analysis of diffraction data only apply to *patterns,* which in turn result only when waves diffract from orderly arrays. Hence crystallography applies for the most part only to crystals, or to molecules which can be got to crystallize.

In spite of this, a certain amount of molecular information can be deduced from the patterns that are generated by fibres and powders. For example, the double-helical structure of DNA was deduced from an X-ray diffraction pattern that had been got from a fibrous sample.

## Electron diffraction

The clear differences between intensities of the diffraction spots can be used in crystal structure determination
Electron crystallography is a method to determine the arrangement of atoms in solids using a transmission electron microscope (TEM). The method was invented by Aaron Klug, who won the Nobel Prize in Chemistry for this, and his studies on virus structures and transfer RNA, in 1982.

The first electron crystallographic protein structure to achieve atomic resolution was bacteriorhodopsin in 1990.

## Examples

### Crystallography in materials engineering

An example of a cubic lattice
Crystallography is a tool that is often employed in materials science. The understanding of crystal structures is needed to understand crystallographic defects.

A number of other physical properties are linked to crystallography. For example, the minerals in clay form small, flat, platelike structures. Clay can be easily deformed because the platelike particles can slip along each other in the plane of the plates, yet remain strongly connected in the direction perpendicular to the plates. Such mechanisms can be studied by crystallographic texture measurements.

Crystallography includes the symmetry patterns which can be formed by atoms in a crystal.

### Biology

X-ray crystallography was the primary method for determining the 3-D molecular structure of biological macromolecules. The most important of these are enzymes, and nucleic acids such as DNA and RNA. In fact, the double helix structure of DNA was worked out from crystallographic data.

The first crystal structure of a macromolecule was solved in 1958 The Protein Data Bank (PDB) is a freely accessible repository for the structures of proteins and other biological macromolecules. Computer programs can be used to help visualize biological molecular structures.

X-ray crystallography has now given way to electron crystallography for macromolecules which do not form large 3-D crystals.