X-ray crystallography

X-ray crystallography is an experimental science used to determine the atomic and molecular structure of a crystal. It works because the internal structure of a crystal causes a beam of incident X-rays to diffract, or bend, in specific directions. By measuring the angles and intensities of this diffraction, a crystallographer can create a three-dimensional map. This map shows the density of electrons within the crystal and the precise positions of the atoms. It also reveals chemical bonds and other details like crystallographic disorder. This method is essential for characterizing the atomic structure of many different materials.

The process of solving a structure involves several rigorous steps. First, scientists must prepare high-quality samples of the material. They then carefully record the intensities of the diffracted X-rays. This data must be processed to remove any artifacts, which are errors in the recording. Next, researchers use various methods, known as direct methods, to obtain an initial estimate of the atomic structure. After this, they use computational techniques, such as difference maps, to complete the picture. The final step is a numerical refinement. This process compares the calculated atomic positions against the experimental data to ensure accuracy.

Historically, humans have admired the symmetry of crystals for centuries. In 1611, Johannes Kepler hypothesized that the hexagonal shape of snowflakes came from regular water particles. In 1669, Nicolas Steno began experimental studies on crystal symmetry. He discovered the law of constancy of interfacial angles, showing that crystal face angles remain the same for a specific type. In 1784, René Just Haüy discovered the law of decrements. He showed that crystal faces result from stacking patterns of identical blocks. This led to the concept of a Bravais lattice, where a single unit cell repeats indefinitely in three directions.

The discovery of X-rays by Wilhelm Röntgen in 1895 changed the course of science. While physicists debated if X-rays were waves or particles, Max von Laue realized they could be used to study crystals. In 1912, von Laue suggested that X-rays had a wavelength comparable to the spacing in a crystal's unit cell. Working with Walter Friedrich and Paul Knipping, he shone X-rays through a copper sulfate crystal. The resulting photographic plate showed a pattern of intersecting circles of spots. This confirmed that X-rays are a form of electromagnetic radiation. Von Laue received the Nobel Prize in Physics in 1914 for this discovery.

Following von Laue, William Lawrence Bragg and his father, William Henry Bragg, made massive advances. In 1912–1913, the younger Bragg developed Bragg's law. This law connects the scattering of X-rays with the evenly spaced planes within a crystal. The father and son shared the Nobel Prize in 1915. Early successes included solving the structure of table salt in 1914. This proved that crystals could be made of ionic compounds rather than just covalently bonded molecules. That same year, the structure of diamond was solved. It showed a tetrahedral arrangement with C–C bond lengths of approximately 1.52 angstroms.

As methods improved, scientists tackled increasingly complex organic and biological molecules. In 1923, the first organic compound, hexamethylenetetramine, was solved. By 1928, Kathleen Lonsdale used the method to study hexamethylbenzene. Her work established the hexagonal symmetry of benzene and helped develop the idea of resonance in chemical bonds. In the 1930s, researchers began solving much larger molecules like phthalocyanine. This molecule is closely related to biological porphyrins, such as chlorophyll. Today, the method is used to map the structures of proteins, nucleic acids like DNA, and even viruses.

Modern X-ray crystallography remains vital for many scientific fields. It is the primary way to differentiate materials that look similar in other experiments. By understanding atomic arrangements, scientists can explain unusual electronic or elastic properties in materials. In medicine, knowing the structure of a protein or virus is the basis for designing new pharmaceuticals. For example, understanding molecular shapes helps in creating drugs to fight specific diseases. The data gathered from these experiments is often deposited in international databases. This allows the global scientific community to continue building on these atomic discoveries.