Crystallography

Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The word crystallography is derived from the Ancient Greek word κρύσταλλος (; "clear ice, rock-crystal"), with its meaning extending to all solids with some degree of transparency, and γράφειν (; "to write"). In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming that 2014 would be the International Year of Crystallography. Before the development of X-ray diffraction crystallography (see below), the study of crystals was based on physical measurements of their geometry using a goniometer. This involved measuring the angles of crystal faces relative to each other and to theoretical reference axes (crystallographic axes), and establishing the symmetry of the crystal in question. The position in 3D space of each crystal face is plotted on a stereographic net such as a Wulff net or Lambert net. The pole to each face is plotted on the net. Each point is labelled with its Miller index. The final plot allows the symmetry of the crystal to be established. Crystallographic methods now depend on analysis of the diffraction patterns of a sample targeted by a beam of some type. X-rays are most commonly used; other beams used include electrons or neutrons. Crystallographers often explicitly state the type of beam used, as in the terms X-ray crystallography, neutron diffraction and electron diffraction. These three types of radiation interact with the specimen in different ways. X-rays interact with the spatial distribution of electrons in the sample. Electrons are charged particles and therefore interact with the total charge distribution of both the atomic nuclei and the electrons of the sample. Neutrons are scattered by the atomic nuclei through the strong nuclear forces, but in addition, the magnetic moment of neutrons is non-zero.

The rule of four: anomalous distributions in the stoichiometries of inorganic compounds

The rule of four: anomalous distributions in the stoichiometries of inorganic compounds