Crystallography

Crystallography is the experimental science of determining the arrangement of atoms in solids. In older usage, it is the scientific study of crystals. The word "crystallography" is derived from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and graphein = write.

Before the development of X-ray diffraction crystallography (see below), the study of crystals was based on the geometry of the crystals. This involves measuring the angles of crystal faces relative to theoretical reference axes (crystallographic axes), and establishing the symmetry of the crystal in question. The former is carried out using a goniometer. The position in 3D space of each crystal face is plotted on a stereographic net, e.g. Wulff net or Lambert net. In fact, 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 the analysis of the diffraction patterns that emerge from a sample that is targeted by a beam of some type. The beam is not always electromagnetic radiation, even though X-rays are the most common choice. For some purposes electrons or neutrons are used, which is possible due to the wave properties of the particles. Crystallographers often explicitly state the type of illumination used when referring to a method, as with the terms X-ray diffraction, 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 the valence electrons, while electrons are charged particles and therefore feel the total charge distribution of both the atomic nuclei and the surrounding electrons. Neutrons are scattered by the atomic nuclei through the strong nuclear forces, but in addition, the magnetic moment of neutrons is non-zero. They are therefore also scattered by magnetic fields. When neutrons are scattered from hydrogen-containing materials, they produce diffraction patterns with high noise levels. However, the material can sometimes be treated to substitute hydrogen for deuterium. Because of these different forms of interaction, the three types of radiation are suitable for different crystallographic studies

Theory
Condensed matter physics
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Phases · Phase transition
[show]States of matter
Solid · Liquid · Gas · Bose-Einstein condensate · Fermionic condensate · Fermi gas · Fermi liquid · Supersolid · Superfluid · Luttinger liquid
[show]Phase phenomena
Order parameter · Phase transition
[show]Electronic phases
Insulator · Mott insulator · Semiconductor · Semimetal · Conductor · Superconductor · Thermoelectric · Piezoelectric · Ferroelectric
[show]Electronic phenomena
Quantum Hall effect · Spin Hall effect · Kondo effect
[show]Magnetic phases
Diamagnet · Superdiamagnet

Paramagnet · Superparamagnet
Ferromagnet · Antiferromagnet
Ferrimagnet · Metamagnet
Spin glass
[show]Quasiparticles
Phonon · Exciton · Plasmon

Polariton · Polaron · Magnon
[show]Soft matter
Amorphous solid · Granular matter ·

Liquid crystal · Polymer
[show]Scientists
Maxwell · Van der Waals · Debye · Bloch · Onsager · Mott · Peierls · Landau · Luttinger · Anderson · Bardeen · Cooper · Schrieffer · Josephson · Landau · Kohn · Kadanoff · Fisher
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An image of a small object is usually generated by using a lens to focus the illuminating radiation, as is done with the rays of the visible spectrum in light microscopy. However, the wavelength of visible light (about 4000 to 7000 angstroms) is three orders of magnitude longer then the length of typical atomic bonds and atoms themselves (about 1 to 2 angstroms). Therefore, obtaining information about the spatial arrangement of atoms requires the use of radiation with shorter wavelengths, such as X-rays. Employing shorter wavelengths implied abandoning microscopy and true imaging, however, because there exists no material from which a lens capable of focusing this type of radiation can be created. (That said, scientists have had some success focusing X-rays with microscopic Fresnel zone plates made from gold, and by critical-angle reflection inside long tapered capillaries.)[1] Diffracted x-ray beams cannot be focused to produce images, so the sample structure must be reconstructed from the diffraction pattern. Sharp features in the diffraction pattern arise from periodic, repeating structure in the sample, which are often very strong due to coherent reflection of many photons from many regularly spaced instances of similar structure, while non-periodic components of the structure result in diffuse (and usually weak) diffraction features.

Because of their highly ordered and repetitive structure, crystals give diffraction patterns of sharp Bragg reflection spots, and are ideal for analyzing the structure of solids.