Crystallography

thumb|A crystalline solid: atomic resolution image of strontium titanate. Brighter spots are columns of [[strontium atoms and darker ones are titanium-oxygen columns.]] thumb|Octahedral and tetrahedral interstitial sites in a face centered cubic structure thumb|Kikuchi lines (physics)|Kikuchi lines in an [[electron backscatter diffraction pattern of monocrystalline silicon, taken at 20 kV with a field-emission electron source]]

unique arrangement of atoms or molecules in a crystalline liquid or solid

Crystallization is a process that leads to solids with a uniform pattern of atoms or molecules, i.e. a crystal. The uniform nature of a crystalline solid can be contrasted with amorphous solids in which atoms or molecules lack regular organization. Crystallization can occur by various routes including precipitation from solution, freezing of a liquid, or deposition from a gas. Attributes of the resulting crystal can depend largely on factors such as temperature, air pressure, cooling rate, or solute concentration.

technique used for determining the atomic or molecular structure of a crystal, in which the ordered atoms cause a beam of incident X-rays to diffract into specific directions

tendency of crystalline materials to split along definite crystallographic structural planes

ability of a solid material to exist in more than one form or crystal structure

series of chemical substances with the same general formula, varying by a single parameter

class of space groups, lattices, point groups, or crystals

two separate crystals sharing some of the same crystal lattice points in a symmetrical manner

mineralogical term for the visible shape of a mineral

thumb|Potential energy surface for silver depositing on an aluminium–[[palladium–manganese (Al–Pd–Mn) quasicrystal surface. Similar to Fig. 6 in Ref.]]

an infinite array of discrete points in three dimensional space generated by a set of discrete translation operations

describing crystal lattice planes

gives the angles for coherent and incoherent scattering from a crystal lattice

Bending of electron beams due to electrostatic interactions with matter

water molecules present in a hydrated compound's crystal structure, without being covalently bound

particular mapping that projects a sphere onto a plane

Epitaxy (prefix epi- means "on top of") is a type of crystal growth or material deposition in which new crystalline layers are formed with one or more well-defined orientations with respect to the crystalline seed layer. The deposited crystalline film is called an epitaxial film or epitaxial layer. The relative orientation(s) of the epitaxial layer to the seed layer is defined in terms of the orientation of the crystal lattice of each material. For most epitaxial growths, the new layer is usually crystalline and each crystallographic domain of the overlayer must have a well-defined orientation

energy change upon formation of one mole of a crystalline compound

symmetry group of a configuration in space

fourier transform of real-space lattices, important in solid-state physics

primitive cell in the reciprocal space lattice of crystals

concept in materials science: the interface between two grains, or crystallites, in a polycrystalline material

quantum system whose ground state is one in which the particles are in repetitive motion

having crystal structures of the same symmetry

primitive cell of crystal lattices with Voronoi decomposition applied

study of the principles of chemistry behind crystals

сonstant in crystallography

means of describing a crystal structure

type of crystal structure

base of crystal structure

physical phenomenon

group of geometric symmetries (isometries) that keep at least one point fixed

after a first nucleation, second step of crystallization consisting in the regular accretion of atoms or ions at the surface of the crystal

thumb|A faceted amethyst Facets () are flat faces on geometric shapes. The organization of naturally occurring facets was key to early developments in crystallography, since they reflect the underlying symmetry of the crystal structure. Gemstones commonly have facets cut into them in order to improve their appearance by allowing them to reflect light. The earliest diamond cutting techniques were simply to polish the natural shape of rough diamonds, often octahedral crystals. It wasn't until the 14th century that faceting, the process of cutting and polishing a gemstone to create multiple flat

mathematical classification of a two-dimensional repetitive pattern

dense arrangement of congruent spheres in an infinite, regular arrangement

vector characterising a dislocation in a crystal lattice

symmetry operation combining reflection across and translation along an axis

an arrangement of non-overlapping spheres within a containing space

sub-branch of optical physics

fraction of volume in a crystal structure that is occupied by the constituent particles

well-formed crystal with sharp and well developed faces

formula for lattice energy of a crystal

notation to represent symmetry in point groups, plane groups and space groups

classification system for crystals

physical phenomenon

distribution of crystallographic orientations of a polycrystalline sample

dimensionless number used in condensed matter physics to describe the attenuation of X-ray scattering or coherent neutron scattering caused by thermal motion

energy conservation during diffraction by atoms

equation that describes how solids transform from one phase to another at constant temperature

a tiling of the plane by regular hexagons and equilateral triangles, with each edge separating both types of shape

equations describing diffraction in a crystal lattice

notation to represent symmetry in point groups

cubic crystal structure of diamond and other substances

file format for representing crystallographic information

X-ray crystallography

mathematical description in crystallography

technique in crystallography