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The smallest repeating unit in a crystal lattice that reflects the symmetry and structure of the entire crystal.

The physical dimensions of unit cells in a crystal lattice, often described by the lengths of the cell edges (a, b, c) and the angles between them (α, β, γ).

A fundamental equation that relates the angles at which X-rays are diffracted by crystal planes, given by $n\lambda = 2d\sin\theta$, where $n$ is an integer, $\lambda$ is the wavelength, $d$ is the distance between crystal planes, and $\theta$ is the diffraction angle.

A technique for determining the atomic and molecular structure of a crystal by diffracting X-ray beams off its crystalline planes.

A notation system that describes the orientation of crystal planes in a lattice, using a set of three integers (hkl).

Describes the symmetry of a crystal structure in three dimensions, considering translational and point symmetries. There are 230 unique space groups.

A classification scheme for crystals based on the symmetry properties of the lattice. There are seven systems: cubic, tetragonal, orthorhombic, hexagonal, trigonal, monoclinic, and triclinic.

A construct used to describe the diffraction pattern of a crystal lattice, where each point represents the diffraction condition for a set of lattice planes.

An operation that moves a crystal in such a way that it looks the same after the operation as it did before. Examples include rotation, reflection, inversion, and translation.

The group of symmetry operations that leave at least one point unmoved, describes symmetry of the molecule regardless of translational motions.

A mathematical operation that transforms crystallographic data from real space to reciprocal space, and is essential in interpreting X-ray diffraction data.

A method where a polycrystalline powder is used for diffraction analysis, producing a series of rings that are unique to the crystal structure of the material.

A method of X-ray diffraction that involves exposing a stationary crystal to a polychromatic beam of X-rays to produce a pattern of spots which can be analyzed for crystal orientation.

The property of being directionally dependent, as opposed to isotropy, which means homogeneous in all directions, often reflected in the physical properties of crystals.