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Brillouin zone, the Glossary

In mathematics and solid state physics, the first Brillouin zone (named after Léon Brillouin) is a uniquely defined primitive cell in reciprocal space.^[1]

22 relations: Bloch's theorem, Bragg plane, Bravais lattice, Computational materials science, Cubic crystal system, Fermi surface, Fundamental domain, Fundamental pair of periods, Hexagonal crystal family, Léon Brillouin, Locus (mathematics), Mathematics, Monoclinic crystal system, Orthorhombic crystal system, Point group, Reciprocal lattice, Solid-state physics, Tetragonal crystal system, Triclinic crystal system, Unit cell, Voronoi diagram, Wigner–Seitz cell.
Electronic band structures
Vibrational spectroscopy

Bloch's theorem

In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves modulated by periodic functions.

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Bragg plane

In physics, a Bragg plane is a plane in reciprocal space which bisects a reciprocal lattice vector, \scriptstyle \mathbf, at right angles. Brillouin zone and Bragg plane are crystallography.

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In geometry and crystallography, a Bravais lattice, named after, is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by where the ni are any integers, and ai are primitive translation vectors, or primitive vectors, which lie in different directions (not necessarily mutually perpendicular) and span the lattice. Brillouin zone and Bravais lattice are crystallography.

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Computational materials science

Computational materials science and engineering uses modeling, simulation, theory, and informatics to understand materials.

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Cubic crystal system

In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube.

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Fermi surface

In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied from unoccupied electron states at zero temperature.

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Fundamental domain

Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action.

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Fundamental pair of periods

In mathematics, a fundamental pair of periods is an ordered pair of complex numbers that defines a lattice in the complex plane.

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Hexagonal crystal family

In crystallography, the hexagonal crystal family is one of the 6 crystal families, which includes two crystal systems (hexagonal and trigonal) and two lattice systems (hexagonal and rhombohedral).

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Léon Brillouin

Léon Nicolas Brillouin (August 7, 1889 – October 4, 1969) was a French physicist.

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Locus (mathematics)

In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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Monoclinic crystal system

In crystallography, the monoclinic crystal system is one of the seven crystal systems.

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Orthorhombic crystal system

In crystallography, the orthorhombic crystal system is one of the 7 crystal systems.

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Point group

In geometry, a point group is a mathematical group of symmetry operations (isometries in a Euclidean space) that have a fixed point in common. Brillouin zone and point group are crystallography.

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Reciprocal lattice

In physics, the reciprocal lattice emerges from the Fourier transform of another lattice. Brillouin zone and reciprocal lattice are crystallography.

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Solid-state physics

Solid-state physics is the study of rigid matter, or solids, through methods such as solid-state chemistry, quantum mechanics, crystallography, electromagnetism, and metallurgy.

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Tetragonal crystal system

In crystallography, the tetragonal crystal system is one of the 7 crystal systems.

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Triclinic crystal system

Triclinic (a ≠ b ≠ c and α ≠ β ≠ γ) In crystallography, the triclinic (or anorthic) crystal system is one of the seven crystal systems.

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Unit cell

In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Brillouin zone and unit cell are crystallography.

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Voronoi diagram

In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects.

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Wigner–Seitz cell

The Wigner–Seitz cell, named after Eugene Wigner and Frederick Seitz, is a primitive cell which has been constructed by applying Voronoi decomposition to a crystal lattice. Brillouin zone and Wigner–Seitz cell are crystallography.

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References

[1] https://en.wikipedia.org/wiki/Brillouin_zone

Also known as Brillouin zones, Constant energy surface, Constant-energy surface, First Brillouin zone, Gamma point, Reciprocal lattice primitive cell, W (Brillouin zone).