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Brillouin zone

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

16 relations: Bloch wave, Bragg plane, Bravais lattice, Computational Materials Science, Crystal system, Fundamental domain, Fundamental pair of periods, Léon Brillouin, Locus (mathematics), Mathematics, Point group, Primitive cell, Reciprocal lattice, Solid-state physics, Voronoi diagram, Wigner–Seitz cell.

Bloch wave

A Bloch wave (also called Bloch state or Bloch function or Bloch wave function), named after Swiss physicist Felix Bloch, is a type of wavefunction for a particle in a periodically-repeating environment, most commonly an electron in a crystal.

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Bragg plane

In physics, a Bragg plane is a plane in reciprocal space which bisects one reciprocal lattice vector \mathbf.

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Bravais lattice

In geometry and crystallography, a Bravais lattice, studied by, is an infinite array of discrete points generated by a set of discrete translation operations described by: where ni are any integers and ai are known as the primitive vectors which lie in different directions and span the lattice.

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Computational Materials Science

Computational Materials Science is a monthly peer-reviewed scientific journal published by Elsevier.

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Crystal system

In crystallography, the terms crystal system, crystal family, and lattice system each refer to one of several classes of space groups, lattices, point groups, or crystals.

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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 define a lattice in the complex plane.

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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) is a set of points whose location satisfies or is determined by one or more specified conditions.

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Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change.

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Point group

In geometry, a point group is a group of geometric symmetries (isometries) that keep at least one point fixed.

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Primitive cell

A primitive cell is a unit cell constructed so that it contains only one lattice point (each vertex of the cell sits on a lattice point which is shared with the surrounding cells, each lattice point is said to contribute 1/n to the total number of lattice points in the cell where n is the number of cells sharing the lattice point).

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Reciprocal lattice

In physics, the reciprocal lattice of a lattice (usually a Bravais lattice) is the lattice in which the Fourier transform of the spatial wavefunction of the original lattice (or direct lattice) is represented.

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Solid-state physics

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

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Voronoi diagram

In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on distance to points in a specific subset of the plane.

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Wigner–Seitz cell

The Wigner–Seitz cell, named after Eugene Wigner and Frederick Seitz, is a type of Voronoi cell used in the study of crystalline material in solid-state physics.

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References

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

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