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Brillouin zone

Index Brillouin zone

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

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

Bloch wave

A Bloch wave (also called Bloch state or Bloch function or Bloch wavefunction), 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 a reciprocal lattice vector, \scriptstyle \mathbf, at right angles.

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Bravais lattice

In geometry and crystallography, a Bravais lattice, named after, is an infinite array of discrete points in three dimensional space 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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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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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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Hexagonal crystal family

In crystallography, the hexagonal crystal family is one of the 6 crystal families, which includes 2 crystal systems (hexagonal and trigonal) and 2 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 (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Monoclinic crystal system

In crystallography, the monoclinic crystal system is one of the 7 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 group of geometric symmetries (isometries) that keep at least one point fixed.

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Primitive cell

In geometry, crystallography, mineralogy, and solid state physics, a primitive cell is a minimum volume cell (a unit cell) corresponding to a single lattice point of a structure with discrete translational symmetry.

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Reciprocal lattice

In physics, the reciprocal lattice represents the Fourier transform of another lattice (usually a Bravais lattice).

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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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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 7 crystal systems.

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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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Redirects here:

Brillouin Zone, First Brillouin zone, Gamma point, Reciprocal lattice primitive cell, W (Brillouin zone).

References

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

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