In geometry and crystallography, a Bravais lattice, named after Auguste Bravais (1850), is an infinite array of discrete points generated by a set of discrete...

a factor 48. The Bravais lattices were studied by Moritz Ludwig Frankenheim in 1842, who found that there were 15 Bravais lattices. This was corrected...

crystallography for lattice planes in crystal (Bravais) lattices. In particular, a family of lattice planes of a given (direct) Bravais lattice is determined...

in physical space, such as a crystal system (usually a Bravais lattice). The reciprocal lattice exists in the mathematical space of spatial frequencies...

face-centered-cubic Bravais lattice, which is not necessarily close-packed when a motif is set onto the lattice points. E.g. the diamond and the zincblende lattices are...

not a Bravais lattice, as there are two nonequivalent sets of lattice points. Instead, it can be constructed from the hexagonal Bravais lattice by using...

hexagonal lattice (sometimes called triangular lattice) is one of the five two-dimensional Bravais lattice types. The symmetry category of the lattice is wallpaper...

nodes of Bravais lattice. The lengths of principal axes/edges, of unit cell and angles between them are lattice constants, also called lattice parameters...

calculation Bethe lattice, a regular infinite tree structure used in statistical mechanics Bravais lattice, a repetitive arrangement of atoms Lattice C, a compiler...

reciprocal lattice vector G {\displaystyle \mathbf {G} } and arbitrary position vector r {\displaystyle \mathbf {r} } in the original Bravais lattice space...

examples. There is only one tetragonal Bravais lattice in two dimensions: the square lattice. Bravais lattices Crystal system Crystal structure Point...

Bravais lattices are represented using conventional primitive cells, as shown below. The other seven Bravais lattices (known as the centered lattices)...

Two monoclinic Bravais lattices exist: the primitive monoclinic and the base-centered monoclinic. For the base-centered monoclinic lattice, the primitive...

The oblique lattice is one of the five two-dimensional Bravais lattice types. The symmetry category of the lattice is wallpaper group p2. The primitive...

Bravais lattice. For example, the cube, truncated octahedron, and rhombic dodecahedron have point symmetry Oh, since the respective Bravais lattices used...

space. In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice is broken up into Brillouin...

rank 3, called the Bravais lattice (so named after French physicist Auguste Bravais). There are 14 possible types of Bravais lattice. The quotient of the...

crystallography, a lattice plane of a given Bravais lattice is any plane containing at least three noncollinear Bravais lattice points. Equivalently, a lattice plane...

intersect at 90° angles, so the three lattice vectors remain mutually orthogonal. There are four orthorhombic Bravais lattices: primitive orthorhombic, base-centered...

arrangement of congruent spheres in an infinite, regular arrangement (or lattice). Carl Friedrich Gauss proved that the highest average density – that is...

noted, giving a complete crystallographic space group. These are the Bravais lattices in three dimensions: P primitive I body centered (from the German Innenzentriert)...

cF8 Rutile structure, tP6 The two (italicised) letters specify the Bravais lattice. The lower-case letter specifies the crystal family, and the upper-case...

The rectangular lattice and rhombic lattice (or centered rectangular lattice) constitute two of the five two-dimensional Bravais lattice types. The symmetry...

image in the imaginary axis. The 14 lattice types in 3D are called Bravais lattices. They are characterized by their space group. 3D patterns with translational...

crystal with the given crystal structure. KCl has a face-centered cubic Bravais lattice. However, the K+ and the Cl− ion have the same number of electrons...

In fact, even within a given crystal system, the composition and Bravais lattice diversifies the number of independent slip systems (see the table below)...

Olivine's crystal structure incorporates aspects of the orthorhombic P Bravais lattice, which arise from each silica (SiO4) unit being joined by metal divalent...

work in crystallography, the conception of Bravais lattices, and the formulation of Bravais law. Bravais also studied magnetism, the northern lights...

three-fold axes, whereas in the second they do not. These are the Bravais lattice types in three dimensions: P – Primitive I – Body centered (from the...

the restriction that a wave function must be periodic on a certain Bravais lattice. Named after Max Born and Theodore von Kármán, this condition is often...