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A simple cubic crystal has only one lattice constant, the distance between atoms, but in general lattices in three dimensions have six lattice constants: the lengths a, b, and c of the three cell edges meeting at a vertex, and the angles α, β, and γ between those edges. The crystal lattice parameters a, b, and c have the
This means that X-rays are seemingly "reflected" off parallel crystal lattice planes perpendicular at the same angle as their angle of approach to the crystal with respect to the lattice planes; in the elastic light (typically X-ray)-crystal scattering, parallel crystal lattice planes perpendicular to a reciprocal lattice vector for the crystal ...
where a is the unit cell edge length of the crystal, ‖ ‖ is the magnitude of the Burgers vector, and h, k, and l are the components of the Burgers vector, = ; the coefficient is because in BCC and FCC lattices, the shortest lattice vectors could be as expressed .
The empty lattice approximation is a theoretical electronic band structure model in which the potential is periodic and weak (close to constant). One may also consider an empty [clarification needed] irregular lattice, in which the potential is not even periodic. [1]
The reciprocal lattices (dots) and corresponding first Brillouin zones of (a) square lattice and (b) hexagonal lattice. In mathematics and solid state physics, the first Brillouin zone (named after Léon Brillouin) is a uniquely defined primitive cell in reciprocal space.
A force field is the collection of parameters to describe the physical interactions between atoms or physical units (up to ~10 8) using a given energy expression. The term force field characterizes the collection of parameters for a given interatomic potential (energy function) and is often used within the computational chemistry community. [ 50 ]
This is based on the fact that a reciprocal lattice vector (the vector indicating a reciprocal lattice point from the reciprocal lattice origin) is the wavevector of a plane wave in the Fourier series of a spatial function (e.g., electronic density function) which periodicity follows the original Bravais lattice, so wavefronts of the plane wave ...
The Hubbard model is based on the tight-binding approximation from solid-state physics, which describes particles moving in a periodic potential, typically referred to as a lattice. For real materials, each lattice site might correspond with an ionic core, and the particles would be the valence electrons of these ions.