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The primitive rectangular lattice can also be described by a centered rhombic unit cell, while the centered rectangular lattice can also be described by a primitive rhombic unit cell. Note that the length a {\displaystyle a} in the lower row is not the same as in the upper row.
A primitive cell is a unit cell that contains exactly one lattice point. For unit cells generally, lattice points that are shared by n cells are counted as 1 / n of the lattice points contained in each of those cells; so for example a primitive unit cell in three dimensions which has lattice points only at its eight vertices is considered to contain 1 / 8 of each of them. [3]
Primitive unit cells are defined as unit cells with the smallest volume for a given crystal. (A crystal is a lattice and a basis at every lattice point.) To have the smallest cell volume, a primitive unit cell must contain (1) only one lattice point and (2) the minimum amount of basis constituents (e.g., the minimum number of atoms in a basis).
The unit cell is defined as the smallest repeating unit having the full symmetry of the crystal structure. [2] The geometry of the unit cell is defined as a parallelepiped, providing six lattice parameters taken as the lengths of the cell edges (a, b, c) and the angles between them (α, β, γ). The positions of particles inside the unit cell ...
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. It is used in the study of crystalline materials in crystallography. Wigner–Seitz primitive cell for different angle parallelogram lattices.
The black boxes outline the unit cell. In mathematics, physics and chemistry, a space group is the symmetry group of a repeating pattern in space, usually in three dimensions. [ 1 ] The elements of a space group (its symmetry operations) are the rigid transformations of the pattern that leave it unchanged.
In crystallography, the monoclinic crystal system is one of the seven crystal systems. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal lengths, as in the orthorhombic system. They form a parallelogram prism. Hence two pairs of vectors are perpendicular (meet at right ...
Finite-difference time-domain (FDTD) or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis technique used for modeling computational electrodynamics (finding approximate solutions to the associated system of differential equations). Since it is a time-domain method, FDTD ...