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The primitive translation vectors of the oblique lattice form an angle other than 90° and are of unequal lengths. Crystal classes. The oblique lattice class ...
Despite this rigid minimum-size requirement, there is not one unique choice of primitive unit cell. In fact, all cells whose borders are primitive translation vectors will be primitive unit cells. The fact that there is not a unique choice of primitive translation vectors for a given lattice leads to the multiplicity of possible primitive unit ...
The translation vectors define ... lattices, the primitive lattice vectors are ... The crystallographic point group or crystal class is the mathematical group ...
Vectors and are primitive translation vectors. The honeycomb point set is a special case of the hexagonal lattice with a two-atom basis. [ 1 ] The centers of the hexagons of a honeycomb form a hexagonal lattice, and the honeycomb point set can be seen as the union of two offset hexagonal lattices.
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.
Let ,, be primitive translation vectors (shortly called primitive vectors) of a crystal lattice, where atoms are located at lattice points described by = + + with , , and as any integers. (So x {\displaystyle \mathbf {x} } indicating each lattice point is an integer linear combination of the primitive vectors.)
Reciprocal space (also called k-space) provides a way to visualize the results of the Fourier transform of a spatial function. It is similar in role to the frequency domain arising from the Fourier transform of a time dependent function; reciprocal space is a space over which the Fourier transform of a spatial function is represented at spatial frequencies or wavevectors of plane waves of the ...
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.