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The primitive translation vectors of the oblique lattice form an angle other than 90° and are of unequal lengths. ... Geometric class, point group Arithmetic class ...
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.)
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 ...
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.
Primitive cell – a repeating unit formed by the vectors spanning the points of a lattice Seed crystal – a small piece of a single crystal used to initiate growth of a larger crystal Wigner–Seitz cell – a primitive cell of a crystal lattice with Voronoi decomposition applied
Instead, it is chosen so the number of orthogonal basis vectors is maximized. This results in some of the coefficients of the equations above being fractional. A lattice in which the conventional basis is primitive is called a primitive lattice, while a lattice with a non-primitive conventional basis is called a centered lattice.
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]
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.