Search results
Results from the WOW.Com Content Network
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]
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.
If the lattice or crystal is 2-dimensional, the primitive cell has a minimum area; likewise in 3 dimensions the primitive cell has a minimum volume. 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.
With this form, the reciprocal lattice as the set of all wavevectors for the Fourier series of a spatial function which periodicity follows , is itself a Bravais lattice as it is formed by integer combinations of its own primitive translation vectors (,,), and the reciprocal of the reciprocal lattice is the original lattice, which reveals the ...
In either case, one needs to choose the three lattice vectors a 1, a 2, and a 3 that define the unit cell (note that the conventional unit cell may be larger than the primitive cell of the Bravais lattice, as the examples below illustrate). Given these, the three primitive reciprocal lattice vectors are also determined (denoted b 1, b 2, and b 3).
The smallest area enclosed in this way is called the Wigner–Seitz primitive cell. For a 3-dimensional lattice, the steps are analogous, but in step 2 instead of drawing perpendicular lines, perpendicular planes are drawn at the midpoint of the lines between the lattice points.
This crystallography -related article is a stub. You can help Wikipedia by expanding it.
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.