Unit cell

The unit cell - in geometry , solid state physics and mineralogy , in particular when discussing the crystal lattice , is the smallest cell corresponding to a single lattice point of a structure with translational symmetry in 2D, 3D or other dimensions. There is a fundamental difference between a primitive and a unit cell when considering the structure of a crystal. A primitive cell is the minimum imaginary volume of a crystal, the parallel transfers ( translations ) of which in three dimensions make it possible to construct a three-dimensional crystal lattice as a whole. A primitive unit cell can only be called if it has the same symmetry elements as the finite volume. Thus, when modeling crystalline structures, it turns out to be more convenient to use just a unit cell, since it reproduces not only the structure, but ultimately the properties of the crystal.

Brave formulated 3 rules for choosing unit cells:

* The symmetry of the unit cell must correspond to the symmetry of the crystal.

* The unit cell must have a maximum number of equal edges and equal angles.

* Provided that the first two rules are fulfilled, the unit cell must have a minimum volume.

The content of the unit cell allows you to characterize the entire structure of the mineral. The part of the structure covered by the unit cell consists of atoms held together by electronic bonds. Such tiny cells, endlessly repeating in three-dimensional space, form a crystal. An elementary cell is not a physical body, it can be moved along the structure parallel to itself, regardless of the choice of the origin, the cell will contain the same atoms in previous quantities, since the structure is periodic. The unit cell is such a minimal period in three dimensions.

The unit cells used in crystallography have the form of parallelepipeds, their shape and size are determined by setting three non-coplanar translations (vectors) of the lattice, that is, three edges of the cell not lying in the same plane. The cell fully defines the grid. The converse is not true: in the same lattice, cell selection can be made differently.

The cell built on the three shortest non-coplanar translations of the lattice is called the main cell. The volume of such a cell is minimal, it contains only one node of the crystal lattice, and therefore refers to primitive cells. Often such a cell turns out to be low symmetric, despite the fact that the symmetry of the structure itself is higher. In this case, choose another, highly symmetric cell of a larger volume, with additional lattice nodes (non-primitive, or centered cell).

Using X-ray diffraction analysis, the unit cell sizes of the mineral, its syngony, type of symmetry and spatial symmetry group are determined, and the crystal structure is also decoded.