Cubic crystal system

The cubic crystal system is one of the seven crystal systems in crystallography. It includes all the point groups, each of which has a threefold rotational axis of rotary inversion, or in four different directions. These four threefold axes in cubic crystals along the four body diagonals of the unit cell, the shape of a cube. Falsely also fourfold rotation axis are given as a property of the cubic crystal system. But this does not, in general, since there are cubic point groups that do not have four-fold symmetry.

Point groups

The cubic crystal system includes point groups. They form the cubic crystal family and can be described by the cubic lattice system.

Grid system

The cubic lattice system has the holohedry. There is only one way to do that in a lattice different threefold axes can exist: the space diagonals of a cube. Therefore, the cubic lattice has three right angles and three equal axes. Thus, there are the following conditions:

Even if the axes are the same length, so they are not always equivalent! The report is prepared in general accordance with the standard prescribed in the International Tables for Crystallography. The cubic lattice system with c (s: cubic ) abbreviated.

Bravais lattice

Cubic centered symmetry: cI

Face-centered cubic lattice: cF

In the cubic there are three Bravais lattices which are in the literature often referred to by its acronym: the primitive (sc for simple cubic ), the body-centered or body-centered ( bcc or bcc for body centered cubic ) and the face-centered cubic (fcc for face centered cubic ) lattice.

Comments regarding the use of the concept lattice

The crystal structure is described by a grid, and a base. The grid (also space lattice or translation lattice period) is the set of all translation vectors, which carry a crystal into itself. The position of the atoms described by the base. Crystalline structures which not only have the same crystal lattice, but in which the same materials are also ( but with different atoms) taken form a structure type. Outside of the literature, this difference between lattice and structure type is not always observed. In the event that there is only one atom in the unit cell, which is on the position ( 0,0,0), one also speaks of a primitive cubic (or body-centered or face-centered ) grid as a structure type. Contains the base more atoms, one also speaks of interpenetrating cubic lattices.

While this use of the term is still reasonable, so there is, in particular the Internet, including terms and related ideas that are definitely wrong.

• The points which are used to represent Bravais lattices, do not represent atoms dar. There are types of structure for which there is no atom at the origin of the grid. ( The best-known type of structure with this property is the hexagonal close -packed ( hcp ) )
• There are no cubic primitive ( - body-centered or face-centered ) crystal systems. The concept of centering refers solely and alone on a grid.
• The terms hcp (hexagonal closed packed ) and ccp ( cubic closed packed ) stand for sphere packings. These correspond to structural types. The information on coordination numbers and packing density also refer only to these types of structures. However, no grid. In particular, fcc is not the same ccp! There are many other structures that have a face-centered cubic lattice. Is only right that the cubic close packing can be described as having a face-centered cubic lattice.

Representation by primitive lattice

The body-centered cubic lattice also may be described by a primitive (but non- cubic ) lattice. The relationship between the primitive and a non- primitive lattice vectors is summarized in the following table. In each case, the lattice constant and are not necessarily the length of the vector. The formula for the calculation can be found in the article to the reciprocal lattice

The reciprocal lattice of a sc lattice is thus again a sc lattice. The reciprocal lattice of a fcc - lattice is a bcc lattice and vice versa.

Description and physical properties of the cubic point groups

For a description of the cubic crystal classes in Hermann- Mauguin symbolism symmetry operations with respect to a given direction ( viewing directions ) are given in the grid system. The sight of the first symbol is the a- axis (<100 > ), the second symbol, the space diagonal (< 111> ) and the third symbol, the face diagonal ( <110 > ).

Characteristic of the cubic space groups is a three ( 3) on the second point of the space group symbol.

For information on the physical properties "-" means prohibited and " " allowed by symmetry. About the magnitude of the effect can be made due to the symmetry no statement, but one can assume that this effect is never exactly disappear.

More cubic crystalline, chemical substances, see Category: Cubic crystal system