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The seven lattice systems and their Bravais lattices in three dimensions. In geometry and crystallography, a Bravais lattice, named after Auguste Bravais (), [1] is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by
The following table gives the crystalline structure of the most thermodynamically stable form(s) for elements that are solid at standard temperature and pressure.Each element is shaded by a color representing its respective Bravais lattice, except that all orthorhombic lattices are grouped together.
Figure 1 – The HCP lattice (left) and the FCC lattice (right). The outline of each respective Bravais lattice is shown in red. The letters indicate which layers are the same. There are two "A" layers in the HCP matrix, where all the spheres are in the same position. All three layers in the FCC stack are different.
The letters A, B and C were formerly used instead of S. When the centred face cuts the X axis, the Bravais lattice is called A-centred. In analogy, when the centred face cuts the Y or Z axis, we have B- or C-centring respectively. [5] The fourteen possible Bravais lattices are identified by the first two letters:
A lattice system is a set of Bravais lattices (an infinite array of discrete points). Space groups (symmetry groups of a configuration in space) are classified into crystal systems according to their point groups, and into lattice systems according to their Bravais lattices.
The degree of translation is then added as a subscript showing how far along the axis the translation is, as a portion of the parallel lattice vector. For example, 2 1 is a 180° (twofold) rotation followed by a translation of 1 / 2 of the lattice vector. 3 1 is a 120° (threefold) rotation followed by a translation of 1 / 3 of ...
Shown above are examples of the hexagonal polytypes 2H, 4H and 6H as they would be written in the Ramsdell notation where the number indicates the layer and the letter indicates the Bravais lattice. [4] The 2H-SiC structure is equivalent to that of wurtzite and is composed of only elements A and B stacked as ABABAB. The 4H-SiC unit cell is two ...
The black-white Bravais lattices characterize the translational symmetry of the structure like the typical Bravais lattices, but also contain additional symmetry elements. For black-white Bravais lattices, the number of black and white sites is always equal. [ 24 ]