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Below each diagram is the Pearson symbol for that Bravais lattice. Note: In the unit cell diagrams in the following table the lattice points are depicted using black circles and the unit cells are depicted using parallelograms (which may be squares or rectangles) outlined in black. Although each of the four corners of each parallelogram ...
The fourteen three-dimensional lattices, classified by lattice system, are shown above. The crystal structure consists of the same group of atoms, the basis, positioned around each and every lattice point. This group of atoms therefore repeats indefinitely in three dimensions according to the arrangement of one of the Bravais lattices.
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.
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.
In either case, there are 3 lattice points per unit cell in total and the lattice is non-primitive. The Bravais lattices in the hexagonal crystal family can also be described by rhombohedral axes. [4] The unit cell is a rhombohedron (which gives the name for the rhombohedral lattice). This is a unit cell with parameters a = b = c; α = β = γ ...
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 rectangular lattice and rhombic lattice (or centered rectangular lattice) constitute two of the five two-dimensional Bravais lattice types. [1] The symmetry categories of these lattices are wallpaper groups pmm and cmm respectively. The conventional translation vectors of the rectangular lattices form an angle of 90° and are of unequal ...
The Bravais lattice of the space group is determined by the lattice system together with the initial letter of its name, which for the non-rhombohedral groups is P, I, F, A or C, standing for the principal, body centered, face centered, A-face centered or C-face centered lattices. There are seven rhombohedral space groups, with initial letter R.