Crystal lattice
Introduction
A crystal lattice is a periodic arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter. The smallest area of the lattice that repeats is the unit cell.
Lattice Systems
In crystallography, the terms crystal system, crystal family, and lattice system each refer to one of several classes of space groups, lattices, point groups, or crystals. Informally, two crystals are in the same crystal system if they have similar symmetries, although there are many exceptions to this.
Crystal systems, crystal families, and lattice systems are similar but slightly different, and there is widespread confusion between them: in particular the trigonal crystal system is often confused with the rhombohedral lattice system, and the term "crystal system" is sometimes used to mean "lattice system" or "crystal family".
Bravais Lattices
In geometry and crystallography, a Bravais lattice, named after Auguste Bravais, is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by:
Photograph of a 3D model of a Bravais lattice.
- An integer number of translations along three in-plane lattice vectors.
- An integer number of translations normal to the plane.
In all, there are 14 possible types of Bravais lattice that fill three-dimensional space.
Lattice Parameters
The lattice parameters are the lengths of the cell edges (a, b, and c) and the angles between them (α, β, and γ). The lattice constants, or lattice parameters, refer to the constant distances between unit cells in a crystal lattice. Lattices in three dimensions generally have three lattice constants, referred to as a, b, and c. However, in the special case of cubic crystal structures, all of the constants are equal and we only refer to a.
Lattice Structures in Materials Science
In materials science, a crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter.