latticeparameters

Lattice parameters are the set of numerical values that define the geometry of a crystal's unit cell. In crystallography, a unit cell is the smallest repeating unit that reconstructs the entire lattice. The lattice parameters consist of three edge lengths a, b, and c, and three interaxial angles alpha, beta, and gamma between the edges (often written as a, b, c, α, β, γ). Together they determine the cell’s size and shape and thus the metric properties of the crystal.

Different crystal systems impose specific constraints on these parameters. In the triclinic system all sides and all angles are generally unequal and not 90 degrees. In monoclinic, two angles are 90 degrees while the third is not. In orthorhombic, a, b, and c are all different with all angles at 90 degrees. In tetragonal, a = b ≠ c with all angles at 90 degrees. In hexagonal, a = b ≠ c, with α = β = 90 degrees and γ = 120 degrees. The rhombohedral (trigonal) system can be described either by equal edges with equal, non-90-degree angles or by a specialized set of lattice parameters.

Measurement and use: Lattice parameters are determined from diffraction data (X-ray, neutron, or electron diffraction) and refined during structure solution. They are typically reported in angstroms for lengths and degrees for angles. Temperature and pressure can alter the parameters, so values are given for specified conditions. The term “lattice constant” is often used for a single parameter, especially in cubic systems, while “lattice parameters” refers to the full set of six values.