Gitterparametre

Gitterparametre, or lattice parameters, are the lengths and angles that define the geometry of a crystal's unit cell. They are commonly denoted a, b, c for the cell edges and α, β, γ for the angles between them. These parameters determine the size and shape of the unit cell and, together with the crystal system, describe how atoms are arranged in three-dimensional space. The unit of length is typically the ångström (Å), and angles are measured in degrees. The cell volume can be calculated from the parameters with the formula V = abc sqrt(1 - cos^2 α - cos^2 β - cos^2 γ + 2 cos α cos β cos γ).

The lattice parameters reflect the symmetry and geometry of the crystal system. In high-symmetry systems, some parameters are equal or fixed in value: for example, in cubic systems a = b = c and α = β = γ = 90°. In tetragonal systems, a = b ≠ c with α = β = γ = 90°. Orthorhombic systems have a ≠ b ≠ c and α = β = γ = 90°. Hexagonal systems have a = b ≠ c, α = β = 90°, γ = 120°. Monoclinic and triclinic systems feature more general angle relationships, with monoclinic typically having α = γ = 90° and β ≠ 90°, and triclinic having all angles and lengths independent of each other. The rhombohedral (trigonal) system is characterized by a = b = c with α = β = γ ≠ 90° in its common description.

Measuring and refining lattice parameters is central to crystallography. They are determined from X-ray diffraction (XRD), neutron diffraction, or electron diffraction data, using methods such as Rietveld refinement for powders or single-crystal XRD. Temperature and pressure changes, as well as phase transitions, can alter the lattice parameters, making them essential for understanding material structure, phase stability, and properties.