latticeparametrien

Lattice parameters, also known as unit cell parameters, are constants that specify the size and shape of a crystal’s repeating unit cell. They are the three edge lengths a, b, and c, and the three interaxial angles α, β, and γ between those edges. Together they define the geometry of the lattice in a given crystal system.

These six numbers determine the unit cell volume and the arrangement of lattice points. Different crystal systems are characterized by constraints on these parameters: cubic (a=b=c and α=β=γ=90°); tetragonal (a=b≠c, α=β=γ=90°); orthorhombic (a≠b≠c, α=β=γ=90°); monoclinic (α=γ=90°, β≠90°); triclinic (α,β,γ all unequal and not 90°); hexagonal (a=b≠c, α=β=90°, γ=120°).

Unit cell parameters are determined experimentally by diffraction methods such as X-ray, electron, or neutron diffraction and refined against observed reflections. They are used to index diffraction patterns, calculate the unit cell volume, and, together with atom positions, to model the crystal structure. Lattice parameters are fundamental inputs to databases and are sensitive to temperature and pressure, varying due to thermal expansion or compression.

Practical uses include material identification, phase characterization, and determination of density (via mass per unit cell). Databases such as ICSD and Pearson’s Crystal Data store standard lattice parameters for many materials.