Kristallsystemens

Kristallsystemens (the crystal systems) are a classification framework in crystallography that describes the geometry and symmetry of a crystal's repeating unit, the unit cell. They are defined by the relative lengths of the cell edges a, b, c and the interaxial angles α, β, γ.

There are seven crystal systems: cubic, tetragonal, orthorhombic, hexagonal, trigonal (rhombohedral), monoclinic, and triclinic. Each system imposes characteristic constraints on a, b, c and α, β, γ: cubic a=b=c and α=β=γ=90°; tetragonal a=b≠c and α=β=γ=90°; orthorhombic a≠b≠c and α=β=γ=90°; hexagonal a=b≠c with α=β=90°, γ=120°; trigonal (rhombohedral) a=b=c with α=β=γ ≠ 90°; monoclinic a≠b≠c with α=γ=90°, β ≠ 90°; triclinic a≠b≠c with α, β, γ all different and none equal to 90°.

These geometric distinctions underlie the 14 Bravais lattices when lattice centering is included (primitive, body-centered, face-centered, etc.), distributed among the crystal systems. The crystal system provides the framework for describing crystal symmetry, while space groups refine this with the full set of symmetry operations.

In practice, crystal systems help mineralogy, solid-state chemistry, and materials science classify crystals, predict properties such as cleavage planes and diffraction patterns, and guide structure determination through X-ray and neutron diffraction.