Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

# Crystal systems

The rotational symmetry of a crystal places constraints on the shape of the conventional unit cell we choose to describe the structure. On this basis we divide all structures into one of 7 crystal systems. For example, for crystals with 4 fold symmetry it will always be possible to choose a unit cell that has a square base with a = b and γ = 90°: There are 14 unique combinations of the 7 crystal systems with the possible types of primitive and non-primitive lattices. These are referred to as the 14 Bravais lattices.

## Crystal systems, lattices and symmetry elements

 Crystal System Defining Symmetry Unit Cell Geometry Triclinic Translational Only a≠b≠c; α≠β≠γ Monoclinic A diad axis (parallel to ) a≠b≠c; α=γ=90°; β>90° Orthorhombic 3 diads (each should be parallel to each axis) a≠b≠c; α=β=γ=90° Trigonal For more information click here 1 triad (parallel to ) a=b≠c; α=β=90°; γ=120° ( or a=b=c; 120° > α=β=γ ≠ 90°) Hexagonal 1 hexad (parallel to ) a=b≠c; α=β=90°; γ=120° Tetragonal One tetrad (parallel to the  vector) a=b≠c; α=β=γ=90° Cubic 4 triads (all parallel to <111> directions) a=b=c; α=β=γ=90° 