The Seven Crystal Systems: Overview

Crystals are classified into seven crystal systems, namely cubic, trigonal, triclinic, monoclinic, orthorhombic, tetragonal, and hexagonal systems.

The simplest of these is the cubic system, where vectors a, b, and c are equal in length and orthogonal to each other. If only two vectors share the same length, it results in a tetragonal system.

In the trigonal crystal system, also called the rhombohedral system, the three lattice vectors are of equal length but inclined at equal, non-90-degree angles.

In a triclinic lattice, the defining vectors have no specific constraints; they are unequal in length and form unequal angles.

On the other hand, a monoclinic lattice necessitates that two of the angles are 90 degrees, while the third angle is not 90 degrees.

An orthorhombic lattice has three mutually perpendicular vectors of different lengths, whereas a tetragonal lattice also has three right angles but features two vectors of equal length.

Lastly, a hexagonal lattice system has two equal‑length vectors that subtend a 120° angle in a basal plane, while the third vector is perpendicular to this plane.