# Crystal Systems

Submitted by ChemPRIME Staff on Thu, 12/16/2010 - 13:33

Unit cells need not be cubes, but they must be parallel-sided, three-dimensional figures. A general example is shown in Figure 1. Such a cell can be described in terms of the lengths of three adjacent edges, a, b, and c, and the angles between them, α, β, and γ.

Figure 1 A generalized unit cell with sides a, b, and c, and angles α, β, and γ.

Crystals are usually classified as belonging to one of seven crystal systems, depending on the shape of the unit cell. These seven systems are listed in table below.

The Seven Crystal Systems.

 Name Relationship Between Edges of Unit Cell Relationship Between Angles of Cell Cubic a = b = c α = β = γ = 90° Tetragonal a = b ≠ c α = β = γ = 90° Orthorhombic a ≠ b ≠ c α = β = γ = 90° Monoclinic a ≠ b ≠ c α = β = 90° ≠ γ Triclinic a ≠ b ≠ c α ≠ β ≠ γ ≠ 90° Rhombohedral a = b = c α = β = γ ≠ 90° Hexagonal a = b ≠ c α = β = 90; γ = 120°

The simplest is the cubic system, in which all edges of the unit cell are equal and all angles are 90°. The tetragonal and orthorhombic classes also feature rectangular cells, but the edges are not all equal. In the remaining classes some or all of the angles are not 90°. The least symmetrical is the triclinic, in which no edges are equal and no angles are equal to each other or to 90°. Special note should be made of the hexagonal system whose unit cell is shown in Figure 2. It is related to the two-dimensional cell encountered previously as the second example of a 2D crystal latticeAn orderly, repeating arrangement of points in 3-D space in which each p;oint has surroundings identical to every other point. A crystal's constituent atoms, molecules, and ions are arranged about each lattice point. structure, in that two edges of the cell equal and subtend an angle of 120°. Hexagonal crystals are quite common among simple compounds. We have already encountered three examples, namely, ice, graphite, and quartz, which are shown again in Figure 3.

Figure 2 The hexagonal unit cell a = b ≠ c, α = β = 90°, γ = 120°.