Crystal Structure

Atoms, ions or molecules in a crystal occupy positions with long-range periodic order. A lattice describes that repeating translational pattern; a basis identifies the particle or group attached to each lattice point. A unit cell is a repeating three-dimensional region that generates the crystal structure by translation.

Common structure descriptions include:

• simple cubic (SC),
• body-centred cubic (BCC),
• face-centred cubic (FCC), and
• hexagonal close-packed (HCP).

Simple cubic

The conventional simple-cubic cell has lattice sites at its eight corners. Each corner is shared by eight cells, so it contributes 1/8 of an atom to one cell: 8 × (1/8) = 1 atom per cell.

• Coordination number: 6.
• Nearest neighbours touch along a cube edge, so a = 2r.
• Packing fraction: π/6 ≈ 0.524, or about 52.4%.

Naturally occurring alpha-polonium is the standard elemental example of simple-cubic packing.

Body-centred cubic

A BCC cell has the same eight shared corner sites plus one whole lattice point at the body centre, giving 8 × (1/8) + 1 = 2 atoms per cell.

• Coordination number: 8.
• Nearest neighbours touch along a body diagonal, so square root of 3 a = 4r.
• Packing fraction: π square root of 3/8 ≈ 0.680, or about 68.0%.

Alpha-iron at room temperature is a familiar BCC metal. A crystal with one species at the corners and a different species at the centre, such as CsCl, is not a BCC Bravais lattice: translating by half a body diagonal exchanges unlike species. It is described by a simple-cubic Bravais lattice with a two-particle basis.

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