InorganicVII

Chapters / Chapter 1 · Solid state / Topic 4 of 14

Atoms per unit cell: SC, BCC, FCC

Chapter 1 · Solid state and crystal structures

corners: 8 x 1/8 = 1total = 1 atomSimple cubic (primitive)
Simple cubic: one atom per cell. The cube is a schematic; atoms are drawn as points, not to scale.

In a simple or primitive cubic lattice the atoms are present at all eight corners of the unit cell. Each corner is shared by eight adjacent cubic cells, so each corner contributes 1/8 of an atom.

8 corners × 1/8 = 1 atom per unit cell
corners: 8 x 1/8 = 1centre: 1 (unshared)total = 2 atomsBody-centred cubic
Body-centred cubic: the centre atom belongs entirely to this cell.

In a body-centred cubic lattice the atoms are at all the corners and at the centre of the unit cell. The centre atom is not shared by any other cell.

8 × 1/8 + 1 = 2 atoms per unit cell
corners: 8 x 1/8 = 1faces: 6 x 1/2 = 3total = 4 atomsFace-centred cubic
Face-centred cubic: 14 lattice points in the drawing, 4 atoms per cell after sharing is counted.

In a face-centred cubic lattice the atoms are at all eight corners and at the centre of each face. There is no atom at the centre of the cube. Each face-centre atom is shared by two adjacent cells, so it contributes 1/2.

Corners: 8 × 1/8 = 1
Faces: 6 × 1/2 = 3
Total = 4 atoms per unit cell