A crystal is built from a small unit that repeats in every direction, called the unit cell. The unit cell of sodium chloride is a cube with edges 564 pm long.
Along each edge of the cube, sodium ions and chloride ions alternate. The chloride ions sit at the corners and at the centres of the faces, so on their own they form a face-centred cubic lattice, and the sodium ions fill the gaps between them.
Each ion is surrounded by ions of the opposite charge, and no two ions of the same charge touch. This pattern continues through the whole crystal.
An ion on a corner of the unit cell is shared by 8 cells, one on a face by 2 and one on an edge by 4, so only 1/8, 1/2 and 1/4 of each belongs to the cell. An ion at the centre is not shared.
The chloride ions sit on the 8 corners and the 6 faces: 8 × 1/8 + 6 × 1/2 = 4. The sodium ions sit on the 12 edges and at the centre: 12 × 1/4 + 1 = 4.
A unit cell therefore holds 4 sodium ions and 4 chloride ions. Their ratio, 1 : 1, matches the formula \mathrm{NaCl}.
In caesium chloride, \mathrm{CsCl}, the unit cell is a cube with a chloride ion at each corner and a caesium ion at the centre. The edge of the cube is 412 pm long.
The cell holds 8 × 1/8 = 1 chloride ion and 1 caesium ion, again in the ratio 1 : 1.
The arrangement looks like a body-centred cubic lattice, but it is not one, because the ion at the centre differs from the ions at the corners. It is made of two simple cubic lattices, one of each ion, fitted inside each other.
The number of oppositely charged ions touching an ion is called its coordination number. In sodium chloride, each ion is surrounded by 6 ions of the other kind, at the corners of an octahedron.
In caesium chloride, each ion is surrounded by 8 ions of the other kind, at the corners of a cube.
The difference comes from the sizes of the ions. A caesium ion (174 pm) is much larger than a sodium ion (102 pm), so more chloride ions (181 pm) fit around it.
Ions of opposite charge touch, so the edge of a unit cell, a, can be worked out from the ionic radii, r_+ for the cation and r_- for the anion.
In sodium chloride, the ions touch along each edge, so a = 2(r_+ + r_-). With r_+ = 102 pm and r_- = 181 pm, a comes to 566 pm, close to the measured 564 pm.
In caesium chloride, the ions touch along the body diagonal, which is \sqrt{3} times the edge, so \sqrt{3}a = 2(r_+ + r_-). With r_+ = 174 pm and r_- = 181 pm, a comes to 410 pm, close to the measured 412 pm.