Crystal Density

The crystal lattice structure of a material allows us to determine how many molecules exist in its unit cell. With this information, alongside the unit-cell parameters - three distance parameters (a, b, c) and three angular parameters (α, β, γ).

Density (ρ) = (Z × M) / (a × b × c × N_A)

where:

• Z is the number of formula units per unit cell
• M is the molar mass of the substance
• a, b, and c are the edge lengths of the unit cell
• N_A is Avogadro’s number

For a simple cubic lattice, atoms are located only at the 8 corners of the cube. Each corner atom is shared by 8 neighboring unit cells, so each contributes 1/8 to a single unit cell.

Z = 8 × (1/8) = 1

For a body-centered cubic lattice, 8 atoms are located at the corners, and 1 atom is present at the center of the cube. Each corner atom is shared by 8 neighboring unit cells, so each atom at the corner contributes 1/8 to a single unit cell. The center atom belongs entirely to the unit cell. So,

Z = (8 × 1/8) + 1 = 2

For a face-centered cubic lattice, 8 atoms are located at the corners, and 6 atoms are present on the faces of the cube. Each corner atom is shared by 8 neighboring unit cells, so each atom at the corner contributes 1/8 to a single unit cell. The atoms at the center of the faces contribute ½ to a single unit cell. So,

Z = (8 × 1/8) + (6 × ½) = 4

The density of solids is expressed in grams per milliliter (g/mL) or grams per cubic centimeter (g/cm³), since 1 milliliter equals 1 cubic centimeter.