More about Crystal Structures

Note that each of the seven crystal systems that we have discussed may have several variants in terms packing of atoms inside each geometrical configuration. For example, the cubic crystal system can have three packing variations as shown below:

Simple Cube	Body Centred Cube	Face Centred Cube

Three variants of the Cubic System

The number of atoms per unit cell depends on the type of packing. For example, the unit cell of simple cubic structure contains 8x1/8 = I atom per cell, whereas the BCC contains 8x1/8 +1 = 2 atoms per unit cell and the FCC contains 8x1/8 + 6x1/2 = 4 atoms.

Knowing all these parameters you can determine the theoretical density of a material which is defined as:

Density ρ = [(number of atoms/unit cell) (atomic mass) ] / [(Volume of unit cell) (Avogadro’s Number)]

For example, Iron has BCC cells,

Hence, no. of atoms per unit cell = 2, atomic mass = 55.84 g/mol, Volume of unit cell = a³ = (2.866 e^-8)³ = 23.54 e^-24
Hence, it’s density should be (2x55.84)/(23.54e^-24)(6.02 e²³) = 7.88 g/cc