Calculation of Density

Once the number of atoms per unit cell (n) and the edge length (a) of a cubic unit cell are known, the crystal's density follows directly from the basic definition of density as mass over volume, applied to a single unit cell:

The mass of the unit cell is the number of atoms belonging to that cell (n) multiplied by the mass of one atom. Since the mass of one atom equals the molar mass M divided by Avogadro's number NA (mass of one atom = M/NA):

For a cubic unit cell, all three edge lengths are equal (a = b = c), so the volume of the unit cell is simply:

Substituting (2) and (3) into (1) gives the working formula used throughout this unit:

This equation links four quantities -- density (rho), atoms per cell (n), molar mass (M) and edge length (a) -- so that if any three of the four are known, the fourth can always be calculated. …