Relation between Lattice Mass and Mass Density of a Cubic Crystal

Here we have to find relationship between lattice constant and mass density for this consider cubic crystal whose unit cell having side a (lattice parameter)

Let ρ be the density of crystal such that

Density (ρ) = mass/volume

Volume of cubic crystal = a³

Let M be the molecular weight of given material, that means M-grams of material having molecules equal to Avogadro’s number (N = 6.022 ×10 ²³).

If there are n molecules per unit cell then weight of n molecules is Mn/N

From above, equation (1) becomes

This is relation between lattice parameter (a) and mass density (ρ).

Volume of unit cell-

a³  =  Mn/Nρ

Number of atoms per unit volume (number density /atomic density/atomic concentration) given as-

n/a³ =  nρ/M

Where,

For SC      n=1

For BCC    n=2

For FCC     n=3

 

Example 1.Calculate the lattice parameter of NaCl crystal has FCC structure from following data

Molecular weight of NaCl=59.45

Density of NaCl= 2170 kg/m ³

Avogadro number (N = 6.023×10 ²³)

For FCC,  n=4-

 

Therefore lattice parameter is  –

Problems for practice: