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: