## Packing Efficiency Chemistry Notes

→ As we know that the constituent particles in crystal lattice are arranged in close packing. Some spaces remain vacant in this state, which are called voids. The percentage of the total space filled by the particles is called packing efficiency or the fraction of total space filled is called packing fraction.

% Packing efficiency

Packing Eficiency in hcp or ccp or fcc Structures :

Length of edge of a unit cell = a
Volume of one sphere = $$\frac{4}{3}$$ (πr3)

∵ fcc stucture is formed from four spheres.
∴ Volume of four spheres = 4 × $$\frac{4}{3}$$ (πr3) = $$\frac{16}{3}$$ (πr3)
∆ ABC AC2 = AB2 + BC2
= a2 + a2
∴ AC = a√2 … (1)
If we see AC then the arrangement of spheres in it is as follows

Hence, the total volume occupied by spheres or particles in fec or ccp or hep structure is 74%. While the empty space i.e. volume of total voids is 26%.

Packing Efficiency in Body Centred Cubic Sturcture (bcc) :

Edge length of unit cell = a
Since bec structure forms from two spheres.
So, Volume of two spheres = 2 × $$\left(\frac{4}{3} \pi r^{3}\right)$$ = $$\frac{16}{3}$$ πr2

In ∆ABC, AC2 = AB2 + BC2
AC2 = a2 + a2
AC2 = 2a2
In ∆ACD, AD2 = AC2 + CD2

If we see AD, then the arrangement of spheres in it is as follows

On putting the value of AD in equation (i),

Hence, the total volume occupied by spheres or particles in bee structure is 68% While, the empty space i.e. volume of total voids is 32%.

Packing Efficiency in Simple Cubic Unit Cell (scc)

Volume of one sphere = $$\frac{4}{3}$$ πr3