Packing efficiency:-

  • The percentage of the total space filled by the particles in the three dimensional close packing is known as the packing efficiency.

Packing fraction:-

  • The total fraction of the space filled in three dimensional close. Packing is called the packing fraction.

1. Calculation of packing efficiency in cubic unit cell (simple cubic):-

In simple cubic unit cell we have the particles present only at the corners thus

Suppose the edge length of the unit cell = a and radius of sphere = r
As sphere are touching each other evidently
=> a = 2r
No. of spheres per unit cell = 1/8 x 8 =1
Volume of sphere = 4/3pr3
Volume of cube = a3 = (2r)3 = 8r3
Packing efficiency [Fractio] = 
So packing efficiency of simple cubic unit cell is = 52.4%

2. Packing efficiency of face centred cubic structure [cubic close packing]:-

As the sphere on the face centre is touching the spheres at the corners evidently AC = 4r
But from right angled triangle ABC

Or packing efficiency = 0.74 x 100 = 74%
Thus the packing efficiency of hcp and ccp structures are 74%.

3. Calculation of packing efficiency of body contred cubic structure:-

As the sphere at the body centre touches the spheres at the corner body diagonal AD = 4r
Further face diagonal

Or packing efficiency = 0.68 x 100 = 68%
Thus the packing efficiency in BCC structure is 68%.

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