**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 = 4/3pr^{3}

Volume of cube = a^{3} = (2r)^{3} = 8r^{3}

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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