Packing Efficiency in CCP and HCP Structures
The packing efficiencies in both types of structures(CCP and HCP) are equally good as in both, atoms or spheres occupy equal fraction (74%) of the available volume.
Now, We calculate the packing efficiency in CCP structure.
Let the unit cell length be 'a' and face diagonal be 'b' as shown in figure.
In triangle ABC, ∠ABC is 90°
therefore, AC2 = b2 = BC2 + AB2
or, b2 = a2 + a2 = 2a2
or, b = √2 a
If 'r' is the radius of the sphere, then-
b = 4r = √2 a
or, a = 4r/√2 = 2√2 r
r = a/2√2
As CCP structure has 4 atoms per unit cell, therefore the total volume of 4 spheres (v) is
v = 4 × 4/3 πr3
Total volume of the unit cell (V) = a3 = (2√2r)3
Now packing efficiency = (v/V) × 100
= 4 × 4/3 × πr3/(2√2r)3] × 100
= [16/3 × πr3/16 × (√2r)3] × 100
= [π/3√2] × 100 = 74%
Therefore, 74% of unit cell is occupied by atoms and the rest 26% is empty space.
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