The packing efficiency of a simple cubic crystal, when biggest void(s) is/are filled with interstitial atoms of appropriate size without causing any distortion, is approximately
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The packing efficiency of a simple cubic crystal is 0.7285
Explanation:
From question, the crystal is simple cube.
∴ a = 2r
Radius of the interstitial atom exactly fitting at the center of the cube:
R = 1/2 × (a√3 - 2r)
R = 1/2 × (a√3 - a)
∴ R = 0.366a
The packing fraction is given by the formula:
Packing fraction = (Volume occupied by sphere)/a³
On substituting the values, we get,
Packing fraction = ((1/8 × 8 × (4πr³)/3) + (1 × (4πR³)/3))/a³
Packing fraction = ((4π × (a/3)³) + (0.366 × a)³)/3a³
∴ Packing fraction = 0.7285
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