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Q.

In face centred cubic (fcc) crystal lattice, edge length is 400 pm. Find the diameter (in pm) of greatest sphere which can be fit into the interstitial void without distortion of lattice.

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answer is 117.2.

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Detailed Solution

For a face centered cubic crystal
$a \sqrt{2} = 4 r$
$\begin{array}{l} r = \frac{\sqrt{2}}{4} a = \frac{a}{2 \sqrt{2}} \\ = \frac{400 \times \sqrt{2}}{4} = 100 \times 1 .414 = 141 .4 pm \end{array}$
For an octahedral void a = 2(r+R)
Diameter of sphere = 2R = a–2r=400–2×14
Diameter = 2R = 400 – 282.8 =117.2 pm

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