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Question

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

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Solution

In fcc lattice, the largest void present is octahedral void.

If the radius of void sphere is R and of lattice sphere is r, then
r=2×4004=141.42 pm

Applying condition for octahedral void

2(r+R)= edge length, a

2R=a2r

2R=400(2×141.42)=117.16

Hence, the diameter of greatest sphere is 117.16 pm.

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