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=a−2r
2R=400−(2×141.42)=117.16
Hence, the diameter of greatest sphere is 117.16 pm.