In face centred cubic (fcc) crystal lattice, edge length is 400 pm. Find the diameter of greatest sp

Question

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

Professor PC Thomas Classes · Answer

In fcc, the largest void is the octahedral void. Radius of lattice sphere $r = \frac{a}{2\sqrt{2}} = 141.42~pm$. For octahedral void, $R = 0.414r = 0.414 	imes 141.42 = 58.55~pm$. Diameter $= 2R = 117.1~pm$. Alternatively, using exact geometry: $2(R+r) = a \Rightarrow 2R = 400 - 282.84 = 117.16~pm$.