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Types of Unit Cell

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Question

In face-centered cubic (fcc) crystal lattice, the edge length of the unit cell is $400 p m$ . Find the diameter of the greatest sphere which can be fitted into the interstitial void without distortion of the lattice.

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Solution

In fcc unit cell,

$a \sqrt{2} = 4 r$

$r = \frac{a \sqrt{2}}{4} = \frac{400 \times \sqrt{2}}{4} = 141.4 p m$

For octahedral void,

$2 (r + R) = a$

$2 R = a - 2 r = 400 - 2 \times 141.4 = 117.16 p m$

Diameter of greatest sphere $= 117.16 p m$

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