Question

An element crystallises in a face-centred cubic (fcc) unit cell with cell edge $a$. The distance between the centres of two nearest octahedral voids in the crystal lattice is:

Answer 1

In fcc octahedral voids are present on edge centres and body centre.


Minimum distance between two octahedral voids $\left(x\right)$:


On applying Pythagoras theorem
$x=\sqrt{{\left(\frac{a}{2}\right)}^2+{\left(\frac{a}{2}\right)}^2}$

$x=\sqrt{2}\frac{a}{2}$

$x=\frac{a}{\sqrt{2}}$