This question requires research $($not discussed in class$).$

A unit cell has several interstitial voids $($or spaces or sites$).$ There are two types of interstitial voids in FCC and BCC cells, namely, octahedral and tetrahedral. However, the octahedral and tetrahedral voids in BCC are not regularly shaped but distorted.

$($a$)$ How many"distorted" octahedral and tetrahedral voids are there in a BCC cell? $(3$ marks$)$

$($b$)$ The centre of one of the tetrahedral voids in a BCC unit cell is located at $(\frac{1}{4},\frac{1}{2},0).$

$($i$)$ Name the Miller indices for the horizontal plane that passes through the centre of the void.

$($ii$)$ Calculate the radius of the largest atom that could fit in the void if the radius of the parent atom in this lattice is $0\mathrm{.}387nm.$ Use a diagram to aid in your analysis.

$(2+5$ marks$)$