Which of the following statements is(are) correct for the diamond structure?

Options

A. Each atom has `4` nearest neighbours and `12` next nearest neighbours.
B. It is relatively empty.
C. The maximum proportion of the available volume which may be filled by hard spheres is only `0.34`.
D. The maximum proportion of the available volume which may be filled by hard sphere is only `0.46`.

Answer

A, B, C

Explanation

`(a, b, c)`
Atom (carbon) laying in the tetrahedral voids touches the surrounding `4` atoms at a distance of `sqrt3a//4`, and the face centre atom has `12` next nearest neighbours at a distance of `a//sqrt2`.
For `PF`,
The packing fraction `(PF) = (8 xx (4)/(3)piR^(3))/(a^(3))`
Where `2R = (sqrt3a)/(4) implies (R)/(a) = (sqrt3)/(8)`
Hence, `PF` is: `(32)/(3)pi ((3sqrt3)/(8 xx 64)) = (sqrt3pi)/(16) ~~ 0.34`