Surface density diamond structure [1 1 1]

[Ulumab]

Homework Statement

Calculate the surface density (planar density) of the Silicon diamond structure in the [1 0 0],[1 1 0],[1 1 1] planes.
Given a = 5.431 A (latice constant)

Hint: For the (111) plane, it should help you to think of the diamond lattice as two interpenetrating FCC lattices.2. The attempt at a solution
I managed to solve [1 0 0] and [1 1 0](2/a^2 and 4/sqrt(2)*a^2) I have also got a result for [1 1 1](2/(sqrt(3)/2*a^2)) but I completely ignored the hint in the description.

 

[ehild]

2. The attempt at a solution
I managed to solve [1 0 0] and [1 1 0](2/a^2 and 4/sqrt(2)*a^2) I have also got a result for [1 1 1](2/(sqrt(3)/2*a^2)) but I completely ignored the hint in the description.

The hint helps to imagine the diamond structure. You do not need it if you know how it looks like.