Find out of 1st,2nd and 3rd coordination number for an atom located at the corner in a simple cubic unit cell

Explanation

Let the desired atoms is A
(i)1st C.N.
1st nearest neighbours are at a distance a (edge length ) from point A.So, 1st C.N.=6

(ii)2nd C.N.
2nd nearest neighbours are at a distance `asqrt2` from point A, as shown . For one plane (let X-Y) `2nd` nearest neighbrous =4

For three planes (XY,YZ and ZX), 2nd C.N. =12
(iii)3rd C.N. :
3rd nearest neighbours are at a distance `asqrt3` from point A , i.e., at the other end of body diagonals (as shown ) .

A is contributed in eight cubes . So, 3rd C.N.=8