The coordination number of systems with disorder cannot be precisely defined.
The first coordination number can be defined using the radial distribution function g(r):
where r is the rightmost position starting from r = 0 whereon g(r) is approximately zero, r is the first minimum. Therefore, it is the area under the first peak of g(r).
The second coordination number is defined similarly:
Alternative definitions for the coordination number can be found in literature, but in essence the main idea is the same. One of those definition are as follows: Denoting the position of the first peak as r,
The first coordination shell is the spherical shell with radius between r and r around the central particle under investigation.