Calculate an order parameter for a given set of atomic coordinates

Just found this: Truskett, T. M., S. Torquato, and P. G. Debenedetti. 2000. "Towards a Quantification of Disorder in Materials: Distinguishing Equilibrium and Glassy Sphere Packings." Physical Review E 62 (1): 993-1001. doi: 10.1103/PhysRevE.62.993.

Eqn 4.1 gives a crystal-independent measure of order $$ T^* = frac{ int_{rho^{1/3}sigma}^{xi_C} left | h(xi) right | dxi }{xi_C - rho^{1/3}sigma} $$

where $h(xi) = g(xi) - 1$ where $g(xi)$ is the radial distribution function, $xi=rrho^{1/3}$ where $r$ is the radial coordinate, $rho = frac N V$ is the number density, and $xi_C$ is a cutoff limited by the size of the box.

I would recommend calculating the structure factor $S(mathbf{q})$ $$ S(mathbf{q}) = frac{1}{N} left| sum_{j=1}^N exp(-i mathbf{q}cdotmathbf{r}_j) right|^2 $$ for a large number of wavevectors $mathbf{q}$ and finding the maximum value of $S$, call it $S_{text{max}}$, amongst those values, excluding $mathbf{q}=0$. Then, as explained on that Wikipedia page, $S_{text{max}}/N$ will be of order $1$ for a regular crystal, and of order $1/N$ for a disordered system, if you have $N$ atoms. The components of the wavevectors will be integer multiples of $2pi/L$ assuming a cubic box of side $L$. You only need to consider components up to $2pi/a$ where $a$ is the atomic diameter. There is no need to include atomic form factors in the calculation, since your atoms are identical.

This is similar to the experimental approach of looking for sharp peaks in the X-ray scattering pattern. If you were interested in identifying the crystal structure, the pattern of sharp peaks would help. But for your purposes, just the fact that there are sharp peaks would be enough.