problens on packing in voids.how to get ratio of cations to anions by no of tetrahedral and / or octahedral voids . what happens when only fraction of voids are filled?

The lattice generally have voids which are filled by cations.
Each voids have different volumes available and considering the cations/anions as a sphere, we calculate the radius of spere that can be filled in this available sphere.
volume of octahedral voids>tetrahedral voids
Higher the radius ratio, so it needs more volume to stay and so it will choose type of void.