[pnicogen1]

So I was trying to figure out the fraction of unoccupied holes in ZnS. What confuses me is this:

For every 4 anionic packing spheres in a FCC, there are 4 octahedral holes, and 8 tetrahedral holes.

4(ZnS) : 4 Zn,4 S. I was originally thinking the 4 S-2 would assume the role of the packing spheres and the Zn would fill octahedral holes since they are larger and more chemically favorable. So the fraction would be 1.0 occupied in octahedral holes. However, this is not true. The filling of octahedral holes is not favorable in ZnS because they fill 50% of the tetrahedral holes.

For future reference/other cpds, how do I tell if a cation will fill the tetrahedral holes or the octahedral holes? I know that there is the radius ratio, but is there another pattern that I can use to determine this?

[pnicogen1]

Also I just calculated the radius ratio using the values in my textbook and came up with 0.517. This means that the cations should fill octahedral holes because of the radius ratio rules

" Cubic 0.732-1.0
Octahedral 0.414-0.732
Tetrahedral 0.255-0.414 "

I really don't understand why the Zn+2 occupies the tetrahedral holes! Please explain...:-(

[AWK]

he Zn would fill octahedral holes since they are larger and more chemically favorable.

First check ionic radii
http://en.wikipedia.org/wiki/Ionic_radius
Then all will be clear

[pnicogen1]

Lol. I mean the octahedral holes are larger than tetrahedral holes, not that Zn was larger than S.
However, the ionic radii values on wiki are different than the ones in my book. 

[AWK]

However, the ionic radii values on wiki are different than the ones in my book.

May be, a few percent.
Wikipedia usually gives quite correct numbers.
Compare with webelements.com