[Rutherford]

A Co oxide cristallizes so that in the hexagonal closed package of oxide anions, Co ions occupy 1/8 of tetrahedral and 1/2 of octahedral interstices. What is the formula of the oxide?
Here is the picture of the package:
http://imageshack.us/photo/my-images/152/viewermu.png/

I didn't have a clue how to start so I saw the answer and there is written that: on 1 oxide anion come 2 tetrahedral (2*1/8=1/4) and 1 octahedral (1/2) interstices. Number of Co ions on 1 oxide anion is 3/4 so it is Co₃O₄.
Now, I am confused. If the red circles are the oxide anions, then they occupy 1T and 3O interstices (only halves of every O interstices).

[AWK]

http://shailendrakrchemistry.files.wordpress.com/2009/12/solid-state-obj.pdf

compare point 24

[cheese (MSW)]

In N close packed spheres (ccp, hcp) there are 2N tetrahedral interstices (holes!) and N octahedral interstices.
Good luck!   

[Rutherford]

How so?

[cheese (MSW)]

O atoms = N
Tetrahedral = ⅛ × 2N (Co^2+)
Octahedral = ½ × N (Co^3+)
X through by 4/N Voilà!
It has what is called a spinel structure.

[Rutherford]

But how can you see that from the picture?

[AWK]

You need good: picture and spatial imagination.

[Rutherford]

Then I will have to remember that:

In N close packed spheres (ccp, hcp) there are 2N tetrahedral interstices (holes!) and N octahedral interstices.

Thanks you two for the help.

[cheese (MSW)]

And it is easier to see with 3D models!
Incidentally it is hexagonal packing.

[Rutherford]

Found this http://www.chemtube3d.com/solidstate/_hcp%28final%29.htm but it isn't helping me  .

[AWK]

Could you do such calculations for cubic close packed cell. The result is exactly the same since this is close packed structures with the same efficiency. Moreover, knowing rules given you by Cheese you can do just simple algebra instead of spatial imaginations.

[Rutherford]

If it is so hard, then I will just remember that on 1 oxygen anion come 2 Tet. and 1 Oct. holes. Thanks again for helping.

[AWK]

A Co oxide cristallizes so that in the hexagonal closed package of oxide anions

!

[Rutherford]

Oxide, right  .