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Offline Rutherford

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Hexagonal package
« on: June 23, 2012, 12:14:45 PM »
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).

Offline AWK

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Re: Hexagonal package
« Reply #1 on: June 23, 2012, 03:49:36 PM »
AWK

Offline cheese (MSW)

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Re: Hexagonal package
« Reply #2 on: June 23, 2012, 07:55:51 PM »
In N close packed spheres (ccp, hcp) there are 2N tetrahedral interstices (holes!) and N octahedral interstices.
Good luck!   :D

Offline Rutherford

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Re: Hexagonal package
« Reply #3 on: June 24, 2012, 04:43:52 AM »
How so?

Offline cheese (MSW)

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Re: Hexagonal package
« Reply #4 on: June 26, 2012, 08:47:13 PM »
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.

Offline Rutherford

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Re: Hexagonal package
« Reply #5 on: June 27, 2012, 04:33:56 AM »
But how can you see that from the picture?

Offline AWK

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Re: Hexagonal package
« Reply #6 on: June 27, 2012, 04:57:57 AM »
You need good: picture and spatial imagination.
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Offline Rutherford

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Re: Hexagonal package
« Reply #7 on: June 27, 2012, 05:13:19 AM »
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.

Offline cheese (MSW)

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Re: Hexagonal package
« Reply #8 on: June 27, 2012, 10:30:40 AM »
And it is easier to see with 3D models!
Incidentally it is hexagonal packing.

Offline Rutherford

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Re: Hexagonal package
« Reply #9 on: June 28, 2012, 06:52:30 AM »
Found this http://www.chemtube3d.com/solidstate/_hcp%28final%29.htm but it isn't helping me  :( .

Offline AWK

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Re: Hexagonal package
« Reply #10 on: June 28, 2012, 09:29:51 AM »
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.
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Offline Rutherford

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Re: Hexagonal package
« Reply #11 on: June 28, 2012, 10:14:38 AM »
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.

Offline AWK

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Re: Hexagonal package
« Reply #12 on: June 29, 2012, 01:06:33 AM »
Quote
A Co oxide cristallizes so that in the hexagonal closed package of oxide anions

!
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Offline Rutherford

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Re: Hexagonal package
« Reply #13 on: June 29, 2012, 05:47:32 AM »
Oxide, right  :-[ .

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