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### Topic: Hexagonal package  (Read 4757 times)

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#### 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).

#### AWK

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

#### 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!

#### Rutherford

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

#### 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.

#### 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?

#### 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.
AWK

#### 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.

#### 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.

#### 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  .

#### 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.
AWK

#### 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.

#### 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

!
AWK

#### Rutherford

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