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Topic: size of tetrahedral holes in bcc  (Read 22654 times)

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Offline maakii

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size of tetrahedral holes in bcc
« on: June 11, 2007, 09:53:47 AM »
Hi everyone!,

I was thinking about the relative sizes of the tetrahedral holes in bcc..but it seems that I am missing something..because I can't seem to figure out how in the world to calculate it and I can't find any websites saying how to do so. Or is my question even relevant in the first place because I don't recall any substances with bcc structure and cations filling up the tetrahedral holes. I think its probably because they are too small. and they are in the path of the octahedral holes too.

But if anyone could hint at how to calculate the size of the tetrahedral holes in bcc, I would be grateful! (;



The one on the bottom depicts what I'm trying to find out.

Offline enahs

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Re: size of tetrahedral holes in bcc
« Reply #1 on: June 11, 2007, 10:37:09 AM »
Maybe you can tell me what the acronym BCC means? I am not familiar with that form.

Offline maakii

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Re: size of tetrahedral holes in bcc
« Reply #2 on: June 11, 2007, 11:45:17 AM »
Oh sorry! Its body centered cubic (bcc), the one that has the 68% packing efficiency

Offline enahs

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Re: size of tetrahedral holes in bcc
« Reply #3 on: June 11, 2007, 06:31:48 PM »
That is what I thought you meant. But I am confused, maybe I misunderstand what you are asking then? But the tetrahedral holes do not come from a single unit, but when you look at how they pack, such as in ccp (cubic closed pack) and hcp (hexagonal close-pack) array?


Offline maakii

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Re: size of tetrahedral holes in bcc
« Reply #4 on: June 11, 2007, 09:08:21 PM »
Yup, the holes only arise when the larger anions are packed together in any style, however, this does not mean that they cannot be represented in a unit cell, for the holes are spaced at regular intervals too right?

As you can see in the second picture, all the white small circles represent the tetrahedral holes in the body centered arrangement, as they are formed by 4 main "spheres" arranged around it in a tetrahedral fashion, as represented by the bold black lines.

In the case of bcc, the octahedral holes would be right smack in the middle of the 4 tetrahedral holes lying on the top face, or at least that's how I see it..(octahedral hole created by the 4 corner "spheres" on the top face, and the 2 spheres on top and below it)

Hope I cleared up some confusion!

Offline AWK

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Offline maakii

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Re: size of tetrahedral holes in bcc
« Reply #6 on: June 13, 2007, 11:26:53 PM »
Hmm, thanks for the links! Although those were also talking about closest packed structures, but not about body centered stuctures, I think that holes in body centered structures are only important if they are octahedral ones, since those are already so small!

Offline AWK

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Re: size of tetrahedral holes in bcc
« Reply #7 on: June 14, 2007, 01:30:12 AM »
In every case a tetrahedral hole is defined as a radius of sphere that can be placed in the hole. If you can describe a tetrahedron (not necessarily regular one) and know radii of spheres at vertices, you can calculate this radius for the hole. My examples showed an ideal case.
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Offline maakii

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Re: size of tetrahedral holes in bcc
« Reply #8 on: June 14, 2007, 02:43:10 AM »
The problem is that I can't visualize what the atom in the tetrahedral hole will be touching..I have a feeling that it will be touching the 2 atoms on the edge of the unit cell, therefore I am able to construct a triangle with sides (r+x), (r+x) and a third side of unit cell length (4r/30.5), however, I do not have any angles to work with..so it is perplexing for me.

Offline AWK

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Re: size of tetrahedral holes in bcc
« Reply #9 on: June 14, 2007, 06:38:47 AM »
Term bcc means - body centered cubic.
Body centered unit cells appear in orthorhombic, tetragonal and cubic cells
In orthorhombic body centered unit cell (in standard setting b>a>c) we have  edges of the following length:
b, a and 4 times 1/2xSQRT(a2+b2+c2) with center of a hole in 1/4a, 1/2b (and other permutations (1/2, 1/4) - these numbers are an approximation) and 0
In tetragonal body centered unit cell we have  edges of the following length:
a, a and 4 times 1/2xSQRT(a2+a2+c2) with center of a hole in 1/4a, 1/2a (and other permutations (1/2, 1/4)- exact numbers) and 0.
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