Coordination Number relating to Atom Size - Why?

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SUMMARY

The Coordination Number (CN) directly influences the size of an atom, with a higher CN indicating a larger atomic volume. For instance, an atom with a CN of 12 occupies more space than one with a CN of 8 or 4. This relationship is not primarily due to quantum mechanical orbital bonding but rather the geometric arrangement of surrounding atoms. Smaller central atoms result in a lower CN, as demonstrated by the analogy of fitting surrounding atoms around a central atom of fixed radius.

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Apoapsis
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Hi everyone.

Could anyone please explain to me why the Coordination Number (number of nearest neighbors - also called bulk coordination number I think) influences the size of an atom. So if a particular atom has a CN of 12 it will occupy more volume than the same atom with a CN of 8 or 4.

Is this something to do with the quantum mechanical orbital bonding? Could it possibly be something how the electron cloud 'stretches out', so to speak, to 'reach' the neighboring atoms? I have searched and I can't find anything which explains this.

Thanks in advance.:redface:
 
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Yes, and no...but mostly no. You don't need to have to think about electronic orbitals to understand why a bigger atom (in a given lattice) will have a larger co-ordination number. For the sake of simplicity and illustrative ability, throw away the lattice and ask yourself how many atoms of unit radius you can stick onto the surface of an atom of radius, say 100 units. Well, it's going to be large (~104 atoms). Next, how many atoms can you stick onto the surface of a unit atom. It's certainly not so large anymore (perhaps no more than 12 atoms).

Moral: The smaller the central atom (with fixed radius of surrounding atoms), the smaller is the CN.
 

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