Coordination Number relating to Atom Size - Why?

[Apoapsis]

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.

 

[Gokul43201]

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.

 

[charng]

The coordination number of an atom refers to the number of atoms that are directly bonded to it in a crystal lattice structure. This number can vary depending on the type of crystal structure and the type of bonding present.

The coordination number can influence the size of an atom because it affects the distance between neighboring atoms. In a crystal lattice, atoms are arranged in a repeating pattern, and the distance between atoms is determined by the strength of the bonds between them. When the coordination number is high, meaning there are more neighboring atoms bonded to the central atom, the distance between atoms is shorter. This results in a smaller atomic size.

On the other hand, when the coordination number is low, the distance between atoms is longer, resulting in a larger atomic size. This is due to the fact that fewer neighboring atoms are bonded to the central atom, allowing for more space between them.

This relationship between coordination number and atomic size is influenced by the quantum mechanical orbital bonding of the atoms. As you mentioned, the electron cloud of an atom can stretch out to reach neighboring atoms and form bonds. When there are more neighboring atoms, the electron cloud is more compact and the bonds are stronger, resulting in a smaller atomic size.

In summary, the coordination number of an atom can affect its size due to the distance between neighboring atoms and the strength of the bonds between them, which is influenced by quantum mechanical orbital bonding. I hope this helps to clarify the concept for you.