In fluorite ($\ce{CaF2}$), the coordination number of $\ce{Ca}$ is $8$, and that of $\ce{F}$ is $4$. Is there any logic behind the ratio of coordination numbers being the same as the stoichiometry of the ions?

  • $\begingroup$ I think it isn't a coincidence that the ratio of cations to anions is 1:2, and the coordination is 8:4. You can have other $\ce{AB2}$ structures, like rutile where the coordination is 6:3. Also, please improve your grammar. $\endgroup$ Oct 28, 2015 at 22:47
  • $\begingroup$ You didn't explained why that happens? $\endgroup$ Oct 28, 2015 at 22:49
  • $\begingroup$ You can, to some extent, rationalise it by looking at the unit cell. For a highly regular structure like that of fluorite, if you reduce the coordination number of Ca to 7, for example, then the ratio of Ca:F will no longer be 1:2. However, I do admit that that is not quite the best "proof". $\endgroup$ Oct 28, 2015 at 23:00
  • $\begingroup$ I just want to know why the ratio of coordination numbers is same as that of ratio of stoichiometric coefficients $\endgroup$ Oct 28, 2015 at 23:02
  • $\begingroup$ Is explanation related to the formula of compound $\endgroup$ Oct 28, 2015 at 23:03

1 Answer 1


Surely there is a logic behind that, and a pretty simple one. Let's take a crystal and count all $\ce{Ca}$ atoms in it. We'll get some huge number N (possibly about as huge as $N_A$). Now how many fluorine atoms are there? Each $\ce F$ is a neighbor of some $\ce{Ca}$, so if we just count all neighbors of all $\ce{Ca}$, we won't miss anything... and will end up with 8N. But wait, each $\ce F$ is a neighbor of four $\ce{Ca}$, so it was counted 4 times! We divide by 4 to compensate for that and happily arrive at 2N, which is consistent with the formula $\ce{CaF2}$.

So yes, it is no coincidence that the ratio of coordination numbers is also the ratio of stoichiometric coefficients.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.