# To what extent are the radius ratio rules valid for predicting the crystal structure of an ionic compound?

The ionic radii of $\ce{Ba^2+}$ and $\ce{O^2-}$ in barium oxide are $\pu{135pm}$ and $\pu{140pm}$, respectively. The ratio of the radius of $\ce{Ba^2+}$ to $\ce{O^2-}$ is approximately $0.964$.

According to the radius ratio rules the solid barium oxide should crystallise in a body-centered cubic type structure (like $\ce{CsCl}$).

But evidently the prototype structure is $\ce{NaCl}$ type.

What is the reason for this anomaly from general trend?

EDIT: I found that every alkaline earth metal oxides (Of the type $\ce{M_{alk.e}O}$) possesses rock salt (halite) structure but only $\ce{MgO}$ obeys the radius ratio rule (it has a radius ratio of about $0.64$ which is well between $0.414$ and $0.732$).

Certainly as we are going down the group the cationic radius is going to increase and so is the radius ratio.

• The mentioned trend is but a crude generalization. – Ivan Neretin Sep 27 '17 at 15:13
• Please elaborate.... – Serotonin Sep 27 '17 at 16:13
• What's to elaborate? Tall guys play basketball, short guys play football; that's an empirical correlation. It is mostly true, but exceptions both ways are plenty. On the other hand, $(a+b)^2=a^2+2ab+b^2$; that's a law. Can it be broken? Not a chance. Well, your trend is not a law. – Ivan Neretin Sep 27 '17 at 17:17
• The reason is basically that the crystal structure was measured and found to be the NaCl structure. Now good luck finding a reason. – Jan Sep 28 '17 at 9:42
• @Serotonin Everything has a reason; it's just that you'll have to wait till someone figures out what the reason is... ;) – paracetamol Sep 29 '17 at 10:03