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My book under the heading of Anti-fluorite structure makes the following remark, about the radius ratio of an ideal Anti-fluorite:

The ideal antifluorite would have a cation-to-anion radius ratio of $0.228$. However, the ideal ratio is not observed in the antifluorite structure, the observed ratio is higher than the ideal.

I do not understand why the ideal radius ratio should be $0.228$. It is clear that since the antifluorite structure has the smaller ion filled into the tetrahedral voids, radius ratio can range from $0.225-0.414$, with $0.225$ being the best fit for this type of void. It is however unclear as to why there is a difference in the ideal radius ratio for antifluorite structure and for the best fit of the tetrahedral void. It would be great if this is clarified. Thanks.

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