By D. W. Budworth and G. Arthur (Auth.)
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6), considered as a packing, consists of a simple cubic array of fluorine ions, with alternate cubic holes filled with calcium ions. As there is one cubic hole per atom (cf. caesium chloride), this ensures the correct 2:1 ratio of anions to cations, and it can be seen that the cations are themselves arranged in face-centred cubic fashion (cf. the sodium chloride structure, where alternate sites in a simple cubic array were shown to be a face-centred cubic arrangement). In fact, the fluorite structure is usually described as a face-centred cubic arrangement of calcium ions with all the tetrahedral holes filled with fluorine.
It will be remembered that the octahedral sites in a closepacked hexagonal structure form a CCC... stacking sequence of close-packed planes, and occupancy of only two thirds of the sites gives a pattern of aluminium ions in each plane which is the same as that of the carbon atoms in the layers of graphite, viz. hexagonal rings with empty centres. ) We can thus distinguish between three types of C plane of aluminium ions by the positions in which the empty places are left and, in order to ensure that each oxygen ion is correctly coordinated by four aluminium ions, these planes, which we can call Cl9 C2 and C 3 , must occur in order.
Because there is some scope for personal preference in interpretation, values given by different authors vary slightly from each other. Values can also be assigned in a similar way to the covalent radii of atoms. These values are applicable to covalently-bonded crystals and molecules. 4. EFFECT OF RADIUS RATIO ON STRUCTURE We have seen that in the sodium chloride structure, the small cations occupy octahedral interstices in a close-packed array of anions. Now the size of an octahedral hole is 0-414 that of the size of the spheres which surround it, so that to decide how good a fit the cations are we must compare this value with that of the ratio of the cation size to the anion size.