We can, as we did for metallic solids, use the concept of packing spheres to study ionic solids. We also need to consider the relative size of the oppositely charged ions and the charges of the ions to determine its structure.
Consider two layers of closely packed anions with the second layer (orange) sitting in the notches of the bottom layer (blue), forming two types of space (or holes) in between the layers (see diagram I above). As the volume of a cation is usually smaller than that of an anion, a cation can fit into either hole, depending on the relative sizes of cations and anions in the crystal. A relatively larger cation occupies an octahedral hole, while a relatively smaller cation lodges in a tetrahedral hole (diagram II), forming ionic compounds with two different arrangements. For each compound, the anion-cation-anion layered structure then repeats itself with the third layer of anions having the same arrangement as the first layer of anions.
For the ionic compound where octahedral holes are filled, each cation has six anions in its vicinity, and each anion has six cations in its vicinity. Therefore, we also call such a structure a 6-6 coordination structure. For the ionic compound where tetrahedral holes are filled, each cation has four anions in its vicinity and each anion has four cations in its vicinity. Therefore, we also call such a structure a 4-4 coordination structure.
If the cation-anion radius ratio is even larger (but still less than 1), the layer of anions must move apart to accommodate the cations (diagram III), such that both cations and anions are in the same layer with every cation in contact with four anions (diagram IV). A second layer has the anions sitting in the notches formed by the anions of the bottom layer (diagram V), with each second-layer cation again in contact with four second-layer anions. The third layer of anions are directly above those in the first layer, giving the crystal an XYXY… structure. In such a structure, each cation has eight anions in its vicinity and each anion has eight cations in its vicinity. Therefore, we also call such a structure a 8-8 coordination structure.
Having seen how cations and anions are packed in a crystal, let’s find the respective unit cells. Firstly, we depict a crystal that has a packing pattern like diagram V in the lattice form (diagram Va), and rotate it for a better view (diagram Vb). Note that some anions are coloured black for contrast.
The space lattice Vb is formed by replicating two interpenetrating cells, a cationic simple cubic unit cell (pink) and an anionic simple cubic unit cell (blue; see diagram Vc). By pairing a cation in the middle of an anionic simple cubic unit cell with one of the anions of that cell, and using that as a basis (diagram Vd), we get the unit cell of V, which is again a simple cubic unit cell (diagram Ve). To maintain charge neutrality within the crystal, the total charges for cations and anions must be equal and opposite. In short, a compound with a relatively high radius ratio like caesium chloride adopts this structure.
A compound with a lower radius ratio (e.g. NaCl) has cations occupying octahedral holes that are formed by layers of anions (see diagram II and IIa below). The result is a space lattice consisting of replications of two interpenetrating cells, a cationic face-centred cubic unit cell and an anionic face-centred cubic unit cell (diagram IIb). By pairing a cation with an anion and using the pair as a basis, we get a face-centred cubic unit cell for NaCl.
For a compound with even lower radius ratio (e.g. ZnS, zinc blende), cations occupy tetrahedral holes formed by layers of anions (see diagram II and IId below). By pairing a cation with an anion and using the pair as a basis, we once again get a face-centred cubic unit cell for zinc blende (diagram IIe).
