Binary ionic solids

Binary Ionic Solids Common Structural Types... 

In the ionic model, binding energies represent the nett effects of attraction between charges on the anions and central cation, repulsion between the anions and all electrons on the cation, and repulsion between the nuclei. The lattice energy, U0, of a binary ionic solid, such as periclase, may be expressed by the Bom equation, one form of which is... 

In fact, trigonal holes are so small that they are never occupied in binary ionic compounds. Whether the tetrahedral or octahedral holes in a given binary ionic solid are occupied depends mainly on the relative sizes of the anion and cation. Next, we will determine the sizes of the octahedral and tetrahedral holes and consider guidelines for their occupation by ions. 

In this section we will consider some specific binary ionic solids to show how these solids illustrate the ideas of ion packing. Because an ionic solid must be neutral overall, the stoichiometry of the compound (the ratio of the numbers of anions to cations) is determined by the ion charges. On the other hand, the structure of the compound (the placement of the ions in the solid) is determined, at least to a first approximation, by the relative sizes of the ions. 

In fact, trigonal holes are so small that they are never occupied in binary ionic compounds. Whether the tetrahedral or octahedral holes in a given binary ionic solid are occupied depends mainly on the relative sizes of the anion and cation. For example, in zinc sulfide the ions (ionic radius = 180 pm) are arranged in a cubic closest packed structure with the smaller ions (ionic radius = 70 pm) in the tetrahedral holes. The locations of the tetrahedral holes in the face-centered cubic unit cell of the ccp structure are shown in Fig. 10.36(a). Note from this figure that there are eight tetrahedral holes in the unit cell. Also recall from the discussion in Section 10.4 that there are four net spheres in the face-centered cubic unit cell. Thus there are twice as many tetrahedral holes as packed anions in the closest packed structure. Zinc sulfide must have the same number of S ions and Zn ions to achieve electrical neutrality. Thus in the zinc sulfide structure only half the tetrahedral holes contain Zn ions, as shown in Fig. 10.36(c). 

Another arrangement adopted by binary ionic solids is the simple cubic arrangement. The simple cubic arrangement is not a closest packed structure and has larger holes than the cubic closest packed arrangement. The simple cubic structure has a cubic hole at the center of the unit cell. The size of the cubic hole is r = 0.732 R of the cubic unit cells considered here, this is the largest hole. 

The criteria given here provide a useful way of rationalizing the structures of binary ionic solids. However, as with all simplified models, we must be aware of the limitations of the model. In developing the criteria given, we have assumed that there are no interactions other than coulombic attractions between the ions. The criteria will fail if this is not the case. Nonetheless, we will find the criteria to be very useful. 

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