Bulk modulus alkali halides

Strongly for the ionic crystals, yet the bulk modulus for the alkali halides varies as d. The cl trend for the bulk modulus will show up in the study of simple metals, and in terms of the pseudopotentials that will be used in the study of simple metals, d" -dependence takes on a particularly fundamental role. In Problem 15-3, the simple metal theory is used to give a good account of the bulk modulus in C, Si, and Gc. It should be noted also that the simple metal theory docs not give a good account of cohesive energy itself there is much cancellation between terms for that property, and there are important contributions (for example, that do not vary as... 

Let us then turn to the ionic solids themselves. Kim and Ciordon (1974) recalculated the total energy for the alkali halides that form rocksalt structures and thereby computed from first principles the lattice spacing, the separation energy (the energy per ion pair required to separate the solid into isolated ions -this comes from the theory more naturally than does the cohesive energy, which is relative to isolated neutral atoms), and the bulk modulus. For KCI, the agreement of the values for the three properties with experimental values is typical of the calculations. The calculated (and in parentheses, the experimental) values for KCI are 3.05 (3.15) A, 175 (166) kcal/mole, and 2.3 (1.9) x 10 dync/cmA Again we may say that the interactions are quite well understood in terms of the microscopic theory. We shall return to the interpretation of these properties in terms of simple models in Section 13-D. 

One feature that should be noted in passing is that the bulk modulus varies approximately as d in contrast to covalent solids, in which it varies as d (We shall see that in metals it also varies as d. ) As a consequence, the bulk modulus for the alkali halides can be given the universal value of 6.7 eV per ion pair. It is not clear what the significance of this empirical rule is. 

Figure 3.3 Bulk modulus as a function of interionic spacing for alkali halides.

The bulk modulus of the alkali halides decreases with decreasing lattice parameter. True or False ... 

Table 15.7 The properties of some alkali halides, ro is the distance between neighbor atoms S is bulk modulus coh is the cohesive energy.

Mitra and Marshall showed that the bulk moduli of 16 alkali halides with the NaCl structure are also equal to a constant/u", where a is the lattice constant and n is closer to three than to four. Whereas Keyes s constant is given by q, no such simple constant could be given for the alkali halides, which are essentially ionically bonded phases. Kittel derived the following expression for the bulk modulus K, applicable to the above alkali halides ... 

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