Alkali halides, radius ratios

Table 7.1 Radius ratios and observed structure types for the alkali metal halides...

In practice, this hard-core model is too simple to predict reliably the ground-state structure of ionic compounds such as the alkali halides that are located in the upper left-hand corner of the AB structure map in Fig. 1.9. Nevertheless, it provides a simple introduction to the importance of the radius ratio in determining structural stability. 

Rg. 4.18 Actual crystal structures of the alkali halides (as shown by the symbols) contrasted with the predictions cl the radius ratio rule. Tie figure is divided into three regions by the lines rjr. 0.414 and r+/h- a 0.732, predicting coordination number 4 (wurizite or zinc blende, upper left), coordination number 6 (rock salt, NaCl, middle), and coordination number 8 (CsCI, lower right). The crystal radius of lithium, and to a lesser extent that of sodium, changes with coordination number, so both ihe radii with C.N. 4 (left) and C.N = 6 Iright) have been plotted. 

Perform radius ratio calculations to show winch alkali halides violate the radius ratio rule. 

The CsCl structure (Fig. 10-5) is observed in alkali halides only when the radius of the cation is sufficiently large to keep its eight nearest-neighbor anions from touching. What minimum value for the ratio of the cation-to-anion radii, r+/r, is needed to prevent this contact ... 

The alkali metals react with many other elements directly to make binary solids. The alkali halides are often regarded as the most typical ionic solids. Their lattice energies agree closely with calculations although their structures do not all conform to the simple radius ratio rules, as all have the rock salt (NaCl) structure at normal temperature and pressure, except CsCl, CsBr and Csl, which have the eight-coordinate CsCl structure. The alkali halides are all moderately soluble in water, LiF being the least so. 

For compounds in which the radius ratio is small, another term may be added to (5) to include also the appreciable effect of anion-anion repulsion. Pauling has indeed proposed such a treatment, analogous to Born s, but refined to include radius-ratio effects in doing so, he has been able to predict just how much the interionic distances in each of the alkali halides should depart from strict additivity. In using his modified treatment further for calculation of lattice energies, he has been able to show that the anomalies in melting points and boiling points, mentioned earlier in this chapter, may be correlated, at least semiquantitatively, with the radius ratios. 

While radius ratio rules generally predict correct structure types for the alkali halides in only about 50% of the cases, the MEG calculations (not even shell stabilized) correctly predict the NaCl structure to be more stable for 15 of the 16 compounds studied. Calculated structural parameters were also in good agreement with experiment, and calculated pressures for the NaCl CsCl transition were in fair agreement with the limited experimental data available. These results indicate that preferred coordination numbers and structural types in alkali halides can be accu-... 

Calculate the radius ratios for the alkali halides. Which fit the radius ratio rules and which violate them (Reference L. C. Nathan, J. Chem. Educ., 1985, 62, 215.)... 

All the alkali metal halides except the cliloride, bromide and iodide of caesium form cubic crystals with the rock salt lattice and show a co-ordination number of 6. The exceptions are also cubic, but have the caesium chloride structure (Fig. 133) characterised by a co-ordination number of 8. The radius ratio for CsCl, Cs /Cl" = 0.93, allows 8 co-ordination, but is so near the ratio for 6 co-ordination that caesium chloride is dimorphous, changing, at 445°, from the caesium chloride to the rock salt structure. The crystalline halides are generally markedly ionic, though, as expected, lithium iodide is somewhat covalent, for iodide is the largest and most easily polarised simple anion and lithium, the smallest alkali metal cation, possesses the strongest polarising power. 

Although there is a general increase in c.n. s of cations with increase in ionic radius a detailed correspondence between c.n. and radius ratio is not observed for simple ionic crystals. For example, all the alkali halides at ordinary temperature and pressure except CsCl, CsBr, and Csl crystallize with the NaCl structure. For Lil and LiBr (and possibly LiCl) the radius ratio is probably less than 0-41, but the radius ratios for the lithium halides are somewhat doubtful because the interionic distances in these crystals are not consistent with constant (additive) radii ... 

However, radius ratio arguments are not quantitatively reliable, and they even fail to account for the structures of some alkali halides. The predicted coordination number is four in Lil and eight in RbCl, although both compounds have the rocksalt structure (CN=6) at normal temperature and pressure. 

The radius ratio r+jr for each of the alkali halides is shown in table 3.03. Consideration of these values reveals that CsCl, CsBr and Csl would, indeed, be expected to have the caesium chloride structure, and that the majority of the remaining halides would be expected to show the sodium chloride arrangement. There are, to be sure, a number of halides with r+jr > 0 7 which, nevertheless, have the sodium chloride rather than the caesium chloride structure. Fig. 3.08, however, emphasizes that energetically there is little difference between these two structures when the radius ratio is large, and there are in any case other factors contributing to the lattice energy which we have so far ignored in our discussion. 

We have already considered in detail the structures of the alkali halides, all of which crystallize with either the sodium chloride or the caesium chloride arrangement ( 3.04 and 3.05). All of these compounds are essentially ionic, and the degree of ionic character depends on the difference in electronegativity of the atoms concerned it is thus a maximum in caesium fluoride and a minimum in lithium iodide. As we have seen, the radius ratio r+jr is the primary factor in determining whether a given halide possesses the sodium chloride or the caesium... 

Radius Ratios and Crystal Structures of Alkali Halides (ISO). 

A comparison of the limiting radius-ratio values given in Table I with the radius ratios of alkali halides in Table II shows that the observed structures are not always as predicted. According to the simple theory, the roeksalt structure should be stable only within the range 0.414 rM/rx 0.732. Thus LiCl (0.33), LiBr (0.31), and Lil (0.28) should have tetra-hedrally coordinated structures, while KF (0.98), RbF (1.09), and CsF (1.24) should have eight or twelve coordinated structures. These disagreements are perhaps not surprising in view of the crudeness of the approximations involved, but more realistic models do not lead immediately to an explanation of the persistence of the roeksalt structure not only in the alkali... 

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