Madelung constant ionic compounds

Fig. 8.15 The Madelung energy in ionic compounds as a function of the radius ratio for CsCl, NaCl and cubic ZnS lattices (assuming the anion radius, / , is held constant).

A compound A+B has a larger Madelung constant per equivalent than a compound Therefore, while, for equal ionic radii, a... 

The enthalpy of formation of an ionic compound can be calculated with an accuracy of a few percent by means of the Born-Land6 equation (Eq. 4.13) and the Bcrn-Haber cycle. Consider NaCI. for example. We have seen that by using the predicted internuclear distance of 283 pm (or the experimental value of 281.4 pm), the Madelung constant of 1.748, the Rorn exponent, n, and various constants, a value of — 755 kJ mol-1 could be calculated for the lattice energy. The heat capacity correction is 2.1 kJ mol-1, which yields U 9i = —757 kJ mol-1. The Bom-Haber summation is then... 

In order for an ionic compound to dissolve, the Madelung energy or electrostatic attraction between the ions in the lattice must be overcome. In a solution in which the ions are separated by molecules of a solvent with a high dielectric constant ( H 0 81.7 ) the attractive force will be considerably less. The process of solution of an ionic compound in water may be considered by a Bom-Haber type of cycle. The overall enthalpy of the process is the sum of two terms, the enthalpy of dissociating the ions from the lattice (the lattice energy) and the enthalpy of introducing the dissociated ions into the solvent (the solvation energy) ... 

The ionic solids NaCl and KC1 form the same type of crystal structure, so they have the same values of the Madelung constant A. We can decide in which compound the ions bind together more strongly by taking the ratio of U for the two compounds. All the constants cancel when the ratio is taken, including the ionic charges, and we are left with... 

The relationship between cubic close-packed (ccp) structures and ionic compounds of type B1 is obvious. Interstitial sites with respect to metal positions are at fractional coordinates of the type 00 and equivalent to the ionic sites in Bl. The Madelung constant of Al type metals with interstitially localized free electrons is therefore the same as that of rocksalt structures. It is noted that the interstitial sites define the same face-centred lattice as the metal ions. 

Further insight into the stability of predominantly ionic compounds can be gained by inspection of the reduced Modelling constant. A " The reduced Madelung constant IS closely related to the derivation of the KapuslinskU equation given earlier (Chapter 4). Templeton showed that if the lattice energy a compound M, X, is formulated as ... 

A number of Madelung constants for a compound appear in the literature. These usually differ from each other in the molecular unit chosen for evaluation (e.g. M X or MX / ) and whether the ionic charges are included in the constant. If... 

For a molecular compound, the Madelung constant is not a useful parameter, and we think that the best way to measure the overall polarity of the molecule is to localize the barycenter of positive and negative charges in the structure. With these two barycenters, an ionic dipolar moment can be computed by looking at the modulus of the vector joining them ... 

A problem in estimating the lattice energy of a hypothetical compound is deciding what ionic structure type to assume. Attempts have been made to use the fact that Madelung constants for MX and MX2 structure types (Table 6.4) are in an... 

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