Born exponents values

The values of the Born exponent, n, for various crystal structures are estimated from compressibility data. The values recommended for use with various ion configurations are shown in Table 7.6. 

Estimate the lattice energy of sodium chloride, using the appropriate data from Appendix F and assuming that the Born exponent is 9. Compare your result with the value given in Eq. 4.8. 

First, obtain an approximate value for the Born exponent, n, from Table 2.5. This is found to be n = 8. 

The enthalpy of formation of an ionic compound can be calculated with an accuracy of a few percent by means of the Born-Land equation (Eq. 4.13) and the Born-Haber cycle. Consider NaCI. for example. Wc 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 Born exponent, n, and various constants, a value of —755kJmor could be calculated for the lattice energy. The heat capacity correction is 2.1 kJ mol", which yields = —757 kJ moP. The Bom-Haber summation is then... 

Table 5.3 Values of the Born exponent, n, given for an ionic compound MX in terms of the electronic configuration of the ions [M ][X ]. The value of n for an ionic compound is determined by averaging the component values, e.g. for MgO, 5 + 9...

Using the values given in Table 5.3, determine an appropriate Born exponent for BaO. 

This expression has its origins in the Born-Lande equation, with a value of 9 for the Born exponent (the value for NaCl) and half the value of the Madelung constant for NaCl the inclusion of the factor v shows why half of A is included. Although the Kapustinskii equation is useful, it is a gross approximation and values obtained in this way must be treated with caution. 

Compared to a simple inverse (r ) dependence on r for the Ecoui term, the relatively high value of n, the Born exponent, indicates that be very small... 

Values of Born Exponents for Various Electronic Configurations... 

Besides this electrostatic attraction there is the repulsion which arises when the ions begin to touch each other. This repulsion originates in the general mutual repulsion of the electron clouds of atoms and ions, which always occurs when the clouds penetrate each other and the electrons do not form any atomic bond with a common electron pair (p. 147). The repulsion is difficult to calculate and so Born represented the repulsion energy by B rn, a function which, provided n is large, increases very rapidly with decreasing distance r, corresponding to almost hard spheres. B in this expression is a still undetermined factor of proportionality while the value of the exponent can be deduced from the compressibility n amounts to about 9. 

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