Born exponents

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. 

The Madelung constant is unique ftk ejj h crystal structure and is defined only for those whose interatomic vectors are fixed by symmetry. The Born exponent, n, can be cslimatcd Hfor alkali halides by the noblc-gas-likc electron configuration of the Vigny It can also be estimated from the compressibility of the crystal system. For NaCl, n equals 9.1. 

This inverse power integer is called the Born exponent (Gould, 1962). Simple power relationships (Israelachvili, 1992) apply to neither polysaccharide intermolecular nor surface forces due to the multiple effects of substituents, branches, kinks, etc. 

Since A, the Madelung constant is almost the same for the two structures, (p. 179), the ionic radius (or interionic distance) for the CsCl structure may be obtained by multiplying the (octahedral) crystal radius (or sum of crystal radii) by [ ]1/(n 1), where n, it will be recalled, is the Born exponent. 

This expression differs from that for the Coulomb energy alone by the inclusion of 1/n, the reciprocal of the Born exponent. It should be emphasized that the expression was derived by considering all ions as point charges as the covalent character of the bonds within the lattice increases, Equation (8) becomes a poorer and poorer approximation. 

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

The Madelung constant and Born exponent appearing in Eq. 1 are related to the specific arrangement of ions in the crystal lattice. The Madelung constant may be considered as a decreasing series, which takes into account the repulsions among... 

The variable n is knovra as the Born exponent, which depends upon the electronic configuration of the ions present. The Born-Lande equation calculates on the basis of the electrostatic attraction between... 

Born exponent 46 Born-Haber cycle 44 Born-Lande equation 45... 

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... 

If valence is thought of as a measure of a bond s attractive force, it should, at equilibrium, be proportional to the repulsive overlap force between the atom cores. Not surprisingly, expressions that have been proposed for the repulsive component of interatomic forces are similar in form to Equations 10.1 and 10.2. Biirgi and Dunitz [16] have shown that Equation 10.1 can be derived from the Morse potential, and Brown and Shannon [8] have shown that the constant, W, in Equation 10.2 is related to the Born exponent [17]. 

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...

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