Madelung ionic electrostatic energy

It was noted in Chapter 4 that the Madelung constant of a structure may be expressed in various ways. The way that is conceptually simplest in terms of the Bom-Lande equation is the simple geometric factor. A, such that when combined with the true ionic charges, Z and Z, the correct electrostatic energy is formulated. It was noted that some workers have favored using another constant, A. combined with the highest common factor of Z and Z. Z -... 

The electrostatic (Madelung) part of the lattice energy (MAPLE) has been employed to define Madelung potentials of ions in crystals (Hoppe, 1975). MAPLE of an ionic solid is regarded as a sum of contributions of cations and anions the Madelung constant. A, of a crystal would then be the sum of partial Madelung constants of cation and anion subarrays. Thus,... 

The experimental trends in bonding and structure which we have discussed in the previous chapter cannot be understood within a classical framework. None of the elements and only very few of the thousand or more binary AB compounds are ionic in the sense that the electrostatic Madelung energy controls their bonding. And even for ionic systems, it is a quantum mechanical concept that stops the lattice from collapsing under the resultant attractive electrostatic forces the strong repulsion that arises as the ion cores start to overlap is direct evidence that Pauli s exclusion principle is alive and well and hard at work ... 

Ionic radii are discussed thoroughly in Chapters 4 and 7. For the present discussion it is only necessary to point out that the principal difference between ionic and van der Waals radii lies in the difference in the attractive force, not the difference in repulsion. The interionic distance in UF, for example, represents the distance at which the repulsion of a He core (Li+) and a Ne core (F ) counterbalances the strong electrostatic or Madelung force. The attractive energy for Lt F"is considerably over 500 kJ mol"1 anti the London energy of He-Ne is of the order of 4 kJ mol-1. The forces in the LiF crystal are therefore considerably greater and the interioric distance (201 pm) is less than expected for the addition of He and Ne van der Waals radii (340 pm). 

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 crystal lattice energy can be estimated from a simple electrostatic model When this model is applied to an ionic crystal only the electrostatic charges and the shortest anion-cation intermiclear distance need be considered. The summation of all the geometrical interactions be/Kveeti the ions is called the Madelung constant. From this model an equatitWjor the crystal lattice energy is derived ... 

The theorem has the important implication that intramolecular interactions can be calculated by the methods of classical electrostatics if the electronic wave function (or charge distribution) is correctly known. The one instance where it can be applied immediately is in the calculation of cohesive energies in ionic crystals. Taking NaCl as an example, the assumed complete ionization that defines a (Na+Cl-) crystal, also defines the charge distribution and the correct cohesive energy is calculated directly by the Madelung procedure. 

Further, it is observed experimentally that electron-pair bonds are frequently associated with anisotropic, i.e. directed, atomic orbitals. This gives rise to open structures. However, the electrostatic (Madelung) energy associated with ionic crystals favors close packing Therefore largely ionic crystals favor more close-packed, two-sublattice structures such as rock salt versus zinc blende. In the case of two-sublattice structures induced by d electrons, electron-pair bonds are generally prohibited by the metallic or ionic outer s and p electrons that favor close packing. Nevertheless, it will be found in Chapter III, Section II that, if transition element cations are small relative to the anion interstice and simultaneously have Rti RCf electron-pair bonds may be formed below a critical temperature. 

Madelung constant — is the factor by which the ionic charges must be scaled to calculate the electrostatic interaction energy of an ion in a crystal lattice with given... 

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