Electrostatic model for ionic lattices

The lattice energy can be estimated by assuming an electrostatic model for the solid state ionic lattice the ions are considered to be point charges. Later in this chapter, we consider to what extent this approximation is true. 

Wood and Blundy (2001) developed an electrostatic model to describe this process. In essence this is a continuum approach, analogous to the lattice strain model, wherein the crystal lattice is viewed as an isotropic dielectric medium. For a series of ions with the optimum ionic radius at site M, (A(m))> partitioning is then controlled by the charge on the substituent (Z ) relative to the optimum charge at the site of interest, (Fig. 10) ... 

Oxidic surfaces in particular develop acid or basic properties which are important in catalysis. We will approach this subject first by taking as a starting point the ionic bond model [2]. The lattice is considered to consist of cations and anions held together by electrostatic interactions. Later we will discuss a more balanced theory that also accounts for covalent bonding aspects. 

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 intemuclear distance need be considered. The summation of all the geometrical interactions between the ions is called the Madelung constant. From this model an equation for the crystal lattice energy is derived ... 

Ionic crystals may be viewed quite simply in terms of an electrostatic model of lattices of hard-sphere ions of opposing charges. Although conceptually simple, this model is not completely adequate, and we have seen that modifications must be made in it. First, the bonding is not completely ionic with compounds ranging from the alkali halides, for which complete ionicity is a very good approximation, to compounds for which the assumption of the presence of ions is rather poor. Secondly, the assumption of a perfect, infinite mathematical lattice with no defects is an oversimplification. As with all models, the use of the ionic model does not necessarily imply that it is true , merely that it is convenient and useful, and if proper caution is taken and adjustments are made, it proves to be a fruitful approach. 

Non-aqueous Solvation.—Structural radii and electron-cloud radii, together with lattice enthalpies and enthalpies of solvation of ionic crystals, have been reviewed.84 The free energies of transfer, AGtr(K+), of potassium ions from water to 14 non-aqueous solvents have been reported, and they were derived from measurements in an electrochemical cell assumed to have a negligible liquid-junction potential. The essentially electrostatic nature of its solvation allows K+ to be used as a model for non-specific solvent-ion interactions. A... 

Considerations of lattice energies calculated using an electrostatic model provide a satisfactory understanding for the fact that ionic compounds are central to the chemistry of Na, K, Rb and Cs. That Li shows a so-called anomalous behaviour and exhibits a diagonal relationship to Mg can be explained in terms of similar energetic considerations. We discuss this further in Section 11.10. 

The purpose of this paper is to calculate the electrochemical potential and the double layer repulsion using a lattice model, applicable to hydrated ions of different sizes, that accounts for the correlation between the probabilities of occupancy of adjacent sites. As the other lattice models,4-7 this model accounts only for the steric, excluded volume effects due to ionic hydration. In feet, short-ranged electrostatic interactions between the ions and the dipoles of the water molecules, as well as the van der Waals interactions between the ions and the water molecules, are responsible for the formation of the hydrated ions. The long-ranged interactions between charges are taken into account through an electrostatic (mean field) potential. The correlation between ions is expected to be negligible for sufficiently low ionic concentrations. 

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