Ionic solid Coulomb potential

FIGURE 2.7 The potential energy of an ionic solid, taking into account the coulombic interaction of the ions and the exponential increase in their repulsion when they are in contact. The minimum potential energy is given by the Born-Meyer equation, Eq. 3. 

The structures of ionic solids may be accounted for quite accurately by the use of a coulombic interaction potential between neighbouring ion pairs together with a suitable ion-core repulsion. 

For the case of ionic solids, the method of Ewald summations [44] is employed to take into account the long-range Coulomb potential of the crystal (Madelung potential). 

Nanomaterials are systems that contain particles with one dimension in the nanometer regime. The past decade has witnessed a growing intense interest from biologists, chemists, physicists, and engineers in the application of these materials -the so-called nanotechnology , which is sometimes referred to as the next industrial revolution [1]. The reasons for such interest are the unusual properties and potential technological applications that are exhibited by these materials when compared to their bulk counterparts [2-10]. In this chapter, attention will be focused onrather simple ionic solids, where the interatomic attractions are predominantly coulombic forces, and the dimensions are predominantly <100 nm. Such systems have been termed nanoionics [11,12]. 

Equation (6.13) was derived on a model of covalent bonds between nearest neighbors. It is not strictly applicable to ionic solids. The repulsion part of the potential energy must be similar for ionic and covalent cases, but the attraction part for ionic solids must also include the sum of the coulombic interactions with the remainder of the lattice. In effect, the number of bonds is increased. To see the magnitude of this effort, compare Equations (6.7) and (6.8) with their counterparts for a diatomic molecule, or ion-pair. 

For ionic solids interacting with Coulomb pair potentials, similar calculations can be carried out. However, this is a rather complex matter because Coulomb, van der Waals attraction and Pauli repulsion should all be taken into account. In addition, there are uncertainties in the choice of suitable pair-potential equation (many inter-atomic potential equations, including Lennard-Iones were tried), and the calculated Gf results are highly dependent on the particular choice of pair-potential model. As an example, Gf = 212m) m 2 was calculated theoretically for the NaCl (100) crystal, which is near to the experimental value of Gf = 190 m) m 2 from extrapolation of the molten salt surface tension values, but far away from Gf = 300 mj m 2, which was found from crystal cleavage experiments. 

The strongest intermolecular interactions are those between ions and between ions and dipoles. We have encountered this ion-ion interaction before in the context of chemical bonding in ionic solids, but it is also a major intermolecular interaction in solutions of ionic compounds, such as aqueous sodium chloride. As discussed in Section 0.1, the interaction between two ions of charge qp, and separated by a distance r is given by the Coulomb potential. 

This contribution to the total molecule/surface interaction is caused by the Coulomb interaction between the charge distributions of the ionic crystal and the adsorbed molecule or, stated differently, by the potential energy of the adsorbed molecule in the electrostatic field above the solid surface. In the theory of intermolecular forces, this interaction is generally expressed by means of a multipole expansion... 

This category of approaches assumes that interactions in the solid can be represented by two or three-body potentials or force-fields between atoms. The interaction is usually obtained by fitting models to results on molecular systems. This is a convenient approach for ionic materials where long range Coulomb forees are strong and for a typical material like Si02 at least eleven parameters are needed to characterize the system. Such a choice of potential, but in the form of y r) = D exp[-a r - eq)]... 

A realistic potential function for an ionic system (gas, liquid, or solid) includes a Bom repulsive term in addition to the coulombic term as... 

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