Interionic potential

The thennodynamic properties are calculated from the ion-ion pair correlation fimctions by generalizing the expressions derived earlier for one-component systems to multicomponent ionic mixtures. For ionic solutions it is also necessary to note that the interionic potentials are solvent averaged ionic potentials of average force ... 

L and W C Mackrodt 1994. Density Functional Theory and Interionic Potentials. Philosophical gazine B69-.871-878. 

The equilibrium between the complexes formed according to Equation (80) depends both on the concentration of fluorine ions and on the potential of interionic interactions, namely the nature of the outer-sphere cations [358]. The influence of the concentration of fluorine ions and of the nature of the outer-sphere cations on the equilibrium in Equation (80) can be demonstrated by the spectral transformations observed at 850°C for M2TaF7 - MF systems, where M = alkali metal [358]. 

All interionic and almost all intermolecular interactions can be traced to the coulombic interaction between two charges (Section 2.4), and throughout the discussion of intermolecular interactions we shall build on Eq. 5 from Section A, the expression for the potential energy Ef of two charges qx and q1 separated by a distance r ... 

The ions in solution are subject to two types of forces those of interaction with the solvent (solvation) and those of electrostatic interaction with other ions. The interionic forces decrease as the solution is made more dilute and the mean distance between the ions increases in highly dilute solutions their contribution is small. However, solvation occurs even in highly dilute solutions, since each ion is always surrounded by solvent molecules. This implies that the solvation energy, which to a first approximation is independent of concentration, is included in the standard chemical potential and has no influence on the activity. 

Experience shows that the potentials of metal electrodes in melts of their own salts (i.e., the activities of the cations) depend on the natnre of the anions. However, the variation in the valnes of activity in melts is not very pronounced. This is dne to the relatively small spread of interionic distances fonnd in different melts (their entire volume is filled up with ions of similar size) compared to the spread found in aqueous solutions. For this reason the electrostatic forces between the ions (which are very significant) do not differ greatly between different melts. 

As only very dilute solutions are considered, where the ions are rarely close together, the interionic potential energy is small (Q, U < kT). Therefore, the exponent factor may be replaced by... 

Sangster MJL, Dixon M (1976) Interionic potentials in alkali halides and their use in simulations of the molten salts. Adv Phys 25(3) 247-342... 

One now has a picture of conduction electrons in the potential of the ions, which is really a collection of pseudopotentials. The energy of the electronic system obviously depends on the positions of the ions. From the electronic energy as a function of ionic positions, say Ue,(R), one could determine the equilibrium ionic configuration (interionic spacing in a crystal or ion density profile... 

Patey, G. N. Valleau, J. P., A Monte Carlo method for obtaining the interionic potential of mean force in ionic solution, J. Chem. Phys. 1975, 63, 2334-2339... 

Equation (87) and analogous equations for AG , AHm, and for surface tensions apply to molten salt mixtures in which the interaction potential can be classed as conformal. These relations may also be used to test whether the ionic interaction potential in aqueous solutions may be considered as conformal. Thus, as will be shown in one simple example, the limits of usefulness of some interionic interaction potentials may be tested in ranges of concentration of salts in water too high to obtain absolute values for the partition functions. A similar test may be made for associations in salt vapors such as... 

We shall, however, keep here the screened Coulomb potential (314) for describing the interionic interaction the most general case will be discussed in Section V-E. 

In this approximation, the B ions pulsate in harmonic oscillation around the equilibrium positions and, consequently, the interionic potential energies, , (2) and Ef(Q), of the ground and excited states are given by... 

The vibrational motion of atoms in diatomic molecules and, by extension, in crystals cannot be fully assimilated to harmonic oscillators, because the potential well is asymmetric with respect to Xq. This asymmetry is due to the fact that the short-range repulsive potential increases exponentially with the decrease of interionic distances, while coulombic terms vary with 1/Z (see, for instance, figures 1.13 and 3.2). To simulate adequately the asymmetry of the potential well, empirical asymmetry terms such as the Morse potential are introduced ... 

Figure 5JO Experimentally observed intracrystalline disorder in (Mg,Fe)2Si04 mixture, compared with theoretical distribution curves generated by interionic potential calculations. = Aikawa et al. (1985) = Smyth and Hazen (1973) = Brown and Prewitt (1973) 0,0, A = Ottonello et al. (1990). From G. Ottonello, F. Princivalle, and A. Della Giusta, Temperature, composition and/o effects on intersite distribution of Mg and Fe in olivines. Physics and Chemistry of Minerals, 17, 301-12, copyright 1990 by Springer Verlag. Reprinted with the permission of Springer-Verlag GmbH Co. KG.

Figure 5.11 Gibbs free energy of mixing in binary join Mg2Si04-Ca2Si04 dXT = 600 °C and P = bar, calculated with a static interionic potential approach. Reprinted from G. Ottonello, Geochimica et Cosmochimica Acta, 3119-3135, copyright 1987, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.

Figure 5.12 shows how and ions are distributed between Ml and M2 sites in the (Mg, Ni)2Si04 mixture at various T (P = I bar). Experimentally observed distributions are compared with the results of static interionic potential calculations carried out at two different values of the hardness factor p (cf. section 1.11.2). 

Table 5.15 Activity of component Ni2Si04 in (Mg, Ni)2Si04 mixture (1) results of interionic potential model (Ottonello et al., 1989) (2) Campbell and Roeder, (1968).

Figure 5,17 Enthalpic interactions in the various binary joins of aluminiferous garnets. calorimetric data results of interionic potential calculations. The corresponding subregular Margules interaction parameters are listed in table 5.26 (from Ottonello et al., in prep.).

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