Polarizability of ions

A. R. Ruffa, Theory of the Electronic Polarizabilities of Ions in Crystals Application to the Alkali Halide Crystals, Phys. Rev., 130,1412 (1963). 

Although we have illustrated the effects of polarizability of ions by considering a few cases where the effects are large, there must be some polarization effect for any combination of ions. However, there is an even more important consideration. It is known that the apparent radius of a given ion depends somewhat on the environment of the ion. For example, an ion surrounded by four nearest neighbors will appear to be slightly different in size from one that is surrounded by six ions of opposite charge. We have treated the ionic radius as if it were a fixed number that is the same in any type of... 

The study of thiourea adsorption on an Hg electrode from ethanolic solutions shows that different supporting electrolytes can make a comparison of the adsorption parameters more difficult. The data obtained for various electrolytes (KF, KPFe, LiCl, NH4NO3, and KCNS) suggest that coadsorption, size, and polarizability of ions strongly influence the interfacial behavior of TU, at high concentration of the ions in particular. The effect of the electrolyte on AG° and parameter A in the Frumkin isotherm is illustrated in Table 6. 

This method may also be applied to the calculation of polarizabilities. Indeed, we arrived at the present formulation of this method when wishing to perform such calculations. More recently,7 it has been applied to the problem of calculating the polarizability of ions having the rare gas structure. Here again the ground state is considered as being described by an antisymmetric function composed of Slater orbitals. The excited orbital was taken to be of the form ... 

Variables 2 and Zj are charges of ions i and j Ay is the Pauling factor defined as Ay = (1 + zjnx + z-Jn i, where nK and nj represent the numbers of electrons in the outermost shell of ions i and j, respectively Cy = (3/2) aiajEiEj/(Ei + Ej) and dy = (9/4e2)Cy(a, 1/Ar1 + atjE/Nj), where a denotes the polarizability of ions, N is the number of the total electrons of an ion, and E is the first ionization potential, evaluated from the Equation Ef = Nle2h2I Tr2mai for ion i, where h and m are the Planck constant and the mass of the ion, respectively. Values of p, b, and cr are estimated from isothermal compressibilities and thermal expansion coefficients of 17 rock-salt-type crystals of alkali halides by Fumi and Tosi (15). 

G. D. Mahan, Solid State Ionics, 1, 29-45 (1980). Polarizability of Ions in Crystals. 

Our interest is how to treat polarizability of ion in the molecular dynamics calculation. There have been paid a lot of attention up to now and three methods to include the effect of the polarizability are considered a shell model method, a modified potential method, a dipole rod method. 

Shannon R. D. (1993) Dielectric polarizabilities of ions in oxides and fluorides. J. Appl. Phys. 73, 348-366. 

The polarizability of ions forming the melt gives rise to light scattering either due to electrostatic field fluctuation around the ion and/or to polarizability changes due to bond formation within the melt (i.e. complex formation). 

Ion The electrostatic polarizability of ions increases with its radius and may be partly responsible polarizability for the adoption of structures where coordination geometries are unsymmetrical, and of structures with high coordination numbers. 

Fia. 52b. Potential curves for field ionization of He at a metal with ij> = 4.50 ev. In an applied field of 4.5 volts/A, isoenergetie switch from atomic (A) to ionic (A+) curve can occur at xc 4.3A. a, —polarizability of atom a+—polarizability of ion. Repulsion of ionic and atomic curves is not indicated in this or following diagrams. 

The terms are conveniently represented graphically the open circles represent the ions, the full circles the molecules, and bonds the 8 or T factors. Every term of the expansion (56) is represented by a succession of connected bonds (chain diagrams) going from one ion to another. We shall extract the terms containing polarizabilities of ions and treat them separately accordingly the first three terms of Eq. (56) are represented as follows ... 

Shepard, R. 1949. Dielectric constants and polarizabilities of ions in simple crystals and barium titanate. Physical Review, 76(8) 1215-1219. 

As noted above, Kossel introduced the idea that the transition from ionic to covalent substances is gradual, the covalence increasing with the mutual polarizing influence of ions. This idea was developed by Fajans and his school who defined the polarizabilities of ions and estimated the polarizing action of cations (Z/r ), but ultimately failed to create a quantitative theory. The reason is obvious [10] there are no completely ionic substances, only intermediate cases, more or less approaching this type. Hence the parameters of ideal ions are not available experimentally, the more so since ionic radii cannot be uniquely defined from interatomic distances (see Chap. 1). Thus the polarization concept remained only qualitative. However, the contribution in the bond energy of the polarizing effect of atoms can be described in the form that has proven itself for the van der Waals interaction (see Sect. 4.4), where the deviation of the A B distance from the mean of A A and B B distances is a function of the difference of the atomic polarizabilities... 

Tessman JR, Kahn AH, Shockley W (1953) Electronic polarizabilities of ions incrysUils. Phys Rev 92 890-895... 

Mahan GD (1980) Polarizability of ions in crystals. Solid State Ionics 1 29-45 Fowler PW, Pyper NC (1985) In-crystal ionic polarizabilities derived by combining experimental and ab initio results. Proc Roy Soc London A 398 377-393 Fowler PW, Madden PA (1985) In-crystal polarizability of CP . J Phys Chem 89 2581-2585 Pyper NC, Pike CG, Edwards PP (1992) The polarizabilities of species present in ionic-solutions. Mol Phys 76 353-372... 

Wilson JN, Curtis RM (1970) Dipole polarizabilities of ions in alkali halide crystals. 1 Phys Chem 74 187-196... 

The polarizability of ions and molecules was in fact introduced by Fajans32 as early as in 1923, but it is understood that various other factors contribute to hard and soft properties. 

The electron polarization Pei in the local electric field E must be also added to the total polarization. If we denote the electron polarizability of ion 4 or 5 by a (0) or a (0), we could get... 

Atoms exist in a molecule in the form of ions no matter whether they arc associated in ionic or co-valent bonds. Like the electrons moving under an electric field, ions can move along the direction of the electric field too. Ions of opposite charges are bound together through chemical bonds, forming a molecule. Under an electric field, those ions will move to the opposite direction, creating dipole moment. The polarizability of ions, a , can be expressed as [5] ... 

This work shows that the use of the RIM allows to describe the local structure of pure silica and a silica-calcia mixture for which measurements are complicated or not possible. However, it has been shown that the calculation of properties such as density exhibit some differences from measurements but the trend is correct and offers, in a first approach, a rather good estimation of it at elevated temperature. For complex systems, including multi-cations with different oxidation degrees, it appears that the polarizability of ions should be included to get more reliable results. 

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