Ionic Refractions

An independent semi-empirical method of determining ionic refractions was suggested by Pauling [164], using the relation between the polarizability and the second-order Stark effect. 

Pauling determined the constant of Eq. 11.40 and calculated ionic refractions. The systems of Fajans and Pauling are similar, being based on the same experimental data, namely, the refractions of rare gases. 

The comparison of the covalent and ionic refractions of the same elements shows that the addition or removal of the valence electrons influences the atomic refraction most. The changes of atomic refractions due to bond ionicity in molecules and crystals have been calculated as 

The accuracy of calculated molar refractions of inorganic compounds has been much improved by taking into account the polarizing effect of atoms (g) and bond metallicity (m) [150], The former was described proceeding from the van der Waals interactions, g = [(Ra — b)/ a] where Ra Rb (see Eq. 4.24). If the smaller ion (A) is the cation, this will lower the refraction, otherwise will increase it. The bond metallicity m, i.e. the delocalized fraction of covalent electrons of A—A bonds in AB 

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Fajans and Wulff, not yet published. Their ionic refraction values for light of infinite wave-length are found by the methods applied by Fajans and Joos to the refraction for the sodium D-lines. 

Atomic and ionic refractivities The contribution that each atom or ion makes to the total refractive index. 

Hertlein (US) in 1896 measured refraction, viscosity, and electrical conductivity of aqueous potassium tri-, tetra-, and pentathionates and decided in favor of uiibranched structures, and so did Martin and Metz (171) in 1924 on the basis of thermochemical measurements. Spacu and Popper (208) in 1939 reported the refraction of sodium tetrathionate Grinberg (186) has later commented on the ionic refraction of tetra thionate as indicating negative charge on the divalent sulfur atoms. However, from Hertlein s measurements the increments per sulfur atom, from tri-to tetra-thionate and tetra- to pentathionate, are about 9 cm3. This is the same as in other series, for example, in the polysulfur dichlorides (72) where the sulfur atoms are hardly negative. 

The measure of polarizability was provided by the abundant data on molecular, ionic and atomic refractions. Refractions in chemistry seem to be of historical importance today. Their long use and the sophisticated level they reached in chemistry provide important hints. Refraction has been recognized as a molecular volume, thus discussion of softness may be reduced to the level of molecular or atomic dimensions, as indeed it was later proposed (Sect. 1.2). Refractions have also been known to be additive, atomic refractions are transferable between molecules. This was but the first indication that atomic softness that should roughly parallel refractions (polarizability), may also be defined for bonded atoms. Examples of atomic and ionic refractions are given in Tables 1 and 2. The increasing order of refraction indeed reflects the expected hardness sequence, the borderline between soft and hard species can be drawn at ca. 2-3 cm /mol. 

Table I. Ionic refractions (Ro) and corresponding hardness indices, n, = (4k oKo ) compared to ionic radii (r,) and hardness parameters derived therefrom. r)2 = Htieori). After Ref. [14]...

The molar refractivity of a compound can be calculated from the contributions of each of the constituent ions. The molar refractivity for the compound A By, for example, is given by the sum of the ionic refractivities of the constituent ions, R , times their concentration in the compound, or, in this case ... 

Since the ionic refractivity depends on the polarizability of the ion, large values are found for the large, low field strength ions such as TT and Pb ". Variations in the ionic refractivity explain many of the major trends in the refractive index of glasses. 

Since a typical glass contains from 50 to 80 atomic percent of anions, the ionic refractivities of the anions are very important in controlling the molar refractivity. The polarizabilities of the common anions increase in the order F < OFl < Cl" < < S " < Se < Te. This... 

Explain why the ionic refractivity of a bridging and a non-bridging oxygen should be different. 

Table 11.9 Ionic refractions (cm /mol) anions the upper lines Rco, the low lines Rd...

An alternative to improving atomic/ionic refractions was to express molecular refraction through bond increments. A system of bond refractions is definitely superior to the system of atomic refractions, as it allows to account for chemical interactions explicitly. The concept of bond refraction was introduced by Bachinskii [183] who suggested that the molar refraction (as well as volumes, heats of combustion, etc) of organic compounds can be calculated of bond increments. According to Bachinskii, Rc-c =l/4f c + l/4 c. = l/47Jc + etc. This method is not quite con-... 

Table S11.12 Empirical values of the crystalline ionic refractions (cm /mol)...

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