Ionic radius ratio

Table 2.3. Ionic Radii Ratios Corresponding to Interstitial Sites...

Inadequacy of the Classical Criterion Derived from the Ionic Radii Ratio... 

Particular case of aluminium, substituting simnltaneonsly Ca and Si" in alite lattice is possible becanse the ionic radii ratio of Al and eqnal 0.36 (51/140) is... 

Cation Anion CN Ionic Radii, pm Ionic Radii Ratio Cage for Cation... 

Therefore, ionic radii ratio = 0.508 (but not for fetrahedral coordination). Now consider the octahedral interstice. 

When three different kinds of spherical ions are present, their relative sizes are also an important factor that controls the stability of a structure. The PbFCl type is an example having anions packed with different densities according to their sizes. As shown in Fig. 7.5, the Cl- ions form a layer with a square pattern. On top of that there is a layer of F ions, also with a square pattern, but rotated through 45°. The F ions are situated above the edges of the squares of the Cl- layer (dotted line in Fig. 7.5). With this arrangement the F -F distances are smaller by a factor of 0.707 (= /2) than the CP-CP distances this matches the ionic radius ratio of rF-/rcl- = 0.73. An F layer contains twice as many ions as a CP layer. Every Pb2+ ion is located in an antiprism having as vertices four F and four... 

Use ionic radius ratios (Tables 6.3 and 6.4) to decide whether the CaF2 or the rutile type is more likely to be adopted by NiF2, CdF2, Ge02, K2S. 

Alternate layers can be occupied by two different kinds of metal atom, then every pair of the face-sharing octahedra contains two different metal atoms this is the ilmenite type (FeTi03). Ilmenite is, along with perovskite, another structure type for the composition AiiMiv03. The space for the A2+ ion is larger in perovskite. Which structure type is preferred can be estimated with the aid of the ionic radius ratio r(A2+)/r(02-) < 0.7 ilmenite... 

Brown (1988) showed that the use of ionic radius ratios generally gives... 

Figure 9.7 Transition pressures at 1,000 °C for various olivines transforming to the P-phase ( modified spinel or wadsleyite) or Y-phase (spinel or ringwoodite) as a function of the ionic radius ratio divalent cation (Fr+) to Si4 or Ge4 (M4 ) (from Syono et al., 1971). Note that the cations acquiring excess CFSE in spinel over olivine (e.g., Fe2+, Co2+, Ni2+) deviate from a linear trend.

Most inorganic chemistry texts list cut-off values for ther+/r ratios corresponding to the various geometries of interstitial sites (Table 2.3). However, it should also be pointed out that deviations in these predictions are found for many crystals due to covalent bonding character. An example for such a deviation is observed for zinc sulfide (ZnS). The ionic radius ratio for this structure is 0.52, which indicates that the cations should occupy octahedral interstitial sites. However, due to partial covalent bonding character, the anions are closer together than would occur from purely electrostatic attraction. This results in an effective radius ratio that is decreased, and a cation preference for tetrahedral sites rather than octahedral. 

In addition to the reinterpretation of Pauling s rules developed by Burdett and McLarnan (1984), there have been a number of other studies related to various aspects of these standard rules. Due to the substantial number of errors in classifying AB compounds in terms of ionic radius ratio (e.g., Phillips, 1970 Tossell, 1980b), there have been numerous attempts to create structure maps that have two atomic quantities as coordinates and that can provide a unique separation of the different structure types. Such atom quantities may be related primarily to size or energy or to some combination of the two. Some of the most important such approaches are those of Mooser and Pearson (1959), Phillips (1970), and Simons and Bloch (1973). 

Fig. 15. Graph of charge to ionic radius ratio vs. pM for the enterobactin analog MECAMS...

Given that the ionic radius of Fe-" is 0.77 A and that of 0- is 1.26 A, predict a likely structure for FeO using ionic radius ratios. 

Particularly in the case of plutonium hydroxide, the amount of plutonium solublized from an internal deposit by biological ligands depends upon the oxidation state of the deposited plutonium. The charge to ionic-radius ratio and the tendency towards hydrolysis decreases in the order32 33) ... 

While not the most toxic, plutonium is the most likely transuranium element to be encountered. Plutonium commonly exists in aqueous solution in each of the oxidation states from III to VI. However, under biological conditions, redox potentials, complexa-tion, and hydrolysis strongly favor Pu(IV) as the dominant species (27, 28). It is remarkable that there are many similarities between Pu(IV) and Fe(III) (Table I). These include the similar charge per ionic-radius ratios for Fe(III) and Pu(IV) (4.6 and 4.2 e/k respectively), the formation of highly insoluble hydroxides, and similar transport properties in mammals. The majority of soluble Pu(IV) present in body fluids is rapidly bound by the iron transport protein transferrin at the site which normally binds Fe(III). In liver cells, deposited plutonium is initially bound to the iron storage protein ferritin and... 

The cations are generally weakly held to the clay mineral surfaces, and can be readily displaced by other cations present in the solution. The cation (base) exchange depends on the ionic strength (charge to ionic radius ratio) and the concentration of fhe solufion. The cation exchange (or adsorption) capacity of a clay mineral reflecfs ifs charge deficiency per unif mass and is a function of the particle composition and of ifs specific surface (Table 7.2). 

Eor ionic crystals, the preference of a cation to occupy a certain interstitial site is primarily governed by the ionic radius ratio of the cation/anion (r+/r ). Since anions are most often larger than cations, this ratio is usually less than... 

Fig. 25. Correlation of structural systematics for RXj compounds with the effects of high pressure, as discussed by Gregorian et al. (1989) using the variation in c/a, ionic radius ratios rjr, and ratios of nearest-neighbor distances for the cations, Re/ a- O trichlorides, ambient pressure, trihydroxides, ambient pressure, A LaClj, at pressures up to 7 GPa.

Owing to its large charge/ionic radius ratio, Ce has a pronounced tendency for hydrolysis and forms a number of 0x0- and hydroxosulfates, some analoguous to Ti and Th compoimds (Lundgren, 1956) (see section 4.6). Nevertheless, many normal sulfates are known as well (Gmelin, 1981b) and some of them have been structurally characterized. Table 12 summarizes the structural information available and table 13 presents a comparison of the Ce O distances in Ce and Ce sulfates the comparison includes the 0x0- and hydroxosulfates of tetravalent cerium. 

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