Ionic radii relationship

In an ideal perovskite structure for an ABO3 compound, the larger, A, ions are surrounded by twelve oxygens and the smaller, B, ions by six oxygens. Eq. (31) shows the ionic radii relationship for a close-packed arrangement. 

Consider the oxidation case in Figure 10.6b for divalent metal cations (M+ ) and oxygen anions if the ionic radius relationship is Ro-i > Rm+ ... 

The type of catalyst influences the rate and reaction mechanism. Reactions catalyzed with both monovalent and divalent metal hydroxides, KOH, NaOH, LiOH and Ba(OH)2, Ca(OH)2, and Mg(OH)2, showed that both valence and ionic radius of hydrated cations affect the formation rate and final concentrations of various reaction intermediates and products.61 For the same valence, a linear relationship was observed between the formaldehyde disappearance rate and ionic radius of hydrated cations where larger cation radii gave rise to higher rate constants. In addition, irrespective of the ionic radii, divalent cations lead to faster formaldehyde disappearance rates titan monovalent cations. For the proposed mechanism where an intermediate chelate participates in the reaction (Fig. 7.30), an increase in positive charge density in smaller cations was suggested to improve the stability of the chelate complex and, therefore, decrease the rate of the reaction. The radii and valence also affect the formation and disappearance of various hydrox-ymethylated phenolic compounds which dictate the composition of final products. 

Bismuth forms both 3+ and 5+ cations, although the former are by far the more common in nature. The ionic radius of Bi is even closer to that of La, than Ac, so again La is taken as the proxy. As noted above, Bi has the same electronic configuration as Pb, with a lone pair. It is unlikely therefore that the Shannon (1976) radius for Bi is universally applicable. Unfortunately, there is too little known about the magmatic geochemistry of Bi, to use its partitioning behavior to validate the proxy relationship, or propose a revised effective radius for Bi. The values of DWD u derived here should be viewed in the light of this uncertainty. 

The linear dependence of the pitting potential on ionic radius is likely a reflection of the similarly linear relationship between the latter and the free energy of formation of aluminum halides.108 It is reasonable to assume that the energy of adsorption of a halide on the oxide is also related to the latter. Hence, one could postulate that the potential at which active dissolution takes place is the potential at which the energy of adsorption overcomes the energy of coulombic repulsion so that the anions get adsorbed. 

Cations in aqueous solutions have an effective radius that is approximately 75 pm larger than the crystallographic radii. The value of 75 pm is approximately the radius of a water molecule. It can be shown that the heat of hydration of cations should be a linear function of Z /r where is the effective ionic radius and Z is the charge on the ion. Using the ionic radii shown in Table 7.4 and hydration enthalpies shown in Table 7.7, test the validity of this relationship. 

Figure 9.3 shows the relationship between ionic radius and proton affinity in a graphical way for monatomic ions having a — 1 charge. It is clear that to a good approximation there is a correlation between the size of the anion and its proton affinity. While this is in no way a detailed study, it is clear that the smaller (and thus harder] the negative ion (with the same type of structure) the more strongly it binds a proton. 

Figure 5.6 Relationship between cell volume and cubed ionic radius of main cation in Vl-fold coordination with oxygen. From Brown (1982). Reprinted with permission of The Mineralogical Society of America.

Fig. 3.1 Relationship between the unit cell volume of various MOOH minerals or synthetic compounds with the diaspore structure and the ionic radius of M ".

Fig. 3.7 Top Relationship between the unit cell edge length a of synthetic goethites and various structurally incorporated metals. Bottom Rate of change of a per mol of substituted metal (= slope of the upper curves) vs. ionic radius of the respective metal cations (Gerth, 1990, with permission).

Li20(s). The other members of the group form mainly the peroxide or superoxide. Lithium exhibits the diagonal relationship that is common to many first members of a group. Many of lithium s compounds are similar to the compounds of Mg. This similarity is related to the small ionic radius of Li+, 58 pm, which is close to the ionic radius of Mg24, 72 pm, but substantially less than that of Na+, 102 pm. 

The linear relationship between unit cell volume and the cube of the ionic radius among a series of isostructural compounds has been emphasized by Shannon and Prewitt (2) as a powerful means of systematizing crystallographic resuTts. The data of Schwartz and Fonteneau et al. (rhs Figure 2) are consistent with the unsubstituted A +B +04 results and thus support the concept of a mean radius r. and by analogy as a predictor, in combination with the appropriate SFM, of the occurrence of particular structure types. 

Figure 5.17. Relationship between the partition coefficient for inner aragonite shell and coexisting extrapallial fluid of the marine mollusc, Pinctada furcata, and ionic radius of the elements. (After Speer, 1983.)...

Ionic radius. The wide variation of metal-oxygen distances within individual coordination sites and between different sites in crystal structures of silicate minerals warns against too literal use of the radius of a cation, derived from interatomic distances in simple structures. Relationships between cation radius and phenocryst/glass distribution coefficients for trace elements are often anomalous for transition metal ions (Cr3+, V3+, Ni2+), which may be attributed to the influence of crystal field stabilization energies. 

Because of steric factors there is not a simple relationship between AG or AH or TAS and the ionic radius . There is then no simple explanation of such observations as tetrad effects, see below, since some such breaks could come about in an apparent series of ion size changes of equal increment. Tetrad breaks may occur at the expected place following ionic size differentials but may also occur elsewhere through the sensitivity of packing problems. 

Beryllium and aluminum show a similar relationship. Here, the ionic radius of aluminum (0.50 A) is considerably greater than that of beryllium (0.31 A), but the charge-per-unit-size values for the two ions are quite close since the charge ratio is 3/2. This time, in situations in which size-to-charge ratio is an important consideration, beryllium and aluminum should behave similarly. (Thus the major difficulties in the early preparation of beryllium compounds were not in their separation from their homologs but rather in their separation from the corresponding aluminum compounds.)... 

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