Shannon radii

However, since only values of rexpti are obtained, it is necessary to assume a value for the ionic radius of either r+ or r- in order to derive the ionic radius of the other. It is usual to assume a value of 1.40 A for the radius of the and 1.94 A for the radius of CP (Pauling, 1948) because these are half the minimum anion-anion distances found in crystal structures. Values for ionic radii (Shannon and Prewitt, 1969 Shannon, 1976 Brown, 1988) are listed in Table V for a coordination number of 6 around the metal atoms. Thus, values of radii are hypothetical, based on the idea of an additivity rule and a few initial assumptions on anion size. 

The concept of atomic or ionic size is one that has been debated for many years. The structure map of Figure 1 used the crystal radii of Shannon and Prewitt and these are generally used today in place of Pauling s radii. Shannon and Prewitt s values come from examination of a large database of interatomic distances, assuming that intemuclear separations are given simply by the sum of anion and cation radii. Whereas this is reasonably frue for oxides and fluorides, it is much more difficult to generate a self-consistent set of radii for sulfides, for example. A set of radii independent of experimental input would be better. The pseudopotential radius is one such estimate of atomic or orbital size. 

From Cantrell (1988), estimated from correlations of lanthanide ionic radii (Shannon, 1976) versus lanthanide carbonate complexation constants, plus the actinide ionic radius estimates of Shannon (1976). 

Averaged over acentric displacements of T. Estimated from ionic radii (Shannon and Prewitt )]. 

A few publications have appeared on phase relationships and/or intermediate phases of AgF-RF3, TIF-RF3, and NH4F-RF3 systems. On the basis of ionic radii (Shannon, 1976), Ag" fits into the alkaline cations between Na and K, while TF and NHl have similar sizes as Rb. Therefore, phases with analogous formulae and structures can be expected. 

We reproduced the dependence of the differences [AfH°(RCl3, cr, 298) — AfH°(R , aq, 298)], taken from Cordfunke and Konings (2001a), on the crystal-chemical radii of R for a CN of 6, however, using the ionic radii (Shannon, 1976) described by a pol5momial of degree 2. This polynomial had the form... 

The compounds, successively synthesized, CpJU(0Ar)(0) and Cp2U(NAr)(0) (Ar = 2,6-diisopropylphenyl Evans et al. 1992c) are, respectively, the first and complexes with terminal monoxofunctional groups as confirmed by the respective electron absorption spectra. The structure of Cp2U(0-2,6-Pr2-C6H3)0 (fig. 31) is analogous to that of the N derivative. The difference in the two U-O (terminal bond distances) 1.859(6) for the U species and 1.844(4) A for is consistent with the difference in the and U ionic radii (Shannon 1976). 

When publishing his tables of effective ionic radii. Shannon referred to the results of the charge density studies and included a second table of crystal radii where the radius of each cation had been increased by addition of 14 pm and the radius of each anion reduced by the same amount. It should be clear that addition of the crystal radii of the cation and anion will produce the same interatomic distance as addition of the traditional effective ionic radii, but Shannon felt that crystal radii correspond more closely to the physical size of the ions in a solid. ... 

The uncertainty of the proper coordination number of any particular plutonium species in solution leads to a corresponding uncertainty in the correct cationic radius. Shannon has evaluated much of the available data and obtained sets of "effective ionic radii" for metal ions in different oxidation states and coordination numbers (6). Unfortunately, the data for plutonium is quite sparse. By using Shannon s radii for other actinides (e.g., Th(iv), U(Vl)) and for Ln(III) ions, the values listed in Table I have been obtained for plutonium. These radii are estimated to have an uncertainty of 0.02 X ... 

The spherical Cu(I) cation (d ° electronic configuration) is thus ideally suited for the formation of double-stranded helicates with LI and L4-L6, because of its lack of directional coordination bonds and its limited electrostatic factor z /R = 1.30 eu A (z is the charge of fhe cation and R is its ionic radius Shannon, 1976), which is compatible with CN = i (Figure 5). The demonstration of this novel concept in coordination chemistry, combined with the undeniable aesthetic appeal of helical strucfures, were at the origin of a considerable enthusiasm leading to the isolation and structural characterization of a plethora of binuclear double-, triple-, and quadruple-stranded helicates during the past two decades (for comprehensive reviews, see Albrecht, 2001 Constable, 1992, 1994, 1996 ... 

Also as a result of the lanthanide contraction, yttrium has an ionic radius comparable to that of the heavier REE species in the holmium-erbium region. If the effective ionic radius (Shannon 1976) of is plotted (0.90 A)., it plots in between element 67 (Ho) and 68 (Er). Scandium (effective ionic radius is 0.745 A), plots outside of the Lanthanide series. As also the outermost electronic arrangement of yttrium is similar to the heavy rare earths, the element behaves chemically like the heavy rare earths. It concentrates during (geo)chemical processes with the heavier REEs, and is difhcult to separate from the heavy REEs. Scandium, on the other hand, has a much smaller atomic radius, and the trivalent ionic size is much smaller than that of the heavy rare earths. Therefore, scandium does not occur in rare earth minerals, and in general has a chemical behavior that is significantiy different from the other rare earth elements (Gupta and Krishnamurthy 2005). 

Shannon and Prewitt base their effective ionic radii on the assumption that the ionic radius of (CN 6) is 140 pm and that of (CN 6) is 133 pm. Also taken into consideration is the coordination number (CN) and electronic spin state (HS and LS, high spin and low spin) of first-row transition metal ions. These radii are empirical and include effects of covalence in specific metal-oxygen or metal-fiuorine bonds. Older crystal ionic radii were based on the radius of (CN 6) equal to 119 pm these radii are 14-18 percent larger than the effective ionic radii. 

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. 

Figure 24. Lattice strain model applied to zircon-melt partition coefficients from Hinton et al. (written comm.) for a zircon phenocryst in peralkaline rhyolite SMN59 from Kenya. Ionic radii are for Vlll-fold coordination (Shannon 1976). The curves are fits to Equation (1) at an estimated eraption temperature of 700°C (Scaillet and Macdonald 2001). Note the excellent fit of the trivalent lanAanides, with the exception of Ce, whose elevated partition coefficient is due to the presence of both Ce and Ce" in the melt, with the latter having a much higher partition coefficient into zircon. The 4+ parabola cradely fits the data from Dj, and Dy, through Dzi to Dih, but does not reproduce the observed DuIDjh ratio. We speculate that this is due to melt compositional effects on Dzt and (Linnen and Keppler 2002), and possibly other 4+ cations, in very silicic melts. Because of its Vlll-fold ionic radius of 0.91 A (vertical line), Dpa is likely to be at least as high as Dwh, and probably considerably higher.

Figure 2.2 A contour plot of the electron density in a plane through the sodium chloride crystal. The contours are in units of 10 6 e pm-3. Pauling shows the radius of the Na+ ion from Table 2.3. Shannon shows the radius of the Na+ ion from Table 2.5. The radius of the Na+ ion given by the position of minimum density is 117 pm. The internuclear distance is 281 pm. (Modified with permission from G. Schoknecht, Z Naiurforsch 12A, 983, 1957 and J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed., 1993, HarperCollins, New York.)...

We focus attention on the fact that the crystal radii (CRs) for the various cations listed in table 1.11 are simply equivalent to the effective ionic radii (IRs) augmented by 0.14 A. Wittaker and Muntus (1970) observed that the CR radii of Shannon and Prewitt (1969) conform better than IR radii to the radius ratio principle and proposed a tabulation with intermediate values, consistent with the above principle (defined by the authors as ionic radii for geochemistry ), as particularly useful for sihcates. It was not considered necessary to reproduce the... 

One reason for the failure of the radius ratio rules is that ions do not behave like hard spheres. Even those that are hard in the Pearson (1973) sense can still be compressed. This is clearly seen in the way the bond length varies with the bond valence. If cation anion bonds can be compressed, so can the distance between the 0 ions in the first coordination sphere. The stronger the cation anion bonds, therefore, the closer the anions in the first coordination sphere can be pulled together (Shannon el al. 1975). 

Shannon and Prewitt (1969) give the 10-coordinate radius of Ba + as 152pm compared to 181pm for Cs+. 

Further, ions are not hard, billiard ball like spheres. Since the wave functions that describe the electronic distribution in an atom or ion do not suddenly drop to zero amplitude at some particular radius, we must consider the surfaces of our supposedly spherical ions to be somewhat fuzzy. A more subtle complication is that the apparent radius of an ion increases (typically by some 6 pm for each increment) whenever the coordination number increases. Shannon10 has compiled a comprehensive set of ionic radii that take this into account. Selected Shannon-type ionic radii are given in Appendix F these are based on a radius for O2- of 140 pm for six coordination, which is close to the traditionally accepted value, whereas Shannon takes the reference value as 126 pm on the grounds that it gives more realistic ionic sizes. For most purposes, this distinction does not mat-... 

The Shannon-Prewitt tabulation also distinguishes between different spin states for ions of the transition elements. For example, the radius of Fe2+ in octahedral six-coordination is 17 pm smaller for the low-spin state as opposed to high-spin. If you study bio-inorganic chemistry in a more advanced text, you will find that this fact is of great importance in understanding the mechanics of the haemoglobin molecule (see Section 9.8). 

The Shannon-Prewitt tables probably provide the most useful and most comprehensive collection of ionic radii. Values are included for improbable species such as Br7+ the sum of its radius and that of O2-gives the observed internuclear distance in BrO. Shannon-Prewitt radii for the more plausible ions in octahedral six-coordination are given in Table 4.2. These are useful for most practical purposes (see Chapter 5) except where octahedral six-coordination is uncommon for the ion in question. 

---