Shannon-Prewitt ionic radii

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. 

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 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. 

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. 

Goldschmidt and, more recently, Shannon and Prewitt, concentrated on the analysis of experimental data (mostly fluorides and oxides) with the aim of obtaining a set of ionic radii which, when combined in pairs (eq. 6.6), reproduced the observed internuclear distances. In view of the approximate nature of the concept of the ionic radius, no great importance should be attached to small differences in quoted values so long as self-consistency is maintained in any one set of data. Some dependence of ionic size oti coordination number is expected if we consider the different electrostatic interactions that a particular ion experiences in differing environments in an ionic crystal. The value r,o for a given ion increases slightly with an increase in coordination number. For example, the Shannon values of rion for Zn are 60, 68 and 74 pm for coordination numbers of 4, 5 and 6, respectively. 

Shannon and Prewitt (Shannon Prewitt, 1969,1970,1976) performed a verification of ionic radii in isotypic compounds, basing on the linear relation between the unit cell volume and the ionic radius (r ). Next, Brisse and Knop (Brisse Knop, 1968) have demonstrated a linear relation between the radius and the cube root of the unit cell volume for... 

The coordination chemistry of tetravalent cerium is in many aspects very similar to the coordination chemistry of tetravalent plutonium. The ionic radius of Ce" " (0.94 A) is within the experimental error identical to the ionic radius of Pu + (Shannon and Prewitt, 1969). Due to the similarity in the charge-to-ionic size ratio, the complex formation constants of tetravalent cerium are essentially the same as those of tetravalent plutonium. Complex formation causes for the two metal systems the same shift of the redox potential. 

Interatomic distances in the (1, l)-type compounds are listed in table 22. The 0-0 distance within a triangular net [0(1)-60(1) in the table], which is equal to the fl-cell dimension, is considerably longer than twice the ionic radius of O [2.8 A after Shannon and Prewitt (1969)], whereas interlayer 0-0 distances [0(1)-30(1), 0(l)-30(2) and 0(2)-30(2)] are in rough accordance with it. This fact indicates that an oxygen ion is in contact with oxygen ions in the adjacent layers but is apart from those in the same layer. 

The primary consideration of the occupancy of polyhedral sites by cations is the ionic size. The ionic radius increases with the coordination number (C.N.). A table of effective ionic radii in sites was compiled (Shannon and Prewitt, 1969). In table 29.5 are listed the known examples of rare earth ions occupying the... 

The beryllium ion has a relatively small ionic radius (0.35 A (Shannon and Prewitt, 1969)). As a consequence of this small size, its hydrolysis reactions begin to occur at a relatively low pH (about 5.3). Only the divalent ion exists in aqueous solution. 

Radium has the largest ionic radius (1.43 A (Shannon and Prewitt, 1969)) and, consequently, has the weakest hydrolytic reactions. As a result of the weak reactions, the stabilities are difficult to measure. Adding to this difficulty is the radioactive nature of radium, with studies needing in many cases to be conducted only using specialised equipment. It is considered that radium will provide the main contribution to the long-term risk, in relation to radiation dose, in the case of the failure of a nuclear waste repository (SKB, 2006). Thus, its reactions in water, including hydrolysis, are quite important. 

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... 

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. 

Figure 3.5 Plot of the association constant of some 1 1 metal cation-hydroxy complexes at zero ionic strength (see Chap. 4) versus the electrostatic function luZon/irti + Toh). where the association reaction is written Af + OH"=A/OH " , and z and r are the charge and radius in nanometers (nm) or angstroms (A) (1 nm = 1 A) of cation M and OH ( oh = 1-40 nm). Cation radii are from Shannon and Prewitt (1969), log values from Baes and Mesmer (1981). The slope of the straight line suggests the contribution of electrostatic (ionic) bonding to the stability of the complexes. The extent to which species plot above this line presumably reflects the increased contribution of covalency to their stabilities.

The experimentally measured anion-cation distances in highly ionic solids can be interpreted on the assumption that each ion has a nearly fixed radius. For example, the difference in anion-cation distance between the halides NaX and KX is close to 36 pm irrespective of the anion X, and it is natural to attribute this to the difference in radii between Na+ and K+. To separate the observed distances into the sum of two ionic radii is, however, difficult to do in an entirely satisfactory way. One procedure is to look for the minimum value in the electron density distribution between neighboring ions, but apart from the experimental difficulties involved such measurements do not really support the assumption of constant radius. Sets of ionic radii are therefore all based ultimately on somewhat arbitrary assumptions. Several different sets have been derived, the most widely used being those of Shannon and Prewitt, based on the assumed radius of 140 pm for O in six-coordination. Values for a selection of ions are shown in Table 1. 

As indicated above, the covalent radius of an element depends on its oxidation state. In a binary ionic compound, MX, containing the positive ion, M. and the negative ion. X, the minimum distance between them is measurable with considerable accuracy by the method of X-ray diffraction. The problem is to divide such a distance into the ionic radii for the individual ions. That ions behave like hard spheres with a constant radius whatever their environment might be is an approximation to the real situation. In compounds which do not exhibit much covalency the approximation is reasonable, and led Shannon and Prewitt to assign radii to O- and F of 140 and 133 pm respectively after their study of many oxides and fluorides. Ionic radii are not assignable to every element, and the generalizations described apply only to those elements which do form ions in compounds, and are subject to their oxidation states (discussed in Chapter 5) and coordination numbers i.e. the number of nearest neighbours they have in the ionic compound). 

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