Radii Shannon-Prewitt

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. 

With regard to each of the following, does it make any difference whether one uses correct radii, such as empirically derived Shannon>Prewitt radii, or whether one uses theoreiically reasonable but somewhat misassigned traditional rudii ... 

Fig. 20. Left hand panel 23 A x 23 A STM image of the (2x1) reconstruction on Nao.67W03(100) taken at +0.4 V sample bias and 1 nA tunnel current. Top right hand panel unrelaxed Nao.sO surface plane. The oxygen ions (large spheres) and sodium ions (small spheres) are assigned their conventional Shannon-Prewitt radii. Bottom right panel schematic of the relaxed (2x1) reconstruction with peroxide-like oxygen ion dimers. Adapted from ref. 298.

Shannon-Prewitt radii for other monoatomic ions at various coordination numbers are recorded in table 3.2. The choice of radius is important when estimating the solvation parameters of highly charged ions such as Al " ". It is also important to note that the estimated radii for transition metal ions such as Mn " " and Fe " " depend on the spin state of the d electrons in the ion. This also leads to important differences in solvation energies. 

Trends in the properties of lanthanides are usually visualized as Z plots although in some cases, plots against orbital angular momentum show linear relationships where the more traditional Z plots are difficult to interpret. The thermodynamic parameters required for a firm underpinning of much of lanthanide chemistry are now in place and most of the important quantities have been determined or reliably estimated. Revised ionic radii are now available and it will be interesting to see whether these replace the classical Shannon-Prewitt radii which have been used for over 30 years. 

Cesium chloride has a radius ratio of 1.08 because, using Shannon-Prewitt radii, the cesium cation is larger than the chloride anion. In this case, we should actually calculate r lr (= 0.93) and assume that the cations form the A-type lattice and the chlorides fill the appropriate holes. Note that 0.93 falls in the cubic hole/C.N. = 8 range of Table 7.4. As shown in Figure 7.21e, the cesium cations form a simple cubic lattice, and the chloride anions occupy the cubic holes. Alternatively, the chloride anions can be pictured as forming the A-type lattice with the cesium cations in the cubic holes. Using the solid lines as the unit cell, note that the coordination number of both the cation and anion is 8. Note also that there is a total of one [8( )] chloride per unit cell and, of course, one cesium cation in the body consistent with a 1 1 stoichiometry. Table 7.9 shows that the greatest correlation (100%) between the known structure and calculated radius ratios occurs for the CsCl structure. 

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). 

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... 

As it can be seen, the difference between these radii is about 0.002 nm, which indicates that the interionic interactions lead to a shortening of bond lengths and if the oxygen ion radius is assumed to be 0.14 nm, the metal ion radii should be smaller by about 0.002 nm. On the other hand, if we assume oxygen ion radius for coordination number 4 as 0.138 nm, i.e., the value proposed by Shannon and Prewitt (Shannon Prewitt, 1969, 1970), then metal ion radii do not differ much from the table values. 

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. 

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... 

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. 

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

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. 

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 Gibbs energy of solvation according to the Born model is given by equation (3.4.6). The constant AlCo /Stiso is equal to 6.945 x lO Jmmol" The radius of Na" " according to Shannon and Prewitt is 116 pm (table 3.1). The factor (1 — l/Sj) is equal to 0.972. The resulting value of AjGi is -581.9 kJmor ... 

Many X-ray diffraction studies of electrolyte solutions have been carried out in aqueous solutions [Gl, 4, 5]. Values of the most probable distance, between the oxygen atom in water and a number of monoatomic ions are summarized in table 5.1. In the case of the cations, this distance reflects the radius of the cation plus the effective radius of the water molecule measured in the direction of the lone pairs on oxygen. In the case of alkali metals, the effective radius of water increases from 122 pm for Li" " to 131 pm for Cs when the Shannon and Prewitt radii are assumed for the cations (see section 3.2), the average value being 127 pm. This result can be attributed to the observation that the coordination number for water molecules around an alkali metal or alkaline metal earth cation changes with cation size and electrolyte concentration. In the case of the Li" " ion, this number decreases from six in very dilute solutions to four in concentrated solutions [5]. Because of the electrostatic character of the interaction between the cation and water molecules, these molecules exchange rapidly with other water molecules in their vicinity. For this reason, the solvation coordination number should be considered as an average. 

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