Shannon’s radii

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 ... 

A nice feature of Shannon s radii - dubbed effective ionic radii by himself - is that the complete set is additive, such that experimental cation-anion distances are, in most cases, correctly reproduced. To allow for this, a few ions must have negative radii but such an unphysical property does not bother the brave crystal chemist. Second, because of the popularity of Pauling s radii, the size of in six-fold coordination is also fixed to 1.40 A, such that traditionalists of ionic radii do not have to rethink. Nonetheless, an alternative, likewise additive, set of crystal radii - not to be confused with Pauling s crystal radii - is generated from Shannon s effective radii by subtracting 0.14 A from all anionic radii and adding this 0.14 A to all the cationic radii (see below). 

How good are these values Shannon s radii reproduce the observed interionic distances in the 17 alkali metal halides with the rock salt structures with an average... 

AR (=Ra-Rc) for selected binary compounds. Da and are the D parameters of anions and cations, respectively, while Rg and Rc are Shannon s crystal radii of anions and... 

Shannon s crystal ionic radii [51], except where otherwise noted. 

In Figure 9(c) the ideal specific areas for flat LaO and CUO2 sheets, calculated from Shannon s ionic radii, are compared. If the regular K2Nip4 stmcture is to be assumed for La2Cu04,... 

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. 

Ion Ro (for S = 37 pm) for different anions (pm) Shannon crystal radii (pm) for different coordination numbers ... 

Shannon s crystal radii, however, better match the experimentally found electron density distribution mentioned at the begiiming. For example, modern X-ray data show that the minimum electron density for LiF ([NaCl] t) e) corresponds to r(Li+) = 0.92 A and r(F ) = 1.08 A. This reflects a significantly larger/smaller lithium/fluorine ion than Pauling s (0.60/1.36 A), Goldschmidt s (0.78/1.33 A) and also Shannon s effective ionic radii (0.76/1.33 A), but it is already quite close to Shannon s crystal radii (0.90/1.19 A). Summarizing, effective ionic radii correspond to the idea of closely packed anions but crystal radii are closer to the real sizes of anions and cations. 

Many mineralogists use Goldschmidt s values. The most comprehensive set of ionic radii is that compiled by Shannon and Prewitt (1969) and revised by Shaimon (1976). Table 4.6 lists Shannon s ionic radii. Although there are several different tabulations they are, for the most part, internally consistent. So it is important to use radii from only one data set. Never mix values from different tabulations. 

Shannon, R.D. and Prewitt, C.T. (1969) Effective ionic radii in oxides and fluorides, Acta Crystallogr B25, 925. Gives the alternatives to Pauling s radii. 

TABLE 5.2 Shannon s ionic radii (pm) for selected ions, according to their coordination number. ... 

Fig. 14. Distribution ratios of rare-earth elements between 0.3 M di-n-octyl-phosphonic acid/benzene and 0.05 M HCl (Peppard et al. 1968) as a function of (a) atomic number, (b) the reciprocal of Templeton and Dauben s (1954) ionic radii, (c) the reciprocal of Shannon s (1976) ionic radii.

The calculated results of tolerance factors for some mixed conducting materials are described in Fig. 2.1. Shannon s ionic radii referring to the coordination numbers 12 (A-site) and 6 (B-site) has been used, although it is known that oxygen deficiency influences the coordination number and therefore the ionic radii. From the results, we can find that the tolerance factors of several popular materials such as LSM, LSCF are close to 1. Therefore the tolerance factor should be considered first in designing a new material. 

In the calculations by means of Kapustinskii s equation, we used a value of 1.81 A for the crystalline radius of the Cl ion in accordance with Shannon s data (Shannon, 1976), in which crystalline radii are given for several R + ions (Sm, Eu k Tm ", and Yb k lattices with various CNs. The radii for CN = 6 are displayed in Figure 28, together with the... 

FIGURE 28 Crystalline radii for the ions O), calculated using the Born-Haber cycle and Kapustinskii s equation from the enthalpies of formation found with the use of Kim and Oishi s scheme (Kim and Oishi, 1979) A, Shannon s data (Shannon, 1976). The solid curve connects the values calculated from the fit of polynomial (28). Reproduced from Chervonnyi and Chervonnaya (2005c) with permission from Pleiades Publishing, Ltd. 

It follows from Figure 28 that the crystalline radii that we calculated for the Sm, Tm, and ions correlate well with Shannon s data (Shannon, 1976). Poorer correlation is observed for the Eu " ion. Two facts are, however, worth noting. First, Shannon (1976) reported the results obtained by comparison methods from the structural parameters of oxide and fluoride crystals. Second, the Eu ion radius versus CN dependence implies that the divalent europium ion radius in a crystal with CN = 6 is 1.15 A rather than 1.17 A. The thus corrected Shannon s data (Shannon, 1976) correlate better with our values for the Eu ion radius. 

In Table 20.7 are listed radii of trivalent actinide ions (coordination number CN 6) derived from measurements on trichlorides by the method of Bums, Peterson, and Baybarz [288]. Determinations of M-Cl distances have been made for M = U, Pu, Am, Cm, and Cf the other values were estimated by use of unitcell data and curve fitting. All these radii are relative to the trivalent lanthanide radii of Templeton and Dauben [396], who employed data from cubic sesquioxides and assumed atomic positions to establish M-O distances. Also included in Table 20.7 are radii of tetravalent actinide ions obtained from the M-O distances calculated from unit-cell parameters of the dioxides [1] by subtracting 1.38 A for oxygen (the value used [396] for the sesquioxides). For comparison. Shannon s ionic radii, derived from oxides and fluorides, and Peterson s tetravalent radii, derived from dioxides, are shown [537,538]. As... 

Usually, this factor is evaluated from Shannon s ionic radii [13] for respective coordination numbers. When the tolerance factor is near unity, the structure is the ideal cubic one. In other cases, orthorhombic or rhombohedral distortions appear. 

Perovskite structure is realized when 0.8 tolerance factor is closer to 1 (0.9 < f < 1.05). However, it is important to realize that ionic approximation is not always valid and several other factors (e.g., Jahn-Teller effect, metal-metal interactions) may strongly affect crystal structure [4]. In other words, it is not possible to predict space group, in which considered material will crystallize only on the basis of calculated value of t. Additionally, there are other ways for calculating tolerance factor one is based on Bond Valence method [14], while the other one uses real interatomic distances determined, for instance, from neutron diffraction studies. Values of t derived from the last method represent in fact the actual degree of distortion of the cell and are usually much closer to 1, comparing to values obtained from Shannon s ionic radii. 

Figure 4. Fits of lattice strain model to experimental mineral-melt partition coefficients for (a) plagioclase (run 90-6 of Blundy and Wood 1994) and (b) elinopyroxene (ran DC23 of Blundy and Dalton 2000). Different valence cations, entering the large cation site of each mineral, are denoted by different symbols. The curves are non-linear least squares fits of Equation (1) to the data for each valence. Errors bars, when larger than symbol, are 1 s.d. Ionic radii in Vlll-fold coordination are taken from Shannon (1976).

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