Ionic radii listed

The ionic radii listed in Tables 6.3 and 6.4 in most cases apply to ions which have coordination number 6. For other coordination numbers slightly different values have to be taken. For every unit by which the coordination number increases or decreases, the ionic radius increases or decreases by 1.5 to 2 %. For coordination number 4 the values are approximately 4 % smaller, and for coordination number 8 about 3 % greater than for coordination number 6. The reason for this is the mutual repulsion of the coordinated ions,... 

CsCl crystallizes in a cubic structure that has a Cl- at each corner and a Cs+ at the center of the unit cell. Use the ionic radii listed in Table 10.1 to predict the lattice constant, a, and compare with the value of a calculated from the observed density of CsCl, 3.97 g/cm3. 

MgS and CaS both crystallize in the NaCl-type lattice (Fig. 10-7). From the ionic radii listed in Table 10.1, what conclusion can you draw about anion-cation contact in these crystals ... 

The use of ionic radii listed in App. 3A is inappropriate in this case because the bonding is almost purely covalent. (See periodic table printed on inside front cover.)... 

Example 12-7. Employ the radius ratio rule using the Pauling ionic radii listed in Table 12.5 to predict the lattice types of (a) CsCI, (b) SrF2, and (c) KBr. 

If the density of this material is 5.24 g/cm, compute its atomic packing factor. For this computation, you will need to use the ionic radii listed in Table 12.3. 

The details of sample preparation, molar volume measurement, and X-ray diffraction analyses have been reported in the preliminary works on molten CeClj and ErCl,. CeClj is known to be hexagonal with a bimolecular unit, in which each Ce atom is surrounded by nine Cl atoms. On the other hand, ErCl, forms a monoclinic crystal, the unit cell of which contains four molecules. The number of the nearest Cl atom around Er atom is six. As shown in Fig. 1, the first peak centered at 0.28 to 0.29nm appeared sharply in the correlation function G(r) for molten CeCl, and the broad peak existed in the range of 0.46 to 0.6nm upon which the shoulder-like peak overlapped in the neighborhood of 0.4nm. According to the ionic radius list by Shannon, the first peak was assignable to the Ce-Cl pair since the ionic radii of Ce (VI) and Cr(VI) were 0.101 and 0.181 nm, respectively, and the... 

Table 5.1 lists some of the atomic properties of the Group 2 elements. Comparison with the data for Group 1 elements (p. 75) shows the substantial increase in the ionization energies this is related to their smaller size and higher nuclear charge, and is particularly notable for Be. Indeed, the ionic radius of Be is purely a notional figure since no compounds are known in which uncoordinated Be has a 2- - charge. In aqueous solutions the reduction potential of... 

The remaining compounds listed in Table II all adopt structures with infinite metal-metal bonded chains consisting of octahedral cluster units fused on opposite edges. However, because of the large difference in effective ionic radius of the cations concerned, very different lattice types are dictated. The compounds NaMoi 06 (19,22) and Bas(Moit06)8 (17) adopt tunnel structures with the Na+ or Ba2+ ions located in sites along the tunnels with 8-fold coordination by oxygen atoms. 

As early as 1920 s Goldschmidt, Pauling and Zachariasen (5—7) observed the additivity of atomic and ionic radii to reproduce the interatomic distances very closely. However, the early lists of ionic radii were based on a cation coordination number of six and a fixed value for the ionic radius of either O - or F. Goldschmidt was first to notice that the radii varied with CN. 

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. 

When comparing ionic porosity of different minerals, for self-consistency, the same set of ionic radii should be used, and the same temperature and pressure should be adopted to calculate the molar volume of the mineral. Table 3-3 lists the ionic porosity of some minerals. It can be seen that among the commonly encountered minerals, garnet and zircon have the lowest ionic porosity, and feldspars and quartz have the highest ionic porosity. More accurate calculation of IP may use actual X-ray data of average inter-ionic distance and determine the ionic radius in each structure. 

In 1967, C. J. Pederson of DuPont deNemours Co. synthesized the cyclic polyethers ( ) These cyclic polyethers are commonly referred to as "crown ethers" (see Figure 3). In solution, crown ethers are extremely effective ligands for a wide range of metal ions. The size of the ring cavity and the ionic radius of the metal affect the stability of the complex. Tables I and II list the cavity diameters for the crown ethers and the ionic radii of a number of metal ions (6-11). 

The size of an arsenic atom depends on its valence state and the number of surrounding atoms (its coordination number). When valence electrons are removed from an atom, the radius of the atom not only decreases because of the removal of the electrons, but also from the protons attracting the remaining electrons closer to the nucleus (Nebergall, Schmidt and Holtzclaw, 1976), 141. An increase in the number of surrounding atoms (coordination number) will deform the electron cloud of an ion and change its ionic radius (Faure, 1998), 91. Table 2.2 lists the radii in angstroms (A) for arsenic and its ions with their most common coordination numbers. 

The examples of minerals affected by Jahn-Teller distortions that are listed in table 6.1 demonstrate that the concept of ionic radius is not a rigorous atomic property when applied to crystal structures containing the Cr2+, Mn3+ and Cu2+ ions. Other consequences of Jahn-Teller distortions in mineral structures are discussed in 6.8.3.2 and elsewhere (Strens, 1966a Walsh et al., 1974). 

The equilibrium distance between an interacting pair is the sum of the van der Waals or ionic radii of two atoms. Hence the ionic radius of the cation is important in all interactions, both nonspecific and electrostatic interactions. The ionic radii of important cations are listed in Table III. The cationic charge, on the other hand, is important only to the electrostatic interactions. 

The values of AGfc calculated above are listed in Table IX and plotted against (l/rA+) in Fig. 3. The straight line is drawn with slope calculated from Eq. (75), using Ds = 78.5, D0 = 1.78, for water at 25°C. The points for iodide ion is clearly unacceptable, as already discussed, but it seems unlikely that any revision will bring AGFC(I) up from zero to the predicted value of ca. 70 kcal mole - h Clearly more data are needed before the continuum theory can be subjected to even an approximate quantitative test, but already we may forecast that the dependence of AGFC on ionic radius will be less sensitive than Eq. (75) implies. 

Most inorganic chemistry texts list cut-off values for ther+/r ratios corresponding to the various geometries of interstitial sites (Table 2.3). However, it should also be pointed out that deviations in these predictions are found for many crystals due to covalent bonding character. An example for such a deviation is observed for zinc sulfide (ZnS). The ionic radius ratio for this structure is 0.52, which indicates that the cations should occupy octahedral interstitial sites. However, due to partial covalent bonding character, the anions are closer together than would occur from purely electrostatic attraction. This results in an effective radius ratio that is decreased, and a cation preference for tetrahedral sites rather than octahedral. 

Ionic radius depends on whether the ion is in the high spin or low spin state. In the Fe oxide structure (and where a choice exists), the ions listed adopt a high spin state. 

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