Radius hypothetical ionic

Here we see clearly the large concentration of density around the oxygen nucleus, and the very small concentration around each hydrogen nucleus. The outer contour is an arbitrary choice because the density of a hypothetical isolated molecule extends to infinity. However, it has been found that the O.OOlau contour corresponds rather well to the size of the molecule in the gas phase, as measured by its van der Waal s radius, and the corresponding isodensity surface in three dimensions usually encloses more than 98% of the total electron population of the molecule (Bader, 1990). Thus this outer contour shows the shape of the molecule in the chosen plane. In a condensed phase the effective size of a molecule is a little smaller. Contour maps of some period 2 and 3 chlorides are shown in Figure 8. We see that the electron densities of the atoms in the LiCl molecule are only very little distorted from the spherical shape of free ions consistent with the large ionic character of this molecule. In... 

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. 

Deviations from the Limiting Law. In Figure 3 results for 1 1 electrolytes with four different ion-sizes are plotted for hypothetical solutions having D = 78.54, T = 25.0°C, density = 1.0 and n = 1. The DH limiting-law is also plotted for comparison. It should be noted that the ionic atmosphere extends outwards from the surface of the central ion, and the parameter a is the mean effective ionic radius rather than the distance of closest approach of the DH theory. 

The relation of H content, n, to lattice parameter for VH is interpreted readily by the hydridic model as indicated in Figure 5, which represents a portion of a hypothetical unit cell in which H-, of radius 1.22 A., is located in an octahedral site in a BCC V+5 cell. The radius of V+5 is 0.48 A., both ionic radii being corrected for fourfold coordination (12). The V-H distance is, of course, the same as that given by the atomic model shown on the right, where the metal and hydrogen radii are, respectively, 0.93 and 0.56 A. (see also Figure 6). 

We start with the influence of ionic radius on partitioning. Consider a hypothetical silicate Y Si cO where is a cation of radius r which fits exactly into the largest cation site without straining the stmcture. The partitioning of Y " between crystal and coexisting silicate melt should be determined principally by the free... 

The assumptions inherent in this are (i) that the lattices considered, both real and hypothetical, are totally ionic, or if not that the nonionic contribution is the same in each, and (ii) that the lattices have the same energy, that is that the ions M and M" have the same radius. Neither of these assumptions can be expected to be completely true, for example Na+, Ne+ and Mg+ are not isoelectronic, but the deviations resulting from the assumptions should be small. Though the results of Grimm and Herzfeld need recalculating, because of the change in the values of... 

We start with the influence of ionic radius on partitioning. Consider a hypothetical silicate Y +SLO... 

Fig. 3. Free energy (-A G) of hydration of alkali ions (curve a) as compared with free energy (-AG) of ligand binding for two hypothetical cases of ligand interaction in a chelating cavity (curves b and c), as a function of the reciprocal ionic radius...

Note Using the tabulated ionic radius of Ca (i.e. that of Ca2+) would be less valid than using the atomic radius of a neighboring monovalent ion, for the problem asks about a hypothetical compound of monovalent calcium. Predictions with the smaller Ca2+ radius (100 pm) differ substantially from those listed above the expected structure changes to rock-salt, the lattice enthalpy to 758 kJmol-1, Af// (CaCl) to —446kJ mol-1 and the final reaction enthalpy to +96 kJ mol-1. 

The simplest argument that TmS is trivalent, TmSe intermediate valent and TmTe divalent under normal conditions comes from comparing the lattice constants of the lanthanide sulfides, selenides and tcllurides as shown in fig. 58 (after Bucher et al. 1975). The lanthanide contraction is the cause for the general trend in the curves and the standard divalent Sm, Eu and Yb ions with their larger ionic radius are the obvious deviations. TmTe lies on the divalent curve, TmS on the trivalent one and TmSe is intermediate and by linear interpolation between a hypothetical divalent and trivalent TmSe one obtains a valency of 2.75. The figure also shows that SmS, in this case by pressure or trivalent rare earth doping, can be intermediate valent, TmSe, in this case by stoichiometry variation, can become trivalent and TmTe, in this case by pressure, oxidation and stoichiometry variation, can become intermediate valent. 

There has been some speculation that an ionic noble-gas compound with the stoichiometry Xe F can be prepared. Using both the Born-Lande and Kapustinsldi equations, estimate the lattice energy for this hypothetical compound. Carefully state all assumptions that you make to establish a value for the ionic radius of Xe. Atomic radii are given in Table 7.3. 

Many ionic systems contain nonspherical ions. For example, anions S04, Cr04 , Mo04, W04 have tetrahedral structure, and anions C03 , NOs" have triangular structure. It is useful to define some concept of effective radii together with an effective parameter describing the degree of nonsphericity to describe these ions. Yashimirskii has proposed a system of so-called thermochemical radius for this purpose. He defined thermochemical ionic radius as follows thermochemical radius is a hypothetical radius of nonspherical ions, by this value a spherical ion... 

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