Ion sphere radius

The ionization potential appears to reduce sharply towards zero with decrease of the ion sphere radius indicating the effect of increased plasma coupling strength. Table 1 gives the energy levels of hydrogen-like Ne in a plasma environment for different plasma densities. 

Figure 12 Plot of orbital energy against the ion sphere radius for hydrogenic ions. Reprinted with permission from [174] 2005, John Wiley Sons, Inc.

Within the framework of the same dielectric continuum model for the solvent, the Gibbs free energy of solvation of an ion of radius and charge may be estimated by calculating the electrostatic work done when hypothetically charging a sphere at constant radius from q = 0 q = This yields the Bom equation [13]... 

Attention will be restricted here to fluorine compounds of the three d-transition series elements, in which the metal ion is octahedrally coordinated. Octahedral coordination, however, is found in nearly all these cases, which is quite reasonable considering the sizes of the ions in question. A close-packed octahedron of fluoride ions of radius 1.33 A adapts a size of its octahedral interstice appropriate to a sphere of radius 0.55 A. Cations having this size and larger ones meet the conditions of a contact between cations and anions. Thus stability is predicted for octahedral coordination until such contacts of ions become possible for coordination numbers higher than 6. For a coordination of 8 fluoride ions this is only the case if the radii of the cations are as large as 0.86 A (square antiprism) or 0.97 A (cube) resp. 

Table 5 Comparison of the critical radius Rc (in au), n (/cm3) and critical pressure Pc (in atm) between the results obtained by using a Debye-Huckel model and an Ion-Sphere (IS) model. Reprinted with permission from [203] Copyright 2006, John Wiley Sons, Inc.

The integral in the expression (48) for stat diverges near R and Rr. Naturally, the down limits in the integration are radii of the solvation spheres near the donor and acceptor (r and rf). If the donor and acceptor are the atomic ions, The radius r at room temperature is approximately,... 

Since Bernal and Fowler,16 the charging radius r0 in the Born equation has been put equal to the Inner Sphere radius, or approximately the ion to water molecule center distance plus 1.4 A. At least for 1+ ions, this gives a fairly good approximation to the Gibbs energy of interaction of the ion with the outer Dielectric Continuum if aT and s are constant throughout the medium. High-valency ions are discussed in Section IV. 

Ion Ionic radius Coordination munber Typical geometry of inner-sphere complex First pA a of [M(H20) ] + , 2 22... 

According to [4] the polyacene molecules with an ionization potential less than 7 eV can be ionized in cages of the X and Y zeolites. The excited molecules are quenched by transition metal ions such as Cu, TF, the active sphere radius of which ranges from 10 to 18 A [3,4 and references therein]. The zeolite lattice participates in both the donation and acceptation of electrons in regard to various substrates in many processes of importance. 

In order to complete the MSA estimate of Iny,- one must add the hard-sphere contribution, which accounts for the fact that work must be done to introduce the ions as hard spheres into the solution. It is obtained from the Percus-Yevick model for non-interacting hard spheres. For the case that all ions (spheres) have the same radius, the result is (see equation (3.9.22))... 

In fact, trigonal holes are so small that they are never occupied in binary ionic compounds. Whether the tetrahedral or octahedral holes in a given binary ionic solid are occupied depends mainly on the relative sizes of the anion and cation. For example, in zinc sulfide the ions (ionic radius = 180 pm) are arranged in a cubic closest packed structure with the smaller ions (ionic radius = 70 pm) in the tetrahedral holes. The locations of the tetrahedral holes in the face-centered cubic unit cell of the ccp structure are shown in Fig. 10.36(a). Note from this figure that there are eight tetrahedral holes in the unit cell. Also recall from the discussion in Section 10.4 that there are four net spheres in the face-centered cubic unit cell. Thus there are twice as many tetrahedral holes as packed anions in the closest packed structure. Zinc sulfide must have the same number of S ions and Zn ions to achieve electrical neutrality. Thus in the zinc sulfide structure only half the tetrahedral holes contain Zn ions, as shown in Fig. 10.36(c). 

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