Crystal ionicity

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. 

Of the three principal classes of crystals, ionic crystals, crystals containing electron-pair bonds (covalent crystals), and metallic crystals, we feel that a good understanding of the first class has resulted from the work done in the last few years. Interionic distances can be reliably predicted with the aid of the tables of ionic radii obtained by Goldschmidt1) by the analysis of the empirical data and by Pauling2) by a treatment based on modem theories of atomic structure. The stability,... 

Metal ion Crystal ionic radius A Complexation constant... 

A typical special feature of the melts of ionic crystals (ionic liquids) are their high concentrations of free ions, of about 25 M. Because of the short interionic distances, considerable electrostatic forces act between the ions, so that melts exhibit pronounced tendencies for the formation of different ionic aggregates ion pairs, triplets, complex ions, and so on. 

The point defects are decisive for conduction in solid ionic crystals. Ionic migration occurs in the form of relay-type jumps of the ions into the nearest vacancies (along the held). The relation between conductivity o and the vacancy concentration is unambiguous, so that this concentration can also be determined from conductivity data. 

In almost all theoretical studies of AGf , it is postulated or tacitly understood that when an ion is transferred across the 0/W interface, it strips off solvated molecules completely, and hence the crystal ionic radius is usually employed for the calculation of AGfr°. Although Abraham and Liszi [17], in considering the transfer between mutually saturated solvents, were aware of the effects of hydration of ions in organic solvents in which water is quite soluble (e.g., 1-octanol, 1-pentanol, and methylisobutyl ketone), they concluded that in solvents such as NB andl,2-DCE, the solubility of water is rather small and most ions in the water-saturated solvent exist as unhydrated entities. However, even a water-immiscible organic solvent such as NB dissolves a considerable amount of water (e.g., ca. 170mM H2O in NB). In such a medium, hydrophilic ions such as Li, Na, Ca, Ba, CH, and Br are selectively solvated by water. This phenomenon has become apparent since at least 1968 by solvent extraction studies with the Karl-Fischer method [35 5]. Rais et al. [35] and Iwachido and coworkers [36-39] determined hydration numbers, i.e., the number of coextracted water molecules, for alkali and alkaline earth metal... 

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

All ions studied are assumed to be spherical, and radii (r) of the bare ions are listed in Table 3. Unless otherwise noted, authorized values of crystal ionic radii or van der Waals radii are adopted [51-57]. 

Element Atomic Number Electronic Configuration Electronegativity Crystal Ionic Radius A°... 

The principal intention of the present book is to connect mechanical hardness numbers with the physics of chemical bonds in simple, but definite (quantitative) ways. This has not been done very effectively in the past because the atomic processes involved had not been fully identified. In some cases, where the atomic structures are complex, this is still true, but the author believes that the simpler prototype cases are now understood. However, the mechanisms change from one type of chemical bonding to another. Therefore, metals, covalent crystals, ionic crystals, and molecular crystals must be considered separately. There is no universal chemical mechanism that determines mechanical hardness. 

This paper starts with a brief description of the Golden ratio and the ( )-based crystal ionic radii and is then followed by the (()-based aqueous ionic radii and hydration lengths. The role of in the sizes of the ions in the crystal and in aqueous solutions and their hydration bonds with water can be seen in Fig. 12.3 for Na" and Cl" ions (used as the examples). 

Table 2.3 gives the self-diffusion coefficients of some important ions in submerged soils and Figure 2.2 shows the values for the elemental ions plotted against ionic potential ( z /r where z is the absolute ionic charge and r the crystal ionic radius). As the ionic potential increases the hydration layer of water molecules around the ion increases, and therefore the mobility tends to decrease. Also, at the same ionic potential, cations diffuse faster than anions. The mobilities... 

Table 2.4 Crystal Ionic Radii and Standard Molar Gibbs Free Energies of Flydration of Ions... 

The molar conductivities of alkali metal ions increase, in most solvents, with increasing crystal ionic radii (Li+[Pg.216]

In 1953 Olson and Konecny (19) studied the conductance of lithium bromide in acetone-water mixtures at 25°C and 35°C. They calculated KD and Ao in the acetone-rich solvents by the Fuoss method and Ao in the water-rich solvents by extrapolation of the phoreogram. They found that as the water content increases Kd increases, Ao decreases but then undergoes an increase, and a increases from slightly less than the sum of the crystal ionic radii to the sum of the radii of the fully hydrated ions. Extrapolation of their data for A0 to zero water content is not reliable because of the large concave upward negative slope however, it would appear to lead to a value of about 220 U l cm2 eq-1. Similar extrapolations of values for Kd and a yield 2.0 X 10 4 and 2.2 A, respectively. 

A separate class of experimental evaluation methods uses biological mechanisms. An artificial neural net (ANN) copies the process in the brain, especially its layered structure and its network of synapses. On a very basic level such a network can learn rules, for example, the relations between activity and component ratio or process parameters. An evolutionary strategy has been proposed by Miro-datos et al. [97] (see also Chapter 10 for related work). They combined a genetic algorithm with a knowledge-based system and added descriptors such as the catalyst pore size, the atomic or crystal ionic radius and electronegativity. This strategy enabled a reduction of the number of materials necessary for a study. 

Lastly, the extensions of the standard implicit solvent model to more sophisticated settings (liquid crystals, ionic solvents, metallic surfaces,...) are briefly dealt with in section 1.2.7. 

Molar ionic conductivity — This quantity, first introduced by -> Kohlrausch, is defined by A = Zi Fui (SI unit Sm2 mol-1), where Zj and 14 are the charge number and -> ionic mobility of an ion, respectively. The molar -> conductivity of an electrolyte M +X (denoted by A) is given by A = u+X+ + i/ A, where A+ and A are the molar ionic conductivities of the cation and anion. The A value of an ion at infinite dilution (denoted by A°°) is specific to the ion. For alkali metal ions and halide ions, their A values in water decrease in the orders K+ > Na+ > Li+ and Br- > Cl- > F-. These orders are in conflict with those expected from the crystal ionic radii, because the smaller ions are more highly hydrated, so that the -> hydrated ions become larger and thus less mobile. Based on Stokes law, the radius of a hydrated ion... 

Solid oxide conductors, such as Zr02, which form the basis of chemical sensors, rely on the presence of defects to induce ionic conductivity (Madou and Morrison, 1989). If every lattice site was occupied with the correct atom, then it would be impossible for any atoms to move within the material. It would be like an auditorium with no empty seats in order for one person to move, everyone would have to move. Similarly, in a perfect crystal, ionic conduction will be difficult if there are no vacant spots for an ion to move into. 

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