Crystal ionicity, measurement

Based on these measurements, a new model of the transfer of hydrophilic ions across the O/W interface was proposed (see Fig. 8). In this model, the hydrophilic ion transfers from W to O with some water molecules associated with the ion. A typical example in Fig. 8 shows that a sodium ion transfers across the NB/W interface with four water molecules. In theoretical treatment of AG II ° W of such a hydrophilic ion, therefore, the transferring species should be regarded as the hydrated ion. In accordance, the radii (rh) of hydrated ions in NB were estimated from the hydration numbers ( ) and crystal ionic radii (r) by... 

KNs. The d.c. electrical conduction of KN3 in aqueous-solution-grown crystals and pressed pellets was studied by Maycock and Pai Verneker [127]. The room-temperature conductivity was found to be approximately 10" (ohm cm) in the pure material. Numerical values for the enthalpies of migration and defect formation were calculated from ionic measurements to be 0.79 0.05 and 1.43 0.05 eV (76 and 138 kJ/mole), respectively. In a subsequent paper [128], the results were revised slightly and the fractional number of defects, the cation vacancy mobility, and the equilibrium constant for the association reaction were calculated. The incorporation of divalent barium ions in the lattice was found to enhance the conductivity in the low-temperature region. Assuming the effect of the divalent cation was to increase the number of cation vacancies, the authors concluded that the charge-carrying species is the cation, and the diffusion occurs by means of a vacancy mechanism. 

It has also been used to study the second sound resonance in smectic A liquid crystals and measure the compression modulus. For measuring the flexocoefficients (ei — 63) and (ei + 63), hybrid-aligned nematic cells have been used extensively. AC techniques avoid problems associated with ionic impurities, but require elaborate numerical fitting of the data. Some observations on the pnblished measurements of flexo-coefHcients are made in Section 2.4, which ends with a few concluding remarks. 

Crystal structure measurements have indicated a predominantly ionic structure for (8.49) where Li + cations are octahedrally coordinated by three solvent molecules and the Li-P distance is too great for covalent bonding to take place. This suggests that a whole series of metallopolyphosphines may, with some metals at least, be capable of existing in phosphide forms. Some of the possible symmetrical arrangements for a P chain are indicated in (8.50). 

Area determination of ionic crystals by measurement of exchange reactions of radioactive tracers was established by Paneth and Vorwerk (1922). When a radioactive tracer is uniformly distributed between the solid surface and a solution... 

The ionic conductivity of LiFeP04 single crystals was measured to be up to four orders of magnitude lower than the electronic conductivity. The anisotropy already observed for the electronic conduction is reproduced for ionic transport. Similar values were found for b- and c-direction whereas the a-axis shows much less conductivity values (Fig. 8.4). 

The ionic mobility and diffusion coefficient are also affected by the ion hydration. The particle dimensions calculated from these values by using Stokes law (Eq. 2.6.2) do not correspond to the ionic dimensions found, for example, from the crystal structure, and hydration numbers can be calculated from them. In the absence of further assumptions, diffusion measurements again yield only the sum of the hydration numbers of the cation and the anion. 

The fact that the water molecules forming the hydration sheath have limited mobility, i.e. that the solution is to certain degree ordered, results in lower values of the ionic entropies. In special cases, the ionic entropy can be measured (e.g. from the dependence of the standard potential on the temperature for electrodes of the second kind). Otherwise, the heat of solution is the measurable quantity. Knowledge of the lattice energy then permits calculation of the heat of hydration. For a saturated solution, the heat of solution is equal to the product of the temperature and the entropy of solution, from which the entropy of the salt in the solution can be found. However, the absolute value of the entropy of the crystal must be obtained from the dependence of its thermal capacity on the temperature down to very low temperatures. The value of the entropy of the salt can then yield the overall hydration number. It is, however, difficult to separate the contributions of the cation and of the anion. 

A measure of shear strength is the shear modulus. For covalent crystals this correlates quite well with hardness (Gilman, 1973). It also correlates with the hardnesses of metals (Pugh, 1954), as well as with ionic crystals (Chin, 1975). Chin has pointed out that the proportionality number (VHN/C44) depends on the bonding type. This parameter has become known as the Chin-Gilman parameter. 

Physical hardness can be defined to be proportional, and sometimes equal, to the chemical hardness (Parr and Yang, 1989). The relationship between the two types of hardness depends on the type of chemical bonding. For simple metals, where the bonding is nonlocal, the bulk modulus is proportional to the chemical hardness density. The same is true for non-local ionic bonding. However, for covalent crystals, where the bonding is local, the bulk moduli may be less appropriate measures of stability than the octahedral shear moduli. In this case, it is also found that the indentation hardness—and therefore the Mohs scratch hardness—are monotonic functions of the chemical hardness density. 

There is another use of the Kapustinskii equation that is perhaps even more important. For many crystals, it is possible to determine a value for the lattice energy from other thermodynamic data or the Bom-Lande equation. When that is done, it is possible to solve the Kapustinskii equation for the sum of the ionic radii, ra + rc. When the radius of one ion is known, carrying out the calculations for a series of compounds that contain that ion enables the radii of the counterions to be determined. In other words, if we know the radius of Na+ from other measurements or calculations, it is possible to determine the radii of F, Cl, and Br if the lattice energies of NaF, NaCl, and NaBr are known. In fact, a radius could be determined for the N( )3 ion if the lattice energy of NaNOa were known. Using this approach, which is based on thermochemical data, to determine ionic radii yields values that are known as thermochemical radii. For a planar ion such as N03 or C032, it is a sort of average or effective radius, but it is still a very useful quantity. For many of the ions shown in Table 7.4, the radii were obtained by precisely this approach. 

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