Ionic solids density

Modern theories of electronic structure at a metal surface, which have proved their accuracy for bare metal surfaces, have now been applied to the calculation of electron density profiles in the presence of adsorbed species or other external sources of potential. The spillover of the negative (electronic) charge density from the positive (ionic) background and the overlap of the former with the electrolyte are the crucial effects. Self-consistent calculations, in which the electronic kinetic energy is correctly taken into account, may have to replace the simpler density-functional treatments which have been used most often. The situation for liquid metals, for which the density profile for the positive (ionic) charge density is required, is not as satisfactory as for solid metals, for which the crystal structure is known. 

Ionic conduction studies in solids date back to the work of Gunterschultze and Betz,50 who derived the empirical relationship between the electric field strength, E = [(o) " (4>o)jV (cf. Fig. lb), in an oxide and the nonohmic ionic current density, j9... 

An X-ray atomic orbital (XAO) [77] method has also been adopted to refine electronic states directly. The method is applicable mainly to analyse the electron-density distribution in ionic solids of transition or rare earth metals, given that it is based on an atomic orbital assumption, neglecting molecular orbitals. The expansion coefficients of each atomic orbital are calculated with a perturbation theory and the coefficients of each orbital are refined to fit the observed structure factors keeping the orthonormal relationships among them. This model is somewhat similar to the valence orbital model (VOM), earlier introduced by Figgis et al. [78] to study transition metal complexes, within the Ligand field theory approach. The VOM could be applied in such complexes, within the assumption that the metal and the... 

In our opinion, this book demonstrates clearly that the formalism of many-point particle densities based on the Kirkwood superposition approximation for decoupling the three-particle correlation functions is able to treat adequately all possible cases and reaction regimes studied in the book (including immobile/mobile reactants, correlated/random initial particle distributions, concentration decay/accumulation under permanent source, etc.). Results of most of analytical theories are checked by extensive computer simulations. (It should be reminded that many-particle effects under study were observed for the first time namely in computer simulations [22, 23].) Only few experimental evidences exist now for many-particle effects in bimolecular reactions, the two reliable examples are accumulation kinetics of immobile radiation defects at low temperatures in ionic solids (see [24] for experiments and [25] for their theoretical interpretation) and pseudo-first order reversible diffusion-controlled recombination of protons with excited dye molecules [26]. This is one of main reasons why we did not consider in detail some of very refined theories for the kinetics asymptotics as well as peculiarities of reactions on fractal structures ([27-29] and references therein). 

Determine the density of a metal or ionic solid from its crystal structure, Examples 5.5 and 5.7. 

Tsang and Falicov (49) have calculated the charge density distribution at corner sites in ionic and rare gas crystal surfaces. For ionic solids, low coordination number surface sites should have large charge density variations... 

Fig. 3. Approximate electron density variation on jellium surfaces with periodic positive charge boundaries. The solid line gives the edge of the uniform ionic charge density. The dashed line indicates the contour where the electron density is equal to one-half its interior value.

It is noteworthy to point out that bonding character for compounds is rarely purely covalent or ionic in nature, especially for inorganic species. Rather, a combination of both bonding modes provides the best description of the electron density for these solids. As you might expect, this will also affect the physical properties of the solid for instance, the hardness of ZnS is significantly greater than what would be expected for a purely ionic solid. 

Figure 2.4. Charge density as function of distance from electrode, for the electrolyte modelled in Fig. 2.3. The three cases represent positive, zero and negative electrode charge. Solid lines are total charge densities, longer dashes are ionic charge densities, and shorter dashes are aqueous charge densities. The curves have been smoothed. From E. Spohr (1999). Molecular simulation of the electrochemical double layer. Electrochimica Acta 44,1697-1705, reproduced with permission from Elsevier.

Cockroft, J. K., Fitch, A. N., and Simon, A. Powder neutron diffraction studies of orientational order-disorder transitions in molecular and molecular-ionic solids use of symmetry-adapted spherical harmonic functions in the analysis of scattering density distributions arising from orientational disorder. In Collected Papers. Summerschool on Crystallography and its Teaching. Tianjin, China. Sept 15-24, 1988. (Ed., Miao, F.-M.) p. 427. Tianjin Tianjin Normal University (1988). 

Determining the ionic structure in the cubic system from ionic radii using the radius-ratio rule Determining the density of the ionic solid from the density of the unit cell Note Usually within 10% of the experimental value... 

Second, being quasibound Inside a potential barrier on the perimeter of the molecule, such resonances are localized, have enhanced electron density In the molecular core, and are uncoupled from the external environment of the molecule. This localization often produces Intense, easily studied spectral features, while suppressing non-resonant and/or Rydberg structure and, as discussed more fully below, has a marked Influence on vibrational motion. In addition, localization causes much of the conceptual framework developed for shape resonances In free molecules to apply equally well to photolonlzatlon and electron scattering and to other states of matter such as adsorbed molecules, molecular crystals, and Ionic solids. 

The experimentally measured anion-cation distances in highly ionic solids can be interpreted on the assumption that each ion has a nearly fixed radius. For example, the difference in anion-cation distance between the halides NaX and KX is close to 36 pm irrespective of the anion X, and it is natural to attribute this to the difference in radii between Na+ and K+. To separate the observed distances into the sum of two ionic radii is, however, difficult to do in an entirely satisfactory way. One procedure is to look for the minimum value in the electron density distribution between neighboring ions, but apart from the experimental difficulties involved such measurements do not really support the assumption of constant radius. Sets of ionic radii are therefore all based ultimately on somewhat arbitrary assumptions. Several different sets have been derived, the most widely used being those of Shannon and Prewitt, based on the assumed radius of 140 pm for O in six-coordination. Values for a selection of ions are shown in Table 1. 

N0 03 is an extremely high density ionic solid with the density 2.7 g/cc at the ambient condition. Figure 10 compares room-temperature isotherms for N2O-III and NO >J03 to 55 GPa with those of CO2-III and CO2-V. At pressures below 15 GPa, N2O-III is relatively soft... 

Figure 4.9 The redox process in compound formation. A, In forming the ionic compound MgO, each Mg atom transfers two electrons to each O atom. (Note that atoms become smaller when they lose electrons and larger when they gain electrons.) The resulting Mg and ions aggregate with many others to form an ionic solid. B, In the reactants H2 and CI2, the electron pairs are shared equally (indicated by even electron density shading). In the covalent product HCl, Cl attracts the shared electrons more strongly than H does. In effect, the H electron shifts toward Cl, as shown by higher electron density (red) near the Cl end of the molecule and lower electron density (blue) near the H end.

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