Ionic crystals applications

Kim, Y.S. and Gordon, R.G. (1974) Theory of binding in ionic crystals Application to alkali-halide and alkaline-earth dihalide crystals Phys. Rev. B9, 3548-3554. 

Pisani [169] has used the density of states from periodic FIP (see B3.2.2.4) slab calculations to describe the host in which the cluster is embedded, where the applications have been primarily to ionic crystals such as LiE. The original calculation to derive the external Coulomb and exchange fields is usually done on a finite cluster and at a low level of ab initio theory (typically minimum basis set FIP, one electron only per atom treated explicitly). 

It is perhaps not too fanciful to compare the stormy history of liquid crystals to that of colour centres in ionic crystals resolute empiricism followed by fierce strife between rival theoretical schools, until at last a systematic theoretical approach led to understanding and then to widespread practical application. In neither of these domains would it be true to say that the empirical approach sufficed to generate practical uses such uses in fact had to await the advent of good theory. 

This by no means exhaustive discussion may serve to indicate the value of the information provided by magnetic data relative to the nature of the chemical bond. The quantum-mechanical rules for electron-pair bonds are essential to the treatment. Much further information is provided when these methods of attack are combined with crystal structure data, a topic which has been almost completely neglected in this paper. It has been found that the rules for electron-pair bonds permit the formulation of a set of structural principles for non-ionic inorganic crystals similar to that for complex ionic crystals the statement of these principles and applications illustrating their use will be the subject of an article to be published in the Zeitschrift fur Kristallographie. 

A set of principles governing the structure of complex ionic crystals, based upon the assumption of a coordinated arrangement of anions about each cation at the comers of an approximately regular polyhedron, is formulated with the aid of considerations based upon the crystal energy. Included in the set is a new electrostatic principle which is of wide application and considerable power. 

Cryptands, 42 122-124, 46 175 nomenclature, 27 2-3 topological requirements, 27 3-4 Cryptate, see also Macrobicyclic cryptate 12.2.2], 27 7-10 applications of, 27 19-22 cylindrical dinuclear, 27 18-19 kinetics of formation in water, 27 14, 15 nomenclature, 27 2-3 spherical, 27 18 stability constants, 27 16, 17 Crystal faces, effect, ionic crystals, in water, 39 416... 

Static Approach. There appears to be only one author, namely Passler (1974a,b, 1975a,b, 1976a,b, 1977a,b, 1978, 1980a,b, 1981), who has extensively worked with the static approximation, Eq. (31), in application to semiconductors, with a very recent additional such treatment by Morante et al. (1982). Other recent work, on rare earth ions in ionic crystals, is, for instance, given by Pukhov and Sakun (1979). 

Certain compounds, whether present in solution or in solid state (as molecular or ionic crystals) emit light when they are excited by photons in the visible or near ultraviolet domain of the spectrum. This phenomenon, called luminescence, is the basis of fluorimetry, a very selective and sensitive analysis technique. The corresponding measurements are made with fluorimeters or spectrofluorimeters and, for chromatographic applications, with fluorescence detectors. 

In 1937, dost presented in his book on diffusion and chemical reactions in solids [W. lost (1937)] the first overview and quantitative discussion of solid state reaction kinetics based on the Frenkel-Wagner-Sehottky point defect thermodynamics and linear transport theory. Although metallic systems were included in the discussion, the main body of this monograph was concerned with ionic crystals. There was good reason for this preferential elaboration on kinetic concepts with ionic crystals. Firstly, one can exert, forces on the structure elements of ionic crystals by the application of an electrical field. Secondly, a current of 1 mA over a duration of 1 s (= 1 mC, easy to measure, at that time) corresponds to only 1(K8 moles of transported matter in the form of ions. Seen in retrospect, it is amazing how fast the understanding of diffusion and of chemical reactions in the solid state took place after the fundamental and appropriate concepts were established at about 1930, especially in metallurgy, ceramics, and related areas. 

For the case of typical ionic crystals aP 1-10, and the weak coupling limit is applicable. The most important conclusion from this treatment is that the weak coupling limit leads to a perturbed Bloch type wave function characterized by equal probability for finding the electron at any point of the medium. Thus, in the case of the ionic crystals, the current description of the polaron is that of a mobile electron followed by lattice polarization. 

Binary compounds formed between metals and group 6 or group 7 elements usually occur in the form of ionic crystals rather than as isolated molecules. The most typical example is, of course, given by the alkali halides, studied by Lowdin in his classic treatise from 1948 [1], Another important class of ionic crystals, with somewhat different properties, are the metal oxides, which play a central role in many contexts in chemistry and physics. To mention only one example, their catalytic properties have long been recognized and subject to extensive study, and have given rise to numerous applications of enormous practical importance. 

In Fig. 3, the values for the electron-number-related static hyperpolarizability fiJN312 obtained for these ionic chromophores (open symbols) have been compared with the same values for the best dipolar, neutral chromophores reported so far (diamonds).31 32 These chromophores, with a reduced number of electrons N equal to 20, have dynamic first hyperpolarizabilities approaching 3000 x 10 30 esu at a fundamental wavelength of 1.064 pm, in combination with a charge transfer (CT) absorption band around 650 nm. It is clear that at this point, the neutral NLOphores surpass the available ionic stilbazolium chromophores for second-order NLO applications, however, only at the molecular level. The chromophore number density that can be achieved in ionic crystals is larger than the optimal chromophore density in guest-host systems. 

The theoretical prediction of the optical absorption profile of a solid using first-principles methods has produced results in reasonable agreement with experiment for a variety of systems [2-4], For example, several ionic crystals were studied extensively, generally using the Hartree-Fock one-electron approximation [5], through the extreme-ultraviolet. Lithium fluoride was the focus of a particularly detailed comparison [6-8], providing excellent confirmation of the applicability of the band theory of solids for optical absorption. 

The most investigated crystals from the polariton point of view are ionic crystals, studied by IR spectroscopy.156 (Other applications of polariton theory are time spectroscopy and nonlinear optics in semiconductors182 and semiconductor-doped glasses.183) The mixed crystals are of the type K(C1, Br)... 

Solid phases of binary systems, like the liquid phases, are very commonly of variable composition. Here, as with the liquid, the stable range of composition is larger, the more similar the two components are. This of course is quite c-ontrary to the chemists notion of definite chemical composition, definite structural formulas, etc., but those notions are really of extremely limited application. It happens that the solid phases in the system water—ionic compound are often of rather definite composition, and it is largely from this rather special case that the idea of definite compositions in solids has become so firmly rooted. In such a system, there are normally two solid phases ice and the crystalline ionic compound. Ice can take up practically none of any ionic compound, so that it has practically no range of compositions. And many ionic crystals... 

In the next section the ideas behind several methods, including the GA and a simulated annealing (SA) approach [19,20], then their implementation used to generate ionic crystal structures are reviewed. This will contain an introduction to the types of move class operators and the various types of cost functions used to modify the current trial structure(s) and to assess the quality of the trial structures, respectively. In the third section recent applications of the GA and SA approaches to closest-packed ionic systems and then to open-framework crystal structures are reviewed. 

Before making application of this formula to tlie perovskites, let us make a brief application to ionic crystals- we summarized the results of this application in Chapter 13 -and to simple tetrahedral solids. In the alkali halides, we focus upon the occupied p states in the halogen ion and calculate the chemical grip associated with interaction of the halogen ion with the alkali, v stales. These arc the same couplings that were included in the calculation of ion softening in Section 14-C. The coupling W2 of Eq. (19-29) becomes the matrix element = 1.84 h /(md ), and 2W i, is to be identified with the = 9.1 h l(nul ) used in Table 14-2. Then (Eq. 19-29) becomes... 

Wolf, G. H., and M. S. T. Bukowinski (1988). Variational stabilization of the ionic charge densities in the electron-gas theory of crystals applications to MgO and CaO. Phys. Chem. Mineral. 15, 209-20. 

During recent years the application of the methods of x-ray and electron diffraction to the determination of the structure of molecules has permitted interatomic distances of a large number of bonds to be obtained and attempts have been made to find simple additive laws which will describe the observed data. In the case of ionic crystals the suggestion was made that each ion could be regarded as a small sphere, which just touch each other in the crystal. To each ion, therefore, there may be ascribed an ionic radius which is maintained by the ion in 1 crystals of a particular type, for example, in which the coordination number of the ion remains the same. For different coordination numbers of a particular ion, it is necessary to give different ionic radii. 

For metal crystals of appreciable size, the number of possible contributions to the alternative bond distributions is extremely large and this results in a considerable contribution to crystal stability from resonance energy. Because orbitals are incompletely occupied, application of an electric field results in electron migration. Solids containing different electronic structures, such that all available orbitals are doubly occupied, are insulators because free migration of electrons is not possible. This is the situation in covalent crystals. Orbital overlap with the production of covalent shared, but incompletely filled, electron bonds does not occur in molecular or ionic crystals, which are therefore not electronic conductors. 

Tsirelson et al. [194] extended Levine s model to account for the different types of bonds in second-order nonlinear susceptibility calculations. Applications to lithium formate deuterate (LiCOOH D2O) and related crystals with and without water molecules showed that the water can play a significant role in X -. They also proposed an expression for X which gave qualitative agreement with experiment for five ionic crystals. 

To calculate the induction and electrostatic contributions to the adsorption energy (V/ and Ve in Eq. (4)) one should first evaluate the electrostatic field at the surface of the crystal. Calculations of electrostatic fields near surfaces of ionic crystals have been done since 1930 (see references in [26]). In the case of amorphous silicates, one may do such an evaluation using effective charges for the anions and cations, as in the interatomic potentials of Eq. (1) and as set out in Refs. [10, llj. Unfortunately this is not applicable to the BS model which excludes cations from consideration. 

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