Ionic crystals solution

Cortona embedded a DFT calculation in an orbital-free DFT background for ionic crystals [183], which necessitates evaluation of kinetic energy density fiinctionals (KEDFs). Wesolowski and Warshel [184] had similar ideas to Cortona, except they used a frozen density background to examine a solute in solution and examined the effect of varying the KEDF. Stefanovich and Truong also implemented Cortona s method with a frozen density background and applied it to, for example, water adsorption on NaCl(OOl) [185]. 

Fig. 17.1. (a) Dislocation motion is intrinsically easy in pure metals - though alloying to give solid solutions or precipitates con moke it more difficult. (b) Dislocation motion in covalent solids is intrinsically difficult because the interatomic bonds must be broken and reformed. ( ) Dislocation motion in ionic crystals is easy on some planes, but hard on others. The hard systems usually dominate. 

Consider next the process depicted in Fig. 10. If an ionic crystal is in contact with a dilute solution, and we take q additional ion pairs into the solution, there will be a change in the cratic term, and at the same lime the change in the free energy AF will receive the contribution qL, that is to say, a contribution consisting of q units each equal to L. 

Consider an ionic crystal in which the anion is a molecular ion. The orientation of this anion in the crystal is completely determined, or determined to a large extent, by the crystal structure and furthermore, its freedom of libration is severely limited by the intense fields of the adjacent ions. When this ion goes into solution, it will have a greater number of possible orientations, and its freedom of libration will be greater. Hence the AS0 for a molecular anion will contain a considerable increment in entropy over and above the cratic term (which is all that we subtract in the case of an atomic ion). This additional increment in entropy is likely to be somewhat different for different species of anion. The best we can do at present is to subtract an amount that is of the right order of magnitude. The question is whether we can, by sub-... 

Fig. 59. Ordinates give in milliliters per gram the volume change accompanying the solution of the ionic crystal at 25°0 abscissas give the square root of the concentration in moles pc liter.

The different hydration numbers can have important effects on the solution behaviour of ions. For example, the sodium ion in ionic crystals has a mean radius of 0 095 nm, whereas the potassium ion has a mean radius of 0133 nm. In aqueous solution, these relative sizes are reversed, since the three water molecules clustered around the Na ion give it a radius of 0-24 nm, while the two water molecules around give it a radius of only 017 nm (Moore, 1972). The presence of ions dissolved in water alters the translational freedom of certain molecules and has the effect of considerably modifying both the properties and structure of water in these solutions (Robinson Stokes, 1955). 

The ionic conductivities of most solid crystalline salts and oxides are extremely low (an exception are the solid electrolytes, which are discussed in Section 8.4). The ions are rigidly held in the crystal lattices of these compounds and cannot move under the effect of applied electric fields. When melting, the ionic crystals break down, forming free ions the conductivities rise drastically and discontinuously, in some cases up to values of over 100 S/m (i.e., values higher than those of the most highly conducting electrolyte solutions). 

The composition and properties of the ions contained in the solution are not the same as those of ions contained in the ionic crystal lattice. It is already known that anhydrous copper sulfate (CuS04) is colorless. This implies that Cu2+ and SCT ions that make up the crystal lattice of the sulfate are colorless. When the Cu2+ ions combine with water molecules during dissolution they turn blue (the color characteristic of copper salt). This color is therefore due to hydrated ions of copper, i.e., ions connected with the water molecules. 

If a substance is to be dissolved, its ions or molecules must first move apart and then force their way between the solvent molecules which interact with the solute particles. If an ionic crystal is dissolved, electrostatic interaction forces must be overcome between the ions. The higher the dielectric constant of the solvent, the more effective this process is. The solvent-solute interaction is termed ion solvation (ion hydration in aqueous solutions). The importance of this phenomenon follows from comparison of the energy changes accompanying solvation of ions and uncharged molecules for monovalent ions, the enthalpy of hydration is about 400 kJ mol-1, and equals about 12 kJ mol-1 for simple non-polar species such as argon or methane. 

In solution theory the specialized distribution functions of this kind should appear in the theory of ion pairs in ionic solutions, and a form of the Bjerrum-Fuoss ionic association theory adapted to a discrete lattice is generally used for the treatment of the complexes in ionic crystals mentioned above. In fact, the above equation is not used in this treatment. Comparison of the two procedures is made in Section VI-D. 

The selection of the solvent is based on the retention mechanism. The retention of analytes on stationary phase material is based on the physicochemical interactions. The molecular interactions in thin-layer chromatography have been extensively discussed, and are related to the solubility of solutes in the solvent. The solubility is explained as the sum of the London dispersion (van der Waals force for non-polar molecules), repulsion, Coulombic forces (compounds form a complex by ion-ion interaction, e.g. ionic crystals dissolve in solvents with a strong conductivity), dipole-dipole interactions, inductive effects, charge-transfer interactions, covalent bonding, hydrogen bonding, and ion-dipole interactions. The steric effect should be included in the above interactions in liquid chromatographic separation. 

The ability of an ionic solid to dissolve depends on its lattice energy, as well as the degree to which its ions can become hydrated. The lattice energy of an ionic crystal is a measure of the strength of its three-dimensional network of bonds. If these interactions are weaker than the solute-solvent attractions, the ionic bonds will be easily disrupted by water molecules. 

One method of introducing ions into solution is by the dissolution of an ionic crystal (e.g., NaCl). Ionic crystals are composed of separate positive and negative ions (Fig. 2.9). The overall dissolution process of an ionic crystal MA (M, A, A ) can be represented by the reaction... 

Ionic Atmosphere, Before considering the distribution of ions in an ionic solution, it is instructive to consider the arrangement (distribution) of ions in an ionic crystal. For example, in a sodium chloride crystal, each ion is surrounded by six nearest neighbors of opposite charge. Each positive Na ion is surrounded by six negative Cl ions, and each negative CP ion is surrounded by six positive Na" ions (Figs. 2.9 and 2.14). 

We will consider in this section how mass transfer proceeds, using crystal growth from a solution phase as a representative example of crystal growth in which heat and mass transfer are coupled. We will use the growth of ionic crystals in aqueous solution in a beaker as an example (Fig. 3.3). 

Ionic crystals can form solid solutions, too. KBr, in the presence of KG1, will form crystals, in which some of the Br ions are substituted by Cl ions. If KC1 is in excess, a KC1 crystal is formed with some of the chlorine ions replaced by bromine ions. Smaller ions, like F , or larger, like I"", do not replace Br ions in KBr in considerable quantities KF and KBr do not form solid solutions, unless at high temperature or between very narrow limits. In chloride bromide systems the composition of the solid solution may range from pure chloride to pure bromide. 

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. 

The ionic radii discussed above are properly "crystal radii," i.e.. the radii exhibited by (he ions in ionic crystals. Although these radii are probably reasonable representations of the radii of contact of the ions in solution w ith the nearest atoms of solvate molecules, especially for ions of low charge density, nevertheless, most Ions in solution have far larger effective radii because they carry with them a sheath of solvent molecules, die tenacity... 

Bulk type I catalysis was found in acid catalysis with the acid forms and some salts at relatively low temperatures. The reactant molecules are absorbed between the polyanions (not in a polyanion) in the ionic crystal by replacing water of crystallization or expanding the lattice, and reaction occurs there. The polyanion structure itself is usually intact. The solid behaves like a solution and the reaction medium is three-dimensional. This is called pseudoliquid catalysis (Sections l.A and VI). The reaction rate is proportional to the volume of the catalyst in the ideal case the rate of an acid-catalyzed reaction is proportional to the total number of acidic groups in the solid bulk. 

Heteropolyanions and isopolyanions are polymeric oxoanions (polyoxometalates) (2, 3, 5, 6). The structure of a heteropolyanion or polyoxoanion molecule itself is called a primary structure (5, 6, 77). There are various kinds of polyoxoanion structure (Section II.A. 1). In solution, heteropoly anions are present in the unit of the primary structure, being coordinated with solvent molecules and/ or protonated. Most heteropolyanions tend to hydrolyze readily at high pH (Section 1I.C). Protonation and hydrolysis of the primary structure may be major structural concerns in solution catalysis. Heteropoly compounds in the solid state are ionic crystals (sometimes amorphous) consisting of large polyanions, cations, water of crystallization, and other molecules. This three-dimensional arrangement is called the secondary structure. For understanding catalysis by solid heteropoly compounds, it is important to distinguish between the primary structure and the secondary structure (5, 6, 17). Recently, it has been realized that, in addition... 

I have not described the calculation of the eigenvalues, which requires the solution of the equations of motion and therefore a knowledge of the force constants. The shell model for ionic crystals, introduced by Dick and Overhauser (1958), has proved to be extremely useful in the development of empirical crystal potentials for the calculation of phonon dispersion and other physical properties of perfect and imperfect ionic crystals. There is now a considerable literature in this field, and the following references will provide an introduction Catlow etal. (1977), Gale (1997), Grimes etal. (1996), Jackson et al. (1995), Sangster and Attwood (1978). The shell model can also be used for polar and covalent crystals and has been applied to silicon and germanium (Cochran (1965)). 

Alan Allnatt s research interests at Western Ontario have been concerned with the statistical mechanics of the transport of matter through crystals. His earliest work centered on obtaining methods for calculating the equilibrium distributions and thermodynamic properties of the point defects (vacancies, interstitials, solutes) that make transport possible. He first studied dilute systems, so the methods could be largely analytical. The methods for ionic crystals,... 

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