Energies ionic crystals

Kapustinskii equation For an ionic crystal composed of cations and anions, of respective charge and z, which behave as hard spheres, the lattice energy (U) may be obtained from the expression... 

Madeluag constant For an ionic crystal composed of cations and anions of respective change z + and z, the la ttice energy Vq may be derived as the balance between the coulombic attractive and repulsive forces. This approach yields the Born-Lande equation,... 

The uncertainties in choice of potential function and in how to approximate the surface distortion contribution combine to make the calculated surface energies of ionic crystals rather uncertain. Some results are given in Table VII-2, but comparison between the various references cited will yield major discrepancies. Experimental verification is difficult (see Section VII-5). Qualitatively, one expects the surface energy of a solid to be distinctly higher than the surface tension of the liquid and, for example, the value of 212 ergs/cm for (100)... 

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]. 

Let us examine the enthalpy terms involved when an ionic crystal MX is dissolved in water. The energy diagram for a Group I halide is as shown in Figure 3.8. 

In periodic boimdary conditions, one possible way to avoid truncation of electrostatic interaction is to apply the so-called Particle Mesh Ewald (PME) method, which follows the Ewald summation method of calculating the electrostatic energy for a number of charges [27]. It was first devised by Ewald in 1921 to study the energetics of ionic crystals [28]. PME has been widely used for highly polar or charged systems. York and Darden applied the PME method already in 1994 to simulate a crystal of the bovine pancreatic trypsin inhibitor (BPTI) by molecular dynamics [29]. 

From these various examples, it is clear that the adsorption energy for a given kind of site can vary quite markedly from one crystal face of the adsorbent to another. For argon on solid xenon (Table 1.1), for example, the most favourable site has a o value of —1251 x 10" J on the (100) face but only -1072 on the (111) face. Such differences are in no way surprising, and they have been found also with ionic crystals. 

The Dissociation of a Molecule into Ions. The Removal of Ions from a Metal Surface. The Removal of Ions from the Surface of an Ionic Crystal. The Solvation Energy of an Ion. Work Done against Electrostatic Forces. Molecules and Molecular Ions Containing One or More Protons. Proton Transfers. The Quantities D, L, Y, and J. Two Spherical Conductors. 

We shall, however, wish to make use of the lattice energies which are tabulated for ionic crystals at the absolute zero of temperature. Now... 

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. 

Lanthanides Elements 57 (La) through 70 (Yb) in the periodic table, 146 Lanthanum, 147 Laser fusion, 528 Lattices in ionic crystals, 249 Lavoisier, Antoine, 14 Law of conservation of energy A natural law stating that energy can neither be created nor destroyed it can only be converted from one form to another, 214... 

The potential energy of an ionic crystal (ions of valence z) may be written = —a(e2z2)/i + R), the first term representing the Coulomb energy, and the second the potential of the repulsive forces. Equation 6 suggests a simple form for [Pg.260]

In deriving theoretical values for inter-ionic distances in ionic crystals the sum of the univalent crystal radii for the two ions should be taken, and corrected by means of Equation 13, with z given a value dependent on the ratio of the Coulomb energy of the crystal to that of a univalent sodium chloride type crystal. Thus, for fluorite the sum of the univalent crystal radii of calcium ion and fluoride ion would be used, corrected by Equation 13 with z placed equal to y/2, for the Coulomb energy of the fluorite crystal (per ion) is just twice that of the univalent sodium chloride structure. This procedure leads to the result 1.34 A. (the experimental distance is 1.36 A.). However, usually it is permissible to use the sodium chloride crystal radius for each ion, that is, to put z = 2 for the calcium... 

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. 

The theoretical treatment of the properties of ionic crystals and molecules has been carried farther than that of other types of atomic aggregates. The Bom theory of crystal energy permits the calculation to within... 

It is impossible to carry out this program of directly evaluating the energy integral except in the simplest cases but rough energy curves for various electronic structures can often be constructed by semi-empirical methods, and the discussion outlined above carried out with them. Thus information regarding the repulsive forces between ions obtained from the observed properties of ionic crystals can be used for ionic states of mole-... 

A similar procedure can be used in predicting interatomic distances in ionic crystals, by evaluating the potential energy of a three-dimensional array of... 

Figure 8-20 reminds us that an ionic crystal contains many ions. All the ions exert electrical forces on one another. To calculate the energy resulting from these forces, we start with Equation, which describes the energy arising from... 

Because of the high electrostatic energy required to maintain them in an ionic crystal such as AgBr, we can safely ignore the following possible defects ... 

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