Lattice energy magnitudes

In the case of ionic solid substances, an important quantity is the free lattice energy AGS, i.e., the energy liberated when one type of crystalline substance is formed from its ionic constituents in the gas phase. This definition implies that this magnitude for a simple 1 1 solid electrolyte is a sum of the real potentials of cation and anion ... 

Hirshfeld and Mirsky (1979) evaluated the relative contributions to the lattice energy for the crystal structures of acetylene, carbon dioxide, and cyanogen, using theoretical charge distributions. Local charge, dipole and quadrupole moments are used in the evaluation of the electrostatic interactions. When the unit cell dimensions are allowed to vary, inclusion of the electrostatic forces causes an appreciable contraction of the cell. In this study, the contributions of the electrostatic and van der Waals interactions to the lattice energy are found to be of comparable magnitude. 

Of interest is the relative contribution of the electrostatic interactions to the total calculated lattice energy. Some of the results are reproduced in Fig. 9.3 (Coombes and Price 1995). It is clear that the contribution increases rapidly for the more polar molecules, and can be pronounced. For formamide, the electrostatic contribution is more than 100% of the lattice energy, as the repulsive and the van der Waals r 6 forces are of approximately equal magnitude and sum to a small, opposite, contribution. 

The concepts required for a quantitative treatment of the reactivity of solids were now clear, except for one important issue. According to the foregoing, point defect energies should be on the same order as lattice energies. Since the distribution of point defects in the crystal conforms to Boltzmann statistics, one was able to estimate their concentrations. It was found that the calculated defect concentrations were orders of magnitude too small and therefore could not explain the experimentally observed effects which depended on defect concentrations (e.g., conductivity, excess volume, optical absorption). Jost [W. Jost (1933)] provided the correct solution to this problem. Analogous to the fact that NaCl can be dissolved in H20... 

The magnitude of a lattice energy depends directly on the charge on the ions and inversely on the distance between ions (that is, on the radii of the ions). In this instance, all the ions in both drawings are doubly charged, either M2+ or O2-, so only the size of the ions is important. 

The magnitude of the lattice energy of an ionic compound depends on the charges and sizes of the ions that make up the compound. Use the Coulomb s Law activity (eChapter 6.6) to determine which ionic compound has the larger lattice energy, LiF or SrTe. (Ionic radii in A for Li+, F, Sr2+, and Te2- are 0.68,1.33,1.13, and 2.21, respectively. Note that 1 A= 100 pm.)... 

As we traverse the series, the lattice energies of LnX2 and LnX3 increase steadily in magnitude, a consequence of the lanthanide contraction since UL is always a little more than twice as great for LnX3 as for LnX2 (as... 

The principal exothermic term in a stepwise thermochemical analysis (such as we found useful in Chapter 5) will be the lattice energy of the product. This is not readily obtainable experimentally (unlike the lattice energies of simple ionic solids) and its magnitude is not amenable to any simple analysis. As we shall see a little later, a purely ionic description of such products is often inappropriate anyway. Let us focus attention on the ease of formation of AX x and BX +1. The removal of X- from AXm will be favoured by ... 

Since lattice energies are comparable for structures containing similar cations in octahedral and tetrahedral sites (cf. NiO and ZnO in fig. 7.1b ), the njnt ratios in table 6.3 indicate that there are higher proportions of transition metal ions in octahedral sites than in tetrahedral sites in magmas despite the fact that lattice energies of silicate crystals and melts are almost two orders of magnitude higher than those of the CFSE s, E0 and Et (cf. fig. 7. lb and d). 

Kapustinskii s equation, of course, cannot be expected to produce values for the lattice energies as exact as those produced by extended calculation. Essentially the Kapustinskii formula ignores all contributions to the lattice energy save Us and Uu. If the ions are nonspherical there is considerable difficulty in choosing a repulsion envelope for the ion and assigning a radius. This difficulty also arises in the extended calculation of the lattice energy but only in calculation of Ur, which is an order of magnitude less than Um- In the Kapustinskii equation this difficulty arises in Um as well. 

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