Lattice energy defined

Energy terms such as ionization energies and lattice energies (defined at 0 K) can be used in Born-Haber cycles to estimate unknown quantities under standard conditions. 

Lennard-Jones potential (Ch. 6) lattice energy defined in the cell theory (Ch. 7) electronic charge, that of positron and electron internal energy per unit volume quadmpolar coupling constant of aliphatic CD bond... 

Does the sublattice in potassium-doped PAc show a characteristic repeat distance If so, does it depend on the doping level Compositional and diffraction data are not unequivocal on this point, but they do suggest that host and dopant lattices are incommensurate (as indeed X-ray diffraction has been established in the caesium sublattice of Cs-doped PAc). This is also the conclusion of simulation calculations, which in addition predict a high mobility for the channel K ions. Since the concept of lattice energy defined in Section 2.2 cannot be used to compare structures with different compositions, we must seek another method of predicting the optimum doping level. 

We have approached this problem in terms of the lattice forming from the ions. However, the lattice energy is defined in terms of the energy required to separate it into the gaseous ions. Therefore, as used in Eq. (7.9), the value for U will be negative because the attraction energy is much larger than the... 

As defined earlier, the lattice energy is positive while the solvation of ions is strongly negative. Therefore, the overall heat of solution may be either positive or negative depending on whether it requires more energy to separate the lattice into the gaseous ions than is released when the ions are solvated. Table 7.7 shows the heats of hydration, AH °hy(, for several ions. 

The lattice energy is defined as the energy required to separate the ions in one mole of an ionic solid. 

To understand the dissolution of ionic solids in water, lattice energies must be considered. The lattice enthalpy, A Hh of a crystalline ionic solid is defined as the energy released when one mole of solid is formed from its constituent ions in the gas phase. The hydration enthalpy, A Hh, of an ion is the energy released when one mole of the gas phase ion is dissolved in water. Comparison of the two values allows one to determine the enthalpy of solution, AHs, and whether an ionic solid will dissolve endothermically or exothermically. Figure 1.4 shows a comparison of AH and A//h, demonstrating that AgF dissolves exothermically. 

The results for the three models are summarized in Table 9.2, which lists the effective Madelung constant n (t, defined by eiectrosuiic = — peff/a the effective Born coefficient, defined by U = — NAncff/a(l — l/neff) and the lattice energy U. 

In molecular crystals, the relative importance of the electrostatic, repulsive, and van de Waals interactions is strongly dependent on the nature of the molecule. Nevertheless, in many studies the lattice energy of molecular crystals is simply evaluated with the exp-6 model of Eq. (9.45), which in principle accounts for the van der Waals and repulsive interaction only. As underlined by Desiraju (1989), this formalism may give an approximate description, but it ignores many structure-defining interactions which are electrostatic in nature. The electrostatic interactions have a much more complex angular dependence than the pairwise atom-atom potential functions, and are thus important in defining the structure that actually occurs. 

With mixed-valence compounds, charge transfer does not require creation of a polar state, and a criterion for localized versus itinerant electrons depends not on the intraatomic energy defined by U , but on the ability of the structure to trap a mobile charge carrier with a local lattice deformation. The two limiting descriptions for mobile charge carriers in mixed-valence compounds are therefore small-polaron theory and itinerant-electron theory. We shall find below that we must also distinguish mobile charge carriers of intennediate character. 

The lattice energy at a half-crystal position (kink site) is defined as the attachment energy and the energy released in forming a slice containing more than two PBCs is denoted by E j These are related to the lattice energy as follows ... 

The electrostatic (Madelung) part of the lattice energy (MAPLE) has been employed to define Madelung potentials of ions in crystals (Hoppe, 1975). MAPLE of an ionic solid is regarded as a sum of contributions of cations and anions the Madelung constant. A, of a crystal would then be the sum of partial Madelung constants of cation and anion subarrays. Thus,... 

The lattice energy U is defined as the energy released (U is therefore negative by thermodynamic convention) when a mole of the requisite free gaseous ions comes together from infinite interionic separation to make up the crystal. If N is Avogadro s number (6.0221 x 1023), we have the Bom-Lande formula ... 

The calculation of lattice energies (and other Coulomb s law energies) is complicated somewhat by the fact that in SI the permittivity (dielectric constant) of a vacuum is no longer defined as one but has an experimentally determined value. Furthermore, for reasons we need not explore at present. Coulomb s law is stated in the form ... 

Ionization energy is defined / V I for isolated, gaseous-state atoms. Other factors, such as lattice energy or solvation energy must be considered when forming ions in a condensed state. 

The lattice energy U of an ionic compound is defined as the energy required to convert one mole of crystalline solid into its component cations and anions in their thermodynamic standard states (non-interacting gaseous ions at standard temperature and pressure). It can be calculated using either the Born-Land6 equation... 

The lattice energy of an ionic crystal may be defined as the energy emitted when the correct number of ions emerge from distant locations and station themselves in their appropriate places in the crystal lattice. For a mole of sodium fluoride, for example, one may obtain such a lattice energy by multiplying the potential energy (as given in Equation... 

Thus the behavior of lattice defects bears some analogy to phase separation in fluids, or to the treatment of adsorption on localized sites. At low relative temperatures, the defects adopt a random distribution if they are sufficiently dilute if their concentration exceeds a certain value they segregate into defect-poor and defect-rich regions which can coexist. The concentration at which this occurs, and the relative temperature scale, depend on what can be represented as a nearest-neighbor attraction in the interaction potentials. The magnitude of the attractive interaction energy defines a critical temperature above which no segregation of defects occurs. 

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