Lattice energy, description

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. 

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 ... 

The band picture of metals developed by physicists accounts very well for conduction and other electric and magnetic properties. The valence bond description of the bonds in metals related to the concepts of chemistry explains much better than the former theory such properties as lattice energies and bond distances. Today, however, the V.B. picture does not lend itself well to a priori quantitative calculations of these properties and it seems doubtful to what extent a bond in solid lithium with a bond order of o. 11 (with respect to the bond order one in a gas molecule) has any fundamental meaning. There is no doubt, however, that in less typical metals and compounds Pauling s theory is valuable as a counterpart to the band picture, just as the V.B. and the M.O. methods are both of great importance for the description of the constitution of organic molecules. 

For application to nonmolecular solids, the bond description is similar but certain modifications are needed. First, the covalent energy must be multiplied by the equivalent number n of two electron covalent bonds per formula unit that must be broken for atomization. The evaluation of n will be discussed in detail presently. Second, the ionic energy must be evaluated as the potential energy over the entire crystal, corrected for the repulsions among adjacent electronic spheres. This is done by using the Born-Mayer equation for lattice energy, multiplying this expression by an empirical constant, a, which is 1 for the halides and less than 1 for the chal-cides, as follows ... 

The lattice energy is a crucial parameter to determine as the calculated value can be compared with the experimental sublimation enthalpy (Eq. 8) (13), as a check of the description of intermolecular interactions between the molecules by the defined potential function. 

For ionic solids, in which both attractive and repulsive electrostatic forces as well as short-range repulsive forces complicate the description of the overall energy, the Bom-Lande equation has been shown to provide an adequate estimate of lattice energy, /. ... 

In this book we avoid the use of the concept of electronegativity as far as possible and base the systemization of descriptive inorganic chemistry on rigidly defined and independently measured thermochemical quantities such as ionization energies, electron affinities, bond dissociation enthalpies, lattice energies and hydration enthalpies. However, some mention of electronegativity values is unavoidable. 

In the description of the intermolecular bonding, the Lennard-Jones 6-12 potential function (8) is one of the most common, consisting of an attractive and repulsive contribution to the van der Waals component of the lattice energy (Vydw) as shown in Equation 1. "A" and "B" are the atom-atom parameters for describing a particular atom-atom interaction and "r" is the interatomic distance. This potential function has formed the basis of a variety of different force fields (9-11) that were utilized in this paper. A modified (10-12 version of this potential can also be employed (10,11) to describe hydrogen bonding. The 10-12 potential is very similar in construction to Equation 1 except that the attractive part is dependent on r ° rather than r. ... 

Such assumptions have been used successfully to calculate the free energy between metallic crystalline phases. For example, Lam et a/.[60]computed the temperature-pressure phase diagram of beryllium. They predicted the static lattice energy using ab initio pseudopotentials and estimated the phonon energy and entropy from the second order elastic constants. Since the electronic contribution to the entropy varies less for insulators than it does for metals, one would expect a better description of the thermodynamics for the materials here than for beryllium. 

More complicated is the description of the melting of copolymers with Ml or partial isomorphism or isodimorphism (Sect. 5.1.10). The changes in concentration in the mixed crystals as well as the melt must be considered and the change of the lattice energy with cocrystalhzation must be known. The simplest description assumes that there is no difference in concentration between melt and crystal, and there is a linear change of the heat of fusion, AH, with concentration. This leads to T = [ 1 - XB(AHj/AHu)]Tm°, where AH is the heat of fusion per repeating unit of the homopolymer. 

We start this second and last chapter on the solid state with a description of the theoretical determination of lattice energy. Next, we consider how the lattice energy can be determined experimentally using the principles of thermochemistry that you learned in previous chemistry courses. A discussion of such topics as the degree of covalent character in ionic crystals, the source of values for electron affinities, the estimation of heats of formation of unknown compounds, and the establishment of thermochemical radii of polyatomic ions follows. We conclude with a special section on the effects of crystal fields on transition metal radii and lattice energies. 

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