Bond energy curve

In 1971 Ducastelle and Cyrot-Lackmann proved a very important moments theorem that captures this crossing behaviour of the bond energy curves. Their moments theorem states that if two eigenspectra have moments that are identical up to some level pQ, that is App = 0 for p < p0, then the two bond energy curves must cross at least (p0 — 1) times as a function of electron count. Thus, we have seen in Fig. 4.5 that the triangle and the linear chain curves cross once, since p0 = 2, whereas the square and the linear chain curves cross twice, since p0 = 3. 

One of the most valuable features of theoretical methods based on classical VB structures is their ability to calculate the energy of a diabatic state. For practical uses, some diabatic bond energy curves of chemical interest can be, for example, the separate dissociation energy curves of the ionic and covalent components of a bond, or the energy curves of the effective VB structures of a... 

Fig. 12.9. Radial distribution (D(R) = TV(contacts)/(47tl d/ )) for N... H and O... H contacts, with non-bonded energy curves shown by ordinate scale on the right. The vertical solid line shows the sum of packing radii. M curves [14]. G curves [46]...

The bond-energy curve for a covalent bond has the same general shape as that shown in Figure 4.1a. The main difference is that we do not have the additional energy term associated with the formation of ions. The forces involved are still electrostatic ... 

Sketch bond-energy curves for two ceramics, one with a high Young s modulus and one with a low Young s modulus. 

Sketch a bond-energy curve for two atoms held together by van der Waals forces. Describe how this curve differs from the one shown in Figure 4.1, which is for ionic bonding. 

The general need is to understand the response of a material to an applied stress. The stress may be applied externally or induced by altering other parameters such as temperature (which can cause a phase transformation). The fundamental idea is the link to bonding. In Chapter 4 we described how the Young s modulus is related directly to the bond-energy curve. In Chapter 12 we described the nature of dislocations in ceramics. 

As described in Chapter 4 the shape of the bond-energy curve depends on the strength and type of the interatomic bonding ... 

FIGURE 4.1 (a) Bond-energy curve for KCI. At infinite separation, the energy is that required to form K+ and Ci" from the corresponding atoms, (b) Force-distance curves for two materiais one where the bonding is strong and one where it is weak. 

A number of semitheoretical models have been proposed to describe the bond-energy curve in ionic-bonded and van der Waals-bonded systems in which the attractive force can be described accurately by an inverse power law. The repulsive potential is described by an exponential or a high order inverse power law. Such potentials are useful for relating physical properties such as the bulk modulus and elastic modulus to the lattice energy. Unfortimately, there are no simple lattice models that can be applied to metallic or covalently bonded systems. 

The bond-energy curve can be approximated by U x) = CxP — Dx in which C represents the harmonic part of the potential and D is the anharmonic part. It is assumed that... 

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