Cohesive energy of solids

From the chemist s point of view, the cohesive energy of solids is their most important property. The cohesive energy (AEcxp) is defined as the energy required to dissociate one mole of solid M(s) into its constituent gas atoms M(g) ... 

Van der Waals forces do not play a great part in the production of stable chemical compounds, but in the cohesion energy of solid and liquid phases, composed of separate molecules as units. This means that many physico-chemical properties such as volatility, solubility, miscibility, viscosity, plasticity and surface tension, which all depend on the intermole-cular interaction, and therefore on the cohesion, are determined by the Van der Waals forces. This holds for most organic compounds and likewise for mixtures and also for many inorganic substances, among them water in the first place. 

Figure 15.5 Cohesive energies of solid noble gases as a function of the unit cell volume. LDA is the local density approximation PBE is approximation by Perdew, Burke, and Ernz-...

We will limit ourselves here to transition metals. It is well known that in these metals, the cohesive properties are largely dominated by the valence d electrons, and consequently, sp electrons can be neglected save for the elements with an almost empty or filled d valence shelP. Since the valence d atomic orbitals are rather localized, the d electronic states in the solid are well described in the tight-binding approximation. In this approximation, the cohesive energy of a bulk crystal is usually written as ... 

The materials for solid solutions of transition elements in j3-rh boron are prepared by arc melting the component elements or by solid-state diffusion of the metal into /3-rhombohedral (/3-rh) boron. Compositions as determined by erystal structure and electron microprobe analyses together with the unit cell dimensions are given in Table 1. The volume of the unit cell (V ) increases when the solid solution is formed. As illustrated in Fig. 1, V increases nearly linearly with metal content for the solid solution of Cu in /3-rh boron. In addition to the elements listed in Table 1, the expansion of the unit cell exceeds 7.0 X 10 pm for saturated solid solutions " of Ti, V, (2o, Ni, As, Se and Hf in /3-rh boron, whereas the increase is smaller for the remaining elements. The solubility of these elements does not exceed a few tenths at %. The microhardness of the solid solution increases with V . Boron is a brittle material, indicating the accommodation of transition-element atoms in the -rh boron structure is associated with an increase in the cohesion energy of the solid. 

Rubber swelling modifies the liquid/solid work of adhesion. Wo, because in addition to the initial liquid/solid interactions, liquid diffusion into the solid produces supplementary liquid/liquid interactions, hquid molecules having passed through the liquid/solid interface. Therefore, to the initial work of adhesion in the absence of swelling, Wq, an additional term corresponding to a fraction of the cohesion energy of the liquid, 2y, should be added. If / is the time of diffusion, the work of adhesion at /, Wo(t), can then be expressed as... 

The surface free energy y is related to the cohesive energy of the solid, AHcoh, and to the number of bonds between an atom and its nearest neighbors that had to be broken to create the surface ... 

In the Introduction the problem of construction of a theoretical model of the metal surface was briefly discussed. If a model that would permit the theoretical description of the chemisorption complex is to be constructed, one must decide which type of the theoretical description of the metal should be used. Two basic approaches exist in the theory of transition metals (48). The first one is based on the assumption that the d-elec-trons are localized either on atoms or in bonds (which is particularly attractive for the discussion of the surface problems). The other is the itinerant approach, based on the collective model of metals (which was particularly successful in explaining the bulk properties of metals). The choice between these two is not easy. Even in contemporary solid state literature the possibility of d-electron localization is still being discussed (49-51). Examples can be found in the literature that discuss the following problems high cohesion energy of transition metals (52), their crystallographic structure (53), magnetic moments of the constituent atoms in alloys (54), optical and photoemission properties (48, 49), and plasma oscillation losses (55). 

Seiler and Dunitz point out that the main reason for the widespread acceptance of the simple ionic model in chemistry and solid-state physics is its ease of application and its remarkable success in calculating cohesive energies of many types of crystals (see chapter 9). They conclude that the fact that it is easier to calculate many properties of solids with integral charges than with atomic charge distributions makes the ionic model more convenient, but it does not necessarily make it correct. 

Overlap between p orbitals leads to cohesive energies of typically less than 0.4 eV molec The much stronger ionic and covalent bonding have binding energies of 10 and 3 eV atom respectively. Finally, physisorption is the weakest form of absorption to a solid surface characterized by a lack of a true chemical bond (chemisorption) between substrate and adsorbate and will be discussed in Chapter 4 (see e.g., Zangwill, 1988). 

For actinide atoms E is of the order of 60.000 Ryds. If the cohesive energy of a solid is required it is necessary first to compute the total energy of the atom, spin polarizing the... 

Equation (1.4) is an expression for the lattice energy of an ionic solid like NaCl, first derived by Born and Mayer. The equation can be used directly for the calculation of cohesive energy of ionic solids provided we know A and p. 

The cohesive force between solid surfaces and the surface energy of solids." Ibid., 13 (7th Ser.) 853-862. 

Van der Waals forces usually contribute significantly to the cohesion energies and interfacial energies of solids and liquids. In those cases, in which determining interactions occur at interatomic spacings, there is no doubt of their mechanical importance. However, there is still doubt about the best way to formulate and compute forces while incorporating details of molecular arrangement. 

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