Surfaces of crystalline solids

In this chapter the special features of surfaces and internal boundaries in single-phase crystalline systems are described. The orientation dependence of the surface functions will be discussed and the use of Wulff plots and stereographic triangles to present the orientation dependence of surface energy will be demonstrated. The various types of internal boundaries (grain boundaries, twin boundaries, etc.) and their thermodynamic properties will be discussed. 

As described in Chapter 2, there are two fundamental quantities that describe surfaces and interfaces. One is the surface energy (y), which is the reversible work involved in creating unit area of new surface at constant temperature, volume and total number of moles (J/m ). The other is the surface stress (a), which is the work involved in reversibly deforming a surface (N/m). We have seen that for pure liquids the two quantities are numerically equal. The phenomena described in this chapter relate mainly to the surface energy. 

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Organic functional groups covalently bound to the surface of crystalline solids or insoluble polymers are subject to special constraints which may alter their reactivity in comparison with analogous small molecules. 

Surfaces of crystalline solids can be specifically defined, thanks to the fact that planes of atoms in crystals can be specifically defined. Some of the ideas from the previous chapter on crystals will be applied here. Finally, we recognize the fact that the presence of certain surfaces speeds up, or catalyzes, some chemical reactions. Again, why It turns out that there can be an interaction between the reactants and the surface itself that decreases the activation energy of the reaction, and therefore speeds up the rate. Catalysis of chemical reactions is an important industrial concern because in industry time is money. The physical chemistry of surfaces provides the basis for understanding why catalysis by surfaces occurs. 

Miller indices are commonly used to describe surfaces of crystalline solids. Figure 22.15 shows some examples. 

Finally, we note that the methods here presented are applicable as well to hard interfaces, e.g., surfaces of crystalline solids or Langmuir-Blodgett films of surfactant molecules on solid supports. 

Langmuir s equation [24] is regularly derived in a variety of ways, of which the most inmitive is based on chemical equilibrium (Chapter 12) rather than phase equilibrium. He originally based it only on the external surface of crystalline solids, not on the internal surface of the pores in crystalline or amorphous solids - by far the most industrially important adsorption application it is most often applied to these internal surfaces. The discussion here is a significant simplification of that he presented. He assumed that at equilibrium the rates of adsorption and desorption were equal and that... 

To examine the effective interaction of urea with specific surfaces of KCl, an approach similar to surface docking developed to predict the influence of additives on the crystal morphology has been employed [21-27], The basis of this approach is to analyze the effect of additives on the individual crystal faces, which are cleaved from a crystal. If the additive has a preferred interaction on a special face, the growth of this face will be slower. As a result, the other fast-growing surfaces will disappear, and eventually, the slow-growing surface will control the morphology. In this way, the additive influences the morphology of crystals. For simulations of surfaces of crystalline solids, slab, and cluster models are nevertheless by far more popular because they are feasible from the computational point of view [28]. However, the cluster models came under scrutiny due to their finite size representation. Slab models rather mimic the infinite surface of solids and are considered to be a better approach than the cluster models. In this study, a conventional array of these alkali... 

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