Point defect: also formation energy

We will be considering primarily inorganic solids but must keep in mind that the same principles also apply to organic solids. Therefore, we intend to examine the nature of point defects in terms of their thermodynamics, equilibria and the energy required for their formation. It will be seen that point defects follow the same physical chemistry laws that apply to inorgcuiic compounds and physical properties in general. 

Our present task is to build on the foundations laid in chap. 7, but now with special reference to the diffusive processes that take place at extended defects. The basic argument will be that by virtue of the more open atomic-level environments near extended defects, the activation energy both for point defect formation and migration will often be reduced relative to bulk values. We will build our case around a fundamental case study through the consideration of diffusion at surfaces. The surface diffusion example will illustrate not only how diffusive processes are amended at extended defects, but will also illustrate the shortcomings of the transition state formalism when the detailed atomic-level mechanisms are not known a priori. 

Note that in LRC, the stable Frenkel pairs may be formed (e.g., under irradiation). The energy spectrum of Frenkel pair formation is somewhat spread due to the spread in energies of vacancies and interstitials formation. The width of this spectrum as well as variations in energy of vacancies and interstitials formation may amount to some eV, and the typical values of the threshold energy of Frenkel pair formation in metallic glasses as well as in crystals may amount to about 25-30 eV. To point defects of a cluster one may attribute also the interstitial and substitutional impurities that locally break the topological and compositional order. 

We have seen above that the kinetics of mineral dissolution is well explained by transition-state theory. The framework of this theory and kinetic data for minerals have shown that dissolution is initiated by the adsorption of reactants at active sites. Until now these active sites have been poorly characterized nevertheless, there is a general consensus that the most active sites consist of dislocations, edges, point defects, kinks, twin boundaries, and all positions characterized by an excess surface energy. Also these concepts have been strongly supported by the results of many SEM observations which have shown that the formation of crystallographically controlled etch pits is a ubiquitous feature of weathered silicates. 

The defects which disrupt the regular patterns of crystals, can be classified into point defects (zero-dimensional), line defects (1-dimensional), planar (2-dimensional) and bulk defects (3-dimensional). Point defects are imperfections of the crystal lattice having dimensions of the order of the atomic size. The formation of point defects in solids was predicted by Frenkel [40], At high temperatures, the thermal motion of atoms becomes more intensive and some of atoms obtain energies sufficient to leave their lattice sites and occupy interstitial positions. In this case, a vacancy and an interstitial atom, the so-called Frenkel pair, appear simultaneously. A way to create only vacancies has been shown later by Wagner and Schottky [41] atoms leave their lattice sites and occupy free positions on the surface or at internal imperfections of the crystal (voids, grain boundaries, dislocations). Such vacancies are often called Schottky defects (Fig. 6.3). This mechanism dominates in solids with close-packed lattices where the formation of vacancies requires considerably smaller energies than that of interstitials. In ionic compounds also there are defects of two types, Frenkel and Schottky disorder. In the first case there are equal numbers of cation vacancies... 

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