Energetics of Defect Formation

The relationship between standard free energy and equilibrium constant for a chemical reaction is as follows  

Since the PV term is negligible in the intrinsic ionization process, E° may be substituted for the enthalpy. E° is the energy necessary to remove an electron from the valence band and place it into the conduction band. Consequently, it is the width of the band gap. 

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The energetics of defect formation can be exploited to make solid solutions to form new compounds. 

This has important consequences for the energetics of defects in metals. For example, the vacancy formation energy within a nearest neighbour pair... 

Anyway, in this manner, we have built a thermodynamic bridge between defect properties, solid and liquid state , that is also mirrored in many semiempirical relationships (e.g. between enthalpy of defect formation and melting point). This, of course, is to be expected, since defect formation contains almost aU the relevant energetic and entropic information. Thus, it is understandable that t3q>ical binary... 

In pure and stoichiometric compounds, intrinsic defects are formed for energetic reasons. Intrinsic ionic conduction, or creation of thermal vacancies by Frenkel, ie, vacancy plus interstitial lattice defects, or by Schottky, cation and anion vacancies, mechanisms can be expressed in terms of an equilibrium constant and, therefore, as a free energy for the formation of defects, If the ion is to jump into a normally occupied lattice site, a term for... 

Catalytic applications of ceria and ceria-based mixed oxides depend primarily upon the nature and concentration of the defects present in the material. Although experimental techniques are available for the study of these defects, the characterization of their physical properties at the atomic level is often very difficult. The most important point defects in ceria are oxygen vacancies, reduced Ce centers and dopant impurities. The formation energy of such defects and the energetics of their mutual interactions within the bulk oxide have been the subject of several computational studies. 

The surfaces of real substrates are inhomogeneous and exhibit surface defects such as steps, kinks, pits etc. These defects do significantly influence not only the energetics of 2D nucleation [3.249], but also the overlapping of growing 2D islands. Thus, the assumptions of the Avrami equation (3.65) are not fulfilled in this case. In the following, the influence of surface inhomogeneities such as monatomic steps on the kinetics of 2D Meads phase formation is briefly discussed. 

A second difficulty with the pair potential description is manifest when we attempt to consider defect formation energies. Specifically, we will also show that the pair potential description implies a formation energy for vacancies that is a vast overestimate relative to the numbers found in experiment. As is true for the elastic moduli, there are modifications that can be considered, but not without a sense that the crucial physics is being ignored. In response to these difficulties, and others, concerted efforts have been made to extend our description of the energetics of... 

An alternative perspective on the subject of point defects to the continuum analysis advanced above is offered by atomic-level analysis. Perhaps the simplest microscopic model of point defect formation is that of the formation energy for vacancies within a pair potential description of the total energy. This calculation is revealing in two respects first, it illustrates the conceptual basis for evaluating the vacancy formation energy, even within schemes that are energetically more accurate. Secondly, it reveals additional conceptual shortcomings associated with... 

In this context, Sayle et al. have used atomistic simulation methods to investigate the interaction of ceria with impurities, particularly rhodium, palladium and platinum. The energetics of the most common valence states for the metal atoms were investigated, as well as the variation of the energy of the impurities with depth below the surface and the tendency of defects to segregate to the surfaces. Fig. 8.9. shows the substitutional defect formation energies as a function of the distance from the (111) and (110) surfaces of Ce02 for C e " ", PcP+ and Sayle etal. found that... 

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