Extended defect structures thermodynamics

Thermodynamic considerations imply that all crystals must contain a certain number of defects at nonzero temperatures (0 K). Defects are important because they are much more abundant at surfaces than in bulk, and in oxides they are usually responsible for many of the catalytic and chemical properties.15 Bulk defects may be classified either as point defects or as extended defects such as line defects and planar defects. Examples of point defects in crystals are Frenkel (vacancy plus interstitial of the same type) and Schottky (balancing pairs of vacancies) types of defects. On oxide surfaces, the point defects can be cation or anion vacancies or adatoms. Measurements of the electronic structure of a variety of oxide surfaces have shown that the predominant type of defect formed when samples are heated are oxygen vacancies.16 Hence, most of the surface models of... 

EM plays a crucial role in the development of thermodynamic data, especially for defective solids, multi-phase solids and solids with coexisting intergrowth structures. These microstructural details, which are essential to catalytic properties, cannot be revealed readily by other diffraction methods which tend to average structural information. The formation of anion vacancies in catalytic reactions and the resulting extended defects are described here, from which an improved understanding of the formation of CS planes and their role in catalysis can be obtained. These general results are applicable to other CS structures. 

Shear Plane-Point Defect Equilibria.—The question of the existence of point defects in compounds where extended defects are known to occur has been controversial. Indeed, it has occasionally been claimed that point defects cannot form in such phases and that they will always be eliminated with the formation of extended structures. We reject these latter arguments as thermodynamically unsound. From a thermodynamic standpoint, the formation of extended defects can be viewed as a special mode of point defect aggregation as such, shear planes will be in equilibrium with point defects, with the position of the equilibrium depending on both temperature and the extent of the deviation from stoicheiometry. Thus, if we assume, as is suggested by our calculations, that anion vacancies are the predominant point defects in reduced rutile (a further point of controversy as mentioned above) then there will exist an equilibrium of the type... 

In this chapter, we will discuss the generation modes of thermodynamically stable point defects and the defect-chemical logic to calculate the equilibrium defect structure of a given system. As a stereotype of systems, we will consider only a binary oxide MO, but the idea and logic can be readily extended to other binary, ternary and higher systems with minor modifications [2-6]. 

Solid State Chemistry (thermodynamic, kinetic, and structural properties of oxides, nonstoichiometry and extended defects in nonmetallic solids, application of high-resolution electron microscopy to solid state chemistry)... 

Stone-Wales wave isomeric mechanism that produces the t -extended dislocation dipole originally applied here to graphene-to-silicene nanoribbons future computational studies, especially at DFT level will be necessary to describe and cross-check the actual bondonic findings regarding the energetic barriers and thermodynamic stability of presently considered SW topological defects in IVA elemental honeycomb and related hetero structures. 

The fluorite structure of CeO forms extended solid solutions with a large number of oxides of metals with valences ranging from 2+ to 6+. The influence of doping with metal cations of various valencies on the thermodynamic properties of defect formation is discussed here. 

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