POINT DEFECTS IN OXIDES

In this section, the phenomenon of point defects, such as vacancies and interstitial, in crystals is briefly introduced. The oxide entropy change (A5) increases when more points defects, also known a imperfections, generate within a crystal. Metal oxides at equilibrium may contain nearly equal numbers of cations and anion vacancies. Thus, the number of point defects (n) producing a minimum free energy change, AG = AHf — TAS, can be modeled by the Arrhenius law [21-23] 

Furthermore, point defects are mobile imperfections at high temperatures, and eventually, their rate of diffusion may obey the Arrhenius law [22] 

It is known that ionic compounds have appreciable electrical conductivity, which is inseparable from diffusion, due to atomic defects, such as Schottky and Frenkel defects to an extent, and ionic migration and diffusion. For instance, Schottky defects are combinations of cation and anion vacancies necessary to maintain ionic electrical neutrality and stoichiometric ionic structure. In general, ions (cations and anions) diffuse into adjacent sites. 

On the other hand, Frenkel defects are combinations of interstitial cations and cation vacancies. Electrical neutrality and stoichiometry are also maintained. Thus, combinations of the type of defects provide the ionic diffusion mechanism for oxide growth, but stoichiometry may not be maintained due to the electrical nature of oxides having either metal-excess or metal-deficit conditions. 

With regard to the case in which ncation(FexO) nanion(FeO), the Schot-tky and Frenkel defects do not prevail as the dominant mechanisms for oxide formation. Instead, cation diffusion and electron migration toward the oxide surface are the dominant mechanisms. Also, some ferric iron (Fe ) cations can be present in the oxide structure and can associate with oxygen 0 anions generating some cation vacancies. This implies that a fraction of ferrous iron Fe+ cations oxidize to Fe+ cations, resulting in a cation deficiency [21]. 

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The question raised by Anderson (1970,1971) and Anderson et al (1973) as to whether anion point defects are eliminated completely by the creation of extended CS plane defects, is a very important one. This is because anion point defects can be hardly eliminated totally because apart from statistical thermodynamics considerations they must be involved in diffusion process. Oxygen isotope exchange experiments indeed suggest that oxygen diffuses readily by vacancy mechanism. In many oxides it is difficult to compare small anion deficiency with the extent of extended defects and in doped complex oxides there is a very real discrepancy between the area of CS plane present which defines the number of oxygen sites eliminated and the oxygen deficit in the sample (Anderson 1970, Anderson et al 1973). We attempt to address these issues and elucidate the role of anion point defects in oxides in oxidation catalysis (chapter 3). 

Gianfranco P. Ab initio theory of point defects in oxide materials structure, properties, chemical reactivity. Solid State Sci. 2000 2 161-79. 

While the effective g value is expressed in terms of three principal values directed along three axes or directions in a single crystal, only the principal values of g can be extracted from the powder spectrum rather than the principal directions of the tensor with respect to the molecular axes. (Therefore it is more correct to label the observed g values as gi, g2, g3 rather than g gyy, in a powder sample.) In the simplest case, an isotropic g tensor can be observed, such that all three principal axes of the paramagnetic center are identical (x = y = z and therefore gi= gi = g-i). In this case, only a single EPR line would be observed (in the absence of any hyperfine interaction). With the exception of certain point defects in oxides and the presence of signals from conduction electrons, such high symmetry cases are rarely encountered in studies of oxides and surfaces. 

Often the most important properties of materials are directly or indirectly connected to the presence of defects and in particular of point defects [18]. These centers determine the optical, electronic and transport properties of the material and usually dominate the chemistry of its surface. A detailed understanding and a control at atomistic level of the nature (and concentration) of point defects in oxides is therefore of fundamental importance to synthesize new materials with well defined properties. This has lead in recent years to the birth of the new field of defect engineering. Of course, before to be created in controlled conditions point defects have to be known in all aspects of their physico-chemical properties. The accurate theoretical description of the electronic structure of point defects in oxides is essential for the understanding of their structure-properties relationship. 

Tuller HL, Bishop SR (2011) Point defects in oxides tailoring materials through defect engineering. Annu Rev Mater Res 41 369-398... 

Sintering governed by lattice diffusion will be dependent upon the concentration of point defects in oxides. Accordingly, sintering rates of an oxide can be optimised by close control of impurities or dopants and the ambient partial pressures of oxygen and of water vapour in cases where proton defects affect the defect structure of the oxide. 

Crystal structure, crystal defects and chemical reactions. Most chemical reactions of interest to materials scientists involve at least one reactant in the solid state examples inelude surfaee oxidation, internal oxidation, the photographie process, electrochemieal reaetions in the solid state. All of these are critieally dependent on crystal defects, point defects in particular, and the thermodynamics of these point defeets, especially in ionic compounds, are far more complex than they are in single-component metals. I have spaee only for a superficial overview. 

Figure 1.13 Point defects in nickel oxide, NiO (schematic) Ni2+ vacancy Ni2+ interstitial Li+ on a Ni2+ site Mg2+ on a Ni2+ site Fe3+ on a Ni2+ site O2- vacancy N3- on an O2-site F on an O2- site free electron free hole.

It is diagnostic of electronic/chemical state, is sensitive to point defects, and can be used to probe the distribution of promoters in catalytic oxides (67). Examples include effects of the distribution of antimony in Sb-Sn02 catalysts (used for selective hydrocarbon oxidation) on the electronic structure of the catalyst and mapping of point defects in titania catalysts. 

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... 

The spectral distribution of the PL from OPS is found to be similar to that of as-prepared PS [Ta6]. In some cases a green band is found and has been ascribed to point defects in Si02 [Ka9]. The slow red-orange band is dominant, while the fast blue-green band contributes significantly to the PL intensity for highly oxidized samples [Kol], While the red band is correlated with the presence of small... 

Non-stoichiometry is a very important property of actinide dioxides. Small departures from stoichiometric compositions, are due to point-defects in anion sublattice (vacancies for AnOa-x and interstitials for An02+x )- A lattice defect is a point perturbation of the periodicity of the perfect solid and, in an ionic picture, it constitutes a point charge with respect to the lattice, since it is a point of accumulation of electrons or electron holes. This point charge must be compensated, in order to preserve electroneutrality of the total lattice. Actinide ions having usually two or more oxidation states within a narrow range of stability, the neutralization of the point charges is achieved through a Redox process, i.e. oxidation or reduction of the cation. This is in fact the main reason for the existence of non-stoichiometry. In this respect, actinide compounds are similar to transition metals oxides and to some lanthanide dioxides. 

VO2 and Ti02) leads to the formation of extended defects, i.e. CS planes, rather than to point defects. In the early literature reports, the definition of CS involved the removal of a complete sheet of anion sites to form an extended CS plane defect (Wadsley 1964, Anderson and Hyde 1967). Consequently, the role played by true point defects in non-stoichiometric oxides was not obvious from these earlier reports and answer to this was sought by Anderson (1970, 1971), Anderson et al (1973) (1.13.2). However, although this definition of CS is a convenient one, the situation is not so straightforward as we now demonstrate. 

More generally, co is independent of the external gas pressure k is the Boltzmann constant (1.38 x 10 erg deg ) and T is the temperature in Kelvin. Furthermore, the equilibrium between co and a collapsed CS plane fault is maintained by exchange at dislocations bounding the CS planes. Clearly, this equilibrium cannot be maintained except by the nucleation of a dislocation loop and such a process requires a supersaturation of vacancies and CS planes eliminate supersaturation of anion vacancies (Gai 1981, Gai et al 1982). Thus we introduce the concept of supersaturation of oxygen point defects in the reacting catalytic oxides, which contributes to the driving force for the nucleation of CS planes. From thermodynamics. 

These studies have led to a new understanding of me fundamental defect processes that occur at me oxide catalyst s surface and of the role of extended CS plane defects in oxide catalysts. Furmermore, me studies suggest mat anion point... 

There is increasing experimental evidence for the superlattice ordering of vacant sites or interstitial atoms as a result of interactions between them. Superlattice ordering of point defects has been found in metal halides, oxides, sulphides, carbides and other systems, and the relation between such ordering and nonstoichiometry has been reviewed extensively (Anderson, 1974, 1984 Anderson Tilley, 1974). Superlattice ordering of point defects is also found in alloys and in some intermetallic compounds (Gleiter, 1983). We shall examine the features of some typical systems to illustrate this phenomenon, which has minimized the relevance of isolated point defects in many of the chemically interesting solids. 

Schottky defects are the predominant equilibrium point defects in stoichiometric zirconia ZrC>2 (see Exercise 8.15). Suppose that the soluble oxide Ta2C>5 is added to ZrCV Assume that cation vacancies form without the formation of any interstitial defects. 

The Role of Point Defects in Silicon Processing. The Balancing Act in Silicon Processing. Both silicon oxidation and the diffusion of impurities occur at high temperatures and involve point defects such as va-... 

Figure 32. Role of silicon point defects in the oxidation reaction (115).

Point defects in the form of cation vacancies () were introduced by Aykan et al. (93-95) into molybdates, tungstates, and vanadates with scheelite-type crystal structures. The authors studied the catalytic properties of more than 30 scheelite-structure phases represented by the formula A1 x< xM04 (M = molybdenum, tungsten, and/or vanadium and A may include Li, Na, K, Ag, Ca, Sr, Ba, Cd, Pb, Bi, and/or arare earth element in quantities appropriate to achieve charge balance for the normal oxidation states). It was found that the defects can be introduced... 

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