Reaction between defects

Many defects are charged, they diffuse through the lattice, if the temperature is high enough, and they can associate with each other to form defect clusters or color centers. Such associates strongly affect the properties of the solid and materials engineers control the defect concentrations in solids to obtain the wanted properties. The following are examples of reactions between defects. 

The quantitative description of most diffusional processes in single-phase media is based upon the assumption of local defect equilibrium. Therefore, in this section we shall first of all examine processes by which defect equilibrium is attained. In this regard, two important fundamental types of defect reactions should be discussed 1. Following a sudden change in temperature or pressure, a reaction between defects and lattice atoms occurs at sites of repeat-able growth such as inner or outer surfaces and dislocations. For a crystal with Schottky disorder, the reaction equation may be formulated as ... 

Macdonald and Franceschetti " made an analysis of small-signal ac impedance measurement which can be apphed also to MIECs. They allow for high frequencies and therefore for the existence of a noimegligible displacement current and deviation from local electroneutrality. They also consider electrodes with partial blocking and internal reaction between defects. The model is limited to dilute concentrations and zero dc bias. 

Diffusion of the molecular gases can be compHcated by reactions with the glass network, especially at the sites of stmctural defects. The diffusion coefficient of water, for example, shows a distinct break around 550°C (110). Above 550°C, the activation energy is approximately 80 kj /mol (19 kcal/mol), but below 550°C, it is only 40 kJ/mol (9.5 kcal/mol). Proposed explanations for the difference cite the fact that the reaction between water and the sihca network to form hydroxyls is not in equiUbrium at the lower temperatures. 

Since corrosion is essentially a reaction between a metal and its environment, the very significant effect of crystal defects and metallurgical structure on certain corrosion phenomena is to be expected. It is no more possible to... 

Catalytic oxidations on the surface of oxidic materials usually proceed according to the Mars-Van Krevelen mechanism [P. Mars and D.W. van Krevelen, Chem. Eng. Sci. 3 (1954) 41], as illustrated in Fig. 9.17 for the case of CO oxidation. Instead of a surface reaction between CO and an adsorbed O atom, CO2 is formed by reaction between adsorbed CO and an O atom from the metal oxide lattice. The vacancy formed is filled in a separate reaction step, involving O2 activation, often on defect sites. 

Consider the surface of a solid. In the interior, we see a certain s mmetry which depends upon the structure of the solid. As we approach the surface from the interior, the symmetry begins to change. At the very surface, the surface atoms see only half the symmetry that the interior atoms do (and half of the bonding as weU). Reactions between solids take place at the surface. Thus, the surface of a solid represents a defect in itself since it is not like the interior of the solid. 

The chemical composihons of the zeolites such as Si/Al ratio and the type of cation can significantly affect the performance of the zeolite/polymer mixed-matrix membranes. MiUer and coworkers discovered that low silica-to-alumina molar ratio non-zeolitic smaU-pore molecular sieves could be properly dispersed within a continuous polymer phase to form a mixed-matrix membrane without defects. The resulting mixed-matrix membranes exhibited more than 10% increase in selectivity relative to the corresponding pure polymer membranes for CO2/CH4, O2/N2 and CO2/N2 separations [48]. Recently, Li and coworkers proposed a new ion exchange treatment approach to change the physical and chemical adsorption properties of the penetrants in the zeolites that are used as the dispersed phase in the mixed-matrix membranes [56]. It was demonstrated that mixed-matrix membranes prepared from the AgA or CuA zeolite and polyethersulfone showed increased CO2/CH4 selectivity compared to the neat polyethersulfone membrane. They proposed that the selectivity enhancement is due to the reversible reaction between CO2 and the noble metal ions in zeolite A and the formation of a 7i-bonded complex. 

Erom the preceding discussion, the distinction between misfit defects shear domains formed by pure shear and CS planes formed by the elimination of anion vacancies in a specific crystallographic plane by shear and the collapse of the oxide lattice on that plane can be understood. This distinction between defects is central to catalytic reaction mechanisms in oxides. However, it is often not made in the literature on oxide catalysis and solid state oxide chemistry. This can result in an incorrect interpretation of observed data and of the role played by lattice oxygen atoms in catalytic reactions. The former are regions containing... 

Pending further detailed information on the constitution of the surface layer, it is possible neverthelsss to get useful qualitative information on the relationship between defect structure of a given semiconducting oxide and its behavior as an adsorbent or catalyst. Thus a semiconductor can be modified by addition of controlled amounts of impurities. If it is then assumed that the direction of the modification is the same at least qualitatively at the surface and in the bulk, a comparison of oxides respectively unmodified and modified in opposite directions can reveal trends of interest as to the requirements of a given surface reaction. This method was first tried by Wagner (27) and further amplified by one of us (28,28a). 

Figure 1-4. The A/AX interface during flow of A-cations across the boundary (g = 0) into the (semiconducting) compound AX. Point defect relaxation reaction between 0< < R reads V + A- = Aa. hit = width of relaxation zone.

If majority point defect concentrations depend on the activities (chemical potentials) of the components, extrinsic disorder prevails. Since the components k are necessarily involved in the defect formation reactions, nonstoichiometry is the result. In crystals with electrically charged regular SE, compensating electronic defects are produced (or annihilated). As an example, consider the equilibrium between oxygen and appropriate SE s of the transition metal oxide CoO. Since all possible kinds of point defects exist in equilibrium, we may choose any convenient reaction between the component oxygen and the appropriate SE s of CoO (e.g., Eqn. (2.64))... 

The temporal evolution of spatial correlations of both similar and dissimilar particles for d = 1 is shown in Fig. 6.15 (a) and (b) for both the symmetric, Da = Dft, and asymmetric, Da = 0 cases. What is striking, first of all, is rapid growth of the non-Poisson density fluctuations of similar particles e.g., for Dt/r = 104 the probability density to find a pair of close (r ro) A (or B) particles, XA(ro,t), by a factor of 7 exceeds that for a random distribution. This property could be used as a good aggregation criterion in the study of reactions between actual defects in solids, e.g., in ionic crystals, where concentrations of monomer, dimer and tetramer F centres (1 to 3 electrons trapped by anion vacancies which are 1 to 3nn, respectively) could be easily measured by means of the optical absorption [22], Namely in this manner non-Poissonian clustering of F centres was observed in KC1 crystals X-irradiated for a very long time at 4 K [23],... 

Up to now we have been discussing in this Chapter many-particle effects in bimolecular reactions between non-interacting particles. However, it is well known that point defects in solids interact with each other even if they are not charged with respect to the crystalline lattice, as it was discussed in Section 3.1. It should be reminded here that this elastic interaction arises due to overlap of displacement fields of the two close defects and falls off with a distance r between them as U(r) = — Ar 6 for two symmetric (isotropic) defects in an isotropic crystal or as U(r) = -Afaqjr-3, if the crystal is weakly anisotropic [50, 51] ([0 4] is an angular dependent cubic harmonic with l = 4). In the latter case, due to the presence of the cubic harmonic 0 4 an interaction is attractive in some directions but turns out to be repulsive in other directions. Finally, if one or both defects are anisotropic, the angular dependence of U(f) cannot be presented in an analytic form [52]. The role of the elastic interaction within pairs of the complementary radiation the Frenkel defects in metals (vacancy-interstitial atom) was studied in [53-55] it was shown to have considerable impact on the kinetics of their recombination, A + B -> 0. 

The oxygen incorporation reaction between oxygen gas and defects in LSFTO is given by... 

Just as the oxygen vacancy and the SC can be considered as a product of the addition or disproportionation reaction of two silicon radicals (fundamental sources of the oxygen deficiency in Si02), so can the peroxide bridge and the DOSG be considered as products of the respective reactions between two oxy radicals (=Si-0-)3Si-0 (fundamental defects containing excess oxygen in silica) ... 

This method using grafting to one silicon atom of SC makes it possible to approach spatially two chemically different groups r and rt and obtain free radical structures of the (=Si-0-)2Si(r )(r) type. This leads to more diverse intermediates on the solid surface and allows one to study new chemical processes involving these intermediates, including intramolecular reactions between r and /y groups. The low-molecular radicals necessary for the first step of SC modification can conveniently be obtained from the saturated H-r molecules, and appropriate defects on the silica surface can be used as... 

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