Oxidation defect equilibrium

Let us imagine equilibrating a fayalite crystal (Fe2Si04) in an atmosphere sufficiently oxidizing to allow a defect equilibrium of the following type to proceed toward the right ... 

Oxidation of zinc to zinc oxide is another example whose kinetics have been interpreted in terms of the Wagner model (Wagner Grunewald, 1938). At 670 K, the reaction has been found to be independent of oxygen pressure between 0.02 and 1 atm. ZnO is a n-type semiconductor, having a stoichiometric excess of zinc accommodated as interstitials the defect equilibrium could be represented as... 

The conductivity measurements show that equilibrium (1) sets in rapidly at temperatures as low as 500°C. Since the melting point of zinc oxide is about 2100°C. and accordingly its Tamman temperature about 900°C., the process under consideration cannot possibly involve the bulk of the crystal because defects could not diffuse rapidly enough through the lattice at such low temperatures. Except at very high temperatures, the defect equilibrium is realized only at the surface of the crystal, that is, in a layer of a few unit cells thickness. 

In other cases, however, and in particular when sublattices are occupied by rather immobile components, the point defect concentrations may not be in local equilibrium during transport and reaction. For example, in ternary oxide solutions, component transport (at high temperatures) occurs almost exclusively in the cation sublattices. It is mediated by the predominant point defects, which are cation vacancies. The nearly perfect oxygen sublattice, by contrast, serves as a rigid matrix. These oxides can thus be regarded as models for closed or partially closed systems. These characteristic features make an AO-BO (or rather A, O-B, a 0) interdiffusion experiment a critical test for possible deviations from local point defect equilibrium. We therefore develop the concept and quantitative analysis using this inhomogeneous model solid solution. 

Manganous Sulfide Nonstoichiometry and defect concentrations are very low in Mni yS of the order of that in nickel oxide. The predominant defect equilibrium is... 

Because oxidation and reduction are reversed reactions each other, which are actually the same process from the thermodynamic point of view, their reaction equations are dependent mutually. For example, if the reduction reaction of Eq. (5.21) is combined with the intrinsic electronic defect equilibrium ... 

The nonstoichiometry of an oxide strongly depends on the presence of alio-valent impurities and dopants affect the number of thermal defects in non-stoichiometric oxides and their electrical conductivity because the solutes have a valence other than the atoms they replace. This is illustrated in the case of lithium and chromium doping of nickel and zinc oxides in equilibrium with gaseous oxygen. 

If the range of homogeneity of the reaction product is sufficiently narrow, then the average diffusion coefficient as defined in eq. (8-9) can be calculated by means of defect thermodynamics, if it is assumed that the defects behave as the solute in ideally dilute solutions. In section 4.2 it was shown how the concentrations of the defect centers depend upon the component activities for a given type of disorder in binary ionic crystals. As an example, let us consider the formation of copper (I) oxide on copper sheet at 1000 °C in an oxidizing atmosphere whenis about 1 torr. The following defect equilibrium can be written ... 

Mizusaki, J., Mori, N., Takai, H., Yonemura, Y., Minamiue, H., Tagawa, H., Dokiya, M., Inaba, H., Naraya, K., Sasamoto, T., and Hashimoto, T. (2000). Oxygen nonstoichiometry and defect equilibrium in the perovskite-type oxides Lai- Sr MnOs+j. Solid State Ionics 129 163-177. 

In stoichiometric oxides, the equilibrium concentration of the defects depends only on temperature. For Frenkel defects at equilibrium ... 

It is important to note that since oxidation and reduction are the same thermodynamic process simply reversed, the reactions written to describe them are not independent. For example, taking the reduction reaction [Eq. (7.21)] in combination with the intrinsic electronic defect equilibrium... 

Strobel P, Capponi JJ, Marezio M, Monod P (1987) High-temperature oxygen defect equilibrium in superconducting oxide YBa2Cu307-x, Solid Slate Commun 64(4) 513-15... 

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]... 

As mentioned above, an exact stoichiometric composition in inorganic compounds is in principle the exception rather than the rule. Oxides in equilibrium with their surroundings are generally nonstoichiometric, except under specific conditions of temperature and activities of the components. However, within our experimental ability to measure the ratio of the constituent atoms, many inorganic compounds may be considered to be so near stoichiometry over large temperature and activity ranges that minor deviations from stoichiometry may often be neglected in a discussion of defect concentrations and defect-controlled properties. 

As illustration let us consider the defect equilibrium for Schottky defects in the oxide MO and where the metal and oxygen vacancies are doubly charged. The defect equation for their formation is given in Chapter 2 as... 

Mizusaki, J., Yoshihiro, M., Yamauchi, S., and Fueki, K. Thermodynamic quantities and defect equilibrium in the perovskite-type oxide solid solution Lai cSr cFe03. 5. J Solid State Chem. 1987, 67, 1-8. 

However, it is unlikely that this defect equilibrium determines the ojgrgen ion vacancy concentration in Mg-doped LaCrOj, as the presence of trivalent cation vacancies in ternary metal oxides is not favored thermodynamically. ... 

Mizusaki J, Mori N, Takai H et al (2000) Oxygtai nonstoichiometry and defect equilibrium in the perovskite-type oxides Lai.xSrxMn03+d. Solid State Ionics 129 163-177... 

O2 is higher than that in H2 at 500-900°C due to the contribution of electron hole conduction in oxidative atmospheres [11-14]. An electron hole is generated in association with the following defect equilibrium ... 

In this method the creation of defects is achieved by the application of ultrashort (10 ns) voltage pulses to the tip of an electrochemical STM arrangement. The electrochemical cell composed of the tip and the sample within a nanometer distance is small enough that the double layers may be polarized within nanoseconds. On applying positive pulses to the tip, the electrochemical oxidation reaction of the surface is driven far from equilibrium. This leads to local confinement of the reactions and to the formation of nanostructures. For every pufse applied, just one hole is created directly under the tip. This overcomes the restrictions of conventional electrochemistry (without the ultrashort pulses), where the formation of nanostructures is not possible. The holes generated in this way can then be filled with a metal such as Cu by... 

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