Electronic Disordering

Within the framework of standard band approach, thermally activated electrons can 

Consequently, a free electron in the conduction band and an itinerant hole in the valence band appear simultaneously  

Alternatively, the process of intrinsic electronic disordering can be represented within the framework of localized electrons model, for example  

The effectively neutral atomic defects may trap or donate electrons, thus acquiring a charge, the sign of which will depend on the chemical nature ofthe defects and their surroundings. The following quasi-chemical reactions provide examples ofthe point-defect ionization processes  

The possible ionization of the Schottky-type defects in NaCl, given by 

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N is here the number of lattice defects (vacancies or interstitials) which are responsible for non-stoichiometry. AHfon is the variation of lattice enthalpy when one noninteracting lattice defect is introduced in the perfect lattice. Since two types of point-defects are always present (lattice defect and altervalent cations (electronic disorder)), the AHform takes into account not only the enthalpy change due to the process of introduction of the lattice defect in the lattice, but also that occurring in the Redox reaction creating the electronic disorder. 

If defects are not independent but interact between each other, the total enthalpy of the lattice is affected by this interaction. AHi ter takes care of the gain or loss of total enthalpy due to the interaction fields. AHi ter is dependent on both N and N (where N is the number of cationic compensating charges, usually related through stoichiometry to N), since both lattice defects and electronic disorder are electrical charges with respect to the lattice. 

After having described the mechanism of electron interchange between the catalyst and the reactive gas molecules, we will show in the following chapters how the electron disorder and the space-charge effects are expected to influence the rate of reaction. The electron interchange between the catalyst and the different species of molecules involves a different mechanism of potentially higher reaction rates than is the case in the homogeneous gas phase reactions. 

Recently Schwab (70) also emphasized the important role of electron defects for catalytic activities of solid oxides. Following this concept, he tried to develop a mechanism for the decomposition of H2O2 and for the oxidation of CO using inverse spinels as catalysts. Since the mechanism of the electron disorder and conductivity in spinels is much more complicated than in simple cubic oxides, it is not surprising that a satisfactory interpretation of these catalytic effects is still lacking,... 

The latter devices are fuel cells that consist of ceramic components which have to fulfill extremely demanding criteria with regard to thermal, mechanical, chemical, and electrical properties. Just consider the electrolyte It does not only have to be thermally stable but also has to be mechanically and chemically compatible with the electrodes. It does not only have to be chemically stable over a very wide redox window but also has to maintain electrolyte properties within that window (redox stability). Owing to the high mobilities of the electronic carriers and the comparatively steep power law dependencies of their concentrations (see Part I), this requires an extremely high ratio of ionic versus electronic disorder at the reference point of p-n minimum (cf. Part I).2... 

Verble, J. L. (1974) Temperature-dependent lightscattering studies of the Verwey transition and electron disorder in magnetite. Phys. Rev. (B), 9,5236—48. 

In Anderson s treatment, no account is taken of changes in the electronic disorder of the compound arising from changes in the stoichiometry. In the sense of the notation used previously this is equivalent to considering the presence of only neutral defects. For a binary compound exhibiting only Frenkel disorder in the metal lattice, the defects are therefore Vm° and Mf, with no defects in chalcogenide lattice. The presentation given here is equivalent to that of Anderson, since we can write ... 

Data for the temperature dependence of the enthalpy of UO2, obtained using drop calorimetry methods, showed a clear peak in the specific heat at 2610 K [87]. However, the structural origin of this feature was questioned by some groups, who proposed an alternative explanation in terms of electronic disorder (small polarons of... 

In order to exclude the influence of gaseous phase at this stage, it is essential to take into consideration a simple example (e.g., silicon) as a semiconducting material with vacancies. Assuming that possible defects of the crystal structure are vacancies and electron defects, the processes of intrinsic electronic disordering, vacancy formation, and vacancy ionization can be written, respectively, as ... 

Let us assume that AH2 > AHi > AH3, as the energy of atomic disorder is normally larger than that needed for intrinsic electronic disordering in turn, the latter is higher with respect to the energetic effects related to defect charging (see Figures 3.3 and 3.4). Under this assumption, it is possible to consider two alternative approximations. 

Assuming that the intrinsic electron disorder proceeds as nil = d + h ,... 

Troisi, A. and Orlandi, G., Charge-transport regime of crystalline organic semiconductors Diffusion limited by thermal off-diagonal electronic disorder, Phys. Rev. Lett., 96, 086601, 2006. 

Perfect electronic order is achieved only at a temperature of OK, where all electrons are in the lowest possible energy levels under the constraint of the Pauli exclusion principle. Any excitation of electrons from their ground state to higher energy levels results in electronic disorder. In ceramics, however, intrinsic electronic disorder refers to the formation of free electrons in the conduction band and holes in the valence band. An intrinsic electronic defect thus consists of a free electron in the conduction band and a free electron hole in the valence band. The concentrations of free electrons (e ) and electron holes (h ) are determined by the band gap and temperature. According to Fermi statistics, the probability of an electron occupying an energy level E, P(E), is expressed as... 

Electronic disorder thermal excitation of electrons from the fully filled valence band to the empty conduction band, which means that electronic conduction by electrons and holes becomes possible. The thermal equilibrium is + /i with... 

Figure 10.7. Calculated equilibrium defect diagrams for a binary oxide MO with Schottky defect pairs. In case (a) the equilibrium constant for vacancies is taken to be much larger than for electronic disorder (Kg = 10 Ki) case (b) gives the concentrations if the Schottky disorder is the smaller. The defect concentrations in regions I and III have a power dependence on the oxygen pressure with the exponent Region II in case (a), which includes the electrolytic domain has an exponent of the defect lines of in case (b) the exponent is...

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