Stoichiometric Point Ionic Defects

The compound will be stoichiometric, with an exact composition of MX10ooo when the number of metal vacancies is equal to the number of nonmetal vacancies. At the same time, the number of electrons and holes will be equal. In an inorganic compound, which is an insulator or poor semiconductor with a fairly large band-gap, the number of point defects is greater than the number of intrinsic electrons or holes. To illustrate the procedure, suppose that the values for the equilibrium constants describing Schottky disorder, Ks, and intrinsic electron and hole numbers, Kc, are 

As the partial pressure of X2 falls away from that at the stoichiometric point, reduction will occur. Anion vacancies and electrons would be expected to be more favored than cation vacancies and holes. The relevant equation is 

The effects of this change will depend upon the equilibrium constants. Suppose that 1017 m-3 of vacancies, and double that number of electrons, is produced by the change in partial pressure. In the present example, the concentration of electrons 

Because it is assumed that Ks is a lot greater than Ke it is reasonable to ignore the minority electronic defects and approximate the electroneutrality Eq. (7.12) by the relation  

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As expected, these equations are similar in form to Eqs. (7.13)-(7.15) and apply to both sides of the stoichiometric composition. They can be plotted as log(defect concentration) versus log pXl graph. A plot of log[Vj J versus log pXl has a slope of — j and passes through the (ionic) stoichiometric point. A plot of log [V J versus log pXl has a slope of I and passes through the (ionic) stoichiometric... 

The technique obviously allows one to measure the stoichiometry range and also the free formation enthalpy. The actual nonstoichiometry within the phase-width can be directly calculated from the defect model. As discussed in Part I, for a simple ionic disorder the nonstoichiometry 8 is a sinh-function in the difference of the chemical component potential to the value of the stoichiometric point (A = 0) (see Part I,2 Section IV). Owing to... 

Point (microscopic) defects in contrast from the macroscopic are compatible with the atomic distances between the neighboring atoms. The initial cause of appearance of the point defects in the first place is the local energy fluctuations, owing to the temperature fluctuations. Point defects can be divided into Frenkel defects and Schottky defects, and these often occur in ionic crystals. The former are due to misplacement of ions and vacancies. Charges are balanced in the whole crystal despite the presence of interstitial or extra ions and vacancies. If an atom leaves its site in the lattice (thereby creating a vacancy) and then moves to the surface of the crystal, it becomes a Schottky defect. On the other hand, an atom that vacates its position in the lattice and transfers to an interstitial position in the crystal is known as a Frenkel defect. The formation of a Frenkel defect therefore produces two defects within the lattice—a vacancy and the interstitial defect—while the formation of a Schottky defect leaves only one defect within the lattice, that is, a vacancy. Aside from the formation of Schottky and Frenkel defects, there is a third mechanism by which an intrinsic point defect may be formed, that is, the movement of a surface atom into an interstitial site. Considering the electroneutrality condition for the stoichiometric solid solution, the ratio of mole parts of the anion and cation vacancies is simply defined by the valence of atoms (ions). Therefore, for solid solution M X, the ratio of the anion vacancies is equal to mJn. 

Analyses of the defect chemistry and thermodynamics of non-stoichiometric phases that are predominately ionic in nature (i.e. halides and oxides) are most often made using quasi-chemical reactions. The concentrations of the point defects are considered to be low, and defect-defect interactions as such are most often disregarded, although defect clusters often are incorporated. The resulting mass action equations give the relationship between the concentrations of point defects and partial pressure or chemical activity of the species involved in the defect reactions. 

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. 

Intrinsic Crystal Self-Diffusion. A simple example of intrinsic self-diffusion in an ionic material is pure stoichiometric KC1, illustrated in Fig. 8.11a. As in many alkali halides, the predominant point defects are cation and anion vacancy complexes (Schottky defects), and therefore self-diffusion takes place by a vacancy mechanism. For stoichiometric KC1, the anion and cation vacancies are created in equal numbers because of the electroneutrality condition. These vacancies can be created... 

Defects in ceramics can be charged, which are different from those in metais. For a simple pure ionic oxide, with a stoichiometric formula of MO, consisting of a metal (M) with valence of +2 and an oxygen (O) with valence of -2, the types of point defects could be vacancies and interstitials of both the M and O, which can be either charged or neutral. Besides the single defects, it is also possible for the defects to associate with one another to form defect clusters. Electronic defects or valence defects, consisting of quasi-free electrons or holes, are also observed in crystalline solids. If there are impurities, e.g., solute atoms Mf, substitutional or interstitial defects of Mf could be formed, which can also be either charged or neutral. 

Determination of nonstoichiometry in oxides is a key point in the search for new materials for electrochemical applications. In recent decades, owing to their current and potential applications (electrodes in fuel cells, insertion electrodes, membranes of oxygen separation, gas sensors, catalytic materials, etc.), various methods of precise characterization of MfECs have been proposed, either the measurement of the defect concentrations and the stoichiometric ratio as functions of the oxide composition, of the surroxmding oxygen pressure and of temperature, or the transport properties. There are different methods to determine the electrical properties of MIECs and, more specifically, the ionic and electronic contributions. The most appropriate method depends on different parameters, i.e., the total electrical conductivity of the studied oxides, the ionic and electronic transport numbers, the... 

N-type nature of ZnO is due to the sensitiveness of ZnO lattice constants to the presence of extended defects (planar dislocations/threading) and structural point defects (interstitials and vacancies) that are commonly found in ZnO resulting in a non-stoichiometric compound. The excess zinc atoms in Zni+dO have the tendency to act as donor interstitials that give its natural N-type conductivity. In ionic form, the excess zinc tends to occupy special Zn interstitial sites with Miller index (1/3, 2/3, 0.875) as shown in fig. 12. These special sites offer passage routes for zinc interstitials to easily migrate within the wurtzite structure [109]. 

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