Schottky pair

FIGURE 5.1 Schematic illustration of intrinsic point defects in a crystal of composition MX (a) Schottky pair, (b) perfect crystal, and (c) Frenkel pair. 

At low temperatures, the site fraction of cation vacancies due to Schottky-pair formation will be negligible and their site fraction will therefore be fixed at the level... 

Consider first an oxygen vacancy. Its effective charge of2e can be neutralized by a cation vacancy with an effective charge — 2e an example of such vacancy compensation is an associated Schottky pair. Alternatively, an oxygen vacancy might be electron-compensated by being associated with two electrons. Similarly a... 

In thermal equilibrium, some ionic crystals at a temperature above absolute zero enclose a certain number of Schottky pair defects, that is, anion and cation vacancies in the structure (see Section 5.7.1) [13]. Since the concentration of Schottky pair defects at equilibrium at an absolute temperature, T, obeys the mass action law, then [16]... 

There are about 106 schottky pairs per cc at room temperature in NaCl. In one cc of NaCl there are about 1022 ions, so there will be one schottky defect per 1016 ions. 

The same defect thermodynamics and diffusion theory can be applied to ionic crystals with one important proviso, which is the need to account for the charges on the ions (and hence effective charges on the defects), and that the crystal must remain electrically neutral overall. This means that the defects will occur as multiplets to satisfy this later condition. For example, in a MX crystal they will occur as pairs the Schottky pair- a cation vacancy and an anion vacancy the cation-Prenkel pair- a cation vacancy and an interstitial cation and the anion-Frenkel pair - an anion vacancy and an interstitial anion. The concentrations of the defects in the pair are related by a solubility product equation, which for Schottky pairs in an MX equation takes the form ... 

Here, c+ and c are the site fractions of the cation and anion vacancies, respectively, Ks is the equilibrium constant for the formation of the Schottky pair, and gs (= g+ + g, the sum of the individual defect formation energies) is the Gibbs free energy to form the pair. In the bulk of a pure crystal, the condition of electrical neutrality demands that the concentrations of each defect in the pair are equal that is ... 

Calculations of the energies of Schottky pair formation and cation migration in KN3 were performed by Royce and coworkers [50], taking into account the charge distribution of the azide ion. 

Defect pairs Schottky pairs of anion and cation vacancies Frenkel pairs of a cation vacancy and the same cation as an interstitial Anti-Frenkel the same as Frenkel but for anions 0... 

If one starts with a pair of cations and anions on regular lattice sites within the crystal. Mm and Oq, one must also take into account that the formation of the Schottky pair results in the formation of two new lattice sites, and the overall equation may thus be written... 

When the Schottky pair dominates the defect structure, we may see from the reaction equation or from the electroneutrality condition that in MO the concentrations of the metal and oxygen vacancies are equal ... 

The most common types of intrinsic point defects are Schottky and Frenkel defects (Figure 3.1). A Schottky defect consists of a vacant cation lattice site and a vacant anion lattice site. To form a Schottky defect, ions leave their normal lattice positions and relocate at the crystal surface, preserving overall charge neutrality. Hence, for a metal monoxide, MO, vacant sites must occur equally in the cation and anion sublattice and form a Schottky pair, whereas in binary metal oxides, MO2, a Schottky defect consists of three defects a vacant cation site and two vacant anion sites. A Frenkel defect forms when a cation or anion is displaced from its regular site onto an interstitial site, where, the resulting vacancy and interstitial atom form a Frenkel defect pair. 

On the basis of these ideas, Macdonald and eo-workers [13,14] developed their model of passivity and its breakdown involving the action of vacancies within the passive layer. It is assumed that cation vacancies migrate from the oxide-electrolyte to the metal-oxide interface, whieh is equivalent to the transport of cations in the opposite direetion. If these vacaneies penetrate into the metal phase at a slower rate than their transport through the oxide, they accumulate at the metal-oxide interface and finally lead to a loeal eoneentration. The related voids lead to stresses within the passive film and its final breakdown. The inward diffusion or migration of eation vacaneies is affeeted by the incorporation of Cl ions at the oxide-electrolyte interface aceording to the following mechanism The concentration c of metal ion V, and vacancies Fq2 are determined by the equihbrium of the Schottky pair formation at the oxide-eleetrolyte interface [Eq. (3)], which causes an inverse dependenee of their eoneentrations [Eq. (4)]. 

The concentration of Schottky defects in a binary salt MX can be readily calculated. From Equation (3.12) it can be seen that the configurational entropy change for introduction of a Schottky pair of anion and cation vacancies is... 

The Tmi xEUxSe mixed crystals have a cubic NaCl structure. The lattice constants for samples with x = 0 to -0.25 are shown in Fig. 211, together with the Vegard-law lines for a variety of valences, Kaldis etal. [2, p. 137], also see Boppart, Wachter [8, p. 36], [9]. Lattice constant and density measurements, as well as X-ray fluorescence and chemical analysis, indicate the existence of Schottky defects, particularly in the Tm-rich part of the system. The vacancy concentration changes smoothly with x in Tmi xEUxSe. The following table presents the lattice constant a, measured and calculated densities Dexp and Dcaic. respectively, number of Schottky pairs nsch. and vacant lattice sites n as a function of x in Tmi xEUxSe ... 

The point defect formation according to the Schottky reaction (formation of Schottky pair ) can be treated analogously ... 

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