Cation-anion vacancy pair formation

Fig. 3-11. Energy for decomposing ionization of compound AB to form gaseous ions A(giD) and via electron-hole pair formation and via cation-anion vacancy pair formation r = reaction coordinate of decomposing ionization e, s semiconductor band gap . vmb) = cation-anion vacancy pair formation energy (Va- Vb-) Lab = decomposing ionization energy of compound AB.

The decomposing ionization of soUd compound AB may also take place through the formation of a cation-anion vacancy pair as follows ... 

The decomposing ionization will take place preferentially by way ofthe electron-hole pair formation, if the formation energy of the electron-hole pair, e, is smaller than the formation energy of the cation-emion vacancy pair, Hv(ab>, and vice versa. In general, compound semiconductors, in which the band gap is small (e,< Jfv(AB>), will prefer the formation of electron-hole pairs whereas, compound insulators such as sodium chloride, in which the band gap is great (e(>Hv(AB>), will prefer the formation of cation-anion vacancy pairs [Fumi-Tosi, 1964]. 

In the case in which the formation of cation-anion vacancy pairs is preferential, the ion levels of A and B ions in solid compound AB are obtained in the same way as Eqns. 3-21 and 3-22 by Eqns. 3-23 and 3-24, respectively ... 

Turning now to the vacancy concentration in Eq. (4.72), recall from Chapter 1, and Eq. (1.48) in particular, that the concentration of vacancies is related to the free energy of formation of the vacancy, so that for a cation-anion vacancy pair, or Schottky defect, the concentration of vacancies, [V7] is given by... 

Walter Haus Schottky (1886-1976) received his doctorate in physics under Max Planck from the Humboldt University in Berlin in 1912. Although his thesis was on the special theory of relativity, Schottky spent his life s work in the area of semiconductor physics. He alternated between industrial and academic positions in Germany for several years. He was with Siemens AG until 1919 and the University of Wurzburg from 1920 to 1923. From 1923 to 1927, Schottky was professor of theoretical physics at the University of Rostock. He rejoined Siemens in 1927, where he finished out his career. Schottky s inventions include the ribbon microphone, the superheterodyne radio receiver, and the tetrode vacuum tube. In 1929, he published Thermodynamik, a book on the thermodynamics of solids. Schottky and Wagner studied the statistical thermodynamics of point defect formation. The cation/anion vacancy pair in ionic solids is named the Schottky defect. In 1938, he produced a barrier layer theory to explain the rectifying behavior of metal-semiconductor contacts. Metal-semiconductor diodes are now called Schottky barrier diodes. 

A cation vacancy may be paired with an anion vacancy. This is called a Schottky defect. An example is the formation of Li+ and F vacancies in LiF. This is illustrated in Figure 5.2A. 

Removal of lattice oxygen from the surface of nickel oxide in vcumo at 250° or incorporation of gallium ions at the same temperature [Eq. (14)] causes the reduction of surface nickel ions into metal atoms. Nucleation of nickel crystallites leaves cationic vacancies in the surface layer of the oxide lattice. The existence of these metal crystallites was demonstrated by magnetic susceptibility measurements (33). Cationic vacancies should thus exist on the surface of all samples prepared in vacuo at 250°. However, since incorporation of lithium ions at 250° creates anionic vacancies, the probability of formation of vacancy pairs (anion and cation) increases and consequently, the number of free cationic vacancies should be low on the surface of lithiated nickel oxides. Carbon monoxide is liable to be adsorbed at room temperature on cationic vacancies and the differences in the chemisorption of this gas are related to the different number of isolated cationic vacancies on the surface of the different samples. 

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 ... 

Besides alkali halides, alkali and alkaline earth azides have been most thoroughly inveistigated for radiation coloration. By irradiation of freshly precipitated potassium azide at 196°C with radiation of A = 2537 A, Tompkins and Young19 obtained bands due to the presence of F-centres and V-centres. Ageing was found to have marked influence on these bands. The proposed mechanism of ageing involves the formation of anion and cation vacancy pairs... 

The Schottky defect, which is unique to ionic compounds, consists of a stoichiometric pair of cation and anion vacancies. For an MO compound with full ionization, its formation equation is expressed as... 

The migration of a lattice atom/ion into an available interstitial site will leave behind a vacancy (Figure 2.49) the formation of such an interstitial/vacancy pair is known as a Frenkel defect. In contrast, Schottky defects are formed through the migration of a cation-anion pair from the crystal lattice framework, leaving behind two vacant lattice sites. For ionic crystals, the overall charge of the crystal must be charge-balanced. That is, if trivalent ions such as La are substituted with divalent cations such as Ca, there must be concomitant placements of divalent anions... 

As described in the previous chapter, the Schottky disorder involves the presence of equivalent amounts of cation and anion vacancies. In an oxide MO this means that the erystal contains equal concentrations of metal and oxygen vacancies. The overall formation of such a defect pair within the crystal involves the transfer of a pair of cations and anions on regular lattice sites from the bulk to the surface. In reality the defects are formed at external and internal surfaces or... 

Fig. 155, p. 334, shows the density of TmxSe at room temperature as a function of x, determined with the buoyancy method, together with theoretical values and calculated for the following defect models 1) vacancies, 2) interstitial defects, 3) antisite defects (Tm occupies both cationic and anionic Schottky vacancies), Kaldis, Fritzler [1, p. 125], [2, p. 83], Fritzler, Kaldis [3], Fritzler et al. [4]. The discontinuity at Tmo.sySe is attributed to the formation of the TmsSe superstructure. The difference between experimental and calculated densities for the compositions Tmo.sySe to Tmi oSe is explained by the increasing number of Schottky vacancy pairs. The existence of both iSchottky pairs and antisite defects is assumed between Tm oSe and Tmi oeSe. Selected numerical values of the experimental density as a function of composition ... 

Various kinds of packing defects exist in the ionic crystals of NaCl type. A pair of cation and anion may be shifted from their stable positions toward the surface of the crystal, thus leaving behind a pair of vacancies. This is called the Schottky defect. The cation may leave its stable position and enter into an interstitial site. The formation of an interstitial cation and a vacancy is called the Frenkel defect. In addition to these two common kinds of defects, the presence of impurity atoms, atoms of varied valence, vacancies, and/or interstitial atoms is also possible. Some other important defects are discussed below. 

In compound crystals, balanced-defect reactions must conserve mass, charge neutrality, and the ratio of the regular lattice sites. In pure compounds, the point defects that form can be classified as either stoichiometric or nonstoichiometric. By definition, stoichiometric defects do not result in a change in chemistry of the crystal. Examples are Schottky (simultaneous formation of vacancies on the cation and anion sublattices) and Frenkel (vacancy-interstitial pair). 

For the Frenkel disorder the predominant defects are either limited to the cations and anions, and the disorder involves the presence of equal numbers of vacancies and interstitial ions in a sublattice in a crystal. In the formation of a Frenkel defect pair, a cation on a normal site is transferred to an interstitial site, and no new lattice sites are created in the process. If, for the sake of illustration, the interstitial ion and the resulting vacancy are assumed to be doubly charged, the formation of a Frenkel defect pair may be written... 

Defect formation mechanisms and concentrations. In the perovskite stmcture ABO3 there are three sublattices two cationic and one anionic. Therefore, the total defect equilibrimn conditions include contribution of all possible defects (vacancies and substituting ions) in each sublattice. For simplicity let us consider the defect formation in typical perovskite solid solutions of the Lai xSrxB03 s composition widely used in SOFC. As the perovskite lattice is formed by cubic close packing of mixed AO3 layers, intrinsic defects are Schottky ones which together with electron-hole pairs are formed in both pure and doped perovskites. Quasichemical reactions of formation of intrinsic defects may be written as follows [12, 13] ... 

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