Schottky vacancy pair

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 ... 

It is also possible for a cation and an anion to move to the smface, forming an electrically neutral cation-anion vacancy. This type of vacancy is known as a Schottky defect and the pair of vacancies is called a Schottky vacancy pair. 

Thermodynamic considerations imply that all crystals must contain a certain number of defects at nonzero temperatures (0 K). Defects are important because they are much more abundant at surfaces than in bulk, and in oxides they are usually responsible for many of the catalytic and chemical properties.15 Bulk defects may be classified either as point defects or as extended defects such as line defects and planar defects. Examples of point defects in crystals are Frenkel (vacancy plus interstitial of the same type) and Schottky (balancing pairs of vacancies) types of defects. On oxide surfaces, the point defects can be cation or anion vacancies or adatoms. Measurements of the electronic structure of a variety of oxide surfaces have shown that the predominant type of defect formed when samples are heated are oxygen vacancies.16 Hence, most of the surface models of... 

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... 

Figure 5.1 Point defects in ionic solids Schottky defect, vacancy pair, Frenkel defect and aliovalent impurity (for definitions see Section 5.2).

Particle irradiation effects in halides and especially in alkali halides have been intensively studied. One reason is that salt mines can be used to store radioactive waste. Alkali halides in thermal equilibrium are Schottky-type disordered materials. Defects in NaCl which form under electron bombardment at low temperature are neutral anion vacancies (Vx) and a corresponding number of anion interstitials (Xf). Even at liquid nitrogen temperature, these primary radiation defects are still somewhat mobile. Thus, they can either recombine (Xf+Vx = Xx) or form clusters. First, clusters will form according to /i-Xf = X j. Also, Xf and Xf j may be trapped at impurities. Later, vacancies will cluster as well. If X is trapped by a vacancy pair [VA Vx] (which is, in other words, an empty site of a lattice molecule, i.e., the smallest possible pore ) we have the smallest possible halogen molecule bubble . Further clustering of these defects may lead to dislocation loops. In contrast, aggregates of only anion vacancies are equivalent to small metal colloid particles. 

One of the causes of point defects is a temperature increase which results in an increased thermal movement of the atoms which can subsequently lead to the atoms escaping from their place in the lattice. Other causes are the effects of radiation and inbuilt, foreign atoms. In an atomic lattice a vacancy can occur due to the movement of an atom, an absence of an atom or molecule from a point which it would normally occupy in a crystal. In addition to this vacancy an atomic will form elsewhere. This combination of an atomic pair and a vacancy is called the Frenkel defect. In ionic crystals an anion and a cation have to leave the lattice simultaneously due to the charge balance. As a result a vacancy pair remains and this is called the Schottky defect. Both defects can be seen in figure 4.8. 

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. 

Schottky defects. In the Schottky defect reaction, electric-charge-equivalent numbers of vacancies are formed on each sublattice. In NaCl, for example, a Schottky defect entails the formation of Na and Cl vacancy pairs (Fig. 6.3a). In general, for an MO oxide, the reaction reads ... 

In Eq. 11.23, Z is the number of distinct orientations of the defect complex it accounts for the configurational entropy. For example, if the vacancies sit on adjacent sites in NaCl, Z would be 12. Figure 11.6 shows calculated concentrations of Schottky defects and vacancy pairs in NaCl and MgO. 

Ks = KJLVa ] and in NiO 0 V, + Vo = MKo]. Schottky equilibrium leads to vacancy pairs and this type of disorder dominates in alkaline halides and in oxides with a halite (NaCl) structure. 

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...

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... 

Another type of defect found in AX materials is a cation vacancy-anion vacancy Schottky defect pair known as a Schottky defect, also schematically diagrammed in Figure 12.19. This... 

Schottky defect In an ionic solid, a defect consisting of a cation-vacancy and anion-vacancy pair, scission. A polymer degradation process by which molecular chain bonds are ruptured by chemical reactions or by exposure to radiation or heat. 

Two point defects may aggregate to give a defect pair (such as when the two vacanc that constitute a Schottky defect come from neighbouring sites). Ousters of defects ( also form. These defect clusters may ultimately give rise to a new periodic structure oi an extended defect such as a dislocation. Increasing disorder may alternatively give j to a random, amorphous solid. As the properties of a material may be dramatically alte by the presence of defects it is obviously of great interest to be able to imderstand th relationships and ultimately predict them. However, we will restrict our discussion small concentrations of defects. 

Yakov Frenkel showed in 1926 that ideal crystals could not exist at temperatures above the absolute zero. Part of the ions leave their sites under the effect of thermaf vibrations and are accommodated in the interstitial space, leaving vacancies at the sites formerly taken up. Such point defects have been named Frenkel defects. These ideas were developed further by Walter Schottky in 1929, who pointed out that defects will also arise when individual ions or ion pairs are removed from the bulk... 

Intrinsic Defects The simplest crystalline defects involve single or pairs of atoms or ions and are therefore known as point defects. Two main types of point defect have been identified Schottky defects and Frenkel defects. A Schottky defect consists of a pair of vacant sites a cation vacancy and an anion vacancy. A Schottky defect is... 

The treatment assumes that the point defects do not interact with each other. This is not a very good assumption because point defect interactions are important, and it is possible to take such interactions into account in more general formulas. For example, high-purity silicon carbide, SiC, appears to have important populations of carbon and silicon vacancies, and Vsj, which are equivalent to Schottky defects, together with a large population of divacancy pairs. 

This is similar in magnitude to the energy of formation of Schottky defects, and so it could be anticipated that a reasonable proportion of the vacancies would be associated into pairs. 

Figure 9.3 Schematic representation of magnetic defects in a ferrimagnetic matrix (a) a pair of vacancies or nonmagnetic impurities similar to a Schottky defect and (b) an antisite defect.

Lattice defects in ionic crystals are interstitial ions and ion vacancies. In crystalline sodium chloride NaCl a cation vacancy Vn - is formed by producing a surface cation NaJ, (Nal - NaJ + Vua ) this is called the Schottky defect. On the other hand, in crystalline silver chloride AgCl a pair of cation vacancy Va,. and interstitial cation Ag is formed, (Ag - Agj + ) this is called the Frenkel... 

For a 1 1 solid MX, a Schottky defect consists of a pair of vacant sites, a cation vacancy, and an anion vacancy. This is presented in Figure 5.1 (a) for an alkali halide type structure the number of cation vacancies and anion vacancies have to be equal to preserve electrical neutrality. A Schottky defect for an MX2 type structure will consist of the vacancy caused by the ion together with two X anion vacancies, thereby balancing the electrical charges. Schottky defects are more common in 1 1 stoichiometry and examples of crystals that contain them include rock salt (NaCl), wurtzite (ZnS), and CsCl. 

Let us also consider the pairing reaction B A -t-V A = [B, V] in an ionic crystal AX, where the dopant BA is a heterovalent cation and V A is the compensating cation vacancy. We define the degree of pairing to be NP = A[B>V T/VB. From the mass balance equation A B = AB+AjB Vj and the condition of electroneutrality jVv + A b = NyA, one finds for the case that the undoped AX crystal exhibits Schottky type disorder (which means that = Ks)... 

Self-diffusion of Ag cations in the silver halides involves Frenkel defects (equal numbers of vacancies and interstitials as seen in Fig. 8.116). In a manner similar to the Schottky defects, their equilibrium population density appears in the diffusivity. Both types of sites in the Frenkel complex—vacancy and interstitial— may contribute to the diffusion. However, for AgBr, experimental data indicate that cation diffusion by the interstitialcy mechanism is dominant [4]. The cation Frenkel pair formation reaction is... 

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... 

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. 

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. 

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]... 

Intrinsic point defects are deviations from the ideal structure caused by displacement or removal of lattice atoms [106,107], Possible intrinsic defects are vacancies, interstitials, and antisites. In ZnO these are denoted as Vzn and Vo, Zn and 0 , and as Zno and Ozn, respectively. There are also combinations of defects like neutral Schottky (cation and anion vacancy) and Frenkel (cation vacancy and cation interstitial) pairs, which are abundant in ionic compounds like alkali-metal halides [106,107], As a rule of thumb, the energy to create a defect depends on the difference in charge between the defect and the lattice site occupied by the defect, e.g., in ZnO a vacancy or an interstitial can carry a charge of 2 while an antisite can have a charge of 4. This makes vacancies and interstitials more likely in polar compounds and antisite defects less important [108-110]. On the contrary, antisite defects are more important in more covalently bonded compounds like the III-V semiconductors (see e.g., [Ill] and references therein). 

A population of vacancies on one subset of atoms created by displacing some atoms into normally unoccupied interstitial sites constitute a second arrangement of paired point defects, termed Frenkel defects (Figure 2(b), (c)). Because one species of atom or ion is simply being redistributed in the crystal, charge balance is not an issue. A Frenkel defect in a crystal of formula MX consists of one interstitial cation plus one cation vacancy, or one interstitial anion plus one anion vacancy. Equally, a Frenkel defect in a crystal of formula MX2 can consist of one interstitial cation plus one cation vacancy, or one interstitial anion plus one anion vacancy. As with the other point defects, it is found that the free energy of a crystal is lowered by the presence of Frenkel defects and so a popnlation of these intrinsic defects is to be expected at temperatures above 0 K. The calculation of the number of Frenkel defects in a crystal can proceed along lines parallel to those for Schottky defects. The appropriate chemical equilibrium for cation defects is ... 

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