Point defects Schottky

Point defects (Schottky, Frenkel, unoccupied lattice sites, misplaced units)... 

BALANCED POPULATIONS OF POINT DEFECTS SCHOTTKY AND FRENKEL DEFECTS... 

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

Materials that contain defects and impurities can exhibit some of the most scientifically interesting and economically important phenomena known. The nature of disorder in solids is a vast subject and so our discussion will necessarily be limited. The smallest degree of disorder that can be introduced into a perfect crystal is a point defect. Three common types of point defect are vacancies, interstitials and substitutionals. Vacancies form when an atom is missing from its expected lattice site. A common example is the Schottky defect, which is typically formed when one cation and one anion are removed from fhe bulk and placed on the surface. Schottky defects are common in the alkali halides. Interstitials are due to the presence of an atom in a location that is usually unoccupied. A... 

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. 

The vacant sites will be distributed among the N lattice sites, and the interstitial defects on the N interstitial sites in the lattice, leaving a conesponding number of vacancies on die N lattice sites. In the case of ionic species, it is necessaty to differentiate between cationic sites and anionic sites, because in any particular substance tire defects will occur mainly on one of the sublattices that are formed by each of these species. In the case of vacant-site point defects in a metal, Schottky defects, if the number of these is n, tire random distribution of the n vacancies on the N lattice sites cair be achieved in... 

It is not necessary for a compound to depart from stoichiometry in order to contain point defects such as vacant sites on the cation sub-lattice. All compounds contain such iirndirsic defects even at the precisely stoichiometric ratio. The Schottky defects, in which an equal number of vacant sites are present on both cation and anion sub-lattices, may occur at a given tempe-ramre in such a large concentration drat die effects of small departures from stoichiometry are masked. Thus, in MnOi+ it is thought that the intrinsic concentration of defects (Mn + ions) is so large that when there are only small departures from stoichiometry, the additional concentration of Mn + ions which arises from these deparmres is negligibly small. The non-stoichiometry then varies as in this region. When the departure from non-stoichio-... 

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 potassium ions that are produced occupy cation lattice sites, but no anions are produced so electrons occupy anion sites. In this situation, the electron behaves as a particle restricted to motion in a three-dimensional box that can absorb energy as it is promoted to an excited state. It is interesting to note that the position of the maximum in the absorption band is below 4000A (400nm, 3.1 eV) for LiCl but it is at approximately 6000 A (600 nm, 2eV) for CsCl. One way to explain this observation is by noting that for a particle in a three-dimensional box the difference between energy levels increases as the size of the box becomes smaller, which is the situation in LiCl. Schottky, Frenkel, and F-center defects are not the only types of point defects known, but they are the most common and important types. 

Figure 1.15 Balanced populations of point defects in an ionic crystal of formula MX (schematic) (a) Schottky defects and (b) Frenkel defects.

A point defect is a localized defect that consists of a mistake at a single atom site in a solid. The simplest point defects that can occur in pure crystals are missing atoms, called vacancies, or atoms displaced from the correct site into positions not normally occupied in the crystal, called self-interstitials. Additionally atoms of an impurity can occupy a normal atom site to form substitutional defects or can occupy a normally vacant position in the crystal structure to form an interstitial. Other point defects can be characterized in pure compounds that contain more than one atom. The best known of these are Frenkel defects, Schottky defects, and antisite defects. 

Despite the fact that not all details of the photographic process are completely understood, the overall mechanism for the production of the latent image is well known. Silver chloride, AgBr, crystallizes with the sodium chloride structure. While Schottky defects are the major structural point defect type present in most crystals with this structure, it is found that the silver halides, including AgBr, favor Frenkel defects (Fig. 2.5). 

At all temperatures above 0°K Schottky, Frenkel, and antisite point defects are present in thermodynamic equilibrium, and it will not be possible to remove them by annealing or other thermal treatments. Unfortunately, it is not possible to predict, from knowledge of crystal structure alone, which defect type will be present in any crystal. However, it is possible to say that rather close-packed compounds, such as those with the NaCl structure, tend to contain Schottky defects. The important exceptions are the silver halides. More open structures, on the other hand, will be more receptive to the presence of Frenkel defects. Semiconductor crystals are more amenable to antisite defects. 

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. 

The energy of formation of defects in PbF2 are anion Frenkel defect, 0.69 eV cation Frenkel defect, 4.53 eV Schottky defect, 1.96 eV. (a) What point defects do these consist of (b) What are (approximately) the relative numbers of these defects in a crystal at 300 K (Data from H. Jiang et al., 2000). 

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... 

Figure 7.9 Brouwer diagram for a phase MX in which Schottky defects are the main point defect type (a) initial points on the diagram, (b) variation of defect concentrations in the near-stoichiometric region, (c) extension to show variation of defect concentrations in the high partial pressure region, (d) extension to show variation of defect concentrations in the low partial pressure region, and (e) complete diagram.

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... 

The notion of point defects in an otherwise perfect crystal dates from the classical papers by Frenkel88 and by Schottky and Wagner.75 86 The perfect lattice is thermodynamically unstable with respect to a lattice in which a certain number of atoms are removed from normal lattice sites to the surface (vacancy disorder) or in which a certain number of atoms are transferred from the surface to interstitial positions inside the crystal (interstitial disorder). These forms of disorder can occur in many elemental solids and compounds. The formation of equal numbers of vacant lattice sites in both M and X sublattices of a compound M0Xft is called Schottky disorder. In compounds in which M and X occupy different sublattices in the perfect crystal there is also the possibility of antistructure disorder in which small numbers of M and X atoms are interchanged. These three sorts of disorder can be combined to give three hybrid types of disorder in crystalline compounds. The most important of these is Frenkel disorder, in which equal numbers of vacancies and interstitials of the same kind of atom are formed in a compound. The possibility of Schottky-antistructure disorder (in which a vacancy is formed by... 

The papers of Wagner and Schottky contained the first statistical treatment of defect-containing crystals. The point defects were assumed to form an ideal solution in the sense that they are supposed not to interact with each other. The equilibrium number of intrinsic point defects was found by minimizing the Gibbs free energy with respect to the numbers of defects at constant pressure, temperature, and chemical composition. The equilibrium between the crystal of a binary compound and its components was recognized to be a statistical one instead of being uniquely fixed. 

Figure 1.10. Point defects (a) formation of a Schottky defect (b) Frenkel defect. (Cottrell 1971 reproduced courtesy of Arnold Publishing.)...

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. 

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

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