Schottky-Wagner defects

The simplest type of defect is called the Schottky or Schottky-Wagner defect, (t is simply the absence of an atom or ion from a lattice site, in an ionic crystal, electrical neutrality requires that the missing charge be balanced in some way. The simplest way is for the missing cation, for example, to be balanced by another Schottky defect, a missing anion, elsewhere (Fig. 7. ID). 

Consider next a stoichiometric compound of composition MX. The following pairs of defects are possible (1) equal numbers of vacancies on M and X sites (Schottky-Wagner defect), (2) equal numbers of vacancies and interstitials on M sites (M-site Frenkel defect), (3) equal numbers of vacancies and interstitials on X sites (X-site Frenkel defect), and (4) equal numbers of M and X interstitials. 

A useful analogy, which has not yet been fully exploited, can be drawn between complementary defect pairs and electrolytes in solution. The Schottky-Wagner approximation (valid for highly dilute defects) corresponds to the Arrhenius strong electrolyte. Thus Wagner represents the nonstoichiometric equilibrium of cuprous oxide as... 

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. 

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. 

In last century the knowledge of defects in a solid, especially an oxide, has been explored comprehensively. The contribution of Schottky and Wagner successfully put the problem on a quantitative basis and promote the discovery of semiconductor transistor. The idea of non-stoichiometry was developed by Berthollet more than a hundred years ago and the controversy between berthollides, which do not obey the Dalton s law, and daltonides, which follow Dalton s law of constant and multiple proportions based originally upon the study of simple ionic and molecular species, encouraged the scientific debates on how existence of point defect in a compound is is it random statistic distribution or the structure related The experimental data are the best way to explore the truth. Indirect and direct observations of atom... 

The defects which disrupt the regular patterns of crystals, can be classified into point defects (zero-dimensional), line defects (1-dimensional), planar (2-dimensional) and bulk defects (3-dimensional). Point defects are imperfections of the crystal lattice having dimensions of the order of the atomic size. The formation of point defects in solids was predicted by Frenkel [40], At high temperatures, the thermal motion of atoms becomes more intensive and some of atoms obtain energies sufficient to leave their lattice sites and occupy interstitial positions. In this case, a vacancy and an interstitial atom, the so-called Frenkel pair, appear simultaneously. A way to create only vacancies has been shown later by Wagner and Schottky [41] atoms leave their lattice sites and occupy free positions on the surface or at internal imperfections of the crystal (voids, grain boundaries, dislocations). Such vacancies are often called Schottky defects (Fig. 6.3). This mechanism dominates in solids with close-packed lattices where the formation of vacancies requires considerably smaller energies than that of interstitials. In ionic compounds also there are defects of two types, Frenkel and Schottky disorder. In the first case there are equal numbers of cation vacancies... 

At the same time, Wagner and Schottky pointed out from the studies in statistical thermod3mamics on the actual crystal and lattice defects that, at any temperature above OK, every solid compoimd only owns a single phase, although its composition changes under certain conditions. There is no thermodjmamic status that the compounds which either compose strictly in accordance with the ideal chemical stoichiometry, or deduce single phase from rules of valence bond. 

The formed products of the reactions of oxidation of metals are stoichiometric ionic conqrounds (Schottky or Frenkel type) or semiconductor, non-stoichiometric compounds. In the last case, usually, we can model these solids in the Wagner approximation of the prevalent defect (see section 2.3.2), which can distinguish the two famihes ... 

The thermodynamic basis for the treatment of point defects was laid down by Frenkel, Schottky and Wagner [1,2]. 

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