Point defect: also

Here the narrow prescription of Chapter 1 is widened to deal with more chemically complex phases, in which the materials may contain mixtures of A, B and X ions as well as chemical defects. In these cases, using an ionic model, it is only necessary that the nominal charges balance to obtain a viable perovskite composition. In many instances these ions are distributed at random over the available sites, but for some simple ratios they can order to form phases with double or triple perovskite-type unit cells. The distribution and valence of these ordered or partly ordered cations and anions are often not totally apparent from difEraction studies, and they are often clarified by use of the bond valence sums derived from experimentally determined bond distances. Information on the bond valence method is given in Appendix A for readers unfamiliar with it Point defects also become significant in these materials. The standard Kroger- fink notation, used for labelling these defects, is outlined in Appendix B. 

In this section, the phenomenon of point defects, such as vacancies and interstitial, in crystals is briefly introduced. The oxide entropy change (A5) increases when more points defects, also known a imperfections, generate within a crystal. Metal oxides at equilibrium may contain nearly equal numbers of cations and anion vacancies. Thus, the number of point defects (n) producing a minimum free energy change, AG = AHf — TAS, can be modeled by the Arrhenius law [21-23]... 

However, most impurities and defects are Jalm-Teller unstable at high-symmetry sites or/and react covalently with the host crystal much more strongly than interstitial copper. The latter is obviously the case for substitutional impurities, but also for interstitials such as O (which sits at a relaxed, puckered bond-centred site in Si), H (which bridges a host atom-host atom bond in many semiconductors) or the self-interstitial (which often fonns more exotic stmctures such as the split-(l lO) configuration). Such point defects migrate by breaking and re-fonning bonds with their host, and phonons play an important role in such processes. 

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. 

Electrical Properties. Generally, deposited thin films have an electrical resistivity that is higher than that of the bulk material. This is often the result of the lower density and high surface-to-volume ratio in the film. In semiconductor films, the electron mobiHty and lifetime can be affected by the point defect concentration, which also affects electromigration. These effects are eliminated by depositing the film at low rates, high temperatures, and under very controUed conditions, such as are found in molecular beam epitaxy and vapor-phase epitaxy. 

Two German physical chemists, W. Sehottky and C. Wagner, founded this branch of materials seience. The story is very clearly set out in a biographical memoir of Carl Wagner (1901 1977) by another pioneer solid-state chemist, Hermann Schmalzried (1991), and also in Wagner s own survey of point defects and their interaction (Wagner 1977) - his last publieation. Sehottky we have already briefly met in connection with the Pohl school s study of colour centres... 

For the deformation of NiAl in a soft orientation our calculations give by far the lowest Peierls barriers for the (100) 011 glide system. This glide system is also found in many experimental observations and generally accepted as the primary slip system in NiAl [18], Compared to previous atomistic modelling [6], we obtain Peierls stresses which are markedly lower. The calculated Peierls stresses (see table 1) are in the range of 40-150 MPa which is clearly at the lower end of the experimental low temperature deformation data [18]. This may either be attributed to an insufficiency of the interaction model used here or one may speculate that the low temperature deformation of NiAl is not limited by the Peierls stresses but by the interaction of the dislocations with other obstacles (possibly point defects and impurities). 

We will be considering primarily inorganic solids but must keep in mind that the same principles also apply to organic solids. Therefore, we intend to examine the nature of point defects in terms of their thermodynamics, equilibria and the energy required for their formation. It will be seen that point defects follow the same physical chemistry laws that apply to inorgcuiic compounds and physical properties in general. 

We have Investigated the structure of solids In the second chapter and the nature of point defects of the solid in the third chapter. We are now ready to describe how solids react. This will Include the mechanisms Involved when solids form by reaction from constituent compounds. We will also describe some methods of measurement and how one determines extent and rate of the soUd state reaction actually taking place. We will also show how the presence and/or formation of point defects affect reactivity In solid state reactions. They do so, but not In the memner that you might suspect. We will also show how solid state reactions progress, particularly those involving silicates where several different phases appear as a function of both time and relative ratios of reacting components. 

The intensity of the dicarbonyl at 2116cm is considerably reduced as compared to the 90 K deposit, indicating that the amount of metal atoms trapped at point defects is reduced for growth at 60 K. The difference in the nucleation sites is also reflected by the lower thermal stability of the systems, which decompose between 80 and 150 K as compared to 200 to 250 K for the 90 K deposits. With isotope mixing experiments the peak at 2087 cm was assigned to a carbonyl with three or more CO ligands, while the peak at 1999 cm is associated to a monocarbonyl [32]. 

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... 

The point defects are decisive for conduction in solid ionic crystals. Ionic migration occurs in the form of relay-type jumps of the ions into the nearest vacancies (along the held). The relation between conductivity o and the vacancy concentration is unambiguous, so that this concentration can also be determined from conductivity data. 

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