Point defect models

In addition to these surveys, the crystal cherrristry and electrocherrrical properties of a wide variety of multinary oxide solid electrolytes and MlECs are described in the studies reported in Reference 90. While defect cherrristry has been successfully employed to model point defect generation and conduction mechartisrrts in norttirtally prrre and doped birtary and ternary compormds, complex defect equilibria occur in concerrtrated solid solutiorts based on ternary comporrrtds artd in mrrltirtary corrtpourtds. Usrrally, these complex defect equilibria are treated with the aid of nrrmerical methods. Examples are the pyrochlores GT, GZT, and YZT as discussed in Section 11.B.4. 

Fig. 5.20. The shock-induced polarization of a range of ionic crystals is shown at a compression of about 30%. This maximum value is well correlated with cation radius, dielectric constant, and a factor thought to represent dielectric strength. A mechanically induced point defect generation and migration model is preferred for the effect (after Davison and Graham [79D01]).

Formula for the chemical potentials have been derived in terms of the formation energy of the four point defects. In the process the conceptual basis for calculating point defect energies in ordered alloys and the dependence of point defect concentrations on them has been clarified. The statistical physics of point defects in ordered alloys has been well described before [13], but the present work represents a generalisation in the sense that it is not dependent on any particular model, such as the Bragg-Williams approach with nearest neighbour bond energies. It is hoped that the results will be of use to theoreticians as well as... 

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). 

Point defects in solids make it possible for ions to move through the structure. Ionic conductivity represents ion transport under the influence of an external electric field. The movement of ions through a lattice can be explained by two possible mechanisms. Figure 25.3 shows their schematic representation. The first, called the vacancy mechanism, represents an ion that hops or jumps from its normal position on the lattice to a neighboring equivalent but vacant site or the movement of a vacancy in the opposite direction. The second one is an interstitial mechanism where an interstitial ion jumps or hops to an adjacent equivalent site. These simple pictures of movement in an ionic lattice, known as the hopping model, ignore more complicated cooperative motions. 

At temperatures of the order 700 - 900 K the surface point defects play the dominant role in controlling the various eledrophysical parameters of adsorbent on the content of ambient medium [32]. As it has been mentioned in section 1.6, these defects are being formed in the temperature domain in which the respective concentration of volume defects is very small. In fact, cooling an adsorbent down to room temperature results violation of uniform distribution due to redistribution of defects. The availability of non-homogeneous defect distribution led to creation of a new model of depleted surface layer based on the phenomenon of oxidation of surface defects [182] which is an alternative to existing model of the Shottky barrier [183]. 

Figure 8.6 summarizes our current knowledge of the appearance of point defects in STM images. The most prevalent point defects on sputtered/annealed Ti02(l 1 0) lxl surfaces have been identified as Ob-vacs, OHb, and OHb pairs and these are shown in a ball model together with an STM image decorated with a number of all three types of defects. 

The ability of STM to image at the atomic scale is particularly exemplified by the two other chapters in the book. Thornton and Pang discuss the identification of point defects at Ti02 surfaces, a material that has played an important role in model catalyst studies to date. Point defects have been suggested to be responsible for much of the activity at oxide surfaces and the ability to identify these features and track their reactions with such species as oxygen and water represents a major advance in our ability to explore surface reactions. Meanwhile, Baddeley and Richardson concentrate on the effects of chirality at surfaces, and on the important field of surface chirality and its effects on adsorption, in a chapter that touches on one of the fundamental questions in the whole of science - the origins of life itself ... 

Compare the theoretical and experimental densities to see which point defect model best fits the data. 

The various types of point defect found in pure or almost pure stoichiometric solids are summarized in Figure 1.17. It is not easy to imagine the three-dimensional consequences of the presence of any of these defects from two-dimensional diagrams, but it is important to remember that the real structure of the crystal surrounding a defect can be important. If it is at all possible, try to consult or build crystal models. This will reveal that it is easier to create vacancies at some atom sites than others, and that it is easier to introduce interstitials into the more open parts of the structure. 

The simplest way to account for composition variation is to include point defect populations into the crystal. This can involve substitution, the incorporation of unbalanced populations of vacancies or by the addition of extra interstitial atoms. This approach has a great advantage in that it allows a crystallographic model to be easily constructed and the formalism of defect reaction equations employed to analyze the situation (Section 1.11). The following sections give examples of this behavior. 

These point defect models need to be regarded as a first approximation. Calculations for stoichiometric GaAs suggest that balanced populations of vacancies on both gallium and arsenic sites, VGa and VAs, exist, as well as defect complexes. Calculation for nonstoichiometric materials would undoubtedly throw further light on the most probable defect populations present. 

When the random-walk model is expanded to take into account the real structures of solids, it becomes apparent that diffusion in crystals is dependent upon point defect populations. To give a simple example, imagine a crystal such as that of a metal in which all of the atom sites are occupied. Inherently, diffusion from one normally occupied site to another would be impossible in such a crystal and a random walk cannot occur at all. However, diffusion can occur if a population of defects such as vacancies exists. In this case, atoms can jump from a normal site into a neighboring vacancy and so gradually move through the crystal. Movement of a diffusing atom into a vacant site corresponds to movement of the vacancy in the other direction (Fig. 5.7). In practice, it is often very convenient, in problems where vacancy diffusion occurs, to ignore atom movement and to focus attention upon the diffusion of the vacancies as if they were real particles. This process is therefore frequently referred to as vacancy diffusion... 

The random-walk model of diffusion needs to be modified if it is to accurately represent the mechanism of the diffusion. One important change regards the number of point defects present. It has already been pointed out that vacancy diffusion in, for example, a metal crystal cannot occur without an existing population of vacancies. Because of this the random-walk jump probability must be modified to take vacancy numbers into account. In this case, the probability that a vacancy is available to a diffusing atom can be approximated by the number of vacant sites present in the crystal, d], expressed as a fraction, that is... 

Models describing the point defect population can be used to determine how the electronic conductivity will vary with changes in the surrounding partial pressure. 

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... 

A block model of defects on a single-crystal surface is depicted in Figure 2.4.17 The surface itself in reality is a two-dimensional defect of the bulk material. In addition, one-dimensional defects in the form of steps which have zero-dimensional defects in the form of kink sites. Terraces, which are also shown in the figure, have a variety of surface sites and may also exhibit vacancies, adatoms, and point defects. Surface boundaries may be formed as a result of surface reconstruction of several equivalent orientations on terraces. 

As also discussed in Chapter 4, dislocations also give rise to diffuse scatter from the near-core region. Point defects of all types also give diffuse scatter. Although we do not yet have complete theories to describe this at present, we can model the diffuse scatter quite well by a Lorentzian function of the form ... 

In point defect models, vacancies and interstitial ions may be responsible for point defects. These defects may be independent of both the composition and external conditions. 

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