Interstitial defects structure

These alternative descriptions of shear-plane formation will be valuable in our discussion of mechanism in Section 4. In the account now presented of the relative stabilities of shear plane and point defect structures we will assume that vacancies are the predominant point defects. However, the arguments we present could be adapted for metal interstitial defect structures. 

The formation of the combination of defects may be described as a chemical reaction and thermodynamic equilibrium conditions may be applied. The chemical notations of Kroger-Vink, Schottky, and defect structure elements (DSEs) are used [3, 11]. The chemical reactions have to balance the chemical species, lattice sites, and charges. An unoccupied lattice site is considered to be a chemical species (V) it is quite common that specific crystal structures are only found in the presence of a certain number of vacancies [12]. The Kroger-Vink notation makes use of the chemical element followed by the lattice site of this element as subscript and the charge relative to the ideal undisturbed lattice as superscript. An example is the formation of interstitial metal M ions and metal M ion vacancies, e.g., in silver halides ... 

The method can be illustrated by reference to a classical 1933 study of the defects present in wilstite, iron monoxide. Wustite adopts the sodium chloride (NaCl) structure, and the unit cell should contain 4 Fe and 4 O atoms in the unit cell, with an ideal composition FeOi.o, but in reality the composition is oxygen rich and the unit cell dimensions also vary with composition (Table 1.1). Because there is more oxygen present than iron, the real composition can be obtained by assuming either that there are extra oxygen atoms in the unit cell (interstitial defects) to give a composition FcO 1 +v, or that there are iron vacancies present, to give a formula Fci-JD. It is... 

Zinc oxide is normally an w-type semiconductor with a narrow stoichiometry range. For many years it was believed that this electronic behavior was due to the presence of Zn (Zn+) interstitials, but it is now apparent that the defect structure of this simple oxide is more complicated. The main point defects that can be considered to exist are vacancies, V0 and VZn, interstitials, Oj and Zn, and antisite defects, 0Zn and Zno-Each of these can show various charge states and can occupy several different... 

There are large numbers of anion excess fluorite-related structures known, a small number of which are listed in Table 4.4. The defect chemistry of these phases is enormously complex, deserving of far more space than can be allocated here. The defect structures can be roughly divided into three categories random interstitials, which in... 

Figure 4.9 Clusters in the fluorite structure (a, b) transformation of a cube into a square antiprism (c, d) transformation of a cube into a cuboctahedron (e) a single square antiprism formed by tbe creation of < 110> interstitial defects (/) an M6F36 cluster in a fluorite structure matrix. Cations in the plane of tbe section are represented by smaller spheres anions above and below the plane are represented by larger spheres.

In conclusion, electron microscopy techniques reveal considerable evidence for variability in composition and defect structures, such as cation and anion vacancies, extended defects, substitutional ions and oxygen interstitials these are common to all of the high temperature superconducting oxides. These defects play an important role in controlling the carrier concentrations and therefore the... 

An iron deficiency could be accommodated by a defect structure in two ways either iron vacancies, giving the formula Fe] /D, or alternatively, there could be an excess of oxygen in interstitial positions, with the formula FeOi+ f. A comparison of the theoretical and measured densities of the crystal distinguishes between the alternatives. The easiest method of measuring the density of a crystal is the flotation method. Liquids of differing densities which dissolve in each other, are mixed together until a mixture is found that will just suspend the crystal so that it neither floats nor sinks. The density of that liquid mixture must then be the same as that of the crystal, and it can be found by weighing an accurately measured volume. 

FIGURE 5.27 (a) The fluorite structure of UO2 with a unit cell marked in bold, (b) Interstitial defect cluster in U02+jf. Uranium positions... 

Since the ratio of number of anions to cations in a unit cell for the Fluorite structure is 1 to 2, the compound Zro.gsCao isOj 5 can be said to be non-stoichiometric. The possible defect types are anion vacancies or interstitial cations. X-ray diffraction studies have definitely confirmed that the former type of defect structure is dominant therefore, there exist oxygen vacancies up to 7.5 per cent. The concentration of oxygen vacancies must depend on Po., as is usual for the metal oxides. 

The defect structure of Fei O with the NaCl-type structure had been estimated to be a random distribution of iron vacancies. In 1960, Roth confirmed, by powder X-ray diffraction, that the defect structure of wiistite quenched from high temperatures consists of iron vacancies (Vp ) and interstitial iron (Fcj) (there are about half as many FCj as Vpe). This was a remarkable discovery in the sense that it showed that different types of crystal defects with comparable concentrations are able to exist simultaneously in a substance, Roth also proposed a structure model, named a Roth cluster, shown in Fig. 1.84. Later this model (defect complex = vacancy -F interstitial) was verified by X-ray diffraction on a single crystal and also by in-situ neutron diffraction experiments. Moreover, it has been shown that the defect complex arranges regularly and results in a kind of super-structure, the model structure of which (called a Koch-Cohen model) is shown in Fig. 1.85 together with the basic structures (a) and (b). 

Fig, 7.15 Mechanisms of ionic conduction in crystals with defect structures (a) vacancy (Schoilky defect) mechanism, (b) interstitial (Frenkel defect) mechanism, (c) inlcrsthialcy (concerted Schottky-Frenkel) mechanism. 

X-ray studies have established that /9-R105 boron has a very porous (only 36% of space is filled in the idealized model) and defective structure with the presence of interstitial atoms and partial occupancies. The B57 fragment can dispose of excess electrons by removal of some vertices to form nido or arachno structures, and individual Bi2a units can gain electrons by incorporating capping vertices that are accommodated in interstitial holes (see Fig. 13.4.11(b)). 

Fig. 1.14. Dumbbell oxygen interstitial defects in ZnO in comparison to the ideal lattice structure and the octahedral oxygen interstitial [114,115]. The structure of the rotated dumbbell interstitial depends on the charge state. Copyright (2005) by the American Physical Society...

In the former case, the ions migrate among the interstitial defects, which may be relevant only to small ions such as Li+. This leads to a transference number close to 1 for the cation migration. In the other case, the lattice contains both anionic and cationic holes, and the ions migrate from hole to hole [39], The dominant type of defects in a lattice depends, of course, on its chemical structure as well as its formation pattern [40-43], In any event, it is possible that both types of holes exist simultaneously and contribute to conductance. It should be emphasized that this description is relevant to single crystals. Surface films formed on active metals are much more complicated and may be of a mosaic and multilayer structure. Hence, ion transport along the grain boundaries between different phases in the surface films may also contribute to conductance in these systems. 

The defective structure in nanocrystalline ceria based catalysts proved to have strong effect on the OSC. Mamontov et al. (2000) reported the neutron diffraction studies of the atomic structures of nanocrystalline powder of ceria and ceria-zirconia solid solution. They found that the concentration of vacancy-interstitial oxygen defects has a direct correlation with the OSC. This effect is stronger than the correlation of surface area with OSC. Zirconia reduces ceria and preserves oxygen defects to retard the degradation of ceria-zirconia in OSC. Yan et al. observed the strong correlation between OSC and the lattice strain in nanosized ceria-zirconia, which could be measured via XRD (Si et al., 2004 Figure 11). 

The MX2+X phases contain interstitial anions. As with the anion-deficient phases, these interstitials are not random point defects, but ordered or clustered. The earliest cluster geometry to be postulated was the [2 2 2] cluster in UO2+J, the prototype anion-excess flnorite phase. The cluster is composed of 2 interstitial oxygen atoms displaced along (110), two interstitial oxygen atoms displaced along (111) in UO2+J (Figure 5). Other cluster geometries have also been proposed in this oxide, and the defect structure of this well studied phase is still not completely resolved. 

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