Extended defect

Extended defects interrupt the continuity of the crystal, generating crystal subgrains whose dimensions depend, in a complex fashion, on the density of extended defects per unit area. Table 4.1 gives examples of reported dislocation densities and subgrain dimensions in olivine crystals from the San Carlos perido-tite nodules (Australia). Assuming a mean dislocation density within 1.2 X 10 and 6 X 10 cm , Kirby and Wegner (1978) deduced that a directional strain pressure of 35 to 75 bar acted on the crystals prior to their transport to the surface by the enclosing lavas. 

Anomalously high extended defect concentrations may be achieved in crystals by submitting them to directional stress. For example, Willaime and Gaudais (1977) induced dislocation densities of 10 cm in sanidine crystals (KAlSi30g triclinic), and Ardell et al. (1973) reached a dislocation density of 10 cm in quartz with the same method. 

In recent years it has been shown that in many defect compounds, particularly oxides, the predominant defects are not random point defects, but rather the defect structure may consist of complexes, microdomains, block structures, or crystallographic shear planes. These extended defects will be described in more detail by Eyring and Tai in Chapter 4 of Volume 3. 

A complex defect may be considered a combination of point defects. For example, in 002 + there is evidence that the excess oxygen is due to defects which consist of a combination of three oxygen interstitials, two oxygen vacancies, and two holes (Uy ions). A complex defect differs from an associate (as discussed in Section 

2) in that it is always assumed to exist in the combined state in the lattice. Equilibria between the complex and isolated defects are not considered. 

The mass action law also may be applied to complex defects. Assuming that the defects in FeOj + were complex defects consisting of two Fe vacancies plus an Fe interstitial/ Kofstad and Hed wrote an equation similar to the following for the formation of complexes  

Five interstices are used because it is assumed that each complex defect will block an additional seven interstices for occupation by other complexes, but the addition of oxygen to the lattice will create two additional interstices (a = 2). Also it is necessary to write a hole as Fe/g since the normal Fep ions used to form holes must be explicitly taken into consideration at high concentrations of defects. Using Eq. (Ill), Kofstad and Hed obtained good agreement with experimental data of as a function of deviation from stoichiometry. A more rigorous treatment of this system was carried out using a modification of Eq. (77). Recent X-ray work has shown that the defects in FeOj are more complex than considered here. However, the mass action law may be applied to other complex defects in the same manner. 

The electron microscopy studies of the superconductive cuprates show that the different families differ from each other by the nature of their defect chemistry, in spite of their great structural similarities. For example, the La2Cu04-type oxides and the bismuth cuprates rarely exhibit extended defects, contrary to YBa2Cu307 and to the thallium cuprates. The latter compounds are characterized by quite different phenomena. 

The well known microtwinning phenomena that are inherent to the structure transition of orthorhombic YBa2Cu307 to tetragonal 

Ftgere 22 Idealized models of junction between twinning dotntia. 

Y-Ba cation ordering a c/3 shifting of the fringes is clearly observed, (b) Idealized model of the defect. 

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Issues associated with order occupy a large area of study for crystalline matter [1, 7, 8]. For nearly perfect crystals, one can have systems with defects such as point defects and extended defects such as dislocations and grain... 

Common teniiinology used to characterize impurities and defects in semiconductors includes point and line defects, complexes, precipitates and extended defects. These teniis are somewhat loosely defined, and examples follow. 

Extended defects range from well characterized dislocations to grain boundaries, interfaces, stacking faults, etch pits, D-defects, misfit dislocations (common in epitaxial growth), blisters induced by H or He implantation etc. Microscopic studies of such defects are very difficult, and crystal growers use years of experience and trial-and-error teclmiques to avoid or control them. Some extended defects can change in unpredictable ways upon heat treatments. Others become gettering centres for transition metals, a phenomenon which can be desirable or not, but is always difficult to control. Extended defects are sometimes cleverly used. For example, the smart-cut process relies on the controlled implantation of H followed by heat treatments to create blisters. This allows a thin layer of clean material to be lifted from a bulk wafer [261. 

If tlie level(s) associated witli tlie defect are deep, tliey become electron-hole recombination centres. The result is a (sometimes dramatic) reduction in carrier lifetimes. Such an effect is often associated witli tlie presence of transition metal impurities or certain extended defects in tlie material. For example, substitutional Au is used to make fast switches in Si. Many point defects have deep levels in tlie gap, such as vacancies or transition metals. In addition, complexes, precipitates and extended defects are often associated witli recombination centres. The presence of grain boundaries, dislocation tangles and metallic precipitates in poly-Si photovoltaic devices are major factors which reduce tlieir efficiency. 

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 precursor of such atomistic studies is a description of atomic interactions or, generally, knowledge of the dependence of the total energy of the system on the positions of the atoms. In principle, this is available in ab-initio total energy calculations based on the loc density functional theory (see, for example, Pettifor and Cottrell 1992). However, for extended defects, such as dislocations and interfaces, such calculations are only feasible when the number of atoms included into the calculation is well below one hundred. Hence, only very special cases can be treated in this framework and, indeed, the bulk of the dislocation and interfacial... 

The kinds of substitution mechanisms that may be relevant to super-low concentration elements such as Pa involve intrinsic defects, such as lattice vacancies or interstitials. Vacancy defects can potentially provide a low energy mechanism for heterovalent cation substitution, in that they remove or minimise the need for additional charge balancing substitutions. Formation of a vacancy per se is energetically unfavourable (e.g., Purton et al. 1997), and the trace element must rely instead on the thermal defect concentration in the mineral of interest, at the conditions of interest. Extended defects, such as dislocations or grain boundaries, may also play a key role, but as these are essentially non-equilibrium features, they will not be considered further here. 

Although several types of lattices have been described for ionic crystals and metals, it should be remembered that no crystal is perfect. The irregularities or defects in crystal structures are of two general types. The first type consists of defects that occur at specific sites in the lattice, and they are known as point defects. The second type of defect is a more general type that affects larger regions of the crystal. These are the extended defects or dislocations. Point defects will be discussed first. 

In addition to the point defects that occur at specific lattice sites, there are types of defects, known as extended defects, that extend over a region of the crystal. The three most important types of extended... 

In addition to movement of lattice members within a crystal, it is also possible for there to be motion of members along the surface. Consequently, this type of diffusion is known as surface diffusion. Because crystals often have grain boundaries, cracks, dislocations, and pores, there can be motion of lattice members along and within these extended defects. 

Jefferson s studies of the pyroxenoids has added greatly to our application of the way in which, through the intermediary of planar - or planar and Kinke - faults one structure is converted into another (45). And Audier, Jones and Bowen (46) have revealed how unit cell strips of Fe C may be accommodated as extended defects in the Fe C structure. Both these carbidic phases can be readily identified by HREM at the interface of iron catalysts used for the disproportionation of CO (to yield C j+CC ). 

III. Neutralization of Deep Level Centers and Extended Defects... 

Apart from its role in interacting with existing defects and impurities, hydrogen has recently been shown to induce defects as well (Johnson et al., 1987). Extended defects (described as platelets ) in the near-surface region were observed after hydrogenation and correlated with the presence of large concentrations of H. Theoretical models will be discussed in Part VIII. Part IX, finally, will contain some conclusions and point out directions for future work. As is the case for so many other topics in semiconductor physics, silicon (Si) has been the material for which the majority of... 

Point defects can, for the sake of cataloging, be considered to be zero dimensional. Extended defects with higher dimensionality can also be described. One-dimensional defects extend along a line, two-dimensional defects extend along a plane, and three-dimensional defects occupy a volume. In this chapter these extended defects are introduced. 

Internal boundaries in a crystal, when disordered, form extended defects. However, if the boundaries become ordered, they simply extend the unit cell of the structure and hence are no longer regarded either as boundaries or defects (Fig. 3.20c). In addition, some boundaries can change the composition of a solid locally and, if present in large numbers, can change the macroscopic composition noticeably. When these are ordered, new series of compounds form. Boundaries that do cause significant composition changes are described in Chapter 4. 

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