Crystals extended defects

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... 

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. 

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. 

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. 

Figure 5.2 Diffusion couple formed by two crystals separated by radioactive material (a) initially and (b) after heating. Short-circuit diffusion occurs down extended defects, and diffusion into the bulk occurs both from the surface and laterally from extended defects.

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... 

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. 

Figure 4J Examples of extended defects in crystals edge dislocation (A) and screw dislocation (B).

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. 

Table 4.2 lists defect energies calculated with the method described above in fayal-ite and forsterite crystals. Note that the energies obtained are on the magnitude of some eV—i.e., substantially lower than the energies connected with extended defects. Note also that, ionic species being equal, the defect energies depend on... 

In extended defects, the displacement vector b (or R) associated with them can be defined from the Burgers Circuit shown in figure 2.4(a), for a simple cubic system (Frank 1951, Cottrell 1971, Amelinckx et al 1978). In the defective crystal (A), a sequence of lattice vectors forms a clockwise ring around the dislocation precisely the same set of lattice vectors is then used to make a second... 

In a perfect crystal, all atoms would be on their correct lattice positions in the structure. This situation can only exist at the absolute zero of temperature, 0 K. Above 0 K, defects occur in the structure. These defects may be extended defects such as dislocations. The strength of a material depends very much on the presence (or absence) of extended defects, such as dislocations and grain boundaries, but the discussion of this type of phenomenon lies very much in the realm of materials science and will not be discussed in this book. Defects can also occur at isolated atomic positions these are known as point defects, and can be due to the presence of a foreign atom at a particular site or to a vacancy where normally one would expect an atom. Point defects can have significant effects on the chemical and physical properties of the solid. The beautiful colours of many gemstones are due to impurity atoms in the crystal structure. Ionic solids are able to conduct electricity by a mechanism which is due to the movement of fo/ 5 through vacant ion sites within the lattice. (This is in contrast to the electronic conductivity that we explored in the previous chapter, which depends on the movement of electrons.)... 

The introduction to this chapter mentions that crystals often contain extended defects as well as point defects. The simplest linear defect is a dislocation where there is a fault in the arrangement of the atoms in a line through the crystal lattice. There are many different types of planar defects, most of which we are not able to discuss here either for reasons of space or of complexity, such as grain boundaries, which are of more relevance to materials scientists, and chemical twinning, which can contain unit cells mirrored about the twin plane through the crystal. However,... 

An extension of the kinetic theory on cases when a mechanical pressure interacts with kinetic processes inside solid volume and on interfaces has wide application interests. The elastic deformations in solid are presented from influence of external forces and from presence of internal defects of crystal structure point defects (vacancy, intersite atoms, complexes of atoms, etc.), extended defects (dislocations and inner interfaces in polycrystals), and three-dimensional defects (heterophases crystals, polycrystals). 

The specific heat of a semiconductor has contributions from lattice vibrations, free carriers and point and extended defects. For good quality semi-insulating crystals only the lattice contribution is of major significance. Defect-free crystals of group III nitrides are difficult to obtain, and thus the specific heat measurements are affected by the contributions from the free carriers and the defects. While the specific heat of AIN is affected by the contribution of oxygen impurities, the data for GaN and InN are affected by free electrons, especially at very low temperatures. 

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