Crystals planar defects

Figure 3.20 Planar defects in solids (a) boundaries between slightly misaligned regions or domains b) stacking mistakes in solids built of layers, such as the micas or clays (c) ordered planar faults assimilated into a crystal to give a new structure and unit cell (shaded).

Figure 3.30 Magnetic domains in a ferromagnetic crystal (schematic). The magnetic dipoles, represented by arrows, are aligned parallel in each domain. The domain walls constitute (approximately) planar defects in the structure.

Ferromagnetic and ferroelectric materials are only two examples of a wider group that contains domains built up from switchable units. Such solids, which are called ferroic materials, exhibit domain boundaries in the normal state. These include ferroelastic crystals whose domain structure can be switched by the application of mechanical stress. In all such materials, domain walls act as planar defects running throughout the solid. 

Frequently the most important planar defects in a crystal are the external surfaces. These may dominate chemical reactivity, and solids designed as catalysts or, for example, as filters must have large surface areas in order to function. Rates of reaction during corrosion are frequently determined by the amount of surface exposed to the corrosive agent. (A further discussion of surface physics and chemistry, although fascinating, is not possible within the scope of this volume.)... 

In a similar fashion, the line and planar defects described above are all, strictly speaking, volume defects. For the sake of convenience it is often easiest to ignore this point of view, but it is of importance in real structures, and dislocation tangles, for instance, which certainly affect the mechanical properties of crystals, should be viewed in terms of volume defects. 

Modular structures are those that can be considered to be built from slabs of one or more parent structures. Slabs can be sections from just one parent phase, as in many perovskite-related structures and CS phases, or they can come from two or more parent structures, as in the mica-pyroxene intergrowths. Some of these crystals possess enormous unit cells, of some hundreds of nanometers in length. In many materials the slab thicknesses may vary widely, in which case the slab boundaries will not fall on a regular lattice and form planar 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... 

Finally, two-dimensional defects can occur in crystals. There are two categories of planar defects stacking faults and grain boundaries. 

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,... 

Fig. 2.13 Lattice image of slightly reduced WO,. The black lines show a kind of planar defect, which corresponds to the shear plane 120. The inset shows a streaked diffraction pattern for the crystal parallel to g(120), indicating the random distribution of shear planes (see also Fig. 2.16).

The driving forces necessary to induce macroscopic fluxes were introduced in Chapter 3 and their connection to microscopic random walks and activated processes was discussed in Chapter 7. However, for diffusion to occur, it is necessary that kinetic mechanisms be available to permit atomic transitions between adjacent locations. These mechanisms are material-dependent. In this chapter, diffusion mechanisms in metallic and ionic crystals are addressed. In crystals that are free of line and planar defects, diffusion mechanisms often involve a point defect, which may be charged in the case of ionic crystals and will interact with electric fields. Additional diffusion mechanisms that occur in crystals with dislocations, free surfaces, and grain boundaries are treated in Chapter 9. 

Experiments demonstrate that along crystal imperfections such as dislocations, internal interfaces, and free surfaces, diffusion rates can be orders of magnitude faster than in crystals containing only point defects. These line and planar defects provide short-circuit diffusion paths, analogous to high-conductivity paths in electrical systems. Short-circuit diffusion paths can provide the dominant contribution to diffusion in a crystalline material under conditions described in this chapter. 

Another contribution to variations of intrinsic activity is the different number of defects and amount of disorder in the metallic Cu phase. This disorder can manifest itself in the form of lattice strain detectable, for example, by line profile analysis of X-ray diffraction (XRD) peaks [73], 63Cu nuclear magnetic resonance lines [74], or as an increased disorder parameter (Debye-Waller factor) derived from extended X-ray absorption fine structure spectroscopy [75], Strained copper has been shown theoretically [76] and experimentally [77] to have different adsorptive properties compared to unstrained surfaces. Strain (i.e. local variation in the lattice parameter) is known to shift the center of the d-band and alter the interactions of metal surface and absorbate [78]. The origin of strain and defects in Cu/ZnO is probably related to the crystallization of kinetically trapped nonideal Cu in close interfacial contact to the oxide during catalyst activation at mild conditions. A correlation of the concentration of planar defects in the Cu particles with the catalytic activity in methanol synthesis was observed in a series of industrial Cu/Zn0/Al203 catalysts by Kasatkin et al. [57]. Planar defects like stacking faults and twin boundaries can also be observed by HRTEM and are marked with arrows in Figure 5.3.8C [58],... 

Ordered arra3rs are not completely uniform but have defects, as do crystals, as shown in Figure 11.16. These defects fall into four main categories (1) point defects or vacancies (i.e., places where a particle is missing) (2) line defects or dislocations, (3) planar defects (i.e., grain boimdaiies), and (4) volume defects like cracks. The point defects are... 

Of these four types, (a)-(c) are observed at the atomic level, whereas bulk defects are easily observed by the naked eye, or using a light microscope. These bulk defects are produced through the propagation of the microscopic flaws in the lattice. For crystals with a planar defect such as polycrystalline solids, the grain boundary marks the interface between two misaligned portions of the bulk crystal (Figure 2.23). 

In this section, we have described the general nature and origin of the contrast observed from planar defects, dislocations, and small inclusions. In the next section, we describe the way to calculate the detailed contrast from a crystal defect. The following sections discuss the results of such calculations for the types of defect commonly observed in minerals. 

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