Dislocations and grain boundaries

Plastic deformation, unlike elastic deformation, is not accurately predicted from atomic or molecular properties. Rather, plastic deformation is determined by the presence of crystal defects such as dislocations and grain boundaries. While it is not the purpose of this chapter to discuss this in detail, it is important to realize that dislocations and grain boundaries are influenced by things such as the rate of crystallization, particle size, the presence of impurities, and the type of recrystallization solvent used. Processes that influence these can be expected to influence the plastic deformation properties of materials, and hence the processing properties. 

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.)... 

This process involves creation of additional sites in the crystal. Cation and anion sites must be created in the same proportion as the ratio of cation to anion sites in the host crystal—in this case, 1 1. These defects can also be formed at point-defect sources such as dislocations and grain boundaries (see Sections 11.4 and 13.4). 

Until now, we have considered an infinite lattice, but a real material has limited dimensions, that is, n n2, n3 has boundaries. However, an infinite array of unit cells is a good approximation for regions relatively far from the surface, which constitutes the major part of the whole material [5], At this point, it is necessary to recognize that a real crystal has imperfections, such as vacancies, dislocations, and grain boundaries. 

Samples presently available are rich in extended defects, dislocations and grain boundaries, and the thermodynamics of growth at low temperatures suggests high densities of at least some of the point defects. 

BET studies of both the commercial and laboratory scale particles discussed above indicate that there is little internal area accessible to BET adsorbate molecules. This holds for both amorphous and polycrystall ine particles. If the individual particles are composed of multiple crystalline substructures, internal defects capable of adsorption would be expected. However, the BET measurements. show that internal pore.s, if they are present, are not accessible to adsorbate gases. A possible explanation is that annealing by solid-state diffusion occuin sufftcienily rapidly al the temperatures of formation to block access of the external gas to dislocations and grain boundaries. However, the origins of the crystallites within the particles and the mechanisms of crystallization tire not understood al present. 

Diffusion at Extended Defects 11.2.1 Background on Short-Circuit Diffusion In chap. 7, we discussed the fundamental role of point defects in diffusion. We also hinted at the serious amendment to diffusion rates that is mediated by the presence of extended defects such as dislocations and grain boundaries (see fig. 9.1). As was noted above, diffusion rates along defects can often be so much larger than those in... 

Fig. 11.10. Schematic of interactions between dislocations and grain boundaries (courtesy of Ian Robertson).

These variables include the amount of general or localized cold working (e.g., scratches) the presence of imperfections such as dislocations and grain boundaries, the latter making grain size a variable and crystal orientation. The latter becomes a variable because different crystal faces exposed to the environment have different arrangements of atoms and, hence, different tendencies to react with the environment. 

In addition to point and electronic defects, ceramic crystals contain dislocations and grain boundaries. 

Scattering is the main cause of resistivity. The electron wave can be scattered in a variety of ways, of which three are of most importance. The first is the interaction of the electron wave with lattice vibrations, called phonons. This is called thermal scattering. As the temperature increases so do the lattice vibrations, and the resistivity rises. At low temperatures the resistivity drops gradually to a finite value, maintained at absolute zero (Figure 13.5), except for the superconductors, described later in this chapter. This is an intrinsic property of a metal and cannot be altered. Structural imperfections present in the solid also contribute to resistivity. These are mainly defects such as dislocations and grain boundaries, or else impurities. As with lattice vibrations, they scatter the electron waves and so increase resistivity. Defects and impurities are extrinsic features that can be removed by careful processing. 

If the number of trap sites is not fixed, as at a void, the trap is referred to as unsaturable from the viewpoint that the trapped hydrogen concentration can increase without limit as the lattice concentration increases [40]. For many traps such as dislocations and grain boundaries, the number of trap sites is fixed, so the capacity of the trap for hydrogen is finite, and the trap is described as saturable. 

Self-diffusion and rates of oxidation [49] creep and sintering are dependent on the presence of ionic defects in Cr203. The self-diffusion of oxygen is much slower than that of chromium. However, recent data [50, 51] are 4-7 orders of magnitude lower than previously pubKshed data, which were dominated by dislocation and grain boundary effects. The new data, obtained for single crystals, show a dependence on pOi corresponding to the reaction... 

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