Crystal imperfections dislocations

The physical properties of tellurium are generally anistropic. This is so for compressibility, thermal expansion, reflectivity, infrared absorption, and electronic transport. Owing to its weak lateral atomic bonds, crystal imperfections readily occur in single crystals as dislocations and point defects. 

It is seen, therefore, that after the passage of a perfect dislocation through a crystal, the crystal matrix will be perfect and dislocation free. This will not generally be true for imperfect dislocations, which invariably leave a stacking fault in their wake. 

Considering the crystal imperfections that are typically found in all crystals, the crystal quality of organic pigments is a major concern. The external surface of any crystal exhibits a number of defects, which expose portions of the crystal surface to the surrounding molecules. Impurities and voids permeate the entire interior structure of the crystal. Stress, brought about by factors such as applied shear, may change the cell constants (distances between atoms, crystalline angles). It is also possible for the three dimensional order to be incomplete or limited to one or two dimensions only (dislocations, inclusions). 

The primary consideration we are missing is that of crystal imperfections. Recall from Section 1.1.4 that virtually all crystals contain some concentration of defects. In particular, the presence of dislocations causes the actual critical shear stress to be much smaller than that predicted by Eq. (5.17). Recall also that there are three primary types of dislocations edge, screw, and mixed. Althongh all three types of dislocations can propagate through a crystal and result in plastic deformation, we concentrate here on the most common and conceptually most simple of the dislocations, the edge dislocation. 

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. 

These forces are the result of elastic stress fields that. exist near every impurity ion or aggregate and crystal imperfection like a dislocation line or grain boundary. These forces are very strong and are mainly responsible for the creation of second phase impurity aggregates in a host of ionic crystals. If the latent image is considered as a second phase formation of Ag° atoms in the silver halide crystal, then it seems that the elastic forces are those that cause the formation of this Ag aggregate. 

The thermal gradient and, hence, stress generated in melt-grown crystals have limited the maximum diameter of GaAs wafers (currently 3-4 inch diameter compared to over 12 inch for Si), because with increased wafer diameters the thermal stress-generated dislocation (crystal imperfection) densities eventually becomes unacceptable for device applications. 

Frank [5.50] was the first to recognize the major role of screw dislocations in the process of the growth of real crystals. Due to the helicoidal structure of this crystal imperfection, a step originates from the point where the screw dislocation line intersects the surface of the crystal face (Fig. 5.26b). This step is constrained to terminate at the dislocation emergence point and winds up into a spiral during the growth process (Fig 5.27). 

Volatile products of a reaction, once generated, can escape readily from surface sites. Additional local deformation of crystal regularity occms in the vicinity of a point of surface termination of a dislocation, in the presence of impurities, or at zones of more complex crystal imperfection or damage. All these factors tend to increase the ease of onset of reaction. Crystal surfaces, particularly in the vicinity of specific sites of imperfection, are often identified as zones of initiation of reaction (nucleation). 

Microscopic observations confirm the existence of compact nuclei which grow in three dimensions [4,7]. The texture of the residual material, the solid "product" of reaction has also been characterized [13]. Because the nucleation step has been associated with crystal imperfections, the distribution of dislocations at the surface of the reactant has been studied [14] by an etch technique. This work was later... 

Preferential dissolution at naturally occurring crystal imperfections, such as dislocations, twinning planes, and other structural defects (Berner and Holdren, 1979 Berner and Schott, 1982 Lasaga, 1981b Brantley et al., 1986 Schott and Petit, 1987 Blum and Lasaga, 1987). 

Thus, a crystal is effectively perfect so long as its degeneracy is less than about 10l018 So, our imperfect real crystals can have innumerable lattice imperfections, dislocations, fractures, and chips and have zero residual entropy, so loyg as "innumer- able" in this case does not mean more than 10 0. Since 10 0... 

The velocity relevant for transport is the Fermi velocity of electrons. This is typically on the order of 106 m/s for most metals and is independent of temperature [2], The mean free path can be calculated from i = iyx where x is the mean free time between collisions. At low temperature, the electron mean free path is determined mainly by scattering due to crystal imperfections such as defects, dislocations, grain boundaries, and surfaces. Electron-phonon scattering is frozen out at low temperatures. Since the defect concentration is largely temperature independent, the mean free path is a constant in this range. Therefore, the only temperature dependence in the thermal conductivity at low temperature arises from the heat capacity which varies as C T. Under these conditions, the thermal conductivity varies linearly with temperature as shown in Fig. 8.2. The value of k, though, is sample-specific since the mean free path depends on the defect density. Figure 8.2 plots the thermal conductivities of two metals. The data are the best recommended values based on a combination of experimental and theoretical studies [3],... 

The role of crystal imperfections in the dimerization of substituted anthracenes has been described in the case of l,8-dichloro-9-methylanthracene.178 Similar studies have now been conducted for the 10-methyl isomer.179 In order to explain how the topochemically forbidden / -dimer (head to tail) is produced from irradiation in the solid phase, optical and electron microscopic examinations of the (010) faces of the orthorhombic crystals of the monomer have been carried out, together with differential-enthalpic and dielectric measurements. Again it is shown that the dimer nuclei appear at emergent dislocations. 

The crystal determines the actual value of b. If b is a perfect lattice vector, then the structure of the crystal will not be changed by the passage of a dislocation. If b is not a lattice vector, then a planar defect (a stacking fault) will be present on one side of the dislocation and a second so-called partial (or imperfect) dislocation will be required to remove the stacking fault. 

In general, real crystals contain inhomogeneities (inclnsions of gaseons, liqnid, or solid impurities) and lattice defects (imperfections, dislocations, grain boundaries, and distortions). They also deviate from the ideal forms, because comers and edges are abraded due to mechanical wear in the crystallizer. The surfaces are often impure due to adhering residues of mother liquor. 

The defects in solids can be classified according to the dimensions of the region of translation symmetry disruption. When one or a few nearest host crystal sites are disturbed, we speak of point (zero-dimensional) defects, called also local defects. Also known are extended defects that introduce structural imperfections in lattice directions - linear (one-dimensional) defects or in the lattice planes planar or two-dimensional defects). The surface of a crystal and dislocations are the important examples of two-dimensional and linear defects, respectively. 

It is well known [73] that plastic deformation in crystals can occur when the applied shear stress can cause one plane of atoms to slip over another plane because there is an imperfect match between these adjacent planes at a particular point in the crystal lattice. These points of imperfection are called dislocations [74] and were identified by electron diffraction techniques to relate to specific crystal defects. Dislocations are observed in polyethylene single crystals by Peterman and Gleiter [75] and give credence to the idea that yield in crystalline polymers can be understood in similar terms to those used by metallurgists for crystalline solids. 

The dislocation is a crystal imperfection in which there is one more atom in the upper row than in the lower row. When shear stresses are applied, there are as many atoms resisting displacement on one side of the dislocation center as there are tending to promote it on the other. Hence, it takes much less energy to cause a dislocation to move across a crystal, than to move one layer of a perfect array of atoms over another. Dislocations are present as defects occurring during solidification, or are generated at cracks or other points of stress concentration when a metal is stressed. 

Positrons diffusing through matter can be captured in special trapping sites. As shown in early studies, these trapping centres are crystal imperfections, such as vacancies and dislocations. The wavefunction of a positron captured in such a defect is localised until it annihilates with an electron of its immediate surroundings into y-rays. Since the local electron density and the electron momentum distribution are modified with respect to the defect-free crystal, the annihilation radiation can be utilised to obtain information on the localisation site. The different positron techniques are based on analysing the annihilation radiation. The principles of the basic positron methods are illustrated in Figure 4.27 [84]. 

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