Crystal imperfections grain boundaries

The nature of the material to be studied, which means its degree of crystallinity and perfectness of crystal structure, may have a significant effect on the thermoanalytical behavior. In spite of identical chemical composition of a certain material the variations with respect to structure, imperfections, grain boundaries, etc. are almost infinite. Of course many of these will not show in normal thermogravimetric analysis, with very sensitive apparatus characteristically different TG curves18, 19 may be obtained however. As an example Fig. 26 shows the thermal decomposition of hydrozincite, Zn5(OH)6(003)2, whereby equal amounts of samples from natural origin and synthetic preparations are compared. 

The defects which disrupt the regular patterns of crystals, can be classified into point defects (zero-dimensional), line defects (1-dimensional), planar (2-dimensional) and bulk defects (3-dimensional). Point defects are imperfections of the crystal lattice having dimensions of the order of the atomic size. The formation of point defects in solids was predicted by Frenkel [40], At high temperatures, the thermal motion of atoms becomes more intensive and some of atoms obtain energies sufficient to leave their lattice sites and occupy interstitial positions. In this case, a vacancy and an interstitial atom, the so-called Frenkel pair, appear simultaneously. A way to create only vacancies has been shown later by Wagner and Schottky [41] atoms leave their lattice sites and occupy free positions on the surface or at internal imperfections of the crystal (voids, grain boundaries, dislocations). Such vacancies are often called Schottky defects (Fig. 6.3). This mechanism dominates in solids with close-packed lattices where the formation of vacancies requires considerably smaller energies than that of interstitials. In ionic compounds also there are defects of two types, Frenkel and Schottky disorder. In the first case there are equal numbers of cation vacancies... 

As early as 1829, the observation of grain boundaries was reported. But it was more than one hundred years later that the structure of dislocations in crystals was understood. Early ideas on strain-figures that move in elastic bodies date back to the turn of this century. Although the mathematical theory of dislocations in an elastic continuum was summarized by [V. Volterra (1907)], it did not really influence the theory of crystal plasticity. X-ray intensity measurements [C.G. Darwin (1914)] with single crystals indicated their mosaic structure (j.e., subgrain boundaries) formed by dislocation arrays. Prandtl, Masing, and Polanyi, and in particular [U. Dehlinger (1929)] came close to the modern concept of line imperfections, which can move in a crystal lattice and induce plastic deformation. 

W.T. Read and W. Shockley. Dislocations models of grain boundaries. In Imperfections in Nearly Perfect Crystals. John Wiley Sons, New York, 1952. 

It is well known that the surface orientation of crystals and imperfections in the surface, like grain boundaries or dislocations, affect largely the reaction rates at electrodes made of metals or semiconductors. Such effects are most pronounced in those reactions where atoms leave their position in a crystal lattice or have to be incorporated into such one. These processes are connected with activation barriers which are particularly high for semiconductors where the chemical bonds between the components of the crystal lattice are highly directed and localized. If we consider photoelectrochemical reactions at semiconductors we have additionally to discuss the influence of these factors on light absorption and its consequences. 

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. 

This value, based on the experimental density, is to be considered the more reliable, since it is based on a measured property of CsCl, while the ionic radii are based on averages over many different compounds. Unit cell dimensions can be measured accurately by x-ray diffraction and from them the theoretical density can be calculated. The measured density is usually lower because most samples that are large enough to measure are not perfect single crystals and contain empty spaces in the form of grain boundaries and various crystalline imperfections. 

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. 

In practice, all crystals have imperfections. If a substance crystallizes rapidly, it is likely to have many more imperfections, because crystal growth starts at many sites almost simultaneously. Each small crystallite grows until it runs into its neighbors the boundaries between these small crystallites are called grain boundaries, which can be... 

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. 

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 mechanism by which defects concentrate impurities is a subject of research that has important bearing on crystal growth, especially related to formation of crystalline materials for use in the electronics industry. Besides imperfections associated with isolated impurities (i.e., point defects), the other major types of structural defects are line defects (both edge and screw), planar defects, grain boundaries, and structural disorder (Wright 1989). The connection between defect formation and impurity uptake is evident in two of these defects in particular the edge defect and point defect. 

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