Crystal imperfections imperfect order

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). 

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. 

Unsubstituted CP crystals all have quite similar chain packings. The crystal sizes are always small (ca. 100 A in all directions) and imperfectly ordered usually, chains are longer than the crystal dimensions. Therefore, the ideal CP is not found in practice chain geometries fluctuate along their length, as well the interchain interactions. This disorder is to be taken seriously in physical study, not as a small perturbation. 

Both Weber and Kulenkampff remark that it is difficult to understand how the Br lines in the higher order spectrum published by Allison and Duane can be explained as due to crystal imperfections. They are quite correct in this criticism. It is the pmpose of this note to make plain that certain portions of the curve referred to are now regarded by the writer as unreliable. In particular, no confidence can be placed in the portion... 

Schultze et al. [3.115-3.120], and Kolb et al. [3.121-3.128]. The experimental results gave evidence of the formation of well-ordered 2D Meads overlayers in the underpotential range depending on the crystallographic orientation and the crystal imperfection density of S. Electrochemical results were first hypothetically interpreted in terms of 2D Meads superlattice structures" [3.87-3.89, 3.93, 3.98], which were also observed in comparative [3.121, 3.122, 3.129-3.133] and ex situ [3,123-3.128] UHV studies. 

Table 8-1 summarizes some of the features of the methods just described. Note that a crystal of any thickness can be examined in reflection, but the information received applies only to a shallow surface layer. Transmission methods, on the other hand, are restricted to rather thin crystals, of the order of 1 mm or less, but these methods reveal imperfections throughout the volume. Note also that the area irradiated, which is related to the area of the incident beam, may differ from the area examined if the crystal is traversed across the beam, as in the Lang projection method. 

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 residual intercalant is retained at crystal imperfections such as crystallite boundaries or twin lines and x-ray diffraction may show graphite reflections only. Residue compounds with large interplanar distances have residual intercalant between the carbon planes . In bromine residue compounds ordered layers of intercalant are found by electron diffraction . Thus there is no distinct borderline between dilute lamellar and residue compounds. 

In addition to the exciton band, energy states may be created between valence and conduction bands because of crystal imperfections or impurities. Particularly important are the states created by the activator atoms such as thallium. The activator atom may exist in the ground state or in one of its excited states. Elevation to an excited state may be the result of a photon absorption, or of the capture of tm exciton, or of the successive capture of an electron and a hole. The transition of the impurity atom from the excited to the ground state, if allowed, results in the emission of a photon in times of the order of 10" s. If this photon has a wavelength in the visible part of the electromagnetic spectrum, it contributes to a scintillation. Thus, production of a scintillation is the result of the occurrence of these events ... 

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. 

Structure Used herein to refer to the molecular-level, crystallographic, three-dimensional arrangement of atoms, as controlled by the chemical bonding. Both long-range and short-range order/disorder, including crystal imperfections and defects, must be considered. 

Complete structural characterization of a material involves not only the elemental composition for major components and a study of the crystal structure, but also the impurity content (impurities in solid solution and/or additional phases) and stoichiometry. Noncrystalline materials can display unique behavior, and noncrystalline second phases can alter properties. Both the long-range order and crystal imperfection or defects must be defined. For example, the structural details which influence properties of oxides include the impurity and dopant content, nonstoichiometry, and the oxidation states of cations and anions. These variables also influence the point-defect structure, which in turn influences chemical reactivity, and electrical, magnetic, catalytic, and optical properties. 

FIGURE 1.4 Representation of linear order (ID) in real space and in reciprocal space. (Adapted from A. Guinier. Theorie et techniques de la radiocristallographie. 2nd ed. Dunod, Paris, 1956, 736 p. X-ray diffraction in crystals, imperfect crystals and amorphous bodies, Dover ed. translation (1994). With permission.)... 

So far we have assumed that crystals have perfect order. In fact, real crystals have various defects or imperfections. These are principally of two kinds chemical impurities and defects in the formation of the lattice. 

Equations (2) and (3) result in Aa/a = -1.7 X 10The lattice constants of pure "BP and BP result in Aa/a = -1.2 X 10 one order smaller than that from the Raman shift, which would be due to such crystal imperfections (57) as lattice distortions and low-angle grains. 

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