Defects of crystal lattices

In a crystal containing twin defects, the crystal lattices continue across the twin boundaries without a break. Another similar defect, the antiphase defect, is formed by a shift of the crystal by half a unit cell along the antiphase boundary. This defect can also contribute to strong image contrast as shown in Figure 10.3b. 

Howie, A., Whelan, M. J. (1962). Diffraction contrast of electron microscope images of crystal lattice defects. 111. Results and experimental confirmation of the dynamical theory of dislocation image contrast. Proc. Roy. Soc., (London), A267, 206-30. 

The defects of crystal structure - that is, aU types of irregularity ofanideal crystal lattice -can be classified based on their size and/or number of dimensions [9,15-19] ... 

Kogure T, Nespolo M (2001) Atomic stractures of planar defects in oxybiotite. Am Mineral 86 336-340 Konishi H, Akai J (1990) HRTEM observation of new complex polytype of biotite from dacites in Higashiyama hills, Niigata, central Japan. Clay Sci 8 25-30 Mauguin MCH (1928) Etude de Micas au moyen du rayons X. Bull Soc fr Mineral Cristallogr 51 285-332 Menter JW (1956) The direct study by electron microscopy of crystal lattices and their imperfections. Proc R Soc London A236 119... 

Dielectric relaxation and dielectric losses of pure liquids, ionic solutions, solids, polymers and colloids will be discussed. Effect of electrolytes, relaxation of defects within crystals lattices, adsorbed phases, interfacial relaxation, space charge polarization, and the Maxwell-Wagner effect will be analyzed. Next, a brief overview of... 

Solids and dipole relaxation of defects in crystals lattices Molecules which become locked in a solid or rigid lattice cannot contribute to orientational polarization. For polar liquids such as water, an abrupt fall in dielectric permittivity and dielectric loss occur on freezing. Ice is quite transparent at 2.45 GHz. At 273 °K, although the permittivity is very similar (water, 87.9 ice, 91.5) the relaxation times differ by a factor of 10 (water, 18.7 x 10 s ice, 18.7 x 10 s). Molecular behavior in ordinary ice and a feature which may be relevant to a wide variety of solids has been further illuminated by the systematic study of the dielectric properties of the nu-... 

There are also applications of quantum theory for instance in the onset of a failure in a material. The failure starts on the atomic scale when an interatomic bonding is stressed beyond its yield-stress threshold and breaks. The initiation and diffusion of point defects in crystal lattice turn out to be a starting point of many failures. These events occur in a stress field at certain temperatures. The phenomena of strain, fatigue crack initiation and propagation, wear, and high-temperature creep are of particular interest The processes of nucleation and diffusion of vacancies in the crystal lattice determines the material behavior at many operation conditions. 

In a crystal lattice there is translation symmetry but in a polycrystalline solid it exists only approximately within one grain. Similar to the outer surfaces of the crystallites, the grain boundaries are two-dimensional defects the crystal lattice stops there. Dislocations are one-dimensional defects and pores are defects in solids having a dimension that is usually three but can be lower. Such higher-dimensional defects (Table 10.1) determine many properties the dislocations in metals affect plasticity and the porosity, if open, determines gas permeability. 

Color centers are simple point defects in crystal lattices, consisting of one or more electrons trapped at an ionic... 

Fig. 92. A schematic presentation of the influence of crystal lattice defects on AKj in the system Pr2Te3-Pr3Te4-Details are explained in the text.

The groups Gd of a supercell model with one point defect for a superceU are sym-morphic, they belong to the crystal class Fd = Sd with all the types of crystal lattices possible for this crystal class. The point sjonmetry of the cycUc-cluster coincides for the host crystal - with the point-symmetry group F, for the defective crystal - with the point-symmetry group Sd-... 

Point defect or zero-dimensional defect. This kind of defects include both the possible existence of vacancies and substituted impurity atoms on their sites of crystal lattice structure and include misplaced parts of atoms with each other in solid compound of AB, namely, A atom occupies the B atomic site, while inversely B atom occupies A, or to say there are misplaced atoms or variable valence ions on the sublattice sites. The interstitial atoms sited in the interstitials of lattice structure are also parts of those point defects. It can further be divided into Schottky defects and Frenkel defect. The former means a metal atomic defect and the original metal atoms are transformed to the metal surface and the latter is composed of an atomic defect and an interstitial atom, as presented in Fig. 3.23. It could be imagined that the existence of inner defects would bring the distortions of lattice, as shown in Fig. 3.24. The issue of point defect is the major subject and key problem for the studies of solid chemistry. 

Concentrations of Schottky defect can be measured with experiment of thermal expansion of metals, namely the determination of thermal expansion coefficient of both the whole crystal and lattice parameters, respectively. The thermal expansion coefficient of the whole crystal includes not only the thermal expansion of crystal lattice itself, but the formation of Schottky defect. Therefore, the difference of two results can reflect both the existence and concentration of Schottky defect. For instance, at conditions near to the melting point, the concentration of Schottky vacant for alumina is about 1 x 10, and formation energy of its vacant is about 0.6eV (leV = 1.60 x 10 J) while that of NaCl is 10 -10 and formation energy is 2 eV, respectively. 

As various irregularities of crystals lattice are discussed above, it is now necessary to analyze their effect and importance in heterogeneous catalysis. There are at least two facts confirming the relation of crystal irregularity with the catalytic active center on catalyst surface. One of them is on those sites where the dislocations and surface point defects occur, and the atomic arrangements would differ from the others sites in catalyst surface, while surface atomic space and the properties of stereochemistry would remain the important factors to decide the catalytic activity. 

Those sites of dislocations of edge and screw are beneficial to the catal3dic reactions. The other is that the electronic factors on those sites of crystal lattice irregularity enhance the high catal3dic activities, because the surface points correlated with the dislocations and defects can modify the electrical properties of solids. 

This is the first book devoted to the theoretical modelling of refractory carbides and nitrides and alloys based on them. It makes use of computational methods to calculate their spectroscopic, electric, magnetic, superconducting, thermodynamical and mechanical properties. Calculated results on the electronic band structure of ideal binary transition-metal carbides and nitrides are presented, and the influences of crystal lattice defects, vacancies and impurities are studied in detail. Data available on chemical bonding and the properties of multi-component carbide- and nitride-based alloys, as well as their surface electronic structure, are described, and compared with those of bulk crystals. 

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