One- and Two-Dimensional Defects in Crystals

On the other hand, the formation of the high pressure phase is preceded by the passage of the first plastic wave. Its shock front is a surface on which point, linear and two-dimensional defects, which become crystallization centers at super-critical pressures, are produced in abundance. Apparently, the phase transitions in shock waves are always similar in type to martensite transitions. The rapid transition of one type of lattice into another is facilitated by nondilTusion martensite rearrangements they are based on the cooperative motion of many atoms to small distances. ... 

Figure 5.88 is an illustration of two-dimensional defects in the form of surfaces and grain boundaries. They either terminate a crystal or separate it from the three-dimensional defects. In polymer crystals, these surfaces and grain boundaries are rarely clean terminations of single-crystalline domains, as one would expect from the unit cell descriptions in Sect. 5.1. The surfaces may contain folds or chain ends and may be traversed by tie molecules to other crystals and cilia and loose loops that enter the amorphous areas, as is illustrated in Figs. 5.87 and 2.98. The properties of a polycrystalline sample are largely determined by the cohesion achieved across such surfaces and the mechanical properties of the interlamellar material, the amorphous defects. 

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. 

Although much work has been done on the three reference substances described here, there are still needs for refinement of heat capacity measurements and frequency spectra fit. Most emjdiasis has been placed on obtaining a picture of the vibrations in the ideal crystal lattice. The questions about vibrations in small and defect crystals has at pre nt only been opened. Historically, the universal Dulong Petit-Rule of heat capacity which fits only well at elevated temperatures was replaced between 1900 and 1920 mainly throi h the work of Einstein, Debye. Nemst, and Lindemaim by a theory with one characteristic constant for each substance, the 0-temperature. The Tarasov treatment of the 1950 s shows that in case of strong anisotropy of forces, as in one or two dimensionally strongly bonded crystals, a second constant... 

A block model of defects on a single-crystal surface is depicted in Figure 2.4.17 The surface itself in reality is a two-dimensional defect of the bulk material. In addition, one-dimensional defects in the form of steps which have zero-dimensional defects in the form of kink sites. Terraces, which are also shown in the figure, have a variety of surface sites and may also exhibit vacancies, adatoms, and point defects. Surface boundaries may be formed as a result of surface reconstruction of several equivalent orientations on terraces. 

Electron transport properties of metal oxides nanoparticles are very important for electrical and electronic applications as well as for understanding the unique one-dimensional carrier transport mechanism. It has been noticed that the diameter of metal oxides nanoparticles, surface conditions, crystal structure and its quality i.e., chemical composition, crystallographic orientation along the film axis etc are important parameters that influence the electron transport mechanism. It is found that conductance of a nano-structure strongly depends on their crystalline structure. For example, in the case of perfect crystalline Si nanowires having four atoms per unit cell, generally three conductance channels are found [51], One-or two-atom defect, either by addition or removal of one or two atoms may disrupt the number of such conductance channel and may cause variation in the conductance. It has been observed that change in the surface conditions of the nanowires can cause remarkable... 

A suitable classification of crystalline defects can be achieved by first considering the so-called point defects and then proceeding to higher-dimensional defects. Point defects are atomic defects whose effect is limited only to their immediate surroundings. Examples are vacancies in the regular lattice, or interstitial atoms. Dislocations are classified as linear or one-dimensional defects. Grain boundaries, phase boundaries, stacking faults, and surfaces are two-dimensional defects. Finally, inclusions or precipitates in the crystal matrix can be classified as three-dimensional defects. 

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. 

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). 

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