Line defects in crystals

B.7 CLASSIFICATION OF LINE DEFECTS IN CRYSTAL/CRYSTAL INTERFACES... 

Line defects in crystals such as screw or edge dislocations are quite common in solid substances. The typical length of all dislocation in 1 m3 of annealed material amounts to 1010 m (10 km in 1 cm3). The so-called dislocation density is defined as ... 

Figure 7.7 Line defects in crystals edge dislocation (left) and screw dislocation (right). Dislocation vector (d) and Burger s vector (b).

As in crystals, defects in liquid crystals can be classified as point, line or wall defects. Dislocations are a feature of liquid crystal phases where tliere is translational order, since tliese are line defects in tliis lattice order. Unlike crystals, tliere is a type of line defect unique to liquid crystals tenned disclination [39]. A disclination is a discontinuity of orientation of tire director field. 

It should be clear that the presence of line defects in a crystal lattice leads to a disruption of the continuity of the lattice just as the presence of point defects affects the packing of a given lattice. The line defect. 

Thermodynamic considerations imply that all crystals must contain a certain number of defects at nonzero temperatures (0 K). Defects are important because they are much more abundant at surfaces than in bulk, and in oxides they are usually responsible for many of the catalytic and chemical properties.15 Bulk defects may be classified either as point defects or as extended defects such as line defects and planar defects. Examples of point defects in crystals are Frenkel (vacancy plus interstitial of the same type) and Schottky (balancing pairs of vacancies) types of defects. On oxide surfaces, the point defects can be cation or anion vacancies or adatoms. Measurements of the electronic structure of a variety of oxide surfaces have shown that the predominant type of defect formed when samples are heated are oxygen vacancies.16 Hence, most of the surface models of... 

Crystal/crystal interfaces possess more degrees of freedom than vapor/crystal or liquid/crystal interfaces. They may also contain line defects in the form of interfacial dislocations, dislocation-ledges, and pure ledges. Therefore, the structures and motions of crystal/crystal interfaces are potentially more complex than those of vapor/crystal and liquid/crystal interfaces. Crystal/crystal interfaces experience many different types of pressures and move by a wide variety of atomic mechanisms, ranging from rapid glissile motion to slower thermally activated motion. An overview of crystal/crystal interface structure is given in Appendix B. 

UST 99] USTINOV A.I., Effect of planar defects in crystals on the position and profile of powder diffraction lines , in SNYDER R.L., FIALA J., BUNGE H.J. (eds.). Defect and microstructure analysis by diffraction, lUCr Monographs on crystallography, no. 10, Oxford University Press, p. 264-317, 1999. 

Line defects in a crystalline material are known as dislocations. Dislocations are formed due to nonequilibrium conditions such as ion implantation and thermal processing. Under equilibrium conditions, there is no requirement for the presence of dislocations or any other defect (except native point defects) in the crystal. An edge dislocation may be viewed also as having an extra half-plane inserted into the crystal (see Fig. 9.9). 

If the sample is crystalline, the scattered intensity depends very strongly on the orientation of the crystals and on their thickness. In bright field, a thin crystal will appear dark when it is correctly oriented for diffraction. If the crystal is not perfectly flat, the contours of correct orientation will appear as dark lines, called bend contours. Variation of intensity such as this in crystalline specimens is called crystallographic or diffraction contrast. Many types of defects in crystals cause localized distortion of the crystal lattice. These defects change the crystal orientation locally and so cause variations in the crystallographic contrast. Detailed information... 

There are several different kinds of defects in crystals. Depending on the type and number of defects in any volume of crystal (that is, the type and density of defects), the physical and chemical properties of the crystal may be altered from the properties of the perfect crystalline form. Defects can be separated on the basis of whether they affect a single point, a line of points, or a plane of points. For simplicity s sake, we will assume that we are considering an atomic crystal, but all crystals—atomic, ionic, molecular—exhibit most of the defects discussed here. 

Vertical and horizontal line defects in samples, (a) ScHieren texture of a 70-pm sample of MBBA (N-(p-methoxy-benzylidene)-p-n-butylaniline) at 20°C in homeotropic anchoring. To induce the vertical line defects an electric field of 6 Vrms 300 Hz applied vertically, (b) Horizontal line defects appeared spontaneously in planar ceU on cooling from the isotropic phase. The subsequent photos illustrate the evolution of a string network in a liquid crystal. The four snapshots have the same size, but were obtained at different times. Notice the progressive dilution of the string network (picture from http //tvww.damtp.cam.ac.uk/user/gr/public/cs phase.html). Bar 100 pm. 

The description of parabolic cyclide surfaces is based upon two confocal parabolas in mutually perpendicular planes, with the vertex of one parabola passing through the focus of the other. These parabolas represent line defects in smectic liquid crystals. Parts of some typical parabolic cyclide surfaces are pictured in... 

The other major defects in solids occupy much more volume in the lattice of a crystal and are refeiTed to as line defects. There are two types of line defects, the edge and screw defects which are also known as dislocations. These play an important part, primarily, in the plastic non-Hookeian extension of metals under a tensile stress. This process causes the translation of dislocations in the direction of the plastic extension. Dislocations become mobile in solids at elevated temperamres due to the diffusive place exchange of atoms with vacancies at the core, a process described as dislocation climb. The direction of climb is such that the vacancies move along any stress gradient, such as that around an inclusion of oxide in a metal, or when a metal is placed under compression. 

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