Classification of defects

Defects in solid include micro defects at atomic or electronic level and microscopic defects could be divided into the following kinds according to defect sizes. 

In an ideal and perfect crystal, all of the electrons would sit on the lowest energy level and energy levels in valence band are completely occupied and conduction bands include no electrons, namely be empty hole. However, in a practical crystal, due to the existence of point defects, which result in the electron current carriers in conduction bands and hole current carriers in valence bands, of which the former is expressed by e and the latter by h. These electrons and holes are also one kind of defects, called as electronic defects. 

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 

Point defects, both vacancies and interstitials, are thermodynamically stable since they lower the Gibbs energy of the crystal. The equilibrium concentrations of point defects rapidly increase with temperature. In metals, vacancies are the predominant point defects in the equilibrium state and their concentrations at high temperatures are much larger than those of interstitials. 

Although crystallization is one of the best ways of purifying chemical substances, yet no crystal is free of impurities. An impurity atom is either incorporated in a crystal structure as an interstitial, or replaces an atom of the main element at the same site. In the latter case, known as the substitution defect, the valence (oxidation state) of the replacing and replaced atoms can be the same or different, in which case a charge compensation is required. Finally, there are so-caUed anti-site defects for example, in a regular AB structure some of the A atoms occupy the sites properly belonging to B, and vice versa. In this case, the periodicity is perturbed with neither a vacancy, nor an interstitial, nor an impurity being present. 

In the enumeration of the types of defect in 1.2 some effort was made to produce a rational classification. The placing of a defect solid in one or other class is undoubtedly somewhat arbitrary, particularly as one solid of definite composition may well contain defect systems of different kinds and these may interact. Moreover, some types of defect have temperature-dependent concentrations and would disappear in the true thermodynamic equilibrium state at 0 i they may be referred to as thermal, indicating their origin. Defects of other kinds that are inherent in the particular solid would be present in the equilibrium state at they have been referred to as biographical defects. Defects of all types 

Cation vacancies plus bound positive holes (i,e., cation of higher charge in neighbourhood of cation vacancy). 

Cation vacancies plus anion vacan-ci in unequal numbers. Electrons and positive holes bound at appropriate vacancies. 

Interstitial atoms with some possible charge transfer. 

Gross departure from stoicheiometry. Diffusion and electrolytic migration of non-metal atom pronounced. 

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Crystalline solids are built up of regular arrangements of atoms in three dimensions these arrangements can be represented by a repeat unit or motif called a unit cell. A unit cell is defined as the smallest repeating unit that shows the fuU symmetry of the crystal structure. A perfect crystal may be defined as one in which all the atoms are at rest on their correct lattice positions in the crystal structure. Such a perfect crystal can be obtained, hypothetically, only at absolute zero. At all real temperatures, crystalline solids generally depart from perfect order and contain several types of defects, which are responsible for many important solid-state phenomena, such as diffusion, electrical conduction, electrochemical reactions, and so on. Various schemes have been proposed for the classification of defects. Here the size and shape of the defect are used as a basis for classification. 

Examination. Sampling plans and procedures for the following classification of defects shall be in accordance eith Standard MIL-STD-105. Continuous sampling plans, in accordance with Standard MIL-STD-1235 may be used if approved by the procuring activity... 

We will not carry this analysis further, since in writing the correction function on the form e(z,y) we have not explicitly included the dependence on derivatives of f. However, we note that this section provides reason for a classification of defect correction schemes by a new concept, called convergence order. A procedure which guarantees the asymptotic inequalities (within some disk)... 

The problem of classification of defects types for nanotubes is essentially more complicated that the same one for graphite monolayer. Removal only one carbon atom can lead to appearance two different kinds of defects, and it can be created also two different types of defects after removal two neighboring atoms. The appearance of defects is accompanied by local and sometimes global changes of nanotubes geometry. All the computations were performed in the framework of semi-empirical PM3-method [1-2],... 

FIGURE 4 Classification of defects. The ordering increases from top to bottom. With increasing ordering the detection sensitivity of XRD increases as does the deviation from the composition of the thermodynamic phase, until it reaches a local minimum for the ordered subphase shown at the bottom. Catalysts often represent the case of the middle scheme and are difficult to characterize by diffraction or by their compositions. This statement also holds also for many catalyst support materials. 

Table 1 gives a summarized classification of defect solid types in so far as present knowledge will allow, a description of the nature of the possible defects in each type, an example of each class and its characteristic properties. In this table the new symbolic representation discussed in the previous section has been used. 

Written in advance, the test plan defines all test procedures with their pass/fail criteria, expected test results, test tasks, test environment for equipment and computers, criteria for acceptance and release to manufacturing, and the persons responsible for conducting these tests. The test plan also specifies those functions excluded from testing, if any. Individual tasks cover functional testing, simulation of incomplete functions as integration proceeds, mathematical proof of results, records of discrepancies, classification of defects and corrective actions. 

Sampling, inspection and classification of defectives is conducted strictly in accordance to.(the AQLs for this are shown... 

Samples of each batch of the finished products shall be selected on at random basis during packaging, and examined for defects, in accordance with a suitable inspection plan which delineates a classification of defects and an acceptable level. 

Company shall have a Quality Control Laboratory to perform the required testing or it shall employ a commercial laboratory to augment its testing capability or capacity. As a minimum a company laboratory shall be capable of performing in-process controls and examination for Classification of Defects. The laboratory activity will be guided by G.L.P. regulation. 

Topology of Director Fields Homotopy Groups and Classification of Defects... 

The classification of defects in nematics represents a straightforward example of the applications of homotopic group theory [14, 15], The reader is referred to reviews of the subject [19-21, 23, 52]. This topological approach confirms the absence of walls, the existence of Mobius lines, the mutual annihilation of thin threads and the existence of singular points. More importantly, it shows that defects combine and merge according to the rules of multiplication of the two-element Abelian group Z2. 

The same result can be obtained for biaxial nematics [42] from a topological point of view, the classifications of defects in cholesterics and biaxial nematics are identical. Calculation of the fundamental group for iR = SO 2i)/D2 requires knowledge beyond the scope of this chapter. We simply present the result (for details, see [2], [37], [42]) ... 

One should bear in mind that the topological classification of defects in cholesteric and other layered media such as smectics and ordinary crystals is limited by the condition of the layers equidistance. As a result, some transformations between defects that belong to the same class require very high energy barriers comparable to the energy barriers between different classes. Transformation X X within the class Cx represents such an example. 

As already mentioned, the layered structure of cholesteric materials imposes certain limitations on the topological classification of defects based on ho-motopy groups a more general theory is still lacking. In this section we discuss macroscopic defects such as focal conic domains and oily streaks whose existence depends crucially on the layered character of ordering. 

We begin with a not particularly realistic example, a two-dimensional nematic. Here the classification of defects is quite illustrative, and in the one-constant approximation (12.20) a calculation of structures with point defects is simple. The equilibrium condition for a point defect, located at the center of the coordinate system, reads... 

ASTM D2562 - Classification of defects in molded parts. 

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