Defect symbolism

Although the results eu e equal as far as utility is concerned, we shedl continue to use our symbolism, for reasons which will become clearer later on. The following Table is a comparison of defect symbolism, as used by prior Authors. Note that our symbolism most resembles that of Kroeger, but not in aU aspects. These prior authors also considered other intrinsic defects that we have not touched, namely interstices and the so-called "anti-structure" occupation. 

The defect symbols can be used in writing quasi-chemical reactions. 

Kroger-Vink Notation for Representing Point Defects in Solids Point Defect Symbol... 

The following compares defect symbolism, as used by prior Authors. Note that our S5ntnbollsm most resembles that of Kroeger, but not in all aspects. 

Fig. 13 a, b. Possible stacking of macromolecular bilayers in the P form crystals of s-PS. The regular succession of bilayers ABAB. .. gives rise to the ordered P" modification (a) defects, corresponding to pairs of bilayers of the kind AA or BB, would characterize the disordered P modification an AA defect is reported in (b). The symbols (/) and ( ) indicate the orientation of the lines connecting the adjacent phenyl rings of each chain inside the macromolecular bilayers A and B, respectively [29]... 

A considerable body of scientific work has been accomplished in the past to define and characterize point defects. One major reason is that sometimes, the energy of a point defect can be calculated. In others, the charge-compensation within the solid becomes apparent. In many cases, if one deliberately adds an Impurity to a compound to modify its physical properties, the charge-compensation, intrinsic to the defect formed, can be predicted. We are now ready to describe these defects in terms of their energy and to present equations describing their equilibria. One way to do this is to use a "Plane-Net". This is simply a two-dimensional representation which uses symbols to replace the spherical images that we used above to represent the atoms (ions) in the structure. 

Having Introduced these examples, let us now examine a method of symbolism useful in characterizing defect reactions in solids. 

Whether you recdize it or not, we have already developed our own symbolism for defects and defect reactions based on the Plane Net. It might be well to compeu e our system to those of other authors, who have also considered the same problem in the past. It was Rees (1930) who wrote the first monograph on defects in solids. Rees used a box to represent the cation vacancy, as did Libowitz (1974). This has certain advantages since we can write equation 3.3.5. as shown in the following ... 

Draw one or more "plane-nets" for the "P" eation eombined with a "U" anion. Indicate all of the possible defects that can appear. Write the symbol of each as you proceed. Include pairs of defects as needed. 

In this book, elastic strain and plastic deformation will be differentiated by both words and symbols. Elastic strain is given the usual symbols e and y for extensional and shear elastic strains, respectively. For plastic shear deformation. 8 will be used, e and 8 are physically different entities, e and y are conservative quantities which store internal energy. 8 is not conservative. The work done to create it is dissipated as heat and structural defects. 

Bile salt export pump (BSEP gene symbol ABCB11) mediates the biliary excretion of nonconjugated bile salts, such as taurocholic acid, glycocholic acid and cholic acid, and therefore is responsible for the formation of the bile acid-dependent bile flow [97, 98]. Its hereditary defect results in the acquisition of PFIC2, a potentially lethal disease which requires liver transplantation [17, 81, 82, 99]. As discussed in Section 12.5.2, the inhibition of BSEP following drug administration may result in cholestasis. 

The flat tire example is pictured using a fault tree logic diagram, shown in Figure 11-12. The circles denote basic events and the rectangles denote intermediate events. The fishlike symbol represents the OR logic function. It means that either of the input events will cause the output state to occur. As shown in Figure 11 -12, the flat tire is caused by either debris on the road or tire failure. Similarly, the tire failure is caused by either a defective tire or a worn tire. 

Turning to pure compounds, such as CaO, MgAl2C>4, or FeS, the same intrinsic defects as described above can occur, but in these cases there is more than one set of atoms that can be affected. For example, in a crystal of formula MX, vacancies might occur on metal atom positions, written VM, or on nonmetal atom positions, given the symbol Vx, or both. Similarly, it is possible to imagine that interstitial metal atoms, written Mi or nonmetal atoms, written X might occur (Fig. 1.3). The different sets of atom types are frequently called a sublattice, so that one might speak of vacancies on the metal sublattice or on the nonmetal sublattice. 

Point defect populations profoundly affect both the physical and chemical properties of materials. In order to describe these consequences a simple and self-consistent set of symbols is required. The most widely employed system is the Kroger-Vink notation. Using this formalism, it is possible to incorporate defect formation into chemical equations and hence use the powerful methods of chemical thermodynamics to treat defect equilibria. 

The position of a defect that has been substituted for another atom in the structure is represented by a subscript that is the chemical symbol of the atom normally found at the site occupied by the defect impurity atom. The impurity is given its normal chemical symbol, and the site occupied is written as a subscript, using the chemical symbol for the atom that normally occupies the site. Thus, an Mg atom on a Ni site in NiO would be written as MgNi. The same nomenclature is used if an atom in a crystal occupies the wrong site. For example, antisite defects in GaN would be written as GaN and NGa. 

The charged defects that most readily come to mind are electrons. In a crystal containing defects, some fraction of the electrons may be free to move through the matrix. These are denoted by the symbol e. The superscript represents the effective negative... 

An effective charge relative to the host lattice is possible with any defect. These are added as superscripts to the appropriate symbol VM, Vx, M , Mx and associated defects such as (VMVX). 

The defect has an effective charge of 1 and it is represented by the symbol Ca a-Not all defects carry effective charges. Frequently, this need not be noted. For instance, suppose that a sodium ion in NaCl, represented by NaNa, is substituted by a potassium ion, represented by KNa. Clearly, the defect will have no effective... 

We use the symbol N2 to denote a configuration of Na defects, that is a particular assignment of the set of N2 defects, all distinguishable, to the lattice sites of the crystal, the latter being all labelled and distinguishable. Although the notation above is rather different from that generally employed in discussions of... 

By adding the symbol 0 (zero) to the described notation, vacant tetrahedral sites can be represented. Examples of formulae of defect tetrahedral structures are ... 

Figure 11.4. Heat of formation and periodic potential energy barriers to defect transport (-A-) divergent boundary conditions (- -) convergent boundary conditions. The filled symbols give the free energy of the stationary states (reprinted with permission from Carbeck and Rutledge. Copyright 1996, American Chemical Society).

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