Normal lattice site

The electrons required to reduce 02 to o - come from individual cations which are thereby oxidized to a higher oxidation state. Alternatively, if suitable interstitial sites are not available, the excess ions can build on to normal lattice sites thereby creating cation vacancies which diffuse into the crystal, e.g. ... 

Extrinsic Defects Extrinsic defects occur when an impurity atom or ion is incorporated into the lattice either by substitution onto the normal lattice site or by insertion into interstitial positions. Where the impurity is aliovalent with the host sublattice, a compensating charge must be found within the lattice to pre-serve elec-troneutality. For example, inclusion of Ca in the NaCl crystal lattice results in the creation of an equal number of cation vacancies. These defects therefore alter the composition of the solid. In many systems the concentration of the dopant ion can vary enormously and can be used to tailor specific properties. These systems are termed solid solutions and are discussed in more detail in Section 25.1.2. 

A somewhat different situation is found in the type of point defect known as a Frenkel defect. In this case, an atom or ion is found in an interstitial position rather than in a normal lattice site as is shown in Figure 7.17. In order to position an atom or ion in an interstitial position, it must be possible for it to be close to other lattice members. This is facilitated when there is some degree of covalence in the bonding as is the case for silver halides and metals. Accordingly, Frenkel defects are the dominant type of defect in these types of solids. 

The notion of point defects in an otherwise perfect crystal dates from the classical papers by Frenkel88 and by Schottky and Wagner.75 86 The perfect lattice is thermodynamically unstable with respect to a lattice in which a certain number of atoms are removed from normal lattice sites to the surface (vacancy disorder) or in which a certain number of atoms are transferred from the surface to interstitial positions inside the crystal (interstitial disorder). These forms of disorder can occur in many elemental solids and compounds. The formation of equal numbers of vacant lattice sites in both M and X sublattices of a compound M0Xft is called Schottky disorder. In compounds in which M and X occupy different sublattices in the perfect crystal there is also the possibility of antistructure disorder in which small numbers of M and X atoms are interchanged. These three sorts of disorder can be combined to give three hybrid types of disorder in crystalline compounds. The most important of these is Frenkel disorder, in which equal numbers of vacancies and interstitials of the same kind of atom are formed in a compound. The possibility of Schottky-antistructure disorder (in which a vacancy is formed by... 

In these equations gv is the change in Gibbs free energy on taking one atom from a normal lattice site to the surface of the crystal and (gt + gv) the change when an atom is taken from a normal lattice site to an interstitial site, both at constant temperature and pressure. cr denotes a site fraction of species r on its sublattice, and is the chemical potential of a normal lattice ion in the defect-free crystal. 

Make a simple estimate of the energy of defect formation in the fluorite structure (a) describe the coordination by nearest neighbours and next-nearest neighbours of an anion both for a normal lattice site and for an interstitial site at the centre of the unit cell shown in Figure 5.3(a). 

In self-diffusion by the vacancy mechanism, a lattice atom moves from a normal lattice site to a vacancy. As shown in Figure 4, the atom must move from the normal lattice site in a to the saddle point position in b to reach the vacancy at c. The energy at the saddle point is greater than that at the equilibrium lattice sites, and the atoms must be sufficiently activated in order to move to b and then to c. The fraction of the lattice atoms activated to the saddle point is related to the Gibbs free energy change between positions a and b. The atom fraction of activated atoms, Xm, is expressed by... 

Figure 4. The sequence a-c shows the movement of the atom from a normal lattice site to an adjacent vacancy. Part d shows the variation of free energy as the atom moves from a to c. (Reproduced with permission from reference 119. Copyright 1981 Academic Press.)...

Protons are retained in the material by combining with oxide ions at normal lattice sites, according to... 

A similar equation holds for the relationship between the number of self-interstitials and the equilibrium constant, Ki. The creation of a self-interstitial on one of N possible interstitial sites leaves a vacancy on one of the N normal lattice sites ... 

Fluorite type oxides are particularly prone to nonstoichio-metric effects. This most commonly occurs in the form of cation nonstoichiometry induced by partial reduction of the cation or by replacement of a portion of the oxide by flnoride. Anion excess phases can occur as a result of cation oxidation or by replacement with higher valence impurities. The dominant defect in this structure involves the migration of oxygen to the large cuboidal interstice resulting in the formation of a vacancy at a normal lattice site. A vacancy of this type is called a Frenkel defect. 

There are two types of lattice defects that occur in all real crystals and at very high concentration in irradiated crystals. These are known as point defects and line defects. Point defects occur as the result of displacements of atoms from their normal lattice sites. The displaced atoms usually occupy sites that are not in the lattice framework they are then known as interstitials. The empty lattice site left behind by the interstitial is called a vacancy. Avacancy produced by displacement of an anion or cation, along with its interstitial ion, is called a Frenkel pair, or simply a... 

High resolution F NMR spectra of samples from the solid solution Caj -xYxF2+x (0.03 < X < 0.32) with a fluorine excess have been acquired by spinning faster than 20 kHz. These F spectra show 4 resonances whose intensities vary with x (Figure 9.9) and correspond to a normal lattice site, a slightly relaxed normal site and 2 distinct interstitial sites (Wang and Grey 1998). The spectra are comparable with that of the... 

The second type of stoichiometric defect involves the movement of an ion on to an interstitial site. An interstitial site is a gap in the lattice, which is not a normal lattice site. The silver halides most commonly possess this type of defect, where the silver cation moves on to the interstitial site. The cation moves into a site in the centre of a cube of cations and anions, as shown in Figure 6.3. 

Defects are incorporated into the halite structure by formation of vacancies on the normal lattice sites. When x = 0.7, there are simply vacancies in the oxide sublattice. When x = 1.25, which can be rewritten by dividing the formula by 1.25 as Ti gO, the vacancies are on the cation sublattice. 

The kick-out mechanism is rather similar to the interstitialcy mechanism. In this case, a host self-interstitial atom diffuses around the lattice. When it reaches a substitutional impurity atom, the self-interstitial pushes the impurity atom into an adjacent interstitial site. The interstitial impurity then diffuses interstitially until it reverts back to a host lattice site by displacing a host atom. It is experimentally difficult to distinguish the kick-out mechanism from the interstitialcy mechanism. The generally accepted view is that the interstitial impurity atoms may tend to diffuse longer distances before returning to the normal lattice sites for the kick-out mechanism, whereas the impurity atoms tend to diffuse interstitially for a relatively short distance before going into the normal lattice sites for the interstitialcy mechanism. 

Fig. 27. Alternative model for hydrogen adsorption on (110) nickel. It is considered less reasonable than that of Fig. 26b. Slight displacements of top layer Ni atoms may perhaps account for the one-half order beams of Fig. 26a. Illustration to scale shows H atoms of diameter 0.74 A bonded to two top layer Ni atoms which have been pulled out of their normal lattice sites along vector displacements marked by the small arrows. View is along close-packed surface direction. Nearest neighbor Ni—Ni bonds joining atoms such as labelled 1 and 2 need to be stretched 8%.

Preservation of regular site ratio the ratio between the numbers of regular cation and anion sites must remain constant and equal to the ratio of the parent lattice.Thus if a normal lattice site of one constituent is created or destroyed, the corresponding number of normal sites of the other constituent must be simultaneously created or destroyed so as to preserve the site ratio of the compound. This requirement recognizes that one cannot create one type of lattice site without the other and indefinitely extend the crystal. For instance, for an MO oxide, if a number of cation lattice sites are created or destroyed, then an equal number of anion lattice sites have to be created or destroyed. Conversely, for an M2O oxide, the ratio must be maintained at 2 1, etc. 

You will note that we have the change in entropy as a function of the differences between normal lattice sites and vacancies. Since we know that Nl Nv, we can write for the entropy of mixing ... 

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