Extrinsic Point Defects

Previous sections of this chapter have shown that it is possible to introduce defects into a perfect crystal by adding an impurity. Such an addition causes point defects of one sort or another to form, but they no longer occur in complementary pairs. Impurity-induced defects are said to be extrinsic. We have also noted that when assessing what defects have been created in a crystal, it is important to remember that the overall charge on the crystal must always be zero. 

If majority point defect concentrations depend on the activities (chemical potentials) of the components, extrinsic disorder prevails. Since the components k are necessarily involved in the defect formation reactions, nonstoichiometry is the result. In crystals with electrically charged regular SE, compensating electronic defects are produced (or annihilated). As an example, consider the equilibrium between oxygen and appropriate SE s of the transition metal oxide CoO. Since all possible kinds of point defects exist in equilibrium, we may choose any convenient reaction between the component oxygen and the appropriate SE s of CoO (e.g., Eqn. (2.64))... 

When the point defect relaxation is diffusion controlled, we can use Eqn. (5.89) to determine k. After setting rAB = aAX (= unit cell dimension), it is found that at even moderate temperatures (= 100°C), x is on the order of a millisecond or less. This r is many orders of magnitude shorter than relaxation times for nonstoichiometric compounds where the point defect pairs equilibrate at external surfaces (Section 5.3.2). In other words, intrinsic defects equilibrate much faster than extrinsic defects if, during the defect equilibration, the number of lattice sites is conserved. 

Diffusion in ionically bonded solids is more complicated than in metals because site defects are generally electrically charged. Electric neutrality requires that point defects form as neutral complexes of charged site defects. Therefore, diffusion always involves more than one charged species.9 The point-defect population depends sensitively on stoichiometry for example, the high-temperature oxide semiconductors have diffusivities and conductivities that are strongly regulated by the stoichiometry. The introduction of extrinsic aliovalent solute atoms can be used to fix the low-temperature population of point defects. 

Extrinsic Crystal Self-Diffusion. Charged point defects can be induced to form in an ionic solid by the addition of substitutional cations or anions with charges that differ from those in the host crystal. Electrical neutrality demands that each addition results in the formation of defects of opposite charge that can contribute to the diffusivity or electronic conductivity. The addition of aliovalent solute (impurity) atoms to an initially pure ionic solid therefore creates extrinsic defects.10... 

In addition, the structure and properties of point defects at low temperatures and at high temperatures may be different (29). The observation of extrinsic-type dislocation loops in dislocation-free, float-zone Si indicate that self-interstitials must have been present in appreciable concentrations at high temperature during or after crystal growth (30, 31). However, it is unclear whether these self-interstitials were present at thermal equilibrium or were introduced during crystal growth by nonequilibrium processes. 

There are many factors which contribute to dielectric loss and in the case of the complex ceramic compounds discussed above, to achieve a satisfying understanding of the relative magnitudes of the various loss mechanisms is challenging. There will be contributions to loss intrinsic to the idealized structural chemistry of the material and it is now clear that this is complicated by a domain structure. There will also be contributions of an extrinsic nature, particularly those associated with departures from the ideal structure, point defects and... 

Crystallinity, like most things, can vary in degree. Even single crystals typically have intrinsic point defects (e.g. lattice site vacancies) and extrinsic point defects (e.g. impurities), as well as extended defects such as dislocations. Defects are critical to the physical properties of crystals and will be extensively covered in later chapters. What we are referring to here with the degree of crystallinity is not the simple presence of defects, but rather the spectmm of crystallinity that encompasses the entire range from crystalline to fully disordered amorphous solids. Table 1.1 lists the various classes. Let s take each of them in the order shown. 

Defects can be further classified into point defects and extended defects. Unassociated point defects are associated with a single atomic site and are thus zero-dimensional. These include vacancies, interstitials, and impurities, which can be intrinsic or extrinsic in nature. Extended defects are multi-dimensional in space and include dislocations and stacking faults. These tend to be metastable, resulting from materials processing. The mechanical properties of solids are intimately related to the presence and dynamics of extended defects. A discussion of extended defects is deferred until Chapter 10. For now, only point defects are covered. Their importance in influencing the physical and chemical properties of materials cannot be overemphasized. 

Nonequihbrium concentrations of point defects can be introduced by materials processing (e.g. rapid quenching or irradiation treatment), in which case they are classified as extrinsic. Extrinsic defects can also be introduced chemically. Often times, nonstoichiometry results from extrinsic point defects, and its extent may be measmed by the defect concentration. Many transition metal compounds are nonstoichiometric because the transition metal is present in more than one oxidation state. For example, some of the metal ions may be oxidized to a higher valence state. This requires either the introduction of cation vacancies or the creation of anion interstitials in order to maintain charge neutrality. The possibility for mixed-valency is not a prerequisite for nonstoichiometry, however. In the alkah hahdes, extra alkah metal atoms can diffuse into the lattice, giving (5 metal atoms ionize and force an equal number... 

From a thermodynamic stability viewpoint, how are extrinsic point defects and extended defects similar ... 

The absorbing sites have been discussed in terms of the cation-anion couples in low coordination on the surface, but no hypothesis has been made regarding the nature of the emitting sites. The emitting sites could be (i) extrinsic impurities on the surface, e.g., TMIS or organic materials (ii) point defects such as trapped electron or hole centers or (iii) sites identical or similar to the absorbing sites. These possibihties have been considered by Coluccia (13). 

All the extrinsic defects modify the concentration of the intrinsic ones compared to the undoped ceria and therefore they modify the rate of the process. In order to get a quantitative model, the concentrations of point defects in ceria must be theoretically expressed as function of the oxygen partial pressure, the amount of foreign cation and physical constants such as equilibrium constants and diffusion coefficients[7,ll]. In the following, only two equilibrium constants will be considered ... 

Fig. 2 illustrates (he room-temperature photoluminescence (PL) spectra recorded from the as-prepared ZnO colloidal solution and the ZnO nanostructure formed after deposition of the colloid on the silicon substrate. An UV band at 385 nm was detected from all ZnO products. In addition, a broad orange-red photoluminescence band centered at around 620 nm could be also observed in some materials. The UV photoluminescence peak at 385 nm is well known to be related to the exciton emission, ihe mechanism of visible emission is suggested mainly due to the present of various point defects, either extrinsic or intrinsic, which can easily form recombination centers. Photoluminescence measurements show that the deposited ZnO nanostructures have the stronger UV emission than the ZnO nanoparticles in the colloidal solutions. The better UV emission characteristic of deposited ZnO is suggested to be due to the lower defect density and oxygen vacancies in ZnO nanocrystals in the first case. Similar results have also been reported previously [8]. In addition, the aqueous surrounding can change the surface states of ZnO nanocrystals. It is well known that surface states may... 

Intrinsic vacancies are much more numerous in metals. For example, in a 1-cm crystal of aluminum at room temperature there are about 9 billion vacancies. In a crystal of silicon in equilibrium at room temperature there are only about 1 x 10 intrinsic vacancies per cubic centimeter. This is considerably less than typical concentrations of extrinsic point defects (dopants) in silicon—about 0.0001% another fortunate fact. 

Fig. 3.3. Illustration of the main proton transfer mechanisms (a) defect mechanism in a densely packed structure (b) loosely packed structure with a high concentration of mobile species (c) quasi-liquid state with a proton jump contribution In (a) the conductivity is favoured by intrinsic (interstitial rabbits) or extrinsic (impurity elephant) point defects. An orientation defect (hippopotamus in the wrong orientation) can also favour disorder of rabbits (Oj for Zr02 CaO, H for KHSO4) (b) the tree sublattice is a perfectly stable loosely packed structure and a high rabbit disorder can exist without affecting the host lattice (e.g. NH4 in p-AljOj) (c) only the mobile species sublattice is considered here these entities are moving with different speeds in different directions and some are hopping such may be the image of a quasi liquid or surface liquid (V205.nH20, HUP).

Point defects are zero-dimensional (Figure 10.6) and they are the only defects that are thermodynamically stable. Line and plane defects are not thermodynamically stable and do not occur in equilibrium states. Point defects determine the extrinsic physical properties of solids such as electrical conductivity, work function, and color as well as the chemical properties such as dififusivity, stoichiometry, and sinter rate. Some examples of point defects are (a) vacancies, where atoms or ions that should be on lattice sites are missing (b) interstitials which are atoms or ions between the regular lattice sites of a solid (c) foreign atoms or... 

For the limiting case (Cd g) > we find that (VAg) — (CdAg). That is, the vacancy concentration is completely fixed by the addition of CdBr2. This is called the region of exclusively extrinsic disorder, as opposed to the region of intrinsic disorder. In the extrinsic region, those physical properties of the crystal which depend upon the point defect disorder are functions only of the concentration of dopant. However, in deriving eq. (4-26), it has been tacitly assumed that point defects do not form complexes. This assumption, as shown later, must eventually be modified. 

Charged defects in solids can interact with one another in an analogous way to the interactions between ions (or between ions and electrons) in a solution. In the solid-state situation, the crystal may be viewed as a neutral medium into which the charged defects are dissolved. This similarity between solution chemical interactions and defect interactions in the solid state has resulted in the field of defect chemistry, which provides basic methods for studying the effects of point defects in solids. The methods are normally applicable to fairly low defect concentrations. Generally, a broad distinction is made between intrinsic defects that are thermally gena-ated in pure compounds and extrinsic defects produced by external influences such as impurities and gaseous atmospheres. References 2 and 3 provide a detailed discussion of point defects and defect chemistry in metal oxides. 

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