Charged vacancy

Additionally, we can have at least four (4) types of charged vacancies and interstitial sites as given in 3.2.2. (Charged surface sites are not common but are included here for the sake of completeness). This gives rise to 12 more charge defect equations or a total of 42 defect equations that we can write ... 

They are usually joined along the 110 plane of the lattice of the face-centered salt crystal, although we have not shown them this way (The 100 plane is illustrated in the diagram). Note that each vacancy has captured an electron in response to the charge-compensation mechanism which is operative for all defect reactions. In this case, it is the anion which is affected whereas in the "F-center", it was the cation which was affected (see equation 3.2.8. given above). These associated, negatively-charged, vacancies have quite different absorption properties than that of the F-center. 

Note that we have written two defect reactions for the case of vacancy formation in Table 3-2. Pyrophosphate is an insulator and the formation of a positively-charged vacancy is much less likely than the vacancy plus a free positive charge. This brings us to a rule found in defect chemistry that seems to be universal, namely ... 

In this diagram, we have shown both charged ions involved in the migrational diffusion process as well as charged vacancies which also add to the overall diffusion process. We must have electroneutrality in diffusion, i.e.- pairs of defects, and using the above example, we can write nine equations, of which the following is just one case ... 

The above electron trapping process promotes the electron transfer effects, which improves the photocatalytic activity of Eu-TiOz. At the same time, the positively charged vacancies (h+) remaining on the dye molecule can extract electrons from hydroxyl species in solution to produce hydroxyl radicals... 

Equations (1.206) and (1.207) describe the ionization of neutral vacancies (Vx, Vm). We assume here that the ionization of V and Vm to Vx and Vm does not take place. In a crystal in thermal equilibrium, electrons and holes will be formed by thermal excitation of electrons from the valence band to the conduction band, and the reverse process is also possible. This process can be expressed by eqn (1.210) as a chemical reaction, (see eqn (1.136)). Such reactions are called creation-annihilation reactions. Equations (1.208) and (1.209) describe the creation-annihilation reactions of neutral vacancies and charged vacancies in a crystal. Equation (1.211) shows the formation reaction of MX from constituent gases. It is to be noted that of these eight equations two are not independent. For example, the equilibrium constants Ks and K x in eqns (1.209) and (1.211) are expressed in terms of the other Ks as... 

For the case of p < [Vm], viz. K > Ki, the neutrality condition in region (II) is approximated to [Vm] = [Vx] ( n, p). The calculated expressions for each concentration are listed in Table 1.6. In this region under this approximation the concentrations of charged vacancies [Vm] and [Vy] are dominant, which may be expected to induce ionic conduction. When p becomes larger than [V ], we get a new region (III), in which the neutrality condition is approximated to p = [Vm]. 

In deriving Eqns. (4.137) and (4.143) we have assumed that only neutral vacancies are present. Charged vacancies can easily be included if necessary. For each of the individual reaction steps, which were already formulated in Eqn. (4.22) (viz. 

In the absence of an electric field the charged vacancy migrates randomly, and its mobility depends on temperature since this determines the ease with which the Na+ surmounts the energy barrier to movement. Because the crystal is highly ionic in character the barrier is electrostatic in origin, and the ion in its normal lattice position is in an electrostatic potential energy well (Fig. 2.17). 

The removal of an O atom or ion from the MgO surface results in a large relaxation of the lattice. For a neutral Fs center there is an outward displacement of the Mg " ions and an inward movement of the second neighbor O ions by 1-2% with respect to the unrelaxed surface. The effect is much more pronounced for charged vacancies, and changes of 5% and 10% in the Mg-0 distances around the cavity are found for Fs and Fj centers, respectively [39]. In the F or F centers one or two electrons are associated with the defect. The extra electron(s) can either be delocalized over the 3s levels of the Mg " ions around the cavity, with partial reduction of these ions and a change of their charged state from Mg to Mg, or can be localized in the vacancy center. 

V l/ ) or (VpbVci/ indicates a charged vacancy pair in PbCl2. 

The concentration of charged vacancies is governed by Fermi-Dirac statistics and is given (using V as an example) by... 

The argument for charged vacancies is analogous. Thus the square root dependence of the composition upon pressure offers no definite information about the charge on the defects. 

Electron spin resonance reveals the unpaired electrons associated with impurities or structural defects and can be used to identify the lattice site positions of these features. Nitrogen is shown to substitute for carbon and acts as a shallow donor. The various ESR triplets due to nitrogen in several SiC polytypes give information on the lattice sites occupied. For the acceptor boron, ESR shows it to occupy Si sites only, in disagreement with DAP photoluminescence measurements which show only boron on carbon sites. It may be that boron substitutes on both sites and the two techniques have sensitivity for only one particular lattice site. The aluminium acceptor is not observed in ESR but gallium has been noted in one report. Transition metals, Ti and V, have been identified by ESR both isolated on Si sites and in Ti-N complexes. Several charged vacancy defects have been assigned from ESR spectra in irradiated samples. 

Our study has led us to the point where we can realize that the primary effect of impurities in a solid is the formation of defects, particularly the Frenkel and Schottky types of associated defects. Thus, the primary effect obtained in purifying a solid is the minimization of defects. Impurities, particularly those of differing valences than those of the lattice, cause charged vacancies and/or interstitials. We can also increase the reactivity of a solid to a certain extent by making it more of a defect crystal by the addition of selected impurities. 

One would expect that equal amounts of each specie would diffuse in opposite directions, thus preserving electroneutrality. While this is true for the reaction in 3.1.68., i.e. - m2+ => <= 5Q=, what of the case for BaSiOs where diffusion is limited to one direction It is not reasonable that the solid should build up a charge as the m2+ ions are diffusing and we must search for compensating species elsewhere. It turns out that charge compensation occurs by diffusion of charged vacancies. 

Note that the charged vacancy diffuses as one of the reacting species to form the defect compound. This situation is quite common in the solid state chemistry of compounds containing multivalent cations. The trivalent Nl3+ also gives rise to anew compound, NiAlOs. Yet the same... 

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