Vacancy compensation

The compound LisZn2Ge3 can be expressed as SLi , 2Zn, SGe in terms of oxidation numbers, or as 8 Li , 2 Zn, 3 Ge with regard to the Zintl-Klemm concept and valence considerations. It closely relates to Li5AlSi2 and the corresponding [Li3Al3Si 5] hexagonal layer in which Zn and Ge would play the role of A1 and Si. With the Zn vacancy compensated by a Hthium dumbbell, the [Li4ZrL4Gei5] anionic network is isoelectronic. 

At greater degrees of reduction, all of the Pr ions are in the trivalent state, and the oxide is in essence an acceptor-doped oxide with oxygen vacancy compensation. Any further reduction must then be accomplished by the transformation of Ce4+ to Ce3+, repeating the previous cycle ... 

The charge compensation is provided by a Ca2+ vacancy which serves to compensate two Eu2+ ions. There are different arrangements for the Eu3+ and the Ca2+ vacancy as illustrated in the figure. The cubic site has the Ca2+ vacancy compensation so distant that the local symmetry of the Eu2+ is not perturbed. The tetragonal site has the vacancy in the nearest neighbor position. The dimer sites have the vacancy in the nearest neighbor positions for two symmetrically located Eu2+ ions. Each of these different Eu2+ sites has different crystal field splittings and spectra. 

There is an equilibrium between the different sites that determines the observed distribution. For example, the ratio of the sites with the cation vacancy nearby to those with the vacancy distant will depend upon the concentration of vacancies by the law of mass action. One can write the conventional equilibrium relationships given by mass action considerations for equilibria between vacancies and probe ion sites with local and distant vacancy compensation. The equilibrium constant will depend on the temperature under which the equilibrium was established. Since all of the sites can be observed by site selective laser spectroscopy, one can measure the equilibrium distributions directly. We find that the sites and their distributions are described excellently by the mass action relationships of conventional equilibria. This work is described in more detail elsewhere (5,6). 

Consider first an oxygen vacancy. Its effective charge of2e can be neutralized by a cation vacancy with an effective charge — 2e an example of such vacancy compensation is an associated Schottky pair. Alternatively, an oxygen vacancy might be electron-compensated by being associated with two electrons. Similarly a... 

Na6Al32VAi051, respectively. This suggests that compared to //-alumina the fi" modification contains an aluminium vacancy compensated by three extra sodium ions in the conduction plane. The consequent higher conductivity of the ft" modification makes it favoured for battery electrolytes. The conductivity of polycrystalline //-alumina at 350 °C (the temperature appropriate to battery operation) is about 5Sm-1 and for polycrystalline //"-alumina about 50 8 m-1. 

Thus the lanthanum dopant is vacancy compensated and no electronic charge carriers are generated. As shown in Fig. 6.10, La substitution results in a marked increase in the resistivity of PZT. 

Empirical calculations carried out for cations show that vacancy compensation is clearly the preferred route, at least for large dopant cations (radius >0.8A). 

Empirical calculations carried out for cations show that vacancy compensation is clearly the preferred route, at least for large dopant cations (radius >0.8A). Formation of interstitials is also ruled out by measurements of true density and comparison with calculated values . For the smaller cations (i.e. Al ), some compensation via dopant interstitial may occur. The reactions described in Eq. 2.18 and 2.21 (for a divalent cation) therefore summarise the main route to defect formation in solid solutions of the type Ce. jMj02,o.5x and Ce, xMx02.x respectively. 

At high PO2, the compensation mechanism switches from electronic to cation vacancy compensation (or self compensation), where the donor charge is compensated by the formation of Sr vacancies [98, 99]. This is accompanied by the formation of a secondary Sr-rich phase. The nature of this phase is not fully determined and is suggested to be either an Sr +i Ti 03 +i phase within the matrix [100] or a separate SrO phase [101]. A separate phase is denoted below simply for clarity ... 

The examples in the previous section show the effects of additions of higher and lower valent oxide to the p-conducting, metal-deficient Mi-yO. Let us also briefly consider the effects of doping an oxygen-deficient oxide MO2-X with higher and lower valent oxides, respectively. The predominating defects in MO2-X are oxygen vacancies compensated by defect electrons. The oxide it thus an n-type electronic conductor. 

We now apply our derived expression for the example case of an oxygen-deficient oxide MOi-x. This contains oxygen vacancies compensated by electrons, and we have earlier shown that the defect concentrations are given by n = 2[Vq ] = 4K. ) Po[ - Since the mobility of... 

As regards electronic structure, Ti02 is an n-type semiconductor and has a small amount of oxygen vacancies compensated by the presence of Ti centers. 

One of the most important features of these materials is that the compensation of the acceptor does not change abruptly from electronic to vacancy compensation, but there is an extensive region in which the compensation is mixed. Here the material is hypostoichiometric 5 now becomes negative and lies between 0 and x/2, where x is the concentration of the acceptor (R III). 

Next there is a region (RIV) where the material is vacancy compensated and... 

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