Charged interstitials

One should note that when a charged-interstitial is present in one sublattice, the other sub-lattice will contain either a like-cheirged interstitial or a llke-chcirged substitutional ion which exactly balances the total charge present in the lattice. Such equations might include one or both of the following equations ... 

Calculations are now carried out routinely using a wide variety of programs, many of which are freely available. In particular, the charge on a defect can be included so that the formation energies, interactions, and relative importance of two defects such as a charged interstitial as against a neutral interstitial are now accessible. Similarly, computation is not restricted to intrinsic defects, and the energy of formation of... 

On the other hand, oxygen diffusion measurements, by use of as a tracer, indicate that singly charged interstitials, O, are the dominant defects of anions. (Anion defects Of are considered as minority defects compared to the cation defects.) The formation of Of is described by the chemical reaction... 

Consider an ionic material that contains a dilute concentration of positively charged ions that diffuse interstitially (interstitial diffusion is described in Section 8.1.4). D is the interdiffusivity of these ions in the absence of any field. As shown in Sections 2.2.2 and 2.2.3, if an electric field, E = —V, is applied, the diffusion potential will be the electrochemical potential given by Eq. 2.41. According to Eq. 2.21, the flux of charged interstitials is... 

The relationship between the intrinsic diffusivity, D, of charged interstitial ions in an ionic solid and the ionic electrical conductivity, p, due to the motion of these ions in the absence of a significant concentration gradient is given by Eq. 3.50 that is,... 

Solution. In this case, the charged cation vacancies, possessing a diffusivity Z v tlon, will respond to the voltage just as the charged interstitials did in Section 3.2.1. The relationship between tIon and p will then be given by the same type of relation as Eq. 3.50 that is,... 

Figure 10.2 Calculated local environment surrounding a doubly charged interstitial in La2Cu04. The calculated interionic separations are La-O 2.3 A, 0-0 2.7 A.

Clearly each mechanism predicts a different dependence of defect concentration on oxygen partial pressure. Since the electrical conductivity depends on the concentration of conduction-band electrons, measurement of electrical conductivity as a function of oxygen partial pressure should serve to define the dependence law and indicate which defect is predominant. Initial experiments of this type carried out between 500 and 700 indicated that the conductivity varied with oxygen partial pressure having exponents between 1/4.5 and 1 /5. This indicates that neither defect mechanism predominates, and the actual structure could involve both singly and doubly charged interstitial cations. ... 

Figure 4.4 Variation of concentration of singly or doubly charged interstitial zinc ions across a ZnO scale for high and low oxygen partial pressures.

The structures within the homologous series Gdj + 2 2n + 3 C have been described in sect. 2 as a ccp arrangement of X and C atoms with Gd atoms in of the octahedral holes, i.e. as ordered defect derivatives of rock salt. That closed-shell situations do not always maximize stability is excellently demonstrated for the w = 1 and n = 2 members of the series because removal of one Gd atom per formula unit would produce closed-shell compounds in each case, Gd3X5C and Gd5X7C2 . Both metal-metal bonding interactions introduced by the three conduction electrons as well as the requirements of the highly charged interstitial atom to have a spherical shell of... 

The point defect chemistry of ZnO is different partly because there are two charge states of Zn, namely 2+ (as in ZnO) and 1+. When we heat ZnO in Zn vapor, we form a Zn-rich oxide, Zni+jf). Experimentally it is found that the excess Zn sits on interstitial sites (as you would expect from the crystal structure). We can write the basic defect equation for the singly charged interstitial as... 

In this case a particle A moves from an A lattice site to an interstitial site whereby, for example, with respect to the unperturbed lattice a single positively charged interstitial particle Aj is formed, a vacancy Vi in the interstitial lattice is destroyed, and a negatively charged vacancy V on an A site is left. This exchange process can be written in the form of a chemical reaction, a so-called disorder reaction... 

The neutral interstitial Mi atoms may be successively ionised to singly, doubly, triply or quadraply charged interstitial ions, e.g. 

Consider an oxide with a stoichiometric composition MO2. Let us further assume for the sake of illustration that when the oxide is nonstoichiometric the important point defects are doubly charged oxygen vacancies and doubly charged interstitial metal ions. (It mat be noted that the metal interstitials are not fully ionised in this case.) The composition of the nonstoichiometric oxide may accordingly be written Mi+y02-x-... 

Figure 3-3. Schematic presentation defect concentrations as a function of oxygen pressure in an oxide MO2 containing both doubly charged oxygen vacancies and doubly charged interstitial metal ions, compensated by electrons.

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