Cations vacancies

Copper(I) oxide [1317-39-1] is 2lp-ty e semiconductor, Cu2 0, in which proper vacancies act as acceptors to create electron holes that conduct within a narrow band in the Cu i7-orbitals. Nickel monoxide [1313-99-17, NiO, forms a deficient semiconductor in which vacancies occur in cation sites similar to those for cuprous oxide. For each cation vacancy two electron holes must be formed, the latter assumed to be associated with regular cations ([Ni " h = Semiconduction results from the transfer of positive charges from cation to cation through the lattice. Conduction of this type is similar... 

The addition of a small amount of cluomium at concentrations less than 1 %, increase the oxidation rate proportionately to the cluomium content. This is to be expected since the replacement of tluee nickel ions in NiO by two chromium ions in Ci 203 will introduce one cation vacancy/CiaOs molecule. 

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. ... 

If n is the concentration of defects (cation vacancies or positive holes) at equilibrium, then, applying the law of mass action to equation 1.157... 

Motion of a cation vacancy Fig. 1.73 Motion of positive holes and cation vacancies... 

Finally we notice that in the p-type oxides CU2O and NiO, the presence of excess oxygen actually provides, through the formation of cation vacancies, a transport mechanism for the metal, while in an /i-type oxide like TiOi, the excess metal, by forming anion vacancies, provides a transport mechanism for oxygen. With /i-type oxides like ZnO and AljO, where the excess metal is accommodated interstitially, a transport mechanism is, of course, provided for the excess component itself. 

The electrical conductivity is proportional to n. Equation 1.168 therefore predicts an electrical conductivity varying as p. Experimental results show proportionality to p and this discrepancy is probably due to incomplete disorder of cation vacancies and positive holes. An effect of this sort (deviation from ideal thermodynamic behaviour) is not allowed for in the simple mass action formula of equation 1.167. 

Consider now the system Cu/CujO in oxygen gas at a pressure p (X signifies the oxide/oxygen interface in Fig. 1.75). Ignoring space charges, x the equilibrium concentration of cation vacancies or positive holes at the CujO/Oj interface, is given by... 

For definiteness, the oxidation of copper to copper(l) oxide may be considered. Our picture of the process is that cation vacancies and positive holes formed at the Cu O/Oj interface by equation, 1.166 are transported to the Cu/CujO interface where they are destroyed by copper dissolving in the non-stoichiometric oxide. We require an expression for the rate of oxidation. 

We denote by x the distance from the metal surface, and by n x) and rip x) the concentrations of cation vancancies and positive holes in the oxide. Let and Vp be their mobilities, and and Dp their diffusion coefficients. Let F x) be the electrostatic field in the oxide. J, the flux of cation vacancies (number crossing unit area per second), will be expressed by... 

The negative sign means that cation vacancies and positive holes move inwards, i.e. in the negative direction of x. For CujO, the positive holes are much more mobile than the cation vacancies, and we can assume that ripVp The oxidation flux is then... 

This equation can be obtained in another way which may be more instructive. Assume that the slow step in the oxidation is the transport of cation vacancies. The positive holes may then be considered to take up their equilibrium distribution, defined by Boltzmann s equation... 

Our picture of the transport process in these thick oxide layers is that there is a uniform concentration gradient of defects (cation vacancies and positive holes) across the layer. But it is important to notice that the oxidation flux is exactly twice that to be expected if diffusion alone were responsible for the transport of cation vacancies. The reason for this is, of course, that the more mobile positive holes set up an electric field which assists the transport of the slower-moving cation vacancies. 

An important aspect of any theory of the oxidation of a pure metal is that it enables us to see how the protective power of the oxide layer can be altered by the introduction of alloying constituents into the metal. According to Wagner s theory, the parabolic rate constant for the system Ni/NiO for example depends upon the concentration of cation vacancies in the oxide in equilibrium with oxygen gas. If this concentration can be reduced, the oxidation rate is reduced. Now this can be done if cations of lower valency than Ni can be got into the oxide (Fig. 1.77). Suppose, for example, that a little Li is added to the Ni. Each Li ion which replaces Ni is a negative... 

Consider Ni exposed to Oj/HjO vapour mixtures. Possible oxidation products are NiO and Ni (OH)2, but the large molar volume of Ni (OH)2, (24 cm compared with that of Ni, 6.6 cm ) means that the hydroxide is not likely to form as a continuous film. From thermodynamic data, Ni (OH)2 is the stable species in pure water vapour, and in all Oj/HjO vapour mixtures in which O2 is present in measurable quantities, and certainly if the partial pressure of O2 is greater than the dissociation pressure of NiO. But the actual reaction product is determined by kinetics, not by thermodynamics, and because the mechanism of hydroxide formation is more complex than oxide formation, Ni (OH)2 is only expected to form in the later stages of the oxidation at the NiO/gas interface. As it does so, cation vacancies are formed in the oxide according to... 

The De Wolff disorder model has been extended to the cation vacancy model for /-Mn02 and -Mn02 by Ruetschi [42]. In this model the occurrence of manganese cation vacancies and the non stoichiometry of electrochemical Mn02 have been taken into account. Furthermore, the vacancy model deals with the explanation of the different water contents of manganese dioxide. Ruetschi makes some simple assumptions ... 

The high reactivity of the active form of Ag2C03 is attributed to the retention of water, incorporated during preparation, in the form of the ions HCOj and OH", with corresponding cation vacancies (VAg+), viz. 

Such defects facilitate movement of C02 within the crystal by transfer from HCOj to OH" and of Ag+ in the cation vacancies. This interpretation is supported [758,759] by the observed increase in reactivity resulting from doping of Ag2C03 with Cd2+, Y3+ or Gd3+, where incorporation of the additive is accompanied by the creation of cation vacancies. 

Macdonald et al.25 28 maintained that the adsorption of chloride ions enhances the formation of cation vacancies of metal ions and their transfer... 

Fig. 8.6 Crystal structures of -Ca3(BN2)2 (s) snd -Sr3(BN2)2 (b). Squares indicate cation vacancies. The related cubic cell of a-Ca3(BN2)2 is highlighted in the structure ofy -Ca3(BN2)2-...

These studies show that the thiospinel structure is quite flexible with opportunity for cation vacancies at the 8 a site. Our investigation on such cation-deficient thiospinels is significant in that it shows that additional vacancies are possible in the 8 a site. Most of the cation-deficient compounds known earlier (predominantly copper compounds) were obtained by extraction of Cu by using various oxidizing reagents. These studies show that such cation-deficient quaternary thiospinels can also be obtained by direct solid-state reactions. 

Frenkel defects (Cation vacancy plus same cation as interstitial)... 

Note that, in general, anions are larger in size than cations due to the extra electrons present in the former. A hexagonal lattice is shown in 3.1.6. with both Frenkel and Schottky defects, as well as substitutional defects. Thus, if a cation is missing (cation vacancy) in the cation sublattice, a like anion will be missing in the anion sub-lattice. This is known as a Schottky defect (after the first investigator to note its existence). 

---