Cu2O, oxygen vacancy

Consider a crystal of CU2O in which the majority of the point defects are capper vacancies. This crystal is placed in 1 atm of air. At constant temperature, the pressure is reduced to 3 torr. Assuming chemical equilibrium, calculate the ratio of copper vacancies at reduced pressure to copper vacancies at atmospheric pressure. You need not consider oxygen vacancies or any interstitials. Becall that in a compound material the ratio of lattice sites must remain fixed. 

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 conductivity of these materials can be controlled by the number of defects. In a /7-type semiconductor such as CU2O, in which vacancies are formed in the cation lattice when the oxygen partial pressure is increased, we can develop relationships between conductivity and oxygen partial pressure. The overall reaction for the formation of vacancies and electron holes can be written in Kroger-Vink notation (cf. Section 1.2.6.1) as... 

It has been shown that at room temperature stoichiometric CU2O will adsorb considerably more oxygen than is needed to form a monolayer (27). Also, the reactivity of the adsorbed oxygen tow ards CO and CO2 decreases with time, which is explained as caused by the penetration of lattice vacancies so far below the surface that reaction is no longer possible. This process can be represented in two stages as follows ... 

B. M. W. Trapnell (Liverpool University) There is some evidence for the formation of localized bonds in chemisorption, rather than of bonds affecting the whole band of the solid. The partial coverage of metals by nitrogen is due to some kind of deficiency of electrons or vacancies in the metal, yet this deficiency must be confined to the surface, as in the band plenty of electrons and vacancies are available. With the oxides, the very small change in conductivity of a CU2O film on oxygen adsorption indicates formation of localized (Cu++0 ) or (Cu++0 ) pairs if band electrons were used, the conductivity change would be enormous. 

Mrowec and Stoldosa and Mrowec et al have investigated the oxidation of Cu to CU2O over a range of temperatures and oxygen partial pressures and their results are shown in Figure 3.12. From this it is clear that the exponent is very close to 1 /4, indicating that neutral cation vacancies are the predominant defect species in CU2O. 

That is, the concentration of cation vacancies is proportional to the eighth root of the partial pressure of oxygen in the case of the above mentioned ideal conditions. Now, in CU2O the transport number of the electronic charge carriers is one, and the diffusion of copper ions via vacancies is rate-determining. Thus, if local defect equilibrium is assumed, it follows from eq. (8-14) that the component diffusion coefficient varies as p l according to the equation ... 

Consider now the system Cu/CujO in oxygen gas at a pressure Px signifies the oxide/oxygen interface in Fig. 1.75). Ignoring space charges, rix the equilibrium concentration of cation vacancies or positive holes at the CU2O/O2 interface, is given by... 

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