Structural vacancies formation

An effect which is frequently encountered in oxide catalysts is that of promoters on the activity. An example of this is the small addition of lithium oxide, Li20 which promotes, or increases, the catalytic activity of the alkaline earth oxide BaO. Although little is known about the exact role of lithium on the surface structure of BaO, it would seem plausible that this effect is due to the introduction of more oxygen vacancies on the surface. This effect is well known in the chemistry of solid oxides. For example, the addition of lithium oxide to nickel oxide, in which a solid solution is formed, causes an increase in the concentration of the major point defect which is the Ni3+ ion. Since the valency of the cation in the alkaline earth oxides can only take the value two the incorporation of lithium oxide in solid solution can only lead to oxygen vacancy formation. Schematic equations for the two processes are... 

The main result of the experimental part of the study, which is shown in Fig. 4, confirms the supposition, which was made in the Introduction above, that one cannot expect formation of structural vacancies in the oxygen sublattice of strontium-alloyed Lai-ySryMnC -s perovskites and, correspondingly, a considerable increase... 

Pala RGS, Metiu H. The structure and energy of oxygen vacancy formation in clean and doped, very thin films of ZnO. J Phys Chem C. 2007 111 12715-22. 

A change originating from the oxygen vacancy is observed in the present theoretical spectra. It is found that the valence fluctuation of Ce possibly caused by the vacancy formation is less effective than the structural change and undistinguishable in the spectra. The local atomic arrangement substantially determines the XANES spectra for Ce02 and CeO] 75. 

M4s(H 2.2, SR 1.84) a = aw.H(l 1 2). The vacancies (non-occupancy positions N) as compared with the Ni2In structure are gN = f/J (5.67.33.25 + 5.33.67.75) while the atom sites are (S.O.O.O + 5.0.0.5) + (5.67.33.75 + 5.33.67.25). The site of the atoms corresponding to As has to be considered as an indication of membership to the NiAs-family. Many members of the NiAs-family contain disordered vacancies, however here we shall consider only structural types with ordered vacancies. According to the mechanism of vacancy formation the non-occupancy increases with increase ofN A. The ordering of the vacancies often lowers the symmetry. The binding is not exactly the same in all members of the NiAs-family. As an example we have aNisb = (3-96 3.96 5.16)A = acu.H(2 2 3/2) = acu.H(2,2,0 - 2,4,0 0,0,5.2 5) this CEC gives a possibility to explain the remarkable fact that in several vacancy variants of NiAs only every second T-atom layer parallel to the basal plane contains vacancies. 

Non-stoichiometric oxides may contain either an excess of metal (e.g. zinc oxide, Zni+jO) or a deficiency of metal (e.g. nickel oxide, Ni,.jO). Some metal oxides (e.g. titanium oxide) may be prepared as either excess-metal or metal-deficit oxides. Excess metal is incorporated in the structure as interstitial cations together with the electrons removed through ionization. In metal-deficit or excess-oxygen oxides, excess oxygen is incorporated in the structure by formation of cation vacancies and positive holes, which may be achieved by oxidation of cations, e.g. 

Defects are incorporated into the halite structure by formation of vacancies on the normal lattice sites. When x = 0.7, there are simply vacancies in the oxide sublattice. When x = 1.25, which can be rewritten by dividing the formula by 1.25 as Ti gO, the vacancies are on the cation sublattice. 

In order to exclude the influence of gaseous phase at this stage, it is essential to take into consideration a simple example (e.g., silicon) as a semiconducting material with vacancies. Assuming that possible defects of the crystal structure are vacancies and electron defects, the processes of intrinsic electronic disordering, vacancy formation, and vacancy ionization can be written, respectively, as ... 

Fig. 7.15. Vacancy formation energies for a series of elements in both the fee and bee structures (adapted from Korzhavyi et al. (1999)).

Using the Morse potential that was fit to the cohesive energy, lattice parameter and bulk modulus of Cu in problem 2 of chap. 4, compute the relaxation energy associated with a vacancy in Cu. In light of this relaxation energy, compute the relaxed vacancy formation energy in Cu and compare it to experimental values. How do the structure and energy of the vacancy depend upon the size of the computational cell ... 

Note that in DRP-structures, the vacancies are unstable as numerical simulation shows [6.35] the property of DRP structures. Because of the difference in LO and elastic deformations, the energies of vacancy formation are different in different sites. Let Ebe the energy of vacancy formation in the jt-type site without the elastic deformations account,- UVfl the correction to the energy of vacancy formation that is due to elastic deformations present, and f Uvli) the distribution function of UVfl values normalized to unity. Then the vacancies concentration in /i-type sites is determined by the relation... 

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