Vacancy definition

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. 

In the region of superconducting compositions in BaPbx.x-B Og, oxygen vacancies have been found to decrease Tc (46)(47). This has definite implications for preparation of high Tc material, but also indicates that the Te may be tuned to any desired transition temperature below the maximum Tc by careful technological treatments. 

Figure 5.1 Point defects in ionic solids Schottky defect, vacancy pair, Frenkel defect and aliovalent impurity (for definitions see Section 5.2).

Dowden (27) considers the active centers for carbonium ion formation to be associated with surface cation vacancies. A proton, derived from water contained in the catalyst, is attracted to the anions surrounding the vacancy. A hydrocarbon molecule is assumed to be held by polarization forces above this lattice defect and the proton will be distributed between the hydrocarbon and the anions, forming a carbonium ion of a definite lifetime. 

From the definition of p and pg, we obtain the following relationship vacancy-ordered structure pg > vacancy-disordered structure p = Pb... 

Since the ratio of number of anions to cations in a unit cell for the Fluorite structure is 1 to 2, the compound Zro.gsCao isOj 5 can be said to be non-stoichiometric. The possible defect types are anion vacancies or interstitial cations. X-ray diffraction studies have definitely confirmed that the former type of defect structure is dominant therefore, there exist oxygen vacancies up to 7.5 per cent. The concentration of oxygen vacancies must depend on Po., as is usual for the metal oxides. 

Fig. 1.73 Basic model structure for the definition of vacancy-ordered structures in the MX-MX2 system." ...

With the introduction of the lattice structure and electroneutrality condition, one has to define two elementary SE units which do not refer to chemical species. These elementary units are l) the empty lattice site (vacancy) and 2) the elementary electrical charge. Both are definite (statistical) entities of their own in the lattice reference system and have to be taken into account in constructing the partition function of the crystal. Structure elements do not exist outside the crystal and thus do not have real chemical potentials. For example, vacancies do not possess a vapor pressure. Nevertheless, vacancies and other SE s of a crystal can, in principle, be seen , for example, as color centers through spectroscopic observations or otherwise. The electrical charges can be detected by electrical conductivity. 

The results of the discussion on the phenomenological thermodynamics of crystals can be summarized as follows. One can define chemical potentials, /jk, for components k (Eqn. (2.4)), for building units (Eqn. (2.11)), and for structure elements (Eqn, (2.31)). The lattice construction requires the introduction of structural units , which are the vacancies V,. Electroneutrality in a crystal composed of charged SE s requires the introduction of the electrical unit, e. The composition of an n component crystal is fixed by n- 1) independent mole fractions, Nk, of chemical components. (n-1) is also the number of conditions for the definition of the component potentials juk, as seen from Eqn. (2.4). For building units, we have (n — 1) independent composition variables and n-(K- 1) equilibria between sublattices x, so that the number of conditions is n-K-1, as required by the definition of the building element potential uk(Xy For structure elements, the actual number of constraints is larger than the number of constraints required by Eqn. (2.18), which defines nk(x.y This circumstance is responsible for the introduction of the concept of virtual chemical potentials of SE s. 

Let us now discuss some details of practical relevance. From the Gibbs phase rule, it is evident that crystals consisting of only one component (A) become nonvariant by the predetermination of two thermodynamic variables, which for practical reasons are chosen to be Pand T. In these one-component systems, it is easy to recognize the (isobanc) concentration dependence of the point defects on temperature. From the definition of the vacancy chemical potential for sufficiently small vacancy mole fractions Nv, namely //v = /A (P, T) + RT- In Vv, together with the condition of equilibrium with the crystal s inerL surroundings (gas, vacuum), one directly finds... 

Figure 2-5. Relative defect (vacancy) fraction as a function of alloy composition rVB (see Eqn. (2.78)), if defects interact differently with nearest neighbors A and B. (I) Ah = 0 (2) Ah — 0.6 R T (for definition of Ah see text).

Chemical diffusion has been treated phenomenologically in this section. Later, we shall discuss how chemical diffusion coefficients are related to the atomic mobilities of crystal components. However, by introducing the crystal lattice, we already abandon the strict thermodynamic basis of a formal treatment. This can be seen as follows. In the interdiffusion zone of a binary (A, B) crystal having a single sublattice, chemical diffusion proceeds via vacancies, V. The local site conservation condition requires that /a+/b+7v = 0- From the definition of the fluxes in the lattice (L), we have... 

This fraction is determined by the step-dance between a specified vacancy and the (tagged) atom during their encounter, which does not end before the atom-vacancy pair has definitely separated. Normally, a new and independently moving vacancy comes along much later and begins the next encounter with the tagged atom. 

Specific kinetic effect. This would apply to the sulfided monolayer catalyst. Cobalt may affect adsorption-desorption properties or intrinsic activity of vacancies. No definitive data exist to support this proposal. 

The two species in the binary solution are designated as B and A. B is the adsorbate molecule and A is the absence of an adsorbed molecule at a particular adsorption site on the zeolite surface, called a "vacancy". Because of its definition, A is equal in size to the B species molecule. As the gas pressure above the zeolite (i.e., Pg) goes to larger values (Pg" Pg0) the solution composition within the cavity goes toward a pure solution of adsorbed gas (X--+1). As the gas pressure above the zeolite goes to smaller values (i.e., VpJ V Q)> the amount of adsorption becomes less (Xg-K)) and the solution composition within the cavity goes toward a pure solution of vacancies (X -+l). This choice of solution species has the proper asymptotic nature. 

---