Structure site vacancies

The smallest imperfections in metal crystals are point defects, in particular vacant lattice sites (vacancies) and interstitial atoms. As illustrated in Fig. 20.21a, a vacancy occurs where an atom is missing from the crystal structure... 

Therefore, the data indicate that Co-Mo-S can be considered as a M0S2 structure with Co atoms located in edge positions. As discussed below, these Co atoms play a direct role in the catalysis. Furthermore, it is generally accepted that the HDS reaction involves adsorption on sulfur vacancies. The low sulfur coordination number (large coordinative unsaturation) estimated from the Co EXAFS may, in fact, reflect that active sites (vacancies) are associated with the Co atoms. 

The diffusion coefficient for a given ion in a crystal is determined, as we have seen, by the atomistic properties of the ion in the structural sites where the vacancy (or interstitial) participating in the migration process is created (see eq. 4.71). The units of diffusion (and/or self-diffusion ) are usually cm sec . Pick s first law relates the diffusion of a given ion A (Jf) to the concentration gradient along a given direction X ... 

Fig. 2. Triangular plot of Ca, Na, and A-site vacancies in pyrochlore from Vishnevogorskii calculated from structural formulae normalized to two B-site cations. Compositions of primary pyrochlore plot near the Ca-Na join (solid symbols). Compositions of the altered areas move toward the Ca-vacancy join, then along this join toward the top of the triangle.

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. 

Ba6B2W30i8 (hhcccc)3 18H. Structure consists (Bm=Gd-Lu, Y) of three octahedra sharing faces which alternate with three octahedra sharingcorners. B-site vacancy is ordered at the central octahedral site of the face-sharing groups of octahedra. 34... 

Ba8Re2W3024 (hhhhchhc)3 24H. Structure consists of groups of three and five face-shared octahedra which are linked through corners (Fig. 4e). B-site vacancy is ordered in alternate face-shared octahedral sites. 35... 

Defects in perovskite oxides can be due to cation vacancies (A or B site), amon vacancies or anion excess. Cation-deficient oxides such as A,WOj give rise to oxide bronze structures, W03 itself representing the limiting case of the A-sile deficient oxide A-site vacancies are seldom ordered in these metallic systems. B-site vacancies are favoured in hexagonal perovskites and ordering of these vacancies gives rise to superstructures in some of the oxides. 

Schottky defects occur when sites that are normally occupied by atoms or ions are left vacant. In order that the crystal structure maintain its electrical neutrality, for every cation-site vacancy there must be an anion-site vacancy. At room temperatures, one in 10 sites is typically vacant, but this adds up to 10 Schottky defects in a 1 mg crystal. A less commonly observed defect is a Frenkel defect, in which an atom or ion is displaced from its site to an interstitial site that is normally unoccupied. In so doing the number of nearest neighbors of one component of the crystal is changed. This type of defect is seen in... 

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... 

First approaches to the quantitative understanding of defects in stoichiometric crystals were published in the early years of the last century by Frenkel in Russia and Schottky in Germany. These workers described the statistical thermodynamics of solids in terms of the atomic occupancies of the various crystallographic sites available in the structure. Two noninteracting defect types were envisaged. Interstitial defects consisted of atoms that had been displaced from their correct positions into normally unoccupied positions, namely, interstitial sites. Vacancies were positions that should have been occupied but were not. 

It seems that the lattice oxygen plays a direct role in the oxidation of CO. Indeed, it was found that the catalytic activity is maximum, if the bond energy of the lattice oxygen is minimum [3], Hence, the oxygen vacancy is also an important factor for the catalytic activity. The partial substitution of the A element can monitor the oxygen vacancy. If Ce(IV) is introduced in the perovskite structure A site vacancies are produced [4]. The partial substitution of B element by R (IV) increases greatly the CO oxidation activity of Lao.TPbo.sMnOs perovskite [5]. 

Fig. 2. Stabilised cubic structure of oxide electrolyte, showing a substituting cation and compensating anion site vacancy.

WO, and ReO, may be regarded as the limiting cases of A-site vacancy perovskites. Both the oxides possess corner-linked framework of the octahedra, but unlike ReO, WO3 is never cubic. It shows several polymorphic transitions starting from the low temperature triclinic structure to more symmetric forms with increasing temperature. The transitions arise from temperature-dependent displacements of the tungsten atom from the centre of the WOg octahedron, ... 

Table 1—Hexagonal Perovskite Oxides Exhibiting B-Site Vacancy-ordering Structural details...

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