Vacancies empty sites

Reviewing the tracer studies on the mechanism of catal3dic hydrodesulfu-risation, it can be concluded that at this time, a general mechanism for these reaction cannot be given. Possibly, it does not exist at all. It is well seen, however, that sulfur-catalyst interaction influences the catalysts behaviour substantially the activity, to a large extent, depends on the Smob/Sirr correlation, S-uptake affects the number of vacancies and consequently the value of the vacancy empty sites ratio. It was seen that H2S treatment affects the catalyst selectivity. There are a number of examples on this, mostly for HDS/hydrogenation selectivity ratio, not referred here. 

Figure B3.2.10. Contour plot of the electron density obtained by an orbital-free Hohenberg-Kolnr teclmique [98], The figure shows a vacancy in bulk aluminium in a 256-site cell containing 255 A1 atoms and one empty site, the vacancy. Dark areas represent low electron density and light areas represent high electron density. A Kolm-Sham calculation for a cell of this size would be prohibitively expensive. Calculations on smaller cell sizes using both techniques yielded densities that were practically identical.

Diffusion and migration in solid crystalline electrolytes depend on the presence of defects in the crystal lattice (Fig. 2.16). Frenkel defects originate from some ions leaving the regular lattice positions and coming to interstitial positions. In this way empty sites (holes or vacancies) are formed, somewhat analogous to the holes appearing in the band theory of electronic conductors (see Section 2.4.1). 

As already illustrated, it is also possible to imagine a defect related to ions in interstices, that is, interstitials. Such defects were first suggested as being of importance by Frenkel and are known as Frenkel defects. In this case, an atom or ion from one sublattice moves to a normally empty site (an interstitial site) in the crystal, leaving a vacancy behind (Fig. IA5b). A Frenkel defect may involve either the... 

To obtain a solid with a high conductivity, it is clearly important that a large concentration, c, of mobile ions is present in the crystal [Eq. (6.1)]. This entails that a large number of empty sites are available, so that an ion jump is always possible. In addition, a low enthalpy of migration is required, which is to say that there is a low-energy barrier between sites and ions do not have to squeeze through bottlenecks. Hence the structure should ideally have open channels and a high population of vacancy defects. 

Particle irradiation effects in halides and especially in alkali halides have been intensively studied. One reason is that salt mines can be used to store radioactive waste. Alkali halides in thermal equilibrium are Schottky-type disordered materials. Defects in NaCl which form under electron bombardment at low temperature are neutral anion vacancies (Vx) and a corresponding number of anion interstitials (Xf). Even at liquid nitrogen temperature, these primary radiation defects are still somewhat mobile. Thus, they can either recombine (Xf+Vx = Xx) or form clusters. First, clusters will form according to /i-Xf = X j. Also, Xf and Xf j may be trapped at impurities. Later, vacancies will cluster as well. If X is trapped by a vacancy pair [VA Vx] (which is, in other words, an empty site of a lattice molecule, i.e., the smallest possible pore ) we have the smallest possible halogen molecule bubble . Further clustering of these defects may lead to dislocation loops. In contrast, aggregates of only anion vacancies are equivalent to small metal colloid particles. 

The BLW method can be considered as an extension of the orbital deletion procedure (ODP) (51,52), a simpler method that can only be applied to carbocations (52) and boranes (51). The ODP consists of representing a resonance structure displaying an electronic vacancy (Lewis acid character) by deleting the primitive basis functions corresponding to the empty site before launching the SCF calculation. As a typical example, the ODP has been applied to calculate the resonance energy of the allyl cation (52). 

Vacancies Vacancies (empty atom sites) are indicated by the symbols Vm and Vx for metal, M, and nonmetal, X, sites respectively. Where confusion may occur with the atom vanadium, the symbol for a vacancy is written Va. Vacancies are created by the removal of neutral atoms from the crystal. This rule also applies to ionic solids. For example, in ionic NiO, Vxi would imply the removal of a Ni + cation together with two electrons, that is, a neutral Ni atom. Similarly, Vo... 

The distribution of the Ce dopant is not uniform. Of the three cation sites in the parent compound, the first two are fully occupied by Bi atoms, while the third is empty. This results in a sequence of cation occupation on the [010] face as shown below in A and B. Site a is 92% Bi, 4% Ce, site b is 88% Bi, 12% Ce, and site c, normally vacant, is 4% Ce occupied. Examination of the oxide environment about site c indicates that there is insufficient room for a Ce cation. Occupation of the site must therefore result in some local disorder, the most likely manifestation thereof being a vacancy in site a (the distance between sites a and c are too short to allow simultaneous occupation). Note also that site a is not 100% occupied. Consequently, about 96% of the time the distribution of cations (Bi/Ce) in Bi, gCe 2 3 12... 

A further point of great interest that emerges from the work of Curtis and from the mechanism depicted in Fig. 4.14 is the concept of latent vacancies and sulfur mobility . This can be related to some recent important considerations on the existence of real anionic vacancies on Co-Mo-S surfaces, a frequently encountered key feature of HDS mechanisms. Tlie Co atom, which is known to be the primary site of attack of thiols in this case, is electronically saturated, but the empty site required for... 

A similar situation arises in recently reported DFT calculations by Byskov et al. [70, 71] that show that if vacancies are introduced in a large cluster model of a MoSj surface by removing sulfur atoms, and relaxation is allowed taking into account several layers of the solid, a spontaneous surface reconstmction process takes place through migration of sulfide ions from the bulk to the surface, so as to fill the empty sites. Thus, although the distinction may be rather subtle, the idea of latent or potential vacancies in a resting state rather than actual physically empty sites around electron rich areas of space seems like an adequate and useful evolution ofthe classical concept of anionic vacancies in HDS catalysts. 

The symbols and yva denote the site fractions of nickel atoms and vacancies, respectively, on the nickel sublattice and the site fraction of sulphur atoms on the sulphur sublattice is always equal to ys = 1 The temperature dependence of the defect interaction parameter Tva Va is given by Equation (V.77). The Gibbs energies of the reference states and g refer to the nickel sublattice completely occupied by Ni atoms (stoichiometric composition NiS) and vacancies (empty nickel sublattice), respectively. 

If attention is focused on the vacancy, a different result is found. Considering the situation in Figure 7.14(a), diffusion can occur by way of any of the atoms around the vacancy moving into the empty site. The vacancy, of course, does not prefer any of its neighbours so that its first jump is entirely random. The same is true of the succeding situation (Figure 7.14b). The vacancy will have no need to prefer a jump to the tracer position. Thus, the vacancy can always move to an adjacent cation site and hence can follow a truly random path. 

X+ = H+ (from an acid), Br+ (from Br2), or HgCh (from HgCl2). = empty site (2e vacancy) ... 

A large number of the ions of one species should be mobile. This requires a large number of empty sites, either vacancies or accessible interstitial sites. As is well known, empty sites are needed for ions to move through the lattice. 

Figure 7.9 Vacancies (light) at the external surface of the nanoshell inside the surface atomic plane (the empty site is considered as a vacancy and has less than a half of empty neighboring sites) (a) if the surface vacancy exchanges places with the atom marked by crosses, it remains inside the facet with the same number of neighbors...

Al. Tracer diffusivities of both components are proportional to the local vacancy concentration (fraction of empty sites)... 

The Flory-Huggins theory uses the lattice model to arrange the polymer chains and solvents. We have looked at the lattice chain model in Section 1.4 for an excluded-volume chain. Figure 2.1 shows a two-dimensional version of the lattice model. The system consists of si,e sites. Each site can be occupied by either a monomer of the polymer or a solvent molecule (the monomer and the solvent molecule occupies the same volume). Double occupancy and vacancy are not allowed. A hnear polymer chain occupies N sites on a string of N-l bonds. There is no preference in the direction the next bond takes when a polymer chain is laid onto the lattice sites (flexible). Polymer chains consisting of N monomers are laid onto empty sites one by one until there are a total tip chains. Then, the unoccupied sites are filled with solvent molecules. The volume fraction of the polymer is related to rip by... 

---