Partially vacant sites

In the structure of La2Fei.76S5 the modifications are more obvious. Only one of the iron chains remains saturated the other three have partial vacancies, two on the octahedral Fe sites, one on the tetrahedral Fe sites, with respective ratios of occupancy of 0.80, 0.74 and 0.39. The tetrahedral sites are the most modified, because all of the Fe atoms which occupy them become five-coordinated by bonding with the neighboring fifth sulfur atom. But, whereas, the tetrahedral Fe located near a partially vacant site of octahedral Fe draws near the sulfur, the tetrahedral Fe located in the neighborhood of a saturated octahedral Fe draws away from it (Besrest et al., 1978). 

Cul) is not due to point defects but to partial occupation of crystallographic sites. The defective structure is sometimes called structural disorder to distinguish it from point defects. There are a large number of vacant sites for the cations to move into. Thus, ionic conductivity is enabled without use of aliovalent dopants. A common feature of both compounds is that they are composed of extremely polarizable ions. This means that the electron cloud surrounding the ions is easily distorted. This makes the passage of a cation past an anion easier. Due to their high ionic conductivity, silver and copper ion conductors can be used as solid electrolytes in solid-state batteries. 

In the first case, the rate of attachment of AB molecules to the surface is proportional to the partial pressure of AB. Moreover, the rate is proportional to the vacant sites concentration. So, the rate of attachment is... 

The mechanism by which oscillations occur also involves the vacant site requirement for reaction. For critical values of the partial pressures, the coverage of one of the reactants decreases leading to an increase in the rate of reaction due to the availability of vacant sites. This accelerates the decrease in coverage until the rate of reaction subsides. The large number of vacant sites then increases the rate of adsorption until the surface coverage returns to its previous state to complete the cycle. 

The effects of forced oscillations in the partial pressure of a reactant is studied in a simple isothermal, bimolecular surface reaction model in which two vacant sites are required for reaction. The forced oscillations are conducted in a region of parameter space where an autonomous limit cycle is observed, and the response of the system is characterized with the aid of the stroboscopic map where a two-parameter bifurcation diagram for the map is constructed by using the amplitude and frequency of the forcing as bifurcation parameters. The various responses include subharmonic, quasi-peri-odic, and chaotic solutions. In addition, bistability between one or more of these responses has been observed. Bifurcation features of the stroboscopic map for this system include folds in the sides of some resonance horns, period doubling, Hopf bifurcations including hard resonances, homoclinic tangles, and several different codimension-two bifurcations. 

The structure of sodium thallide NaTl can be understood as a diamond-like framework of T1 atoms, whose vacant sites are completely filled with Na atoms. Figure 13.7.2(a) shows the structure of NaTl, in which the Tl-Tl covalent bonds are represented by solid lines. The T1 atom has three valence electrons, which are insufficient for the construction of a stable diamond framework. The deficit can be partially compensated by the introduction of Na atoms. The effective radius of the Na atom is considerably smaller than that in pure metallic sodium. 

The [(MQ)]i+ c(TQ2)2 family has n = 2 and features a van der Waals gap between the two adjacent (TQ2) slabs. Because the van der Waals gaps between the double MS2 slabs are empty, the compounds can be exfoliated and intercalated in analogy to the parent MS2 compounds. The octahedral holes in the van der Waals gap of monoclinic (PbS)i,i4(NbS2)2 are partially occupied by additional Nb. Thus, for the parent binary TQ2 compounds tetrahedral and/or octahedral vacant sites within the gap are available for metal intercalation (donor species) as for instance, alkali metals or transition metals such as Mn, Fe, Co. One could also say that the [MQ] slab is, in itself, an intercalated entity (donor species) between two TQ2 slabs. The crystal chemistry of the ternary misfit chalcogenides is similar to that of their parent binary chalcogenides, and this is reinforced by the phenomenon of polytypism which is occurring for both famihes. Examples of Q-multilayered derivatives where m = 2, is [((Pbi, Sb, S)2]l.l4(NbS2) withx 0.2.136... 

A second factor is formed by the partial gas phase pressures of A and B2. When the adsorption of A is faster than adsorption of B2, vacant sites will preferentially be covered by A, which will inhibit front generation as well as front propagation. Therefore, in order to obtain oscillations and pattern formations, B2 adsorption always has to be faster than A adsorption. 

In obtaining a rate law for the rate of adsorption, the reaction in Equation (10-2) can be treated as an elementary reaction. The rate of attachment of the earbon monoxide molecules to the surfaee is proportional to the number of eollisions that these molecules make with the surface per seeond. In other words, a specific fraction of the moleeules that strike the surfaee become adsorbed. The eol-lision rate is, in turn, direetly proportional to the earbon monoxide partial pressuire, Pqq. Since carbon monoxide moleeules adsorb only on vacant sites and not on sites already oeeupied by other earbon monoxide moleeules, the rate of attaehment is also direetly proportional to the eoneentration of vacant sites, C,. Combining these two faets means that the rate or attaehment of carbon monoxide moleeules to the surfaee is direetly proportional to the product of the partial pressure of CO and the eoneentration of vaeant sites that is,... 

When the carbon monoxide molecule dissociates upon adsorption, it is referred to as the dissociative adsorption of carbon monoxide. As in the case of molecular adsorption, the rate of adsorption here is proportional to the pressure of carbon monoxide in the system because this rate governs the number of gaseous collisions with the surface. For a molecule to dissociate as it adsorbs, however, two adjacent vacant active sites are required rather than the single site needed when a substance adsorbs in its molecular form. The probability of two vacant sites occurring adjacent to one another is proportional to the square of the concentration of vacant sites. These two observations mean that the rate of adsorption is proportional to the product of the carbon monoxide partial pressure and the square of the vacant-site concentration, Pco u-... 

It is this exothermic step that probably is the source of the preference for linear hydroformylation products over branched ones. The structure of the comparable 18-electron branched intermediate 7 is about 2 kcal/mol less stable than 7, according to Jiao s calculations. This difference leads ultimately to the anti-Markovnikov, linear aldehyde over the branched-chain isomer. Although -elimination is possible now, the high partial pressure of CO present in the reaction vessel tends to stabilize 7 and prevent loss of CO that would generate the vacant site necessary for elimination to occur. 

The concentradon of Species A on the surface is governed be the adsorption of A and B from the gas phase when the adsorption driving force is the product of the gas phase partial pressure and the concentration of vacant sites, Cy... 

Term A is a product of kinetic and adsorption/desorption equilibrium constants. The kinetic contribution is given by the forward rate constant of the slowest step. In the example above, equilibrium constants are included only for those reactants that adsorb on the catalytic surface. Term B is written in terms of partial pressures and represents the forward rate minus the backward rate. All reactant partial pressures appear in the forward rate, and all product partial pressures appear in the backward rate, regardless of whether or not each gas adsorbs. The equilibrium constant in the backward rate is based on gas-phase partial pressures. Term C represents the vacant-site fraction on the catalytic smface and includes a contribution from each component that adsorbs. The exponent of this adsorption term in the denominator of the rate law corresponds to the number of active sites that are required in the rate-limiting step. 

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