Maximum site occupancy

Lemonnier J-F, Guenee L, BemardineUi G, Vigier J-F, Bocquet B, Piguet C. Planned failures from the principle of maximum site occupancy in lanthanide helicates. Inorg Chem. 2010 49 1252-1265. 

The measured Q.S. values for the surface sites of AU55 give nuclear splittings of 21 mK, 13 mK, and 4 mK for the PPhj coordinated sites, the Cl coordinated sites, arid the bare surface sites respectively. From these values, and the known site occupations, the nuclear quadrupole contribution to the zero field specific heat by these three two-level systems [143] has been calculated directly [144], This value is 5 times as large as that experimentally observed [54]. The maximum value of a linear term in the specific heat of AU55 has been estimate to be no more than one fifth of the bulk value [144]. 

Figure 15 Observation times / necessary for following various single-file mean diffusion paths - plotted against the site occupancy 0, as calculated on the basis of Eqs. (40) and (13) with D = 10 " m s and = 0.5 nm. The shaded area represents the region of maximum observation time accessible by PFG NMR. (From Ref. 162.)...

The existence of two attached states, A M and A P-M, has provided the basis for a family of attractive hypotheses to explain the separation of the maintenance of maximum force and maximum shortening velocity. As in other systems, continuous occupation of the receptor sites produces only a transient elevation of the... 

A clear example of this effect is found in the Li4 3,Al,Si04 solid solutions (Garcia, Torres-Trevino and West, 1990), scheme 1, Fig. 2.2. Single phase solid solutions form over the entire range x = 0-0.5. At X = 0, in stoichiometric Li4Si04, all the Li sites are full and the conductivity is low. As x increases, one particular set of Li sites in the crystal structure starts to empty and is completely empty at x = 0.5, i.e. at Li2.5Alo.5Si04. The effect on the ionic conductivity of this variation is dramatic, as shown in Fig. 2.3. A broad conductivity maximum occurs around x = 0.25, at which composition the mobile Li" sites are half-full (Mc = 0.5, where is the occupancy of the site by ions). To either side, the conductivity becomes very small as x 0 (n,. 1) and x -> 0.5 (tie 0) respectively. ... 

Figures 10—13 give further confirmation that the maximum energy for Mn occupation of tetrahedral sites in a ccp oxide occurs when the Mn valence is +4 (i.e., d filling), independent of cation ordering. Figures...

The Maximum-Entropy Principle. The mean-field and the quasi-chemical approximations can be extended to larger clusters. Using the derivation of Section 3.1.3 to obtain a quasi-chemical approximation for a cluster with more sites is quite cumbersome. In this section we present an approach that is new and that unifies various approximations to deal with multi-site probabilities. It is based on the maximum-entropy principle. Suppose we have a cluster of n sites with occupations Xi, X2,. .., X . We define an entropy... 

It is also of interest to use MAS NMR for the study of the thermal treatment of zeolites which are not in the ammonium-exchanged form. In an X-ray study, Pluth and Smith (179) found electron density at the center of the sodalite cages in dehydrated zeolites Ca-A and Sr-A and attributed this to a partial occupancy of these sites by a four-coordinated aluminous species. No such effect was found in zeolite A exchanged with monovalent cations. Corbin et al. (180) used 27A1 MAS NMR to examine commercial samples of K-A, Na-A and (Ca,Na)-A, as received (see Fig. 41). For K-A and Na-A, only framework tetrahedral Al species were observed, with chemical shifts of 57 and 52 ppm respectively. However, in (Ca,Na)-A an additional intense resonance at 78 ppm, typical of AlfOH) but definitely not due to framework aluminum, was also found (see Fig. 41). A much weaker signal, also at 78 ppm, was detected in zeolite Sr-A its intensity increased greatly on heating the sample to 550°C. Freude et al. (183) came to very similar conclusions in their NMR study of heat-treated zeolite Ca-A. They found that maximum framework dealumination occurs at 500°C and corresponds to ac. 17% of total Al. 

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