Inequivalent sites

One of the most promising techniques for studying transition metal ions involves the use of zeolite single crystals. Such crystals offer a unique opportunity to carry out single crystal measurements on a large surface area material. Suitable crystals of the natural large pore zeolites are available, and fairly small crystals of the synthetic zeolites can be obtained. The spectra in the faujasite-type crystals will not be simple because of the magnetically inequivalent sites however, the lines should be sharp and symmetric. Work on Mn2+ in hydrated chabazite has indicated that there is only one symmetry axis in that material 173), and a current study in the author s laboratory on Cu2+ in partially dehydrated chabazite tends to confirm this observation. 

In the more complex situations, (b) and (c) of Fig. 3.6, where the partially occupied sites are separated by inequivalent sites that are either empty or filled with mobile ions, fast ionic motion requires that the mobile-ion potential at the intervening sites be nearly the same as that at the partially occupied sites. (Of course, if the intervening sites are occupied by stationary ions, the ions in the partially occupied sites are immobilised.) From the constructions in Fig. 3.6, it is clear that the electrostatic forces between the mobile ions tend to smooth the potential where the inequivalent sites are filled with mobile ions whereas the local relaxation energy AH enhances the potential difference of the inequivalent sites where they are empty. 

In systems containing a number of physically inequivalent sites, Mossbauer effect spectroscopy (MES) can often allow the determination of the properties of the individual sites. This also proved to be the case here [24],... 

Two types of mixed-valence compounds must be distinguished at the outset those with mixed valency on energetically equivalent sites and those in which the different valences occupy inequivalent sites. Section 1.2.3 deals with the former case. Sect. 1.2.5 with the latter. 

In some cases, mixed valence states may appear simultaneously on two different atoms because of an overlap of the redox energies associated with the two atoms. In the ilmenite FeTi03, the valence states Fe " and Ti are stabilized with an ordering of Fe and Ti on crystallographically inequivalent sites FeV03, on the other hand, has the corundum structure with Fe and V randomly distributed on equivalent sites with the valence states Fe and This observation places the top of the Fe " 3d band (level) below the bottom of the Ti 3 d band, but above the top of the 3 d band, so charge transfers of the type... 

In this expression the ( -factors of site i are functions, through (27), of the probabilities Pi T) of the atomic configurations T of /-orbitals at the same site. They are equal to 1 if orbital a or (3 does not belong to this subset, i.e. for extended states. Ur is a proper combination of Coulomb direct and exchange contributions Uao-pa, accounting for the interaction energy which arises as prefactors of expressions (29), and which can be seen for e.g. on simplified case of (31). As in our previous simpler models, the probabilities Pi(T) are the variational parameters and one has to minimize Eg with respect to each of them (and at each inequivalent site) according to... 

The material YCaA104 is of interest for solid state lasers. The orientational dependence of the HFEPR spectra at 250 GHz was measured32 for an iron-doped crystal using a goniometer in a quasi-optical spectrometer at 253 K The spectra of Fe3+, S — 5/2, revealed the existence of two magnetically inequivalent sites of roughly equal concentration. Only the site with its z-axis along the c-axis of the crystal was studied in detail and was found to have a 0-factor close to 1.99 and a ZFS of about 29 GHz. 

The HFEPR of Ni2+ in the host Ni2CdCl6.2H20 was studied in a single crystal. The orientation dependence of the spectra at 250 GHz was measured32 using a goniometer in a quasi-optical spectrometer at 253 K. Two inequivalent sites were detected with the magnetic axes of both sites parallel to the c-axis. The 0-factor of both sites was close to 2.24 but the ZFS were -6.781 and -30.97 GHz. 

At 60 °C, 25% of the ester groups undergo one (or an odd number of) n-flip at a frequency higher than 10 kHz, with no more than 25° deviation in the flip angle. The flips are accompanied by rotational readjustments with an amplitude of ca. 20° around the local chain axis. The flips occur between energetically inequivalent sites (thus they are active in dynamic mechanical and dielectric relaxation experiments). 

In the above, ijk denote the Cartesian coordinates of a molecule, IJK those of a crystal (a unit cell), 7Vt is the number of molecules in a unit volume occupying each particular inequivalent site in the unit cell,/ is the number of inequivalent positions of a molecule in a unit cell, and Ng is the number of equivalent positions in a unit cell. The directional cosines are used to transform each of the molecular 0 components to those of the new coordinate system (bUK) and the contributions are summed. 

Figure 24 Representation of possible silicate anion structures for the species identified by b-n-j connectivites deduced from the 2D 29Si INADEQUATE spectrum.The solid lines represent silicon-oxygen-silicon linkage and closed circles (A, B and C) are inequivalent site within each anion illustrating connectivities.

The metallic states in molecular crystals are realized first of all by the charge transfer (CT) between segregated donors and acceptors. The actual conduction can be along either donors or acceptors in the case of ETjX, e.g. on ET donors. In the presence of several inequivalent sites in a unit cell, some site(s) can have a different amount of carrier density from the other site(s), which is termed as CD, or CO. 

Solid-state NMR has emerged as a powerful tool in the analysis of polymorphic drug forms. CP-MAS spectroscopy can be used to identify the number of crystallographically inequivalent sites in a unit cell and to understand the molecular structure on the basis of the chemical shifts. Fig. 14 shows the solid-state spectra of two forms of lamivudine. Form II shows a relatively simple spectrum in which there is only one molecule in the crystallographic asymmetric unit. 

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