Condensed Empty Clusters

The structures of ordered TiO and of NbO are closely related to the rocksalt structure but with 1/6 and 1/4 of the respective positions of both M and O atoms being unoccupied. The reduced lattice energy due to the vacancies has to be compensated for by M-M bonding. The proportion of vacancies therefore increases with the number of d electrons available for M-M bonding. The rock-salt structure is stable for d systems (e. g. TiN, NbC, etc), the structure of the TiO d system lies between the rocksalt structure and the structure of the NbO d system. 

There is an interesting relation between TiO and compounds composed of discrete electron deficient clusters which are stabilized by interstitial atoms. TiO is an obvious borderline case. Having only a few electrons which can be used for M-M bonding, the arrangement with only empty clusters is easily transformed into a (statistically disordered) rocksalt structure at elevated temperature. Now, a portion of the ligand atoms plays the role of the interstitials. 

5 Discrete and Condensed Transition Metal Clusters in Solids 

Pereas our knowledge on bligomeric dusters built from corner sharing [Nb60i2] monomers is restricted to this one example, there exists a rich chemistry of polymers (Thble 5-4). 

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Y4CI0 (Mattausch et al., 1980). The structure is a doubly rare example of condensed empty clusters of the M0X3 type in which the exposed (side) triangular faces are capped by halide two rows of chlorine at the top and... 

Condensed Empty Clusters 405 ftble 5-5. Optimal electron numbers for condensed Nb60]2 dusters. [16]... 

Such examples of empty or metal-centered condensed cubic clusters suggest that larger clusters with additional layers could be prepared, leading ultimately to an... 

Simon, A. (1985). Empty, Filled, and Condensed Metal Clusters, J. Solid State Chem. 57, 2-16. 

At the beginning of the desorption process, some condensate is removed from the wider pores (i.e. unoccupied bonds) near the surface. As the pressure is reduced, the vapour-filled pores (occupied bonds) form clusters, which eventually extend across the particle. The stage at which a spanning cluster is formed across the particle corresponds to the percolation threshold, when the pore emptying becomes rapid. This stage corresponds to the knee of an H2 hysteresis loop. 

In the case of adsorption of a vapor by a porous material, a three phase system in terms of SAS is produced pore/adsorbed film or capillary condensed vapor/solid. Since the s.l.d. of H2O and D2O are known while the pore space s.l.d. equals to zero, contrast matching conditions are achieved if an appropriate mixture of H2O/D2O that has the same s.l.d. as the solid is used as the adsorbate. In this case the adsorbed film as well as the condensed cluster of pores will cease to act as scatterers, and only the remaining empty pores will produce measurable scattering. In terms of SANS, contrast matching reduces the solid/film/pore system to a binary one [1]. By determining a number of scattering curves corresponding to the same sample equilibrated at various relative pressures, for both the adsorption and desorption branches of the adsorption isotherm, a correlation of the two methods could be possible. If the predictions of the Kelvin equation are in accordance with the SAS analysis, a reconstruction of the adsorption isotherm can be obtained from the SAS data [2]. 

Fig. 15. Illustrations of modified HK adsorption models, (a) Geometric representation slit pore filled with adsorbate [110]. (b) Two-stage HK mesopore isotherm model [114] in which capillary condensation (1) to the filled state (2) is preceded by a wetting transition (3) from an empty state (4) to an intermediate condition characterized by film growth on the pore walls (5). (Reproduced with permission from S. Ramalingam, E. S. Aydil, and D. Maroudas. Molecular dynamics study of the interactions of small thermal and energetic silicon clusters with crystalline and amorphous silicon surfaces. Journal of Vacuum Science and Technology B, 2000 19 634-644. Copyright 2001, AVS.)...

Core-level spectroscopies are the appropriate tools to study the electronic distribution around free atoms and the changes induced in this distribution on condensation or on the formation of compounds involving other elements. These spectroscopies are also very useful to track the formation of clusters which finally coalesce to form well-defined solid phases. For the R, X-ray absorption spectroscopy is very useful because of the simplicity of the final multiplet structure, as the transitions obey dipole selection rules. Generally, two types of transitions are observed one in which the 4f electron participates in the transition and another in which it remains as a spectator. In the former case, a transition of a d electron to the empty f shell is involved. This leads to the formation of the nd 4f - d 4f + ( = 3,4) multiplets which are in fact finger prints of the R atom configurations. In the same way, the transitions from p levels scan the empty sd states of the conduction band. 

Gd2Br2C is just one example from the broad condensed cluster chemistry of the rare earth metals which has come to light in recent years. From the above, it is obvious that this chemistry lies on the borderline of M-M bonded cluster compounds and salts. The clusters can exist as any combination of empty or filled and discrete or condensed. Bonding within these clusters ranges from M-M bonded species that may be stabilized by additional strong heteropolar bonding... 

Figure 5-48. Schematized bonding in systems with discrete and condensed clusters (i) empty metal clusters in an environment of nonmetal atoms, (ii) clusters with interstitial atoms in an environment of nonmetal atoms, and (iii) bare clusters with interstitial atoms (see text).

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