The Ga Cluster

Under similar reaction conditions used for the synthesis of the above-mentioned A177R2o2 cluster 63, the Ga cluster Gag4R2o4 [R = N(SiMe3)2] 83 [4], is obtained from a metastable GaBr solution and LiN(SiMe3)2. The molecular structure of 83 is illustrated in a similar fashion to that of 63 in Figure 2.3-28(a). 

Li clusters up to L15 are detected under the same conditions as mentioned above. There is no indication of anomalously low stabilities for Li3 or Li5 which are missing in the gas clustering series, Li2 to Li] 5, of Kimoto and Nishida (14) Table II summarizes data on Li clusters. 

Figure 2 Mass spectra of the Ga cluster (a) and the Ga23 2002, with permission from Elsevier)...

The final equation obtained by Becker and Doting may be written down immediately by means of the following qualitative argument. Since the flux I is taken to be the same for any size nucleus, it follows that it is related to the rate of formation of a cluster of two molecules, that is, to Z, the gas kinetic collision frequency (collisions per cubic centimeter-second). 

Cluster research is a very interdisciplinary activity. Teclmiques and concepts from several other fields have been applied to clusters, such as atomic and condensed matter physics, chemistry, materials science, surface science and even nuclear physics. Wlrile the dividing line between clusters and nanoparticles is by no means well defined, typically, nanoparticles refer to species which are passivated and made in bulk fonn. In contrast, clusters refer to unstable species which are made and studied in the gas phase. Research into the latter is discussed in the current chapter. 

The fonnation of clusters in the gas phase involves condensation of the vapour of the constituents, with the exception of the electrospray source [6], where ion-solvent clusters are produced directly from a liquid solution. For rare gas or molecular clusters, supersonic beams are used to initiate cluster fonnation. For nonvolatile materials, the vapours can be produced in one of several ways including laser vaporization, thennal evaporation and sputtering. 

The thennal evaporation source was the earliest used to produce metal clusters in the gas phase [H, 12 and 13], mostly for clusters of the alkalis and other low melting point materials. In this technique, a bulk sample is simply... 

Rare-gas clusters can be produced easily using supersonic expansion. They are attractive to study theoretically because the interaction potentials are relatively simple and dominated by the van der Waals interactions. The Lennard-Jones pair potential describes the stmctures of the rare-gas clusters well and predicts magic clusters with icosahedral stmctures [139, 140]. The first five icosahedral clusters occur at 13, 55, 147, 309 and 561 atoms and are observed in experiments of Ar, Kr and Xe clusters [1411. Small helium clusters are difficult to produce because of the extremely weak interactions between helium atoms. Due to the large zero-point energy, bulk helium is a quantum fluid and does not solidify under standard pressure. Large helium clusters, which are liquid-like, have been produced and studied by Toennies and coworkers [142]. Recent experiments have provided evidence of... 

Spence T G, Trotter B T, Burns T D and Posey L A 1998 Metal-to-ligand charge transfer in the gas phase cluster limit J. Phys. Chem. A 102 6101... 

Duncan M A 1997 Synthesis and characterization of metal-carbide clusters in the gas phase J. duster Soi. 8 239... 

Transport Disengaging Height. When the drag and buoyancy forces exerted by the gas on a particle exceed the gravitational and interparticle forces at the surface of the bed, particles ate thrown into the freeboard. The ejected particles can be coarser and more numerous than the saturation carrying capacity of the gas, and some coarse particles and clusters of fines particles fall back into the bed. Some particles also coUect near the wall and fall back into the fluidized bed. 

Circulating fluidized beds (CFBs) are high velocity fluidized beds operating well above the terminal velocity of all the particles or clusters of particles. A very large cyclone and seal leg return system are needed to recycle sohds in order to maintain a bed inventory. There is a gradual transition from turbulent fluidization to a truly circulating, or fast-fluidized bed, as the gas velocity is increased (Fig. 6), and the exact transition point is rather arbitrary. The sohds are returned to the bed through a conduit called a standpipe. The return of the sohds can be controUed by either a mechanical or a nonmechanical valve. 

Nucleation is the growth of clusters of molecules that become a thermodynamically stable nucleus. This process is dependent on the vapor pressure of the condensable species. The molecular clusters undergo growth when the saturation ratio, S, is greater than 1, where saturation ratio is defined as the actual pressure of the gas divided by its equilibrium vapor pressure. S > 1 is referred to as a supersaturated condition (14). 

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