Free clusters

Our approach is similar to that employed in research of free cluster ions in the gas phase, where various measurements are conducted on the cluster which is mass selected out of the size-distributed clusters generated by laser sputtering. Based on the chemical compositions of the isolated MFCs, we discuss the determining factors of core size in connection with the formation processes. Some core-size dependent properties of the MFCs are also presented. 

The Wade rules can be applied to ligand-free cluster compounds of main-group elements. If we postulate one lone electron pair pointing outwards on each of the n atoms, then g — 2n electrons remain for the polyhedron skeleton (g = total number of valence elec-... 

The solvent-free cluster 17 crystallizes in the monoclinic space group P21/c and comprises a hexagonal Mg6P6 prism with disordering... 

Studies on the extracted FeMo cofactor has allowed researchers to answer questions about the intrinsic reactivity associated with free clusters.31 The reference 31... 

Just as in our abbreviated descriptions of the lattice and cell models, we shall not be concerned with details of the approximations required to evaluate the partition function for the cluster model, nor with ways in which the model might be improved. It is sufficient to remark that with the use of two adjustable parameters (related to the frequency of librational motion of a cluster and to the shifts of the free cluster vibrational frequencies induced by the environment) Scheraga and co-workers can fit the thermodynamic functions of the liquid rather well (see Figs. 21-24). Note that the free energy is fit best, and the heat capacity worst (recall the similar difficulty in the WR results). Of more interest to us, the cluster model predicts there are very few monomeric molecules at any temperature in the normal liquid range, that the mole fraction of hydrogen bonds decreases only slowly with temperature, from 0.47 at 273 K to 0.43 at 373 K, and that the low... 

P. Borowski, J. Jaroniec, T. Janowski, and K. Wolinski. Quantum cluster equilibrium theory treatment of hydrogen-bonded liquids water, methanol and ethanol. Mol. Phys. 101, 1413-21 (2003). [This paper suggests the need for more accurate treatment of free cluster rotations that become hindered librations at normal liquid densities, thus reducing the populations of larger clusters.]... 

The red shift of the 0-0 band induced by formation of a given PhOH (NH3) cluster is larger in the case of <- S0 than in that of the Tj - S0 transitions. Moreover, the red shift of the St - S0 transition in matrices is larger than in the free clusters. 

In this work we study a number of isolated clusters which may be relevant for understanding the clustering in the liquid alloys. Of course, the behaviour of those clusters in the alloy may be more complicated due to the interaction with the condensed medium, but by studying free clusters we expect to obtain useful information about the tendency of the atoms to cluster in the alloy. A preliminary calculation [9] using the Density Functional Formalism (DFT) [10, 11] and a simplified model for the cluster structure [12] has confirmed the high stability of the A4Pb and A4Pb4 species (with A = Li, Na, K, Rb, Cs). However, the drastic simplification of the cluster structure used in that model calls for more accurate calculations. Consequently, in this work we report the results of ab initio molecular-dynamics DFT calculations. 

The variations of abundance in the mass spectrum of small Pb clusters have been explained by ab initio density functional calculations. A study of free clusters formed by Pb and Na helps to explain the observation of an exceptionally abundant NagPb cluster in gas phase experiments. It also gives strong support to the presence of Na4Pb and Na4Pb4 clusters in the liquid alloys. 

Direct conductivity measurements are difficult to apply to free clusters, and even to two-dimensional systems. 

For free-clusters, the cluster size distribution can be measured by the time-of-flight mass spectrometer for cluster films deposited on substrate by the cluster beam, the measurement of size distribution and observation of nanostructure are mostly done using transmission electron microscopy (TEM). In this section we will focus on the latter and pay special attention to FePt, CoPt clusters which have high anisotropy Tl0 phase after annealing [43-45]. For the TEM observations, FePt, CoPt nanoclusters, produced in a gas-aggregation chamber, in which high pressure Ar gas ( 0.5-lTorr) was applied and cooled by LN2, were directly deposited onto carbon-coated films supported by Cu grids. 

C6o molecules in water also form colloidal clusters based on 3.4 nm diameter (carbon atoms) icosahedral arrangements of thirteen CWI molecules.5 Here the Ceo molecules are necessarily separated by water molecules to form clusters with this diameter.10 Such an arrangement is shown in Figure 2 within an expanded, but now strain-free, cluster of water icosahedral clusters. The water network is formed by tetrahedral tricyclo decamer (H20)io structures connecting groups of four Cm molecules. The modeled diameter of the cluster... 

Contrary to this chemical cluster growth is the formation of naked, ligand free clusters in a more physical sense. Considering the cluster growth in Fig. 8 and 9, it is to be recognized that both five-fold symmetry and hexagonal (hep) or cubic (ccp) structures are realized. While in smaller clusters the icosahedral and cuboctahedral symmetry are... 

Access to clusters of principally all elements in the periodic table has opened new possibilities for test of calculations and comparison with available experimental data and what is known from surface science. The geometry of the free clusters will, as discussed above, be determined by the electronic properties of the constituent atoms. This means that clusters of alkali and coinage metals will in a first approximation be determined by the free electrons while clusters of transition elements will be determined by the balance between the nd and (n -k l)s valence electrons. Noble gas atoms will behave as hard spheres, which under certain thermodynamic conditions can form larger clusters of icosahe-dral symmetry [134,135]. The geometry of these free clusters are quite different what one obtains if the cluster is constructed as a piece of the lattice known for the corresponding solid. 

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