D-cluster

Fig. 2. Vacuum processing chamber configuration (a) batch coater (b) load-lock coater (c) in-line coater (d) cluster tool (e) roU coater (batch) and (f) roU coater (air-to-air), [[ccsq]] represents the isolation valve with transfer tooling [[artl]], the motion of fixturing and [[art2]], the access door.

Cs2Ti4Nb6Clis06. (c) A tetrameric propellerlike (Ti4CI]206) unit in Cs2Ti4Nb6Chg06 built from four (TiLj) octahedra that share edges, (d) Cluster unit in PbLusNbeChsOe. 

Figure 5.25 The strongest (innermost) nF->- ohf interactions in (HF) chain (a)-(c) and cyclic (d) clusters (cf. Fig. 5.23), with estimated second-order stabilization energies in parentheses. These innermost interactions best approximate the limiting case of an infinite cyclic structure.

EISEN, M.B., SPELLMAN, P.T., BROWN, P.O., BOTSTEIN, D., Cluster analysis and display of genome-wide expression patterns, Proc. Natl. Acad. Sci. USA, 1998, 95, 14863-14868. 

We have also analysed the liquid in terms of 3-D clusters, and we have found that the most abundant structures, for all the considered temperatures, are those in which one water molecule is hydrogen bonded to... 

Fig. 1 Schematic drawing to show the concept of system dimensionality (a) bulk semiconductors, 3D (b) thin film, layer structure, quantum well, 2D (c) linear chain structure, quantum wire, ID (d) cluster, colloid, nanocrystal, quantum dot, OD. In the bottom, it is shown the corresponding density of states [A( )] versus energy (E) diagram (for ideal cases).

Let us now consider a given contribution to ,w) proportional to Xr and involving d clusters. We associate with it a diagram with r — 1 intermediate states. On account of the formal property of the eigenvectors... 

Hence, each of the r — n + d sums over k "absorbs one of the r factors F-1 introduced by the dLm (see Eq. 63). We conclude from this that each diagram with d "clusters contributing to Tgy -B) is proportional to Va n. However, as is expected on the basis of the rules stated by Prigogine and Balescu,15 only the diagrams where d = 1 contribute to the transport equation for [Pg.343]

Only the proximal (P) and distal (D) clusters can be involved, as the 3Fe clnster has too high a redox potential. In [NiFe] hydrogenases, the proximal clnster is the only one which is strictly conserved in all enzymes. Hence, we assnme that the proximal cluster is indispensible for the primary, rapid reaction of H2 with the enzyme. Its short distance to the active site enables a clearly EPR-detectable spin-spin interaction of the unpaired spin of the reduced Fe-S cluster with the Ni-based spin (see Section 7.10). It is stressed here that when performing these reactions under eqnilibrinm conditions, no change of the redox states of the Fe-S clnsters can be observed (see below). 

Subbarao, D. Clusters and Lean-Phase Behaviour. Powder Technol. 46 (1986) 101-7. 

Figure 7.11 Some basic types of roll arrangements (a) two-high, (b) three-high, (c) four-high, (d) cluster, (e) tandem rolling with three stands, and (f) planetary milling. McGraw-Hill Encyclopedia of Science and Technology, Vol. 11, 8th ed., p. 54. Copyright 1997 by McGraw-HiU.

Figure 17.18. (A) Carbon contents in an entire microaggregate from an alfisol at Arnot Forest in Upstate New York (500-nm resolution). (B) Detail of the microaggregate (red box in A) (50-nm resolution). (C) X-ray map of B. (D) Cluster map [3 components, 20 clusters, without first component PCA GUI 1.0 developed by Lerotic et al. (2004)]. (E) Individual clusters from D numbers in each cluster map correspond to spectra shown in Figure 17.19 (J. Lehmann, unpublished data 2006, measured as described in Lehmann et al., 2007). See color insert.

TABLE 6.4 Effective Fractal Dimension Obtained from Reorganization of 3-D Cluster-Cluster Aggregates"... 

The electronic structure of microcrystalline silicon of one-dimensional (1-D), 2-D, and 3-D clusters were calculated using the Discrete-Variational (DV)-Xa Molecular-Orbital method. The calculated results are discussed with respect to the effect of the size and the number of dimensions on the energy levels of molecular orbitals. The energy-gap (Eg) between the highest-occupied molecular orbital (HOMO) and the lowest-unoccupied molecular orbital (LUMO) decreases with the increase of cluster size amd the number of dimensions. It is found that including silicon 3d orbitals as basis sets decreases the Eg value. The results show that the components of silicon 3d orbitals in the unoccupied levels near LUMO are over 50 per cent. The calculated results predict that the Eg value will be close to the band gap of crystalline silicon when a 3-D cluster contadns more than 1000 silicon atoms with a diameter of 4nm. 

In order to elucidate the relation between the Eg value and both of the number of dimensions and size of silicon clusters, we treated three types of clusters, that is, one-dimensional (1-D), 2-D, and 3-D silicon clusters, where we defined a 1-D cluster as a zig-zag chain, a 2-D cluster as a planar cluster, and a 3-D cluster as a ball-shaped cluster. The infinite size of 3-D cluster is close to crystalline silicon. 

Figure 1 Models of (a) 1-D, (b) 2-D, and (c) 3-D silicon clusters. Si2He, SiioH22, and Si2oH42 are shown as examples for 1-D clusters, Si2oH3<, SisoHyo are shown as examples for 2-D clusters, and SisHi2, SiasHsg, and SinHeo are shown as examples for 3-D clusters.

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