Face centered cubic packing

A simple and general method for the preparation of surfactant-free, thiol-functionalized iridium nanoparticles was reported by Ulman and coworkers in 1999 [11], The synthesis consisted of a reduction of the dihydrogen hexachloroiri-date (IV) H2lrCl6 H20 precursor by lithium triethylborohydride ( super-hydride ) in the presence of octadecanethiol (C18H37SH) in tetrahydrofuran (THF) (Scheme 15.1). The obtained iridium nanoparticles were crystaUine with fee (face-centered cubic) packing, and showed a wider size distribution with diameters ranging from 2.25 to 4.25 nm. 

Equation (48) has been derived under the assumption that the volume fraction can reach unity as more and more particles are added to the dispersion. This is clearly physically impossible, and in practice one has an upper limit for , which we denote by max. This limit is approximately 0.64 for random close packing and roughly 0.71 for the closest possible arrangement of spheres (face-centered cubic packing or hexagonal close packing). In this case, d in Equation (46) is replaced by d(j>/[ 1 — (/m[Pg.169]

Third, the notion (and reality) of such structural infractions as twins and coherent intergrowths - as is seen by Yacaman et al. in a 923-atom nanoalloy of AuPd [35] - is meaningless in our molecular bimetallic nanoparticles. In the nanoaUoys of Yacaman et al. [35, 42] and others [43], one may discern directly, by aberration-corrected electronic microscopy, thin bands of hexagonal close-packed and face-centered cubic packed sheets. In a typical molecular nanoparticle of the kind that we have studied (also by aberration-corrected electron microscopy [39]), it is directly established (in line with theoretical predictions [44]) that a single bimetallic cluster of RUj Pt does indeed possess molecular character. Furthermore, when six or more such clusters coalesce into larger entities containing ca 200 atoms they adopt the regular crystalline, and faceted state of a bulk metal. 

A detailed analysis of the behavior of hollow-sphere foams is available in [18,19], The theoretical performance of hollow-sphere foams is on par with that of closed-cell foams. Since hollow-sphere foams can be produced with fewer defects, they have the potential to perform up to three times better than existing closed-cell foams at a relative density of 10% and ten times better below a relative density of 5% [17], The behavior of simple cubic packed (SC) and face-centered cubic packed (FCC) hollow-sphere foams is shown in Figure 1. The FCC hollow-sphere foam generally represents the best performance of optimally bonded hollow spheres that was measured in this work and SC hollow-sphere foam generally represents the performance of non-optimally bonded, random packed hollow spheres [17]... 

The side length in the unit cell is denoted b and the radius of the atoms is denoted r. SC simple cubic packing, BCC Body-centered cubic packing, FCC Face-centered cubic packing, HCP Hexagonal closest... 

Figure 6. Wire frame representation of the layer structure of linked Mo72Feioj units with emphasized Fe-O-Fe bridges along the a axis in 8 (only the metal atoms are shown Fe centers, black spheres). The unit cell is also depicted, showing the approximate face-centered cubic packing of the cluster spheres.

The answer is a clear "yes", and we have already witnessed the relationship between the NaCl structure and the face-centered cubic packing (see Section 1.1) by filling the octahedral holes of the latter. The rigorous mathematical apparatus to fully exploit these structural relationships is given by group theory, in particular the theory of space groups which, unfortunately. 

FIGURE 2.32 Schematic, dimensions, and coordinate system of the computational domain simulated for carbon spheres with (a) simple cuhic, (h) hody-centered cubic, and (c) face-centered cubic packings. Shaded areas represent carhon spheres of diameter d. Five unit cells are shown here for illustration purposes. (Reprinted from Electrochimica Acta, 56, Wang, H. N., J. Varghese, and L. Pilon, Simulation of electric double layer capacitors with mesoporous electrodes Effects of morphology and electrolyte permittivity, 6189-6197, Copyright 2011, with permission from Elsevier.)... 

Some values ofr) and o are shown in Table 13.1.2 including the two extreme cases. Actually, water and n-hexadecane have the lowest and highest packing density, respectively, of the common solvents. As is seen, there is an appreciable free volume, which may be expressed by the volume fraction 13 -11 , where 13 0 is the maximum value oft) calculated for the face-centered cubic packing of HS molecules where all molecules are in contact with each other is tIq = nV2 / 6 = Q74. Thus, 1 -13 0 corresponds to the minimum of unoccupied volume. Since 13 typically is around 0.5, about a quarter of the total liquid volume is empty enabling solvent molecules to change their coordinates and hence local density fluctuations to occur. 

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