FCC packing

Let us call the arrangement of spheres shown in Figure 9.33 as A. The next layer may be arranged as B or C. Let us consider the case of B. The third layer will be A or C, etc. In the former case, alternation of the layers gives a scheme ABABAB... (hcp-packing) in the latter it gives AB-CABC... (fcc-packing). More complicated alternations are possible, for example, ABCBABCB..., ABCABABCAB..., etc. 

It is convenient to allocate PBU/C for hep- and fcc-packings as a combination of N octahedral (Figure 9.30c) and 2N tetrahedral (Figure 9.30a) units (where N is the number of spheres in a packing). Such a combination allows filling of space without gaps and overlaps, which is a requirement for PBUs. 

The structure of both gamma-AI2O3 and eta-Al203 is a more or less skew FCC packing of oxygen ions with Al-ions distributed somewhat disordered in the holes between the 0-ions. The disorder is the reason why AI2O3 can disolve other ions. 

Figure 3 Plot of AU and the area ratio R = AVBc/AVBb as a function of the Pt-Pt coordination number N, as obtained from the EXAFS analysis. Also shown is the estimated dispersion, cluster diameter and number of atoms/particle as estimated assuming spherical clusters and FCC packing. Data are shown for the acidic supports (LTL[K/A1=0.63] zeolite and CI-AI2O3, SiOi) and for the basic supports (LTL [K/A1=1.25] zeolite and K-AI2O3, K-Si02).

Miguez, H., Meseguer, R, Lopez, C. et al.. Control of the photonic crystal properties of the FCC-packed submicrometer Si02 spheres by sintering, Adv. Mater., 10, 480, 1998. 

The vertical dashed line in the phase diagram signals a different kind of solid-solid transition. It turns out that for 5 < 0.15 the icosahedral interior becomes energetically less optimal, and it is replaced by a decahedral arrangement of monomers. These stmetures can also possesses extended fcc-packed fractions (Sfcc/deca) ... 

Figure Bl.21.1. Atomic hard-ball models of low-Miller-index bulk-temiinated surfaces of simple metals with face-centred close-packed (fee), hexagonal close-packed (licp) and body-centred cubic (bcc) lattices (a) fee (lll)-(l X 1) (b)fcc(lO -(l X l) (c)fcc(110)-(l X 1) (d)hcp(0001)-(l x 1) (e) hcp(l0-10)-(l X 1), usually written as hcp(l010)-(l x 1) (f) bcc(l 10)-(1 x ]) (g) bcc(100)-(l x 1) and (li) bcc(l 11)-(1 x 1). The atomic spheres are drawn with radii that are smaller than touching-sphere radii, in order to give better depth views. The arrows are unit cell vectors. These figures were produced by the software program BALSAC [35]-...

The important point to note here is that the gas-phase mass-transfer coefficient fcc depends principally upon the transport properties of the fluid (Nsc) 3nd the hydrodynamics of the particular system involved (Nrc). It also is important to recognize that specific mass-transfer correlations can be derived only in conjunction with the investigator s particular assumptions concerning the numerical values of the effective interfacial area a of the packing. 

Danckwerts and Gillham did not investigate the influence of the gas-phase resistance in their study (for some processes gas-phase resistance may be neglected). However, in 1975 Danckwerts and Alper [Trans. Tn.st. Chem. Eng., 53, 34 (1975)] showed that by placing a stirrer in the gas space of the stirred-cell laboratoiy absorber, the gas-phase mass-transfer coefficient fcc in the laboratoiy unit could be made identical to that in a packed-tower absorber. When this was done, laboratoiy data obtained for chemically reacting systems having a significant gas-side resistance coiild successfully be sc ed up to predict the performance of a commercial packed-tower absorber. 

If it is assumed that the values of fcc,. nd a have been measured for the commercial tower packing to be employed, the procedure for using the laboratory stirred-ceU reactor is as follows ... 

It would be desirable to reinterpret existing data for commercial tower packings to extract the individual values of the interfacial area a and the mass-transfer coefficients fcc and /c in order to facilitate a more general usage of methods for scaling up from laboratory experiments. Some progress in this direction has afready been made, as discussed later in this section. In the absence of such data, it is necessary to operate a pilot plant or a commercial absorber to obtain kc, /c , and a as described by Ouwerkerk (op. cit.). 

Principles of Rigorous Absorber Design Danckwerts and Alper [Trans. Tn.st. Chem. Eng., 53, 34 (1975)] have shown that when adequate data are available for the Idnetic-reaciion-rate coefficients, the mass-transfer coefficients fcc and /c , the effective interfacial area per unit volume a, the physical solubility or Henry s-law constants, and the effective diffusivities of the various reactants, then the design of a packed tower can be calculated from first principles with considerable precision. 

Another method for the determination of the structure of the crystal lattice is SAXS [30,31]. Figure 6 shows the specific SAXS profiles of microsphere film (MC2). The cubic packing values (dl/di) are listed in Table 3. Three clear peaks appeared at 0.35, 0.42, and 0.66 degrees in Fig. 6. The dl/di values of the second and third peaks are >/4/3 and >/U/3, respectively. These values are peculiar to the FC(T structure. Thus, the lattice structure of the microspheres is an estimated FCC. As both... 

At each temperature one can determine the equilibrium lattice constant aQ for the minimum of F. This leads to the thermal expansion of the alloy lattice. At equilibrium the probability f(.p,6=0) of finding an atom away from the reference lattice point is of a Gaussian shape, as shown in Fig. 1. In Fig.2, we present the temperature dependence of lattice constants of pure 2D square and FCC crystals, calculated by the present continuous displacement treatment of CVM. One can see in Fig.2 that the lattice expansion coefficient of 2D lattice is much larger than that of FCC lattice, with the use of the identical Lennard-Lones (LJ) potential. It is understood that the close packing makes thermal expansion smaller. 

Minimum Fluidization Velocity (Umf). The lowest velocity at which the full weight of catalyst is supported by the fluidization gas. It is the minimum gas velocity at which a packed bed of solid particles will begin to expand and behave as a fluid. For an FCC catalyst, the minimum fluidization velocity is about 0.02 ft/sec. 

Golf balls and oranges pack naturally in an FCC structure. 

Fig. 16.—Antiparallel packing arrangement of 3-fold sodium pectate (13) helices, (a) Stereo view of two unit cells roughly normal to the fcc-plane. The helix at the center (open bonds) is antiparallel to the two in the front (tilled bonds). Intrachain hydrogen bonds stabilize each helix. Sodium ions (crossed circles) and water molecules (open circles) connect adjacent helices, (b) A view of the unitcell contents down the t -axis highlights the ions and water molecules located between the helices.

The formation of a 3D lattice does not need any external forces. It is due to van der Waals attraction forces and to repulsive hard-sphere interactions. These forces are isotropic, and the particle arrangement is achieved by increasing the density of the pseudo-crystal, which tends to have a close-packed structure. This imposes the arrangement in a hexagonal network of the monolayer. The growth in 3D could follow either an HC or FCC struc-... 

The electron transport properties described earlier markedly differ when the particles are organized on the substrate. When particles are isolated on the substrate, the well-known Coulomb blockade behavior is observed. When particles are arranged in a close-packed hexagonal network, the electron tunneling transport between two adjacent particles competes with that of particle-substrate. This is enhanced when the number of layers made of particles increases and they form a FCC structure. Then ohmic behavior dominates, with the number of neighbor particles increasing. In the FCC structure, a direct electron tunneling process from the tip to the substrate occurs via an electrical percolation process. Hence a micro-crystal made of nanoparticles acts as a metal. 

FCC. Face-centered cubic the FCC structure is a close-packed structure. 

Table 2.2 CALPHAD-type representation of the thermodynamic properties of face-centred cubic (FCC), liquid and hexagonal close-packed (HCP) aluminium of the form (after Dinsdale [18]) ...

Figure 2.12 6/ -G, (A1 FCC) of hexagonal closed-packed (HCP) aluminium and aluminium melt relative to that of face-centred cubic aluminium [18].

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