Fee packing

It is not hard to understand why many metals favor an fee crystal structure there is no packing of hard spheres in space that creates a higher density than the fee structure. (A mathematical proof of this fact, known as the Kepler conjecture, has only been discovered in the past few years.) There is, however, one other packing that has exactly the same density as the fee packing, namely the hexagonal close-packed (hep) structure. As our third example of applying DFT to a periodic crystal structure, we will now consider the hep metals. 

Figure 14 Face-centered cubic (fee) packing of crystaUine Ceo-(a) At room temperature the Cgo molecules rotate essentially isotropically, but below 260 K a phase transition occurs from fee to simple cubic, in which the Cgo molecules jump between symmetry equivalent positions, (b) At 5 K all rotation is frozen and the resulting inter-Cso contact is between a six-six ring fusion and a pentagonal face. (Reprinted with permission of Macmillan from W.I.F. David et al. )...

Localized fee packing is also found in the insoluble Ceo films formed on a water surface by controlled evaporation of Ceo solutions. These films consist of rigid close-packed layers of fiillerene molecules with a reported thickness of 4-8 molecules. 

A very large structure family derives from the basic motif of a cube of 3D comer-connected octahedra realized in the ReOs stmcture or from its distorted variants, the VP3 and IrPs type, mentioned in the previous chapter (Table 1, Pigure 5). The main derivatives are generated by ordered occupation of the octahedral sites and/or by filling the central cavity with a large cation, which becomes part of the fee packing of the anions. Less frequently, the order of vacancies on the octahedral sites is observed. 

P4-9 Sargent Nigel Ambercromby. Scoundrels Incorporated, a small R D company has developed a laboratory scale process for the elementary, solid-cata-lyzed-gas-phase reaction A + B C -F D (names coded for proprietary reasons). The feed is equal molar in A and B with the entering molar flow r e of A is 25 mol/min and the volumetric feed is 50 dm /min. Engineers at Scoundrels calculated that an industrial scale packed bed reactor with 500 kg of a very rare and expensive metal catalyst will yield a 66% conversion when run at 32 C and a feed pressure of 25 atm. At these conditions the specific reaction rate is 0.4 dm /mol-min-kg catalyst. Scoundrels sells this process and catalyst to Queless Chemicals who then manufactured fee packed bed. When Oueless put the process onstream at the specifications provided by Scoundrels, they could only achieve 60% conversion with 500 kg catalyst. Unfortunately the reaction was carried out at 3U°C rather than 32°C. The... 

The mean particle diameter of metal particles could be extimated, in the hypothesis of fee packing and cubocthaedral geometry, around 11 A, consisting of 30 atoms clusters [23]. Chlorine is adsorbed on MgO support as Cf ions, probably close to the metallic particles a similar behavior is already reported in literature for analogous systems based on Pd [19]. After the catalytic test, a considerable increase in the particle size is observed (CN(Pt) = 9.9). In fee packing and in the hypothesis of cuboctahedral particles, such a CN value corresponds to a mean particle diameter of about 30 A, which means a maximum of 30% surface atoms and an even smaller Iraction of metal atoms in contact with the support surface. 

We have hep packing of S ions for wurtzite and fee packing of S " for zinc blende. In both structures Zn ions are located in half the tetrahedral interstices to maximize their separation. ... 

It was a surprise to find that a sample of packing 0.537 did not give fee packing in space, but rhep instead, whereas it gave fee on earth. Also, samples crystallized quicker in space than on earth. For example, a glassy packing of 0.619 volume fraction remained random for a year on Earth whereas it crystallized in space in 4 d. Some of these odd effects require further investigation. One possible cause of these problems is the time required for the crystallization process, which is considered next. 

The 1 /2(110) slip vector corresponds to two inter-anion distances, but the anions are not evenly spaced, because of the nonideality of the fee packing (see Figure 9.19). 

Fig. 7.24 Polymerization of fee packed Ceo molecules via [2 + 2] cycloaddition. The orthorhombic 2D polymer is obtained by topochemical polymerization of Cgo within the 100 planes. The rhombohedrai 2D polymer is formed by the polymerization within the 111 planes...

Figure 2.12. Representations of hexagonal close-packing (hep) and face-centered cubic (fee) packing. Reproduced with permission from Silberberg, M. S. Chemistry The Molecular Nature of Matter, 2nd ed., McGraw-Hill New York, 2000.

DOM materials are prepared using colloidal crystal templates [2-8]. The colloidal crystal (opal structure) templates consist of monodispersed spheres with face-centered closed (fee) packing. When 3D network of voids in colloidal crystals is filled by targeted materials and subsequentiy the colloidal crystals are removed, a replica of the colloidal crystal (inverse opal structure) is produced (Figure 6.2). 

Size of polymer spheres and formation of colloidal crystals (fee packing) of polymer spheres were confirmed by SEM. 

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