Packing crystalline

In either of these close-packed structures, each sphere has 12 nearest neighbors 6 in the same plane, 3 in the dimples above, and 3 in the dimples below. The expanded views in Figure 11-30 show the different arrangements of the hexagonal and cubic close-packed crystalline types, hi the hexagonal close-packed structure, notice that the third layer lies directly above the first, the fourth above the second, and so on. The layers can be labeled ABAB. 

Colorless or light yellow metal at ordinary temperatures it occurs in hexagonal close-packed crystalline form, known as alpha-gadolinium alpha form transforms to a body-centered cubic allotropic form, beta-gadolinium upon heating at 1,262°C density 7.90 g/cm melting point 1,313°C vaporizes at 3,266°C vapor pressure 9.0 torr at 1,800°C (calculated) electrical resistivity 134.0 microhm-cm at 25°C Poisson ratio 0.259 modulus of elasticity 8.15x106 psi thermal neutron absorption cross section 46,000 barns insoluble in water dissolves in acid (reacts). 

It follows from what has been said above that free-volume is a value that is determined by both hole volume and empty volume, the latter being connected with the packing mode. In this case an empty volume ve = vr — vw, where vr is the real (observed) volume at temperature T and vw the volume of the substances as calculated from the Van der Waals dimensions obtained by an X-ray diffraction method or from the gas-kinetic collision cross-section3. Then the expansion volume vex = v - v0, where v0 is the volume occupied by the molecules at 0 K in a close-packed crystalline state. 

In the case of metal clusters, for example, valence electrons show the shell structure which is characteristic of the system consisting of a finite number of fermions confined in a spherical potential well [2]. This electronic shell structure, in turn, motivated some theorists to study clusters as atomlike building blocks of materials [3]. The electronic structure of the metallofullerenes La C60 [4] and K C60 [5] was investigated from this viewpoint. This theorists dream of using clusters as atomlike building blocks was first realized by the macroscopic production of C60 and simultaneous discovery of crystalline solid C60, where C60 fullerenes form a close-packed crystalline lattice [6]. 

The followers of a phase transformation toughening (PTT) state that the change from a less densely packed crystalline structure (f)) to a more packed one (a) (i) promotes microvoiding in the earliest stages of the deformation and (ii) facilitates plasticity due to its exothermic character [72,78,193]. 

The value for close-packed crystalline Si is about 2.3 [29], and above 3.0 nm for traditional polymers [30]. Strohmeir s method [31] for calculating the thickness from the normal emission spectrum then yields ... 

The very heavy shades such as blacks and navies cannot be dyed by conventional methods on polyester fibres, even with the help of carriers. Since the difficulty is the slow diffusion of the larger dyestuff molecules into the closely packed crystalline structure of the fibre, the obvious approach is to present simple molecules and cause them to combine to form a coloured pigment after they have entered. Brenthols and Naphthol AS products are not adsorbed by polyesters from aqueous solutions of their sodium salts. A limited measure of success was achieved by immersing the goods in a suspension of naphthoic acid anilide derivatives and then coupling with a diazotized base. The results were more successful, however, when coupling components with smaller molecules were used and a- and /3-naphthoIs, applied from suspension, were satisfactory but jS-hydroxynaphthoic acid proved to be the most suitable. 

In a solid state and in a hot melt, being still or moving slowly, polyethylene molecules preserve this bean shape. Besides, in the solid state HDPE is a semicrystalline polymer, that is it contains both well-packed, crystalline areas and amorphous regions (Fig. 9.2). 

Figure 9.2 A typical presentation of the solid state HDPE [1]. Both well-packed, crystalline areas, and amorphous regions are seen.

From the angle-dependence of the XPS signal, Muller el al. conclude that Au remains to a large extent at the surface of 5T films if Au is evaporated in short intervals [39], This guarantees an effective heat dissipation with negligible temperature increase. There is a strong dependence of the Au diffusion into the anT film on the film structure. As expected, the diffusion is much smaller in densely packed crystalline films if compared to only z-oriented films (compare Section 3.3). 

The regularity of the cellulose chain and extensive hydrogen bonding between hydroxyl groups of adjacent chains cause cellulose to be a tightly packed crystalline material which is insoluble and infusible. As a result, cellulose cannot be processed in the melt or in solution. However, cellulose derivatives in which there is less hydrogen bonding are processable. 

In native starches, branched amylopectine molecules form die crystalline phase and die eventually present amylose constitutes die amorphous state. Pairs of the branches with a degree of polymerisation of 26 fold into the native, parallel oriented double-helices, which build a planar-hexagonal packed crystalline phase. In the metastable B-structure, one of three sites of this packing are filled by water and in the stable A-structure the hexagonal... 

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