Shape of the crystallites

Surface thermodynamics can explain some unusual shapes of the crystallites on the support, such as the extended planar structure, as well as the existence of a two dimensional phase on the support in equilibrium with the crystallites. It also allows one to derive an expression for the thickness of the planar crystallites. The two dimensional phase, which it predicts to exist, is responsible for the Ostwald ripening mechanism, by which the small crystallites lose atoms to the two dimensional phase and the large ones gain atoms from the two dimensional phase. The surface thermodynamics also provides an explanation for the dynamics of rupture of a thin film located on a support, thus shedding some light about the formation of Fe crystallites on alumina during heating in H2 in places in which no crystallites were present before (the specimen was previously heated in O2). 

Typical snapshots illustrating evolution of the distribution of crystallites are shown in Figure 13. At early stages (see, e.g.. Fig. 13a for /=10 MCS), the crystallites look like bilayer islands. With increasing time, the height of crystallites becomes larger (Fig. 13b). At the latest stages, the shape of the crystallites is pyramidal (Fig. 13c). 

Conventional theory of powder diffraction assumes completely random distribution of the orientations among the infinite amount of crystallites in a specimen used to produce a powder diffraction pattern. In other words, precisely the same fraction of the specimen volume should be in the reflecting position for each and every Bragg reflection. Strictly speaking this is possible only when the specimen contains an infinite number of crystallites. In practice it can be only achieved when the number of crystallites is very large (usually in excess of 10 to lO particles). Nonetheless, even when the number of crystallites approaches infinity, this does not necessarily mean that their orientations will be completely random. The external shape of the crystallites plays an important role in achieving randomness of their orientations in addition to their number. 

The scope of the present paper is to emphasize that the interactions between support, metal and atmosphere are responsible for both the physical (size distribution, shape of the crystallites, wettability of the substrate by the crystallites and vice versa), the chemical and the catalytic (suppression of chemisorption, increased activity for methanation, etc.) manifestations of the supported metal catalysts. In the next section of the paper, a few experimental results concerning the behaviour of iron crystallites on alumina are presented to illustrate the role of the strong chemical interactions between the substrate and the compounds of the metal formed in the chemical atmosphere. Surface energetic considerations, similar to those already employed by the author (7,8), are then used to explain some of the observed phenomena. Subsequently, the Tauster effect is explained as a result of the migration, driven by strong interactions,... 

The primary particles may be illustrated as formed from coacervates of the crystallites, probably interlinked by dissolved polymeric species. Critical nucleus sizes for crystallization from aqueous solutions extend from the stable oligomeric species to polymers of 100 to 1000 ions/molecules. During the condensation, the shape of the crystallites is induced on the particulate structures formed... 

The concentration of B5 sites is very sensitive to the shape of the crystallite. For various crystals containing 683 atoms, van Hardeveld and Hartog (20) calculate a number of B5 sites ranging from 76 to 0 for example, 36 for a sphere, 76 for a cubooctahedron, 13 for a cube, and 0 for many other possible arrangements. 

The quantitative information provided by PPG NMR about the existence of additional transport resistances on the external surface of the zeolite crystallites (surface barriers) results from a comparison of the values for the intracrystalline mean life time determined directly (viz. Tintra) by an analysis of the time dependence of the spin-echo attenuation (and, hence, of the propagator), and determined indirectly (viz. tP ) from the intracrystalline diffusivity on the assumption that molecular exchange between different crystallites is controlled by intracrystalhne diffusion. On the additional assumption that the shape of the crystallites may be approximated by spheres with a mean square radius (R ) one has in the latter case [87,103]... 

The ultimate microstructure of a solid will depend on how quickly different crystal faces develop. This controls the overall shape of the crystallites, which may be needle-like, blocky or one of many other shapes. The shapes will also be subject to the constraint of other nearby crystals. The product will be a solid consisting of a set of interlocking grains. The size distribution of the crystallites will reflect the rate of cooling of the solid. Liquid in contact with the cold outer wall of a mould may cool quickly and give rise to many small crystals. Liquid within the centre of the sample may crystallise slowly and produce large crystals. Finally, it is important to mention that the microstructure will depend sensitively on impurities present. This aspect is discussed in Chapters 4 and 8. 

The shape of nanocrystallites of natural cellulose is a subject of discussion. In several studies the cross-sectional shape of the crystallites was depicted as a square or rectangle. However, recent studies have shown that the most likely cross-sectional shape of the crystallites of natural cellulose is a hexagon (Ding and Himmel, 2006 loelovich, 1991 Yang et al., 2011). Three groups of planes (100), (110), and (110) are located on the surface of crystallites, allowing the co-crystallization process of adjacent crystallites in different lateral directions (loelovich, 1991). The co-crystallization process observed during extraction and hydrolysis of cellulose leads to an increase in lateral sizes of crystallites. 

Half life time for crystallization of acetal has been found to be 27.7 minutes. At 4 minutes after crystallization started, 10% of crystallinity was obtained. What is the shape of the crystallite What is the type of nucleation ... 

The contributions of the examination with X-rays to the problems of gel structure and swelling have been particularly important. Various applications mentioned in the proceeding sections will serve to demonstrate this statement (p. 549) and few need be added at this place The most outstanding contributions were those concerning the question as to whether or not crystalline structures are present, under what conditions they appear or disappear, and what are the changes to which the lattice structure of the crystalline component is subjected under various conditions. Reliable quantitative information on the size and the shape of the crystallites which might, in theory, also be derived from X-ray diffraction patterns under favourable conditions, have been seldom, if ever, obtained. 

The shape of the crystallites themselves is usually anisometric, their greatest dimension coinciding with the direction of the chains. They have the form of lamellae rather than that of rodlets (cf. Fig. 90 in the next section) owing to the different magnitude of the intermolecular forces in the various directions perpendicular to the chain. The lamellar planes correspond.to the crystallographic planes with the densest population of those atoms or groups, which contribute most to intermolecular cohesion (as, for instance, the hydroxylgroups in cellulose). 

The strongly anisotropic shape of the crystallites favors the development of a texture parallel to the surface of the Ag tube in powder-in-tube (PIT) processing, and this is highly desirable for the superconducting properties. The Ag content also serves as a source of pinning centers that hinder the flux line motion. 

Table 3>1. Average lateral size, density, and shape of the crystallites of the passive film formed on Ni(l 11) in 0.05 M H2SO4 by a potential step in the passive region.

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