Crystal systems Crystallite

Intentional seeding is a common practice among chemists who wish to coax the crystallization of a compound from solution or from the melt small crystals or crystallites of the desired material (seeds) are added to the system (e.g. Pavia et al. 1988 Shriner et al. 1997). In this way, the rate-limiting nucleation step, which may be extremely slow, can be accelerated. For this method to be applied, it is of course necessary that a sample of the desired crystalline material is available that is, the compound must have been already crystallized in a previous experiment. When polymorphic forms of a substance are known to occur, intentional seeding with one of the polymorphs is a useful and often the most successful way of preferentially producing it rather than the other form(s). 

The above practice is rather straightforward for a single-crystal experiment, but often provides doubtful results when only powder diffraction data are available. The basic reason is that the powder diffraction pattern is onedimensional, owing to the collapse of the reciprocal lattice of the individual crystallites onto the 26 axis. Consequently, reflections with the same r/ / modulus (i.e. with the same interplanar spacing d ki- indeed dhki= l/ rM /l) will overlap on the 29 axis. For convenience, we quote in Table 7.2 the algebraic expressions of d ki for the various crystal systems. 

The Avrami equationhas been extended to various crystallization models by computer simulation of the process and using a random probe to estimate the degree of overlap between adjacent crystallites. Essentially, the basic concept used was that of Evans in his use of Poisson s solution of the expansion of raindrops on the surface of a pond. Originally the model was limited to expansion of symmetrical entities, such as spheres in three dimensions, circles in two dimensions, and rods in one, for which n = 2,2, and 1, respectively. This has been verified by computer simulation of these systems. However, the method can be extended to consider other systems, more characteristic of crystallizing systems. The effect of (a) mixed nucleation, ib) volume shrinkage, (c) variable density of crystallinity without a crystallite, and (random nucleation were considered. AH these models approximated to the Avrami equation except for (c), which produced markedly fractional but different n values from 3, 2, or I. The value varied according to the time dependence chosen for the density. It was concluded that this was a powerful technique to assess viability of various models chosen to account for the observed value of the exponent, n. 

With the discovery of the lamellar form of polymer crystallites, it was widely heralded, with minor exceptions, that the chains crystallized in a regularly folded array with complete adjacent reentry. " Thus the basal plane was presumed to have a very smooth interfacial structure. For bulk crystallized systems a sequence of chain units would be allowed to escape on occasion as a defect and join a neighboring crystallite. The concept of regular chain folding, where the chains... 

Although a discussion of the properties of crystals formed in dilute solution is not a major topic in this chapter, they are of great importance, both as entities in themselves and in relation to bulk crystallized systems. Of particular importance in the present context is the level of crystallinity that is attained and the structure of the non-crystalline region. The lamellar-like platelets that are formed in dilute solution and the chain orientation within the crystallites is well established. Based almost solely on the observation of lamellae, and the concept of regularly folded chains, a completely... 

In the sense employed here, the perfect phase possesses the lowest free energy consistent with the constraints imposed on the system. Hence the presence of equilibrium type defects, such as lattice vacancies, is automatically included. The possibility that nonequilibrium type defects may exist in the macroscopic crystal or crystallite that eventually develops is not pertinent to the problem of nucleus formation. 

For shape memory applications, crystals formed upon cooling of the semicrystalline polymer act as physical crosslinks by which a permanent or equilibrium shape can be set. In a complementary fashion, the miscible amorphous phase governs temporary shape fixing. In turn, crystallization kinetics, crystallite size, and degree of crystallinity collectively determine kinetics of permanent shape setting and shape memory performance characteristics. Thus, it is possible to tailor the shape memory properties of a system by varying the composition and the thermal history of such blends[9], leading us to the present study focused on crystallization kinetics from melt-miscible crystalline-amorphous blends. 

As with any system, there are complications in the details. The CO sticking probability is high and constant until a 0 of about 0.5, but then drops rapidly [306a]. Practical catalysts often consist of nanometer size particles supported on an oxide such as alumina or silica. Different crystal facets behave differently and RAIRS spectroscopy reveals that CO may adsorb with various kinds of bonding and on various kinds of sites (three-fold hollow, bridging, linear) [307]. See Ref 309 for a discussion of some debates on the matter. In the case of Pd crystallites on a-Al203, it is proposed that CO impinging on the support... 

According to Hosemann-Bonart s model8), an oriented polymeric material consists of plate-like more or less curved folded lamellae extended mostly in the direction normal to that of the sample orientation so that the chain orientation in these crystalline formations coincides with the stretching direction. These lamellae are connected with each other by some amount of tie chains, but most chains emerge from the crystal bend and return to the same crystal-forming folds. If this model adequately describes the structure of oriented systems, the mechanical properties in the longitudinal direction are expected to be mainly determined by the number and properties of tie chains in the amorphous regions that are the weak spots of the oriented system (as compared to the crystallite)9). 

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