Sizes of Crystallites

Knowledge of sizes of ciystallites and non-crystalline domains is very important because it allows clarify the models of super-molecular structure of cellulose, in particular of elementary fibrils of cellulose. There are several methods for measuring the size of the crystallites electron microscopy (EM), atomic force microscopy (AFM),WAXS,etc. 

However, the EM and AFM methods require prior isolation of the free crystallites, for example by hydrolysis of the cellulose fibers, which distorts the native structure. Moreover, contrasting and shading substances used in the EM investigations of cellulose cause significant errors at the measurement of the crystallite sizes. When using AFM, the sample undei oes the mechanical stresses under influence of the sharp tip, which can misrepresent the actual sizes of the crystallites. 

WAXS method is considered as a simple and convenient method for determining the size of the crystallites without their isolation from cellulose. The X-ray measurement method of average size of small crystallites is based on Scherrer s equation  

Scherrer s equation was developed in 1918 in order to calculate the size of nanocrystallites from measuring the width at half maximum of XRD peaks (Scherer, 1918). Even after nearly 100 years, this equation is widely used nowadays, although it has considerable limitations, namely the following  

To determine the actual sizes of crystallites, an improved WAXS method should be used taking into consideration the contribution both of instrumental factor (h] and also of paracrystalline distortions (A] in the experimental width [5] of the peak  

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Measurements conducted on samples, made of other grades of steel have shown that the shift of frequency characferistics of the applied signal are closely connected with sizes of crystallite grains and may be applied for the determination of parameters of the material structure. 

In addition to purely energetical heterogeneity one should also take into account some basic aspects of possible heterogeneities resulting from geometrical effects. The simplest and yet experimentally quite important geometric effects are due to the finite size of crystallites. Experimental measurements ave clearly demonstrated that the size of typical crystallites may be quite small (of the order of 50-100 A [116,132] and quite large (of the order of 10 A [61]. 

The effects due to the finite size of crystallites (in both lateral directions) and the resulting effects due to boundary fields have been studied by Patrykiejew [57], with help of Monte Carlo simulation. A solid surface has been modeled as a collection of finite, two-dimensional, homogeneous regions and each region has been assumed to be a square lattice of the size Lx L (measured in lattice constants). Patches of different size contribute to the total surface with different weights described by a certain size distribution function C L). Following the basic assumption of the patchwise model of surface heterogeneity [6], the patches have been assumed to be independent one of another. 

The optical properties of tubular blown film depends greatly on the surface irregularities and the size of crystallites domain in film, which, in turn, are dependent on... 

The numerical data, as determined by the authors, characterizing the dependence of the degree of crystallinity and the size of crystallites on the draw ratio of the fiber, are presented in Table 4. 

Many of the properties of a polymer depend upon the presence or absence of crystallites. The factors that determine whether crystallinity occurs are known (see Chapter 2) and depend on the chemical structure of the polymer chain, e.g., chain mobility, tacticity, regularity and side-chain volume. Although polymers may satisfy the above requirements, other factors determine the morphology and size of crystallites. These include the rate of cooling from the melt to solid, stress and orientation applied during processing, impurities (catalyst and solvent residues), latent crystallites which have not melted (this is called self-nucleation). 

X-ray diffraction of pigment powder lends itself to the determination of pigment crystallinity. It is thus possible not only to determine the chemical configuration of a crystalline compound, but also the lattice system of the crystal through the diffraction pattern, in other words, the crystal quality size of crystallites, structural defects (Fig. 18). 

One of the primary limitations of PET is related to its slow rate of crystallization from the melt. A consequence of this is that relatively long cycle times are required to provide crystallinity in PET. When this is achieved, it is often accompanied by opacity and brittleness, due to the relatively large size of crystallites formed by thermal crystallization. Crystallinity itself is often desirable in moulded parts, due to the higher thermal and mechanical stability associated with it. Crystallinity is especially desirable when parts are intended to be subjected to elevated temperatures since if the PET components are amorphous they will anneal at temperatures above 80 °C. 

The normalized peak-shape function PS introduced by equation (1) must be determined in order to figure out the dependence of PS on several crystallite parameters, such as average size of crystallites, misorientation of crystallites in the sample etc. These parameters lead to a broadening of reflections, which must be taken into account. 

With nickel catalysts, the extent of the multiple exchange increases with increase of temperature, reduction of the ratio of deuterium to hydrocarbon, and increased size of crystallite. 

Table I. Dependence of the Degree of Nickel Reduction to Metal and the Size of Crystallites on the Nature of a Catalyst Support (45)...

As is shown in the first part of the paper it is believed that Xe absorbs only in noncrystalline regions of polymers. Therefore it can be expected that crystalline domains form a diffusion barrier for Xe. For the right sizes of crystallites this would imply that the Xe diffusion coefficients are dependent on the diffusion time. Such effects have been found in some catalysts [25]. Attempts to detect similar phenomena in semi-crystalline polymers so far failed, possibly because the systems chosen here do not have the right internal crystalline structure (in the PBT/PTMO case) or the crystallites are too small (in the case of EPDM). Results on semi-crystalline non-elastomer polymers will be published elsewhere. 

Nanostructured materials (continued) synthesis for advanced catalysts, 2-3 synthesis of TiC>2 by aerosol process, 6 varying grain size of crystallites, 4 Nanowires... 

Figure IS. Increase in size of crystallites supported on SiC>2 with increasing amount of NiO [83]. The SiC>2 used had a surface area of 415m2g l, pore volume l.l2cmJg. The samples were obtained by pore volume impregnation with an aqueous solution of nickel nitrate. Calcination was at 773 K for 4h. The size of the crystallites was determined by electron microscopy.

Phases present Unit cell contents Size of crystallites... 

The kinematical approach is simple, and adequately and accurately describes the diffraction of x-rays from mosaic crystals. This is especially true for polycrystalline materials where the size of crystallites is relatively small. Hence, the kinematical theory of diffraction is used in this chapter and throughout this book. 

Fio. 28. Frequency factor (A) for hydrogenation of benzene, size of crystallite (D ), and lattice defect (ij) of palladium on aluminosilicate catalyst prepared by cation exchange versus temperature of reduction of the catalyst. Calcined temperature before reduction was kept constant at 300°. 

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