Crystallite size, diffraction

Crystallite Size. From the width of the peaks the computer can determine the size of the crystaUites in the sample. The smaller the crystaUite size, the broader are the diffraction peaks. This kind of analysis is important for determining particulate size of certain materials (eg, sUica) where a range of crystaUite size may be a health hazard if inhaled into the lungs. 

Fig. 7.3. Crystallite size determined from x-ray diffraction line broadening studies show substantial shock-induced reductions. The chemical reactivity of such powders would be expected to be greatly enhanced [86M02].

This conclusion was additionally confirmed by Palczewska and Janko (67) in separate experiments, where under the same conditions nickel-copper alloy films rich in nickel (and nickel films as well) were transformed into their respective hydride phases, which were proved by X-ray diffraction. The additional argument in favor of the transformation of the metal film into hydride in the side-arm of the Smith-Linnett apparatus consists of the observed increase of the roughness factor ( 70%) of the film and the decrease of its crystallite size ( 30%) after coming back from low to high temperatures for desorbing hydrogen. The effect is quite similar to that observed by Scholten and Konvalinka (9) for their palladium catalyst samples undergoing the (a — j8) -phase transformation. 

Many studies have been made of the rates of water evolution from layer-type silicate minerals which contain structural hydroxyl groups (clays and micas). Variations in composition of mineral specimens from different sources hinders comparison of the results of different workers. Furthermore, the small crystallite sizes and poor crystallinity that are features of clays limit and sometimes prevent the collection of ancillary observations (e.g. microscopic examination and diffraction measurements). 

The suppression of C60 crystallite formation in mixed LB films was attempted by mixing C60 and amphiphilic electron donor compounds [259]. Observation of the C60 LB film transferred horizontally by TEM clearly showed 10-40-nm-size crystallites. The diffraction pattern gave an fee lattice with unit cell length 1.410 nm. Examination of the mixed films with arachidic acid by TEM showed extensive crystallite formation. Mixed LB films of three different amphiphilic derivatives of electron donors with C60 were examined. One particular derivative showed very little formation of C60 crystallites when LB films were formed from monolayers of it mixed with C60 in a 1 2 ratio, while two others reduced C60 crystallite formation but did not eliminate it. 

Nanocrystals titania was prepared by sol-gel method. X-ray diffraction result is shown in Figure 1, all samples were anatase phase. Based on Sherrer s equation, these samples had crystallite sizes about 7 nm. From XRD results, it indicated that titania samples showed the similar of crystallinity because the same ordering in the structure of titania particles make the same intensity of XRD peaks. 

The properties of titania particles were investigated using X-ray diffraction (XRD, Model D/MAX-RB, Rigaku Ltd.), scanning electron microscopy (SEM, Model 535M, Philips Ltd.), transmission electron microscopy (TEM, Model 2000EX, JEOL Ltd.). The crystallite sizes were estimated by Scherrer s equation and the composition of rutile phase in titania were estimated from the respective integrated XRD peak intensities. 

X-Ray diffraction has an important limitation Clear diffraction peaks are only observed when the sample possesses sufficient long-range order. The advantage of this limitation is that the width (or rather the shape) of diffraction peaks carries information on the dimensions of the reflecting planes. Diffraction lines from perfect crystals are very narrow, see for example the (111) and (200) reflections of large palladium particles in Fig. 4.5. For crystallite sizes below 100 nm, however, line broadening occurs due to incomplete destructive interference in scattering directions where the X-rays are out of phase. The two XRD patterns of supported Pd catalysts in Fig. 4.5 show that the reflections of palladium are much broader than those of the reference. The Scherrer formula relates crystal size to line width ... 

The amount of variation in reactivity which may be tolerated is small, since a reasonable balance has to be struck between rapid and uniform reaction on the one hand and practical working times on the other. Sorrell Armstrong (1976) found that the mean crystallite diameter could be determined adequately by X-ray diffraction, using line-broadening as an indication of crystallite size, and also by electron microscopy. These techniques were able to distinguish between suitable and unsuitable oxide powders. 

The analysis of XRPD patterns is an important tool studying the crystallographic structure and composition of powder compounds including the possibility to study deviation from ideal crystallinity, i.e. defects. Looking at an X-ray powder diffractogram the peak position reflects the crystallographic symmetry (unit cell size and shape) while the peak intensity is related to the unit cell composition (atomic positions). The shape of diffraction lines is related to defects , i.e. deviation from the ideal crystallinity finite crystallite size and strain lead to broadening of the XRPD lines so that the analysis of diffraction line shape may supply information about sample microstructure and defects distribution at the atomic level. 

In the simplest approach T is the full width of the peak (measured in radians) subtended by the half maximum intensity (FWHM) corrected for the instrumental broadening. The correction for instrumental broadening is very important and can be omitted only if the instrumental broadening is much less than the FWHM of the studied diffraction profile, which is always the case in presence of small nanoclusters. The integral breadth can be used in order to evaluate the crystallite size. In the case of Gaussian peak shape, it is ... 

The crystalline lamellar thickness Dc obtained by StrobPs method is initially 1.4 nm and grows to about 2.0 nm, which is roughly equal to the crystallite size in the chain direction of 2.8 nm estimated from the wide-angle X-ray diffraction (WAXD) [7]. Interestingly, the persistence length /p = 1.45 nm just before crystallization measured by SANS (also see Fig. 11) [9,10] is almost equal to the crystal thickness. 

The catalysts were characterized by inductively coupled plasma emission spectroscopy (ICP-ES Perkin Elmer Optima 3300RL) to determine cobalt content, x-ray diffraction (XRD Bruker A-500) with crystallite size determination using the Rietveld method, and temperature-programmed reduction (Zeton Altamira AMI-200) using 30 ml/min 10% H2/Ar and a ramp rate of 10°C/min. Surface area... 

Preferred orientation of the particles must be minimized. One of the most effective ways to achieve this is to reduce the particle size by grinding the sample [1], As already discussed in Section III.A, however, grinding can disorder the crystal lattice. Grinding can also induce other undesirable transitions, such as polymorphic transformations [59]. In order to obtain reproducible intensities, there is an optimum crystallite size. The crystallites have to be sufficiently small so that the diffracted intensities are reproducible. Careful studies have been carried out to determine the desired crystallite size of quartz, but no such studies have been reported for pharmaceutical solids [60]. Care should be taken to ensure that the crystallites are not very small, since decreased particle size can cause a broadening of x-ray lines. This effect, discussed earlier (Eq. 9), usually becomes apparent when the particle size is below 0.1 jum. 

Table 5 Changes in the crystallite size of some polycyclic pigments in coatings or plastics coloration as a result of heat exposure (calculated from the X-ray diffraction spectra).

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