Sherrer equation

To better understand the differences in their catalytic behavior, the catalysts were characterized by XRD and UV-vis DRS. Unfortunately, except for the peak at 77.6° 26 (311 diffraction), the other Au diffraction peaks overlapped with those of y-Al203. The size of the coherent domains of Au, listed in Table I, were estimated using the width of this diffraction peak and the Debye-Sherrer equation. They showed that catalysts of both groups A and C had small coherent domains, whereas those of group B had large domains. 

Three LaCoOs samples (1,11, and 111) with different specific surface areas were prepared by reactive grinding. In the case of LaCoOs (1), only one step of grinding was performed. This step allowed us to obtain a erystalline LaCoOs phase. LaCoOs (11) and LaCoOs (111) were prepared in two grinding steps a first step to obtain perovskite crystallization and a second step with additive to enhanee speeific surface area. The obtained compounds (perovskite + additive) were washed repeatedly (with water or solvent) to free samples from any traee of additive. The physical properties of the three catalysts are presented in Table 10. LaCoOs (1) was designed to present a very low specific surface area for comparison purposes. NaCl used as the additive in the case of LaCoOs (11) led to a lower surface area than ZnO used for LaCoOs (111), even if the crystallite size calculated with the Sherrer equation led to similar values for the three catalysts. The three catalysts prepared were perovskites having specific surface areas between 4.2, 10.9 and 17.2 m /g after calcination at 550 °C. A second milling step was performed in the presence of an additive, yielding an enhanced specific surface area. 

Dl, particle size calculated from the Sherrer equation Sjh, specific surface area calculated assuming cubic particles and a density of LaCo03 equal to 7.29 D2, equivalent cubic particle size calculated from BET surface area. P, perovskite C, cobalt oxide. 

X-Ray diffraction pattern show that Pt (0) clusters average size on Sherrer equation is 7 - 10 nm. For Pt/SWNT clusters size is 4 nm (Fig. 6). It is necessary to mark that the sizes of Pt clusters of traditional catalysts 10 % Pt/C are more (100-200 nm). 

The observed lattice parameter for the Pt-Ru/C sample follows from the presence of a solid solution of Pt and Ru. According to the variation of afcc with composition for Pt-Ru bulk alloys, an atomic fraction of 45% Ru should be present in the carbon supported alloy. An average particle size for the metal crystallites of 23 A and 20 A in the Pt/C and Pt/Ru/C catalysts, respectively, was determined from the broadening of the (220) diffraction peak by using the Debye-Sherrer equation. 

Figure 3.123 Size-dependent evolution of powder XRD patterns for CoPt3 nanoc stals. The average nanoc stal sizes were calculated using the Debye-Sherrer equation. Reproduced with permission from Ref [55] 2003, American Chemical Society.

After the sample is analyzed the XRD pattern is analyzed using available computer software to measure the interplanar d spacings, and corresponding line intensities. The X-ray pattern of the sample may be compared to reference samples stored in the computer for identification. Crystallite size is also determined using the Sherrer equation. 

TEM and EDX. According to XRD (Table 9) and TEM data (Fig. 55), the increase of calcination temperature is accompanied by porosity annealing and the increase of particle size of both components. Estimation of the particle sizes for separate phases in nanocomposites from X-ray diffraction patterns using Sherrer equation revealed that for composite systems domain sizes of P and F phases remain on a nanoscale level even after sintering at 1200 °C (Table 9). As judged by TEM data, the nanocomposites prepared via ultrasonic dispersion route are characterized by uniform spatial distribution of P and F domains in composites (Fig. 

The X-ray powder diffraction patterns were recorded with a Philips diffractometer equipped with a proportional counter, by using a Ni-filtered CuK radiation. The samples were examined without any previous pretreatment. The crystallinity degree was determined by a procedure developed in our laboratories (ref. 4). The method was based on the comparison between the integrated intensities of two different spectral ranges, specifically affected by the crystalline and by the amorphous fractions of the solid respectively. In this manner the necessity of external standards, having known crystallinity, can be avoided. The crystallite size was determined from the half width of the peaks by using the Sherrer equation after correcting for the mud the... 

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 sharpness of XRD peaks is corresponding with the size of metal nanoparticles. Sherrers s equation is used to estimate the crystalline size of metal nanoparticles. Note that the size estimated from XRD peak width is some times larger than the size measured by TEM, especially when the size is very small. If the size estimated from XRD peak width is smaller than that directly measured by TEM, the particles could be polycrystalline. 

XRD data for selected samples are shown in Table 1. The interplanar spacings, doo2 and doo4, were evaluated from the positions of the 002 and 004 peaks respectively by applying Bragg s equation. The crystallite size Lc along the c-axis was calculated from the 002 peak using the Sherrer formula... 

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