Debye-Scherrer equation

Figure 1 is a TEM photograph of the Cu (10wt%)/Al2O3 catalyst prepared by water-alcohol method, showing the dispersed state of copper and was confirmed the particle sizes from XRD data. Figure 2 is X-ray diffraction patterns of above-mention catalysts, was used to obtain information about phases and the particle size of prepared catalysts. Metal oxide is the active species in this reaction. Particle sizes were determined fix)m the width of the XRD peaks by the Debye-Scherrer equation. 

Chemical composition of fresh HTs was determined in a Perkin Elmer Mod. OPTIMA 3200 Dual Vision by inductively coupled plasma atomic emission spectrometry (ICP-AES). The crystalline structure of the solids was studied by X-ray diffraction (XRD) using a Siemens D-500 diffractometer equipped with a CuKa radiation source. The average crystal sizes were calculated from the (003) and (110) reflections employing the Debye-Scherrer equation. Textural properties of calcined HTs (at 500°C/4h) were analyzed by N2 adsorption-desorption isotherms on an AUTOSORB-I, prior to analysis the samples were outgassed in vacuum (10 Torr) at 300°C for 5 h. The specific surface areas were calculated by using the Brunauer-... 

Determined by X-ray fluorescence spectroscopy Full width at half maximum (FWHM) of (003) plane 5 Crystallite size (t) calculated from (003) plane using Debye-Scherrer equation... 

The particle diameter D is related to the full width at half maximum A by the Debye-Scherrer equation D = 0.9 XIA cos0, where 20 is the diffraction angle and X is the X-ray wavelength. Table 27.1 lists the particle size and lattice plane spacing calculated using the strongest (h,k,l) peak for the Fe, W, Mo carbides, nitrides, oxynitrides and oxycarbides. It is important to note that the calculated particle size using the Debye-... 

For nanocrystals, the interpretation of lattice parameter shifts is complicated by the very small dimensions of the crystallites. Because of the small crystal dimensions, the diffraction peaks are broadened as described by the Debye-Scherrer equation (106), making accurate assessment of small shifts more challenging. Systematic errors such as zero-point or sample-height offsets can also cause artificial shifts in lattice constants (107). The inclusion of an internal... 

Powder X-ray diffraction (XRD) is performed on a Siemens D5005 diffractometer with Cu Ka radiation. The particle size is calculated from the X-Ray line broadening, using the Debye-Scherrer equation. DRS is measured by Perkin-Elmer Lambda 20 UV-visible spectophotometer at room temperature in the wavelength region between 200 and 800 nm. Raman spectra are recorded on a Broker RFS 100 with 2 cm resolution. 

Average crystallite size calculated from the broadening of XRD reflections using the Debye-Scherrer equation. Total weight loss at 900°C given by TGA. Au mean particle size obtained by transmission electron microscopy. Reaction rates given at 80°C for the oxidation of CO, the oxidation of CO and the oxidation of H2 under PROX conditions and the oxidation of H2. 

X-Ray powder diffraction experiments were carried out using a Siemens D5000 X-Ray Diffractometer equipped with a CuK X-Ray source. The interplanar distances (d) and the particle sizes (1) were calculated by the Bragg and the Debye-Scherrer equations, respectively. Activity tests for the WGSR were carried out in a tubular quartz reactor loaded with 100 mg of catalyst. The feed gases (5% CO, 15% H2O, He to balance, total flow rate 100 cm min ) were introduced to the catalyst bed at a space velocity of 60,000 h at several temperatures between 200 and 500°C. 

The XRD pattern of pure gum Arabica powder specimen is shown in Figure 12.3. It shows the overall amorphous nature of gum Arabica. The intensity peak corresponds to 26 = 18.893° is the peak in Radial Distribution Function (RDF). The Debye-Scherrer equation given in Equation 12.2 is employed to compute coherent length ... 

XRD is a fast and nondestructive test which is frequently used to characterise thermoset materials and their composites. Crystalline materials are characterised by sharp peaks, whereas amorphous materials show broad humps. Thus, the degree of crystallinity can be estimated. When a crystalline material such as clay is dispersed in a thermoset matrix, one can study the intercalation and exfoliation behaviour (see subsequent chapters). If the crystallites of the power are very small, the peaks of the pattern will be broadened. From this broadening one can determine an average crystallite size using the Debye-Scherrer equation ... 

The phase composition and crystallite size was calculated with the help of diffraction peaks by using Debye-Scherrer equation d = k /(JCos 0 by using a line broading method. Where d is the crystallite size, k a constant of 0.9, X the x-ray wavelength of Cu which is 1.5406 A, 0 the Bragg angle in degree and p the full width half maxima (FWHM). The XRD pattern shows broad... 

People often use the x-ray diffraction (XRD) technique to estimate the crystal size based on the crystallite facets. For Pt, the prominent crystalline surfaces are the (111), (200), and (220) and (311), respectively. Based on the broadening of the x-ray diffraction peaks, the crystallite sizes are calculated according to the Debye-Scherrer equation. 

Another example of a DMC-catalyzed esterification reaction is the esterification of free fatty acids with glycerol [32]. This reaction again used Zn-Fe(II)-DMC as a catalyst yet the activity of the material could be tuned by varying the synthesis temperature. As such, DMCs with different acidities (as evidenced by NHj-TPD), crystallite sizes (calculated from the Debye-Scherrer equation), particle sizes (studied with scanning electron microscopy (SEM)), and BET (Brunauer, Emmett and Teller) specific surface areas were obtained. The highest catalytic conversions were observed for the catalysts synthesized at elevated temperatures these materials featured both the highest specific surface area and the largest number of acid sites. 

The average grain size determined from the XRD using the Debye-Scherrer equation was 42-46 nm, depending on the reaction conditions. XPS was used to confirm the presence of Ag(0) in the samples by the presence of Ag3ds/2 and Ag3d3/2 peaks. 

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