Particle-size broadening

Figure 12.19 [55] is a plot of the viscosity as a function of volume fraction for ever-broadening particle size distributions [56]. Furnas... 

The XRD line broadening particle size measurements were confirmed by TEM, the new method of preparation giving a fine uniform dispersion of metal particles. 

Figure C2.17.10. Optical absorjDtion spectra of nanocrystalline CdSe. The spectra of several different samples in the visible and near-UV are measured at low temperature, to minimize the effects of line broadening from lattice vibrations. In these samples, grown as described in [84], the lowest exciton state shifts dramatically to higher energy with decreasing particle size. Higher-lying exciton states are also visible in several of these spectra. For reference, the band gap of bulk CdSe is 1.85 eV.

Besides phase identification XRD is also widely used for strain and particle size determination in thin films. Both produce peak broadenings, but they are distinguishable. Compared to TEM, XRD has poor area resolution capability, although by using synchrotron radiation beam diameters of a few pm can be obtained. Defect topography in epitaxial films can be determined at this resolution. 

Scherrer equation to estimate the size of organized regions Imperfections in the crystal, such as particle size, strains, faults, etc, affect the X-ray diffraction pattern. The effect of particle size on the diffraction pattern is one of the simplest cases and the first treatment of particle size broadening was made by Scherrer in 1918 [16]. A more exact derivation by Warren showed that. 

The influence of the sample volume on the zone broadening is more pronounced for media of smaller particle size (due to their inherent low zone... 

If the secondary stream contains emulsifier it can function in three ways. When the emulsion feed is started quickly the added emulsifier can serve to lengthen the particle formation period and hence to broaden the particle size distribution. When the emulsion feed is started later and added in such a manner that the emulsifier is promptly adsorbed on existing particles, one can obtain quite narrow size distributions. If the emulsion feed is started later but added rapidly enough to generate free emulsifier in the reaction mixture a second population of particles can be formed, again yielding a broad size distribution. 

When applied to the XRD patterns of Fig. 4.5, average diameters of 4.2 and 2.5 nm are found for the catalysts with 2.4 and 1.1 wt% Pd, respectively. X-ray line broadening provides a quick but not always reliable estimate of the particle size. Better procedures to determine particle sizes from X-ray diffraction are based on line-profile analysis with Fourier transform methods. 

Bulk characterization of calcined precursors and reduced catalysts was carried out by X-ray diffractometry using Cu K radiation. Reduced catalysts were first passivated by exposure to N2O as described above. Line-broadening analysis was carried out on the Fe(llO) reflection to obtain the iron particle size. Overlap with the MgO(200) reflection limited its usefulness to the more highly-loaded catalysts. 

Iron particle size from X-ray line broadening and percentage-reduction/CO-chemisorption ... 

The chemical analyses of the samples are reported in Table 2. The X-ray diffraction spectra of these solids do not show the presence of any Cu oxide phase with size larger than 3-4 nm, excepted in the cases of Cu(3)Si02 and Cu(4)Zr02 on one side, Cu(146)Na(6)FAU-10 and Cu(146)Na(28)MFI-15 on the other side, where the lines characteristic of CuO do appear with a line broadening corresponding to a particle size of about 4 nm. 

A were packed. They were individually calibrated. All three 3000 A columns showed similar peak separation characteristics for particle sizes between 312 nm and 5TQnm. However, peak broadening was much larger for one of the 3000 A 0olumns. This column was discarded. Of the remaining two 3000 A columns, one was subjected to the following ... 

The interaction of adsorbed thiol molecules with gold nanoparticles as a function of the mean particle size has also been studied [180]. Monochromated X-ray Photoelectron Spectroscopy (MXPS) measurements showed the attachment of the thiol sulfur headgroup onto the cluster surface leading to a positive BE shift in the Au 4f corelevel. No line width broadening could be observed indicating that the thiol-gold interaction affects the whole... 

The Crystallite Size and the Scherrer Formula. The Scherrer formula is based on a restricted assumption assuming that the peak shape is dominated by size effects. The problem of Bragg line broadening, originating from particle size, was first investigated by Scherrer [30] who derived the well-known and widely used law ... 

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