X-ray diffraction line broadening

Table 7.2. Shock-modified powders X-ray diffraction line broadening.

Fig. 7.2. X -ray diffraction line broadening studies in inorganic powders by Morosin and co-workers show evidence for large plastic deformation with residual strain characteristic of cold-worked metals [86M02].

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].

Most surface area measurements are based on the interpretation of the low temperature equilibrium adsorption of nitrogen or of krypton on the solid using the BET theory [33,269,276—278]. There is an extensive literature devoted to area determinations from gas adsorption data. Estimates of surfaces may also be obtained from electron micrographs, X-ray diffraction line broadening [279] and changes in the catalytic activity of the solid phase [ 280]. 

Transmission electron micrographs (TEM) of submicrometer-size particles show faceted particles, and selected area electron diffraction (SAED) patterns of isolated particles show that they are formed by a small number of crystallites (Fig. 9.2.14a), This result is consistent with the mean size of the crystallites, which can be inferred from the x-ray diffraction lines broadening analysis using a William-son-Hall plot (35) in order to take into account the contribution of microstrains to the line broadening. Over the whole composition range, the mean crystallite size is in the range 40-60 nm for particles with a mean diameter in the range 200-300 nm (Table 9.2.5) (33). 

WIDE-ANGLE X-RAY DIFFRACTION LINE-BROADENING FOR CRYSTALLITE SIZE AND STRAIN... 

Fig. 7. The average particle sizes of copper ( ), its CuO precursor (O), and zinc oxide (A) determined from X-ray diffraction line broadening (41). [Reprinted with permission from J. Phys. Chem. 83, 3118 (1979). Copyright (1979) American Chemical Society.]...

For supported metal catalysts, no simple calculation is possible. A direct measurement of the metal crystallite size or a titration of surface metal atoms is required (see Example 1.3.1). TWo common methods to estimate the size of supported crystallites are transmission electron microscopy and X-ray diffraction line broadening analysis. Transmission electron microscopy is excellent for imaging the crystallites, as illustrated in Figure 5.1.5. However, depending on the contrast difference with the support, very small crystallites may not be detected. X-ray diffraction is usually ineffective for estimating the size of very small particles, smaller than about 2 nm. Perhaps the most common method for measuring the number density of exposed metal atoms is selective chemisorption of a probe molecule like H2, CO, or O2. 

State of Dispersion of Metal. Chemisorption of carbon monoxide at 23 °C and x-ray diffraction line broadening have been used to measure... 

Table I summarizes the characteristics of nickel catalysts prepared onto these supports. For brevity these catalysts will be referred to by a notation in the form aA-fi. For example, 7AAP-573 represents a 7 wt % Ni catalyst supported on A O 2A1P0 reduced at 573 K for 1 h. Incidentally, this sample did not reduce under these conditions and was excluded from further kinetic studies. Notations for the other catalysts are shown in the first column of Table I. All samples were reduced at the specified temperature for 1 h unless noted otherwise. The percent reduction was determined by measuring oxygen uptake at 673 K in a commercial thermogravimetric system (Cahn 113). The average particle size was determined by either X-ray diffraction line broadening or magnetic measurements (see below).

The Particle Dimensions of ZnO and Cu as Determined from X-Ray Diffraction Line Broadening ... 

It has been shown that the addition of lead to a chromia-promoted magnetite WGS catalyst enhances the activity for WGS (4 ), A study of the solid state changes which occur upon this substitution was made to probe the active sites..of the catalyst. Through a combination of oxidation studies, Mossbauer spectroscopy, and X-ray diffraction line broadening, a model for the. catalyst was developed. It was concluded that Pb was present as Pb " at tetrahedral sites. The Pb substitution resulted in the expansion of the tetrahedral sites, contraction of the octahedral sites, and the oxidation of some Fe to Fe. The resulting octahedral cations became more covalent in nature, and since the octahedral cations have been reported to be the active sites for CO oxidation over ferrites... 

CHE 00] CHEARY R.W., DOORYHEE E., LYNCH P., ARMSTRONG N., DLIGATCH S., X-ray diffraction line broadening from thermally deposited gold films , J. Appl. Cryst, vol. 33, p. 1271-1283,2000. 

KLI 88] KLIMANEK P., KUZEL R., X-ray diffraction line broadening due to dislocations in non-cubic materials. I. General considerations and the case of elastic isotropy applied... 

X-ray diffraction (XRD) is mostly used for bulk structure analysis, yet it has one feature which makes it suitable for size determination, if the concentration of the active component is large enough. Figure 7.21 shows how x-ray diffraction lines broaden as the crystallite size decreases. Quantitatively, a number average size is obtained from... 

FIgttre 7.21. X>ray diffraction line broadening of dispersed crystallites. 

The metal in a supported metal catalyst may be characterized by electron microscopy (providing a distribution of crystallite sizes), X-ray diffraction line broadening (providing an average size for crystallites larger than about 4 nm), and specific chemisorption (titration) with compounds such as H2 or CO [providing an estimate of the exposed metal area (v5. the total surface area of metal plus support)]. 

A chemisorption teclmique developed by Koinai et al., based on CO methanation, was successfrilly used to analyze noble metal dispersions of both fresh and vehicle-aged Pt/Rli and Pd/Rli commercial automotive three-way catalysts. The teclmique is relatively rapid (< 2 hours), extremely sensitive, and largely free from complications due to adsorption of CO on non-noble metal components of the washcoat (support, promoters, stabilizers, etc.). Particle sizes of the vehicle-aged catalysts, calculated by applying the spherical particle assumption to the dispersions measured by the CO methanation method, agreed well with particle sizes calculated from x-ray diffraction line-broadening data. These results indicate that the CO methanation teclmique can be applied routinely to obtain fast and accurate measurements of noble metal surface areas in automotive catalysts retrieved from tlie field, even tliose with metal dispersions ca. 2% or less. 

The X-ray diffraction studies of Krause failed to reveal the presence of crystalhne Tl. Krause suggested that diffraction effects from T1 were not observed because the metal is amorphous. However, even if the colloidal particles are crystalline, sufficiently smaU particle size results in X-ray diffraction lines broadened enough to be undetectable. Before concluding that the absence of Tl diffraction lines means that the Tl is amorphous, it is also necessary to know the fractional decomposition and so the expected intensities of the Tl lines. 

Alternatively, average crystallite size distributions can be determined from X-ray diffraction line broadening (9,10). Small-angle X-ray scattering (SAXS) permits the determination not only of particle sizes and particle size distributions, but also of particle shape as well as the specific surface area of the metal and of the support. 

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