X-ray line-broadening

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. 

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

Other metals on silica supports have been investigated less extensively than platinum and nickel, and average particle diameters have only been estimated by gas adsorption methods, supported in a few cases by X-ray line broadening data. Thus, rhodium, iridium, osmium, and ruthenium (44, 45) and palladium (46) have all been prepared with average metal particle diameters <40 A or so, after hydrogen reduction at 400°-500°C. 

Reduction Metal content after reduction (%) d , from x-ray line broadening (A) dvS, fromH2 Metal particle chemisorption size distribution at room temp. from electron (A) micrographs Number of B5 sites per mg of Ni Number of B6 sites per cm2 of Ni surface... 

From the surface area S, the mean particle size dvs, is calculated as dvs = 6/Sp where p is the density of the metal. The weight mean diameter dy, = Mid// 23 i nid/ was determined from the degree of X-ray line broadening. 

X-ray line broadening provides a quick but not always reliable estimate of the particle size. As Cohen [9] points out, the size thus determined is merely a ratio of two moments in the particle size distribution, equal to /. Both averages are weighted by the volume of the particles, and not by number or by surface area, as would be more meaningful for a surface phenomenon such as catalysis. Also, internal strain and instrumental factors contribute to broadening. 

The internal surface area of a porous inorganic membrane is often significantly affected by the heat treatment temperature. Leenaars, Keizer and Burggraaf (1984) have shown that, even if the crystallite size of the membrane precursor particles remains essentially the same (from the X-ray line-broadening measurements), the surfaee area of a transition-phase alumina membrane decreases with increasing calcination temperature. Con-... 

G.K. Williamson, W.H. HaU, X-ray line broadening from filed aluminum and wolfram, ... 

TEM and differential X-ray line broadening (expressed by the ratio of the width at half height of the 104 relative to that of the 110 reflection) indicate that the thickness of the platy Al-hematite crystals decreases as Al/(Fe-t Al) increases (Schwertmann et al., 1977 Barron et al., 1984). It is this change in morphology, rather than the structural Al, which governs the IR spectra, in particular the shape factor and the absorp-... 

Z. f Polymere 215 57-60 Wolska, E. Schwertmann, U. (1989) Nonstoi-chiometric structures during dehydroxylation of goethite. Z. Kristallogr. 189 223—237 Wolska, E. Schwertmann, U. (1989 a) Selective X-ray line broadening in the goethite-de-rived hematite phase. Phys. Stat. Sol. A 114 K11-K16... 

In this investigation, only electron inelastic scattering and x-ray line broadening were chosen for substantial correction. There were two principal reasons first, these broadening mechanisms account for the largest part of the distortion, and, second their contributions are easily determined or approximated. 

X-ray line broadening 0.07 Detecting primary crystallite size... 

Transmission and scanning electron microscopy are employed for a direct study of microclusters while the distribution of sizes (or average diameter) is provided by sedimentation and other techniques. The average particle diameter is obtained by the Brunauer-Emmett-Teller (BET) surface-area method and by X-ray line broadening. 

Table 1 gives the average sizes of nickel crystallites measured by X-ray line broadening analysis on (111) reflections, before and after the five hydrogenation runs. They increase moderately and even decrease for RNiFe. This confirms that the BET area loss could be due in part to a poisoning which reduces the capacity of nitrogen adsorption. However, measurements of the metallic surface area should also be done to confirm possible surface poisoning. 

The typical BET surface area of the freshly prepared iron carbide catalyst is approximately 70 m2 g 1. The surface area of the precipitated catalyst and ultrafine catalyst before pretreatment was 140 m2 g 1 and 250 m2 g 1, respectively however, following pretreatment with CO the surface areas dropped to 32 m2 g 1, and 64 m2 g-1, respectively. The particle sizes of the iron carbide and precipitated catalysts after 170 h, determined by X-ray line broadening, were 27 nm and 30 nm, respectively. The ultrafine catalyst had an average particle size of 25 nm after 240 h of synthesis. These particle sizes correspond to a surface area of about 40 m2 g-1. 

FIGURE 18 Average crystallite size measurement by X-ray line broadening. The width of characteristic X-ray lines decreases markedly as cerium dioxide powder is sintered. The crystallites grow from an initial size of 50 to 400 A after heating in air for several hours. 

Several physical methods may be used to provide indirect estimates of the degree of dispersion. Sizes of particles, or of single crystallites, or of magnetic domains determined, respectively, by electron microscopy, X-ray line broadening, and magnetization measurements, can be used for this purpose but, in all cases, assumptions must be introduced into the calculations. 

Further problems can arise because of uncertainties concerning the stoichiometry of the adsorption reaction. For most metals it is assumed that the surface stoichiometry with H2 is H/M = 1. However, there is evidence especially for very small metal particles (of the order of 1 -5 nm) that the stoichiometry can exceed H/M = 1. For quantitative measurements of surface area it is necessary to establish the chemisorption stoichiometry and structure. In practice it is usually possible to achieve approximate estimate of the surface area by some other independent method (for example, from particle size analysis by X-ray line broadening or by TEM). In the case of CO, the CO/M ratio is generally taken as 1.0, but the true value may depend on the particle size and on the particle morphology. With N2O the N2O/M ratio at monolayer coverage is usually assumed to be 0.5, but once again there is no certainty about the validity of this particular assumption. 

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