Diffraction patterns small particles

Determination of the structures of nanocrystals should ideally follow from X-ray diffraction, but small particles do not diffract well owing to their limited size. The peaks in the diffraction pattern are less intense and are broad. Structural studies are therefore based on high resolution transmission electron microscopy (HRTEM), extended X-ray absorbtion fine structure (EXAFS),... 

Cationic quaternary ammonium compounds such as distearyldimethylammonium-chloride (DSDMAC) used as a softener and as an antistatic, form hydrated particles in a dispersed phase having a similar structure to that of the multilayered liposomes or vesicles of phospholipids 77,79). This liposome-like structure could be made visible by electron microscopy using the freeze-fracture replica technique as shown by Okumura et al. 79). The concentric circles observed should be bimolecular lamellar layers with the sandwiched parts being the entrapped water. In addition, the longest spacings of the small angle X-ray diffraction pattern can be attributed to the inter-lamellar distances. These liposome structures are formed by the hydrated detergent not only in the gel state but also at relatively low concentrations. 

Figure 14-15 shows three X-ray diffraction patterns obtained from small crystalline particles of metallic copper, aluminum, and sodium. The qualitative similarity of the patterns given by copper and aluminum shows that they have the same crystal packing. Careful measurements of the spacing of the lines indicate that the atoms... 

Diffraction patterns having relatively well-defined sharp spots can be obtained from small unit-cell crystals with an incident beam of diameter 10-158. Such patterns have been used in the study of the structures of small metal particles (22). For particles 10-20A diameter the electron beam can illuminate the whole of the particle... 

The extent to which small particles of Pd and Pt show evidence of oxidation after exposure to air Is also highly variable. It Is difficult to confirm the evidence of X-ray diffraction and EXAFS (25) that most particles In the 15-20A size range consist entirely of oxide. We have found that such particles usually give single crystal patterns attributable to the metals. There Is, however, considerable evidence that, in the case of Pt on alumina, the Pt crystals have a well-defined epitaxial relationship with the crystallites (20-50A diameter) of the nominally "amorphous" alumina substrate. 

The possibility of obtaining single crystal diffraction patterns from regions of very small diameter can obviously be an important addition to the means for investigating the structures of catalytic materials. The difficulty arises that data on individual small particles is usually, at best, merely suggestive and at worst, completely meaningless. What is normally required is statistical data on the relative frequencies of occurrence of the various structural features. For adequate statistics, it would be necessary to record and analyse very large numbers of diffraction patterns. 

In catalyst characterization, diffraction patterns are mainly used to identify the crystallographic phases that are present in the catalyst. Figure 6.2 gives an example where XRD readily reveals the phases in an Fe-MnO Fischer-Tropsch catalyst [7], The pattern at the top is that of an MnO reference sample. The diffraction pattern of the reduced Fe-MnO catalyst shows a peak at an angle 29 of 57°, corresponding to metallic iron, and two peaks which are slightly shifted and broadened in comparison with the ones obtained from the bulk MnO reference. The Mossbauer spectrum of the reduced catalyst contains evidence for the presence of Fe2+ ions in a mixed (Fe,Mn)0 oxide [7], and thus it appears justified to attribute the distortion of the XRD peaks to the incorporation of Fe into the MnO lattice. Small particle size is another possible reason why diffraction lines can be broad, as we discuss below. 

Figure 11. Anomalous diffraction pattern of a small metallic particle, showing 2.46 A spots.

Many investigations of small particles or of other materials may involve the collection and analysis of diffraction patterns from very large numbers of individual specimen regions. For small metal particles, for example, it may not be sufficient to obtain diffraction patterns from just a few particles unless there is reason to believe that all particles are of the same composition, structure, orientation and size or unless these parameters are not of interest. More commonly, it is of interest to obtain statistics on the variability of these parameters. The collection of such... 

Figures 2 (b) and (c) show a diffraction pattern obtained from a particle of diameter 1.5 nm and a diffraction pattern calculated for a multiply twinned, decahedral particle. The conclusion drawn from the study of many such observed and calculated patterns obtained from gold particles in the size range of 1.5 to 2 nm contained in a plastic film is that very few particles are multiply twinned, many have one or two twin planes but more than half are untwinned (16). This suggests that, at least for this type of specimen, there is no confirmation of the theoretical prediction that the multiply twinned form is the equilibrium state for very small particles.

For small particles supported on thin films of amorphous or microcrystalline materials it is not easy to determine whether there is any consistent correlation between the particle orientation and the orientation of the adjacent locally ordered region of the substrate. For some samples of Pt and Pd on gamma-alumina, for example, nanodiffraction shows that the support films have regions of local ordering of extent 2 to 5 nm. Patterns from the metal particles often contain spots from the alumina which appear to be consistently related to the metal diffraction spots. 

Z-4A), and zeolite H-ZSM-5. The interlayer distance varied by the intercalation was determined from X-ray diffraction patterns. The interlayer space of the crystalline zeolite is separated by the three-dimensional cage structures. The mean diameters of particles were approximately 1 ym. Such small particles formed very stable suspensions with no sign of sedimentation over the time course of the kinetic measurements. The analytical techniques used to obtain the equilibrium concentration are described elsewhere (10-22). All samples were equilibrated for 24-72 h after preparation. The temperature was controlled at 25 °C. 

Optical examination of etched polished surfaces or small particles can often identify compounds or different minerals hy shape, color, optical properties, and the response to various etching attempts. A semi-quantitative elemental analysis can he used for elements with atomic number greater than four by SEM equipped with X-ray fluorescence and various electron detectors. The electron probe microanalyzer and Auer microprobe also provide elemental analysis of small areas. The secondary ion mass spectroscope, laser microprobe mass analyzer, and Raman microprobe analyzer can identify elements, compounds, and molecules. Electron diffraction patterns can be obtained with the TEM to determine which crystalline compounds are present. Ferrography is used for the identification of wear particles in lubricating oils. 

Highly-broadened XRD peaks and electron diffraction patterns indicate that ferrihy-drites are characterized by small crystal size and/or low structural order. TEM shows single spherical particles, ca. 4-6 nm in size (Fig. 4.17). At higher magnification (HRTEM), 6-line ferrihydrite appeared as single crystals with a hexagonal outline and... 

HREM methods are powerful in the study of nanometre-sized metal particles dispersed on ceramic oxides or any other suitable substrate. In many catalytic processes employing supported metallic catalysts, it has been established that the catalytic properties of some structure-sensitive catalysts are enhanced with a decrease in particle size. For example, the rate of CO decomposition on Pd/mica is shown to increase five-fold when the Pd particle sizes are reduced from 5 to 2 nm. A similar size dependence has been observed for Ni/mica. It is, therefore, necessary to observe the particles at very high resolution, coupled with a small-probe high-precision micro- or nanocomposition analysis and micro- or nanodiffraction where possible. Advanced FE-(S)TEM instruments are particularly effective for composition analysis and diffraction on the nanoscale. ED patterns from particles of diameter of 1 nm or less are now possible. 

Note that both the x-ray diffraction and Mossbauer characterization do not reveal the presence of phases other than Fe304 with the present statistics of the respective data sets. The presence of a very small amount of FeO(OH) is suggested in the electron diffraction pattern. It is not known whether FeO(OH) exists on the surface of the particles and/or as an independent particle to date. 

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