Diffraction patterns indexing

FIG. 20-24 High -resolution TEM image of Si nanowires produced at 500 C and 24.1 MPa in supercritical hexane from gold seed crystals. Inset Electron diffraction pattern indexed for the <111> zone axis of Si indicates <110> growth direction. [Reprinted with permission from Lu et al. Nano Lett., 3(1), 93-99 (2003). Copyright 2003 American Chemical Society. ]... 

FIG. 3 X-ray diffraction pattern of a microcrystaliine powder of Cgo- Inset (upper left) is a single-crystal electron diffraction pattern Indexed with Miller indices compatible with the X-ray pattern. The pattern is from a thin platelet such as those in Fig. 1 with the electron beam perpendicular to the flat face. 

TABLE 11.5 Sample data for X-ray diffraction pattern indexing, using 2 = 1.54 A. ... 

Analysis and inspection of SAED directly on screen is often enough for identification for chrysotile and a possible amphibole , but computer-aided measurement and analysis are required for detailed diffraction pattern indexing. 

In the two cases, the antiwear films are polycrystalline, as clearly pointed out by electron diffraction patterns. Indexations of these last ones reveal that microcrystals are mainly carbonate phases, respectively strontianite and calcite. In the case of the OCABS film, electron microdiffraction patterns carried out between well-identified nanocrystallites demonstrate the existence of an amorphous phase responsible for the cohesion of the film. This phase, not identified by ATEM, probably corresponds to (amorphous) calcium oxide species recently detected by TOE SIMS analyses [46]. 

The index of refraction of allophane ranges from below 1.470 to over 1.510, with a modal value about 1.485. The lack of characteristic lines given by crystals in x-ray diffraction patterns and the gradual loss of water during heating confirm the amorphous character of allophane. Allophane has been found most abundantly in soils and altered volcanic ash (101,164,165). It usually occurs in spherical form but has also been observed in fibers. 

The crystal group or Bravais lattice of an unknown crystalline material can also be obtained using SAD. This is achieved easily with polycrystalline specimens, employing the same powder pattern indexing procedures as are used in X-ray diffraction. ... 

Since the first structure determination by Wadsley [56] in 1952 there has been confusion about the correct cell dimensions and symmetry of natural as well of synthetic lithiophorite. Wadsley determined a monoclinic cell (for details see Table 3) with a disordered distribution of the lithium and aluminium atoms at their respective sites. Giovanoli et al. [75] found, in a sample of synthetic lithiophorite, that the unique monoclinic b-axis of Wadsley s cell setting has to tripled for correct indexing of the electron diffraction patterns. Additionally, they concluded that the lithium and aluminum atoms occupy different sites and show an ordered arrangement within the layers. Thus, the resulting formula given by Giovanelli et al. 

The task of predicting a reasonable structure for this alloy was carried out with no information about the powder X-ray diffraction pattern except that one group of investigators had said that it could not be indexed by any Bravais lattice. The prediction of the structure was made entirely on the basis of knowledge of the effective radii of metal atoms and the principles determining the structure of metals and intermetallic compounds. 

X-ray diffraction patterns were recorded on a Philips PW1820 diffractometer with Cu-Ka radiation (X = 0.154 nm). The collected sample was indexed very well as cubic a-Mn203 bixbyite (JCPDS 41-1442, la-3, a = 0.941 nm) (Fig. 1). The morphologies were visualized by scanning electron microscopy (SEM) (Fig. 1). The abundant well-defined hexagonal-like plates with the sizes from several hundred nanometers to a few micrometers were formed during hydrothermal treatment, which kept initial shape after 700 °C-calcination (Fig. 1). The hexagonal plates are about 50 nm thick with smooth surfaces. 

Recent developments and prospects of these methods have been discussed in a chapter by Schneider et al. (2001). It was underlined that these methods are widely applied for the characterization of crystalline materials (phase identification, quantitative analysis, determination of structure imperfections, crystal structure determination and analysis of 3D microstructural properties). Phase identification was traditionally based on a comparison of observed data with interplanar spacings and relative intensities (d and T) listed for crystalline materials. More recent search-match procedures, based on digitized patterns, and Powder Diffraction File (International Centre for Diffraction Data, USA.) containing powder data for hundreds of thousands substances may result in a fast efficient qualitative analysis. The determination of the amounts of different phases present in a multi-component sample (quantitative analysis) is based on the so-called Rietveld method. Procedures for pattern indexing, structure solution and refinement of structure model are based on the same method. 

In the same paper (Yamamoto 1996) an authoritative description is given of several interrelated topics such as super-space group determination, structure determination, indexing of diffraction patterns of quasicrystals, polygonal tiling, icosahedral tiling, structure factor calculation, description of quasicrystal structures, cluster models of quasicrystals. 

The obtained low index surfaces were examined by Laue back reflection X-ray diffraction photograph method. Figures 2—10 show the obtained photographs. They represent a typical diffraction pattern for each surface and show that the quality of the each surface is high. The areas of the low index surfaces are 0.028, 0.024 and 0.025 cm for Ptdll), (110) and (100), respectively. 

To determine the phase properties of the calcined bimetallic nanoparticles, a detailed x-ray diffraction (XRD) study was carried out. The XRD data of AuPt/C showed that the diffraction patterns for the carbon-supported nanoparticles show a series of broad Bragg peaks, a picture typical for materials of limited structural coherence. Nevertheless, the peaks are defined well enough to allow a definitive phase identification and structural characterization. The diffraction patterns of Au/C and Pt/C could be unambiguously indexed into an fcc-type cubic lattice occurring with bulk gold and platinum. We estimated the corresponding lattice parameters by carefully determining... 

Fig. 8 Examples of diffraction patterns of poorly crystalline LDHs that can best be indexed as one layer polytypes. Reprinted with permission from [118]. Copyright American Chemical Society...

From a comparison of various spot electron diffraction patterns of a given crystal, a three-dimensional system of axis in the reeiproeal lattice may be established. The reeiproeal unit cell may be eompletely determined, if all the photographs indexed. For this it is sufficient to have two electron diffraction patterns and to know the angle between the seetions of the reeiproeal lattice represented by them, or to have three patterns which do not all have a particular row of points in common (Fig.5). Crystals of any compound usually grow with a particular face parallel to the surface of the specimen support. Various sections of the reciprocal lattice may, in this case, be obtained by the rotation method (Fig.5). 

Figure 4. Indexing of an electron diffraction pattern representing a coordinate and noncoordinate planes of reciprocal lattice.

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