Diffraction pattern definition

What is the resolution of the diffraction pattern, namely what is the family of Bragg planes in the crystal of smallest interplanar spacing that is represented by a measurable intensity in the diffraction pattern Definition of measurable intensity may here become a contentious question. 

Crystalline forms presenting large amounts of disorder of the kind (ii) or (iii) are generally called mesomorphic modifications (Section 3.6), in analogy with the ordered liquids (smectic and nematic). In these cases the lack of periodicities in one or two dimensions (e.g., along the chain axes or along the directions normal to the chain axes) prevents the definition of a unit cell. Typical features in the X-ray diffraction patterns of mesomorphic forms are diffuse halos on the equator or on the layer lines depending on the kind of disorder present. 

Figure 2.34 Definition of up/down order parameter R from X-ray powder diffraction patterns of iPP samples170,175 (a) unannealed sample (b) sample annealed at 167°C. (Reprinted with permission from Ref. 170. Copyright 1992 by Springer-Verlag.)... 

In addition to the crystalline clays described earlier, there are some materials that act like clays but do not have crystalline structure. Amorphous clays do not have a definite X-ray diffraction pattern and are differentiated from the crystalline clays on this basis. They are composed of mixtures of alumina, silica, and other oxides and generally have high sorptive and cation exchange capacities. Few soils contain large amounts of amorphous clays [2],... 

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... 

Figure la. Examples of ED patterns a - Diffraction pattern of mosaic single crystals, microcrystallites in the film are a little disoriented around definite directions. 

Diffraction patterns may always be multiplied by a constant factor without changing the physics of the system. In MSLS this is a scaling factor which is needed to scale the observed and calculated intensities to the same order of magnitude. This scaling factor is one of the relinable parameters. However, one has to take care with the definition of this factor. It should be defined in such a way that it is not dependent on the change of any other parameter in the refinement procedure, in particularly the crystal thickness and the absorption parameter. Therefore the actual scaling factor, C, was expressed as function of c, the parameter which was used in the refinement process ... 

Now let us assume that a monochromatic source of flux is placed in the plane of the entrance slit so that there is no constant phase relationship between the fields at any two given points in the slit. This, in itself, is a contradiction, because a perfect source monochromaticity implies both spatial and temporal coherence. By definition of coherence, a constant phase relationship would result. To eliminate the possibility of such a relationship, we must require the source spectrum to have finite breadth. Let us modify the assumption accordingly but specify the source spectrum breadth narrow enough so that its spatial extent when dispersed is negligible compared with the breadth of the slits, diffraction pattern, and so on. Whenever time integrals are required to obtain observable signals from superimposed fields, we evaluate them over time periods that are long compared with the reciprocal of the frequency difference between the fields. We shall call the assumed source a quasi-monochromatic source. 

With increasing diffuseness of the diffraction pattern the possibilities of interpretation obviously become more restricted but even in the extreme cases of glass-like substances and liquids it is possible to draw definite conclusions on the manner of association of the atoms, at any... 

We call this Pt(100) surface reconstructed. Surface reconstruction is defined as the state of the clean surface when its LEED pattern indicates the presence of a surface unit mesh different from the bulklike (1 x 1) unit mesh that is expected from the projection of the bulk X-ray unit cell. Conversely, an unreconstructed surface has a surface structure and a so-called (1 x 1) diffraction pattern that is expected from the projection of the X-ray unit cell for that particular surface. Such a definition of surface reconstruction does not tell us anything about possible changes in the interlayer distances between the first and the second layers of atoms at the surface. Contraction or expansion in the direction perpendicular to the surface can take place without changing the (1 x 1) two-dimensional surface unit cell size or orientation. Indeed, several low Miller index surfaces of clean monatomic and diatomic solids exhibit unreconstructed surfaces, but the surface structure also exhibits contraction or expansion perpendicular to the surface plane in the first layer of atoms (9b). 

Electron diffraction studies by Roche et al.96) of annealed fibres have revealed a fibre repeat of 1,24 nm which remains constant even when the processing conditions are varied. This value is in good agreement with the length of 1.247 nm of t-bisthiazole as measured by the C(8) to C(5 )separation by Wellmann et al. 97). This implies that the PBT chain has the fully extended conformation, since the fibre repeat consists of only one repeat unit. The electron diffraction patterns have also been interpreted in terms of monoclinic and triclinic unit cells but a more definite assignment may be possible with more highly ordered fibres. 

Two types of X-ray studies are commonplace X-ray powder analysis and crystal structure determination. Even in powders, the regular arrangement of atoms within the solid leads to characteristic diffraction patterns. X-ray powder patterns may therefore be used to characterize solids in much the same way that a UV or IR spectrum will give useful information but not necessarily a definitive structure. 

Professor Tadakoro s recent book(l ) illustrates the considerable advantages and benefits to be gained by coupling infra-red spectroscopy with fibre x-ray diffraction. The increasing availability of Fourier transform infra-red spectrometers allows the same thick samples, suitable for x-ray work, to be used in the spectrometer thus ensuring that both sets of information emanate from the same structure. The delightful selected area electron diffraction patterns obtained from polysaccharides by Dr. Chanzy (2), which exhibit such remarkable resolution and definition, indicate the importance and value of the modern application of electron micro-... 

PrOj so Between PrO170 and Pr01-83 the phase diagram has not been resolved. Tensiometric measurements suggest a stable phase at PrO1-80 at low temperature. X-ray diffraction patterns usually show broad lines which are definitely complex. It is believed that there may be some stable phases in this region which have not yet been isolated. 

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