Diffraction broadening

It is qualitatively very helpful if instead of having to solve the equations or simulate the solutions every time, we can get some physical understanding which reduces the task. Ray optics is one such method we look at the geometrical optics before the physical optics. Rays are reasonable concepts if diffraction broadening is not too great, that is, for a ray path, where A is the width of... 

Amorphous NA No diffraction Broadened spectra Broadened spectra Glass transition seen. No birefringence,... 

BAL 99] BALZAR D., Voigt function modeling diffraction broadening analysis , in R.L. SNYDER, J. FIALA, H.J. BUNGE (eds.). Defect and microstructure analysis by diffraction, lUCr Monographs on crystallography, no. 10, Oxford University Press, 1999. 

Crystallite sizes were estimated from X-ray diffraction broadening using the Scherrer equation and/or TEM. Surface areas were calculated by the Brunauer-Emmett-Teller (BET) method. Pore sizes were calculated by the Barrett-Joyner-Halenda (BJH) method. 

Many fonns of disorder in a surface structure can be recognized in the LEED pattern. The main manifestations of disorder are broadening and streaking of diffraction spots and diffuse intensity between spots [1]. 

The discussion of diffraction so far has made no reference to the size of the 2D grating. It has been assumed that the grating is infinite. In analogy with optical or X-ray diffraction, finite sizes of the ordered regions on the surface (finite-sized gratings) broaden the diffracted beams. From an analysis of the diffracted-beam shapes, the types of structural disorder in the surface region can be identified and quantified. - ... 

Diffraction is usefiil whenever there is a distinct phase relationship between scattering units. The greater the order, the better defined are the diffraction features. For example, the reciprocal lattice of a 3D crystal is a set of points, because three Laue conditions have to be exactly satisfied. The diffraction pattern is a set of sharp spots. If disorder is introduced into the structure, the spots broaden and weaken. Two-dimensional structures give diffraction rods, because only two Laue conditions have to be satisfied. The diffraction pattern is again a set of sharp spots, because the Ewald sphere cuts these rods at precise places. Disorder in the plane broadens the rods and, hence, the diffraction spots in x and y. The existence of streaks, broad spots, and additional diffuse intensity in the pattern is a common... 

The analogy of a crystal surface as a diffraction grating also suggests how surface defects can be probed. Recall that for a diffraction grating the width of a diffracted peak will decrease as the number of lines in the grating is increased. This observation can be used in interpreting the shape of RHEED spots. Defects on a crystal surfr.ee can limit the number of atomic rows that scatter coherendy, thereby broadening RHEED features. 

Because defects limit the order on a surface, they will alter the dif action pattern, primarily by broadening diffracted beams. Methods have been developed, mostly in the LEED literature, to analyze the shape of diffracted beams to gain information on step distributions on surfaces. These methods apply equally well to RHEED. 

Scherrer equation to estimate the size of organized regions Imperfections in the crystal, such as particle size, strains, faults, etc, affect the X-ray diffraction pattern. The effect of particle size on the diffraction pattern is one of the simplest cases and the first treatment of particle size broadening was made by Scherrer in 1918 [16]. A more exact derivation by Warren showed that. 

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].

Simulated SWCNT ED patterns will be presented below. Tbe most striking difference with tbe MWCNT ED patterns is tbe absence of tbe row of sharp oo.l reflexions. In tbe diffraction pattern of ropes there is still a row of sharp reflexions perpendicular to the rope axis but which now corresponds to the much larger interplanar distance caused by the lattice of the tubes in the rope. The ho.o type reflexions are moreover not only asymmetrically streaked but also considerably broadened as a consequence of the presence of tubes with different Hamada indices (Fig. 3). 

Fig. 3. (a) Diffraction pattern of a well formed rope (superlattice) of armchair-like tubes. Note the presence of superlattice spots in the inset (b). The broadening of the streaks of 1010 type reOexions is consistent with a model in which the SWCNTs have slightly different chiral angles. 

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]. 

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