Diffraction coherence length

Though the crystallinity of cw-polyacetylene is remarkably high, there are strong indications of disorder. It is generally accepted that diffraction line broadening is a combined result of crystallite size and disorder in polyacetylene, A quantitative evaluation of the separate contributions is hardly feasible due to the limited number of separate reflections, but it is common practice to consider the number obtained from the Scherrer equation to be a diffraction coherence length rather than a crystallite size. No more than approximately 10 peaks are observed in diffraction, and there is considerable overlap of reflections.. The number of higher layer lines observable in oriented patterns is only... 

Values for deuleraied polyacetylene, (CD) , measured al 4.2 K diffraction coherence lengths = 130 A (along the chain axis), Lj, = 70 A (perpendicular to the chain axis)... 

The values of the diffraction coherence length ( crystallite size ) calculated from the width of the various reflections observed for the crystalline powders, lie in the range 30-70 A. For the stretched NMP-cast EB-11 film, a value of 150 A is found from the (002) reflection, i.e. along the chain direction. 

This is attributed to the different nature of the bonding of sulphur to silver as compared to gold and the slightly different packing density. The coherence length detennined with He atom diffraction was found to be 12 mn [162]. 

X-ray diffraction peaks were rather broad with coherence lengths as low as 20 nm and this was attributed to rapid quenching. It was proposed that the carbon atoms are arranged in polyyne chains (n = 4) along the c-axis. The density of Carbolite (1.46 g-cm ) is lower than values for other carbynes and for diamond and graphite - hence the name - and this was attributed to a rapid quenching process. 

Figure 16 shows the dependence of the SH intensity at 45° incidence of p-polarized fundamental light on the number of deposited bilayers. The SH intensity increases quadratically with the film thickness of up to 400 bilayers (2 pm), as predicted theoretically in the case of the nonlinear slab with a thickness much smaller than the coherence length. The quadratic dependence demonstrates that the highly ordered noncentrosymmetric molecular orientation, which was confirmed in the relatively thin LB film from the SHG and X-ray diffraction measurements, was preserved in the alternating LB film with the thickness enough to be applied to the nonlinear waveguide devices. 

To recognize island formation one takes advantage of the difference between coherent and incoherent diffraction from a set of N identical scatterers. If the waves scattered off the individual scatterers are incoherent in their phases, the observed intensity will be proportional to N (addition of intensities). If, however, these scattered waves are coherent, the intensity will be proportional to N (addition of amplitudes). Incoherence occurs either when the incident wave arrives with incoherent phases at different scatterers, which occurs in practice for scatterers separated by at least the coherence length of the incident beam, or when the scatterers themselves are located incoherently, i.e. are disordered. 

The crystallinity of m-polyacetylene has been estimated to be 76-84% by x-ray diffraction while trans-polyacetylene is 71-79 %6). Observations on Durham polyacetylene 445) showed that the diffraction peak narrowed, and the interchain -spacing decreased, during isomerization and annealing. The x-ray coherence length, a measure of the crystallite size perpendicular to the chains, increased from 2.6 nm to 7.1 nm, compared with 30 nm for polyethylene. 

Table 1 Coherence Lengths and Crystalline Fractions Inferred from Diffraction Results8...

The 20 A diameter monodisperse crystallites isolated Ifom S. pombe and C. glabrata have been calculated to contain 85 CdS pairs in the lattice coated with approximately 30y-EC peptides (Figure 10). The particle size was determined using transmission electron microscopy and powder X-ray analysis. The analysis of the X-ray diffraction patterns was inconclusive in discriminating between a four-coordinate zinc blende and six-coordinate rock salt lattice structure. The presence of a short coherence length (8 A) can be attributed either to internal disorder or to deviation from pure crystallinity. The absorption red edge of the crystallites is located at about 320 inn. The other properties characteristic of semiconductor nanoparticulates such as luminescence with emission near 460 mn, and electron transfer to methyl viologen... 

X-ray diffraction studies of these drawn films demonstrated a high degree of structural order, which improves with the draw ratio the structural coherence length perpendicular to the draw direction increases by about a factor of two as the films are drawn, from 10 nm at = 4 to 20 nm at = 15 [4]. Consistent with the chain orientation and the improved structural order, the anisotropy (a,/aj) in the electrical conductivity increased with the draw ratio, approaching 250 as X.—>15 (although cth increased dramatically as a function of X, remains... 

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