Bragg diffraction peaks

For the evaluation of the response of the sensor, we selected several vapors of different polarity. The vapors included water (H20), acetonitrile (ACN), toluene, and dichloromethane (DCM). Solvent polarity and refractive index of tested vapors are listed in Table 4.346 47. The spectral range for the evaluation of the vapor responses of the colloidal crystal film was selected as 700 995 nm, which covered only the fundamental Bragg diffraction peak on the (111) planes of the colloidal crystal film to further reduce effects from possible stacking defects in the film as suggested in the literature44. 

A standard method for confirming coherence of the layers is the study of x-ray diffraction spectra. If the layers are coherent and there are enough of them to provide a relatively strong Bragg diffraction pattern, satelhtes due to superlattice (see Chapter 16) formation should appear on each side of the Bragg diffraction peak. Although detailed treatments can be found in the literature, we present below a simplified but rather useful formula for the determination of layer periodicity. 

The chemistry of Scheme 2 produces a cubic pore structure with long-range periodicity and unit cell parameter (Ko) of 8.4 nm. The material show a relatively large number of Bragg peaks in the X-ray diffraction (XRD) pattern, which can be indexed as (211), (220), (321), (400), (420), (332), (422), (431), (611), and (543) Bragg diffraction peaks of the body-centered cubic Ia-3d symmetry (Fig. 1). 

Fig. 1 Low-angle powder XRD pattern of cubic mesostructured germanium. The Bragg diffraction peaks consistent with the body-centered Ia-3d unit cell with a = 8.4 nm...

Name Abbreviation used in XRD patterns Chemical formula 2-theta (Cu Ktr) position and intensity of the strongest Bragg diffraction peaks ... 

The small angles XRPD patterns of the precursor U as well as of the hybrid material Mu present one Bragg diffraction peak (Fig. 4b), which corresponds to a characteristic Watson-Crick (U)2wc dimer. The two other possible stmctures, the reverse Watson-Crick dimer (U)2rwc and the quartet (U)4 (see Fig. 3), do not correlate with the experimental distance. 

Ideally, a Bragg diffraction peak is a line without width as shown in Figure 2.19b. In reality, diffraction from a crystal specimen produces a peak with a certain width as shown in Figure 2.19a. The peak width can result from instrumental factors and the size effect of the crystals. Small crystals cause the peak to be widened due to incompletely destructive interference. This phenomenon can be understood by examining the case illustrated in Figure 2.20. 

The degree of crystallinity can be determined if the intensities due to the amorphous scattering can be separated, by an appropriate method, from the Bragg diffraction peaks due to crystalline phases. The broadening of diffraction peaks due to crystal imperfections and the consequent overlapping of the diffraction peaks, however, make accurate determination of the degree of crystallinity sometimes difficult. 

The second term in the last member of (3.43) gives the Bragg diffraction peaks. The fact that Zo(s) is simply multiplied by P (s) 2 means that the widths of the diffraction peaks are not broadened, and only their heights are modified. A good approximation to p(r) is a Gaussian function, given in (1.102), with a representing the root-mean-square displacement of atoms about their mean positions. In such a case, P (s) 2 can be represented by... 

Fell et al. [72] studied the correlation between the composition and the strucmre of co-polymers of hexyl and octyl thiophenes, obtained by chemical polymerization with FeCl3, and performed also a comparative study of the corresponding polymer mixtures [71 ]. The co-polymers, P[(HT) x(OT) ], of molar fractions x = 0, 0.3, 0.5 and 1.0, were cast from chloroform solutions into films that could be stretch oriented, and were also obtained in the form of stretched threads. Diffraction studies showed patterns very similar to those from the pure polymers, with well developed direction dependent Bragg diffraction peaks, and direction dependent diffuse features. Whereas the b-axis parameter stayed almost constant throughout the series, the a-axis parameter was found to vary linearly with the molar fraction x. 

The crystallinity of polyurethane can be observed as intense (clear) Bragg diffraction peaks in WXRD patterns which are obtained using the... 

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