Bragg reflection, distributed

Total internal reflection Distributed Bragg reflection... 

Figure 10-12. Lcfi hand side Slruclure of a PPV microcavily. A thin film of ihe conjugated polymer is deposited on top of a highly reflective distributed Bragg refieclor (DBR). The second mirror is then fabricated by evaporation of a silver layer. Right hand side Emission spectra of the microcavily at excitation cnetgics or 0.0S pJ (dashed line) and l. l pJ (solid line), respectively. Laser pulses ol duration 200-300 ps and a wavelength of 355 nm were used for optical excitation (according to Ref. [39]).

Fig. 9. X-ray intensity distributions (arbitrary scale) from aggregates formed by different polyglutamine peptides (Q , for n = 8,15, 28, 45) polyGln45 (dried), polyGln28 (vapor hydrated), polyGln15 (vapor hydrated), and polyGlng (lyophilized). The vertical bars indicate the positions of the Bragg reflections. The first interference peak for slab stacking of Q8 is indicated by. See Sharma et al. (2005) for further details.

In general, the orientations of the crystallites in such materials are distributed about a particular direction, termed the fibre axis. This disorientation results in azimuthal spreading (or arcing) of the Bragg reflections, which complicates the task of measuring their integrated intensities. 

Experimental determination of charge density relies mostly on X-ray diffraction although other techniques have been applied in some instances. X-ray diffraction arises from scattering by electrons and therefore carries information on the distribution of electronic charge in real space [10]. The intensity of a Bragg reflection, 7(h), at a given temperature, is proportional to the square of its structure factor,... 

Not all of the Bragg reflections, I[hkl), are unique in intensity. Georges Friedel noted that the intensity distribution in the diffraction pattern is centrosymmetric (diagrammed in Figure 4.15). 

Unit cell dimensions are obtained from measurements of 29 values of several Bragg reflections for which the indices h, k, and I are known. Values of 26 are measured as accurately as possible, and, since the wavelength A. of the radiation used is known, a value of dhu may be found by Bragg s Law, Equation 3.2 (Chapter 3). The value of is related to the unit cell dimensions and, if 26 values are measured for several reflections, values of the unit cell dimensions may be derived. The selected group of reflections chosen to do these calculations should contain a distribution of Miller indices and they should have relatively high 29 values ... 

It is somewhat surprising that, in spite of what has been said in earlier chapters about the loss of phase information in the X-ray diffraction experiment, the intensity distribution contains information on whether the structure is centrosymmetric or noncentrosymmetric. This information is important when there is a spaoe group ambiguity in which one possibility is centrosymmetric, while the other is not (see Chapter 4. Arthur J. C. Wilson - noted that, while the intensities of Bragg reflections on the average depend only on the atomic contents of the unit cell, the distribution of intensities is different depending on whether the structure is centrosymmetric or noncentrosymmetric. The intensities... 

FIGURE 8.5. (a) The probability P E) of iJ having certain values depends on whether the structure is centrosymmetric (solid line) or noncentrosymmetric (broken line). Thus, if values are known, a plot of the number with different ranges of I E I will indicate the centrosymmetry (or lack of it) in the crystal structure, (b) The cumulative distribution curves for centrosymmetric and noncentrosymmetric crystals N Z) is the fraction of Bragg reflections with intensities (or E p values) less than or equal to Z times the mean intensity. 

Distribution of intensities The overall variation in the intensities of the Bragg reflections obtained on X-ray diffraction of a crystal. Intensities from a non-centrosymmetric crystal tend to be clustered more tightly around the mean than do those from a centrosymmetric one. This information forms the basis for one test for the presence or absence of a center of symmetry in the crystal. 

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