Bragg rod profile

Figure 3.59. Top and side-view of the experimental set-up for grazing incidence X-ray diffraction measurements on Langmuir monolayers. The footprint of the Incident beam is indicated by the darker area. Only the crossed-beam area ABCD contributes to the detected scattering. The Seller eollimator selects a horizontal scattering angle of 20 the position-sensitive detector (PSD) has its axis vertical and measures the Bragg rod profiles. In this geometry one has the ability to determine the lateral (q ) as well as the vertieal (q ) components of the scattering vector. (Redrawn from J. Als-Nielsen and K. KJaer, loc. clt.

Figure 12 (a) Schematic representation of how the projection of Bragg rods leads to the asymmetric shape shown in the Warren lineshape figure illustrated in panel (b). The origin of this asymmetry is discussed in the text. This diffraction pattern uses a Lorentzian profile for the structure factor of the Bragg rod. (Reprinted with permission Arnold, Chanaa, Clarke, Cook and Larese 2006, American Physical Society)... 

As we shall see, the hairy platelets formed by the crystalline-amorphous diblock copolymers consist of an inner crystalline core and an outer brush. This lateral profile gives rise fo a form factor that modulates the profiles of the Bragg rods. The form factor relates directly to the volume fractions b(z) of the brush and coordinate perpendicular to the platelet surface. In terms of these quantities the core brush form factor is given by ... 

Thus, the amphtude is modified by a prefactor, which simplifies the computation of the total amphtude. Figure 3.4.2.12 shows the effect on the rod profiles for different values of fi roughness leads to a decrease in amphtude in-between the bulk Bragg peaks. Since the intensity is small to begin with, surface roughness may make it impossible to dishnguish the intensity in the tails of the rods from the bacl ound. 

Equation (3.4.2.26) seems to describe a different crystal truncation rod profile than the 2sin 7rl profile derived in Section 3.4.2.2.3. Summing over the bulk Bragg peaks along I in Eq. (3.4.2.27), however, leads to the earlier result [21]. For this derivation, one needs to use the mathematical equality... 

The summation is therefore most accurate when an odd number of experimental terms is chosen. Figure 3.4.2.15 shows the small deviation from the genuine CTR profile if the contributions from the three nearest Bragg peaks are used. If, in a real experiment, only few terms can be measured, it is better to use the shape function of Eq. (3.4.2.26) to describe the rod profile or to correct for the difference with a... 

Figure 7.3. (a) In situ X-ray reflectivity vs. time (measured at the anti-Bragg condition, shown in inset at top) during dissolution of orthoclase feldspar, KAlSi308, (001) cleavage surface at extreme pH values. The removal of successive monolayers (ML) is noted for each set of data, (after [100]) (b) in situ crystal truncation rod diffraction profiles for a freshly cleaved orthoclase (001) surface (circles) and after reaction at pH = 2.0 (1 and 15 ML dissolved) (diamond and square) and pH = 12.9 (2 ML dissolved) (triangle) (after [103]). (Figures provided by P. Fenter.)... 

Figure 3.4.2.6 The (10) crystal truncation rod of Si(lll). Because of the internal structure of the unit cell, the profile has more variation in intensity than that shown in Figure 3.4.2.4 and not all integer values of / correspond with a bulk Bragg peak.

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