Bragg additivity

A mixture or compound can be treated as consisting of thin layers of pure elements in the correct proportion according to their mass fractions Wj (Bragg additivity) ... 

For local deviations from random atomic distribution electrical resistivity is affected just by the diffuse scattering of conduction electrons LRO in addition will contribute to resistivity by superlattice Bragg scattering, thus changing the effective number of conduction electrons. When measuring resistivity at a low and constant temperature no phonon scattering need be considered ar a rather simple formula results ... 

In addition to the dynamic disorder caused by temperature-dependent vibration of atoms, protein crystals have static disorder due to the fact that molecules, or parts of molecules, do not occupy exactly the same position or do not have exactly the same orientation in the crystal unit cell. However, unless data are collected at different temperatures, one cannot distinguish between dynamic and static disorder. Because of protein crystal disorder, the diffraction pattern fades away at some diffraction angle 0max. The corresponding lattice distance <7mm is determined by Bragg s law as shown in equation 3.7 ... 

In addition to relaxing the fabrication tolerances, the mixed Bragg order implementation induces a coherent diffraction component in the vertical direction23. Although this mechanism reduces the overall Q of the cavity, it facilitates the observation and measurement of the resonator emission. 

From LEED measurements of H monolayers adsorbed on Fe(110) Imbihl et al. proposed a phase diagram as shown in Fig. IS. In addition to lattice gas and lattice fluid phases, two commensurate ordered phases were identifled, denoted as (2 x 1) and (3 x 1) in the figure (cf. Fig. 16). The shaded regions are interpreted as incommensurate phases or as phases composed of antiphase domains their signature is that the LEED spot does not occur at the Bragg position but rather the peak is splitted and satellites appear (Fig. 17). 

The change in intensity of the Bragg reflections can be monitored as a function of time, since data collection times can be as little as 10 s. This is well within the average reaction time for the intercalation reactions of LDHs. From these data, both qualitative and quantitative information regarding the mechanism and kinetics of a reaction can be obtained. A wide variety of reactions have been monitored using EDXRD [15,20-25], in addition to the intercalation reactions of LDHs. 

Similar experiments have been performed with fumaric and maleic acids (trans and cis l,4-but-2-enedicarboxylic acid). Identical observations were made - at the beginning of the reaction, a broad Bragg reflection centered at 10.0 A is seen to grow in to the patterns. This corresponds to the second stage intercalates of maleate and fumarate. Upon continued addition of the dicarboxylates, a phase at 12.9 A appears. This is the maleate intercalate basal... 

Fig. 17 Integrated intensity of the Bragg reflections at 15.1 A ( ) and 14.2 A (T) as a function of time during the addition of aU three benzecarboxylic acids to hexagonal LiAl - Cl. Reproduced with permission from Chem Mater (1998) 10 351-356...

Initially, the starting material, which exhibits a strong Bragg reflection at 8.7 A, is observed. As addition of the guest solution continues, a peak at 14.8 A evolves. This is the first stage intercalate of 1,2-BDA, with all interlayer spaces occupied by the dicarboxylate. No second stage intermediates are observed. Continued addition of 1,2-BDA causes a reduction in the intensity of the 14.8 A reflection, and a reflection with a d-spacing of at 11.2 A to evolve. 

For gas targets (atomic and molecular) the theory yields quite reasonable predictions of proton stopping cross sections as compared with experiment. Moreover, since chemical binding effects are naturally incorporated in the theory, the construction of tables of the velocity-dependence of CAB contributions to 5 for different compounds allows - once and for all - the estimate of 5 for protons in materials with similar CAB components without resource to Bragg s additivity rule. 

A peak caused by the addition of Bragg reflections from the A and B components of the MQW. This is the zero-order or average mismatch peak, from which the average composition of the A-i-B layers may be obtained by differentiation of Bragg s law. 

So far, we have seen that if we measure the Bragg angle of the reflections and successfully index them, then we get information on the size of the unit cell and, if it possesses any translational symmetry elements, also on the symmetry. In addition, we have seen that the intensity of each reflection is different and this too can be measured. In early photographic work, the relative intensities of the spots on the film were assessed by eye with reference to a standard, and later a scanning microdensitometer was used. In modern diffractometers, the beam is intercepted by a detector, either a charge coupled device (CCD) plate or a scintillation counter, and the intensity of each reflection is recorded electronically. 

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