Multiple Bragg diffraction

In the Aufhellung effect,there is a depletion of intensity of In the Umweganregung effect,the intensity of is in- 

In the multiple Bragg diffraction experiment the phase angle Osum is measured. It is expressed as  

As we stressed earlier, relative phases are a function of the choice of unit cell origin. A Bragg reflection does not have an absolute phase angle, but only one relative to the chosen origin. If another origin were chosen, the intensity of the Bragg reflection would remain the same, but the relative phase angle would be different. 

When direct methods are used, origin-defining phases are arbitrarily chosen according to rules developed to define the unit-cell origin. The probabilities of the phases of various structure invariants (triplets, which are origin-independent) are assessed. The E map is then calculated with respect to the chosen unit-cell origin. 

From the Patterson and heavy-atom methods, once the direction of the first vector to be selected has been assigned, the origin of the unit 

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Measurement of multiple Bragg diffraction. Some sets of phases may be derived from experimental measurements of i/ -scan profiles of reflections exhibiting the effects of multiple Bragg diffraction. Groups of relative phases have absolute values that can be detected by this method which is currently in the developmental stage, and is only applicable to those sets of Bragg reflections that display the effect. 

Multiple Bragg diffraction Further diffraction of a Bragg reflection by a second set of lattice planes. This occurs when two reciprocal lattice planes lie simultaneously on the surface of the Ewald sphere. It affects the intensity of the Brage reflection and a detailed analysis of the effect can lead to some phase information. 

Shen, Q., and Colella, R. The current status of phase determination by means of multiple Bragg diffraction. Acta Cryst. A42, 533-538 (1986). 

For certain minerals with multiple element substitutions on lattice sites, electron channeling experiments can provide estimates of site occupancy using a similar thin-film analysis technique. This latter approach, termed ALCHEMI, utilises an orientational dependence of X-ray emission from specific elements on crystallographic sites. Conventional thin-film analyses, which measure the concentration of elements in a sample, do not require specific, known orientations of a sample, and are best obtained from randomly-oriented or non-Bragg diffracting crystals and with a convergent beam which minimises channeling effects. 

Solving the crystal structure using either heavy atom or direct techniques does not always work in a straightforward fashion even when the well-resolved and highly accurate diffraction data from a single crystal are available. The complicating factor in powder diffraction is borne by the intrinsic overlap of multiple Bragg peaks. The latter may become especially severe when the unit cell volume and complexity of the structure increase. 

The division of intensities of the overlapped Bragg reflections is only critical when they are needed to calculate Patterson-, Fourier- or E-map(s). There is no need in their separation during a least squares refinement of structural parameters because each point of the diffraction profile is simply taken as a sum of contributions from multiple Bragg reflections. ... 

Considering Eq. 2.48 and taking into account the one-dimensionality of powder diffraction data, which introduces multiple Bragg reflection overlaps, the expanded form of Eq. 7.2 in the simplest case, i.e. when the powder is a single phase crystalline material, becomes... 

Bragg diffraction XSW measurements were made of uranyl adsorbed on calcite (1014) from a pH 10.5 solution (Sturchio et al. 2001). The coherent fractions obtained range from 0.14 to 0.65. The lower values of the coherent fractions may imply adsorption at multiple sites, although the highest value indicates a high probability of adsorption at a single dominant site. The mean value of the measured coherent position in all measurements was 0.84 0.02. This position was independent of dissolved U(VI) concentration, and corresponds to a distance between the U atom and the calcite (1014) plane of 2.55 0.06 A. These results are consistent with U(VI) adsorption at the calcite surface mainly as a monodentate inner-sphere uranyl-carbonate surface complex. Steric considerations imply that the observed U(VI) surface complex may occur both at edge sites (< 441 > and < 481 > ) and on terrace areas adjacent to Ca vacancies. 

The diffractimi contrast is widely used to identify structural defects and lattice parameters ( lattice parameters ). Information about the nature of these defects can be obtained by diffraction contrast, where multiple Bragg reflectiOTis can assist in... 

Polymers invariably form helical structures, and the helix symmetry is denoted by u, indicating that there are u repeat units in V turns of the helix. The helix pitch is denoted by P and the molecular repeat distance is c = vP. X-ray diffraction patterns from non-crystalline specimens contain diffracted intensities restricted to layer lines that are spaced by 1/c. On a diffraction pattern from a polycrystalline specimen, diffraction signals, or Bragg reflections, occur only at discrete positions on the layer lines, the positions being related to the lateral dimensions of the unit cell of the crystal. The meridian (vertical axis) of the diffraction pattern is devoid of diffracted intensity unless the layer line number J, is a multiple of u, so that u can be determined straightforwardly. The diffracted intensities can be calculated using standard expressions (2), for model structures (i.e. given the atomic coordinates). 

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