Indexing Bragg reflections

A fiber diffraction pattern of the potassium salt is shown in Figure 2 ( 8). Sharp Bragg reflections extend to approximately 3.0 A resolution with meridional intensities on the 6th and 9th layer lines. The diffraction pattern can be indexed on the basis of a... 

Elastic neutron diffraction was first performed (analyzer in Fig. 1 set to zero energy transfer) to establish the structure of the monolayer at low temperature. Three Bragg reflections were observed which could be indexed by a triangular lattice having a nearest-neighbor distance about 10% smaller than required for a 3 X /3 R30° commensurate structure (every third carbon hexagon in the graphite basal plane occupied). 

Figure 5. Diffraction from an uniaxially oriented specimen of stretched calf thymus DNA (courtesy M. H. F. Wilkins). The molecules are approximately 14, helices with c = 10.6 nm. The Bragg reflections on the equator can be indexed on the basis of a rhombic net with a = b = 2.30 nm.

Figure 1. The indexing of 6 -Zr W, 6M004O,. The indices were calculated from the TREOR program. The tick marks under the pattern were demonstrations of the failed index by known structural models. The tick marks were the allowed Bragg reflection positions of space groups of P(-3)c (the lowest), Pa(-3) (middle low), P2 3 (middle up) and P 2,2, 2, (top) models of ZrWjO, or ZrMo20j. The inset emphasizes that both indices 110 and 101 can not be indexed by any structure.

FIGURE 3.15. An X-ray diffraction photograph of the lac repressor protein with some Bragg reflections indexed (hkl). Note the intensity variation among different Bragg reflections. Unit cell dimensions are a = 164, b = 162, c = 75 A, / = 125°. In the indexing, h is chosen to point horizontally to the right, and k is vertical and points up. 

FIGURE 7.1. The relative orientations of the reciprocal lattice of a crystal (expressed as a and b ), and its indexed X-ray diffraction pattern (expressed as h and k). In the diffraction pattern the intensities of the diffracted beams (/) (the blackness of spots on X-ray film, for example) and the directions of travel (sin 6) (positions of spots on the X-ray film) are measured. Note the relationship of a to h, and b to k. From the positions of spots on the photographic film it is possible to deduce the dimensions of the reciprocal lattice, hence of the crystal lattice, hence the indices hkl of each Bragg reflection. 

Laue Large number of Bragg reflections with one crystal setting. More difficult to index. 

Area detector Can measure large numbers of data at the same time. Computer indexing of Bragg reflections. Reasonably precise data. 

Note that is a factor needed to account for the enhancement of intensities of certain classes of Bragg reflections with at least one index zero, i.e., certain classes of Bragg reflections that have an average intensity higher than the average. 

Figure 4.22. Indexed PDF card (also see Figure 4.20, middle). Every observed Bragg reflection has been indexed and the corresponding F30 figure of merit (see section 5.5.1 in Chapter 5) is excellent. Based on these and other established criteria, the quality mark assigned by the ICDD editor is Quality Data , which usually is a good indicator that the included digitized pattern may be trusted in positive phase identification.

The difficulty and reliability of indexing are closely related to the absolute accuracy of the array of d Hki values, i.e. to the absolute accuracy with which positions of Bragg reflections have been determined. For... 

Zone search method begins with searching for one-dimensional and two-dimensional zones and then builds three-dimensional zones using common rows in two-dimensional lattices. When a three-dimensional zone (lattice) is found, it is used in an attempt to index all observed Bragg reflections. This automatic indexing technique is more sophisticated when compared to a trial-and-error approach, but it is still based on Eq. 5.1. First, the analysis of numerical relationships between the observed Q-values is made to identify zones that are invariant with respect to two indices, for example AOO, h 0, OkO and so on. Second, these are combined to identify zones which are invariant with respect to one index and, finally zones where all three indices... 

The correct solution must result in a high figure of merit (although not necessarily the highest) and most, if not all diffraction peaks should be indexed. Unindexed Bragg reflections must be explained, for example, by low intensity, by noticeably different peak widths, or they should be identified as corresponding to an impurity phase. 

The indexing process in this case should be finalized by using the found lattice parameters to assign indices to the weak Bragg reflections that have been eliminated from the indexing and by refinement of the lattice parameters employing all available experimental data. This can be easily done following the procedure described earlier in section 5.4. 

First, is to verify the correctness of indexing, which is easily established by visually comparing the observed and calculated" patterns to ensure that every observed peak has a matching calculated Bragg reflection. 

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