Bragg pattern

Figure 4. Diffraction from a screw-disordered" arrangement of poly U poly A poly U molecules. The Bragg pattern from the fiber containing these triple-stranded polynucleotide molecules corresponds to a trigonal cell with a = b = 2.71 nm c = 3.65 nm. The molecules are 12, helices.

Figure 18.2 Bragg pattern recorded on an image plate at the beginning of swelling (a) first-order and (b) second-order reflections are visible. Both arcs exhibit (c) a pronounced spot that originates from die orientation of the lamellae parallel to the capillary sui ce. (d) The central elongated stripes close to the beam stop are an artefact that results ftom the total reflection of the primary beam at the surface of the glass eapillary.

Fig. 1. Structures of (O) atoms and corresponding electron and x-ray diffraction patterns for (a) a periodic arrangement exhibiting translational symmetry where the bright dots and sharp peaks prove the periodic symmetry of the atoms by satisfying the Bragg condition, and (b) in a metallic glass where the atoms are nonperiodic and have no translational symmetry. The result of this stmcture is that the diffraction is diffuse.

How is the diffraction pattern obtained in an x-ray experiment such as that shown in Figure 18.5b related to the crystal that caused the diffraction This question was addressed in the early days of x-ray crystallography by Sir Lawrence Bragg of Cambridge University, who showed that diffraction by a crystal can be regarded as the reflection of the primary beam by sets of parallel planes, rather like a set of mirrors, through the unit cells of the crystal (see Figure 18.6b and c). 

Figure 4 Diffraction patterns (Bragg-Brentano geometry) of three superconducting thin Aims ( 2- im thick) anneaied for different times. The temperatures for 0 resistance and for the onset of superconductivity are noted.

Figure 5 Bragg>Brentano diffraction pattern for magnetic media used in a demonstration of 1-Gb/in magnetic recording. The iines show a deconvoiution of the data into individual diffraction peaks, which are identified.

Figure 5 Raw diffraction data at the start (bottom) and completion (top) of the in-sHu decomposition of slag experiments. Most of the peaks in the pattern are due to the parent slag phase. Bragg peaks due to titanium oxide (T) and iron metai (Fe) are marked.

Figure 7-3. Flow pattern in a baffled helical screw system. (Source Holland F. A. and Bragg, R. Fluid Flow for Chemical Engineers, 2nd ed., Edward Arnold, 1995.)...

As one may infer from the quotation, W. L. Bragg realized that a crystal can act as an x-ray grating made up of equidistant parallel planes (Bragg planes) of atoms or ions from which unmodified scattering of x-rays can occur in such fashion that the waves from different planes are in phase and reinforce each other. When this happens, the x-rays are said to undergo Bragg reflection by the crystal and a diffraction pattern results. 

In the powder diffraction technique, a monochromatic (single-frequency) beam of x-rays is directed at a powdered sample spread on a support, and the diffraction intensity is measured as the detector is moved to different angles (Fig. 1). The pattern obtained is characteristic of the material in the sample, and it can be identified by comparison with a database of patterns. In effect, powder x-ray diffraction takes a fingerprint of the sample. It can also be used to identify the size and shape of the unit cell by measuring the spacing of the lines in the diffraction pattern. The central equation for analyzing the results of a powder diffraction experiment is the Bragg equation... 

Fig. 2.—Different types of diffracting specimens (a) a single crystal (left) composed of three-dimensionally periodic unit-cells and its diffraction pattern (right) containing Bragg reflections of varying intensities.

In contrast to single-crystal work, a fiber-diffraction pattern contains much fewer reflections going up to about 3 A resolution. This is a major drawback and it arises either as a result of accidental overlap of reflections that have the same / value and the same Bragg angle 0, or because of systematic superposition of hkl and its counterparts (-h-kl, h-kl, and -hkl, as in an orthorhombic system, for example). Sometimes, two or more adjacent reflections might be too close to separate analytically. Under such circumstances, these reflections have to be considered individually in structure-factor calculation and compounded properly for comparison with the observed composite reflection. Unobserved reflections that are too weak to see are assigned threshold values, based on the lowest measured intensities. Nevertheless, the number of available X-ray data is far fewer than the number of atomic coordinates in a repeat of the helix. Thus, X-ray data alone is inadequate to solve a fiber structure. 

Figure 8. A schematic representation of the elements of the X-ray diffraction pattern from relaxed muscle. These reflections are interpreted to arise from various repeating structures in the muscle. Bragg s law, which states that...

---