Debye-Scherrer diffraction patterns

Considering the fact that the X-ray diffraction pattern of a crystal depends on its lattice structure, pigment powders can be analyzed with a Debye-Scherrer diffraction camera to establish a correlation between X-ray diffraction and crystal modification. It is synthetically not possible to produce a defined crystal modification of a new pigment. Attempts to modify the preparative procedure or to apply different aftertreatment may result in a pigment of two or more crystalline forms, different not only in lattice structure, but also in color and performance. 

Figure 4 corresponds to PETPg (Ag2S stained) with 12 different selected areas and corresponding diffraction patterns. One can see that 5 patterns have the same orientation, 3 are practically at right angles from the latter, 2 have an intermediate orientation and the last 2 are highly disoriented, with one Debye Scherrer type pattern. 

The Debye-Scherrer powder patterns of the active adrenal steroids may serve as further substantiating evidence for identification. It must be remembered, however, that these steroids may occur in various crystal forms. Consequently, lack of identity of the x-ray diffraction patterns of an unknown compound and an authentic substance may not necessarily prove lack of chemical identity of the two steroids. On the other hand, if the two patterns are identical, it is probable that the two steroids have the same chemical and crystalline structure. 

In addition, an interesting, although negative, result has come from powder diffraction studies of the hexachloro compounds. We have examined Debye—Scherrer photographs of several samples known to contain predominantly hexachlorodibenzo-p-dioxins and have identified the patterns of at least three crystalline phases therein. (There are 10 possible isomers of hexachlorodibenzo-p-dioxin.) These patterns have been checked carefully against the calculated d-spacings and intensities of the 1,2,3,7,8,9-hexa isomer described by Cantrell, Webb, and Mabis (I) and also against an observed pattern supplied by Cantrell and believed to be from the low temperature phase of the same material. Yet to date we... 

Figure 1 is a TEM photograph of the Cu (10wt%)/Al2O3 catalyst prepared by water-alcohol method, showing the dispersed state of copper and was confirmed the particle sizes from XRD data. Figure 2 is X-ray diffraction patterns of above-mention catalysts, was used to obtain information about phases and the particle size of prepared catalysts. Metal oxide is the active species in this reaction. Particle sizes were determined fix)m the width of the XRD peaks by the Debye-Scherrer equation. 

XRD on battery materials can be classified as powder dififaction, a technique developed by Peter Debye and Paul Scherrer. In powder dififaction the material consists of microscopic crystals oriented at random in all directions. If one passes a monochromatic beam of X-rays through a fiat thin powder electrode, a fraction of the particles will be oriented to satisfy the Bragg relation for a given set of planes. Another group will be oriented so that the Bragg relationship is satisfied for another set of planes, and so on. In this method, cones of reflected and transmitted radiation are produced (Fig. 27.2). X-ray diffraction patterns can be recorded by intercepting a... 

The X-ray powder diffraction pattern of sodium valproate was determined by visual observation of a film obtained with a 143 2 mm Debye-Scherrer Powder Camera (Table IV). An Enraf-Nonius Difractis 601 Generator 38 KV and 18 MA with nikel filtered copper radiation A = 1.5418, was employed (4). 

Figure 5.8 A Debye-Scherrer powder camera for X-ray diffraction. The camera (a) consists of a long strip of photographic film fitted inside a disk. The sample (usually contained within a quartz capillary tube) is mounted vertically at the center of the camera and rotated slowly around its vertical axis. X-rays enter from the left, are scattered by the sample, and the undeflected part of the beam exits at the right. After about 24 hours the film is removed (b), and, following development, shows the diffraction pattern as a series of pairs of dark lines, symmetric about the exit slit. The diffraction angle (20) is measured from the film, and used to calculate the d spacings of the crystal from Bragg s law.

The arrangement of helices in the solid and liquid crystalline states of poly(a-phenylethyl isocyanide) were determined by X-ray and electron diffraction. Well-defined diffraction patterns were obtained from oriented films using selected area electron diffraction. Intermolecular and intramolecular patterns were calculated from the five Debye-Scherrer rings. All the reflections were indexed in terms of a pseudo-hexagonal triclinic unit cell, with... 

Local Orientation. The most striking observation of this work is that the selected area diffraction patterns are not in general of a Debye-Scherrer type. Among the various hypotheses which can be drawn to understand such a fact, the most probable one is that the sections are not truly transverse ones indeed, if one supposes the existence of a cylindrical symmetry at the level of each selected area, 0.5 to 1 ym in diameter (the symmetry axis being always parallel to the fiber axis) the "detectable" network main planes have to be parallel to 1he "c" axis of the individual... 

There are two different ways to get local diffraction patterns "Debye-Scherrer" type (such patterns are obtained if ( y ) is found within (E). In the first case (figure 15 the orientation of the local symmetry axis ( A ) is very close to that of (I) with the consequence tRat the whole cone ( e ) is located within the cone (C) even if the local orientation is relatively good, i.e., angle 0 is small. In the second case, the local orientation is poorer, i.e., 0 is fairly large. 

A polycrystalline thin film does not have any preferred orientation (Figure 6.4 (c)). In such a case, the diffraction from the crystal is not a spot but a so-called Debye-Scherrer ring. Therefore, the sample does not have to be inclined to obtain the diffraction pattern. Conventional 2 0-6 scans move the scattering vector H in the radial direction along the film surface normal. Thus, these scans give sufficient information when the film is polycrystalline. The obtained diffracted intensity must be corrected in terms of the absorption and the Lorentz polarization. These two terms and the obtained diffracted intensity have the following relation ... 

Figure 1. Test micrograph showing the displacement of the unscattered beam (small dots) in the selected area diffraction (SAD) pattern when it occurs in polar coordinates (Philips EM 300). The tilt has been fixed at the 002 Bragg angle for carbon ( 0.3°) and the azimuth changed by small increments. The 000 spot displaces along a practically perfect circle which corresponds to the 002 Debye Scherrer ring. Such a device allows exploration of any position in the SAD pattern, even when neither sharp nor intense hkl reflections are visible. The SAD pattern of an asphaltene heat-treated at 500°C has been superimposed to the test micrograph. Various positions of a 0.13 A aperture are shown.

Much of the early work was done before the need for high resolution diffraction equipment was generally recognized, and the Debye-Scherrer techniques available at that time may well have failed to reveal the fine detail at present being recorded. The very ease with which powder patterns can be recorded, and indexed for phases of high symmetry in terms of a particular unit cell, does not in itself mean that a structure is satisfactorily determined by analogy with others of similar composition and crystallographic constants. It is of equal importance... 

Fig. 6 (a) Observed Debye-Scherrer X-ray powder diffraction patterns (Cu-Ka) of the nestled C,4AsF6, (6) quartz capillary background, (c) calculated (10/) diffuse scattering, (d) simulated pattern with (00/) and (11/) crystal reflections, and (10/) diffuse scattering... 

The x-ray diffraction patterns were obtained by mounting the sample particles on a glass filament in a 114.59-mm diameter powder camera (Debye-Scherrer) and irradiating with Cu-Ka x-rays at 30 kV and 15 mA for periods of time ranging from 8 to 24 h. 

The x-ray powder diffraction method dates back to Debye and Scherrer who were the first to observe diffraction from LiF powder and succeeded in solving its crystal structure. Later, HulF suggested and Hanawalt, Rinn and FreveP formalized the approach enabling one to identify crystalline substances based on their powder diffraction patterns. Since that time the powder diffraction method has enjoyed enormous respect in both academia and industry as a technique that allows one to readily identify the substance both in a pure form and in a mixture in addition to its ability to provide information about the crystal structure (or the absence of crystallinity) of an unknown powder. 

Figure 2.12 The Ewald sphere method illustrates the ring pattern of diffraction from a powder specimen. The Debye ring recorded by the Elull-Debye-Scherrer method results from randomly oriented crystals in the powder specimen, in which reciprocal lattice points of (hkl) touch the Ewald sphere surface in various directions to form individual rings. It is equivalent to rotating a reciprocal lattice along an incident beam axis. (Reproduced with permission from R. Jenkins and R.L. Snyder, Introduction to X-ray Powder Diffractometry, John Wiley Sons Inc., New York. 1996 John Wiley Sons Inc.)...

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