Cone pattern, diffraction

Figure 8.28 Schematic diagram showing (a) diffraction from a single crystal, (b) from four crystals at different orientations with respect to the incident beam and (c) from a polycrystalline powder giving rise to a pattern of concentric cones of diffraction, often presented as a one-dimensional plot of intensity vs diffraction angle (reproduced by permission of The Royal Society of Chemistry).

Figure 7 (a) Bragg reflection from a set of lattice planes, (b) The cone of diffracted X-rays from a powder specimen. The cone contains all X-rays reflected from one particular family of lattice planes in all crystals which are correctly oriented, (c) The form of a powder pattern (asymmetric film mounting)... 

PowderSD Powder3D 1.0 A multi pattern data reduction and graphical presentation software, B. Hinrichsen, R.E. Dinnebier and M. Jansen, 2004 http //www.fkf.mpg.de/xray/ html/powder3d.html Integration of full 2D cones of diffraction under development... 

The powdered sample (200-300 mesh) in the form of a cylinder is placed in the path of a narrow beam of essentially monochromatic x-rays. The diffraction pattern is recorded on a photographic film at right angles to the incident beam. The powder contains fine, randomly oriented crystals. Hence, the requirements of Equation 14.7 (the proper d) are fulfilled by many of these crystal orientations. The random orientation results in a circular cone of diffracted beam for a given reflecting plane with the incident beam as the axis. Since there are planes at different angles in the crystal, several different cones are observed. The film strip is too narrow to... 

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... 

Use of the precession technique should promote a decrease of multi-beam effects and an improvement of the situation with the inaccuracy of orientation. In this case we will have full set of orientations along the surface of cone and the diffraction pattern will be the sum of all patterns for every direction of the beam. 

HMX when dissolved in coned sulfuric acid, produces a red-violet color in the presence of ferrous ions (ferrous ammonium sulfate) (Refs 25 27). HMX may also be detected by its infrared spectrogram and x-ray diffraction pattern Quantitative Determination ... 

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. 

As a result 0 and co (angle between ( A ) and (I)) have equivalent values and again cone (C) surrounds cone ( ). The first case may correspond to PETP in which there would be a noticeable dispersion of the local symmetry axis around fiber axis. This could explain the relatively frequent variations in the orientation of the diffraction pattern in the specific case of PETP. The second case would correspond to 66 polyamide which has local variations of orientation and less overall orientation than in PETP. The two cases are presented in figure 15. 

The existence of the intensity maxima within the cones of scattering have been our experimental cornerstone for measuring the well-defined separation between the clay plates. The second remarkable feature of a comparison between parts (a) and (b) of Figure 11.1 is that the diffraction pattern from the polymer-added sample is much sharper it exhibits a more pronounced first-order diffraction maximum and a strong second-order diffraction maximum, which is rare for a pure aqueous sample [5], This effect was also observed for all the PVME-added samples and means that... 

---