Debye rings

Fig. 8.1.8 Electron micrograph of SijN4 UFPs and the electron diffraction pattern, where two series of Debye rings, (A) and (B), correspond to a- and P-S13N4, respectively. (From Ref. 38. Reprinted with permission of the Society of Materials Science, Japan.)...

From half width of the intensity distribution measured along the Debye ring of reflection derived from a distance between polymer chains obtained by X-ray diffraction, the practical standard value of parallelism degree in orientation was determined to be 0.92. 

Figure 2.31. The origin of the powder diffraction eone as the result of the infinite number of the completely randomly oriented identical reciprocal lattice vectors, d hki, forming a circle with their ends placed on the surface of the Ewald s sphere, thus producing the powder diffraction cone and the corresponding Debye ring on the flat screen (film or area detector). The detector is perpendicular to both the direction of the incident beam and cone axis, and the radius of the Debye ring in this geometry is proportional to tan20.

Assuming that the number of crystallites approaches infinity (the randomness of their orientations has been postulated in the previous paragraph), the density of the scattered wavevectors, kj, becomes constant on the surface of the cone. The diffiacted intensity will therefore, be constant around the circumference of the cone base or, when measured by a planar area detector as shown in Figure 2.31, around the ring, which the cone base forms with the plane of the detector. Similar rings but with different intensities and diameters will be formed by other independent reciprocal lattice vectors, and these are commonly known as the Debye rings. ... 

Assuming that the diffracted intensity is distributed evenly around the base of each cone (see the postulations made above), there is usually no need to measure the intensity of the entire Debye ring. Hence, in a conventional powder diffraction experiment, the measurements are performed only along a narrow rectangle centered at the circumference of the equatorial plane of the Ewald s sphere, as shown in Figure 2.32 and indicated by the arc with an... 

The Lorentz factor takes into account two different geometrical effects and it has two components. The first is owing to finite size of reciprocal lattice points and finite thickness of the Ewald s sphere, and the second is due to variable radii of the Debye rings. Both components are functions of 0. 

From the locations of Debye rings on the film plus their varying intensity (degree of darkening), it is possible to identify the material and to establish its crystal structure. Given the analogue nature of the film, it is nearly as easy to grasp the overall structure of the diffraction pattern, as it is... 

Figure 3.15. The schematic of a powder diffractometer with the vertical goniometer axis, cylindrical sample in the transmission mode and image plate detector (IPD). Solid arrows show the incident beam path. Rings indicate intercepts of Debye cones with the IPD. F -focal point of the x-ray source, M - monochromator, C - collimator, DR - Debye rings.

To obtain an insight into the effect of the draw ratio on the molecular orientation of the Vectra phase, wide angle x-ray diffraction, WAXD, was utilized and the results for the Ultem/Vectra 70/30 sheet drawn in the first zone are shown in Figure 11. For the sample with the lowest draw ratio, a sharp Debye ring corresponding to a d-spacing of 0.46 nm is observed. This observation is in agreement with previous data on Vectra reported in the literature (10). As the draw ratio increases, the azimuthal dependence of the... 

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.)...

The pinhole method has the advantage that an entire Debye ring, and not just a part of it, is recorded on the film. On the other hand, the range of 0 values which are recorded is rather limited either low-angle or high-angle reflections may be obtained, but not those in the median range of 9 (see Fig. 6-12). In the transmission method, the value of 9 for a particular reflection is found from the relation... 

Fig. 6-11 Transmission pinhole photograph of an aluminum sheet specimen. Filtered copper radiation. (The diffuse circular band near the center is caused by white radiation. The nonuniform blackening of the Debye rings is due to preferred orientation in the specimen see Chap. 9.)...

The camera shown in Fig. 5-3 has a motor to rotate the specimen for such integration. The sectored disc on the cassette of this camera is designed for recording two or more partial patterns on one film for comparative purposes. After the first pattern is made, the specimen is changed, the disc is rotated about the collimator by an amount sufficient to cover the previously exposed portion of film and uncover an unexposed portion, and the second exposure is made. Or the disc may be removed, if one wishes to record complete Debye rings from a single specimen. 

Diffraction of the continuous spectrum. Each crystal in a powder specimen forms a weak Laue pattern, because of the continuous radiation component of the incident beam. This is true whether or not that particular crystal has the correct orientation to reflect the characteristic component into the Debye ring. Many crystals in the specimen are therefore contributing only to the background of the photograph and not to the diffraction ring, and the totality of the Laue patterns from all the crystals is a continuous distribution of background radiation. If the incident radiation has been so chosen that very little fluorescent radiation is... 

A transmission pinhole photograph is made of copper with Cu Ka. radiation. The film measures 4 by 5 in. What is the maximum specimen-to-film distance which can be used and still have the first two Debye rings completely recorded on the film ... 

Several methods have been proposed for the estimation of grain size purely in terms of various geometrical factors. For example, an equation may be derived which relates the observed number of spots on a Debye ring to the grain size and other such variables as incident-beam diameter, multiplicity of the reflection, and specimen-film distance. However, many approximations are involved and the resulting equation is not very accurate. The best way to estimate grain size by... 

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