Polycrystalline specimens

Interplanar Spacings. Diffractometer alignment procedures require the use of a well-prepared polycrystalline specimen. Two standard samples found to be suitable are silicon and a-quartz (including Novaculite). The 26 values of several of the most intense reflections for these materials are listed in Table 7.6 (Tables of Interplanar Spacings d vs. Diffraction Angle 26 for Selected Targets, Picker Nuclear, White Plains, N.Y., 1966). To convert to d for Ka or to d for Ka2, multiply the tabulated d value (Table 7.6) for Ka by the factor given below ... 

The crystal group or Bravais lattice of an unknown crystalline material can also be obtained using SAD. This is achieved easily with polycrystalline specimens, employing the same powder pattern indexing procedures as are used in X-ray diffraction. ... 

It is particularly helpful that we can take the Cu-Ni system as an example of the use of successive deposition for preparing alloy films where a miscibility gap exists, and one component can diffuse readily, because this alloy system is also historically important in discussing catalysis by metals. The rate of migration of the copper atoms is much higher than that of the nickel atoms (there is a pronounced Kirkendall effect) and, with polycrystalline specimens, surface diffusion of copper over the nickel crystallites requires a lower activation energy than diffusion into the bulk of the crystallites. Hence, the following model was proposed for the location of the phases in Cu-Ni films (S3), prepared by annealing successively deposited layers at 200°C in vacuum, which was consistent with the experimental data on the work function. 

Polymers invariably form helical structures, and the helix symmetry is denoted by u, indicating that there are u repeat units in V turns of the helix. The helix pitch is denoted by P and the molecular repeat distance is c = vP. X-ray diffraction patterns from non-crystalline specimens contain diffracted intensities restricted to layer lines that are spaced by 1/c. On a diffraction pattern from a polycrystalline specimen, diffraction signals, or Bragg reflections, occur only at discrete positions on the layer lines, the positions being related to the lateral dimensions of the unit cell of the crystal. The meridian (vertical axis) of the diffraction pattern is devoid of diffracted intensity unless the layer line number J, is a multiple of u, so that u can be determined straightforwardly. The diffracted intensities can be calculated using standard expressions (2), for model structures (i.e. given the atomic coordinates). 

How are these crystals arranged in supramolecular aggregates That is, what is their morphology and the microstructure in a polycrystalline specimen ... 

So far it has been assumed that well-formed crystals with plane faces, suitable for accurate setting by the optical method, are available. Such crystals form the ideal experimental material for any detailed crystallographic investigation but it is possible, even when the crystal symmetry is low, to proceed with far less promising material—with ill-formed crystals, or writh irregular crystal fragments, or even with polycrystalline specimens. The additional problems presented by such specimens will now be considered. 

The creep rate when boundary sliding is rate-limiting has been treated and discussed by Beere [13, 14]. If a viscous constitutive relation is used for grainboundary sliding (i.e., the sliding rate is proportional to the shear stress across the boundary), the macroscopic creep rate is proportional to the applied stress, and the bulk polycrystalline specimen behaves as a viscous material. An analysis of the sliding-controlled creep rate of the idealized model in Fig. 16.4 is taken up in Exercise 16.2. 

Oriented, polycrystalline specimens. If, for example, all Az = A = 0 the array would be a three-dimensionally ordered domain i.e. a "single crystal". The most highly organized fibers are ones in which many such domains are oriented with only the helix axes parallel. As I indicated above, such fibers provide X-ray diffraction patterns like those from a rotated single crystal. The not-quite-perfect parallelism of the domains causes the intensity to be distributed along arcs instead of concentrated in spots (see Fig. 2). 

IR transmission spectra (T) of the thin polycrystalline specimens or powders were measured using IR microscope of the Fourier-spectrometer at room temperature in the spectral range of 600 5,000 cm-1. Optical absorption spectra were calculated as -ln(T). Figure 11.11 demonstrates normalized absorption spectra of fulleranes C60Hx with x = 36, 42, 48 and 60 together with the well known spectrum of fullerit... 

Figure 3.13 Spectral patterns for a paramagnetic ion in a polycrystalline specimen with (a) an axially symmetric and (b) a rhombic g-tensor, shown as absorption (top) and first derivative (bottom) lineshapes. Solid curves indicate idealised line shapes, whereas the dashed curves represent typical experimental patterns.

Only two recent studies will be discussed, one dealing with the influence of pressure of oxygen on the formation of nuclei and the other with the influence of dislocations in the metal. Benard, Gronlund, Oudar and Duret (75) studied the oxidation of the individual grains in a polycrystalline specimen of copper and proposed that the nucleation process is an intermediate stage in the formation of oxide films of uniform thickness as follows there are three stages in the formation of the oxide film (1) the incubation of nuclei, (2) the growth of nuclei,... 

Fig. 8. Calculated (open symbols) and experimental (solid diamonds) values of the work function for the 4d transition metals. These calculations are considerably more sophisticated than the older ones shown in Figs. 5-7, and they reproduce several properties of these metal surfaces very well. The calculated values are for different single-crystal faces, as indicated the experimental values refer to polycrystalline specimens. [Reproduced with permission from Methfessel et al. (29). Copyright 1992 American Physical Society.]...

Chemisorbed NH3 dissociates much more readily and many authors have studied the kinetics of dissociation. Loffler and Schmidt have studied the kinetics under molecular beam conditions on a polycrystalline specimen and on several low-index faces of a single crystal [(111), (100), (110), (210)]. The rate between 330 and 930 °C is strongly retarded by hydrogen and can be fitted by a Langmuir-Hinshelwood expression with competitive H2 and NH3 adsorption. 

Figure 3.34 Images of polycrystalline specimen of thallium chloride (a) SAD ring pattern and (b) bright-held image in which the dark circle (50 //m diameter) indicates the area selected for diffraction. (Reproduced with permission from M. von Heimandahl, Electron Microscopy of Materials, Academic Press, New York. 1980 Elsevier B. V.)...

What kind of diffraction patterns you should expect if an SAD aperture includes a large number of grains in a polycrystalline specimen Why ... 

The x-ray spectrometer can also be used as a tool in diffraction analysis. This instrument is known as a diffractometer when it is used with x-rays of known wavelength to determine the unknown spacing of crystal planes, and as a spectrometer in the reverse case, when crystal planes of known spacing are used to determine unknown wavelengths. The diffractometer is always used with monochromatic radiation and measurements may be made on either single crystals or polycrystalline specimens in the latter case, it functions much like a Debye-Scherrer camera... 

The extinction effect can operate, not only in single-crystal specimens, but also in the individual grains of polycrystalline specimens. Extinction may be assumed to be absent in ground or filed powders and is usually negligible in finegrained polycrystalline specimens. If its presence is suspected in the latter, the specimen can always be reduced to powder by grinding or filing. 

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