Unit cell from rotation photographs

The size and shape of the unit cell is determined, usually from rotation photographs and... 

Unit cell dimensions from rotation photographs 150... 

From a comparison of various spot electron diffraction patterns of a given crystal, a three-dimensional system of axis in the reeiproeal lattice may be established. The reeiproeal unit cell may be eompletely determined, if all the photographs indexed. For this it is sufficient to have two electron diffraction patterns and to know the angle between the seetions of the reeiproeal lattice represented by them, or to have three patterns which do not all have a particular row of points in common (Fig.5). Crystals of any compound usually grow with a particular face parallel to the surface of the specimen support. Various sections of the reciprocal lattice may, in this case, be obtained by the rotation method (Fig.5). 

If the spacings of the arcs on a powder photograph do not lead to identification, the determination of unit cell dimensions from the powder photograph may be attempted the methods are described in Chapter VI. If crystals large enough to be handled individually can be picked out of the specimen, single-crystal rotation photographs may be taken and used for identification this also is dealt with in Chapter VI. 

In fibres of some polymers, made under certain conditions, the crystalline regions are found to be tilted with respect to the fibre axis in a well-defined crystallographic direction. This is a very valuable feature, because the diffraction patterns of specimens in which this type of orientation occurs are of precisely the same form as tilted crystal diffraction patterns of single crystals rotated round a direction inclined to a principal axis. The unit cell cannot be obtained directly, for 90° oscillation tilted crystal photographs are required for direct interpretation, but unit cells obtained by trial can be checked by the displacements of diffraction spots from the layer lines this is a severe check, and consistent displacements would leave no doubt of the correctness of a unit cell. This procedure played an effective part in the determination of the unit cell of polyethylene terephthalate (Daubeny, Bunn, and Brown, 1954). 

In addition to this information, however, the diffraction pattern also provides information on the quality of the crystal lattice and the thermal motion of the atoms in the unit cell. Figure 3 shows examples of the diffraction patterns that would be observed under various circumstances for the lattice shown in Fig. 2. The examples assume diffraction from the (010) and (100) planes of the lattice that are, respectively, planes parallel to the jcz-plane (Fig. 2A) and yz-plane (not shown). A diffraction pattern for a crystalline sample is recorded by rotating a crystal in the x-ray beam to record systematically the reflections from the various lattice planes. To see the diffracted intensities for the example under consideration, the crystal would be mounted with its z-axis parallel to the x-ray beam and then rotated about the jr-axis to obtain reflections from the (010) planes with spacings of d(0k0) and about the y-axis to obtain reflections from the (100) planes with spacings of d h00). All of the reflections are recorded on a single frame of a two-dimensional detector or a single piece of photographic film. 

A rotating cylinder electrode (RCE) with a cylindrical or pseudo-cylindrical counterelectrode around it essentially has the geometry of a parallel plate cell. The RCE was developed as a specialty tool for uniform fast electrodeposition in turbulent flow, and for the removal of metal ions from effluents with recovery of the metal in the form of a foil, flake, or powder [61-63]. In the first application, RCE cathodes became the major tool for silver removal from photographic fixer solutions in compact, high-rate units [64], and enabled the recycling of fixer and resale of more than 98 wt% of the silver. Typically, such cells had a stainless steel RCE cathodes of 10-20 cm diameter rotating at speeds up to 1400 rpm, stationary graphite anodes, and were operated at 50 A. 

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