Oriented specimens unit cell determination

The information stored in the specimen database is sufficient to identify the particular specimen and the material from which it is made. Other parameters provide information on the orientation of the specimen and on its unit cell parameters. These latter parameters are used by the data collection tasks and the crystal geometry calculation function to determine diffraction angles, the angles between crystal planes, etc. The user can store information on several specimens in the specimen database, thus permitting him to easily remount and rerun a specimen after looking at the collected data. 

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 drawn metal wires the fibre axis is usually not a crystal axis. The problem of the determination of crystal orientation in such specimens (and in rolled metal sheets), though closely related to those dealt with here, is outside the scope of this book. (The unit cell dimensions, and indeed the complete structures of such crystals, are usually known, and the problems that arise are questions of correlation of physical properties with orientation.) See Schmid and Boas, 1935 Orowan, 1942. 

Lattice Type. From the angles at which X rays are diffracted by a crystal, it is possible to deduce the interplanar distances d using Eq. (3). To determine the lattice type and compute the unit-cell dimensions, it is necessary to deduce the Miller indices of the planes that show these distances. In the case of a powder specimen (where all information concerning orientations of crystal axes has been lost), the only available information regarding Miller indices is that obtainable by application of Eqs. (5) and (6). 

The orientation of crystalline stems with respect to the interface of the microstructure in block copolymers depends on both morphology and the speed of chain diffusion, which is controlled by block copolymer molecular weight and the crystallization protocol (i.e. cooling rate). In contrast to homopolymers, where folding of chains occurs such that stems are always perpendicular to the lamellar interface, a parallel orientation was observed for block copolymers crystallized from a lamellar melt phase perpendicular folding was observed in a cylindrical microstructure. Both orientations are shown in Fig. 8. Chain orientation can be probed via combined SAXS and WAXS on specimens oriented by shear or compression. In PE, for example, the orientation of (110) and (200) WAXS reflections with respect to Bragg peaks from the microstructure in the SAXS pattern enables the unit cell orientation to be deduced. Since PE stems are known to be oriented along the c axis, the chain orientation with respect to the microstructure can be determined. 

Determination of Cell Constants, Crystal System, and Space Group. The requirements on specimen preparation are a bit less demanding when a powder pattern is used to determine the cell constants only as long as lines are not fully missing, because preferred orientation is so heavy. Unfortunately, an unknown unit cell cannot always be determined in this simple way. The method is most suitable for the cubic case. Squaring the Bragg equation gives ... 

The density method is undoubtedly employed most frequently for the determination of fibre crystallinity. Needless to say, the fibre must be free of voids and a correction for the presence of Ti02 delustrant must be used. As already mentioned, the unit cell dimensions (and hence the density of the crystalline regions) are often influenced by the crystallization conditions. Similarly, the density of the noncrystalline regions may be influenced by their orientation. Consequently, realistic values of crystallinity can be obtained only when average densities of crystalline and noncrystalline portions are determined independently for each specimen. ... 

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