Crystal rotation method

Figure 5-5. Crystal rotation method according to Bragg (upper left) and the production of a fiber diagram (lower right) by X-ray measurements. K, crystal PH, photographic film P, primary ray F, fiber M, meridian 0, center LO, LI, L2 zeroth, first, and second planes. LO, the equator.

Drawn fibers and films show X-ray diffraction pictures which are similar to the Bragg crystal rotation photographs (Figure 5-5). The crystal rotation method was originally carried out in order to orient favorably as many crystal planes as possible with regard to the X-ray beam. In drawn fibers and films, the molecular axes he mainly in the direction of elongation (see Section 5.6). A ray that impinges normal to the draw direction will... 

Figure 5.11 Schematic diagram of the crystal rotation method of pretilt angle measurement.

The best compromise seems to be fast- rotation for the crystal and slow or no rotation for the crucible. Of all the possible methods of stirring the melt, the static-crucible method seems to be the best, and this is the method used by most crystal-growers. The next best method seems to be rotating the crucible at a slow rate, counter to the direction of the crystal rotation. It is clear that crystal- rotation needs to dominate the stirring pattern so that mixing of the melt continues while the crystal is growing. 

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). 

Resolution of helicenes has also been performed by the very laborious method of picking single crystals 4,5 29,79,80). After recrystallization of the partially resolved mixture the procedure can be repeated, until no more variation in optical rotation occurs. Because some helicenes crystallize into racemic crystals by lamellar intergrowth of pure P and pure M forms (see Sect. 6) the crystal picking method is not always applicable, however. A [7]-heterohelicene was partially resolved by crystallization from the chiral solvent54) (—>x-pinene. 

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. 

Fig. 91. Graphical method for determining values for non-equatorial reflections of monoclinic crystal rotated round c.

Single-crystal rotation photographs. The method found most convenient for finding the unit cell dimensions of crystals of low symmetry is to send a narrow monochromatic X-ray beam through a single... 

Few calculations of three-dimensional convection in CZ melts (or other systems) have been presented because of the prohibitive expense of such simulations. Mihelcic et al. (176) have computed the effect of asymmetries in the heater temperature on the flow pattern and showed that crystal rotation will eliminate three-dimensional convection driven by this mechanism. Tang-born (172) and Patera (173) have used a spectral-element method combined with linear stability analysis to compute the stability of axisymmetric flows to three-dimensional instabilities. Such a stability calculation is the most essential part of a three-dimensional analysis, because nonaxisymmetric flows are undesirable. 

In 1848, Louis Pasteur noticed that a salt of racemic ( )-tartaric acid crystallizes into mirror-image crystals. Using a microscope and a pair of tweezers, he physically separated the enantiomeric crystals. He found that solutions made from the left-handed crystals rotate polarized light in one direction and solutions made from the right-handed crystals rotate polarized light in the opposite direction. Pasteur had accomplished the first artificial resolution of enantiomers. Unfortunately, few racemic compounds crystallize as separate enantiomers, and other methods of separation are required. 

The Laue method involves a stationary crystal and polychromatic ( white ) X rays. In the other camera methods, monochromatic radiation is used. In these cases the crystal may be oscillated over a small angular range (oscillation method) or rotated 360° about an axis (rotation method). The layer lines so formed may be selected individually. In the Weissenberg method, the oscillation of the crystal is coupled with a movement of the photographic film. The Buerger precession method, by a more complex motion of the instrument, produces an undistorted and magnified picture of the reciprocal lattice. 

Bragg X ray method. The X ray examination of crystals using a single large crystal rotated through a small angle around an axis in a crystal face. 

In the powder method, the crystal to be examined is reduced to a very fine powder and placed in a beam of monochromatic x-rays. Each particle of the powder is a tiny crystal, or assemblage of smaller crystals, oriented at random with respect to the incident beam. Just by chance, some of the crystals will be correctly oriented so that their (1(X)) planes, for example, can reflect the incident beam. Other crystals will be correctly oriented for (110) reflections, and so on. The result is that every set of lattice planes will be capable of reflection. The mass of powder is equivalent, in fact, to a single crystal rotated, not about one axis, but about all possible axes. 

The preceding remarks apply just as well to the powder method as they do to the case of a rotating crystal, since the range of orientations available among the powder particles, some satisfying the Bragg law exactly, some not so exactly, are the equivalent of single-crystal rotation. 

Fig. 8-19 Crystal rotation axes for the diffractometer method of determining orientation...

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