Method rotating crystal

Spinning a crystal during measurement of WAXS patterns is an old method that turns any scattering pattern into a fiber pattern. The rotational axis becomes the principal axis. Thereafter isotropization of the scattering data is simplified because the mathematical treatment can resort to fiber symmetry of the measured data. In the literature the method is addressed as the rotating-crystal method or oscillating-crystal method. 

It should be clear that the Darwin equation with its special LoRENTZ-polariza-tion factor as reported by Warren ([97], Eq. (4.7)) is only valid for unpolarized laboratory sources and the rotation-crystal method. An application to different setup geometries, for example to synchrotron GIWAXS data of polymer thin films is not appropriate. 

Laue method Rotating-crystal method Powder method... 

The chief use of the rotating-crystal method and its variations is in the determination of unknown crystal structures, and for this purpose it is the most powerful tool the x-ray crystallographer has at his disposal. However, the complete determination of complex crystal structures is a subject beyond the scope of this book and outside the province of the average metallurgist who uses x-ray diffraction as a laboratory tool. For this reason the rotating-crystal method will not be described in any further detail, except for a brief discussion in Appendix 1. 

Fig. Al-9 Reciprocal-lattice treatment of rotating-crystal method.

Members of this group, unlike x-ray crystallographers, are not normally concerned with the determination of complex crystal structures. For this reason the rotating-crystal method and space-group theory, the two chief tools in the solution of such structures, are described only briefly. 

In the monochromatic rotating crystal method it has been feasible to record complete data sets from a protein crystal on a timescale of half an hour or less using an SR source (see chapter 10). Ultimately, the total data collection time in the monochromatic method is set by the mechanical overheads of the angular rotation speed of the crystal and by the necessity to replace film cassettes or transfer detector images to computer mass store and to refresh the detector. 

The reflection or spot bandwidth is the narrow range of wavelengths extracted from the overall, much broader bandpass required to stimulate fully the RLP. It is directly akin to the rocking width in the monochromatic rotating crystal method. 

The most powerful method that can be used to determine unknown crystal structures is the rotating crystal technique. In this method a single crystal of good quality (of at least 0.1 mm in the smallest dimension) is mounted with one of its axes normal to a monochromatic beam of x-rays and rotated about in a particular direction. The crystal is surrounded by cylindrical film with the axis of the film being the same as the axis of rotation of the crystal. By repeating this process of rotation in a number of directions, the rotating crystal method can be used to determine an unknown crystal structure. 

It is unlikely that you will ever need to use the rotating crystal method to determine an unknown structure since most materials you are likely to crystallize have structures that have been determined. This will not be true for a newly developed compound, and is rarely true for proteins and other biological macromolecules. 

In the rotating crystal method, a single crystal is used with dimensions of the order of 0.1 to 0.5 mm (smaller than the diameter of the primary beam). The importance of undesired phenomena such as absorption of the beam and extinction (Section 3.3.2) increases with the size of the crystal. The crystal executes a rotation about a lattice line [(77 IT] of the translation lattice. Hence, the crystal must be precisely aligned. The planes of the reciprocal lattice whose lattice points hkl satisfy the equation... 

The Lorentz factor L 9) is contained in the term g(6) of equation (3.52). The lower the rate of passage of the point through the sphere, the higher is the integrated intensity. The point (000) always lies on the sphere, independent of the position of the crystal. Consequently, L(0) = oo. If the rotation axis does not lie in the reflecting plane, we obtain a speed v which is lower than that in equation (3.58). Hence L 6) depends on the experimental technique used. For the rotating crystal method (Section 3.5.2), with the rotation axis parallel to c and the primary beam perpendicular to c, the result for the nth layer is ... 

Laue method 2. Rotating crystal method W. H. and W. L. Bragg 3. Powder method Debye-ScWrer, Hull 4. Goniometer method Weissenberg, Schiebold, Dawson... 

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