Single crystals Laue diffraction pattern from

A Laue X-ray diffraction pattern from a protein crystal. A stationary crystal is irradiated with very intense white, multiwavelength X rays from a synchrotron source. The diffraction pattern is rich in information. A single 0.1 ms X-ray pulse may provide a pattern with enough information to determine a three-dimensional structure. 

You can see from Fig. 9.8 that a Laue diffraction pattern is much more complex than a diffraction pattern from monochromatic X rays. But modern software can index Laue patterns and thus allow accurate measurement of many diffraction intensities from a single brief pulse of X rays through a still crystal. If the crystal has high symmetry and is oriented properly, a full data set can in theory be collected in a single brief X-ray exposure. In practice, this approach usually does not provide sufficiently accurate intensities because the data lack the redundancy necessary for high accuracy. Multiple exposures at multiple orientations are the rule. 

One exception is the so-called Laue technique, in which white radiation is employed to produce diffraction patterns from stationary single crystals. 

In CBED, zone-axis patterns (ZAP) can be recorded near the relevant zone axis and the pattern may also include a higher-order Laue zone (referred to as a HOLZ). The radius of the first HOLZ ring G is related to the periodicity along the zone axis [c] and the electron wavelength, by = 2/kc. CBED can thus provide reciprocal space data in all three (x,y,z) dimensions, typically with a lateral resolution of a few nanometres. As in any application, corroborative evidence from other methods such as HRTEM and single-crystal x-ray diffraction, where possible, can be productive in an unambiguous structural determination of complex and defective materials such as catalysts. We illustrate some examples in later sections. 

The formalism of the reciprocal lattice and the Ewald construction can be applied to the diffraction at surfaces. As an example, we consider how the diffraction pattern of a LEED experiment (see Fig. 8.21) results from the surface structure. The most simple case is an experiment where the electron beam hits the crystal surface perpendicularly as shown in Fig. A.5. Since we do not have a Laue condition to fulfill in the direction normal to the surface, we get rods vertical to the surface instead of single points. All intersecting points between these rods and the Ewald sphere will lead to diffraction peaks. Therefore, we always observe diffraction... 

Radiation and particles, i.e. x-rays, neutrons and electrons, interact with a crystal in a way that the resulting diffraction pattern is always centrosymmetric, regardless of whether an inversion center is present in the crystal or not. This leads to another classification of crystallographic point groups, called Laue classes. The Laue class defines the symmetry of the diffraction pattern produced by a single crystal, and can be easily inferred from a point group by adding the center of inversion (see Table 1.10). 

Laue equations once again indicate that a periodic lattice produces diffraction maxima at specific angles, which are defined by both the lattice repeat distances (a, b, c) and the wavelength (A,). Laue equations give the most general representation of a three-dimensional diffraction pattern and they may be used in the form of Eq. 2.20 to describe the geometry of diffraction from a single crystal. 

From optics we know that diffraction only occurs if the wavelength is comparable to the separation of the scatterers. In 1912, Friedrich, Knipping and Max von Laue performed the first X-ray diffraction experiment using single crystals of copper sulfate and zinc sulfite, proving the hypothesis that X-rays are em-waves of very short wavelength, on the order of the separation of the atoms in a crystalline lattice. Four years later (1916), Debye and Scherrer reported the first powder diffraction pattern with a procedure that is named after them. 

This uses a multipole wiggler and will have operational modes for focussed Laue diffraction work and monochromatic experiments. The small source sizes should allow an equivalently small focal spot from a grazing incidence mirror system. Exposure times in the microsecond range for a macromolecular crystal should be feasible. Depending on the current achieved in single bunch mode it may be possible, at least for smaller unit cell sizes, to record a Laue pattern from one of the single bunches with an intrinsic time resolution therefore of the bunch width. (Feasibility experiments of this kind have been conducted at CHESS but on an undulator (Szebenyi et al 1989).)... 

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