Laue first order

Any arrangement with oxygen atoms at (d) requires that there be no first-order reflections from planes with h + k + l odd. The presence of such reflection on Laue photographs eliminates such arrangements. 

Examination of the Laue data of Table II shows that with only one exception first-order reflections occurred only from planes with h -(- k -(-even. This would indicate the body-centered lattice T", except for the... 

The Laue data (Table I) contain first-order reflections only from planes with all indices odd. This fact, together with the absence of reflections with mixed indices on oscillation photographs, shows the lattice to be face-centered. Of the two face-centered space groups isomorphous with point group Td, Td and Td, the latter requires that no odd-order reflections occur from planes (khl) with h — lc. The numerous observed... 

In this section we will discuss perturbation methods suitable for high-energy electron diffraction. For simplicity, in this section we will be concerned with only periodic structures and a transmission diffraction geometry. In the context of electron diffraction theory, the perturbation method has been extensively used and developed. Applications have been made to take into account the effects of weak beams [44, 45] inelastic scattering [46] higher-order Laue zone diffraction [47] crystal structure determination [48] and crystal structure factors refinement [38, 49]. A formal mathematical expression for the first order partial derivatives of the scattering matrix has been derived by Speer et al. [50], and a formal second order perturbation theory has been developed by Peng [22,34],... 

The Whole-Pattern symmetry is the symmetry which takes into account all the features present on a high S5mimetry zone axis diffraction pattern (i.e. the disks, the lines inside the disk and the Kikuchi lines). As mentioned above, in order to identify a 3D S5mimetry, the pattern should, at least, display the First-Order Laue Zone. In the example given on figure 2a, this FOLZ is weak, but clearly visible and the Whole Pattern displays a 3D-4mm S5munetry. 

In many cases, the crystal retains enzymatic activity. In some cases, the activity of the enzyme in the crystal is the same as that in solution. The methods used for initiating reactions for study by the Laue method are used to measure activity. For example, pH-jump the acylenzyme indolylacryloyl-chymotrypsin was crystallized at a pH at which it is stable. On changing the pH to increase the reactivity, the intermediate was found to hydrolyze with the same first-order rate constant as occurs in solution the reactions of crystalline ras p21 protein, glycogen phosphorylase, and chymotrypsin have been initiated by photolysis.52 Glyceraldehyde 3-phosphate dehydrogenase has also identical reaction rates in the crystal and solution under some conditions.53... 

If we consider a given reflecting plane of spacing d there is an associated set of Miller indices (h, k, 1). Now 2h, 2k, 21 may be beyond the resolution limit and h, k, 1 may also have no common integer divisor. That is, hkl is an inner point of first order. Hence, the Laue spot that results will contain hkl only. 

The spacing between the reciprocal lattice layer, iL, can be calculated easily from the radius of the FOLZ (first order Laue zone) ring (Fig. 2) (7, as described by Steeds [9] ... 

There are several types of diffraction patterns in a CBED pattern the whole pattern using small camera length, the bright-field (BF) pattern, dark-field (DF) pattern. In the whole pattern, you can see several rings surrounding a central ZOLZ pattern. These rings correspond to first-order Laue zone (FOLZ) and... 

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. 

While the methods for acquiring of X-ray diffraction data have not changed since the first diffraction studies by von Laue, improvements in their components have made them more efficient and user friendly, so that crystal structures of much larger and more complicated molecules can now be determined. For example, during the years since 1912, X-ray sources have evolved from sealed tubes that produce only a nominal flux of radiation to synchrotron sources that produce radiation that is several orders of magnitude more intense. The first structural studies were done on crystals of simple salts containing only a few atoms in each unit cell and therefore relatively small numbers of Bragg reflections were available... 

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. 

Fig. 3 Ewald construction. The white half-circle indicates the Ewald sphere in two dimensions. The points of intersection between the reciprocal lattice rods and the Ewald sphere form the set of reciprocal lattice points (bright) which obey Bragg s law and appear as diffraction spots in the diffraction pattern. Zero-, first- and second-order Laue zone are indicated. Eor electron diffraction in TEM, the ratio between the radius of the Ewald sphere and the reciprocal lattice unit is larger than visualized in the figure. (View this art in color at www.dekker. com.)...

In 1912, when M. Lane suggested to W. Friedrich and P. Knipping the irradiation of a crystal with an X-ray beam in order to see if the interaction between this beam and the internal atomic arrangement of the crystal could lead to interferences, it was mainly meant to prove the undulatoiy character of this X-ray discovered by W.C. Rontgen 17 years earher. The experiment was a success, and in 1914 M. Laue received the Nobel Prize for Physics for the discovery of X-ray diffraction by crystals. In 1916, this phenomenon was used for the first time to study the structure of polycrystalhne samples. Throughout the 20 century. X-ray diffraction was, on the one hand, studied as a physical phenomenon arrd explained in its kinematic approximation or in the more general context of the dynamic theory, and on the other, implemented to study material that is mainly solid. 

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