Dynamic crystal diffraction

The crystal stmcture of glycerides may be unambiguously determined by x-ray diffraction of powdered samples. However, the dynamic crystallization may also be readily studied by differential scanning calorimetry (dsc). Crystallization, remelting, and recrystallization to a more stable form may be observed when Hquid fat is solidified at a carefully controlled rate ia the iastmment. Enthalpy values and melting poiats for the various crystal forms are shown ia Table 3 (52). 

Peng, L.-M. (1997) Anisotropic thermal vibrations and dynamical electron diffraction by crystals, Acta Cryst. A, 53, 663-672. 

Electron dynamic scattering must be considered for the interpretation of experimental diffraction intensities because of the strong electron interaction with matter for a crystal of more than 10 nm thick. For a perfect crystal with a relatively small unit cell, the Bloch wave method is the preferred way to calculate dynamic electron diffraction intensities and exit-wave functions because of its flexibility and accuracy. The multi-slice method or other similar methods are best in case of diffraction from crystals containing defects. A recent description of the multislice method can be found in [8]. 

Sinkler, W., Bengu, E., Marks, L. D. (1998), Appheation of Direet Methods to Dynamical Electron Diffraction Data for Solving Bulk Crystal Structures", Acta Cryst. A54, 591-605. 

J. Jansen, D. Tang, H.W. Zandbergen and H. Schenk, MSLS, a least-squares procedure for accurate crystal structure refinement from dynamical electron diffraction patterns. Acta Cryst. A54 91-101,1998. 

S. Bing-Dong, F. Hai-Fu, L. Fang-Hua, Correction for the Dynamical Electron Diffraction Effect in Crystal Structure Analysis, Acta Crystallogr., A49,877-880,1993. 

Kulda J (1984) A novel approach to dynamical neutron diffraction by a deformed crystal. Acta Cryst A40 120-126... 

Figure 4 Temperature dependence of selected atomic displacement parameters for the Mg, Si, Al and O atoms in pyrope garnet. Analysis of the displacement parameters obtained from accurate single-crystal diffraction data allow evaluation of the zero-point energy contribution, separation of static and dynamic effects, and detection of anharmonic vibrational contributions to the atomic motion.

In these studies, as in the case of nematic liquid crystals, the dynamic grating diffraction also contains a fast decaying component due to the density contribution, (0n/0p) (see Fig. 9.13). This component decays in about 100 ns. Its peak magnitude is about twice that of the thermal component, which decays in a measured time of about 30 ps for the grating constants of 11 pm used in the experiment. 

In these studies using dynamical grating diffraction techniques, picosecond laser pulses are used to induce density, temperature, and orientational-flow effects in nematic liquid crystals. 

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

In the concepts developed above, we have used the kinematic approximation, which is valid for weak diffraction intensities arising from imperfect crystals. For perfect crystals (available thanks to the semiconductor industry), the diffraction intensities are large, and this approximation becomes inadequate. Thus, the dynamical theory must be used. In perfect crystals the incident X rays undergo multiple reflections from atomic planes and the dynamical theory accounts for the interference between these reflections. The attenuation in the crystal is no longer given by absorption (e.g., p) but is determined by the way in which the multiple reflections interfere. When the diffraction conditions are satisfied, the diffracted intensity ft-om perfect crystals is essentially the same as the incident intensity. The diffraction peak widths depend on 26 m and Fjjj and are extremely small (less than... 

The key here was the theory. The pioneers familiarity with both the kinematic and the dynamic theory of diffraction and with the real structure of real crystals (the subject-matter of Lai s review cited in Section 4.2.4) enabled them to work out, by degrees, how to get good contrast for dislocations of various kinds and, later, other defects such as stacking-faults. Several other physicists who have since become well known, such as A. Kelly and J. Menter, were also involved Hirsch goes to considerable pains in his 1986 paper to attribute credit to all those who played a major part. 

The most important experimental task in structural chemistry is the structure determination. It is mainly performed by X-ray diffraction from single crystals further methods include X-ray diffraction from crystalline powders and neutron diffraction from single crystals and powders. Structure determination is the analytical aspect of structural chemistry the usual result is a static model. The elucidation of the spatial rearrangements of atoms during a chemical reaction is much less accessible experimentally. Reaction mechanisms deal with this aspect of structural chemistry in the chemistry of molecules. Topotaxy is concerned with chemical processes in solids, in which structural relations exist between the orientation of educts and products. Neither dynamic aspects of this kind are subjects of this book, nor the experimental methods for the preparation of solids, to grow crystals or to determine structures. 

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