X-ray diffraction imaging

As an X-ray diffraction image map helps identify the lattice structure of a crystal, the autocovariance function of a 2D separation map may help recognize the chemical structure of complex mixtures. 

Certain mathematical techniques can determine molecular structure from X-ray diffraction images, such as this X-ray diffraction image of a protein. [Alfred Pasleka/Photo Researchers, Inc.]... 

Figure 13.20 Orientated monodomain X-ray diffraction images from the dodecyloxy analogue of the compound shown in Figure 13.19 at (a) 104 °C and (b) 82 °C corresponding to hexagonal and rectangular columnar phases respectively (reprinted with permission from [11] 2004 American Chemical Society).

Fig. 4. Direct tomographic, energy-dispersive X-ray diffraction imaging system. Suitcase enters device at left of Figure where spatial landmarks for registration purposes are measured by pre-scanner. In main housing centre-right of Figure, a primary cone-beam executes a meander scan, either of a region-of-interest or suitcase in its entirety. Illustration courtesy of GE Security, Germany.

X-ray diffraction imaging in its early days followed a similar path to target medical diagnostic applications. Several investigators found remarkable differences between the diffraction profiles of healthy and diseased tissue in the skeleton [11] and breast [12], to name just two examples. Dose considerations however, particularly compared with MRI, have prevented up to now the widespread application of XDI in diagnostic radiology. 

Fig. 17. Two-dimensional generic cross-section for energy-dispersive direct tomographic X-ray diffraction imaging.

Fig. 21. Geometrical configuration for next-generation X-ray diffraction imaging.

Fig. 23. Simulated energy-dispersive X-ray diffraction imaging profile for diffraction line at 1.2nm 1.

G Harding (2005) The design of direct tomographic, energy-dispersive x-ray diffraction imaging (XDI) systems. SPIE 59230R. 

The book includes several chapters on vapor and trace detection chemiluminescence, mass spectrometry, ion mobility spectrometry, electrochemical methods, and micro mechanical sensors, such as microcantilevers. Other chapters deal with bulk detection techniques neutron techniques, nuclear quadrupole resonance, X-ray diffraction imaging, millimeter-wave imaging, terahertz imaging, and laser techniques. Special chapters are devoted to personnel portals and to biological detection. 

Figure 8 X-ray diffraction images, (a) A precession photograph of muconate lactonizing enzyme. The fourfold symmetry in the diffraction pattern is clearly visible. This gives an undistorted view of the reciprocal lattice but are no longer used because they are not as efficient as rotation images, (b) A rotation image of hen s egg white lysozyme. This easily obtainable image gives a distorted projection of the reciprocal lattice, but this is no obstacle for modern programs.

FIGURE 30.10 Example of an X-ray diffraction image. The characteristic pattern of diffraction spots is caused by the fact that X-rays diffracted from different unit cells in the crystal should scatter in phase. 

Fig. 1.7 Phase diagram of 1,4-phenylene bis(4-((2,5,8,ll,14,17-hexaoxanonadecan-19-yl)oxy) benzoate) and water (redrawn after [25]). The abbreviation D stands for dystetic, Iso for isotropic and Cr for crystalline. The inset shows a two-dimensional X-ray diffraction image of an aligned sample of the lyotropic SmC analog phase. The direction of an applied magnetic field H is indicated (adapted from [25], Copyright 1988 Taylor Francis, www.tandfonline.com)...

According to multi-crystal XRD theory, the diffraction intensity yd of a point in any X-ray diffraction image, can be expressed by the equation ... 

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