Coherent X-ray scatter

CXRS entered the commercial market in the mid-to-late 1990s after a long development period. The basic principles have been known for many years, but practical development faced many hurdles. Most explosives have a crystalline structure. Because the crystals are small and randomly orientated, the structure is sometimes referred to as poly crystalline. These crystals exhibit a strong coherent scatter at certain angles that depend on the X-ray energy and the crystal lattice spacing. This coherent scatter (also called diffraction) is a property of the crystal lattice and is unrelated to 

CXRS can also be employed in an angular dispersive mode (or both angular dispersive and energy dispersive). In this mode, a single-energy photon source. 

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Abbott and R.W. Conners, Simulation of x-ray imaging systems for lugjage inspection in Proc. 2nd Explosives Detection Technology Symposium Aviation Security Technology Conference, 12—15 November 1996, Atlantic City, NJ, FAA (1997) 248—253. 

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X-ray attenuation occurs via four basic modes of interaction, shown schematically in Figure 4. Coherent X-ray scatter (CXRS) is an energy preserving interaction between an X-ray photon and an entire atom or crystalline matrix. Incoherent or Compton scatter represents a direct interaction between an X-ray and an... 

Prototype coherent X-ray scatter used for explosives detection... 

Figure 25 Schematic illustration for a system based on energy-dispersive coherent X-ray scatter (CXRS). Observation of the scattered photons is restricted to a fixed angle via a pinhole collimator. The spectrum from a highly energy resolving detector will show peaks at particular energies that are characteristic of the polycrystalline target. Computerized identification techniques can be used to identify the target substance.

According to Eq. (1.16), the elastic coherent X-ray scattering amplitude is the Fourier transform of the electron density in the crystal. The crystal is a three-dimensional periodic function described by the convolution of the unit cell density and the periodic translation lattice. For an infinitely extended lattice,... 

The coherent X-ray scattering component of a given molecular configuration measured in system L (laboratory system) is written as... 

Sandy, A. R., Lurio, L. B., Mochrie, S. G. J., Malik, A., Stephenson, G. B., Pelletier, J. F., and Sutton, M. (1999). Design and characterization of an undulator beamline optimized for small-angle coherent X-ray scattering at the advanced photon source. J. Synchrotron Radiat. 6, 1174-1184. 

H Strecker, G Harding, H Bomsdorf, J Kanzenbach, R Linde and G Martens (1993) Detection of explosives in airport baggage using coherent x-ray scatter. SPIE 2092 (Eds Harding, Lanza, Myers and Young), 399—410. 

ID Jupp, P T Durrant, D Ramsden, T Carter, G Dermody, I B Pleasants and D Burrows (2000) The non-invasive inspection of baggage using coherent x-ray scattering. IEEE Trans. Nucl. Sci. 47, 1987-1994. 

G Harding and B Schreiber (1999) Coherent x-ray scatter imaging and its applications in biomedical science and industry. Radiat. Phys. Chem. 56, 229-245. 

H Bomsdorf, T Mueller and H Strecker (2004) Quantitative simulation of coherent x-ray scatter measurements on bulk objects. J. X-ray Sci. Technol. 12, 83-96. 

The charge density p(r) is the fundamental property measured in a coherent X-ray scattering experiment, as is commonly employed in the determination of a crystal structure. This follows since the operator which describes the interactions of X-rays with the electrons is, to a very good approximation (the Bom approximation), given by a sum of one-electron interactions... 

The one-electron density, p(r), expresses the probability of finding one electron in a volume element centered at r, the remaining electrons being anywhere. It is a fundamental physical property measured in coherent X-ray scattering experiments or calculated with quantum chemical methods. It is involved in very important theorems such as the electrostatic expression of the Helfinann-Feynman theorem [40-43] which enables the calculation of the forces on nuclei and the Hohenberg-Kohn theorem [44] which is at the root of the Density Functional Theory (DFT). The one electron density can be be written as the sum of the spin contributions ... 

Fig. 6.14 Coherent X-ray scattering pattern from a colloidal suspension of gold nanoparticles. Left half shovis a single-shot coherent pattern, where distinct speckles are clearly visible. Right Ita//shows a scattering ring obtained from a sum of 50 successive shots, which is smooth and largely resembles data from conventional SAXS experiments...

Sandy AR, Lurio LB, Mochrie SGJ, MalikA, Stephenson GB, Pelletier JF, Sutton M (1999) Design and characterization of an undulator heamline optimized for small-euigle coherent X-ray scattering at the Advanced Photon Source. J Synchrotron Radiat 6 1174-1184. doi 10.1107/S0909049599009590... 

The specific surface Ssp of silver blacks was determined by the BET method through the adsorption of N2. The specific surface of supported Ag catalysts was calculated from the data on chemisorption of O2. Size distribution of Ag particles was obtained by transmission electron microscope JEM-100 CX and the SAXS method (KRM-1 apparatus). An average value of the regions of coherent X-ray scattering was determined through the widening of X-ray lines registered with a DRON type apparatus. Spectra of diffused reflection were recorded by the Shimadzu UV-300 spectrometer. 

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