Electron diffraction distribution

In principle, it is possible to calculate the detailed three-dimensional electron density distribution in a unit cell from the three-dimensional x-ray diffraction pattern. 

Figure 5.2 The modification of the electron energy distribution curve by the presence of diffraction limits in a crystal. The lower filled band is separated from upper unoccupied states in a semiconductor by a small energy difference, so that some electrons can be promoted to conduction by an increase in temperature...

Auger Electron Diffraction, AED, is an exact analogy to XPD, providing basically the same information. Instead of measuring the angular distribution of the ejected photoelectrons one uses the Auger electrons (Chapter 5). 

Since the first structure determination by Wadsley [56] in 1952 there has been confusion about the correct cell dimensions and symmetry of natural as well of synthetic lithiophorite. Wadsley determined a monoclinic cell (for details see Table 3) with a disordered distribution of the lithium and aluminium atoms at their respective sites. Giovanoli et al. [75] found, in a sample of synthetic lithiophorite, that the unique monoclinic b-axis of Wadsley s cell setting has to tripled for correct indexing of the electron diffraction patterns. Additionally, they concluded that the lithium and aluminum atoms occupy different sites and show an ordered arrangement within the layers. Thus, the resulting formula given by Giovanelli et al. 

SP 58 The Radial Distribution Method of Interpretation of Electron Diffraction Photographs of Gas Molecules... 

Because of the difficulty of obtaining satisfactory photometer records of electron diffraction photographs of gas molecules, we have adapted and extended the visual method to the calculation of radial distribution curves, by making use of the values of (4t sin d/2)/X obtained by the measurement of ring diameters (as in the usual visual method) in conjunction with visually estimated intensities of the rings, as described below. Various tests of the method indicate that the important interatomic distances can be determined in this way to within 1 or 2% (probable error). 

It is shown by empirical tests that the radial distribution function given by a sum of Fourier terms corresponding to the rings observed on an electron diffraction photograph of gas molecules... 

AOTF w/c RMs bearing the silver, silver iodide and silver sulfide nanoparticles were depressurized slowly and the nanoparticles in the cell were collected and re-dispersed in ethanol. Finally, the sample grids for the TEM (FEl TECNAl G ) measurements were prepared by placing a drop of ethanolic dispersion of nanoparticles on the copper grid. The morphology and size distribution of the silver, silver iodide, and silver sulfide nanoparticles were determined by TEM at an operation voltage of 200kV. The crystallinity of the silver, silver iodide, and silver sulfide nanoparticles was studied by electron diffraction techniques. 

The diffraction pattern obtained in the detector plane when the beam scan in a STEM instrument is stopped at a chosen point of the image comes from the illuminated area of the specimen which may be as small as 3X in diameter. In order to form a probe of this diameter it is necessary to illuminate the specimen with a convergent beam. The pattern obtained is then a convergent beam electron diffraction (CBED) pattern in which the central spot and all diffraction spots from a thin crystal are large discs rather than sharp maxima. Such patterns can normally be interpreted only by comparison with patterns calculated for particular postulated distributions of atoms. This has been attempted, as yet, for only a few cases such as on the diffraction study of the planar, nitrogen-rich defects in diamonds (21). 

The most important information about the nanoparticles is the size, shape, and their distributions which crucially influence physical and chemical properties of nanoparticles. TEM is a powerful tool for the characterization of nanoparticles. TEM specimen is easily prepared by placing a drop of the solution of nanoparticles onto a carbon-coated copper microgrid, followed by natural evaporation of the solvent. Even with low magnification TEM one can distinguish the difference in contrast derived from the atomic weight and the lattice direction. Furthermore, selective area electron diffraction can provide information on the crystal structure of nanoparticles. 

Larsen, F.K. and Hansen, N.K. (1984) Diffraction studies of the electron density distribution in beryllium metal, Acta Cryst., B40, 169-179. 

Feil, D. (1991) X-ray diffraction and charge distribution application to the electron density distribution in the hydrogen bond, In TheApplication of Charge Density Research to Chemistry and Drug Design, Jeffrey, G.A. and Piniella, J.F. (Eds.), NATO ASI Series B250, Plenum Press, New York. 

Destro,R., Bianchi,R., Gatti,C. andMerati,F. (1991)TotalelectronicchargedensityofL-alaninefrom X-ray diffraction at 23 K, Chem. Phys. Lett., 186, 47-52 Iversen, B.B., Larsen, F.K., Souhassou, M. and Takata, M. (1995) Experimental for the existence of non-nuclear maxima in the electron-density distribution of metallic beryllium. A comparative study of the maximum entropy method and the multipole refinement method, Acta Cryst., B51, 580-591 and references therein. 

For the crystalline materials, high resolution X-ray diffraction experiment is a powerful tool to derive accurate electron density even for large systems like zeolites. In this study, we are interested in the experimental electron density distribution in the scolecite CaAl2Si3O10 3H20 in order to make comparison with its sodium analogue natrolite Na2Al2Si3Oi0 2H20 for which the electron density has been reported recently [1,2],... 

X-ray crystallographic experiments measure the intensity of the diffraction peaks resulting from the X-rays scattered by electron clouds, which is related to the thermal average of electron density distributions in the crystal by a Fourier transform ... 

In general, all observed intemuclear distances are vibrationally averaged parameters. Due to anharmonicity, the average values will change from one vibrational state to the next and, in a molecular ensemble distributed over several states, they are temperature dependent. All these aspects dictate the need to make statistical definitions of various conceivable, different averages, or structure types. In addition, since the two main tools for quantitative structure determination in the vapor phase—gas electron diffraction and microwave spectroscopy—interact with molecular ensembles in different ways, certain operational definitions are also needed for a precise understanding of experimental structures. 

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