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Scattering Equation (scattering + equation)

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Chemistry75%

Selected Abstracts

A new approach to calculating powder diffraction patterns based on the Debye scattering equation

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 1 2010
Noel William Thomas
A new method is defined for the calculation of X-ray and neutron powder diffraction patterns from the Debye scattering equation (DSE). Pairwise atomic interactions are split into two contributions, the first from lattice-pair vectors and the second from cell-pair vectors. Since the frequencies of lattice-pair vectors can be directly related to crystallite size, application of the DSE is thereby extended to crystallites of lengths up to ~200,nm. The input data correspond to unit-cell parameters, atomic coordinates and displacement factors. The calculated diffraction patterns are characterized by full backgrounds as well as complete reflection profiles. Four illustrative systems are considered: sodium chloride (NaCl), ,-quartz, monoclinic lead zirconate titanate (PZT) and kaolinite. The effects of varying crystallite size on diffraction patterns are calculated for NaCl, quartz and kaolinite, and a method of modelling static structural disorder is defined for kaolinite. The idea of partial diffraction patterns is introduced and a treatment of atomic displacement parameters is included. Although the method uses pair distribution functions as an intermediate stage, it is anticipated that further progress in reducing computational times will be made by proceeding directly from crystal structure to diffraction pattern. [source]

A comparative study on low-energy elastic electron-NHx (x = 1,2,3) collisions

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 13 2008
L. M. Brescansin
Abstract In this work, a theoretical study on elastic electron-NHx (x = 1,2,3) collisions in the low-energy range is presented. More specifically, calculated elastic differential, integral, and momentum transfer cross-sections are reported in the (1,30)-eV energy range. An optical potential composed of static, exchange, and correlation,polarization contributions is used to represent the electron-target interaction whereas the iterative Schwinger variational method and the method of continued fractions are used to solve the scattering equations. Comparison of the calculated cross-sections for electron scattering by these targets shows that the results are very similar to each other at higher incident energies. This similarity indicates that the interaction between the scattering electron and the central Nitrogen is dominant. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source]

Scattering and absorption of electromagnetic waves on a plane with hemispherical bosses

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 11 2007
Xiaoxiong Gu
Abstract We apply multiple scattering equations to study the scattering of electromagnetic waves on a perfectly conducting plane surface with a random dense distribution of hemispherical bosses. We derive a multipole solution up to third order to analyze close range interactions between nearby bosses. Results show significant improvement of accuracy compared with the traditional dipole approximation solution. Absorption on a lossy embossed surface is obtained from the field solution for the perfectly conducting surface. The surface current and absorption enhancement factor are further computed numerically. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2681,2686, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22855 [source]