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MATHEMATICAL STUDY OF METAL NANOPARTICLE SIZE DETERMINATION BY SINGLE X-RAY LINE PROFILE ANALYSIS

N. Aldea1,* , B. Barz2, T. D. Silipas1, F. Aldea3, Z. Wu4

Affiliation

  1. National Institute of R&D of Isotopic and Molecular Technologies, P.O. Box. 700, RO 400293 Cluj-Napoca, Romania
  2. University of Missouri - Columbia, 223 Physics Building, MO 65211, USA
  3. Agriculture and Medicine Veterinary University, Department of Mathematics and Computer Science, RO 400372 Cluj-Napoca, Romania
  4. Coordination Laboratory of National Center for Nanoscience and Nanotechnology, Synchrotron Radiation Facilities of Beijing Electron Positron Collider, China

Abstract

The new theoretical outline for determination of the metal crystallite nanosize and lattice strain from X-ray diffraction line profile broadening is discussed. Emphasis is made on the rigorous analysis of the line profiles in terms of Fourier transform. Fermi generalized distribution function for single X-ray line profile approximation is used in order to determine the crystallite size and the lattice strain by the deconvolution technique. The microstructural parameters are obtained by the use of the Warren and Averbach theory and are included in the general form of the Fourier transform of the true sample. A comparison of microstructural models of the supported nickel catalysts determined by various analytical approximations is presented. Practical examples that emphasize the influence of the ideal standard line profiles of supported nickel catalysts as experimental samples are given. The measurements were performed on Beijing Synchrotron Radiation Facilities..

Keywords

Deconvolution, Fourier transform, X -ray diffraction, Metal crystallite size, Microstrain.

Submitted at: Oct. 3, 2005
Accepted at: Nov. 24, 2005

Citation

N. Aldea, B. Barz, T. D. Silipas, F. Aldea, Z. Wu, MATHEMATICAL STUDY OF METAL NANOPARTICLE SIZE DETERMINATION BY SINGLE X-RAY LINE PROFILE ANALYSIS, Journal of Optoelectronics and Advanced Materials Vol. 7, Iss. 6, pp. 3093-3100 (2005)