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Weaknesses of the pseudo-Voigt distribution used in the characterization of nanostructured materials based on the powder X-ray diffraction method

N. ALDEA1,* , B. BARZ2, F. ALDEA3

Affiliation

  1. National Institute for Research and Development of Isotopic and Molecular Technologies, P.O. Box 700 Cluj-Napoca 5, Romania
  2. University of Missouri-Columbia, 223 Physics Building MO 65211
  3. University of Agricultural Sciences and Veterinary Medicine, Cluj-Napoca, Calea Manastur 3-5, Romania

Abstract

The diffraction line broadening in X-ray powder pattern is analyzed by using the pseudo-Voigt distribution as well as the Generalized Fermi Function facilities. X-ray line broadening investigations of supported gold catalysts have been limited to finding the average crystallite size from the integral width or the full width at half maximum of the diffraction line. In the case of supported gold catalysts, it is generally difficult to perform satisfactory intensity measurements of the higher order (hkl) reflections. Therefore, the classical method of Warren and Averbach cannot be applied. In this paper we develop an analytical relation based on the pseudo-Voigt distribution that gives the Fourier transform of the true sample function. From the comparison analysis of the Fourier transform of the true sample function and its general relation we point out the weakness of the Voigt distribution used in the case of Au/SiO2 catalyst. The same problem occurs on other nanostructured materials investigated by powder X-ray diffraction method. A reliable solution for this problem is to use the generalized Fermi function instead of Voigt distribution..

Keywords

Supported gold catalysts, X-ray diffraction, Mathematical model, Voigt distribution.

Submitted at: Nov. 15, 2006
Accepted at: March 15, 2007

Citation

N. ALDEA, B. BARZ, F. ALDEA, Weaknesses of the pseudo-Voigt distribution used in the characterization of nanostructured materials based on the powder X-ray diffraction method, Journal of Optoelectronics and Advanced Materials Vol. 9, Iss. 3, pp. 651-654 (2007)