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Effect of a crystallite size distribution on X‐ray diffraction line profiles and whole‐powder‐pattern fitting
Author(s) -
Langford J. I.,
Louër D.,
Scardi P.
Publication year - 2000
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s002188980000460x
Subject(s) - crystallite , nanocrystalline material , diffraction , line (geometry) , materials science , powder diffraction , dispersion (optics) , distribution (mathematics) , transmission electron microscopy , particle size distribution , mineralogy , analytical chemistry (journal) , crystallography , optics , mathematics , chemistry , physics , mathematical analysis , geometry , particle size , nanotechnology , chromatography
A distribution of crystallite size reduces the width of a powder diffraction line profile, relative to that for a single crystallite, and lengthens its tails. It is shown that estimates of size from the integral breadth or Fourier methods differ from the arithmetic mean of the distribution by an amount which depends on its dispersion. It is also shown that the form of `size' line profiles for a unimodal distribution is generally not Lorentzian. A powder pattern can be simulated for a given distribution of sizes, if it is assumed that on average the crystallites have a regular shape, and this can then be compared with experimental data to give refined parameters defining the distribution. Unlike `traditional' methods of line‐profile analysis, this entirely physical approach can be applied to powder patterns with severe overlap of reflections, as is demonstrated by using data for nanocrystalline ceria. The procedure is compared with alternative powder‐pattern fitting methods, by using pseudo‐Voigt and Pearson VII functions to model individual line profiles, and with transmission electron microscopy (TEM) data.