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Precise determination of full Grain Size Distribution from diffraction peak profile as a result of kinematical theory of diffraction for polidispersive nanomaterials

Roman Pielaszek ,  Witold Łojkowski 

Polish Academy of Sciences, High Pressure Research Center (UNIPRESS), Sokolowska 29/37, Warszawa 01-142, Poland


Size of crystallites strongly influences diffraction peak profiles, especially in range of nanometers. In present work we show that classical methods of determination of the average crystallite size from peak width (Scherrer method) or shape (Warren-Averbach method) are accurate only for monodispersive powders. Systematical deviations of measured grain size in polidispersive (real) case ranges between few tens percent and infinity.

In general case of a polycrystals having (wide) Grain Size Distribution (GSD), traditional powder diffraction theory based on interference equation of kinematical theory of diffraction is inprecise (contains a number of approximations). We show new approach (based on Debye equation as a starting point) that allowed derivation of exact formula for a peak profile for polycrystalline powder with Grain Size Distribution. The formula is entirely analytical and mathematically precise.

This formula was then transformed and gave simple method of determination of full Grain Size Distribution of a crystalline powder. To determine GSD one has to measure peak widths at 1/5 and 4/5 of its maximum (FW1/5M and FW4/5M). Simple analytical expression evaluates directly average <R> and dispersion σ of the Grain Size Distribution as a function of measured peak widths FW1/5M and FW4/5M.

Examples of evaluation of diffraction data using FW1/5;4/5M method are given.


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Related papers

Presentation: oral at E-MRS Fall Meeting 2003, Symposium B, by Roman Pielaszek
See On-line Journal of E-MRS Fall Meeting 2003

Submitted: 2003-04-29 22:17
Revised:   2009-06-08 12:55