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New analytical approximation of diffraction size broadened peak profile for spherical crystallites with a lognormal distribution
Author(s) -
Popa N. C.,
Teodorescu C. M.,
Frunza S.
Publication year - 2010
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/s0021889810024829
Subject(s) - log normal distribution , crystallite , diffraction , mathematics , volume (thermodynamics) , distribution (mathematics) , statistical physics , materials science , mathematical analysis , physics , optics , chemistry , crystallography , statistics , thermodynamics
A new analytical approximation of the diffraction peak size profile due to the lognormal distribution of spherical crystallites is derived. In comparison with the existing approximation constructed with the condition of conserving the volume‐averaged column length of the exact profile [Popa & Balzar (2002). J. Appl. Cryst. 35 , 338–346], the new approximation conserves both volume‐ and area‐averaged column lengths. Moreover, it is a better approximation for large distribution dispersions. Like the old approximation, the present one is appropriate for implementation in the whole powder pattern fitting codes, Rietveld included.