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Deconvolution of X‐ray diffraction profiles by using series expansion
Author(s) -
SánchezBajo F.,
Cumbrera F. L.
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/s0021889899015575
Subject(s) - deconvolution , diffraction , series expansion , series (stratigraphy) , crystallite , fourier transform , fourier series , hermite polynomials , mathematical analysis , mathematics , lattice (music) , physics , optics , algorithm , chemistry , crystallography , paleontology , biology , acoustics
The deconvolution of X‐ray diffraction profiles is a basic step in order to obtain reliable results on the microstructure of crystalline powder (crystallite size, lattice microstrain, etc .). A procedure for unfolding the linear integral equation h = g f involved in the kinematical theory of X‐ray diffraction is proposed. This technique is based on the series expansion of the `pure' profile, f . The method has been tested with a simulated instrument‐broadened profile overlaid with random noise by using Hermite polynomials and Fourier series, and applied to the deconvolution of the (111) peak of a sample of 9‐YSZ. In both cases, the effects of the `ill‐posed' nature of this deconvolution problem were minimized, especially when using the zero‐order regularization combined with the series expansion.