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Flat‐specimen effect as a convolution in powder diffractometry with Bragg–Brentano geometry
Author(s) -
Ida T.,
Kimura K.
Publication year - 1999
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/s0021889899003222
Subject(s) - powder diffractometer , convolution (computer science) , diffractometer , window function , geometry , lattice constant , powder diffraction , optics , function (biology) , materials science , diffraction , mathematics , divergence (linguistics) , physics , mathematical analysis , nuclear magnetic resonance , scanning electron microscope , statistics , spectral density , machine learning , evolutionary biology , artificial neural network , computer science , biology , linguistics , philosophy
The flat‐specimen effect on the peak profile in powder diffractometry with Bragg–Brentano geometry can quantitatively be treated as a convolution with an asymmetric window function. The formula of the window function and a practical method for numerical calculation of the convolution are proposed. By applying the model function given by the convolution of the pseudo‐Voigt function with asymmetric window functions based on vertical (axial) divergence and the flat‐specimen effect, experimental profiles measured with a conventional diffractometer are fairly well reproduced with only a few parameters. When this function is applied to the analysis of experimental diffraction profiles of a lanthanum hexaboride (LaB 6 ) standard sample measured with a conventional powder X‐ray diffractometer, the lattice constant is estimated as a = 4.15685 (2)–4.15693 (2) Å at 299 (1) K, without the use of any other standard material or preceding correction of systematic instrumental errors, while the specified value is a = 4.15695 (6) Å.