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Effect of sample transparency in powder diffractometry with Bragg–Brentano geometry as a convolution
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/s0021889899008894
Subject(s) - convolution (computer science) , voigt profile , divergence (linguistics) , optics , function (biology) , geometry , materials science , powder diffraction , mathematics , diffraction , mathematical analysis , computational physics , physics , chemistry , crystallography , spectral line , quantum mechanics , linguistics , philosophy , machine learning , evolutionary biology , artificial neural network , computer science , biology
The effect of transparency and finite thickness of the sample on the peak profile in powder diffractometry with Bragg–Brentano geometry is treated as a convolution with an asymmetric aberration function. The formula of the aberration function and a practical method for numerical calculation of the convolution are proposed. The model function for the total profile is given by triple convolution of the pseudo‐Voigt function with asymmetric functions based on vertical (axial) divergence, horizontal (equatorial) divergence and sample transparency. The validity of the model profile function is examined by fitting the Cu K α X‐ray diffraction profile of diluted lanthanum hexaboride (LaB 6 ) standard samples (SRM660) of 0.5 mm thickness, the transparency of which is varied by mixing with different amounts of starch; all the parameters that may affect the shape of the profile function are treated as fixed parameters. Even in the case of heavily distorted profiles of highly transparent samples with the inverse linear absorption coefficients μ −1 = 0.34 and 1.19 mm, experimental profiles are fairly well reproduced by the model function, typically within several % in R factor. It is also demonstrated that the lattice constants of the transparent samples are precisely evaluated by applying this model function.