Effect of sample transparency in powder diffractometry with Bragg–Brentano geometry as a convolution

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 Kα X-ray diffraction profile of diluted lanthanum hexaboride (LaB₆) 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.