Flat-specimen effect as a convolution in powder diffractometry with Bragg-Brentano geometry

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 (LaB₆) 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.