The deconvolution of overlapping reflections by the procedure of direct fitting

A deconvolution procedure applicable to overlapping reflections has been developed. The procedure is based on direct fitting of the calculated intensities to the observed ones. The calculated intensity at each scattering angle is assumed to be the sum of (1) background and (2) contributions from individual reflections given as the convolution of the true data functions for the pure diffraction profiles by the observed instrument function. Both expressions for background and pure diffraction profiles contain adjustable parameters. The Gauss-Newton method is employed in minimization, and gives a rapid convergence of the parameters. The procedure has been applied to deconvolution of overlapping reflections from yttria-stabilized tetragonal ZrO₂, giving the average crystallite size and microstrain successfully. Examination of truncation effects reveals that the truncations of the functions for instrumental spread and for pure diffraction profiles make the true data functions more Loretzian and increase the integrated intensities, while the calculated background level is affected little. These errors can be suppressed if the convoluted functions of the strong reflection retain > 99% of their profile areas.