Crystallite size distribution in supported catalysts

A Method of Background Subtraction for the Analysis of Broadened Profiles

This method for precisely determining the background level of broadened x-ray profiles assumes that the background under the peak can be approximated by a straight line, and the decay in the tails several profile widths from the peak follows a Cauchy-like law. It uses a plot of I(s)s2 vs. s2 where I(s) is the intensity and the scattering vector s = 2cosθo sin(θ-θo)/ƛ where θo is the centroid, θ the Bragg angle and X the x-ray wavelength. The true background is determined by the slope of the linear portion of the plot and its extension to s2=0 gives the rate of decay of the tails. Results on synthesized and experimental profiles show that the method is useful for Warran-Averbach analysis, because it avoids spurious oscillations and the “hook” effect in the plot of the corrected Fourier coefficients, and makes it possible to correct for overlapping tails of adjacent reflections.