Diffraction peak profiles from spherical crystallites with lognormal size distribution

Abstract

An efficient and accurate method to evaluate the theoretical diffraction peak profiles from spherical crystallites with lognormal size distribution (SLN profile) is presented. Precise results can be obtained typically by an eight-term numerical integral for any values of the parameters, by applying an appropriate substitution of the variable to the integral formula. The calculated SLN profiles have been verified by comparison with those calculated by inverse Fourier transform from the exact analytical solution of the Fourier-transformed SLN profile. It has been found that the shape of the SLN profile strongly depends on the variance of size distribution. When the logarithmic standard deviation ω of the size distribution is close to 0.76, the SLN profile becomes close to a Lorentzian profile, and `super-Lorentzian' profiles are predicted for larger values of ω, as has been concluded by Popa & Balzar [J. Appl. Cryst.(2002),35, 338–346]. The intrinsic diffraction peak profiles of an SiC powder sample obtained by deconvolution of the instrumental function have certainly shown `super-Lorentzian' line profiles, and they are well reproduced by the SLN profile for the value ω = 0.93.