Evaluation of Crytallite Size Distribution by Powder Diffraction Method

Abstract

　Analytical methods for evaluating crystallite size distribution by powder diffraction method have been investigated. A rapid numerical method for evaluating the exact theoretical diffraction peak profiles from collection of spherical crystallites with log-normal size distribution has been developed. The method is based on an efficient computer algorithm to evaluate the integral formula for peak profile functions, and it can be applied to estimate the broadness of the size distribution by a least squares curve-fitting method to the experimental size-broadened diffraction peak profiles within practical computing time. Theoretical frameworks and practical numerical methods for simulating the experimental diffraction peak profiles affected by the instrumental aberration have also been developed. It has been found that the observed powder diffraction peak profiles are reasonably simulated by convolution of intrinsic profiles with the instrumental functions. Accurate formulas for the instrumental aberration function of a high-angular-resolution synchrotron powder diffractometer with flat analyzer crystals as well as a laboratory powder X-ray diffractometer have been derived. Even though the spectroscopic distribution of the monochromated synchrotron beam is narrower than the laboratory X-ray source, it is still the dominant factor affecting the experimental diffraction profile. The asymmetric spectroscopic distribution of the X-ray provided by the beamline 4B2 at the KEK Photon Factory (PF) in Tsukuba was evaluated by measuring the diffraction peak profiles of standard reference crystalline powder of Si (NIST SRM640b). A new analytical method based on deconvolution by fast-Fourier-transform to remove instrumental aberration from experimental data has been developed. The segmented intensity data collected with the multiple-detector-system of the synchrotron powder diffractometer (MDS) at the beamline 4B2 at KEK-PF are affected by the different instrumental function for each detection system. The variations of the instrumental functions have been successfully adjusted by applying a Fourier-based modification on the raw diffraction intensity data.