Electron Diffraction Based Analysis of Phase Fractions and Texture in Nanocrystalline Thin Films, Part I: Principles

A method for phase analysis, similar to the Rietveld method in X-ray diffraction, was not developed for electron diffraction (ED) in the transmission electron microscope (TEM), mainly due to the dynamic nature of ED. Nowadays, TEM laboratories encounter many thin samples with grain size in the 1–30 nm range, not too far from the kinematic ED conditions. This article describes a method that performs (semi)quantitative phase analysis for nanocrystalline samples from selected area electron diffraction (SAED) patterns. Fractions of the different nanocrystalline components are determined from rotationally symmetric ring patters. Both randomly oriented nanopowders and textured nanopowders, observed from the direction of the texture axis produce such SAED patterns. The textured fraction is determined as a separate component by fitting the spectral components, calculated for the previously identified phases with a priori known structures, to the measured distribution. The Blackman correction is applied to the set of kinematic diffraction lines to take into account dynamic effects for medium grain size. Parameters of the peak shapes and the other experimental parameters are refined by exploring the parameter space with the help of the Downhill-SIMPLEX. Part I presents the principles, while future publication of Parts II and III will elaborate on current implementation and will demonstrate its usage by examples, respectively.