Advanced electron crystallography through model-based imaging

Publication Type:

Journal Article


IUCrJ, Volume 3, Number 1 (2016)



experimental design, quantitative analysis, statistical parameter estimation, structure refinement, transmission electron microscopy


The increasing need for precise determination of the atomic arrangement of non-periodic structures in materials design and the control of nanostructures explains the growing interest in quantitative transmission electron microscopy. The aim is to extract precise and accurate numbers for unknown structure parameters including atomic positions, chemical concentrations and atomic numbers. For this purpose, statistical parameter estimation theory has been shown to provide reliable results. In this theory, observations are considered purely as data planes, from which structure parameters have to be determined using a parametric model describing the images. As such, the positions of atom columns can be measured with a precision of the order of a few picometres, even though the resolution of the electron microscope is still one or two orders of magnitude larger. Moreover, small differences in average atomic number, which cannot be distinguished visually, can be quantified using high-angle annular dark-field scanning transmission electron microscopy images. In addition, this theory allows one to measure compositional changes at interfaces, to count atoms with single-atom sensitivity, and to reconstruct atomic structures in three dimensions. This feature article brings the reader up to date, summarizing the underlying theory and highlighting some of the recent applications of quantitative model-based transmisson electron microscopy.