We recently described a data analysis method for precise (∼0.1 Å random error in the mean for a 200 kV instrument with a 3 Å FWHM probe size) size measurements of small clusters of heavy metal atoms on supports as imaged in a scanning transmission electron microscope, including an experimental demonstration using clusters that were primarily triosmium or decaosmium. The method is intended for low signal-to-noise ratio images of radiation-sensitive samples. We now present a detailed analysis, including a generalization to address issues of particle anisotropy and biased orientation distributions. In the future, this analysis should enable extraction of shape as well as size information, up to the noise-defined limit of information present in the image. We also present results from an extensive series of simulations designed to determine the method's range of applicability and expected performance in realistic situations. The simulations reproduce the experiments quite accurately, enabling a correction of systematic errors so that only the ∼0.1 Å random error remains. The results are very stable over a wide range of parameters. We introduce a variation on the method with improved precision and stability relative to the original version, while also showing how simple diagnostics can test whether the results are reliable in any particular instance.
- Data processing/image processing
- Microscopic methods, specifically for catalysts and small particles
- Scanning transmission electron microscopy (STEM)