Catalyst particle sizes from Rutherford scattered intensities

We show that the number of atoms in a small supported catalyst cluster can be estimated from the strength of electron scattering into a high angle annular detector in the STEM. The technique is related to the Z contrast methods developed by Crewe, Wall, Langmore and Isaacson. It works best for high atomic number catalyst particles when supported on low atomic number supports, such as Pt on γ-aluminium oxide. The method is particularly useful for detecting and measuring particles in the sub-nanometre size range where bright field images are unreliable. Unlike the Z contrast methods, a high angle annular detector is used, which avoids intensity modulations arising from Bragg reflections. The signal is mostly high angle diffuse scattering, which is predominantly Rutherford scattering, and is proportional to the number of atoms probed by the beam, weighted by their individual scattering cross-sections. Scattering strengths of individual clusters are computed from digitized high angle annular detector images. Data for Pt on γ-aluminium oxide, when plotted as imaged area^1/2 against intensity^1/3, define a straight line. Such plots provide calibration of the intensity increment per atom without the need of external calibration, although assumptions about particle morphology must be made. Reliable results require high signal-to-noise and optimum sampling of the specimen. For an STEM probe size of 0.35 nm, Pt clusters containing as few as three atoms can be detected when supported on typical, 20 nm thick, γ-aluminium oxide supports.