The atomic lensing model: extending HAADF STEM atom counting from homogeneous to heterogeneous nanostructures

Abstract

Counting the number of atoms in each atomic column from different viewing directions has proven to be a powerful technique to retrieve the 3D structure of homogeneous nanostructures [1]. In order to extend the atom counting technique to heterogeneous materials, this work presents a new atomic lensing model facilitating both atom counting and 3D compositional determination in such materials. In the quantitative evaluation of high angle annular dark field scanning transmission electron microscopy (HAADF STEM) images the so‐called scattering cross‐section (SCS) has proven to be a successful performance measure [1–3]. Its monotonic increase with thickness can be used to count the number of atoms in homogeneous materials with single atom sensitivity [4]. However, for heterogeneous materials, small changes in atom ordering in the column can change the SCS (Fig. 1), significantly complicating atom counting. This depth dependency requires a quantitative method to predict SCSs of all possible 3D column configurations, already more than 2 million for a 20 atoms thick binary alloy. Image simulations can provide this information, but the amount of required simulations makes it an impossible task in terms of computing time. Therefore, a new atomic lensing model is developed based on the principles of the channelling theory [5], where each atom is considered to be an electrostatic lens resulting in an extra focussing effect on the probe. This model allows one to predict the SCSs of mixed columns based on the lensing factors of the individual atoms in monotonic atomic columns. As compared to a linear model neglecting channelling, this new approach leads to a significant improvement in the prediction of SCSs which is not restricted to the number of atom types (Fig. 2) and can be used for a wide range of detector angles (Fig. 3). The power of the atomic lensing model to accurately predict SCSs enables one to extend the atom counting technique to heterogeneous materials. Here, simulated SCSs can be matched to the measured experimental SCSs. Next, the 3D structure can be determined by combining atom counts from different viewing directions. In this presentation, this technique will be demonstrated on experimentally recorded images of an Au@Ag nanocrystal. Another advantage of the atomic lensing model is its ability to accurately predict the atom ordering in the column from experimental SCSs (Fig. 1). Therefore, it opens up the possibility to extract 3D information from a single image. This ability will be presented on a simulated image of an Au@Ag nanorod. In conclusion, a new atomic lensing model is developed which is of great importance for extending the atom counting technique from homogeneous to heterogeneous nanostructures.