Prediction of the morphology of nano particles based solely on atom counting data

The framework to determine the morphology of nano particles from atomically resolved electron microscopy images and atom counting data is introduced. Focus is placed on electron microscopy data avoiding advanced geometry optimization of the particle. The problem is solved by simulated annealing with different fitness functions assessed. Even for small particles the solution space rapidly becomes too large to be exhausted. The concept of site occupation probabilities, $p_i$, is then used to analyze a subset, typically very few hundred solutions. This is shown to be sufficient to reach a relative error of below 10% for $p_i>0.5$ already with 100 solutions allowing to determine with high confidence and low statistical error realistic average shapes also for nano particles of a few thousand atoms. These particles typically exhibit a well defined core covered by a layer of sites that are not occupied in each solution. It is further demonstrated that sites with high probability to contain a vacancy can be identified assuming the presence of a vacancy. If a vacancy is actually present in a particle its position can be identified with rather high fidelity. Finally, it is shown that the procedure can cope with the statistical error or ambiguities inherent in atom counting data based on noisy, low dose electron microscopy images.