Using convolutional neural networks for stereologicalcharacterization of 3D hetero-aggregates based onsynthetic STEM data

Abstract The 3D nano/microstructure of materials can significantly influence their macroscopic properties. In order to enable a better understanding of such structure-property relationships, 3D microscopy techniques can be deployed, which are however often expensive in both time and costs. Often 2D imaging techniques are more accessible, yet they have the disadvantage that the 3D nano/microstructure of materials cannot be directly retrieved from such measurements. The motivation of this work is to overcome the issues of characterizing 3D structures from 2D measurements for hetero-aggregate materials. For this purpose, a method is presented that relies on machine learning combined with methods of spatial stochastic modeling for characterizing the 3D nano/microstructure of materials from 2D data. More precisely, a stochastic model is utilized for the generation of synthetic training data. This kind of training data has the advantage that time-consuming experiments for the synthesis of differently structured materials followed by their 3D imaging can be avoided. More precisely, a parametric stochastic 3D model is presented, from which a wide spectrum of virtual hetero-aggregates can be generated. Additionally, the virtual structures are passed to a physics-based simulation tool in order to generate virtual scanning transmission electron microscopy (STEM) images. The preset parameters of the 3D model together with the simulated STEM images serve as a database for the training of convolutional neural networks, which can be used to determine the parameters of the underlying 3D model and, consequently, to predict 3D structures of hetero-aggregates from 2D STEM images. Furthermore, an error analysis is performed with respect to structural descriptors, e.g., the hetero-coordination number. The proposed method is applied to image data of TiO2-WO3 hetero-aggregates, which are highly relevant in photocatalysis processes. However, the proposed method can be transferred to other types of aggregates and to different 2D microscopy techniques. Consequently, the method is relevant for industrial or laboratory setups in which product quality is to be quantified by means of inexpensive 2D image acquisition.