A deep learning approach for quantum dots sizing from wide-angle X-ray scattering data

Disclosing the full potential of functional nanomaterials requires the optimization of synthetic protocols and an effective size screening tool, aiming at triggering their size-dependent properties. Here we demonstrate the successful combination of a wide-angle X-ray total scattering approach with a deep learning classifier for quantum dots sizing in both colloidal and dry states. This work offers a compelling alternative to the lengthy process of deriving sizing curves from transmission electron microscopy coupled with spectroscopic measurements, especially in the ultra-small size regime, where empirical functions exhibit larger discrepancies. The core of our algorithm is an all-convolutional neural network trained on Debye scattering equation simulations, incorporating atomistic models to capture structural and morphological features, and augmented with physics-informed perturbations to account for different predictable experimental conditions. The model performances are evaluated using both wide-angle X-ray total scattering simulations and experimental datasets collected on lead sulfide quantum dots, resulting in size classification accuracies surpassing 97%. With the developed deep learning size classifier, we overcome the need for calibration curves for quantum dots sizing and thanks to the unified modeling approach at the basis of the total scattering method implemented, we include simultaneously structural and microstructural aspects in the classification process. This algorithm can be complemented by incorporating input information from other experimental observations (e.g., small angle X-ray scattering data) and, after proper training with the pertinent simulations, can be extended to other classes of quantum dots, providing the nanoscience community with a powerful and broad tool to accelerate the development of functional (nano)materials.