Quantitative 3D Characterization of Functionally Relevant Parameters in Heavy-Oxide-Supported 4d Metal Nanocatalysts

Accurate 3D nanometrology of catalysts with small nanometer-sized particles of light 3d or 4d metals supported on high-atomic-number oxides is crucial for understanding their functionality. However, performing quantitative 3D electron tomography analysis on systems involving metals like Pd, Ru, or Rh supported on heavy oxides (e.g., CeO2) poses significant challenges. The low atomic number (Z) of the metal complicates discrimination, especially for very small nanoparticles (1–3 nm). Conventional reconstruction methods successful for catalysts with 5d metals (e.g., Au, Pt, or Ir) fail to detect 4d metal particles in electron tomography reconstructions, as their contrasts cannot be effectively separated from those of the underlying support crystallites. To address this complex 3D characterization challenge, we have developed a full deep learning (DL) pipeline that combines multiple neural networks, each one optimized for a specific image-processing task. In particular, single-image super-resolution (SR) techniques are used to intelligently denoise and enhance the quality of the tomographic tilt series. U-net generative adversarial network algorithms are employed for image restoration and correcting alignment-related artifacts in the tilt series. Finally, semantic segmentation, utilizing a U-net-based convolutional neural network, splits the 3D volumes into their components (metal and support). This approach enables the visualization of subnanometer-sized 4d metal particles and allows for the quantitative extraction of catalytically relevant structural information, such as particle size, sphericity, and truncation, from compressed sensing electron tomography volume reconstructions. We demonstrate the potential of this approach by characterizing nanoparticles of a metal widely used in catalysis, Pd (Z = 46), supported on CeO2, a very high density (7.22 g/cm3) oxide involving a quite high-atomic-number element, Ce (Z = 58).

Image Quality Metrics PSNR is defined [1] as: Where MAXI=2 B -1, with B the number of bits used for the representation of image intensity values (dynamic range).Note that MSE (Mean-Squared Error) measures the average quadratic deviation between the two digital, MxN, images which are compared.In our case I(x,y) would correspond to the noise-free image whereas K(x,y) would correspond to the image obtained after denoising.Therefore, PSNR quantifies, in decibels, how large is the maximum signal to MSE ratio.Typical values fall in the 20-40 dB range, the quality of the denoising method increasing with PSNR.
The Structural SIMilarity (SSIM) index [2] has been used to calculate the agreement between the reconstructions and the original synthetic models.This index takes values between 0 and 1; the higher the values the more similar the images, where a value 1 means that both images can be considered identical.SSIM index takes into account for the comparison three characteristics of the images: luminance, contrast and structure.
[2] Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, "Image quality assessment: From error visibility to structural similarity."IEEE Transactions on Image Processing, vol. 13, no. 4, pp. 600-612, 2004.This step becomes crucial when we are dealing with data in which an external reference is required, as it is the case of microscopy and more particularly of HAADF-STEM ET.

Additional Figures & Tables
To train the U-net GAN structure, both G and D were trained.For G the synthetic models, denoised using the ESRGAN network, were reconstructed using the CS-TVM3D algorithm, Figure SI 4b.Then each slice was on-purpose misaligned in both shift and tilt axis rotation to reproduce the so-called "arc" effect.
For D, the perfect 3D synthetic models, without any distortion, were used as input, Figure SI 4a.The latter were used as the ground truth which the D uses to provide the correct answer to G.This training provides a final prediction, Figure SI 4c.SSIM values close to 1 were in general obtained.
Around 6000 images have been used for this training.In fact, 80% of these images were used for training and 20% to validate the predictions.

Figure
Figure SI 2.-(first, leftmost column) Ground truth projected model; (second column) noised Ground truth projected model after adding different levels of poisson (l) and Gaussian (s) noise; (third column) after denoising using VST-UWT; (fourth column) after denoising using RIDnet; (fifth column) after denoising using ESR-GAN.

Figure
Figure SI 4.-A representative slice of one of the synthetic models: (a) without any distortion.Ground truth; (b) the reconstructed slice without correction of misalignment (c) the reconstructed slice after misalignment correction.

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Figure SI 5.-Perspective views of the 3D reconstruction of an aggregate of the Pd/CeO2 catalyst.

Figure
Figure SI 7.-Representative HR-HAADF (top) and HR BF-STEM images (bottom) of Pd nanoparticles supported on CeO2 NC.

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Figure SI 8.-Comparison of the PSDs obtained from the tomographic 3D (bars in blue) and conventional 2D (bars in red) analysis.

Table SI -
1. Estimation of PSNR and SSIM values for noised and denoised models using VTS-UWT, RIDnet and ESRGAN algorithms.Table SI 2. Different properties of the centroids obtained from K-means clustering obtained from the analysis of the aggregate shown in Figure SI 5.