Predicting the 3D microstructure of SOFC anodes from 2D SEM images using stochastic microstructure modeling and CNNs

TL;DR

The paper tackles the challenge of inferring 3D SOFC anode microstructures from inexpensive 2D SEM images by combining a low-parameter stochastic 3D model with physics-based SEM simulation and CNNs. It builds a ground-truth mapping from six model parameters $\{\lambda_Y,\lambda_Z,p_1,p_2,p_3,p_4\}$ to 2D SEM appearances using Nebula, generating a large synthetic dataset of 2000 microstructures and their SEM images. Three CNNs are trained to recover parameter subsets from 256×256 SEM cutouts, enabling rapid generation of 3D realizations whose geometrical descriptors closely match ground truth on validation data and reasonably on real data, with some caveats for certain descriptors and outliers. The approach reduces reliance on expensive 3D tomography and avoids phase-based segmentation, offering a practical route for rapid 3D reconstruction and microstructure optimization in SOFC anodes and potentially other materials. Future work includes incorporating secondary electron channels, extending to other materials, and integrating alternative imaging simulators such as X-ray CT.

Abstract

The 3D microstructure of solid oxide fuel cell anodes significantly influences their electrochemical performance, but conventional methods for acquiring high-resolution microstructural 3D data such as focused ion beam scanning electron microscopy (FIB-SEM) are costly in both time and resources. In contrast, obtaining 2D images, such as from scanning electron microscopy (SEM), is more accessible, though typically providing insufficient information to accurately characterize the 3D microstructure. To address this challenge, we propose a novel approach that predicts the 3D microstructure from 2D SEM images. The presented method utilizes a low-parametric 3D model from stochastic geometry to generate a large number of virtual 3D microstructures and employs a physics-based SEM simulation tool to obtain the corresponding 2D SEM images. By systematically varying the underlying model parameters, a large dataset can be generated to train convolutional neural networks (CNNs). By doing so, we can statistically reconstruct the 3D microstructure from 2D SEM images by drawing realizations from the stochastic 3D model using the predicted model parameters. In addition, we conducted an error analysis on key geometrical descriptors to quantitatively evaluate the accuracy and reliability of this stereological prediction tool.

Figures (6)

• Figure 1: Workflow of the present paper.
• Figure 2: Stochastic microstructure model realization and corresponding SEM image. Realization of the stochastic 3D microstructure model (left) of size $20µm \times 20µm \times 20µm$, top slice ($20µm \times 20µm$) of the realization (middle) and the corresponding SEM image ($20µm \times 20µm$) obtained by Nebula using the settings described in Section \ref{['subsec:SEM']}. In the 3D rendering, the pore space is transparent, the CGO phase is depicted in the brighter gray and nickel is colored in dark gray, whereas in the 2D slice, the pore space is black, the CGO phase is white and the nickel phase is gray.
• Figure 3: Schematic visualization of the network architecture. The subnetwork $f$ extracts features out of the input image, whereas subnetwork $g$ processes these features to predict the model parameters.
• Figure 4: Accuracy of CNN predictions. Comparison of ground truth and difference between prediction and ground truth for the parameters $\lambda_Z, \lambda_Y$ (left), $p_1, p_3$ (middle) and $p_2, p_4$ (right) on the validation set $V$. Positive values on the y-axis indicate an overestimation of the model parameter by the CNNs, while negative values show an underestimation.
• Figure 5: Geometrical descriptor analysis of original and generated microstructures. Comparison of geometrical descriptors, computed from the original segmented 3D image and the generated structure, respectively: volume fraction (first row), mean chord length (second row), geodesic tortuosity (third row), specific surface area (fourth row), and specific triple phase boundary length (bottom row), where $\varepsilon, \mu, \tau, S, \rho$ are the descriptors computed on the original structure and $\tilde{\varepsilon}, \tilde{\mu}, \tilde{\tau}, \tilde{S}, \tilde{\rho}$ are the descriptors computed on the structure that has been predicted by the CNN. The first four descriptors are computed for the CGO phase (left), the nickel phase (middle), and the pore space (right).