Unsupervised Generative Adversarial Network for 3-D Microstructure Synthesis from 2-D Image

Three-dimensional microstructure reconstruction is indispensable for understanding the performance and reliability of SOFC electrodes. Not only the microstructure parameters, but also SOFC electrochemical characteristics such as overpotentials can be calculated when combined with numerical simulations. The most common method to analyze 3-D structures with a feature size of 0.01 – 10 μm is a focused ion beam - scanning electron microscope (FIB-SEM). However, there's a tradeoff between reconstruction volume size and resolution. Besides, in order to obtain high quality reconstruction, accumulation of know-hows for pre and post-processing is required. Therefore, fast screening of the microstructures is not easy for FIB-SEM due to the difficulty of measurement. On the other hand, a single SEM image can be obtained very easily. An arising question is if it is possible to extract properties of microstructures and numerically synthesize 3-D model directly from a single 2-D SEM image.

In recent years, machine learning techniques have become a powerful tool for image processing. Nevertheless, applications of machine learning in the field of porous materials, in particular fuel cells and batteries are still limited. The previous works concentrated on relatively simple artificial neural networks (ANN), but the class of neural networks that can effectively analyze visual images is the convolutional neural network (CNN). Gayon-Lombardo et al. (1) demonstrated a successful application of generative adversarial network (GAN) based on CNN layers to fabricate synthetic 3-D SOFC microstructures. It is indicated that the GAN-based approach can be very effective, but the algorithm requires 3-D teaching data (GAN^3Dto3D).

In the scope of this research, a novel method for fabrication of synthetic 3-D microstructure directly from a 2-D SEM image is proposed (Fig. 1A). The GAN^2Dto3D network consists of a 3-D microstructure generator and a discriminator which operate on 2-D data. Each microstructure fabricated by the generator is treated as a set of individual cross-sectional 2-D images. The discriminator checks the validity of each 2-D slice in the generated microstructure in all spatial directions (height, width and thickness). Patches extracted from a real 2-D cross-section image are used as training data. In each training iteration, new random patches are extracted to increase the number of available training data. Additionally, the training images are augmented by random horizontal and vertical flipping. As all of the cross-section of the newly generated microstructure has to be statistically equivalent to the real 2-D cross-section, the generated 3-D microstructure is smooth in all spatial directions.

The GAN^2Dto3D approach is tested on the dataset of real SOFC microstructures. For the real microstructure, a set of nickel (Ni) – gadolinium doped ceria (GDC) microstructures was fabricated. All composite anode samples were prepared with NiO (AGC Seimi, Japan) and GDC (Gd_0.1Ce_0.9O ShinEtsu, Japan) powders mixed in a designated proportion and sintered at 1350 ^oC. Differences in the structure are due to the initial anode slurry composition and packing density. The solid phase fractions were controlled by GDC share in the composite in the range of 30 – 70 vol.%, and their porosity was controlled by isostatic pressing (2). 3-D microstructures were reconstructed by FIB-SEM and used as the ground truth data for the validation of GAN^2Dto3D model. The results of the GAN^2Dto3D algorithm applied to generate two synthetic microstructures with different GDC share and the porosity are shown in Fig. 1B and 1C. The size of the generated microstructures is 64 × 64 × 64 voxels, which is equivalent to 6.4 × 6.4 × 6.4 µm. The real microstructures reconstructed with FIB-SEM are shown for comparison. The proposed GAN algorithm produces realistic microstructures, which indicates that GAN has a great potential to enable fast evaluation of various samples without carrying out complex FIB-SEM measurements.

1. Gayon-Lombardo, L. Mosser, N. P. Brandon, and S. J. Cooper, npj Comput. Mater., 6, 1–11 (2020).

2. Komatsu, A. Sciazko, and N. Shikazono, J. Power Sources, 485, 229317 (2021).

Figure 1