(Digital Presentation) Synthesizing Electrode Microstructures with Predefined Spatial Gradients By Conditional Generative Adversarial Networks
Authors: Yamagishi Rena , Sciazko Anna , Komatsu Yosuke , Shikazono Naoki 
Published: July 2022

Recent progress of manufacturing techniques in the field of solid oxide fuel cells (SOFCs) enables fabrications of complex multi-sized gradient microstructures with the spatially varied properties. Methods using additive manufacturing, layer-by-layer deposition, tape casting, nano-imprint, pulse laser deposition and laser engraving, etc. provide possibilities to fabricate 3D structures with flexible design. Moreover, the spatially optimized structures can provide better mechanical and thermal properties, enhance diffusion and improve electrochemical reaction kinetics. In particular, multi-layered electrode designs are attracting increasing interest.
The layered electrode design and optimization require effective methods to fabricate synthetic microstructures with property gradients. The generative adversarial network (GAN) proves its usabilities in fabricating artificial microstructures belonging to the same class as the training data [1] and reconstructing 3D structures from 2D image [2], etc. The applications primarily focus on the structures with uniform spatial properties identical to the training sample. The Wasserstein GAN was recently applied for the fast inverse design of two-phase homogenous microstructures with user-defined properties [3]. In this study, an approach using conditional GAN (C-GAN) is proposed to flexibly generate multi-phase structures with predefined gradients.
The proposed method is tested on the microstructures of porous nickel-gadolinium doped ceria (Ni-GDC) SOFC anodes. The C-GAN training dataset consists of real Ni-GDC microstructures with varied Ni and GDC compositions (GDC share in the range of 30 – 70 vol%) and with varied porosity [4]. In total, 10 different samples were prepared and sintered at 1350 oC in air atmosphere and further reduced in the H2 flow at 800 oC. The fabricated electrodes had significantly different microstructural properties and electrochemical performance. The samples were infiltrated with epoxy resin to enable clear phase recognition, polished to expose cross-section and characterized by the scanning electron microscope (SEM). The SEM images were segmented prior to the C-GAN training.
The C-GAN was trained with patches of 256 x 256 pixels which were randomly extracted from SEM images of each sample. The sample with Ni : GDC = 50 : 50 vol% was excluded from the training data and used only for testing. The generator network input consists of 4 variables: random noise vector, Ni share in composite, porosity and particle size (Fig. 1A). The particle size is controlled by the magnification of the training images. The Ni volume fraction and porosity are calculated separately for each patch during the iterative training process.
The primary version of the trained C-GAN network generates homogenous artificial microstructures with the patch size of 256 x 256 pixels identical to the training data. The fabricated microstructures (Fig. 1B) show excellent visual and good statistical agreements with the real samples. It is possible to reproduce not only the volumetric fractions, but also the surface area density and triple phase boundary density of the real Ni-GDC electrodes (Fig. 1C). The C-GAN can fabricate not only the microstructures belonging to the training dataset, but also samples with other compositions.
Although the C-GAN generator was trained based on patches with 256 × 256 pixels, it can be used for the fabrication of larger structures by increasing the size of the generator input. By adjusting the generator input matrix consisting of the Ni share, porosity and particle size, various microstructure patterns can be fabricated including linear gradients (Fig. 1D) and layered structures (Fig. 1E). Those structures have a significance for the SOFC anodes design as layered designs are conventionally incorporated in SOFC electrodes, e.g. support and active anode layers. In addition, it was shown that the graded structures have superior performance compared with the isotropic anodes [5].
The proposed framework provides a convenient tool for generating realistic microstructures with wide range of predefined properties. Further, it can be coupled with the existing simulation tools to evaluate the wide range of graded and layered microstructural designs.
[1] A. Gayon-Lombardo, L. Mosser, N. P. Brandon, and S. J. Cooper, npj Comput. Mater., 6, 1–11 (2020).
[2] A. Sciazko, Y. Komatsu, and N. Shikazono, ECS Trans., 103, 1363–1373 (2021).
[3] X. Lee, et al., Nature Computational Science, 1, 229, (2021).
[4] Y. Komatsu, A. Sciazko, and N. Shikazono, J. Power Sources, 485, 229317 (2021).
[5] Z. Yan, et al., ECS Trans.,
91, 2055, (2019).

Fig. 1. A) Schema of C-GAN network, B) synthetic homogenous microstructures fabricated by C-GAN, C) TPB dependence on the Ni and pore volume fractions, D) synthetic structure with predefined gradient and E) synthetic layered structure.

Figure 1