The Artemis program and future space exploration necessitate sustainable infrastructure on extraterrestrial bodies. Due to the high cost of transporting materials, using in-situ resources like lunar regolith as cement-like binders is crucial. However, the hydration behavior of these binders in space is poorly understood. Previous studies investigated cement solidification in microgravity, revealing insights into hydration chemistry and microstructural formation without gravity's influence. To fully understand how microstructure affects the mechanical properties of cement, both experimental and numerical methods are necessary. Tricalcium silicate (C₃S), a major component of Ordinary Portland Cement (OPC), significantly impacts the hydration process and subsequent properties of hardened cement paste. However, the high porosity and small size of space-returned C₃S samples limit conventional characterization techniques, making numerical modeling the primary method for evaluating mechanical properties. This requires accurate 3D representations of the microstructure, traditionally obtained through micro-computed tomography (micro-CT). Micro-CT, however, is expensive for statistical analysis of multiple samples and may be limited by sample size or material contrast. Two-dimensional imaging is insufficient to capture 3D features. Therefore, a cost-effective method for 3D microstructure reconstruction from 2D exemplars is needed. This study uses a deep learning-based texture synthesis architecture to generate 3D microstructures of C₃S samples hydrated in both microgravity (µg) and earth (1g) environments. These reconstructed volumes, acting as RVEs, will allow for the numerical evaluation of mechanical properties. The significant difference in microstructural morphology between 1g and µg samples highlights the need for this deep learning approach to create a statistically large ensemble of microstructures for design purposes, using high-resolution SEM images from the NASA PSI database.

Microstructure reconstruction methods are broadly categorized as statistical modeling-based, visual features-based, and AI-based. Statistical methods use stochastic optimization to match statistical features (probability, lineal-path, and cluster functions) of the exemplar to the reconstructed 3D microstructure. Alternatively, physical descriptors (grain and pore size) can be matched. AI-based methods, particularly deep learning approaches using Convolutional Neural Networks (CNNs), are increasingly popular due to their ability to handle image data. Material-system-dependent methods train networks on images specific to a material, while material-system-independent (transfer learning) approaches use pre-trained weights from computer vision datasets. Texture synthesis methods, which characterize the exemplar as a Markov Random Field (MRF), are efficient, single-pass approaches that preserve material descriptors and handle anisotropic materials. Solid Texture Synthesis (STS) methods generate 3D textures from 2D exemplars using various approaches. A recent framework uses a compact solid texture generator with a multi-scale architecture, optimizing a perceptual slice-based loss function using VGG-19 activations. This approach is computationally efficient for synthesizing 3D microstructures.

The study involved C₃S hydration experiments in both microgravity (on the ISS) and 1g conditions, using a w/c ratio of 2.0 and lime-water. Space samples hydrated for 42 days before return to Earth. Backscattered Electron (BSE) micrographs (500x magnification, 0.54 µm resolution) of fracture surfaces from both conditions were obtained and stored in the NASA PSI database. Image analysis was performed to quantify the volume fractions of C-S-H, portlandite (CH), and porosity. Micro-CT imaging was conducted using a Zeiss Xradia 620 Versa X-ray Microscope. A deep learning-based 3D reconstruction framework, adapted from Gutierrez et al. (2020), was employed. This framework uses a CNN-based generator network (G) that synthesizes a solid microstructure texture (v) from multi-channel 3D white noise input (Z). The network uses convolutional, concatenation, and upsampling operations in a multi-scale architecture. The generator parameters (θ) are optimized using a 3D slice-based loss function (Equation 1), comparing feature maps (F) of 2D slices of the generated solid (v_d,n) and the exemplar (u_d) using a pre-trained VGG-19 network as the descriptor (D). The loss function minimizes the difference in Gram matrices (G) of the feature maps. Training involved optimizing θ using the Adam algorithm with a multi-step learning rate scheduler. The method was applied to both grayscale 1g and µg BSE micrographs. Greyscale histogram-based image segmentation with overflow method and sigma filtering (σ = 2.0) were used to identify phase boundaries in the BSE images for both 1g and µg samples. The low-order probability distribution functions (two-point correlation function, S₂(r); lineal-path function, L₂(r); and two-point cluster function, C₂(r)) were used for quantitative validation, comparing reconstructed volumes with micro-CT virtual samples.

Image analysis revealed a significantly higher porosity (70% vs. 47%) and distinct elongated plate-like portlandite morphology in the µg samples compared to 1g samples. Qualitative comparison showed that the deep learning-based reconstruction successfully captured the visual characteristics of both 1g and µg samples, especially the elongated portlandite morphology in µg samples. The loss function converged after 1500 iterations for both samples. Reconstructed volumes showed good agreement with micro-CT virtual data in terms of both visual appearance (Fig. 5) and quantitative assessment using low-order probability functions (Figs. 6, 7). The statistical descriptors S₂(r), C₂(r), and L₂(r) were used to characterize the spatial distribution of portlandite and porosity in both reconstructed and micro-CT volumes. For the 1g sample, the reconstructed volumes accurately represented the uniform distribution of the portlandite phase and the isotropic nature of porosity. For the µg sample, minor variations were observed in S₂(r) and C₂(r), reflecting the elongated morphology of portlandite. However, the overall agreement in the probability distribution functions indicated that the deep learning method successfully generated a statistically equivalent representation of the microstructure. A sensitivity study on exemplar size and resolution showed that a 256x256 pixel exemplar was sufficient for the 1g sample, while a 512x512 pixel exemplar was recommended for the µg sample to adequately capture the elongated portlandite crystals. The reconstructed volumes can be used as RVEs in micromechanical models, and this method is computationally efficient and can be extended to other materials.

The findings address the research question by demonstrating the feasibility of using a deep learning-based approach to accurately reconstruct the 3D microstructure of cement samples hydrated in microgravity, even with limited experimental data. The ability to generate statistically representative ensembles of microstructures overcomes the limitations of traditional micro-CT methods, particularly in terms of cost and the challenges associated with characterizing small or highly porous samples. The good agreement between the reconstructed volumes and micro-CT data validates the effectiveness of the approach and suggests its potential application to other materials science problems. The successful capture of the distinct elongated portlandite morphology in the microgravity samples highlights the method's ability to represent complex microstructural features. The use of low-order probability functions provides a quantitative measure of the similarity between reconstructed and measured microstructures, enabling a comprehensive validation of the deep learning model.

This study presents a computationally efficient and material-system-independent deep learning approach to reconstruct 3D microstructures from limited 2D SEM data. The method successfully generated RVEs of space-cured cement samples, capturing unique microstructural features like elongated portlandite crystals. Quantitative analysis using low-order probability functions validated the results, making this approach valuable for future materials research in space and other areas with limited samples. Future work will focus on incorporating higher-order evaluation metrics and validating the methodology with other multiphase materials.

The study primarily used low-order probability functions for quantitative validation. While these functions capture important microstructural characteristics, higher-order descriptors might provide a more comprehensive evaluation. The use of a pre-trained VGG-19 network as the descriptor may not be optimal for all materials, and exploring other networks could enhance the reconstruction accuracy. The presence of checkerboard artifacts in some reconstructions, typical of generative texture-based methods, could also be addressed in future studies through modifications to the loss function. The sensitivity study indicated the optimal exemplar size, however, this should be considered in relation to the material. The choice of resolution and field of view are interdependent and may influence the reconstruction.