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1. Composition design of high-entropy alloys with deep sets learning

   https://doi.org/10.1038/s41524-022-00779-7  

   Zhang, Jie; Cai, Chen; Kim, George; Wang, Yusu; Chen, Wei (April 2022, npj Computational Materials)

   Abstract High entropy alloys (HEAs) are an important material class in the development of next-generation structural materials, but the astronomically large composition space cannot be efficiently explored by experiments or first-principles calculations. Machine learning (ML) methods might address this challenge, but ML of HEAs has been hindered by the scarcity of HEA property data. In this work, the EMTO-CPA method was used to generate a large HEA dataset (spanning a composition space of 14 elements) containing 7086 cubic HEA structures with structural properties, 1911 of which have the complete elastic tensor calculated. The elastic property dataset was used to train a ML model with the Deep Sets architecture. The Deep Sets model has better predictive performance and generalizability compared to other ML models. Association rule mining was applied to the model predictions to describe the compositional dependence of HEA elastic properties and to demonstrate the potential for data-driven alloy design. 

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2. A Strategic Design Route to Find a Depleted Uranium High-Entropy Alloy with Great Strength

   https://doi.org/10.3390/met12040699  

   Zhang, Weiran; Li, Yasong; Liaw, Peter K.; Zhang, Yong (April 2022, Metals)

   The empirical parameters of mixing enthalpy (ΔHmix), mixing entropy (ΔSmix), atomic radius difference (δ), valence electron concentration (VEC), etc., are used in this study to design a depleted uranium high-entropy alloy (HEA). X-ray diffraction (XRD), scanning electron microscopy (SEM), and transmission electron microscopy (TEM) were used to assess the phase composition. Compression and hardness tests were conducted to select alloy constituents with outstanding mechanical properties. Based on the experimental results, the empirical criteria of HEAs are an effective means to develop depleted uranium high-entropy alloys (DUHEAs). Finally, we created UNb0.5Zr0.5Mo0.5 and UNb0.5Zr0.5Ti0.2Mo0.2 HEAs with outstanding all-round characteristics. Both alloys were composed of a single BCC structure. The hardness and strength of UNb0.5Zr0.5Mo0.5 and UNb0.5Zr0.5Ti0.2Mo0.2 were 305 HB and 1452 MPa, and 297 HB and 1157 MPa, respectively. 

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3. Insights on phase formation from thermodynamic calculations and machine learning of 2436 experimentally measured high entropy alloys

   https://doi.org/10.1016/j.jallcom.2022.165173  

   Wang, Chuangye; Zhong, Wei; Zhao, Ji-Cheng (September 2022, Journal of Alloys and Compounds)

   Both CALPHAD (CALculation of PHAse Diagrams) and machine-learning (ML) approaches were employed to analyze the phase formation in 2,436 experimentally measured high entropy alloy (HEA) compositions consisting of various quinary mixtures of Al, Co, Cr, Cu, Fe, Mn, and Ni. CALPHAD was found to have good capabilities in predicting the BCC/B2 and FCC phase formation for the 1,761 solid-solution-only compositions, excluding HEAs containing an amorphous phase (AM) or/and intermetallic compound (IM). Phase selection rules were examined systematically using several parameters and it revealed that valency electron concentration (VEC) < 6.87 and VEC > 9.16 are the conditions for the formation of single-phase BCC/B2 and FCC, respectively; and CALPHAD could predict this with essentially 100% accuracy. Both CALPHAD predictions and experimental observations show that more BCC/B2 alloys are formed over FCC alloys as the atomic size difference between the elements increases. Four machine learning (ML) algorithms, decision tree (DT), k-nearest neighbor (KNN), support vector machine (SVM), and artificial neural network (ANN), were employed to study the phase selection rules for two different datasets, one consisting of 1,761 solid-solution (SS) HEAs without AM and/or IM phases, and the other set consisting of all the 2,436 HEA compositions. Cross validation (CV) was performed to optimize the ML models and the CV accuracies are found to be 91.4%, 93.1%, 90.2%, 89.1% for DT, KNN, SVM, and ANN respectively in predicting the formation of BCC/B2, BCC/B2 + FCC, and FCC; and 93.6%, 93.3%, 95.5%, 92.7% for DT, KNN, SVM, and ANN respectively in predicting SS, AM, SS + AM, and IM phases. Sixty-six experimental bulk alloys with SS structures are predicted with trained ANN model, and the accuracy reaches 81.8%. VEC is found to be most important parameter in phase prediction for BCC/B2, BCC/B2 + FCC, and FCC phases. Electronegativity difference and FCC-BCC-index (FBI) are the two additional dominating features in determining the formation of SS, AM, SS + AM, and IM. A separation line ΔH_mix=28.97×VEC-246.77 was found in the VEC-vs-ΔH_mix plot to predict the formation of single-phase BCC/B2 or FCC with a 96.2% accuracy (ΔH_mix = mixing enthalpy). These insights will be very valuable for designing HEAs with targeted crystal structures. 

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4. Elastic constants from charge density distribution in FCC high-entropy alloys using CNN and DFT

   https://doi.org/10.1063/5.0229105  

   Mirzaee, Hossein; Soltanmohammadi, Ramin; Linton, Nathan; Fischer, Jacob; Kamrava, Serveh; Tahmasebi, Pejman; Aidhy, Dilpuneet (October 2024, APL Machine Learning)

   While high-entropy alloys (HEAs) present exponentially large compositional space for alloy design, they also create enormous computational challenges to trace the compositional space, especially for the inherently expensive density functional theory calculations (DFT). Recent works have integrated machine learning into DFT to overcome these challenges. However, often these models require an intensive search of appropriate physics-based descriptors. In this paper, we employ a 3D convolutional neural network over just one descriptor, i.e., the charge density derived from DFT, to simplify and bypass the hunt for the descriptors. We show that the elastic constants of face-centered cubic multi-elemental alloys in the Ni–Cu–Au–Pd–Pt system can be predicted from charge density. In addition, using our recent PREDICT approach, we show that the model can be trained only on the charge densities of simpler binary and ternary alloys to effectively predict elastic constants in complex multi-elemental alloys, thereby further enabling easier property-tracing in the large compositional space of HEAs. 

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5. High-throughput machine learning - Kinetic Monte Carlo framework for diffusion studies in Equiatomic and Non-equiatomic FeNiCrCoCu high-entropy alloys

   https://doi.org/10.1016/j.mtla.2023.101966  

   Huang, Wenjiang; Farkas, Diana; Bai, Xian-Ming (December 2023, Materialia)

   Sluggish diffusion is postulated as an underlying mechanism for many unique properties in high-entropy alloys (HEAs). However, its existence remains a subject of debate. Due to the challenges of exploring the vast composition space, to date most experimental and computational diffusion studies have been limited to equiatomic HEA compositions. To develop a high-throughput approach to study sluggish diffusion in a wide range of non-equiatomic compositions, this work presents an innovative artificial neural network (ANN) based machine learning model that can predict the vacancy migration barriers for arbitrary local atomic configurations in a model FeNiCrCoCu HEA system. Remarkably, the model utilizes the training data exclusively from the equiatomic HEA while it can accurately predict barriers in non-equiatomic HEAs as well as in the quaternary, ternary, and binary sub-systems. The ANN model is implemented as an on-the-fly barrier calculator for kinetic Monte Carlo (KMC) simulations, achieving diffusivities nearly identical to the independent molecular dynamics (MD) simulations but with far higher efficiency. The high-throughput ANN-KMC method is then used to study the diffusion behavior in 1,500 non-equiatomic HEA compositions. It is found that although the sluggish diffusion is not evident in the equiatomic HEA, it does exist in many non-equiatomic compositions. The compositions, complex potential energy landscapes (PEL), and percolation effect of the fastest diffuser (Cu) in these sluggish compositions are analyzed, which could provide valuable insights for the experimental HEA designs. 

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