Active Learning Discovery of High Temperature Oxidation Resistant Refractory Complex Concentrated Alloys

Abstract

Refractory complex concentrated alloys (RCCAs) are of significant interest for advanced high-temperature applications, owing to their broad compositional range and potential for attractive mechanical properties and oxidation resistance. However, their compositional complexity poses significant challenges to conventional alloy discovery methodologies. In this study, an active learning framework is introduced that integrates Gaussian process regression with Bayesian global optimization to accelerate identification of oxidation-resistant RCCAs. Focusing on aluminum-containing quaternary systems, alloy and oxide descriptors were used to predict oxidation performance at 1000$^\circ$C. Beginning with a dataset of 81 experimentally validated RCCAs, this framework was used to iteratively select alloy batches (five alloys per batch) with optimization based on a balance between exploration and exploitation to minimize associated experimental costs. After six iterations, two alloys were identified (nominal Al$_{30}$Mo$_5$Ti$_{15}$Cr$_{50}$ and Al$_{40}$Mo$_5$Ti$_{30}$Cr$_{25}$) that exhibited specific mass gains less than 1 mg/cm$^2$ at 1000$^\circ$C in air. Both of these alloys formed adherent external $α$-Al$_2$O$_3$ scales and exhibited parabolic oxidation kinetics consistent with diffusion-limited scale growth. Furthermore, our multiobjective analysis demonstrates that these alloys simultaneously achieve high specific hardness ($>0.12$ HV$_{0.5}$m$^3$/kg) and thermal expansion compatibility with thermal barrier coating systems, positioning them as promising bond coat candidates. This work underscores the efficacy of active learning in traversing complex compositional landscapes, and offers a scalable strategy for the development of advanced materials suitable for extreme environments.

Figures (19)

• Figure 1: Schematic illustration of the rapid active learning workflow for discovering oxidation-resistant RCCAs, revealing the iterative batch process of combining existing data, Gaussian Process Regression, batch Bayesian optimization, experimental synthesis, and data augmentation for selecting five new alloys for each iteration or batch.
• Figure 2: Predicted and experimentally-measured specific mass gain values for 24 h of oxidation at 1000° C in ambient air for 30 alloys evaluated across six batches. Solid circles represent experimental values with error bars, open circles show GPR predictions with error bars, and colors denote different batches (Batch 1: green, Batch 2: blue, Batch 3: cyan, Batch 4: red, Batch 5: magenta, Batch 6: brown). The red dashed line indicates the target threshold (1 mg/cm$^2$) for oxidation resistance.
• Figure 3: Continuous specific mass gain curves vs. time during oxidation in ambient air at 1000° C over 24 h (from TGA experiments), and post-oxidation specimen photographs, of selected alloys (nominal alloy compositions indicated). (a) Al$_5$Nb$_{65}$Zr$_5$Ti$_{25}$ (Batch 1, green) and Al$_{15}$Mo$_{35}$Ti$_{40}$Cr$_{10}$ (Batch 4, blue). (b) Al$_5$Hf$_5$Ti$_{85}$Cr$_5$ (Batch 2, green) and Al$_{20}$Mo$_{10}$Nb$_5$Ti$_{65}$ (Batch 3, blue). (c) Al$_{20}$Mo$_5$Ta$_5$Ti$_{70}$ (Batch 2, green) and Al$_{30}$Ta$_5$Ti$_{50}$Cr$_{15}$ (Batch 3, blue). (d) Al$_{30}$Mo$_5$Ti$_{15}$Cr$_{50}$ (Batch 5, blue) and Al$_{40}$Mo$_5$Ti$_{30}$Cr$_{25}$ (Batch 6, green).
• Figure 4: (a) Expected Improvement (EI) values for design space alloys across the six active learning batches, with each dot representing an alloy candidate, with high-EI candidates in Batches 3 and 4 highlighted using distinct symbols, and with black circles indicating selected alloys. (b) The Exploration-to-exploitation ratio ($|$exploration/exploitation$|$) across the six active learning batches.
• Figure 5: Raman spectra of representative alloys revealing peak signatures for $\alpha$-Al$_2$O$_3$ (a characteristic fluorescent doublet indicated in the dotted rectangle), rutile TiO$_2$, Nb$_2$O$_5$, and WO$_3$.