A D V A N C E D M A T E R I A L S & P R O C E S S E S | M A R C H 2 0 2 3 1 8 mechanical properties of any composition they are interested in within the five-element system. In addition, based on the ML-model, the database provides an easy way for users to screen out their ideal candidates. They can specify selected requirements of density, phase stability, bulk modulus, and shear modulus. As HEAs are attracting extensive attention because of their superior properties—exceptional ductility and fracture toughness—they also possess a much larger compositional space than conventional alloys, which provides more opportunities to improve specific properties. But this opportunity also poses some challenges, as this approach may consume many computational resources for complex systems, limiting the construction of property maps for the corresponding materials. Although most of this article provides specifics about the quinary Al-Co-CrFe-Ni alloy system, the HEA_ML tool allows researchers to expand beyond the five-element system to address high-order systems, including anywhere from 10 to 20 elements. TESTING AND DEVELOPMENT OF THE HEA_ML Density functional theory (DFT) calculations are the backbone of the research that led to the product development. They provided the direct simulation results of the phase stability and the elastic properties of 200 specific compositions (200 points) in this five-element system. The research that the author and his student, Songge Yang, conducted on DFT calculations was published in Journal of Phase Equilibria and Diffusion in July 2021 and Journal of Alloys and Compounds in September 2022[1,2]. This work showed that the FCC alloys’ lattice parameter increases with the addition of Fe and Cr, and decreases with Ni and Co. In addition to the enthalpy of formation at 0 K, the shape distortion rate was another essential parameter to evaluate the crystal stability. The results showed the addition Fig. 1 — With the special quasi-random structures, the key compositions were calculated via the DFT approach; ML is adopted to predict the phase stability and elastic properties. of Cr destabilizes the FCC lattice and caused symmetry breaking. Finally, the result of Pugh’s ratio revealed that most of the FCC alloys show ductile behavior ( > 1.75), especially for the alloys around Fe3Ni, FeCo, and Fe2NiCo ( > 2.5). The brittle behavior ( < 1.75) was located around Fe3Cr and Fe2CoCr. Cr2NiCo and Cr2FeNiCo are considered promising compositions to be tried and verified experimentally, because of the higher bulk modulus and moderate shear modulus. MACHINE LEARNING MODELING Machine learning adopted the DFT calculation results as the input, and created a full composition database. With the database the author and his student, Guangchen Liu, developed, users are able to gain a better understanding of the mechanical properties of any composition they are interested in, within the five-element system. Their work in this area is currently in the manuscript phase and will be published in early 2023. It explores how DFT calculations, although widely used in high-entropy materials, may consume many computational resourc- es for complex systems, and limit the construction of property maps for the corresponding materials over a full composition range. In their work the most common Al-Co-Cr-Fe-Ni system (both FCC and BCC) was selected for investigation. They formulated a materials design strategy that combines DFT calculation results and machine learning models to establish a robust database of properties (e.g., phase stabilities and elastic constants) starting from unary, binary, ternary, and quaternary, then extending into high-order systems. It is expected that analyzing and screening this database will further the discovery and design of new high-entropy materials. As illustrated in Fig. 1 on the top of the iceberg, the team used Vienna Ab initio Simulation Package (VASP) and Alloy Theoretic Automated Toolkit (ATAT) to construct the special quasi-random structures (SQS) and got the elastic constants and enthalpy of formation for 200 key compositions. Subsequently, they used machine learning with Pytorch and Optuna to get the full composition elastic properties. The information below the iceberg shows knowledge about the HEA over a full composition range was obtained from a well-trained model, and the corresponding software was developed with the knowledge embedded. Figure 2 shows the full composition prediction based on 300,000 points in the Al-Co-Cr-Fe-Ni system. Out of which, the points in “rainbow” colors are the ones that fit the HEA definition. The images show the full map of phase stability, bulk modulus, and shear modulus for BCC and FCC HEAs. With that information, screening and identity of the HEAs candidates can be determined.
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