DOI: 10.5281/zenodo.17074832
title: Supporting Dataset for the Article "Beyond Interpolation: Integration of Data and AI-Extracted Knowledge for High-Entropy Alloy Discovery"

description: Discovering novel high-entropy alloys (HEAs) with desirable properties is challenged by the vast compositional space and the complexity of phase formation mechanisms. Several inductive screening methods that excel at interpolation have been developed; however, they struggle with extrapolating to novel alloy systems. This study introduces a framework that addresses the extrapolation limitation by systematically integrating knowledge extracted from material datasets with expert knowledge derived from scientific literature using large language models (LLMs). Central to our framework is the elemental substitution principle, which identifies chemically similar elements that can be interchanged while preserving desired properties. To model and combine evidence from these multi-source knowledge, we employ the Dempster--Shafer theory, which provides a mathematical foundation for reasoning under uncertainty. Our framework consistently outperforms conventional phase selection models that rely on single-source knowledge across all experiments, showing notable advantages in predicting phase stability for compositions containing elements absent from training data. Importantly, the framework intends to effectively complement the strengths of the existing methods. Moreover, it provides interpretable reasoning that elucidates element substitutability patterns critical to alloy stability in HEAs formation. These results highlight the framework's potential for knowledge transfer and extrapolation, offering an efficient approach to exploring the vast compositional space of HEAs with enhanced generalizability and interpretability.

Experiments are conducted considering four computational datasets of quaternary alloys, one experimental dataset of quaternary alloys, and one experimental dataset of quinary high-entropy borides (HEB). HEBs are single-phase ceramics containing multiple transition metal cations randomly distributed on the metal sublattice of a boride structure, offering unique combinations of metallic and ceramic properties. Despite different bonding mechanisms, HEBs exhibit similarly high elemental selectivity as HEAs--boron's restrictive bonding requirements create stringent constraints on metal selection, analogous to the selective substitutability patterns in metallic HEAs, making them suitable for testing our framework's core principle of managing uncertainty in highly selective multi-component systems.

$\mathcal{D}_{0.9T_{m}}$ and $\mathcal{D}_{\text{1350K}}$: These computational datasets include \emph{all possible quaternary} alloys generated from a set of 26 elements: Fe, Co, Ir, Cu, Ni, Pt, Pd, Rh, Au, Ag, Ru, Os, Si, As, Al, Re, Mn, Ta, Ti, W, Mo, Cr, V, Hf, Nb, and Zr. The stability of these alloys is predicted using methods proposed by Chen \emph{et al.} at two different temperatures: $0.9\,T_m$ (approximately $90\%$ of the melting temperature $T_m$ of the alloy) and $1350\,( K)$. These predictions are obtained via a high-throughput computational workflow, which employs a regular-solution model using binary interaction parameters derived from \textit{ab initio} density functional theory (DFT) to compute and compare Gibbs free energies of solid solutions against competing intermetallic phases.$\mathcal{D}_{Mag}$ and $\mathcal{D}_{T_C}$: These computational datasets comprise 5,968 quaternary high-entropy alloys (HEAs), each formed by selecting four elements from a set of 21 transition metals: Fe, Co, Ir, Cu, Ni, Pt, Pd, Rh, Au, Ag, Ru, Os, Tc, Re, Mn, Ta, W, Mo, Cr, V, and Nb. Their magnetizations ($\mathcal{D}_{Mag}$) and Curie temperatures ($\mathcal{D}_{T_C}$) in the body-centered cubic (BCC) phase are computed using the Korringa--Kohn--Rostoker coherent approximation method. These datasets are derived from an original pool of $147,630$ equiatomic quaternary HEAs. $\mathcal{D}_{\text{HEA}}^{\text{exp}}$:  The experimental dataset includes 55 experimentally verified quaternary HEAs from peer-reviewed publications. The dataset includes both HEA (40 alloys) and non-HEA (15 alloys) compositions, providing balanced representation for validation.$\mathcal{D}_{\text{HEB}}^{\text{exp}}$: The experimental dataset includes 19 experimentally verified quinary HEBs from peer-reviewed publications. The dataset includes 15 quinary systems forming HEB.