Data-driven framework maps high-entropy alloys for extreme heat resistance

High-entropy alloys, the deliberately chaotic metal mixtures that have fascinated materials scientists for two decades, may finally have a shortcut through their near-infinite design space. A new study published in Results in Engineering by Esmaeil Khorasani-javadi, Amir Hossein Karimi and Ahmad Ali Amadeh of the University of Tehran presents a physics-informed, literature-data-driven framework that links the composition of these alloys directly to their resistance against two of the most brutal enemies of hot-section engineering: high-temperature oxidation and molten-salt hot corrosion. Instead of relying on machine-learning black boxes, the researchers built a curated meta-dataset from published experiments on bulk alloys and coatings, spanning temperatures from 500 K up to a scorching 1673 K, and interrogated it through the lens of well-established thermodynamic descriptors.

The stakes could hardly be higher. Gas turbine blades, rocket engine components and next-generation nuclear systems all demand materials that survive in air, steam and sulfur-rich combustion products while retaining their mechanical integrity. Conventional superalloys are approaching their compositional limits, and the Edisonian trial-and-error approach that produced them is no longer viable when each new candidate alloy occupies a point in a hyper-dimensional space of five or more principal elements. High-entropy alloys, defined as mixtures of at least five major elements in near-equiatomic proportions, offer an enormous but bewildering playground, and the new work aims to bring navigable order to it.

At the heart of the framework lies a set of interlocking descriptors that together capture the physics of these complex solids. The valence electron concentration, or VEC, acts as a first-order predictor of crystal structure, steering alloys toward face-centered cubic phases at high values and body-centered cubic or even hexagonal structures at lower ones. The atomic size mismatch parameter quantifies the lattice distortion that arises when atoms of different radii share a single crystal lattice, a hallmark of the high-entropy class. The thermodynamic stability parameter Omega weighs entropy-driven solid-solution stabilization against enthalpy-driven compound formation, while the mixing enthalpy and configurational entropy describe the chemical interactions and randomness of the elemental cocktail. Electronegativity difference and density round out the picture, capturing bonding character and its consequences for oxide-scale behavior.

The team assembled their database with unusual care, distinguishing bulk alloys fabricated by vacuum arc melting and induction casting from coatings deposited by high-velocity oxy-fuel spraying, atmospheric plasma spraying and laser cladding. Each entry recorded phase constitution, oxide scale chemistry and morphology, oxidation kinetics classified by linear, parabolic or logarithmic rate laws, exposure time and environmental chemistry, including molten salts such as sodium sulfate, sodium chloride and vanadium pentoxide. Entries with incomplete reporting or kinetically inconsistent behavior were filtered out, and a multi-tier validation compared trends across independent studies to confirm reproducible mechanisms such as the formation of protective alumina and chromia scales or the damaging role of volatile oxides like molybdenum trioxide and vanadium pentoxide.

The resulting stability maps reveal something striking: environmental resistance is not governed by any single parameter but by their synergistic combination. Protective oxides cluster within a narrow window of moderate lattice distortion, roughly 4.5 to 6.5 percent atomic size mismatch, and intermediate VEC values between about 5 and 7. Push lattice distortion too high and the resulting strain generates defects and fast diffusion pathways that undermine the oxide layer. Push VEC too far and the alloy shifts toward structures with poor oxide adhesion. Density follows a similar parabolic logic, with mid-density alloys around 7 to 7.5 grams per cubic centimeter showing optimal behavior, while refractory-rich heavy alloys risk scale spallation under thermal stress.

Hot corrosion tells a subtly different story. While oxidation datasets spread broadly across the thermodynamic space of mixing enthalpy and entropy, the molten-salt corrosion data cluster tightly, suggesting that salt-induced degradation tolerates only a narrow stability window. According to the Lux-Flood acid-base framework, vanadium pentoxide and sodium sulfate act as oxide-ion acceptors, dissolving protective scales through fluxing reactions. Compositions with Omega values between roughly 1.5 and 2.2 showed a stronger tendency to form protective oxides and spinel phases, whose chemical stability and low ionic diffusivity shield the underlying metal. The overlap between the oxidation and corrosion domains hints that alloys balancing entropy stabilization with controlled chemical interactions can resist both attack modes simultaneously.

Perhaps the most practical output is a new semi-quantitative descriptor, the Oxidation-Hot Corrosion Resistance Factor, or OCRF. This dimensionless index folds together the mixing enthalpy normalized by temperature, the melting-temperature ratio, the logarithm of the Omega parameter, and the combined lattice-distortion and electronegativity terms into a single screening number. Across the literature-derived datasets, higher OCRF values correlated with better resistance rankings for both oxidation and hot corrosion, and refractory alloys rich in niobium, tantalum, titanium, molybdenum and tungsten scored well thanks to their high melting temperatures. The authors are careful to stress that the factor is a comparative guide, not a universal law, since salt fluxing, volatilization and spallation introduce chemistry that no purely thermodynamic index can fully capture.

The framework also delivers a concrete design window for high-performance HEA coatings: VEC between 7.2 and 7.8, atomic size mismatch of 4 to 6 percent, Omega above 1.1, mixing enthalpy between minus 5 and minus 15 kilojoules per mole, and configurational entropy of at least 12.5 joules per mole-kelvin. Aluminum, chromium and silicon emerge as the essential oxide formers, with hafnium, yttrium and rare-earth additions improving scale adhesion, while copper, excess molybdenum or tungsten, and manganese promote segregation, volatile oxides or non-protective scales. The team validated the approach experimentally by depositing TiCrAlSiZr-based coatings on stainless steel via cathodic arc evaporation and cycling them at 800 degrees Celsius for 96 hours; the coating with the higher calculated OCRF indeed showed the slower parabolic oxidation kinetics.

Economics and sustainability thread through the analysis as well. The authors classify elements into four cost tiers, quantify price volatility and supply concentration using the Herfindahl-Hirschman Index, and argue that recyclability must become a basic design principle for high-temperature alloys. Whether impurities partition into slag, gas or metal during recycling depends on Gibbs free energies and activity coefficients, meaning that thermodynamic compatibility with existing recycling streams should be considered at the composition-design stage rather than as an afterthought.

The study’s broader message is that the era of designing alloys one descriptor at a time is ending. By showing that oxidation and hot-corrosion resistance emerge from the nonlinear interplay of electronic structure, lattice distortion, thermodynamic stability and environmental chemistry, the work offers a template for rational, physics-informed alloy discovery. The authors call for controlled, systematic datasets and integration with machine learning and uncertainty quantification to refine the OCRF and test its transferability across alloy families. If successful, the framework could compress years of empirical iteration into a computational screening step, accelerating the arrival of alloys tough enough for the hottest, most corrosive corners of the energy transition.

Subject of Research: Data-driven design of high-entropy alloys for high-temperature oxidation and hot-corrosion resistance

Article Title: Data-driven engineering of high-entropy alloys for high-temperature environmental resistance

Article References: Khorasani-javadi, E., Karimi, A. H., & Amadeh, A. A. (2026). Data-driven engineering of high-entropy alloys for high-temperature environmental resistance. Results in Engineering, 32, Article 113284. https://doi.org/10.1016/j.rineng.2026.113284

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113284

Keywords: high-entropy alloys, oxidation resistance, hot corrosion, thermodynamic descriptors, refractory alloys, coatings, alloy design, valence electron concentration, lattice distortion, molten salts, materials informatics, OCR factor