High Entropy Alloys: Design & Applications

Updated 2 August 2025

High-entropy alloys are multicomponent metallic systems formulated with equiatomic concentrations to stabilize simple solid solutions via high configurational entropy.
They leverage advanced computational methods such as DFT screening, machine learning, and CALPHAD to predict phase stability and guide compositional design.
These alloys exhibit unique mechanical and functional properties, enabling applications in superconductivity, thermoelectricity, and sustainable metallurgy through innovative processing techniques.

High-entropy alloys (HEAs) are a class of multicomponent metallic materials characterized by their exploitation of high configurational entropy to stabilize simple solid solutions—such as face-centered cubic (FCC), body-centered cubic (BCC), or hexagonal close-packed (HCP) structures—over the formation of complex intermetallic or multiphase assemblages. Unlike conventional alloys, which are based on one principal element with minor alloying additions, HEAs are formulated by mixing typically five or more elements in equiatomic or near-equiatomic concentrations, resulting in extensive lattice disorder, severe local distortions, and unique sets of mechanical, chemical, and functional properties. The HEA paradigm has expanded the designable compositional space in metallurgy and inspired a wide array of new alloy families, including high-entropy steels, superalloys, intermetallics, and even entropy-engineered thermoelectric compounds.

1. Thermodynamic Foundations and Entropic Stabilization

The stability of HEAs is fundamentally dictated by a competition between enthalpic driving forces favoring phase separation or intermetallic compound formation and the configurational entropy that favors solid-solution formation. The total Gibbs free energy of mixing is given by: $\Delta G_{\mathrm{mix}} = \Delta H_{\mathrm{mix}} - T\Delta S_{\mathrm{mix}}$ The ideal configurational entropy per mole for an $n$ -component system is: $\Delta S_{\mathrm{mix}} = -R\sum_{i=1}^n x_i \ln x_i$ where $x_i$ is the atomic fraction of component $i$ . In equiatomic HEAs with $n\geq5$ , $\Delta S_{\mathrm{mix}}$ is sufficiently large ( $>1.5R$ ) to counterbalance moderately unfavorable mixing enthalpies and thus stabilize highly disordered, single-phase solid solutions at elevated temperatures (Feng et al., 2017, Torralba et al., 24 Feb 2025). This entropic stabilization is maximal for simple lattice types (e.g., BCC, FCC) and can even override phase separation tendencies seen in binary subsystems. Experimental studies confirm that for the Cr–Mo–Nb–V system, the configurational entropy stabilizes a single BCC phase from $T\approx1700\,\mathrm{K}$ up to melting, while a C15 Laves intermetallic forms reversibly at lower temperatures (Feng et al., 2017).

The free energy includes vibrational and electronic contributions as well: $F(T,V) = F^c + F^v + F^e$ with $F^c$ from configurational entropy, $F^v$ the vibrational free energy (integrated over the phonon density of states), and $F^e$ the electronic free energy, sensitive to differences in the density of states near the Fermi level.

2. Crystal Structure Selection and the Role of Allotropy

Recent data-driven analyses have demonstrated that within the high-entropy regime, the majority crystal structure of the non-allotrope forming elements is a strong predictor of the resulting solid-solution phase (Kaufmann et al., 29 Aug 2024). Analysis of 434 experimental HEA compositions shows that, for alloys reported as FCC, the majority of non-allotrope elements are also FCC (61.5%), and for BCC alloys, over 90% of non-allotrope elements are BCC. Thermodynamic modeling of over 1,400 virtual alloys reveals that only a very small fraction with mixed non-allotrope types stabilize as true single-phase HEAs; the vast majority become multiphase. These findings imply that, under the high entropy condition, allotropy serves as a robust screening tool for predicting both phase stability and resulting crystal structure, surpassing empirical rules based on atomic size mismatch, VEC, or enthalpy alone.

3. Methodologies for Composition and Phase Prediction

The multidimensional compositional space and the exponential number of possible HEA permutations demand advanced computational and phenomenological approaches:

High-throughput ab initio screening: Over 650,000 equimolar quinary alloys have been screened using DFT-based binary regular solution models, yielding chemical maps that identify >30,000 stable single-phase HEAs (mainly BCC) and rationalize the underlying mixing enthalpy, melting point, and competitive formation of intermetallics (Chen et al., 2022).
Empirical descriptors: Parameters such as atomic size mismatch ( $\delta$ ), enthalpy of mixing ( $\Delta H_{\mathrm{mix}}$ ), valence electron concentration (VEC), and the $\Omega$ parameter ( $\Omega = T_m \Delta S_{\mathrm{mix}} / |\Delta H_{\mathrm{mix}}|$ ) are widely used for accessibility but yield limited predictive accuracy outside of training data sets (Qi et al., 2020).
Binary phase diagram mining and ML partitioning: Machine learning models trained on phenomenologically derived parameters—phase field parameter (PFP) and phase separation parameter (PSP), extracted from binary phase diagrams—achieve single-phase HEA prediction rates of over 80% and have been validated on entirely new compositions with a 77% success rate (Jie et al., 2019); these models are computationally light and robust to database imperfections.
CALPHAD and first-principles thermodynamics: Combination of CALPHAD (TCHEA5/6) for multicomponent phase equilibrium prediction and DFT for binary/ternary interaction parameters is standard for both first-order screening and refining phase selection maps (Kaufmann et al., 29 Aug 2024).

4. Microstructure, Defect Physics, and Mechanical Behavior

HEAs' unique “atomic-scale randomness” introduces scale-dependent fluctuations in local composition, significantly impacting defect energies and mechanical behavior (Nöhring et al., 2020). Every atom acts effectively as a solute, causing the energy of defects such as stacking faults, dislocation cores, and grain boundaries to fluctuate spatially. For a defect interacting with $N$ sites, the standard deviation of its energy is: $\sigma = \sqrt{\sum_j\sum_X c_X (1 - c_X) \left(\Delta U_X^\mathrm{(SF)}(j)\right)^2}$ This atomic-scale randomness can drastically lower the energetic barriers for localized plastic events—such as dislocation cross-slip—even when the average stacking fault energy is high, leading to unexpected improvements in ductility. Multiple strengthening mechanisms—including solid solution, precipitation/dispersion, strain-hardening, and grain-boundary barriers—combine synergistically, giving HEAs a superior strength-ductility balance over wide temperature ranges (Shang et al., 2021).

5. Functional Properties and Application Domains

Beyond mechanical integrity, HEAs have demonstrated performance across a range of functional regimes:

Superconductivity: Select HEAs, particularly those rich in 4 $d$ and 5 $d$ transition metals, are weakly-coupled type-II superconductors with tunable $T_c$ up to 4.4 K (e.g., Re $_{0.56}$ Nb $_{0.11}$ Ti $_{0.11}$ Zr $_{0.11}$ Hf $_{0.11}$ , HCP lattice), robust under high pressures and with superconducting properties correlated to valence electron count and crystal symmetry (Marik et al., 2019, Sun et al., 2019).
Thermoelectricity: Multi-principal element alloys enable the “entropy engineering” paradigm: increased configurational disorder causes strong phonon scattering and band structure tuning, which can dramatically reduce lattice thermal conductivity $\kappa_L$ and optimize the figure of merit $ZT = (\alpha^2 T)/(\rho \kappa)$ (Poon et al., 2019). Complex chalcogenide and HALF-Heusler MPEAs achieve $ZT > 2$ through such mechanisms.
Surface functionality and solar applications: HEAs (e.g., FeMnNiAlCr) intrinsically form high-efficiency surface oxide absorbers for solar-thermal applications, simultaneously exhibiting high-temperature mechanical strength (2–3× greater than stainless steel at $700^\circ$ C), outstanding creep resistance, and optical-to-thermal conversion efficiency approaching 87% after severe thermal cycling. Corrosion resistance in molten salts is also exceptional, with $<2\%$ weight loss after high-temperature immersion (Gao et al., 2023).
Hydrogen embrittlement resistance: Certain HEAs (notably the Cantor and hcp–PGM variants) display exceptional resistance to hydride formation—even under extreme pressures—comparable to or surpassing high-performance CuBe alloys, making them candidates for hydrogen transport and storage infrastructures (Glazyrin et al., 15 Jan 2024).

6. Alloy Design: Sustainability, Waste Recycling, and Process Innovation

The HEA paradigm unlocks the potential for sustainable metallurgy by enabling direct alloying from multicomponent industrial or electronic waste streams (Torralba et al., 2023, Torralba et al., 24 Feb 2025). Computational thermodynamics (CALPHAD) and phenomenological screening protocols allow for the prediction and realization of high-performance HEAs using commodity scrap, reducing dependence on critical raw materials and facilitating large-scale recycling. Metal injection moulding (MIM) using commodity powders (e.g., Ni625, Invar36, and CoCrF75) successfully yields single-phase FCC HEAs with promising mechanical properties, illustrating the scalability of HEA processing on an industrial basis (Meza et al., 3 Jul 2024).

Furthermore, recent reimagining of the alloy design framework emphasizes moving beyond composition-centric approaches. The integration of advanced data generation, AI-driven optimization, and microstructure-centric models (incorporating SFE, lattice misfit, and anti-phase boundary energies) catalyzes the discovery of advanced alloys with tailored microstructures, directly addressing requirements in high-performance and sustainable applications (Torralba et al., 24 Feb 2025).

7. Nucleation, Growth, and the Role of Atomic-Scale Order

Atomic electron tomography has directly visualized nucleation and growth phenomena in HEAs, revealing that nuclei form with a gradient in bond-orientational order (BOO) from core to boundary, with local structural order strongly correlated to local chemical environment (Yuan et al., 15 Apr 2025). The new “gradient nucleation pathways” (GNP) model unifies classical nucleation theory and multi-step nucleation models by allowing the nucleation barrier to increase progressively through evolving intermediate states: $AG = -\int a(r)\Delta g\, dV + \int |\nabla a(r)| \gamma\, dV$ This approach rationalizes the persistence of partial order, transient nuclei, and the dynamic evolution of microstructure upon coalescence or twin boundary formation. The GNP framework is anticipated to guide future microstructural engineering of HEAs for both structural and functional optimization.

In summary, high-entropy alloys represent a foundational shift in alloy design, enabled by entropic stabilization, complex phase selection mechanisms, and advanced data-driven design tools. The expansive compositional landscape, combined with the capacity to engineer not just composition but microstructure and function (including sustainability features), marks HEAs as a cornerstone in the transitions underway in materials science and sustainable metallurgy.