High-Entropy Alloy Design Guide & Calculator

Introduction to high-entropy alloy design

Use this high entropy alloy calculator and guide to translate a nominal composition into atomic percentages, weight percentages and theoretical batch quantities, then examine three commonly used alloy design descriptors. Start with a research question, compare candidate compositions and document the processing route before turning a calculation into a procurement specification.

What are high-entropy alloys?

High-entropy alloys (HEAs) belong to the broader family of multi-principal-element alloys (MPEAs). Conventional alloy design usually starts with one dominant base element and smaller additions. MPEA design explores several substantial constituents together. A frequently used compositional definition of HEAs involves five or more principal elements at roughly 5–35 at% each, but definitions vary and neither an element count nor an entropy threshold establishes a material’s phases or performance. Four-component NbMoTaW is often discussed in refractory HEA research despite not meeting that five-element definition.

Equiatomic and non-equiatomic compositions

An equiatomic composition assigns equal numbers of atoms to each element: five elements give 20 at% each. Non-equiatomic compositions deliberately vary those fractions to investigate phase balance, processing or properties. Neither approach is inherently superior. Atomic percent describes the share of atoms; weight percent describes the share of mass. Equal at% generally gives unequal wt% because atomic weights differ.

Applications and processing routes

Researchers investigate these alloys for structural performance, high-temperature service, corrosion and wear, irradiation response, catalysis and functional thin films. These are research directions rather than universal HEA advantages. Common routes include arc or induction melting, casting and homogenization; mechanical alloying and powder consolidation; gas atomization and additive manufacturing; and sputter deposition. Cooling rate, atmosphere, impurities, segregation and heat treatment influence the resulting material.

The interactive tool below uses the same engine, atomic-weight data and saved-composition library as our existing HEA composition calculator. Normalization is explicit, and all example compositions are nominal.

Alloy design parameters: definitions and data

All descriptors use atomic fractions cᵢ = at%ᵢ / 100, including when the input is weight percent. Fractions sum to one. Zero-concentration entries are excluded from the constituent count and sums; the limit of c ln(c) at zero is zero.

Ideal configurational mixing entropy

ΔS_mix = −R Σ cᵢ ln(cᵢ), with R = 8.31446261815324 J/(mol·K). The calculator reports J/(mol·K), ΔS_mix/R and the number of positive-concentration elements. This is per mole of atoms for ideal random mixing on one substitutional lattice. An equiatomic N-component composition has ΔS_mix/R = ln(N). It is a model value, not a measurement of total entropy.

Atomic size mismatch

r_avg = Σ cᵢrᵢ; δ = 100 × √[Σ cᵢ(1 − rᵢ/r_avg)²]. The result is a percentage. We use the tabulated atomic radii in ångströms from Guo and Liu (2011), Table 1, restricted to 15 verified metallic elements. This follows the paper’s metallic atomic-radius convention for this subset, rather than mixing covalent, ionic and metallic radii. Radii depend on their definition and environment; δ is not a direct measurement of local lattice strain.

Valence electron concentration

VEC = Σ cᵢ VECᵢ. We use the same Table 1 dataset: s+d valence electron counts for the selected transition metals and 3 for Al. VEC here means electrons per atom under that convention, rather than oxidation state or a free-electron carrier density.

Verified radius (Å) / VEC pairs: Al 1.432 / 3; Ti 1.462 / 4; V 1.316 / 5; Cr 1.249 / 6; Mn 1.350 / 7; Fe 1.241 / 8; Co 1.251 / 9; Ni 1.246 / 10; Cu 1.278 / 11; Zr 1.603 / 4; Nb 1.429 / 5; Mo 1.363 / 6; Hf 1.578 / 4; Ta 1.430 / 5; W 1.367 / 6. The published Mn radius is retained as listed; substituting another radius convention will change δ.

If any positive-concentration element lacks reference data, δ and VEC are unavailable; the tool never calculates a partial weighted average. Composition conversion and entropy still work for supported atomic-weight elements. Atomic weights reuse CIAAW’s abridged standard atomic weights. The number of displayed digits does not imply equivalent scientific accuracy.

Mixing enthalpy, Ω and electronegativity mismatch are future extensions. They are not calculated here: reliable interaction data and clearly defined models are needed first.

How to interpret the results

Entropy is one contribution to free energy

Increasing the number of equally populated constituents increases ideal configurational entropy. However, phase stability depends on Gibbs free energy, including enthalpy, temperature and other entropy contributions. Chemical ordering, short-range correlations, phase separation and different sublattices can invalidate the ideal random-mixing assumption. A large ΔS_mix does not guarantee a single-phase solid solution.

Size mismatch is a comparative descriptor

δ summarizes the spread of selected elemental radii relative to their weighted mean. Compare candidates only with a consistent radius dataset. A small δ does not rule out intermetallic phases; a large δ does not establish amorphization or a particular strength. Local relaxation and chemical interactions are not captured by this single number.

FCC and BCC tendencies from VEC

For the transition-metal alloy families studied by Guo et al. (2011), higher VEC was associated with face-centered cubic (FCC) solid solutions and lower VEC with body-centered cubic (BCC) solid solutions. Commonly quoted empirical ranges are VEC ≥ 8 for FCC and VEC < 6.87 for BCC, with mixed tendencies between them. These are correlations from particular datasets, not universal decision boundaries. Ordered phases, intermetallic compounds, other crystal structures and multiphase microstructures remain possible. The calculator deliberately reports VEC without assigning a phase label.

Validate the processing–structure–property relationship

Use CALPHAD with an appropriate assessed database to investigate candidate equilibria and transformations. Then consider solidification, cooling rate, homogenization, deformation, annealing and thin-film growth conditions. Verify phases with X-ray diffraction (XRD) and complementary microscopy or chemical analysis as needed. Phase fractions, segregation, texture, grain size, porosity and impurities all matter. These screening tools cannot substitute for CALPHAD, XRD or experimental validation, and they do not predict mechanical properties or guarantee supply.

Example alloy systems

Each link loads an equiatomic nominal composition into the existing calculator on this page. Form, processing route and acceptance criteria must be specified separately.

CoCrFeMnNi — Cantor alloy

Nominal composition: 20 at% of each element. The Cantor alloy is a reference system for concentrated solid-solution research, including deformation, ductility, fracture, diffusion and phase stability. Melting and subsequent thermomechanical processing require attention to segregation, Mn loss and heat-treatment history. Published observations for a particular specimen do not guarantee the structure of a new melt, powder or film. Load CoCrFeMnNi.

AlCoCrFeNi — aluminum-containing HEA

Nominal composition: 20 at% each. Al-containing CoCrFeNi systems are studied to understand ordering, phase balance, hardness, oxidation and mechanical response as Al content varies. Equiatomic AlCoCrFeNi is one point within that wider composition space. Aluminum oxidation, segregation and ordered-phase formation merit attention during melting, powder production and heat treatment. Load AlCoCrFeNi.

NbMoTaW — refractory HEA

Nominal composition: 25 at% each. This refractory system is studied for elevated-temperature deformation, strength retention and phase stability. Its four constituents illustrate why the broader MPEA label can be useful. High melting temperatures, density differences, chemical homogeneity, oxygen control and consolidation requirements complicate manufacture. Room-temperature ductility and oxidation resistance require independent evaluation. Load NbMoTaW.

TiZrNbHfTa — refractory multicomponent alloy

Nominal composition: 20 at% each. Often written TaNbHfZrTi, this system is studied for deformation behavior, thermomechanical processing and phase stability in refractory alloys. Ti, Zr and Hf make interstitial contamination and atmosphere control especially relevant. Homogenization and subsequent heat treatment can change microstructure. Neither the name nor calculated VEC establishes a guaranteed phase constitution. Load TiZrNbHfTa.

From alloy design to material procurement

A nominal alloy composition is the starting point for a technical inquiry. State whether the requested composition is an input charge or a required final analysis, the allowable element tolerances, impurity limits and required certification. Manufacturing may require allowance for oxidation, volatilization and other losses; the theoretical batch calculation does not supply those corrections.

For custom alloy sputtering targets, specify target dimensions, backing or bonding needs and intended deposition conditions. Target composition and deposited-film composition may differ because of process-dependent sputtering and transport. For high-entropy alloy powder, define particle size distribution, morphology, oxygen limits and intended consolidation or additive process. Review Basis Materials’ high-entropy alloy materials and custom material composition and form options for available inquiry paths.

Custom compositions, powder, sputtering targets and other forms are subject to a material-specific feasibility review; not every composition or form is currently available. Use the calculator’s Request a Custom Alloy Quote button to carry the nominal formula, at%, wt%, requested form, quantity, dimensions or particle size, required purity, application and additional specifications into our existing Request a Quote workflow. Review the prefilled information and add your contact details there. No inquiry is sent until you submit the form.

Prepare a composition and request a custom alloy quote

Frequently asked questions

Practical answers for composition design and research material inquiries.

References and further reading

• Cantor et al. (2004), Microstructural development in equiatomic multicomponent alloys. DOI: 10.1016/j.msea.2003.10.257.
• Guo and Liu (2011), Phase stability in high entropy alloys: Formation of solid-solution phase or amorphous phase. Table 1 supplies the radius and VEC values used here. DOI: 10.1016/S1002-0071(12)60080-X.
• Guo et al. (2011), Effect of valence electron concentration on stability of fcc or bcc phase in high entropy alloys. DOI: 10.1063/1.3587228.
• Senkov et al. (2010), Refractory high-entropy alloys. DOI: 10.1016/j.intermet.2010.05.014.
• Senkov et al. (2011), Microstructure and room temperature properties of a high-entropy TaNbHfZrTi alloy. DOI: 10.1016/j.jallcom.2010.11.129.
• Miracle and Senkov (2017), A critical review of high entropy alloys and related concepts. DOI: 10.1016/j.actamat.2016.08.081.