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FAQ

What formula notation is supported?

HEACalculator uses a flexible chemical formula parser that handles several common styles:

Style Example Notes
Equimolar (symbol-only) FeCoCrNi All elements treated as equal fractions
Explicit atom counts Fe25Co25Cr25Ni25 Counts are normalized internally
Fractional counts Al0.5CoCrFeNi Decimal counts are allowed
Nested brackets (FeCo)2CrNi or [FeCo]2CrNi Round or square brackets with multipliers
Mixed counts Fe10Co20Cr30Ni40 Any non-negative integer or decimal counts

Element symbols must start with an uppercase letter (Fe, not fe). Spaces are ignored, so Fe Co Cr Ni and FeCoCrNi are the same alloy. Quote a formula that contains spaces on the command line (e.g. HEACalculator search single "Fe25 Co75"), otherwise the shell splits it into separate arguments.

What happens when I don't specify atom fractions?

If you provide a formula without numeric counts (e.g. FeCoCrNi), all elements are assumed to be equimolar. Internally the formula is treated as Fe1Co1Cr1Ni1 and the fractions are normalized to sum to 1.

How many elements are supported?

There is no hard limit on the number of components. However:

  • The mixing enthalpy and formation enthalpy databases cover a finite set of binary pairs. If a pair is missing, the values that need it (and the models that use them) are reported as N/A (null in JSON), and everything else is still calculated. See Some results show N/A.
  • The solid-solution criteria were calibrated almost entirely on alloys with four to seven principal elements, most with five or six. Results for binary or ternary alloys are an extrapolation and should be read with care.

Which prediction model should I trust?

None of them is reliable across all alloy families, and no criterion has emerged as the most reliable. Each was calibrated on its own set of alloys, and they often disagree for the same composition: for AlCoCrFeNi, two report a solid solution, two an intermetallic, and four multiple phases.

Rather than picking one:

  • Report all eight results, not only the ones that match your expectation.
  • Give more weight to criteria whose original papers include alloys similar to yours (see the references).
  • Treat agreement between criteria as supporting evidence, not proof, and confirm important predictions with CALPHAD calculations or experiments.

Does HEACalculator account for temperature effects?

Most parameters (density, VEC, δ, mixing enthalpy and entropy, and the other composition descriptors) do not depend on temperature: they are computed from the composition and tabulated element and binary-pair data. The exceptions are:

  • omega is evaluated at the estimated melting temperature \(T_m\).
  • omega_at(T) can be called with an arbitrary temperature.
  • Model 6 compares the 0 K DFT formation enthalpies against the entropy bound \(-T\,\Delta S_{\text{mix}}\), evaluated at \(T = 0.55\,T_m\).
  • Model 7 defaults to an annealing temperature of \(0.55\,T_m\) and \(k_2 = 0.6\); both can be changed with model_7(k_2=..., annealing_temperature=...).

Can I use HEACalculator as a Python library?

Yes. Install the package and import directly:

from HEACalculator import HEACalculator

hea = HEACalculator("AlCoCrFeNi")
print(hea.thermo.mixing_enthalpy)

To calculate many alloys in parallel, use HEACalculator.screen. See Parallel screening.

See the Usage page for full examples.

How do I cite HEACalculator?

If you use HEACalculator in your research, please cite the following:

Sarıtürk, D., Kalay, Y. E., & Arróyave, R. (2026). HEACalculator: An Open-Source Python Tool for Thermodynamic Property Calculation and Solid Solution Prediction in High-Entropy Alloys. arXiv. https://doi.org/10.48550/arXiv.2606.19661

Sarıtürk, D. (2019). HEACalculator. Zenodo. https://doi.org/10.5281/zenodo.3590318

BibTeX 
@misc{sariturk_2026_arxiv,
  author    = {Sarıtürk, Doğuhan and Kalay, Yunus Eren and Arróyave, Raymundo},
  title     = {{HEACalculator}: An Open-Source {Python} Tool for Thermodynamic Property Calculation and Solid Solution Prediction in High-Entropy Alloys},
  year      = 2026,
  publisher = {arXiv},
  doi       = {10.48550/arXiv.2606.19661},
  url       = {https://doi.org/10.48550/arXiv.2606.19661},
}

@software{sariturk_2019_3590318,
  author    = {Sarıtürk, Doğuhan},
  title     = {HEACalculator},
  year      = 2019,
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.3590318},
  url       = {https://doi.org/10.5281/zenodo.3590318},
}

You should also cite the original papers for any specific prediction models you rely on. See the Overview page for the full reference list.

What license is HEACalculator released under?

HEACalculator is distributed under the GNU General Public License v3.0 or later (GPL-3.0-or-later). See the LICENSE file for details.

How do I report a bug or request a feature?

Open an issue on GitHub: github.com/dogusariturk/HEACalculator/issues