HEA-Bench

hea-bench

Open, interpretable tools for computing the standard high-entropy-alloy (HEA) and high-entropy-oxide (HEO) thermodynamic and geometric descriptors and the classic empirical phase-prediction rules, from any composition. Every descriptor is a transparent closed-form expression over a curated element-property table, validated against the primary literature. The fitted predictions (hardness, phase prediction sets) carry calibrated uncertainty and flag alloys unlike their training data.

Try it now: https://dfieser.github.io/hea-bench/. No install, it runs entirely in your browser, and every library feature works there: the calculator for alloys, oxides and ceramics with property and phase predictions, the experimental dataset, alloy search and experiment planning, and the benchmark.

The equimolar Cantor alloy CoCrFeMnNi, as the browser app reports it. The Python library, the desktop app and this page print the same digits, and a parity suite keeps it that way.

Using an AI coding agent to integrate this? See

AGENTS.md for a machine-oriented guide to the API,

exact return types and units, the fastest path to each task, and the

mistakes to avoid.

What it computes

For any composition it reports:

• Core descriptors: mixing entropy ΔS mix , atomic-size mismatch δ, mean melting temperature T m , Miedema mixing enthalpy ΔH mix , valence-electron concentration VEC, Yang–Zhang Ω, Pauling electronegativity mismatch Δχ, Mansoori excess entropy S E , ΔG ss , ΔG max , King Φ, Ye φ.
• Phase-prediction rules: Yeh entropy, Zhang δ, Guo–Liu VEC, Yang–Zhang Ω, King Φ, Ye φ, Senkov–Miracle κ, the Tsai σ-phase window and Sheikh ductility.
• Miedema formation enthalpies: compound / solid-solution / amorphous, decomposed into chemical, elastic, structural, and topological terms.
• Your own elements and pair values: any descriptor or rule, for a composition with an element or pair enthalpy that is not tabulated.
• High-entropy oxides (hea_bench.oxides + the apps' Oxides mode): rock-salt, perovskite, fluorite, and pyrochlore formability descriptors over Shannon ionic radii with automatic charge-balance oxidation-state assignment: per-sublattice configurational entropy, cation size disorder, Goldschmidt t / octahedral μ / Bartel τ, the fluorite radius-dispersion rule, and the pyrochlore radius-ratio window.

Element coverage: 55 elements for alloys (Ag Al Au Be Bi Ca Ce Co Cr Cu Dy Er Fe Ga Gd Ge Hf Ho In Ir La Li Lu Mg Mn Mo Nb Nd Ni Os Pb Pd Pr Pt Re Rh Ru Sb Sc Si Sm Sn Sr Ta Tb Th Ti Tm U V W Y Yb Zn Zr, covering the full experimentally active rare-earth HEA palette plus the nuclear, solder, and HE-BMG corners); the Miedema pair table covers 75 (1484 of our 1485 pairs; the lone Th-U gap is reported, never zeroed); the oxide module's Shannon table covers 94.

How a number gets made

No fitted model sits anywhere in this chain. Each descriptor is a closed-form expression over curated tables, and the report carries the literature source of every input alongside the value.

flowchart LR

A["Composition CoCrFeMnNi"] --> B["Curated element tables 55 elements, 1484 Miedema pairs"] B --> C["Closed-form descriptors ΔS, δ, VEC, ΔH, Ω, Φ, φ, Λ, γ, κ"] C --> D["Empirical phase rules Yeh, Zhang, Guo-Liu, Yang-Zhang, King, Ye"] C --> E["Report per-value provenance, content-hashed result ID"] D --> E

Four ways to run it, each with every feature

Every feature is in all four parts, so pick whichever suits you and you lose nothing. That is a standing project rule, and CI enforces it: tests/test_feature_parity.py fails whenever a public feature lacks its library function, its MCP tool or a working app surface, a headless browser uses every tab of the built site, the built desktop exe goes through the same steps before it is attached to a release, and a freshly installed wheel answers every MCP tool. pip install hea-bench alone has no dependencies and covers everything except the fitted models and the MCP server; the [all] extra adds scikit-learn and the MCP SDK for those.

All four share one calculation core. The browser/desktop core (web/hea-calculator-core.js) is a pure-JS port of the Python library, and tests/test_web_parity.py guarantees the two match on all 1484 binary pairs and the canonical multi-element fixtures, while tests/test_web_oxides_parity.py does the same for the oxide module, down to identical warning messages. The app's Dataset, Design and Benchmark tabs and its predictions panel run the Python package itself, unchanged, inside the page (Pyodide, web/hea-engine-worker.js), and tests/test_web_engine.py checks that it returns exactly what CPython returns.

Quick start (Python)

pip install hea-bench

import hea_bench as hb

cantor = {"Co": 0.2, "Cr": 0.2, "Fe": 0.2, "Mn": 0.2, "Ni": 0.2}

hb.smix(cantor) # 13.381 J/(mol·K) = R · ln 5 hb.delta(cantor) # 3.164 % atomic-size mismatch hb.vec(cantor) # 8.0 valence electrons hb.mixing_enthalpy(cantor) # -4.16 kJ/mol (Miedema) hb.omega(cantor) # 5.79 (Yang–Zhang) hb.delta_chi(cantor) # 0.138 Pauling electronegativity mismatch hb.s_excess(cantor) # 0.318 J/(mol·K) (Mansoori excess entropy) hb.delta_g_max(cantor) # -8.00 kJ/mol (most-negative Miedema pair) hb.phi_king(cantor) # 3.533 (King 2016 proxy) hb.phi_ye(cantor) # 34.82 (Ye 2015 proxy)

Apply the canonical rules

from hea_bench.rules import guo_vec, king_phi, yang_omega, ye_phi, zhang_delta zhang_delta.predict(cantor) # 'single-phase' yang_omega.predict(cantor) # 'single-phase' guo_vec.predict(cantor) # 'FCC' king_phi.predict(cantor) # 'solid_solution' ye_phi.predict(cantor) # 'solid_solution'

These Cantor-alloy values are pinned in the test suite as the canonical sanity check. The rules are simple empirical surrogates, fast screens rather than predictions, so treat their output accordingly.

Descriptor backends (optional interop)

Descriptors can also be computed through a pluggable backend. The default (native) is this package's own stdlib implementation; with pip install "hea-bench[interop]" the same interface drives an installed HEACalculator (GPLv3, installed at the user's choice), so a workflow standardized on its numbers can keep them while using everything downstream here:

from hea_bench.descriptors.backend import get_backend

get_backend("heacalculator").compute(cantor) # same names, their reference data

hea-bench describe Al0.3CoCrFeNi --backend native

The two backends vendor different reference data (radius conventions differ most), so same-named values legitimately differ; the measured, per-descriptor comparison lives in docs/backend-agreement.md. Quantities whose implementations differ structurally are deliberately not mapped onto each other, and the benchmark's published baselines use the native backend unchanged.

Quick start (oxides)

from hea_bench import oxides

Rost 2015 "J14" entropy-stabilized rock salt

j14 = oxides.describe_rock_salt({"Mg": 1, "Co": 1, "Ni": 1, "Cu": 1, "Zn": 1}) j14"descriptors" # 13.382 J/(mol·K) = R·ln 5 j14["oxidation_states"] # all 2+ by charge balance

Jiang 2018 single-phase high-entropy perovskite

pvk = oxides.describe_perovskite({"Sr": 1}, {"Zr": 1, "Sn": 1, "Ti": 1, "Hf": 1, "Mn": 1}) pvk"descriptors" # 0.979, inside the 0.92–1.04 window pvk"verdicts" # 'perovskite' (τ = 3.72 < 4.18)

Each describe_* report carries the solved oxidation states, the Shannon radii actually used, every descriptor, the formability verdicts with their windows, and any warnings. See examples/02_oxides_walkthrough.py for the full tour, including the fluorite and pyrochlore screens and oxidation-state overrides.

Quick start (ceramics, experimental)

hea_bench.ceramics extends the calculator to rock-salt carbides and nitrides and AlB2-type diborides, composition-only and honest about what that buys:

from hea_bench import ceramics

hec = ceramics.describe_rock_salt_carbide({"Ti": 1, "Zr": 1, "Hf": 1, "Nb": 1, "Ta": 1}) hec["vec_per_formula_unit"] # 8.4, with annotated literature reference points hec["entropy"] # all normalization conventions, labelled

Reports carry the metal-sublattice entropy in every published normalization convention (papers switch between them without warning), VEC with annotated reference points rather than a verdict (the literature marks points, not one window), and explicit notes on what is deferred: the size-mismatch descriptor (the field computes it from DFT binary-cell bond lengths, and adopting a cited table is real curation work), and entropy-forming-ability or DEED, which are DFT-ensemble quantities this package cannot and does not claim to reproduce. Background, citations, and a license audit of candidate ceramics datasets: docs/ceramics.md.

Quick start (AI agents, MCP)

LLM agents hallucinate descriptor values; this server grounds them. hea_bench.mcp_server exposes every feature of the package over the Model Context Protocol as 24 deterministic tools. The calculator: parse_composition, batch alloy_descriptors (with the Miedema enthalpies) and alloy_rules, both taking custom elements and pair values, omega_sensitivity, oxide_report, ceramic_report, element_data and `element_cove