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, with no fitted model and no black box. Every number is a transparent closed-form expression over a curated element-property table, validated against the primary literature.

Try it now: https://dfieser.github.io/hea-bench/. No install, it runs entirely in your browser.

^{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.
• Miedema formation enthalpies (browser/desktop apps): compound / solid-solution / amorphous, decomposed into chemical, elastic, structural, and topological terms.
• 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<br/>CoCrFeMnNi"] --> B["Curated element tables<br/>55 elements, 1484 Miedema pairs"]
    B --> C["Closed-form descriptors<br/>ΔS, δ, VEC, ΔH, Ω, Φ, φ, Λ, γ, κ"]
    C --> D["Empirical phase rules<br/>Yeh, Zhang, Guo-Liu, Yang-Zhang, King, Ye"]
    C --> E["Report<br/>per-value provenance, content-hashed result ID"]
    D --> E

Four ways to run it

The three surfaces 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.

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"]["s_config"]       # 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"]["goldschmidt_t"]  # 0.979, inside the 0.92–1.04 window
pvk["verdicts"]["bartel"]            # '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