Alloy Phase Equilibrium

pycalphad: TDB equilibrium calculations

When to use

Use for equilibrium phase fractions and compositions at a fixed bulk elemental mole composition, specified pressure, and a list of finite temperatures. The bundled helper executes real pycalphad equilibria, checks mass balance, repeats at greater sampling density, and exports each stable composition set separately.

Equilibrium is constrained by the selected database, components, phases, and conditions. It does not predict precipitation rates, retained metastable microstructures, or properties of phases missing from the database. Successful numerical checks do not establish the database's experimental accuracy.

Workflow

1. Identify the TDB's source, license, assessment/publication, valid temperature/pressure and composition range, and required elements. Use the user's database for real alloys. The bundled assets/ideal-cu-ni.tdb is an original hypothetical teaching model, not an assessed Cu-Ni database.
2. Inspect database elements and phases. Select the relevant phases deliberately; record exclusions because they can turn the calculation into a metastable constrained result. Include VA where required by sublattice models. Vacancies are not an independent bulk mole fraction. Keep coupled order/disorder definitions in the TDB, but do not select both partners as separate candidates when the ordered model already includes the disordered contribution; the helper rejects such filtered candidate lists.
3. Copy assets/equilibrium.json. Specify exactly N-1 elemental mole fractions and one dependent non-vacancy element. The dependent fraction is 1 - sum(independent fractions); fractions are not silently normalized. Set K and Pa. Convert weight percentages or mass fractions before using this helper.
4. Declare the database temperature interval from its assessment if known, or set database_temperature_range_k to null if unknown. This is user-supplied evidence, not a range automatically inferred from every TDB function. Requests outside a declared interval fail. Check pressure and composition validity separately.
5. Run the calculation. Check finite Gibbs energies, phase fractions summing to one, reconstructed bulk composition, and stability to doubled pdens (phase-constitution sampling density). Near transitions, refine temperatures and sampling density further.
6. Deliver phase fractions with their molar basis, phase compositions, database hash, conditions, excluded phases, and any numerical or assessment limitations.

Read references/model-and-validation.md for the analytic example, basis conversion, native Model/Workspace/property/plot contracts, miscibility-gap handling, and convergence limits.

Execute the tested example

From the collection root:

uv run --no-project --python 3.12 --with pycalphad==0.11.2 --with numpy==2.5.3 \
  python skills/pycalphad/scripts/equilibrate.py \
  skills/pycalphad/assets/ideal-cu-ni.tdb \
  skills/pycalphad/assets/equilibrium.json equilibrium-result

Tested on Python 3.12, pycalphad 0.11.2, and NumPy 2.5.3. Use a new output directory. All thermodynamic calculations are local; the script does not upload a TDB.

For the supplied hypothetical model at X(Ni)=0.5 and 101325 Pa:

Temperature	Equilibrium result
900 K	FCC_A1 only
1100 K	0.5 FCC_A1 + 0.5 LIQUID; X(Ni) approximately 0.527307 and 0.472693 respectively
1300 K	LIQUID only

The suite verifies analytic common-tangent compositions, a noncentral lever-rule case, Gibbs energy, mass balance, both single-phase limits, and actual same-phase miscibility gap vertices. These validate the computational workflow, not real Cu-Ni metallurgy.

Outputs and acceptance

• report.json: settings and versions, TDB/settings SHA-256, excluded database phases, requested, solver-imposed, and reconstructed bulk compositions, per-temperature baseline/refined results, and checks. Experimental validity is not evaluated by the helper.
• phase-equilibria.csv: one row per stable vertex per temperature and sampling run, including phase name, molar phase fraction, and elemental mole fractions. Its Gibbs energy column is the whole-system molar Gibbs energy, repeated for each vertex; it is not the individual phase energy.

Unused pycalphad vertices have blank names and NaN values; those are omitted. Named vertices with invalid values cause failure. Multiple vertices with the same phase name are retained because a miscibility gap can contain two composition sets of one phase. Vertex indices do not track the same physical phase continuously across temperatures.

In stable 0.11.2, pycalphad clips independent mole fractions to [1e-10, 1-1e-10]. Each result records solver_bulk_mole_fractions and the largest absolute difference from the requested bulk in composition_condition_adjustment_absolute_error. Mass-balance checks still compare against the requested composition; a tighter tolerance can therefore fail at an endpoint. Do not claim exact pure-component or ultratrace results from a clipped multicomponent calculation.

all_checks_passed requires each run's phase-sum and bulk-composition residuals within mass_balance_tolerance, phase totals stable within phase_fraction_tolerance, and system Gibbs energy stable within gibbs_energy_tolerance_j_per_mol when pdens doubles. This comparison does not certify the global minimum or track individual composition-set movement within a same-phase miscibility gap; inspect their exported compositions too. Failed checks remain visible in the report rather than being relabeled as convergence.

Boundaries and upstream contracts

The helper handles elemental mole fractions, one composition, one pressure, and up to 1000 explicit positive temperatures. It validates selected phases through pycalphad's phase-compatibility rules; incompatible or automatically filtered order/disorder phase sets produce an explicit error. It does not silently remove requested phases.

Charged-species constraints, externally imposed chemical potentials, custom models, activity reference-state changes, and database optimization require additional modeling and are outside this helper's tested scope. Do not extrapolate the pedagogical asset to real material selection or heat-treatment decisions.

• Equilibrium dataset semantics
• Phase fractions and composition basis
• Equilibrium and sampling API
• Ordering examples
• Stable 0.11.2 source

Upstream latest documentation currently describes 0.11.3 development builds. The bundled helper and the reference's native examples were exercised against stable 0.11.2 on 2026-10-01; the release's source was checked against the installed wheel. No remote thermodynamic calculation or database-fetch API is used. Database loads a local path, file-like object, or TDB text; a URL is not a supported download shortcut.