Record what the method directly measured, then separately document the equilibrium, phase-identity, and composition interpretation (Kattner, 2020).
Evidence-led assessment
CALPHAD model-building practice, connected across time.
A curated, cited handbook for evaluating evidence; constructing temperature, composition, magnetic, liquid, and multisublattice Gibbs-energy models; fitting parsimoniously; and challenging uncertainty and extrapolation.
The durable lessons
This is an open-tdb synthesis of the cited literature, not a consensus standard. The papers differ in scope, but they repeatedly converge on the following habits.
Use crystallography, site occupancy, thermochemistry, metastable evidence, and intended extrapolation—not only fit quality (Hari Kumar & Wollants, 2001).
Start with unary references and directly constrained phase properties; add complexity only when residual structure and independent evidence require it (Hari Kumar & Wollants, 2001).
Check phase rule, invariant reactions, tie lines, sections, projections, and bounding binaries before asking optimization to fit a ternary picture (Dovbenko et al., 2020).
Document method- and dataset-level weights. Statistical weighting can reveal conflicts, but cannot replace physical evaluation (Paulson et al., 2020).
Inspect metastable curves, chemical potentials, endmember limits, higher-order projections, and database compatibility (Schmid-Fetzer et al., 2007).
Map parameters and observations to prediction sensitivity; inspect identifiability and covariance before claiming precision (Otis et al., 2021).
Carry parameter uncertainty into phase boundaries and other outputs; test whether local linearization is adequate (Ury et al., 2022).
Retain data provenance, exclusions, transformations, model rationale, weights, parameter history, validation cases, and software versions (Schmid-Fetzer et al., 2007).
Scopesystem, phases, domain, uses
Inventorydirect and interpreted evidence
Critiquemethod, sample, consistency
Modelphysics and extrapolation
Optimizestaged fit with weights
Challengesensitivity, projections, reuse
Construct the Gibbs-energy model in layers
Every adjustable term should have a role, an evidence source, a validity domain, and a stress test. Add complexity only after the simpler model leaves a reproducible, physically meaningful discrepancy.
Use one documented unary set and lattice-stability convention throughout the database. Do not repair a binary fit by silently changing shared unary functions (Dinsdale, 1991).
Keep reference, ideal configurational, excess, magnetic, pressure, defect, and ordering contributions identifiable so each can be tested independently (Hillert, 2001).
Use the lowest Redlich–Kister order and fewest reciprocal or higher-order terms supported by residual structure and independent evidence.
A constant interaction is enthalpy-like; a linear T term is entropy-like. Add curvature only when heat capacity or temperature-spanning equilibria constrain it (Kaptay, 2017).
Constrain transition temperatures and moments, then verify ferro-, antiferro-, paramagnetic, and nonmagnetic limits instead of letting chemical terms absorb magnetic behavior (Xiong et al., 2012).
Use an ordinary substitutional description unless thermochemistry, structure, or anomalous heat capacity supports association, ionic, quasichemical, or two-state physics (Becker et al., 2014).
Use symmetry, reciprocal relations, DFT, analogues, or physically justified constraints; label what is calculated, assumed, or fitted and test every endmember corner (Hillert, 2001).
Scan all composition edges and broad temperature ranges, including metastable states. Reject unintended miscibility gaps, phase restabilization, and divergent derivatives (Sundman et al., 2020).
Before adding a term, identify the independent observation that constrains it; inspect covariance, profile behavior, or posterior correlation after fitting (Otis et al., 2021).
S = −∂G/∂T · H = G + TS · Cₚ = −T∂²G/∂T²These identities are executable validation rules, not notation. For every unary, endmember, and interaction temperature function, calculate and plot all four quantities over and beyond the intended range.
Temperature-function rules
- State the valid temperature interval and reference convention.
- Use the fewest basis terms that reproduce independent
G,H,S,Cₚ, and equilibrium evidence. - At an artificial piecewise join, require continuity of
Gand its first derivative; test heat-capacity continuity unless a real transition warrants a discontinuity. - Respect physical low-temperature limits when the domain approaches 0 K; a room-temperature polynomial is not automatically a third-generation model (Roslyakova et al., 2016).
- Test far outside the fitted range for derivative blow-up and nonphysical phase restabilization.
Fit and release gates
- Fit phase formation and mixing enthalpy before adding entropy-like or heat-capacity terms where the evidence permits.
- Withhold at least one informative dataset or projection for validation.
- Plot residuals by data type, source, temperature, composition, and phase.
- Calculate metastable Gibbs-energy differences, activities/chemical potentials, site fractions, invariant reactions, and higher-order sections.
- Record the final parameter-to-evidence map, covariance or uncertainty representation, software version, and numerical test grid.
How many sublattices?
There is no phase-wide magic number. Treat the crystallographically complete model as the starting hypothesis, then reduce internal degrees of freedom only with explicit physical evidence and validation.
Decision procedure
- List distinct Wyckoff sites, multiplicities, coordination, symmetry, charge constraints, and known vacancies or interstitials.
- List the ordered states, antisites, defects, site preferences, homogeneity range, and phase properties the model must reproduce.
- Assign one candidate sublattice per thermodynamically distinguishable site. Even a terminal solution can need several when inequivalent sites show different occupation (Joubert & Crivello, 2019).
- Merge sites only if their occupancy trends, local environments, allowed constituents, and energetic response are equivalent for the intended components and domain.
- Preserve site ratios, configurational entropy, composition mapping, disordered limits, and every required order parameter after a merge.
Evidence and validation
- Best evidence: diffraction/site occupancy versus composition and temperature, crystallography, defect chemistry, DFT endmembers and occupation swaps, thermochemistry, and ordering transitions.
- Reject a reduction if it fits boundaries but fails site fractions, entropy, endmember topology, or a higher-order element's site preference (Campbell et al., 2014).
- For σ: five crystallographic sites are the full structural starting point. A validated three-sublattice grouping can be parsimonious in a specific system (Jacob et al., 2018), while a bond-based five-sublattice description can reduce parameters without deleting crystallographic sites (Pereira dos Santos et al., 2023).
- Document: full candidate, every grouping constraint, parameter counts, excluded configurations, and side-by-side validation.
Order–disorder must share one thermodynamic limit
The ordered and disordered descriptions must become exactly compatible when symmetry-related sublattices have equal site fractions. The choice and number of sublattices must be able to represent every required ordered structure.
Construction
Identify the parent lattice, ordered derivative structures, symmetry-related sites, site ratios, and order parameters. Split the Gibbs energy into a composition-only disordered contribution and a constitution-dependent ordering contribution.
At equal site fractions, require the ordering contribution to vanish and recover the independently assessed disordered Gibbs energy exactly (Kusoffsky et al., 2001; Sundman, 2017).
Stress tests
Test symmetry-equivalent permutations, every endmember, the disordered limit, transition order and temperature, metastable ordered states, and multicomponent extrapolation. Use DFT for endmember ordering energies but retain experimental transition evidence.
Do not compensate for a wrong sublattice topology with extra interactions; change the structural model first.
Fewer parameters, without flattening the physics
Complex CEF phases can generate combinatorial endmember surfaces. Parsimony means choosing a physically structured basis whose terms transfer across systems—not merely deleting terms until optimization becomes easy.
Effective bond energy route
EBEF rewrites the reference surface using effective bond energies while retaining the configurational entropy. It can keep a crystallographically faithful multisublattice model and reduce required parameters (Dupin et al., 2018).
Compare rank, condition number, fitted-parameter count, cross-validation error, and higher-order predictions against the conventional endmember basis.
Evidence from complex TCP phases
A five-sublattice σ assessment used DFT plus matrix inversion and reproduced higher-order data without ternary phase terms (Pereira dos Santos et al., 2023). Later work extended EBEF to simultaneous μ and σ descriptions and reported fewer adjustable/ternary parameters (Pereira dos Santos et al., 2025).
Withhold configurations and equilibria: fewer parameters are an advantage only when the reduced basis remains identifiable and predictive.
Vacancy-bearing intermetallics need special care
Vacancies are internal degrees of freedom in a crystal model. Treating a pure-vacancy configuration as though it were an ordinary chemical endmember can create nonphysical minima or catastrophic stability.
Model construction
Start from crystallographic sublattices and distinguish constitutional vacancies, thermal vacancies, antisites, and composition-changing defects. Write the site-fraction/content mapping explicitly.
Do not assign zero to a pure-vacancy endmember merely for convenience; inspect its physical reference and consequences (Oates et al., 2008).
Required stress tests
Scan every sublattice edge and corner, calculate equilibrium vacancy content versus temperature and composition, and test for multiple stationary points, discontinuities, or unintended stabilization.
Treat vacancy content as an internal variable and verify the physical uniqueness of the solution (Ågren & Hillert, 2019).
Curated paper library
Filter by theme or search titles, authors, contributions, and practice notes. “Access” describes the source located during this review; it does not grant reuse rights.
How this guide was assembled
The selection favors guidance, critical evaluation, foundational model papers, quality assurance, uncertainty/sensitivity methods, and analyses of failure modes or parsimonious alternatives.
Search scope. Web, DOI, publisher, NIST, and CALPHAD-community searches combined CALPHAD with best practice, assessment, experimental interpretation, optimization, sensitivity, uncertainty, reference state, lattice stability, heat capacity, temperature dependence, liquid, magnetism, Compound Energy Formalism, order–disorder, site occupancy, sublattice count, vacancy, sigma, TCP, parameter reduction, and effective bond energy terms. Primary papers and publisher/agency records were favored; MSI guidance documents were also included. The fixed review date supports reproducible updates.
Interpretation boundary. Each record separates the paper’s contribution from an actionable practice statement synthesized for open-tdb and a caution. The handbook rules are a reasoned open-tdb synthesis, not a formal consensus standard. Readers should consult the linked paper before applying a recommendation. This page does not reproduce paper text or imply that every linked work is openly licensed.