{"id":"77a1376d-c27a-4196-bbf6-582a9fbbcf5d","arxiv_id":"2507.16627","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Cr-Fe and Fe-Mo are reassessed with Wyckoff-resolved five-sublattice sigma and mu and three-sublattice C14 models plus DFT endmember enthalpies, reproducing measured sigma site occupancies.","lead":"The authors assembled thermodynamic descriptions for all ten binary alloys in the Cr-Fe-Mo-Nb-Ni system and rebuilt two of them, Cr-Fe and Fe-Mo, with crystal-structure-resolved sublattice models for the brittle TCP phases, supported by 513 DFT-computed enthalpies. If the models hold, alloy designers gain a more reliable foundation for simulating Fe- and Ni-based superalloys and additively manufactured graded materials.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Sigma and C14 sublattice models are stated inconsistently; the reported site-fraction agreement may depend on the wrong Wyckoff mapping.","rationale":"The reader's weakest-assumption diagnosis is also the one I find most load-bearing. The paper's central contribution is the complete Wyckoff-based sublattice models; the headline quantitative evidence is the site-fraction agreement. That evidence collapses to a label-matching claim, and the manuscript gives conflicting label orderings. This is not a matter of disagreement with consensus; it is internal inconsistency. It is also testable: the TDB, DFT tables, and experimental site fractions are available, so verifying the ordering is a finite computational check. I do not see a reason to reject the paper outright: the modeling work is otherwise transparent, DFT settings are specified, and much of the database is adopted from prior publications. But the inconsistency should be resolved before the claimed agreement can be accepted. Because the reader already imposed CONDITIONAL on essentially this basis, I would keep the verdict CONDITIONAL until the check is performed. The only nuance I add is that the agreement is fit-based as well as label-dependent; that reinforces, rather than replaces, the reader's concern.","tokens_in":26250,"tokens_out":6335,"duration_ms":61565,"concrete_test":"Extract the sigma and C14 parameters from the supplied TDB and compute Cr-Fe sigma site fractions at 973 K over 50.5–53.8 at.% Fe with PyCalphad/Thermo-Calc. Compare each computed sublattice occupancy to the Cieslak et al. data for the five Wyckoff sites (2b,4f,8i1,8i2,8j) under all 120 possible assignments of the five model sublattices. The reported MAE values are credible only if the assignment that matches the TDB's sublattice order reproduces the reported MAEs and is not beaten by a clearly different permutation. Also verify that the C14 sublattice size ratios in the TDB match the normalized Wyckoff multiplicities (2a:6h:4f = 1:3:2); if they do not, the 'complete' C14 model is mis-specified.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's headline evidence—Wyckoff-resolved site occupancies for sigma in Cr-Fe 'in excellent agreement' with Cieslak et al. (MAE 0.011–0.024, Sect. 5.1) and Yakel (MAE 0.0288, Fig. S10)—is only meaningful if each CEF sublattice in the optimized TDB is assigned to the same physical Wyckoff site that the experimental data label. The manuscript does not fix this assignment consistently. Section 2.5 gives Fe-Mo sigma as (Fe,Mo)4(Fe,Mo)4(Fe,Mo)2(Fe,Mo)4(Fe,Mo)1, while Table 2 gives the present-work sigma model as (Cr,Fe,Mo)1(Cr,Fe,Mo)2(Cr,Fe,Mo)4(Cr,Fe,Mo)4(Cr,Fe,Mo)4; these two orders cannot both be the Wyckoff order 2b,4f,8i1,8i2,8j in Table 1. For C14, Section 2.5 states (Fe,Mo)1(Fe,Mo)1(Fe,Mo)2 but Table 2 states (Cr,Fe,Mo)1(Cr,Fe,Mo)2(Cr,Fe,Mo)3, and neither matches the 1:3:2 multiplicity pattern of the C14 Wyckoff positions in Table 1. Because the experimental site-fraction data were used in the optimization (Sect. 3.1.1), the reported MAEs are residuals for fitted data; if the sublattice labels were accidentally permuted, a good fit to mislabeled sites proves nothing about the physical model, and the DFT endmember enumeration would be keyed to the wrong sites as well.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a consolidated CALPHAD thermodynamic database for the ten Cr-Fe-Mo-Nb-Ni binary systems, with a focus on remodeling the Cr-Fe and Fe-Mo systems using complete sublattice models for the TCP phases sigma, mu, and Laves_C14 based on their Wyckoff positions. The TCP endmember enthalpies are computed from DFT (PBE-GGA) and integrated with experimental thermochemical and phase-equilibrium data. The abstract highlights improved accuracy of the models, citing 'excellent agreement' of predicted sigma-site occupancies in Cr-Fe with experiments and a better description of the Fe-Mo solidus. The paper also adopts and slightly modifies earlier models for the other eight binaries. Claims are supported by figures of phase diagrams, thermochemical comparisons, and tables of invariant reactions. The full TDB file and DFT endmember data are promised as supplementary material but are not actually visible in the supplied manuscript.","tokens_in":26578,"tokens_out":9084,"duration_ms":83611,"significance":"If the claims hold, this is a genuinely useful contribution: it provides a self-consistent thermodynamic database for a five-component system of technological importance, upgrades simplified TCP-phase models to Wyckoff-resolved forms, and supplies a large, internally consistent set of DFT endmember enthalpies (243+243+27 endmembers). The use of DFT-derived endmember energies is an independent component that does not reduce to a fit of the same experimental data, giving the central claim partial grounding. The reported invariant reactions and solidus improvements are consistent with established experimental ranges and plausible. However, the headline site-occupancy validation is weakened by two issues: it is a residual of a fit (the cited experimental occupancy data were used in the optimization) and the sublattice-to-Wyckoff mapping is stated inconsistently between the text and the model tables. These issues must be fixed before the paper can be accepted, but they are correctable within the manuscript's scope.","major_comments":[{"comment":"The Fe-Mo sigma model is written in Section 2.5 as (Fe,Mo)4(Fe,Mo)4(Fe,Mo)2(Fe,Mo)4(Fe,Mo)1, whereas Table 2 lists the present-work sigma model as (Cr,Fe,Mo)1(Cr,Fe,Mo)2(Cr,Fe,Mo)4(Cr,Fe,Mo)4(Cr,Fe,Mo)4. These orderings are not equivalent: the latter is 1:2:4:4:4 (matching the reduced Wyckoff multiplicities 2b,4f,8i1,8i2,8j from Table 1), while the former is 4:4:2:4:1. Because the site-fraction comparisons in Fig. 1 and the MAEs in Section 5.1 are the abstract's headline evidence, the authors must state explicitly the mapping from each CEF sublattice index to the experimental Wyckoff label and ensure that Section 2.5, Table 2, and the TDB file use the same ordering. If the Section 2.5 ordering is a typo, it must be corrected; otherwise the claimed agreement could be an artifact of permuted sublattice labels.","section":"§2.5 and Table 2"},{"comment":"The Cieslak et al. and Yakel et al. site-fraction data are described in Section 3.1.1 as having been incorporated into the modeling. Consequently, the MAE values in Section 5.1 (0.011 to 0.024 for Cieslak et al., and 0.0288 for Yakel et al.) are residuals for fitted data, not independent predictions. The abstract's phrase 'predicted site occupancies ... show excellent agreement' therefore overstates the evidence. The authors should rephrase the claim as reproducing or consistent with the measured site fractions, and ideally include a validation set (for example, hold out one composition or temperature) to demonstrate predictive skill.","section":"§3.1.1 and §5.1"},{"comment":"Section 4.1 states that all DFT-calculated endmember enthalpies are given in the supplementary TDB file, and the supplemental-material section announces a TDB file, but the supplied supplementary pages contain only figures; the TDB file and the optimized model parameters are not reproduced anywhere in the manuscript. Without those data, the DFT endmember energies (the main independent input) and the actual implemented sublattice models cannot be inspected by the reader. The authors should include the TDB file as supplementary material or, if that is impossible, tabulate the key endmember formation enthalpies and the fitted interaction parameters in an appendix.","section":"§4.1 and Supplemental Material"},{"comment":"The claimed improvement in the Fe-Mo solidus description is based on a narrow margin. The present model is quoted as predicting 59.7 to 91.1 at.% Mo over 2191 to 2753 K, whereas the experimental range is given as 60.0 to 90.0 at.% Mo; this means the model overshoots the experimental range by 0.3 to 1.1 at.% on both ends. The text should quantify the deviations of both the present model and the Rajkumar et al. model from the individual experimental solidus points, and state whether the residual differences are within the reported experimental uncertainty. As written, 'more accurately reflecting experimental trends' leaves this comparison under-specified.","section":"§5.2"},{"comment":"No validation of the PBE-GGA endmember enthalpies against experimental formation enthalpies or alternative calculations is provided. Given that GGA is known to carry systematic errors of the order of 5 to 10 kJ/mol-atom for intermetallic compounds, and that these enthalpies enter Eq. 5 as the endmember energies, the authors should report at least a sanity check for a few well-characterized phases (for example, the formation enthalpy of sigma-CrFe or Fe2Mo against calorimetric data). This would substantiate the claim that the DFT set provides reliable input.","section":"§4.1"}],"minor_comments":[{"comment":"In the text after Fig. 4, the invariant reactions are referred to as being summarized in 'Table 3', but Table 3 is titled 'Details of DFT-based first-principles calculations' and the invariant reactions appear in Table 4; the cross-reference is incorrect.","section":"§5.1"},{"comment":"Section 5.1 refers to 'site 2a' when describing the sigma phase, while Table 1 lists the first sigma Wyckoff position as 2b. These labels should be unified across the text, figures, and tables.","section":"§5.1 and Table 1"},{"comment":"Equation (4) appears to be incomplete: the ideal mixing term RT(x_Cr ln x_Cr + x_Fe ln x_Fe) is written without a preceding '+' and without the x_Fe G_Fe term; the expression should be checked for missing algebraic terms.","section":"Eq. (4)"},{"comment":"There are several typographical errors: the abstract uses 'complied' instead of 'compiled', Table 1's caption spells 'strucutre' for 'structure', and Section 2.9 contains a full-width comma after 'MoNi4'.","section":"Throughout"},{"comment":"The numbering of the supplementary figures is inconsistent with the in-text references: for example, the in-text reference to Fig. S1 as the Cr-Mo phase diagram conflicts with the supplemental list in the main text, where Fig. S1 is described as a phonon density-of-states figure. Renumber the supplement so that each figure number is unique and matches the text.","section":"Supplemental Material"}],"recommendation":"major_revision","confidential_remarks":"This manuscript appears to be a database-oriented CALPHAD paper rather than a methodological breakthrough. The core idea is sound and the DFT endmember set is substantial, but the paper's most visible claim (sigma site occupancy agreement) is weakened by being a residual of a fit and by an inconsistent sublattice labeling. The promised TDB file is not actually available in the provided version, which is a serious transparency issue for a database paper. With the mapping fixed, the fitted-data framing corrected, and the TDB made accessible, the paper would be a legitimate journal contribution. I recommend major revision rather than rejection, because the problems are local and fixable rather than fundamental to the formalism."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new thing here is the reassessment of Cr-Fe and Fe-Mo with complete Wyckoff-based sublattice models: five-sublattice sigma and mu, three-sublattice C14, supported by 513 DFT endmember enthalpies. That is a real amount of new, reproducible input, and the paper is transparent about which earlier assessments it adopts for the other eight binaries. The assembled database, if the TDB file is cleaned and actually shipped, is useful for anyone doing CALPHAD in Fe- and Ni-based superalloys or compositionally graded AM parts. Credit where due: the data selection is careful, the formalism is standard, and the DFT endmembers do give the work independent grounding.\n\nThe soft spots are real but mostly correctable. First, the abstract and Section 5.1 call the sigma site occupancies 'predicted' and 'excellent agreement,' but the Cieslak and Yakel data were explicitly included in the optimization (Section 3.1.1). Those MAEs are residuals for fitted data, not predictions. That is an overstatement, not a fatal flaw, but it should be fixed.\n\nSecond, the sublattice models are stated inconsistently. Section 2.5 gives Fe-Mo sigma as (Fe,Mo)4(Fe,Mo)4(Fe,Mo)2(Fe,Mo)4(Fe,Mo)1, while Table 2 gives the present-work sigma as (Cr,Fe,Mo)1(Cr,Fe,Mo)2(Cr,Fe,Mo)4(Cr,Fe,Mo)4(Cr,Fe,Mo)4. These are different orderings of the same multiplicities, and the order matters if you compare to Wyckoff-resolved experimental site fractions. Same problem for C14 in Section 2.5, which says (Fe,Mo)1(Fe,Mo)1(Fe,Mo)2, and mu, which says (Fe,Mo)2(Fe,Mo)2(Fe,Mo)2(Fe,Mo)6(Fe,Mo)1—neither matches the normalized Wyckoff ratios in Table 1 or Table 2. The Table 2 models look correct; the text is sloppy. But a reader cannot tell which was actually used in the optimization, and the site-fraction comparison is only meaningful if the mapping is right. The authors need to fix this and preferably state the Wyckoff order explicitly.\n\nThird, the supplementary material section contains text about BCC-Nb phonons and Nb-Ni ML potentials that belongs to a different manuscript. That is a production error, but it is in the paper and undermines confidence.\n\nSome comparison metrics are marginal or favor prior models: Fe-Mo activity MAEs are slightly worse than Rajkumar et al., and the BCC enthalpy of formation in Cr-Fe is slightly worse than Jacob et al. against Dench. That is fine, but the 'improved accuracy' claim is not uniformly supported.\n\nOverall: the core modeling work is sound and the DFT database is a contribution. The paper deserves a serious referee, but it needs revision before publication: fix the sublattice ordering, remove the word 'predicted' for fitted quantities, clean the supplementary text, and actually provide the TDB file. If those are addressed, this becomes a good database paper.","headline":"Real DFT-endmember CALPHAD work underneath a sloppy manuscript: the Cr-Fe and Fe-Mo reassessments deserve review, but the site-fraction 'prediction' is a fit and the sublattice models are stated inconsistently.","tokens_in":27226,"tokens_out":3443,"would_cite":true,"duration_ms":35407,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that Wyckoff-resolved five-sublattice models backed by DFT endmember enthalpies reproduce measured sigma-phase site occupancies in Cr-Fe and move the Fe-Mo solidus closer to experiment.","keywords":["CALPHAD modeling","topologically close-packed phases","sigma phase","mu phase","Laves C14","DFT formation enthalpies","Cr-Fe system","Fe-Mo system"],"falsifier":"Measure site occupancies of sigma in Cr-Fe at a composition and temperature not used in the fit, for example a new long anneal near 45 at.% Fe at 1000 K, with atom-probe tomography or neutron diffraction and compare site by site with the model; if the pattern of high- and low-occupancy sites is permuted relative to prediction, the Wyckoff-to-sublattice ordering is wrong. A cheaper check is to recompute the 513 endmember formation enthalpies with a different exchange-correlation functional: if predicted invariant temperatures shift by more than the few kelvin claimed, the PBE energies are doing load-bearing work the paper does not quantify.","tokens_in":1966,"feed_emoji":"⚙️","tokens_out":7095,"duration_ms":149981,"temperature":0.7,"pith_summary":"The paper tries to establish that the brittle topologically close-packed (TCP) phases in the Cr-Fe and Fe-Mo binaries cannot be described accurately by lumping several crystallographic sites together, and that giving each Wyckoff position its own sublattice, backed by DFT-computed endmember formation enthalpies, fixes the problem. If the claim is right, CALPHAD thermodynamic databases for the five-element Cr-Fe-Mo-Nb-Ni system can predict not only which TCP phases appear but also how chromium, iron, and molybdenum distribute among the individual atom sites of those phases. That matters because TCP phases like sigma drain refractory elements from superalloy matrices and embrittle the material, and additive manufacturing of graded Fe-to-Ni parts needs a database that works across the whole composition range. The headline evidence is that sigma-phase Fe occupancies in Cr-Fe match experimental data on all five Wyckoff sites with mean absolute errors between 0.011 and 0.024, and that the Fe-Mo solidus range moves closer to measured values.","feed_headline":"New models predict atom positions in brittle alloy phases","feed_subtitle":"Wyckoff-based models match measured sigma site occupancies and sharpen the Fe-Mo solidus.","key_machinery":"The load-bearing machinery is the complete sublattice model of a TCP phase under the compound energy formalism, a Gibbs-energy expansion in which every sublattice has its own ideal-mixing term: one sublattice for each Wyckoff position, so that each crystallographic site can develop its own occupancy. For $\\sigma$, for example, the model is a five-sublattice formula $(\\mathrm{Cr}, \\mathrm{Fe}, \\mathrm{Mo})_1(\\mathrm{Cr}, \\mathrm{Fe}, \\mathrm{Mo})_2(\\mathrm{Cr}, \\mathrm{Fe}, \\mathrm{Mo})_4(\\mathrm{Cr}, \\mathrm{Fe}, \\mathrm{Mo})_4(\\mathrm{Cr}, \\mathrm{Fe}, \\mathrm{Mo})_4$ instead of the simplified $(\\mathrm{Cr}, \\mathrm{Fe})_{10}(\\mathrm{Cr}, \\mathrm{Fe})_4(\\mathrm{Cr}, \\mathrm{Fe})_{16}$ form; mu gets five sublattices and C14 gets three. The Gibbs energy of each endmember in the compound energy sum is supplied by DFT-based phonon and quasiharmonic calculations, giving 243 $\\sigma$, 243 mu, and 27 C14 formation enthalpies. The role of this machinery is to make model outputs commensurate with site-resolved experiments: each predicted site fraction is tied to a named Wyckoff position, so agreement or disagreement is per-site rather than averaged.","core_discovery":"The central discovery is a self-consistent thermodynamic description of the ten binaries in Cr-Fe-Mo-Nb-Ni, with the two most problematic binaries remodeled. In Cr-Fe, sigma is modeled as a five-sublattice compound with formula (Cr,Fe,Mo)1(Cr,Fe,Mo)2(Cr,Fe,Mo)4(Cr,Fe,Mo)4(Cr,Fe,Mo)4, one sublattice per Wyckoff position, so the predicted site fraction of Fe on each position can be compared directly with the measured atom distributions in the paper's two sigma site-occupancy datasets. The reported mean absolute errors are 0.011 to 0.024 at 973 K against one dataset and 0.0288 overall at 923 K against the other. For Fe-Mo, the same treatment is applied to sigma, mu, and Laves_C14, and the resulting model places the solidus at 59.7 to 91.1 at.% Mo between 2191 and 2753 K, closer to the experimental 60.0 to 90.0 at.% Mo range than the previous model. Formation enthalpies of the 243 sigma, 243 mu, and 27 C14 endmembers come from DFT calculations rather than ad hoc assignments.","pith_inferences":["A stronger test than the paper's would be to hold out one of the two site-occupancy datasets, or a new measurement, during fitting and then compare; the paper's error metrics are computed against data that also helped set the model parameters.","If the sublattice ordering in the model formulas is correct, the same five-sublattice machinery should transfer to sigma phases in higher-order Cr-Fe-Mo-Nb-Ni alloys, predicting how Mo and Nb partition among sites, a quantity that governs TCP embrittlement.","The paper leaves the R phase, which has eleven Wyckoff positions, in a simplified model; applying the same complete-sublattice philosophy there with DFT endmember enthalpies is the immediate next step the argument points toward.","A systematic DFT functional check, such as comparing PBE enthalpies with a meta-GGA, would bound how much of the improved agreement comes from the sublattice structure versus from the DFT energies."],"forward_implications":["Cr-Fe sigma-phase predictions now resolve all five Wyckoff sites separately, so future site-occupancy experiments can be checked site by site instead of against lumped averages.","The Fe-Mo solidus is pulled from 55.6 to 89.8 at.% Mo in the previous model to 59.7 to 91.1 at.% Mo, within about 1 at.% of the measured 60.0 to 90.0 at.% range, improving liquid-solid boundary predictions in Mo-bearing steels and superalloys.","Replacing arbitrary endmember enthalpy values with DFT-computed values removes a systematic source of error that would otherwise propagate into ternary and higher-order databases built on these binaries.","Using the same Wyckoff-based five-sublattice models for Cr-Fe, Fe-Mo, Fe-Nb, and Nb-Ni makes the quinary database internally consistent for ternary extrapolation.","The 973 K and 923 K sigma site-fraction checks give quantitative per-site error metrics that future CALPHAD assessments can use as a baseline."],"supporting_citations":[{"why":"It supplies the previous simplified three-sublattice sigma model for Cr-Fe that the present five-sublattice model is built to beat.","marker":"[14]"},{"why":"It supplies the previous simplified Fe-Mo model whose solidus and phase boundaries are compared throughout the paper.","marker":"[15]"},{"why":"It provides the 973 K sigma site-fraction measurements used to judge the Cr-Fe site-occupancy predictions.","marker":"[34]"},{"why":"It provides the 923 K sigma atom-distribution data used as the second site-occupancy check.","marker":"[6]"},{"why":"It supplies the SGTE pure-element lattice stabilities that keep the new models consistent with the rest of the database.","marker":"[35]"},{"why":"It defines the compound energy formalism on which the Wyckoff-based sublattice models are built.","marker":"[156]"},{"why":"It provides the quasiharmonic and equation-of-state method used to turn DFT energies into endmember thermodynamic data.","marker":"[150]"},{"why":"It defines the PBE exchange-correlation functional used for all 513 endmember enthalpy calculations.","marker":"[154]"}],"fun_headline_variants":["Wyckoff-based models match sigma site occupancies in Cr-Fe","DFT-supported CALPHAD models refine Fe-Mo solidus","New models predict atom positions in sigma and mu phases","Better Cr-Fe and Fe-Mo phases from DFT-backed CALPHAD"],"cache_read_input_tokens":29056,"weakest_assumption_plain":"The claim stands on the assumption that the order of sublattices in each model formula matches the order of the Wyckoff sites as measured, so every predicted site fraction is assigned to the right atom column; it also assumes the DFT endmember enthalpies are accurate enough that the fit does not have to absorb systematic energy errors.","fun_headline_variants_meta":{"raw":{"variants":["Wyckoff-based models match sigma site occupancies in Cr-Fe","DFT-supported CALPHAD models refine Fe-Mo solidus","New models predict atom positions in sigma and mu phases","Better Cr-Fe and Fe-Mo phases from DFT-backed CALPHAD"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001419,"raw_usage":{"total_tokens":5738,"prompt_tokens":961,"completion_tokens":4777,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":577,"completion_tokens_details":{"reasoning_tokens":4702}},"tokens_in":577,"tokens_out":4777,"duration_ms":36164,"temperature":1.0,"reasoning_tokens":4702,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T15:07:33.781320+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure site occupancies of sigma in Cr-Fe at a composition and temperature not used in the fit, for example a new long anneal near 45 at.% Fe at 1000 K, with atom-probe tomography or neutron diffraction and compare site by site with the model; if the pattern of high- and low-occupancy sites is permuted relative to prediction, the Wyckoff-to-sublattice ordering is wrong. A cheaper check is to recompute the 513 endmember formation enthalpies with a different exchange-correlation functional: if predicted invariant temperatures shift by more than the few kelvin claimed, the PBE energies are doing load-bearing work the paper does not quantify.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It provides the 973 K sigma site-fraction measurements used to judge the Cr-Fe site-occupancy predictions."},{"cited_title":"Marcus, M.E","cited_arxiv_id":null,"evidence_quote":"It defines the PBE exchange-correlation functional used for all 513 endmember enthalpy calculations."}],"review_version":1}