{"id":"25103f74-7d95-4c1f-a65c-b8be65e115d5","arxiv_id":"2608.10465","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"The authors combine a Jacobi-Legendre machine-learning potential with exact enumeration of configurations to predict that disordered fcc Ni-Pd is a metastable solid solution at room temperature and becomes thermodynamically stable around 600 K.","lead":"Using a compact machine-learning interatomic potential with 873 parameters, the authors computed the finite-temperature stability of nickel-palladium alloys by explicitly summing over tens of thousands of atomic configurations. The approach is a candidate route to screening disordered and high-entropy alloys at finite temperature without the usual ideal-entropy approximations.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Neglecting finite-temperature magnetic free energy in ferromagnetic Ni-Pd is not bounded by the JLP validation and can shift the claimed 500-700 K stability onset or room-temperature metastability.","rationale":"The paper's strongest element is the workflow itself: a compact 873-parameter JLP with convincing validation on 16-atom cells, including relaxed-energy RMSE near 1.9 meV/atom and vibrational free-energy RMSE of 0.64-3.14 meV/atom. The MLIP surrogate is not the weak link. The load-bearing concern lies in the thermodynamic model assembled in Section III E: Eq. (15) sums over configurations with only E(σ)+F_vib(σ,T), at fixed 0 K volume, and the authors explicitly state that electronic and magnetic free energies are not included. Ni is a ferromagnet with a Curie temperature close to the claimed stability-onset window, so the magnetic free energy of Ni-Pd is neither negligible nor cancelling in formation free energies. An omitted term of a few meV/atom is enough to move the ΔG zero-crossing materially, since the reported JLP phonon error is already ~1-3 meV/atom at these temperatures. The reader's conditional verdict already captures this incompleteness; nothing in my reading moves the verdict to reject or accept. I would additionally encourage the authors to release code, trained model, and data, and to report a finite-size extrapolation of the configurational entropy, but those are secondary to the magnetic free-energy concern.","tokens_in":27025,"tokens_out":9703,"duration_ms":106124,"concrete_test":"Recompute ΔG(T,x) from Section III E with an explicit finite-temperature magnetic free energy added to Eq. (15), e.g. from a classical Heisenberg or disordered-local-moment model fitted to spin-polarized DFT, or from measured magnetization and heat-capacity data for Ni-Pd, including the corresponding magnetic free energy for the pure fcc elemental references. Then track the temperature/composition region where ΔG crosses zero. If the onset moves outside 500-700 K, or if the sign of ΔG at 300 K changes at any composition, the central claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section III E evaluates Eqs. (15)-(17) with only configurational and harmonic-vibrational free energy at fixed 0 K volume, and the text explicitly defers magnetic contributions as 'where necessary'. For Ni-Pd this is not a small correction: pure Ni is ferromagnetic with TC around 631 K, inside the claimed 500-700 K stabilization window, and the magnetism of Ni_xPd_1-x is composition-dependent. The finite-temperature magnetic free energy of the alloy relative to the fcc elemental references is therefore T- and x-dependent and can be of order a few to tens of meV/atom in this window, comparable to or larger than the free-energy differences that determine the ΔG zero-crossings in Fig. 11. This term is not bounded by the JLP or phonon validation: Fig. 10(d) reports 0.64-3.14 meV/atom RMSE on vibrational free energies, but that validates the surrogate against a DFT calculation that also omits the finite-T magnetic contribution. Because the 0 K spin-polarized DFT energies already contain ground-state magnetism, the omission does not cancel in formation free energies. Without an estimate of F_mag(T,x), the quantitative claims of room-temperature metastability and of stability onset between 500 K and 700 K are not established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a complete machine-learning workflow for finite-temperature phase-stability and mechanical-property prediction in disordered alloys, using Ni-Pd as the prototype. A Jacobi-Legendre potential (JLP) with 873 linear parameters is fitted to 1,059 DFT calculations on 8-atom cells and strained elemental cells, then validated on 673 held-out 16-atom supercells, achieving energy RMSEs of about 1.9 meV/atom (unrelaxed) and 1.6 meV/atom (relaxed), and vibrational free-energy RMSEs from 0.64 meV/atom at 300 K to 3.14 meV/atom at 1500 K. The authors then enumerate all 99,268 symmetry-inequivalent configurations in 24-atom cells, relax each with the JLP, compute harmonic phonon free energies, and evaluate the canonical partition function with configurational plus vibrational contributions. From this they predict that the fcc solid solution is thermodynamically stable across the full composition range above a critical temperature between 500 K and 700 K, is metastable at room temperature, and becomes stable first at the Pd-rich end. They also compute heat capacities and thermally averaged elastic constants, and propose a scaling route to high-entropy alloys.","tokens_in":27242,"tokens_out":5027,"duration_ms":53051,"significance":"If the quantitative thermodynamic predictions are reliable, this is a significant advance: an 873-parameter linear JLP trained on small cells is shown to reproduce DFT-level energies, relaxed structures, and vibrational free energies on larger held-out cells, and it enables explicit enumeration of the configurational ensemble without invoking ideal-mixing entropy or a single SQS representative. The validation is solid and unusually complete for a machine-learning-potential paper: independent 16-atom test sets, structural parity checks, symmetry comparison after relaxation, and a large DFT phonon reference set. The finite-temperature stability prediction is concrete and falsifiable, and the throughput numbers (99,268 relaxations, 14.3 million force evaluations in 12 hours) make the proposed workflow attractive for multicomponent alloys. However, the central stability claim rests on approximations whose magnitudes are not bounded within the manuscript, most notably the neglect of finite-temperature magnetic free energy in a system with Ni-rich ferromagnetism.","major_comments":[{"comment":"The central finite-temperature stability claim neglects the magnetic free energy. Equations (15)-(17) include only configurational and harmonic vibrational contributions, and the text states that electronic and magnetic terms can be added 'where necessary'; for Ni-Pd they are necessary. Pure Ni has a Curie temperature around 631 K, inside the claimed 500-700 K stabilization window, and the magnetism of Ni_xPd_{1-x} is composition-dependent. The finite-temperature magnetic free energy of the alloy relative to the fcc elemental references is therefore T- and x-dependent and can plausibly be of order a few to tens of meV/atom in this window, which is comparable to the free-energy differences controlling the ΔG zero-crossings in Fig. 11. The vibrational free-energy validation in Fig. 10(d) does not bound this term, because the DFT phonon reference also omits the finite-T magnetic contribution; the ground-state magnetism already contained in the spin-polarized DFT energies does not cancel in formation free energies. Without an estimate or bound on F_mag(T,x), the quantitative claims of room-temperature metastability and of stability onset between 500 K and 700 K are not established.","section":"Section III E, Eqs. (15)-(17), Fig. 11"},{"comment":"The partition function is evaluated only for 24-atom supercells, and Appendix B shows that the maximum configurational entropy for this cell size is about 0.62 k_B/atom at equiatomic composition, roughly 10% below the ideal-mixing value of 0.693 k_B/atom, with comparable deficits at other compositions. Since the paper attributes the Ni-rich side of the stability onset to configurational entropy, this systematic finite-size entropy deficit can bias the predicted critical temperature; the 16-atom versus 24-atom comparison in Section III E shows a trend but not convergence. A quantitative finite-size correction, an extrapolation to larger cells, or an explicit error estimate on the resulting ΔG is needed to support the specific claim that the onset occurs between 500 K and 700 K rather than, for example, being shifted by the missing entropy.","section":"Section III E and Appendix B"},{"comment":"Equations (15)-(17) are evaluated at the 0 K equilibrium volume for all temperatures, with harmonic vibrations only, while the quasi-harmonic treatment in Section III H is applied to a representative configuration rather than to the full ensemble used for the phase-stability analysis. Thermal expansion and anharmonicity typically change vibrational free energies by several meV/atom at 600-700 K, which is again comparable to the ΔG differences in Fig. 11. The manuscript acknowledges these approximations, but it does not quantify how much they could shift the stability onset or the room-temperature metastability boundary; a bound from the QHA calculations, or at least from the volume dependence of the free energy at the relevant compositions, is needed before the quantitative central claim can be considered established.","section":"Section III E and Section III H"}],"minor_comments":[{"comment":"The reported stress units are dimensionally inconsistent: the text gives training and test stress RMSEs in 'eV/atom' and 'meV/atom', while stress is an energy per volume (eV/Å^3 or GPa), and the force units appear truncated as 'meV/'. Please standardize the units in the text and figure legends.","section":"Section III A, Fig. 6"},{"comment":"The text states that NiPd_3 has Eform ~ 1.5 eV/atom and is 'just below the stability line'; since the convex-hull boundary is at zero formation energy, this must be ~1.5 meV/atom (as also suggested by Fig. 9).","section":"Section III C"},{"comment":"The relaxation convergence criterion is reported as 'forces on each atom are less than 0.02 eV/atom', and later as 0.005 eV/Å; forces should be in eV/Å, and the two statements should be made consistent.","section":"Section II B"},{"comment":"'trail' should be 'trial' throughout the hyperparameter-optimization section and in the Fig. 5 caption.","section":"Fig. 5 and Section II D"},{"comment":"'one has to bare in mind' should read 'one has to bear in mind'.","section":"Section III I"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the journal's scope and the methodology is a natural application of the authors' previously published JLP formalism; I see no novelty-disclosure concern. The main risk to the published version is the magnetic free-energy omission, which is fixable by adding a bounded estimate (e.g., a simple mean-field or disordered-local-moment calculation) or by explicitly weakening the quantitative claims. The finite-size entropy and fixed-volume issues are also addressable with sensitivity estimates. If the authors provide such bounds, the paper would be a valuable contribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things you should know. First, this is a solid workflow paper: a compact linear Jacobi-Legendre potential, trained on 8-atom cells, generalizes cleanly to 16-atom cells (~1.9 meV/atom energy RMSE, 1.6 meV/atom after relaxation, 0.64–3.14 meV/atom on vibrational free energies) and is then pushed through 99,268 relaxations and 14 million force evaluations in 24-atom supercells. The throughput claim is real, and the per-configuration phonon treatment is a genuine step beyond SQS-plus-ideal-entropy. Second, the headline quantitative claim—stability onset between 500 and 700 K, room-temperature metastability—is not as robust as the framing suggests. The free energy omits finite-temperature magnetic contributions in a ferromagnetic system whose Ni end has TC ~631 K, inside the claimed window, and the 24-atom cell's configurational entropy is still ~10% below ideal mixing. Both omissions shift ΔG by a few to tens of meV/atom in the relevant temperature range, and neither is bounded by the validation, because the DFT reference also omits the finite-T magnetic term.\n\nThe new combination is exact enumeration of all symmetry-distinct configurations at finite T with per-configuration harmonic vibrations from an interpretable, linear potential. The JLP itself was published earlier, so the contribution is the workflow and the Ni-Pd prototype result. The paper is honest about many limitations: it discusses the fixed 0 K volume, tests QHA on a representative configuration, and openly reports the noisy shear elastic constants. The qualitative conclusion, complete miscibility with stability first at the Pd-rich end, is plausible and consistent with the known phase diagram.\n\nThe main soft spot is magnetism. Section III E explicitly defers electronic/magnetic terms to \"where necessary,\" but for Ni-Pd it is necessary to bound them. Spin-polarized DFT contains the ground-state magnetic energy, so the omission does not cancel in formation free energies. An approximate F_mag(T,x), even from a mean-field or effective-Hamiltonian estimate, would materially strengthen the central claim. Second, the 24-atom finite-size entropy shortfall is acknowledged but dismissed as minor; at 700 K the shortfall relative to ideal mixing is worth several meV/atom, so the dismissal is too quick. A simple extrapolation of configurational entropy to the thermodynamic limit would help. Third, no code, data, or trained model is released, which limits reproducibility and reuse.\n\nOverall, the paper deserves a serious referee. The workflow is valuable, the validation is honest, and the central claim is plausible but not fully established. I would send it to review and ask for the magnetic estimate, an entropy extrapolation, and a data release.","headline":"A useful high-throughput workflow for finite-T alloy thermodynamics whose headline Ni-Pd stability onset is underbounded by omission of magnetic free energy and finite-size entropy.","tokens_in":27879,"tokens_out":3485,"would_cite":true,"duration_ms":32752,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Fcc Ni-Pd is thermodynamically stable across the full composition range only above a critical temperature between 500 K and 700 K, and metastable at room temperature.","keywords":["machine learning potentials","disordered alloys","phase stability","finite-temperature thermodynamics","Ni-Pd","vibrational free energy","configurational entropy","elastic constants"],"falsifier":"Measure the heat capacity or the order-disorder transition of Ni-Pd alloys across the composition range by calorimetry or in situ diffraction: the predicted 500-700 K stability onset should appear as a composition-dependent feature, with Ni-rich compositions losing stability at higher temperatures than Pd-rich ones. A more direct computational falsifier is to repeat the free-energy sum in 32-atom or larger supercells, or with quasiharmonic volume relaxation and magnetic contributions, and check whether the room-temperature metastability and the roughly 600 K stabilization survive; the 24-atom cell's entropy deficit of about 10% corresponds to an energy scale of tens of meV/atom.","tokens_in":26719,"feed_emoji":"🌡️","tokens_out":10645,"duration_ms":88597,"temperature":0.7,"pith_summary":"This paper argues that a single compact machine-learned potential can settle a question normally reserved for much heavier computation: whether a disordered alloy is thermodynamically stable at a given temperature. Using Ni-Pd as a test case, it claims the fcc solid solution is metastable at room temperature and becomes stable only above roughly 600 K, with Pd-rich compositions stabilizing first. If true, finite-temperature phase stability does not have to be guessed from ideal-mixing entropy; the partition function can be built by explicitly enumerating every symmetry-distinct configuration, each carrying its own harmonic vibrations, at a cost low enough to be practical. The payoff would be a high-throughput route to phase diagrams and mechanical properties of multicomponent alloys, including high-entropy alloys.","feed_headline":"Ni-Pd alloys become thermodynamically stable above ~600 K","feed_subtitle":"A compact machine-learned potential maps finite-temperature alloy stability by summing nearly 100,000 configurations with vibrations.","key_machinery":"The load-bearing object is the Jacobi-Legendre potential (JLP), a cluster expansion truncated at three-body order in which pair terms use Jacobi polynomials and angular terms use Legendre polynomials; the model is linear in its coefficients, so training is a regression and inference is very fast. The thermodynamic machinery is the coarse-grained partition function $Z_\\alpha(\\{x_i\\},T)=\\sum_\\sigma \\exp[-(E_\\alpha(\\sigma)+F^{\\rm vib}_\\alpha(\\sigma,T))/k_B T]$, which replaces ideal-mixing entropy with an explicit sum over all symmetry-distinct configurations, each weighted by its own harmonic vibrational free energy. The 24-atom enumeration supplies the exact configurational entropy of that finite system, up to about 10% below the ideal-mixing limit at equiatomic composition; systematic comparisons at fixed supercell size keep composition trends meaningful.","core_discovery":"The central discovery is that fcc Ni-Pd, while fully miscible when quenched from the melt, is thermodynamically metastable at room temperature and becomes stable only above a critical temperature between 500 K and 700 K, with stability appearing first on the Pd-rich side. This is established by training a Jacobi-Legendre polynomial cluster-expansion potential with 873 parameters on density-functional-theory data from 8-atom cells, then using it to relax all 99,268 symmetry-distinct configurations of a 24-atom supercell and adding each configuration's harmonic vibrational free energy to form the partition function. The resulting Gibbs free energy of formation matches DFT where the comparison is made, and the explicit enumeration gives the exact configurational entropy for the finite supercell instead of the ideal-mixing approximation. The same potential also reproduces relaxed geometries and gives elastic constants within about 10% of DFT, while entropy and heat-capacity curves reveal competition between the solid solution and long-period L1$_0$ ordered forms of NiPd and NiPd$_3$.","pith_inferences":["Editorial inference: the same explicit-enumeration pipeline could resolve whether other 'fully miscible' binaries are in fact metastable at room temperature; the Ni-Pd result suggests that many experimentally known solid solutions may be entropy-stabilized rather than ground-state alloys.","Editorial inference: the claim that stability begins at the Pd-rich end is testable by calorimetry or diffraction across several compositions; one should see the first loss of thermodynamic stability on cooling at the Ni-rich side.","Editorial inference: scaling the model to ternary and quaternary alloys multiplies the number of clusters by about 2.7 and 5.6, but the real bottleneck is the combinatorial growth of distinct supercell configurations, so subcell sampling or active learning will be needed before the method reaches high-entropy alloys.","Editorial inference: the paper's fixed-volume harmonic treatment leaves out magnetic and anharmonic free energies; for a magnetic element like Ni those terms could plausibly move the 600 K onset, and comparing the predicted heat-capacity peaks with measured calorimetry would settle the size of the correction."],"forward_implications":["Above roughly 600 K, quenching Ni-Pd from the melt should produce a thermodynamically stable fcc solid solution across the whole composition range, while at room temperature the solution is metastable with respect to ordered intermetallic phases.","Because the stability onset is composition-dependent, Pd-rich alloys should remain stable at lower temperatures than Ni-rich ones; experiments probing phase stability as a function of composition can test this asymmetry directly.","Vibrations shift the order-disorder transition down: the heat-capacity peak moves from about 700 K to 500 K at 75% Pd and from about 350 K to 250 K at 50% Pd, so ignoring vibrational free energy would overestimate transition temperatures by up to roughly 30%.","The configurational entropy of a 24-atom cell falls about 10% short of the ideal-mixing value at equiatomic composition, so the predicted 500-700 K stability window is likely to shift slightly when larger supercells are used.","Configuration-averaged elastic constants change sharply near the configurational transition temperatures, coupling mechanical response to the same entropy-driven stability physics."],"supporting_citations":[{"why":"Supplies the Jacobi-Legendre cluster-expansion formalism from which the potential is built.","marker":"[39]"},{"why":"Provides the configurational-plus-vibrational free-energy framework and notation used for phase stability.","marker":"[17]"},{"why":"Experimental Ni-Pd phase diagram and lattice constants used as reference for miscibility and melting range.","marker":"[41]"},{"why":"Justifies the coarse-grained partition function combining static and vibrational free energies and quantifies vibrational effects on transition temperatures.","marker":"[64]"},{"why":"Tree-search algorithm generating all symmetry-distinct site-occupancy configurations and their multiplicities for the 16- and 24-atom supercells.","marker":"[43]"},{"why":"Finite-displacement phonon method used to obtain vibrational free energies for every configuration.","marker":"[51]"},{"why":"Special quasirandom structure approach that this explicit-enumeration method aims to surpass.","marker":"[8]"},{"why":"Configurational-entropy density-of-states approach contrasted with the ideal-mixing approximation.","marker":"[16]"}],"fun_headline_variants":["Ni-Pd fcc: metastable at 300 K, stable at 600 K","Machine-learned potential predicts Ni-Pd stability threshold","Exact entropy: key to Ni-Pd finite-temperature stability","Ni-Pd transitions to stable fcc above 600 K","Compact ML model maps Ni-Pd alloy free energy"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing bet is that a tiny 24-atom sample of alloy, vibrating harmonically at its zero-temperature size and ignoring magnetism and volume changes, faithfully represents what the real, macroscopic alloy does; if those ignored effects shift the energy balance by more than a few tens of meV per atom, the predicted 500-700 K stability window could move or disappear.","fun_headline_variants_meta":{"raw":{"variants":["Ni-Pd fcc: metastable at 300 K, stable at 600 K","Machine-learned potential predicts Ni-Pd stability threshold","Exact entropy: key to Ni-Pd finite-temperature stability","Ni-Pd transitions to stable fcc above 600 K","Compact ML model maps Ni-Pd alloy free energy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000289,"raw_usage":{"total_tokens":1724,"prompt_tokens":1009,"completion_tokens":715,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":625,"completion_tokens_details":{"reasoning_tokens":627}},"tokens_in":625,"tokens_out":715,"duration_ms":7051,"temperature":1.0,"reasoning_tokens":627,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T14:20:23.804307+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the heat capacity or the order-disorder transition of Ni-Pd alloys across the composition range by calorimetry or in situ diffraction: the predicted 500-700 K stability onset should appear as a composition-dependent feature, with Ni-rich compositions losing stability at higher temperatures than Pd-rich ones. A more direct computational falsifier is to repeat the free-energy sum in 32-atom or larger supercells, or with quasiharmonic volume relaxation and magnetic contributions, and check whether the room-temperature metastability and the roughly 600 K stabilization survive; the 24-atom cell's entropy deficit of about 10% corresponds to an energy scale of tens of meV/atom.","supporting_citations":[{"cited_title":"Shapeev, Aidan P","cited_arxiv_id":null,"evidence_quote":"Supplies the Jacobi-Legendre cluster-expansion formalism from which the potential is built."},{"cited_title":"281, 120415 (2024)","cited_arxiv_id":null,"evidence_quote":"Provides the configurational-plus-vibrational free-energy framework and notation used for phase stability."},{"cited_title":"Domina and S","cited_arxiv_id":null,"evidence_quote":"Experimental Ni-Pd phase diagram and lattice constants used as reference for miscibility and melting range."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Justifies the coarse-grained partition function combining static and vibrational free energies and quantifies vibrational effects on transition temperatures."},{"cited_title":"Castelli, Rune Christensen, Marcin Dułak, Jesper Friis, Michael N","cited_arxiv_id":null,"evidence_quote":"Tree-search algorithm generating all symmetry-distinct site-occupancy configurations and their multiplicities for the 16- and 24-atom supercells."},{"cited_title":"Kresse and D","cited_arxiv_id":null,"evidence_quote":"Finite-displacement phonon method used to obtain vibrational free energies for every configuration."},{"cited_title":"Wei, L.G","cited_arxiv_id":null,"evidence_quote":"Special quasirandom structure approach that this explicit-enumeration method aims to surpass."},{"cited_title":"255, 119031 (2023)","cited_arxiv_id":null,"evidence_quote":"Configurational-entropy density-of-states approach contrasted with the ideal-mixing approximation."}],"review_version":1}