{"id":"976ace80-730e-4fad-9f36-e1c22226efd8","arxiv_id":"1908.02654","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Thermodynamic calculations predict strong preferential oxidation in refractory high entropy alloys and carbides, driven by differences in oxide stability, with the effect weaker in carbides.","lead":"This paper predicts which metal in a multi-metal alloy will oxidize first at high temperatures, showing that the metal with the most stable oxide dominates the scale even when the oxide stabilities are close. The work offers a design rule for choosing oxidation-resistant high-entropy alloys and ceramics.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Multicomponent predictions rely on constraining the oxide solution activity to unity, which forces coexistence of oxides that an unconstrained minimization would reduce; recomputing Tables 1–2 without this constraint is the decisive check.","rationale":"The reader correctly identified the Section 2.2 activity-unity constraint as the weakest link, and my reading agrees. The paper is honest about the approximation and explicitly says the unconstrained minimization collapses to HfO2, which reveals that the mixed-oxide compositions in the multicomponent tables are products of an imposed coexistence condition. That condition is not a standard thermodynamic model for a solution phase, so the quantitative outputs are not yet established as true equilibrium predictions. The qualitative preferential-oxidation claim is well supported by the analytical binary results and by the unconstrained limiting behavior, so the verdict should remain CONDITIONAL rather than REJECT: the theoretical tendency is credible, but the specific multicomponent scale compositions and depletion profiles need a constraint-free check before they can be accepted quantitatively. The paper also honestly defers to the companion experimental paper, and the ideal-versus-real comparison in Table 3 is a step in the right direction, though it does not cover the cases where the constraint is most consequential.","tokens_in":13226,"tokens_out":9183,"duration_ms":110515,"concrete_test":"Recompute the ternary and quinary equilibria behind Tables 1 and 2 with no activity-unity constraint, defining the oxide scale as a genuine multi-component solution phase with composition-dependent activities (e.g., FTOxid database or published binary interaction parameters) and performing an unconstrained free-energy minimization. Compare the resulting oxide mole fractions and alloy depletion with Tables 1 and 2; if the unconstrained scale is essentially pure HfO2 or the compositions shift substantially, the quantitative central claim is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing assumption is in Section 2.2: the oxide solution phase was given an activity constrained to unity, and the authors state that without this constraint the minimization would produce only HfO2, with the other oxides reduced by Hf. This constraint is what allows Tables 1 and 2 to report mixed-oxide scales (e.g., 35.9% HfO2, 35.9% ZrO2, 4.05% TiO2 in Table 2) and the corresponding depletion patterns. The analytical binary treatment in Section 2.1 is different: it gives each oxide a composition-dependent activity equal to its mole fraction, so the Hf–Zr result of 2.4% ZrO2 is a genuine ideal-solution equilibrium. The FactSage ternary and quinary calculations, by contrast, are constrained equilibria rather than free minima of a real solution phase. The central qualitative claim that the most stable oxides form preferentially is actually reinforced by the unconstrained result, which is essentially pure HfO2, so the concern is not about the existence of preferential oxidation. The concern is about the quantitative scale compositions and the inference that the scale is a solid solution whose composition is set by relative oxide stabilities. The paper's one ideal-versus-real test (Table 3, Zr–Ti at 1773 K) does not probe the multi-component cases where the activity constraint matters most.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a thermodynamic framework for predicting preferential oxidation in refractory high-entropy alloys and carbides. It combines an analytical equilibrium-constant approach for binary systems (composition balance diagrams) with FactSage free-energy minimization for ternary and quinary systems, assuming ideal solution thermodynamics for both substrate and oxide. The central claims are that a large tendency toward preferential oxidation exists even when oxide stabilities are similar, that the effect is reduced in carbides relative to alloys, and that preferential depletion can destabilize the substrate by reducing configurational entropy. The paper is Part I of a two-part study, with the companion experimental part referenced but not included.","tokens_in":13483,"tokens_out":8325,"duration_ms":87486,"significance":"If the quantitative predictions were reliable, the paper would provide a useful design tool for refractory high-entropy materials and a thermodynamic rationale for experimentally observed preferential oxidation. The analytical treatment of binary systems, such as the Hf-Zr composition balance diagram, is clean and derives directly from tabulated thermodynamic data with no fitted parameters. The paper also makes its assumptions explicit, which is commendable. However, the multicomponent free-energy calculations rely on an ad hoc constraint on oxide activity, and the validation against real solution data covers only a binary case. The qualitative conclusion that the most stable oxides form preferentially is likely robust and consistent with the binary analysis, but the quantitative multicomponent predictions are not on the same footing and require substantial caveats.","major_comments":[{"comment":"The central quantitative predictions for the ternary and quinary alloys are generated under the constraint that the activity of the oxide solution phase is unity. As the authors state, without this constraint the free-energy minimization would yield only HfO2, with the other oxides reduced by Hf. This means that the mixed-oxide compositions in Tables 1 and 2 (e.g., 35.9% HfO2 and 35.9% ZrO2 in Table 2) are not free-energy minima of the modeled system; they are imposed by the constraint. Consequently, the paper's claim that the oxide scale composition is set by relative oxide stabilities rather than by the substrate composition is not established for multicomponent systems by these calculations. To make the quantitative predictions defensible, the authors should either use a real thermodynamic solution model for the multicomponent oxide phase that allows coexistence without constraint, or explicitly present Tables 1 and 2 as constrained metastable coexistence calculations and justify the constraint on physical grounds (e.g., kinetic inhibition of the reduction of pre-formed oxide layers).","section":"2.2, Tables 1 and 2"},{"comment":"The validation of the ideal-solution approximation against real oxide solution data is limited to the binary Zr-Ti system, where the activity constraint is not needed because the equilibrium is governed by the composition-dependent activity of a single oxide solution phase. This case does not test the multicomponent calculations in Tables 1 and 2, where the activity constraint is the key modeling choice. Therefore, the statement in Section 4.3 that 'this approach can sufficiently predict the extent of preferential oxidation in refractory materials' is not supported by the evidence presented. The authors should either provide a multicomponent case with a real solution database (e.g., the HfO2-ZrO2-TiO2 ternary) or temper this conclusion to reflect the limited validation.","section":"3.4, Table 3 and Section 4.3"},{"comment":"The prediction that preferential oxidation is reduced in carbides relative to alloys is presented for the TiC-TaC system with the partial pressure of CO fixed at 1 atm. In an actual oxidation process, pCO is an output of the reaction and is determined by the carbon activity in the carbide, the oxygen partial pressure, and the thermal conditions. The quantitative extent of the reduction in preferential oxidation therefore depends on this freely chosen parameter. The authors should either determine pCO self-consistently from the equilibrium conditions or provide a sensitivity analysis over a plausible range of pCO values to demonstrate that the qualitative conclusion holds. As presented, the carbide-specific numbers are conditional on an arbitrary choice.","section":"3.2, Figure 6"}],"minor_comments":[{"comment":"The sentence 'The activity of the oxide solution phase was constrained to be unity' is ambiguous. It should be clarified whether the activity of each end-member component is set to 1, or whether the phase itself is treated as a pure phase of fixed composition. This clarification is important because the interpretation of the minimization results depends on it.","section":"2.2"},{"comment":"The y-axis is described as 'set arbitrarily to display the slopes of the tie lines,' but the axis is not labeled in the figure. Please add a label such as 'Tie-line slope (arbitrary units)' to avoid confusion.","section":"Figure 2 caption"},{"comment":"The basis for the output mol% is unclear for the combined 'Ti sub-oxides (TiO, Ti2O3)' entry. State whether the percentages are on a mole-of-cations basis or a mole-of-oxide-formula-units basis, and verify that the cation mass balance between the oxide and the depleted alloy is satisfied for all elements.","section":"Table 2"},{"comment":"The equilibrium constant expression includes pCO as a dimensional quantity. It should be normalized by the standard-state pressure (e.g., pCO/1 atm) so that the equilibrium constant is dimensionless.","section":"Equation (15)"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper you'd want to know about: Backman et al. give the HEA oxidation community a practical way to anticipate which elements will be preferentially oxidized, using Gaskell composition balance diagrams plus FactSage free energy minimization. The cleanest new result is that even small differences in oxide stability (e.g., HfO2 vs ZrO2) produce strong preferential oxidation, and that carbide reactants reduce this tendency compared to metals because CO formation changes the energetics. That is a useful design rule, and the analytical part is reproducible from standard thermodynamic data.\n\nThe paper does several things well. It is explicit about its assumptions—ideal solutions, neglect of oxygen solubility, solid-state phases. The binary analytical treatment in Section 2.1 is a genuine ideal-solution equilibrium, with each oxide's activity set by its mole fraction. The comparison of ideal vs real oxide data in Table 3 is a sensible check, and the paper doesn't oversell it. The citation pattern is fine; the self-citation [13] is prior thermodynamic assessment, not a hidden prop.\n\nThe soft spot is real, and the authors themselves disclose it: Section 2.2 states that the oxide solution phase activity was constrained to unity, and that without this constraint the minimization would yield essentially pure HfO2. That means Tables 1 and 2 are not free minima of an ideal solution; they are constrained equilibria that force coexistence of multiple oxide components. The consequence is that the specific percentages (e.g., 35.9% HfO2, 35.9% ZrO2, 4% TiO2) and the associated substrate depletion numbers should be read as illustrative of what happens if a mixed scale is forced to exist, not as predictions of what nature will actually form. The central qualitative point—that the most stable oxides dominate and the substrate is depleted—is actually reinforced by the unconstrained result, so the paper's main message survives. But the quantitative machinery for the multicomponent cases is weaker than the paper's framing suggests.\n\nThe Table 3 ideal-vs-real test doesn't probe the multicomponent constrained cases; it's a binary case where the constraint isn't needed. And the pCO=1 choice in the carbide diagrams, while reasonable, is an input assumption. None of this is disqualifying—the paper is honest and the limitations are stated in the text.\n\nWho is this for? Researchers designing refractory HEAs and carbides for high-temperature oxidation resistance, and experimentalists who want a thermodynamic frame for interpreting scales. It deserves a serious referee, and the companion experimental paper should be read alongside it. My own take: treat the binary diagrams as solid predictions; treat the ternary/quinary tables as hypotheses to be tested, with the activity constraint flagged clearly.\n\nRecommendation: send to peer review, but ask the authors to recompute Tables 1–2 without the activity constraint, or at minimum to present the unconstrained result alongside the constrained one.\n\nBest,","headline":"Useful thermodynamic framework for preferential oxidation in refractory HEAs, but the multicomponent numbers come from a constrained equilibrium rather than a free minimum—qualitative story solid, quantitative tables need caveats.","tokens_in":13973,"tokens_out":2541,"would_cite":true,"duration_ms":27408,"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 predicts that oxidation of refractory high-entropy alloys and carbides selectively removes the elements whose oxides are most thermodynamically stable, so the oxide scale composition is set by oxide stabilities rather than the…","keywords":["high temperature oxidation","preferential oxidation","refractory high entropy alloys","high entropy carbides","thermodynamic modeling","free energy minimization","composition balance diagrams","ultra-high temperature ceramics"],"falsifier":"Oxidize an equimolar Hf-Zr-Ti alloy at 1773 K and measure the cation fractions in the scale: the paper predicts a HfO2-ZrO2 scale with only about 0.005 mol% TiO2 and strong Hf depletion in the alloy beneath the scale. Finding a TiO2-rich scale, or substantial Ta and Nb oxides in the quinary Hf-Zr-Ti-Ta-Nb case, would falsify the claim.","tokens_in":13021,"feed_emoji":"🔥","tokens_out":7518,"duration_ms":74413,"temperature":0.7,"pith_summary":"Refractory high-entropy alloys and ceramics are candidate materials for extreme-temperature service, but their oxidation behavior has been poorly mapped. This paper argues that the dominant thermodynamic driver is the large spread in the stabilities of the constituent oxides: even elements in the same periodic group, whose oxide free energies differ by only tens of kilojoules per mole, should oxidize very selectively. The calculations quantify that selectivity for binary, ternary, and five-component alloys and for carbide analogs, and show that the effect weakens when the starting material is a carbide. A sympathetic reader would care because preferential oxidation changes the scale composition and depletes the substrate, which can destroy the solid solution that gives these materials their properties.","feed_headline":"Oxide stabilities, not alloy mix, set scale chemistry","feed_subtitle":"Even small stability gaps drive selective oxidation and deplete the underlying alloy.","key_machinery":"Composition balance diagrams built from exchange reactions such as $\\mathrm{Hf} + \\mathrm{ZrO_2} \\leftrightarrow \\mathrm{HfO_2} + \\mathrm{Zr}$, with the ideal-solution equilibrium constant $K = [X_{\\mathrm{HfO_2}}][X_{\\mathrm{Zr}}]/[X_{\\mathrm{ZrO_2}}][X_{\\mathrm{Hf}}]$. Each tie line connects an alloy composition to the oxide composition and oxygen partial pressure that coexist with it. The second tool is free-energy minimization treating substrate and oxide scale as ideal solid solutions; the oxide solution activity is constrained to unity, forcing all oxide constituents to coexist rather than letting the most stable oxide reduce the others. Together these yield quantitative oxide compositions, substrate depletions, and interfacial oxygen partial pressures.","core_discovery":"On the paper's own terms, the central discovery is that thermodynamic driving forces alone set the oxide scale composition of refractory high-entropy materials. At 2073 K, a 50-50 Hf-Zr alloy is predicted to form an oxide scale containing only about 2.4 mol% ZrO2 even though HfO2 and ZrO2 stabilities differ by only about 64 kJ per mole of O2; at 1773 K, a Ti-Ta alloy of any composition forms almost pure TiO2 until Ti is depleted, and a Ta-Mo alloy forms almost pure Ta2O5. For the equimolar quinary Hf-Zr-Ti-Ta-Nb alloy, free energy minimization predicts a scale composed almost entirely of HfO2, ZrO2, and Ti suboxides, with Ta2O5 and Nb2O5 below about 1 mol%, and corresponding Hf, Zr, and Ti depletion in the alloy. The same calculations for carbides place the oxide composition closer to the substrate composition, because CO formation raises the oxygen potential and compresses the free-energy differences. The paper also shows that configurational entropy, the usual rationale for high-entropy stability, is far too small to offset these driving forces.","pith_inferences":["If the predictions hold, alloy design can rank oxidation behavior from periodic-table positions alone: group IV elements will be consumed first, and oxidation resistance may be engineered by controlling the abundance of the most stable oxide formers.","The same exchange-equilibrium logic should extend to borides and silicides, where the gaseous or liquid oxidation products differ; carbides and alloys give two bounding cases, with borides falling between them.","A direct test is to grow a scale on a Hf-Zr binary at 2073 K and check the predicted 2.4% ZrO2 equilibrium composition, or to track the interfacial oxygen partial pressure, which the diagrams predict quantitatively.","Real non-ideality in oxide solutions may shift the numerical compositions, but because the driving-force differences are so large compared with typical excess energies, the qualitative hierarchy of stable-oxide formers enriched in the scale and depleted in the substrate should survive."],"forward_implications":["For a 50-50 Hf-Zr alloy at 2073 K, the equilibrium scale should be about 97.6% HfO2 and only about 2.4% ZrO2, so a Hf-depleted zone forms beneath the scale.","In an equimolar Hf-Zr-Ti-Ta-Nb alloy, the scale should consist almost entirely of group IV oxides and Ti suboxides, with Ta and Nb oxides below about 1 mol%, and the alloy should be depleted in Hf, Zr, and Ti.","The substrate's configurational entropy drops by roughly 60% in the oxidation-affected zone in the quinary case, from 13.4 to 5.8 J/mol·K, which can destabilize the solid solution and form secondary phases such as Ta2C or Nb2C.","Carbide analogs should show less preferential oxidation than the corresponding alloys, so alloy and carbide behavior bracket what might be expected for borides and other high-entropy ceramics.","Because the effect is thermodynamic, it should appear in the early stages of oxidation and at the oxide-alloy interface regardless of slower kinetic limitations."],"supporting_citations":[{"why":"Supplies the equilibrium-constant method for metal-oxide exchange reactions used to build the composition balance diagrams.","marker":"[15]"},{"why":"Supplies the FactSage free-energy minimization software and thermodynamic databases used for the multicomponent calculations.","marker":"[16]"},{"why":"Provides the prior thermodynamic assessment and the free energies of formation for the group IV, V, and VI oxides used throughout the paper.","marker":"[13]"},{"why":"Reports experimental preferential oxidation in refractory complex concentrated alloys consistent with the thermodynamic ordering predicted here.","marker":"[11]"},{"why":"First-principles surface oxidation study that observed preferential oxidation consistent with the thermodynamic favorability ranking.","marker":"[14]"},{"why":"Experimental Ti-Ta oxidation study showing a TiO2 scale with Ta enrichment near the interface, used to support the composition balance diagram predictions.","marker":"[33]"},{"why":"Provides Ta2O5-TiO2 solid solubility data that mark the real-system solubility regions on the composition balance diagrams.","marker":"[29]"},{"why":"Supports the role of configurational entropy in stabilizing solid solutions, the basis for the predicted destabilization after selective depletion.","marker":"[35]"}],"fun_headline_variants":["Even tiny stability gaps trigger selective oxidation in high-entropy alloys","Oxide scale composition is set by thermodynamics, not entropy","Carbides resist preferential oxidation better than alloys","Small stability gaps drive big oxide selectivity in refractory alloys"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculations assume the oxide scale is an ideal mixture whose components are all forced to coexist; if real oxide mixing is imperfect, or if the most stable oxide reduces the others, the predicted compositions change.","fun_headline_variants_meta":{"raw":{"variants":["Even tiny stability gaps trigger selective oxidation in high-entropy alloys","Oxide scale composition is set by thermodynamics, not entropy","Carbides resist preferential oxidation better than alloys","Small stability gaps drive big oxide selectivity in refractory alloys"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000728,"raw_usage":{"total_tokens":3282,"prompt_tokens":989,"completion_tokens":2293,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":605,"completion_tokens_details":{"reasoning_tokens":2229}},"tokens_in":605,"tokens_out":2293,"duration_ms":17857,"temperature":1.0,"reasoning_tokens":2229,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:37:58.979401+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Oxidize an equimolar Hf-Zr-Ti alloy at 1773 K and measure the cation fractions in the scale: the paper predicts a HfO2-ZrO2 scale with only about 0.005 mol% TiO2 and strong Hf depletion in the alloy beneath the scale. Finding a TiO2-rich scale, or substantial Ta and Nb oxides in the quinary Hf-Zr-Ti-Ta-Nb case, would falsify the claim.","supporting_citations":[{"cited_title":"Gaskell, D.E","cited_arxiv_id":null,"evidence_quote":"Supplies the equilibrium-constant method for metal-oxide exchange reactions used to build the composition balance diagrams."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the FactSage free-energy minimization software and thermodynamic databases used for the multicomponent calculations."},{"cited_title":"Backman, E.J","cited_arxiv_id":null,"evidence_quote":"Provides the prior thermodynamic assessment and the free energies of formation for the group IV, V, and VI oxides used throughout the paper."},{"cited_title":"Butler, K.J","cited_arxiv_id":null,"evidence_quote":"Reports experimental preferential oxidation in refractory complex concentrated alloys consistent with the thermodynamic ordering predicted here."},{"cited_title":"Osei-Agyemang, G","cited_arxiv_id":null,"evidence_quote":"First-principles surface oxidation study that observed preferential oxidation consistent with the thermodynamic favorability ranking."},{"cited_title":"Park, D.P","cited_arxiv_id":null,"evidence_quote":"Experimental Ti-Ta oxidation study showing a TiO2 scale with Ta enrichment near the interface, used to support the composition balance diagram predictions."},{"cited_title":"Waring, Effect of Oxide Additions on the Polymorphism of Tantalum Pentoxide (System Ta2O5-TiO2), (1968)","cited_arxiv_id":null,"evidence_quote":"Provides Ta2O5-TiO2 solid solubility data that mark the real-system solubility regions on the composition balance diagrams."}],"review_version":1}