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REVIEW 3 major objections 4 minor 38 references

Part I: Theoretical Predictions of Preferential Oxidation in Refractory High Entropy Materials

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Pith's one-line read 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…

desk verdict 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. read the letter →

arxiv 1908.02654 v2 pith:MFNLUM5B submitted 2019-08-07 cond-mat.mtrl-sci

Lavina Backman , Joshua Gild , Jian Luo , Elizabeth J. Opila This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords hightemperatureoxidationpreferentialrefractoryentropyalloyscarbidesthermodynamicmodelingfreeenergyminimizationcompositionbalancediagramsultra-highceramics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

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.

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 (3)
  1. [2.2, Tables 1 and 2] 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).
  2. [3.4, Table 3 and Section 4.3] 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.
  3. [3.2, Figure 6] 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.
minor comments (4)
  1. [2.2] 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.
  2. [Figure 2 caption] 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.
  3. [Table 2] 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.
  4. [Equation (15)] 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.

Circularity Check

1 steps flagged · score 6.0 of 10

Multicomponent scale predictions are conditional on an activity-unity constraint that forces coexistence of the input oxides; without that constraint the minimization returns only HfO2.

  1. self definitional [Section 2.2 (Methodology: Free Energy Minimization Calculations), affecting Tables 1-2 and Discussion 4.2]
    "The activity of the oxide solution phase was constrained to be unity. This approximation imposed the coexistence of, for instance, a rutile Ti oxide constituent in solution with the tetragonal Hf and Zr oxides; without this constraint, the free energy minimization calculations would have resulted in the most stable product phase being HfO2, i.e., HfO2 as having an activity of one, and the other oxide phases as having been reduced by Hf."

    Tables 1 and 2 present mixed-oxide scale compositions, e.g. 65.6% HfO2, 34.4% ZrO2 and 4.70e-3% TiO2 for the ternary alloy, as outputs of free-energy minimization. However, the minimization is run with the activity of every oxide constituent constrained to unity, which the paper states 'imposed the coexistence' of the input oxide phases. The paper itself admits that without this constraint the calculation would yield only HfO2, with the other oxides reduced by Hf. Therefore the qualitative prediction that the scale is a multicomponent oxide mixture containing the input oxides is not derived from the free-energy surface; it is built into the calculation as a constraint.

full rationale

The paper is not fitted to its own output: the analytical binary composition balance diagrams (Section 2.1, Figures 2-6) follow from standard equilibrium constants with tabulated FactSage data, and the Hf-Zr analytical result (2.4% ZrO2 from a 50-50 alloy) is a genuine ideal-solution equilibrium. Figure 1 and Figure 7 are adapted from the authors' prior assessment [13], but that assessment is itself based on independent database thermodynamic values, so the self-citation is not load-bearing in a circular way. The central claim that large thermodynamic differences favor preferential oxidation is robust and is even reinforced by the paper's own admission that unconstrained minimization would give essentially pure HfO2; it also has independent experimental support cited in the introduction. The circular element is confined to the quantitative multicomponent free-energy-minimization results in Tables 1 and 2. Section 2.2 explicitly imposes an activity-unity constraint that forces the coexistence of the input oxide constituents, and the paper states that removing this constraint gives only HfO2. Hence the predicted mixed-oxide scale compositions are conditional on an imposed assumption rather than being derived from an unconstrained free-energy minimum. The one ideal-versus-real test in Table 3 (Zr-Ti at 1773 K) is a genuine check but does not probe the multicomponent cases where the activity constraint is most influential. Overall, this is partial circularity: the qualitative preferential-oxidation prediction is independent, while the specific multicomponent scale compositions reduce by construction to the coexistence constraint.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

No free parameters are fitted to data; all numbers come from the FactSage thermodynamic database and the chosen ideal solution model. The one manually fixed value is pCO = 1 atm for the carbide case. The main assumptions are ideal solution mixing, the activity-unity constraint on the oxide solution, local equilibrium, and neglect of oxygen solubility. There are no newly invented physical entities.

free parameters (1)
  • pCO (partial pressure of CO) = 1 atm
    Fixed to simplify the TiC-TaC composition balance diagram (Section 3.2); the equilibrium constant depends on pCO^1/7, so the diagram shifts with this choice.
assumptions (6)
  • domain assumption Ideal solution behavior for alloy and oxide solid solutions (activity coefficients equal to unity).
    Used in the analytical approach (Section 2.1, Equation 12) and in FactSage calculations (Section 2.2). Real alloys and oxides may have non-ideal mixing.
  • ad hoc to paper The oxide solution phase activity is constrained to unity.
    Introduced in Section 2.2 so that multiple oxide constituents coexist in the scale; without it the minimization produces only HfO2.
  • domain assumption Local equilibrium at the oxide-substrate interface controls the oxide composition.
    Section 2.2 says results reflect the local equilibrium near the interface; oxidation kinetics are ignored.
  • domain assumption Oxygen solubility in the metallic alloy and carbide lattice is negligible.
    Section 2.1 explicitly states oxygen solubility, which can be up to 30 at.% in Ti-O, is not considered.
  • domain assumption Vibrational entropy changes from mixing are negligible compared to configurational entropy.
    Section 1 states this assumption, drawing on prior HEA analysis.
  • domain assumption Thermodynamic data from FactSage databases are accurate for the pure substances and real oxide solutions used.
    All quantitative results rely on these databases (Section 2.2).

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Cite this review

Pith. "Pith review of Part I: Theoretical Predictions of Preferential Oxidation in Refractory High Entropy Materials." pith.science (2026). https://pith.science/paper/MFNLUM5B

@misc{pith2026190802654,
  author       = {Pith},
  title        = {Pith review of: Part I: Theoretical Predictions of Preferential Oxidation in Refractory High Entropy Materials},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MFNLUM5B}},
  note         = {Machine review of arXiv:1908.02654}
}
read the original abstract

High entropy materials, which include high entropy alloys, carbides, and borides, are a topic of substantial research interest due to the possibility of a large number of new material compositions that could fill gaps in application needs. There is a current need for materials exhibiting high temperature stability, particularly oxidation resistance. A systematic understanding of the oxidation behavior in high entropy materials is therefore required. Prior work notes large differences in the thermodynamic favorability between oxides formed upon oxidation of high entropy materials. This work uses both analytical and computational thermodynamic approaches to investigate and quantify the effects of this large variation and the resulting potential for preferential component oxidation in refractory high entropy materials including group IV-, V- and VI-element based alloys and ceramics. Thermodynamic calculations show that a large tendency towards preferential oxidation is expected in these materials, even for elements whose oxides exhibit a small difference in thermodynamic favorability. The effect is reduced in carbides, compared to their alloy counterparts. Further, preferential oxidation in high entropy refractory materials could result in possible destabilization of the solid solution or formation of other, competing phases, with corresponding changes in bulk material properties.

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