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arxiv: 2403.00705 · v2 · submitted 2024-03-01 · ❄️ cond-mat.mtrl-sci

Temperature-dependent thermodynamic properties of CrNbO4 and CrTaO4 by first-principles calculations

Shuang Lin , Shun-Li Shang , Allison M. Beese , Zi-Kui Liu This is my paper

Pith reviewed 2026-05-24 03:08 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords CrNbO4CrTaO4thermodynamic stabilityDFTquasiharmonic phonondecomposition temperaturethermal expansionrefractory alloys
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The pith

First-principles calculations find CrNbO4 and CrTaO4 thermodynamically stable up to 1706 K and 1926 K before decomposing.

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

The paper applies density functional theory with the PBE+U method and the quasiharmonic phonon approach to compute temperature-dependent thermodynamic properties of CrNbO4, CrTaO4, and related binary oxides. It merges the resulting formation energies with the SGTE SSUB5 database to locate the upper temperature limits of stability. The calculations also yield thermal expansion coefficients consistent with experiments and indicate lower chromium volatilization when these compounds form.

Core claim

By combining the formation energy predicted by DFT with the existing SGTE Substances Database (SSUB5), the CrNbO4 and CrTaO4 are found to be thermodynamic stable up to 1706 K and 1926 K and decompose into Cr2O3 and Nb2O5 or Ta2O5 at those temperatures, respectively.

What carries the argument

Quasiharmonic phonon approach combined with PBE+U density functional theory calculations to obtain formation energies and thermodynamic properties.

Load-bearing premise

Merging DFT formation energies with the SSUB5 database accurately determines the decomposition temperatures without large errors from neglected anharmonic effects, magnetic entropy, or database inconsistencies.

What would settle it

Experimental measurement of the actual decomposition temperatures of CrNbO4 and CrTaO4 under controlled conditions to check agreement with the predicted 1706 K and 1926 K values.

read the original abstract

In the present work, the density functional theory (DFT) in the generalized-gradient approximation developed by Perdew, Burke, and Ernzerhof (PBE) +U method, i.e., PBE+U, was employed to predict temperature-dependent thermodynamic properties of the rutile-type oxides CrNbO4 and CrTaO4 as well as the binary oxides Cr2O3, Nb2O5, and Ta2O5 via the quasiharmonic phonon approach (QHA). Calculated thermodynamic properties of the binary oxides were benchmarked with experimental data, showing high accuracy except for the negative thermal expansion (NTE) of Nb2O5, attributed to its polymorphic complexity. By combining the formation energy predicted by DFT with the existing SGTE Substances Database (SSUB5), the CrNbO4 and CrTaO4 are found to be thermodynamic stable up to 1706 K and 1926 K and decompose into Cr2O3 and Nb2O5 or Ta2O5 at those temperatures, respectively. The temperature dependence of linear thermal expansion coefficients for CrNbO4 and CrTaO4 are predicted, and their mean values from 500 K to 2000 K are found to be 6.0*10-6/K and 5.04*10-6/K, respectively, in agreement with experimental observations in the literature. The gas-phase species and their vapor pressure are calculated, indicating that the formation of CrTaO4 and CrNbO4 reduces chromium volatilization, which is critically important to design enhanced Refractory high entropy alloys (RHEAs) with enhanced oxidation resistance.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 3 minor

Summary. The manuscript employs PBE+U DFT calculations combined with the quasiharmonic approximation to compute temperature-dependent thermodynamic properties (including formation energies, heat capacities, entropies, and thermal expansion) for CrNbO4, CrTaO4, Cr2O3, Nb2O5, and Ta2O5. Binary-oxide results are benchmarked against experiment (with noted failure to reproduce negative thermal expansion in Nb2O5). DFT-derived 0 K formation energies for the ternary phases are merged with temperature-dependent Gibbs energies from the SSUB5 database to locate decomposition temperatures of 1706 K (CrNbO4) and 1926 K (CrTaO4) via ΔG_rxn(T)=0 for reactions such as 2 CrNbO4 → Cr2O3 + Nb2O5. Linear thermal expansion coefficients and vapor pressures are also predicted, with implications for refractory high-entropy alloy oxidation resistance.

Significance. If the reported decomposition temperatures prove robust, the work supplies practically useful data for designing oxidation-resistant RHEAs by quantifying reduced Cr volatilization upon ternary-oxide formation. The benchmarking of binary properties against experiment and the hybrid DFT+database strategy are strengths that enhance applicability; the explicit prediction of mean thermal expansion coefficients (6.0×10^{-6}/K and 5.04×10^{-6}/K) offers testable outputs. The central stability claims, however, rest on unverified energetic consistency between the new PBE+U calculations and the external SSUB5 reference.

major comments (3)
  1. [Thermodynamic stability analysis] Thermodynamic stability section (description of ΔG_rxn(T)=0 construction): the decomposition temperatures are obtained by combining PBE+U formation energies (for ternaries and implicitly for binaries) with SSUB5 G(T) for the binary end-members. No table or text compares the PBE+U formation energies of Cr2O3, Nb2O5, and Ta2O5 against the values implicit in SSUB5; an unaccounted constant offset of even 10–20 meV/atom would rigidly shift the zero-crossing temperature by ~100 K, directly affecting the headline claims of 1706 K and 1926 K.
  2. [Computational methods] Computational methods section (PBE+U setup): the Hubbard U value(s) employed for Cr, Nb, and Ta are neither stated nor subjected to sensitivity tests. Because formation energies enter linearly into ΔG_rxn(T), the absence of U justification or convergence data undermines in the precise numerical stability limits.
  3. [Results, binary oxides benchmarking] Results for Nb2O5 (QHA benchmarking paragraph): the explicit statement that negative thermal expansion is not reproduced due to polymorphic complexity is acknowledged, yet the same QHA data for Nb2O5 are used in the decomposition reaction. This introduces a potential systematic error in the entropy and Cp contributions to ΔG_rxn(T) that is not quantified.
minor comments (3)
  1. [Abstract and Methods] The abstract and main text should explicitly state the U values and any convergence criteria (k-points, cutoff, supercell size) used for the phonon calculations.
  2. [Figures] Figure captions for thermal-expansion plots would benefit from inclusion of the temperature range and comparison to any available experimental points for the ternaries.
  3. [Discussion] A short discussion of possible anharmonic corrections or magnetic entropy contributions at the reported decomposition temperatures (>1700 K) would strengthen the error analysis.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and valuable comments on our manuscript. We address each of the major comments below and indicate the revisions we will make to strengthen the paper.

read point-by-point responses

  1. Referee: Thermodynamic stability section (description of ΔG_rxn(T)=0 construction): the decomposition temperatures are obtained by combining PBE+U formation energies (for ternaries and implicitly for binaries) with SSUB5 G(T) for the binary end-members. No table or text compares the PBE+U formation energies of Cr2O3, Nb2O5, and Ta2O5 against the values implicit in SSUB5; an unaccounted constant offset of even 10–20 meV/atom would rigidly shift the zero-crossing temperature by ~100 K, directly affecting the headline claims of 1706 K and 1926 K.

    Authors: We agree that a direct comparison of the 0 K formation energies is necessary to assess consistency. In the revised manuscript, we will add a table listing the PBE+U formation energies for Cr2O3, Nb2O5, and Ta2O5 alongside the corresponding SSUB5 values (converted to the same reference state). This will quantify any offset and allow us to discuss its effect on the decomposition temperatures. We note that while an offset would shift the absolute values, the methodology remains consistent for predicting the relative stability of the ternary phases. revision: yes

  2. Referee: Computational methods section (PBE+U setup): the Hubbard U value(s) employed for Cr, Nb, and Ta are neither stated nor subjected to sensitivity tests. Because formation energies enter linearly into ΔG_rxn(T), the absence of U justification or convergence data undermines in the precise numerical stability limits.

    Authors: We acknowledge that the specific U parameters were not detailed in the original submission. We will revise the Computational Methods section to explicitly report the Hubbard U values used for Cr, Nb, and Ta, along with references to the literature from which they were selected to ensure reproducibility. A full sensitivity analysis on U would require substantial additional calculations; however, we will add a note on the expected cancellation of U-dependent errors in the reaction energies ΔG_rxn(T). revision: partial

  3. Referee: Results for Nb2O5 (QHA benchmarking paragraph): the explicit statement that negative thermal expansion is not reproduced due to polymorphic complexity is acknowledged, yet the same QHA data for Nb2O5 are used in the decomposition reaction. This introduces a potential systematic error in the entropy and Cp contributions to ΔG_rxn(T) that is not quantified.

    Authors: We recognize the limitation in applying QHA to Nb2O5 given its polymorphic nature and the resulting discrepancy in thermal expansion. To address this, we will expand the discussion in the revised manuscript to quantify the discrepancy between our QHA results and experimental Cp and entropy data for Nb2O5 at relevant temperatures. We will then estimate the propagation of this error into ΔG_rxn(T) and the resulting uncertainty in the decomposition temperature for CrNbO4. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation merges independent DFT results with external database

full rationale

The paper's central stability temperatures are obtained by combining new PBE+U formation energies (computed for CrNbO4, CrTaO4 and the binaries) with the pre-existing SSUB5 Gibbs energies for the binary end-members. This merge does not reduce to a self-definition or a fitted parameter renamed as a prediction; the crossing temperature ΔG_rxn(T)=0 inherits its value from the external database rather than from any equation internal to the present work. No self-citation is invoked as a load-bearing uniqueness theorem, no ansatz is smuggled via prior work by the same authors, and the QHA phonon calculations are benchmarked directly against experiment. The derivation is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central stability claim rests on (1) the accuracy of PBE+U formation energies for the ternaries, (2) the quasiharmonic approximation for all temperature dependence, and (3) the external SSUB5 Gibbs-energy functions for the binaries. No new entities are postulated.

free parameters (1)
  • Hubbard U correction
    Value chosen for Cr, Nb, Ta d-states; not reported in abstract but required for PBE+U calculations.
axioms (2)
  • domain assumption Quasiharmonic approximation suffices to capture thermal expansion and heat capacity up to 2000 K
    Invoked when temperature-dependent properties are obtained via QHA.
  • domain assumption SSUB5 database entries for Cr2O3, Nb2O5, Ta2O5 are accurate enough to combine with new DFT formation energies
    Used to locate the decomposition temperatures.

pith-pipeline@v0.9.0 · 5850 in / 1652 out tokens · 39781 ms · 2026-05-24T03:08:22.802508+00:00 · methodology

discussion (0)

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Reference graph

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