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REVIEW 4 major objections 3 minor 68 references

High-entropy perovskites, architectured by s0/d0/d10 cations, as novel electrolytes for solid oxide fuel cells

T0 review · 4 major / 3 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read This paper introduces three high-entropy perovskites as rare-earth-free fuel-cell electrolytes and claims the mixed s0/d0/d10 composition, (Ba0.50Sr0.50)(Ti0.33Zr0.33Sn0.33)O3, delivers the best performance, reaching 0.53 W cm−2 at 973 K wi

desk verdict Interesting, honest experimental report — but the headline s0/d0/d10 design rule is not supported by the main-text data once electrolyte thickness is taken into account. read the letter →

arxiv 2607.16616 v1 pith:3BZMZBVA submitted 2026-07-18 cond-mat.mtrl-sci physics.chem-ph

Ho Truong Nam Hai , Rishad Kunafiev , Kwati Leonard , Kaveh Edalati This is my paper · ORCID
classification cond-mat.mtrl-sciphysics.chem-ph
keywords high-entropyoxidesperovskiteelectrolytessolidoxidefuelcellsprotonicceramicsevereplasticdeformationrare-earth-freed0/d10cationsoxygenvacancies
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

This paper aims to establish that high-entropy perovskite oxides made only from abundant s-block and d-block metals can serve as proton-conducting electrolytes for solid oxide fuel cells. The central claim is that a composition mixing empty d-shell cations (Ti, Zr) with a filled d-shell cation (Sn) on the perovskite B-site outperforms both all-d0 and all-d10 analogues. The best cell reaches a peak power density of 0.53 W cm−2 at 973 K, with an open-circuit voltage near the theoretical value and an ohmic resistance of 0.5 Ω cm2. The authors attribute this to localized electronic heterogeneity that suppresses electron hopping, combined with extrinsic oxygen vacancies and favorable metal–oxygen bond lengths. If correct, this would provide a rare-earth-free, low-cost electrolyte design rule for protonic ceramic fuel cells.

What carries the argument

The central object is the ABO3 high-entropy perovskite family (Ba0.5Sr0.5)(M1,M2,M3)O3, where the A-site holds s0 cations (Ba, Sr) and the B-site contains either d0 cations (Ti, Zr, Hf), d10 cations (Ga, In, Sn), or a mix. The active mechanism is the electronic contrast between d0 and d10 B-site cations: the localized mixture of unoccupied and filled d-states suppresses electron hopping, reducing current leakage, while extrinsic oxygen vacancies and longer Ba–O bonds (favorable for hydroxide-ion rotation) promote proton transport. This mechanism is probed with X-ray absorption near-edge structure, extended X-ray absorption fine structure, X-ray photoelectron spectroscopy, and electron spin r

What would settle it

Fabricate the two dense electrolytes (d0 and d0/d10) to the same thickness and density under identical sintering conditions, then measure electronic transference numbers using Hebb–Wagner or oxygen-blocking electrodes; if the d0/d10 cell no longer shows lower leakage or higher power density, the electronic-configuration rule is refuted. Alternatively, vary the Sn fraction in the Ti/Zr host and check whether current leakage scales with d10 content.

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Extended reading notes

Core claim

The central claim is that a high-entropy perovskite with mixed s0/d0/d10 B-site cations — specifically (Ba0.50Sr0.50)(Ti0.33Zr0.33Sn0.33)O3 — acts as an effective proton-conducting electrolyte, while the analogous all-d0 (Ba0.50Sr0.50)(Ti0.33Zr0.33Hf0.33)O3 and all-d10 (Ba0.50Sr0.50)(Ga0.33In0.33Sn0.33)O3−δ are inferior. The paper argues that the coexistence of empty and filled d-orbitals on the B-site creates localized electronic heterogeneity that blocks electron transfer and current leakage, while oxygen vacancies and tuned metal–oxygen bond lengths promote proton transport. The best cell reaches a maximum power density of 0.53 W cm−2 at 973 K with an ohmic resistance of 0.5 Ω cm2 and an

Load-bearing premise

The central claim rests on the assumption that the performance differences among the three cells come from the B-site electronic configuration, yet the cells also differ in electrolyte thickness, sintering conditions, and void density, and the supposedly worst material was the only one that failed to densify.

Editorial extensions

If this is right

  • If the claim is correct, rare-earth-free high-entropy perovskite electrolytes can reach competitive protonic fuel-cell power densities without yttrium, cerium, or lanthanides.
  • The s0/d0/d10 mixing rule offers a chemistry-agnostic design criterion for suppressing electronic leakage in proton-conducting oxides.
  • High-pressure torsion synthesis produces homogeneous, dense thin electrolytes with extrinsic oxygen vacancies that persist after sintering, a route that could be applied to other ceramic electrolytes.
  • The all-d10 composition (Ga/In/Sn) is not viable as an electrolyte because of void formation and volatilization at sintering temperatures, suggesting these elements need reformulation or lower-temperature processing.
  • The measured activation energy of about 0.3 eV for ohmic resistance supports proton, rather than oxygen-ion, conduction in the mixed-cation perovskite.

Reading between the lines

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

  • The performance ordering is not fully controlled: the three cells differ in electrolyte thickness (7.4, 5.8, 9.8 µm), sintering temperature, screen-printing passes, and void content, and the worst-performing cell was the only one that failed to densify. A matched-thickness, matched-density comparison would isolate the electronic-structure effect.
  • If the d0/d10 contrast is the operative mechanism, then replacing Sn with another d10 cation (e.g., In or Ga) in a Ti/Zr host should preserve the low-leakage behavior; this is a testable compositional prediction.
  • The same d0/d10 design rule might extend beyond fuel-cell electrolytes to any mixed ionic-electronic conductor where suppressing electronic conductivity while preserving ionic transport is desirable, such as separation membranes or sensors.
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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

4 major / 3 minor

Summary. The manuscript reports three high-entropy perovskite oxides — (Ba0.50Sr0.50)(Ti0.33Zr0.33Hf0.33)O3 (s0/d0), (Ba0.50Sr0.50)(Ga0.33In0.33Sn0.33)O3−δ (s0/d10), and (Ba0.50Sr0.50)(Ti0.33Zr0.33Sn0.33)O3 (mixed s0/d0/d10) — synthesized by high-pressure torsion and calcination, and integrated as electrolyte layers in anode-supported fuel cells. The authors report cubic Pm3m phases, dense microstructures for two of the three cells, and a maximum power density of 0.53 W·cm−2 at 973 K for the mixed s0/d0/d10 composition, which they attribute to heterogeneous local electronic structure, favorable Ba–O bond lengths, and extrinsic oxygen vacancies that suppress electronic leakage and promote proton transport. The paper also introduces HPT as a synthesis route for fuel-cell electrolytes and compares the best cell with literature PCFCs.

Significance. If the central comparative claim were established, the work would be significant: it demonstrates a rare-earth-free, high-entropy perovskite electrolyte with a competitive intermediate-temperature PCFC power density and a potentially generalizable design rule (mixed empty/filled d-shell B-site cations). The synthesis route is novel and the characterization set is unusually broad: Rietveld-refined XRD, TEM/FFT, SEM/STEM-EDS, XAS/XANES/EXAFS, XPS, ESR, EIS/DRT, and full-cell I–V data. The measured 0.53 W·cm−2 peak power density is a concrete, falsifiable result. However, as detailed below, the evidence that the best composition is intrinsically superior, and that the s0/d0/d10 architecture is the cause, is not currently supported by the main-text data.

major comments (4)
  1. [§3.3, Fig. 5d and Fig. S7] The reported OCV values are mutually inconsistent with the stated ionic transference numbers. The text reports measured OCVs of 1.13 V and 1.17 V at 873 K, while the theoretical Nernst value under the stated conditions is 1.14 V. If t_i ≈ 0.96, the measured OCV should be ≈ 1.09 V, not 1.17 V. An OCV above the theoretical Nernst value is physically impossible for a well-sealed cell with the stated gas compositions. This discrepancy invalidates the 'negligible current leakage' claim and the t_i ≈ 0.96 statement. The authors should reconcile the Nernst calculation, the measured OCV, and the transference-number definition, or present direct leakage/transference measurements (e.g., Hebb–Wagner or EMF with gas concentration cells).
  2. [§3.3, Figs. 5 and 6] The claim that the lower ohmic resistance of the (Ba0.50Sr0.50)(Ti0.33Zr0.33Sn0.33)O3 cell is 'primarily attributable to intrinsic electrolyte resistance rather than to reduced electrolyte thickness' is contradicted by the paper's own numbers. Using σ = t/Rohm with thicknesses of 5.8 µm and 7.4 µm and wet Rohm values of 0.75 and 0.90 Ω·cm² at 873 K gives σ ≈ 7.7×10⁻⁴ S/cm for BTZS and σ ≈ 8.2×10⁻⁴ S/cm for BTZH. At 973 K the values are essentially identical (≈1.16 vs. ≈1.14 mS/cm). The lower ASR is therefore explained by the thinner electrolyte. The supplementary Fig. S6 is not in the main text, and without its Rohm and thickness values one cannot evaluate the claimed thickness control. This is load-bearing: the central design-rule claim rests on intrinsic conductivity, not on cell geometry.
  3. [§2.2 and Fig. 5] The performance comparison across the three cells is confounded by uncontrolled fabrication variables. The three electrolytes differ not only in B-site electronic configuration but also in electrolyte thickness (7.4, 5.8, and 9.8 µm), sintering temperature and time (1673 K/10 h, 1653 K/10 h, and 1573 K/5 h), screen-printing passes (2, 2, and 6), and void content. The s0/d10 cell is acknowledged to be void-laden and is thus not a fair test of the electronic-architecture hypothesis. Effectively, the design rule is tested by only two dense cells (BTZS vs. BTZH), which differ by one B-site element plus thickness and sintering schedule, with a single cell per composition and no error bars. At minimum, the authors should report replicate cells and a thickness-matched comparison with identical sintering and printing conditions, or explicitly acknowledge that the current data cannot isolate the
  4. [§3.3, Eq. (4), and Discussion] The evidence for proton transport is indirect. The Arrhenius analysis in Eq. (4) is applied to the total ohmic area-specific resistance of full cells, which includes electrode, contact, and electrolyte contributions; it is not an intrinsic electrolyte conductivity measurement. The ~0.3 eV activation energy therefore does not by itself establish that proton migration dominates charge transport. The paper itself acknowledges that Hebb–Wagner/EMF transference-number measurements, proton conductivity under humidified vs. dry atmospheres, and hydration studies are needed. Because the central design rule is about suppressing electronic leakage and promoting proton transport, this missing evidence is not merely cosmetic; it should be supplied or the claims should be scaled back accordingly.
minor comments (3)
  1. [Abstract and §2.2] There are typographical errors: 'pprofiles' in Fig. 1 caption and 'into into' in the Conclusions. The manuscript should be proofread.
  2. [Table 3] The table header states 'OCV (V vs. SCE)', but the values are open-circuit voltages of solid oxide fuel cells, not potentials versus a saturated calomel electrode. The unit should be simply 'V' or 'V vs. NHE/H2' if a reference is intended.
  3. [§3.3, Fig. S6] The claim about the 10.6 µm BTZS cell in the main text relies entirely on supplementary Fig. S6. Since this is used to counter the thickness confound, the figure and its Rohm/thickness data should be moved to the main text or at least fully described with numerical values in the supplementary.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claims are direct measurements, and the s0/d0/d10 interpretive framework is applied post hoc rather than derived from the data by construction.

full rationale

The paper's main results—OCV, Rohm from EIS, and peak power density—are measured quantities, not outputs of a fitted model that re-inserts the conclusion. The best-performing composition (Ba0.50Sr0.50)(Ti0.33Zr0.33Sn0.33)O3 is identified empirically, and the XAS/XPS/EXAFS observations are then used to correlate performance with electronic structure; there is no equation in which the claimed design rule is defined in terms of the performance metric or vice versa. The mechanistic statements citing the group's prior work (refs 27-31) are literature-based interpretive support, not a derivation step that forces the experimental outcome. The main weakness—that the lower ASR of the thinner BTZS cell may be explained by thickness rather than intrinsic conductivity—is a confound and a scientific inference issue, not a definitional or fitted-input circularity; it does not satisfy the requirement of exhibiting a specific reduction such as Eq. X = Eq. Y by construction. No circular step can be exhibited from the manuscript text, so the appropriate finding is no significant circularity.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

No invented physical entities are introduced. The core free parameters are outputs of equivalent-circuit and Arrhenius fits on which the performance comparisons rest. The assumptions are standard characterization interpretations (Nernst OCV, XPS/ESR vacancy signatures, Shannon radii, >1.5R entropy criterion) plus the group's own s0/d0/d10 design heuristic (refs [22],[27-31], largely self-authored) and the HPT-vacancy persistence claim (refs [55,56], self-authored reviews). The load-bearing interpretive moves — OCV/t_i ⇒ negligible electron leakage, Ea ≈ 0.3 eV ⇒ proton transport — are flagged by the authors themselves as needing direct measurement.

free parameters (3)
  • Activation energy Ea (per cell) = ≈ 0.3 eV (773–973 K)
    Fitted from ln R vs 1000/T Arrhenius plots of ohmic resistance (Eq. 4, Fig. 6c/f/i). Interpreted as proton migration energy and used to assert proton-dominant conduction — a load-bearing interpretation the paper itself lists as needing direct measurement.
  • EIS equivalent-circuit elements (Rohm, RHF/RMF/RLF, CPE parameters) = Rohm = 0.5/0.65/2.0 Ω·cm² at 973 K
    Fitted to impedance spectra with circuit L(Ro)(RHFQHF)(RMFQMF)(RLFQLF) (§3.3, Fig. 6). The Rohm values are the quantitative basis of the 'best electrolyte' claim; no fit uncertainties are given, and fitting error is admitted to be high for the GaInSn cell.
  • DRT deconvolution parameters = Table S1
    Distribution-of-relaxation-times fits assign impedance arcs to electrode vs electrolyte processes and support the attribution of the high-frequency arc to the electrolyte; reported without uncertainties.
assumptions (7)
  • standard math Nernst equation with PH2O = 1.9 kPa and wet air gives theoretical OCV 1.14 V at 873 K
    Used in §3.3 to compute theoretical OCV and the ionic transference number t_i. Measured OCV of 1.17 V exceeds it, implying an inconsistency among the Nernst computation, the gas conditions, or the measurement.
  • domain assumption Ea ≈ 0.3 eV identifies proton migration in oxide lattices
    §3.3 cites refs [49-51] and concludes proton transport dominates. The paper concedes at the end of §4 that direct proton-conductivity measurements were not performed.
  • domain assumption Higher-binding-energy O 1s XPS peak and ESR g = 2.008 signal indicate oxygen vacancies
    §3.1, refs [39,40]. Standard literature interpretation; the paper itself states XPS cannot reliably quantify vacancies.
  • domain assumption Configurational entropy > 1.5R defines a high-entropy oxide
    Used in §3.1 (Table 1) to classify the three materials as high-entropy; criterion from refs [23,24].
  • domain assumption Mixed d0/d10 B-site cations suppress electron hopping because electrons cannot easily hop between them
    Central design heuristic stated in §1 and §4, citing refs [22],[28-31] — mostly the authors' own prior papers. Used to interpret the high OCV/t_i as 'negligible' electronic leakage.
  • domain assumption HPT processing generates extrinsic oxygen vacancies that survive sintering at 1573–1673 K
    §4 attributes vacancies in the stoichiometric compositions to HPT, citing refs [55,56] (self-authored reviews) and [33]. No direct vacancy quantification is provided.
  • standard math Shannon ionic radii at CN 12 (A-site) and CN 6 (B-site) correctly predict perovskite stability via tolerance and octahedral factors
    Equations (2) and (3) and Table 1; standard crystallographic geometric criterion [32].

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Pith. "Pith review of High-entropy perovskites, architectured by s0/d0/d10 cations, as novel electrolytes for solid oxide fuel cells." pith.science (2026). https://pith.science/paper/3BZMZBVA

@misc{pith2026260716616,
  author       = {Pith},
  title        = {Pith review of: High-entropy perovskites, architectured by s0/d0/d10 cations, as novel electrolytes for solid oxide fuel cells},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3BZMZBVA}},
  note         = {Machine review of arXiv:2607.16616}
}
read the original abstract

Solid oxide fuel cells enable efficient conversion of hydrogen into electricity. However, the limited availability of materials for their cathode, anode, and electrolyte remains a concern. This study introduces three high-entropy oxide perovskites as novel electrolyte materials for fuel cells (Ba0.50Sr0.50)(Ti0.33Zr0.33Hf0.33)O3 with s0/d0 cations, (Ba0.50Sr0.50)(Ga0.33In0.33Sn0.33)O3 with s0/d10 cations, and (Ba0.50Sr0.50)(Ti0.33Zr0.33Sn0.33)O3 with mixed s0/d0/d10 cations. Through sequential sintering by high-pressure torsion processing and calcination, these perovskites were synthesized and then printed with a thickness of about 6-10 microns on a Ni-SrZr0.5Ce0.4Y0.1O3 substrate as an anode and then coated with Ba0.5La0.5CoO3 as a cathode. Electrochemical analysis and impedance spectroscopy show that (Ba0.50Sr0.50)(Ti0.33Zr0.33Sn0.33)O3 with s0/d0/d10 cations exhibits the best performance with negligible current leakage and lowest ohmic resistance, while its maximum power density reaches 0.53 W.cm-2 at 973 K. Complementary synchrotron X-ray absorption and photoelectron spectroscopy analyses indicate that the superior performance of (Ba0.50Sr0.50)(Ti0.33Zr0.33Sn0.33)O3 correlates with its heterogeneous electronic structure characterized by tailored unoccupied d-orbital states, and favorable local metal-oxygen bond lengths and extrinsic oxygen vacancies. This investigation demonstrates the significance of high-entropy perovskites with mixed s0/d0/d10 cations as new rare-earth metal-free ion-conducting electrolytes, particularly for protonic solid oxide fuel cells.

Figures

Figures reproduced from arXiv: 2607.16616 by the authors.

Figure 4
Figure 4. Distorted local electronic structure in the vicinity of cations in high-entropy perovskites. XAS (left side) and EXAFS (right side) graphs for (a, b) Ba L3, (c, d) Ti K, (e, f) Hf L3, (g, h) Sn L3, (i, j) Ga K edges of (Ba0.50Sr0.50)(Ti0.33Zr0.33Hf0.33)O3, (Ba0.50Sr0.50)(Ti0.33Zr0.33Sn0.33)O3 and (Ba0.50Sr0.50)(Ga0.33In0.33Sn0.33)O3-, and their corresponding binary oxides [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Dense fuel cells with high open-circuit voltage using high-entropy perovskites as electrolytes. Cross-sectional SEM micrographs of cells fabricated using (a) (Ba0.50Sr0.50)(Ti0.33Zr0.33Hf0.33)O3, (b) (Ba0.50Sr0.50)(Ti0.33Zr0.33Sn0.33)O3, and (c) (Ba0.50Sr0.50)(Ga0.33In0.33Sn0.33)O3- electrolytes and (d) corresponding open-circuit voltage profiles. The micrograph in (a) was taken by back-scattered electrons, and mic… view at source ↗
Figure 6
Figure 6. Low ohmic resistance under wet conditions and at high temperature for fuel cells fabricated using high-entropy perovskites as electrolytes. EIS spectra of fuel cells with (a, b) (Ba0.50Sr0.50)(Ti0.33Zr0.33Hf0.33)O3, (d, e) (Ba0.50Sr0.50)(Ti0.33Zr0.33Sn0.33)O3 and (g, h) (Ba0.50Sr0.50)(Ga0.33In0.33Sn0.33)O3- electrolytes achieved (a, d, g) at 873 K under dry and wet conditions, and (b, e, h) at different temperature… view at source ↗

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Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.