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arxiv: 2604.13768 · v1 · submitted 2026-04-15 · ❄️ cond-mat.mtrl-sci

Anion Ordering and Phase Stability Govern Optical Band Gaps in BaZr(S,Se)3

Erik Fransson , Michael Xu , Prakriti Kayastha , Kevin Ye , Ida Sadeghi , Rafael Jaramillo , James M. LeBeau , Lucy Whalley
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Paul Erhart
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classification ❄️ cond-mat.mtrl-sci
keywords phaseanionbandcompositionorderingstabilitybazrcrystal
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The pith

Composition, crystal structure, and anion ordering jointly determine the optical band gaps in BaZr(S,Se)3.

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

The paper examines mixing thermodynamics and phase stability in BaZr(S,Se)3 chalcogenide perovskites using molecular dynamics, Monte Carlo simulations with machine-learned potentials, and scanning transmission electron microscopy. It identifies stable ordered structures, particularly alternating layers of sulfur and selenium at around 33% sulfur, that persist at room temperature. These factors, combined with selenium alloying, allow the optical band gap to be tuned between 1.6 and 1.9 eV, with ordering reducing the gap by about 0.12 eV and polymorph variations causing shifts up to 0.4 eV. This control is relevant for developing stable, lead-free materials for solar energy conversion and other optoelectronic uses.

Core claim

Analysis of the dielectric function and absorption coefficient shows that composition, crystal structure, and anion ordering jointly control the optical band gap in BaZr(S,Se)3. Selenium alloying enables tuning between approximately 1.6 and 1.9 eV, anion ordering within a given composition reduces the gap by about 0.12 eV, and variations between structural polymorphs give rise to band gap differences of up to 0.4 eV. Free energy calculations produce a temperature-composition phase diagram with a nonperovskite delta phase in the Se-rich limit and a perovskite phase in the S-rich limit, separated by a broad two-phase region. An unusual ordered structure persists at room temperature, most_promi

What carries the argument

Anion ordering in the form of alternating sulfur and selenium layers within the perovskite lattice, which stabilizes specific phases and modulates the dielectric response and absorption.

Load-bearing premise

The machine-learned interatomic potentials accurately reproduce the anion mixing energetics, ordering preferences, and phase stability of real BaZr(S,Se)3 without significant systematic errors.

What would settle it

High-resolution scanning transmission electron microscopy images of BaZr(S,Se)3 at 33% sulfur showing no evidence of alternating S-Se layers, or optical absorption measurements on composition-matched samples with and without ordering showing no 0.12 eV band gap difference.

Figures

Figures reproduced from arXiv: 2604.13768 by Erik Fransson, Ida Sadeghi, James M. LeBeau, Kevin Ye, Lucy Whalley, Michael Xu, Paul Erhart, Prakriti Kayastha, Rafael Jaramillo.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

Chalcogenide perovskites have emerged as promising lead free materials for photovoltaic and thermoelectric applications. Among them, BaZrS3 has attracted particular attention due to its thermal and chemical stability, favorable optoelectronic properties, and low thermal conductivity. Here, we combine molecular dynamics and Monte Carlo simulations based on machine learned interatomic potentials with scanning transmission electron microscopy to investigate mixing thermodynamics and phase stability in the BaZr(S,Se)3 system. We identify an unusual ordered structure that persists at room temperature, most prominently at 33% S, where S and Se atoms form alternating layers within the crystal. Free energy calculations yield the temperature composition phase diagram, including a nonperovskite delta phase in the Se rich limit and a perovskite phase in the S rich limit, separated by a broad two phase region. Analysis of the dielectric function and the absorption coefficient demonstrates that composition, crystal structure, and anion ordering jointly control the optical band gap. Selenium alloying enables tuning between approximately 1.6 and 1.9eV, while anion ordering within a given composition reduces the gap by about 0.12eV. Lastly, variations between structural polymorphs give rise to band gap differences of up to 0.4eV.

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

2 major / 3 minor

Summary. The manuscript investigates mixing thermodynamics and phase stability in BaZr(S,Se)3 chalcogenide perovskites by combining machine-learned interatomic potential (MLIP) based molecular dynamics and Monte Carlo simulations with scanning transmission electron microscopy. It reports an unusual ordered anion structure (alternating S/Se layers) that persists at room temperature, most prominently at 33% S, derives a temperature-composition phase diagram featuring a perovskite phase in the S-rich limit, a non-perovskite delta phase in the Se-rich limit, and a broad two-phase region, and shows via dielectric-function and absorption-coefficient analysis that composition, crystal structure, and anion ordering jointly control the optical band gap, with Se alloying enabling tuning between ~1.6 and 1.9 eV, ordering reducing the gap by ~0.12 eV, and polymorph variations producing differences up to 0.4 eV.

Significance. If the MLIP energetics are reliable, the work provides concrete, falsifiable predictions for how anion ordering and polymorph selection can be used to engineer band gaps in thermally stable, lead-free chalcogenide perovskites, which is relevant for photovoltaic and thermoelectric applications. The combination of simulation-derived phase diagrams with direct microscopy observation of ordering is a methodological strength.

major comments (2)
  1. [MLIP development and validation] The central claims on phase boundaries, the 0.12 eV ordering-induced gap reduction, and the 0.4 eV polymorph spread all rest on the fidelity of the MLIP to the true anion mixing enthalpies and ordering preferences. No hold-out validation metrics, direct DFT recomputation of mixing energies or free-energy differences for the specific supercells and compositions used in the Monte Carlo runs, or error bars on the reported gaps are supplied (see abstract and the MLIP training/results sections). Systematic bias in the potential would propagate directly into the dielectric-function calculations.
  2. [Optical properties and phase diagram results] Table or figure reporting the phase diagram and band-gap values: the absence of uncertainty estimates on the quoted tuning ranges (1.6–1.9 eV, 0.12 eV, 0.4 eV) and on the location of the two-phase region makes it impossible to judge whether the claimed effects exceed the computational uncertainty.
minor comments (3)
  1. [Abstract and optical analysis] Clarify the precise compositions at which the 1.6 eV and 1.9 eV gaps are obtained and whether these correspond to fully ordered or disordered configurations.
  2. [Phase diagram discussion] Provide a brief definition or structural description of the non-perovskite delta phase and its relation to the perovskite polymorphs.
  3. [Experimental methods] The STEM imaging conditions and quantitative comparison between simulated and experimental ordering patterns should be expanded for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments, which have helped us identify areas where additional details will strengthen the presentation. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: The central claims on phase boundaries, the 0.12 eV ordering-induced gap reduction, and the 0.4 eV polymorph spread all rest on the fidelity of the MLIP to the true anion mixing enthalpies and ordering preferences. No hold-out validation metrics, direct DFT recomputation of mixing energies or free-energy differences for the specific supercells and compositions used in the Monte Carlo runs, or error bars on the reported gaps are supplied (see abstract and the MLIP training/results sections). Systematic bias in the potential would propagate directly into the dielectric-function calculations.

    Authors: We agree that more explicit validation of the MLIP is necessary to support the central claims. In the revised manuscript we will add a dedicated validation subsection that reports hold-out test-set errors for energies and forces. We will also recompute mixing energies and free-energy differences with direct DFT for a representative subset of the supercells and compositions used in the Monte Carlo runs, and we will include error bars on the optical gaps derived from ensemble averaging over multiple configurations. These additions will allow readers to assess potential systematic bias. revision: yes

  2. Referee: Table or figure reporting the phase diagram and band-gap values: the absence of uncertainty estimates on the quoted tuning ranges (1.6–1.9 eV, 0.12 eV, 0.4 eV) and on the location of the two-phase region makes it impossible to judge whether the claimed effects exceed the computational uncertainty.

    Authors: We acknowledge that uncertainty quantification is required to evaluate the robustness of the reported ranges. In the revision we will augment the phase-diagram figure and the band-gap tables with statistical error bars obtained from the Monte Carlo sampling and from variations across different anion configurations in the dielectric-function calculations. This will make clear that the quoted effects (including the 0.12 eV ordering-induced shift) lie outside the estimated computational uncertainty. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on independent simulations, microscopy, and dielectric calculations

full rationale

The derivation chain proceeds from MLIP training on DFT data, to Monte Carlo sampling of structures and phase diagrams, to separate dielectric-function computations on those structures, cross-checked by STEM. No equation or result is shown to equal its input by construction, no fitted parameter is relabeled as a prediction, and no load-bearing premise reduces to a self-citation. The optical-gap tunability ranges (0.12 eV ordering effect, 0.4 eV polymorph spread) are outputs of the dielectric analysis rather than tautological restatements of the fitted energetics. This is the normal, non-circular case for a simulation-plus-experiment study.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, preventing identification of specific fitted parameters or additional axioms. The central claims rest on the domain assumption that ML interatomic potentials trained on DFT data suffice for thermodynamics and ordering in this system.

axioms (1)
  • domain assumption Machine-learned interatomic potentials can accurately model the potential energy surface and mixing thermodynamics for BaZr(S,Se)3.
    Invoked to justify the use of MD and MC simulations for phase stability and ordering.

pith-pipeline@v0.9.0 · 5559 in / 1432 out tokens · 56068 ms · 2026-05-10T13:26:02.254032+00:00 · methodology

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