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arxiv: 2605.19414 · v2 · pith:UAT6YHR6new · submitted 2026-05-19 · ❄️ cond-mat.mtrl-sci

Octahedral Tilting in Halide Double Perovskites: Disentangling Lone-Pair Chemistry and Geometric Effects

Mehmet Baskurt , Erik Fransson , Madeleine Lindvik , Paul Erhart , Julia Wiktor This is my paper

Pith reviewed 2026-05-20 04:50 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords halide double perovskitesoctahedral tiltingGoldschmidt tolerance factorlone-pair chemistryphase stabilitymachine-learned potentialsstructural dynamics
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The pith

Octahedral tilting in halide double perovskites correlates primarily with the Goldschmidt tolerance factor.

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

The paper examines octahedral tilting and phase stability across 57 halide double perovskites at zero temperature. It establishes that both the size of the tilt angles and the energy favoring the tilted tetragonal phase track the Goldschmidt tolerance factor t most directly. Lone-pair cations appear tied to stronger tilting, yet this link is largely indirect because those cations tend to shift ionic radii and therefore move t away from unity. Materials lacking lone pairs can still show pronounced tilting when t is sufficiently far from one. Machine-learned potentials then connect the zero-temperature energetics to finite-temperature behavior, showing higher transition temperatures and consistent soft phonon modes for compounds with stronger tilt stabilization.

Core claim

The authors establish that both the magnitude of the tilt angles and the energetic preference for tilted phases correlate primarily with the Goldschmidt tolerance factor t. The presence of stereochemically active lone-pair cations also correlates with enhanced tilting, yet this trend largely reflects that lone-pair chemistries in HDPs occur together with ionic sizes that shift t away from unity. Several compounds without lone pairs nevertheless exhibit strong octahedral tilting, and the zero-temperature trends align with finite-temperature transition temperatures and phonon spectra.

What carries the argument

The Goldschmidt tolerance factor t, a geometric ratio of ionic radii that quantifies how well the A-site cation fits the perovskite cage and thereby controls the driving force for octahedral tilting.

If this is right

  • Compounds with tolerance factors farther from unity show larger tilt angles and greater energetic preference for the tilted phase.
  • Materials with more strongly stabilized tilted phases exhibit higher transition temperatures to the cubic structure.
  • Phonon spectra at 350 K display soft and broad modes that follow the same ordering as the zero-temperature tilt angles and energies.
  • Strong tilting occurs in multiple compounds that lack stereochemically active lone pairs.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Structural design of halide double perovskites can target desired tilt behavior by adjusting ionic radii to set the tolerance factor rather than relying on lone-pair chemistry.
  • The same geometric dominance may appear in other perovskite families when tolerance factor is systematically varied.
  • Testing the trends under chemical doping or pressure would provide a direct check on whether t remains the controlling variable.

Load-bearing premise

The machine-learned interatomic potentials trained on the studied compounds accurately capture finite-temperature phonon spectra, soft modes, and transition temperatures without introducing artifacts that alter the observed trends with tolerance factor.

What would settle it

Observation of a halide double perovskite with tolerance factor near unity that nevertheless displays large tilt angles and low transition temperature driven by lone-pair activity alone.

Figures

Figures reproduced from arXiv: 2605.19414 by Erik Fransson, Julia Wiktor, Madeleine Lindvik, Mehmet Baskurt, Paul Erhart.

Figure 1
Figure 1. Figure 1: FIG. 1. Overview of the double-halide perovskite struc [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Pearson correlation matrix ( [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Relationships between structural distortion and energetic stability in the double-halide perovskite dataset: (a) [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Distributions of structural, energetic, and geometric descriptors grouped by the number of stereochemically active lone [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Temperature dependence of the lattice parame [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Phonon spectral energy distribution (SED) at 350 K for the cubic phase of (a) Cs [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

Halide double perovskites (HDPs) have emerged as promising alternatives to their lead-based counterparts. However, their structural dynamics is less explored than that of conventional halide perovskites. In this work, we investigate octahedral tilting at 0 K and the relative stability of tetragonal and cubic phases of a set of 57 halide double perovskites (HDPs). By combining structural and energetic descriptors with simple geometric metrics, we identify the main trends controlling the stabilization of one-tilt tetragonal phases across this family. We find that both the magnitude of the tilt angles and the energetic preference for tilted phases correlate primarily with the Goldschmidt tolerance factor $t$. The presence of stereochemically active lone-pair cations also correlates with enhanced tilting; however, this trend largely reflects that lone-pair chemistries in HDPs occur together with ionic sizes that shift $t$ away from unity. Consistent with this picture, we observe several compounds without lone pairs that nonetheless exhibit strong octahedral tilting. Finally, using machine-learned interatomic potentials, we connect the 0 K tilting energetics to finite-temperature behavior: compounds with more strongly stabilized tilt phases exhibit higher transition temperatures, and phonon spectra at 350 K reveal soft and broad modes that are consistent with the trends in tolerance factors, tilt angles, and tilt energies at 0 K. Our results provide a systematic reference for structure-stability relationships in HDPs and clarify when lone-pair chemistry is correlated with, rather than the primary cause of, octahedral tilting.

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 / 2 minor

Summary. The manuscript investigates octahedral tilting in a set of 57 halide double perovskites (HDPs) at 0 K and finite temperatures. It reports that both the magnitude of the tilt angles and the energetic preference for one-tilt tetragonal phases correlate primarily with the Goldschmidt tolerance factor t. The presence of stereochemically active lone-pair cations correlates with enhanced tilting, but this is attributed to the associated shifts in ionic radii that move t away from unity rather than a direct chemical effect. Several lone-pair-free compounds are noted to exhibit strong tilting. Machine-learned interatomic potentials are then used to connect the 0 K energetics to finite-temperature behavior, showing higher transition temperatures and soft/broad phonon modes at 350 K for compounds with stronger tilt stabilization.

Significance. If the central correlations hold after addressing validation gaps, the work supplies a systematic reference for structure-stability relations in HDPs and clarifies when lone-pair chemistry is correlated with rather than causative of tilting. This has direct relevance for the design of lead-free optoelectronic materials. The scale of the study (57 compounds) and the explicit attempt to link 0 K tilt energetics to finite-T observables via MLIPs are strengths, provided the potentials are shown to be free of systematic bias.

major comments (2)
  1. [Finite-temperature extension] Finite-temperature section: No details are given on the training set composition, hyperparameters, validation metrics (e.g., force errors on soft modes), or cross-validation against DFT for anharmonic effects and transition barriers in the machine-learned interatomic potentials. Because these potentials are trained on the studied HDPs and are used to establish that stronger 0 K tilt stabilization produces higher transition temperatures and t-consistent soft modes at 350 K, any systematic error correlated with ionic size or lone-pair presence would directly undermine the finite-T extension of the central claim.
  2. [Results on correlations] Results on correlations (near the discussion of lone-pair vs. t effects): The manuscript states that the lone-pair trend largely reflects shifts in t and cites several lone-pair-free compounds with strong tilting, but provides no quantitative disentanglement such as partial correlation coefficients, multivariate regression, or a table isolating the variance explained by t after controlling for lone-pair presence. This leaves the 'disentangling' claim qualitative and load-bearing for the paper's title and abstract.
minor comments (2)
  1. [Abstract] Abstract: The selection criteria for the 57 HDPs, the range of t values sampled, and any reported error bars or standard deviations on tilt angles and energies are not stated, limiting assessment of the robustness of the reported trends.
  2. [Figures] Figure clarity: Ensure that plots of tilt angle or energy versus t clearly distinguish lone-pair-containing from lone-pair-free compounds (e.g., via symbols or colors) so that the secondary nature of the lone-pair effect is visually evident.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. We address each major comment below and will revise the manuscript to incorporate the requested information and analyses.

read point-by-point responses

  1. Referee: Finite-temperature section: No details are given on the training set composition, hyperparameters, validation metrics (e.g., force errors on soft modes), or cross-validation against DFT for anharmonic effects and transition barriers in the machine-learned interatomic potentials. Because these potentials are trained on the studied HDPs and are used to establish that stronger 0 K tilt stabilization produces higher transition temperatures and t-consistent soft modes at 350 K, any systematic error correlated with ionic size or lone-pair presence would directly undermine the finite-T extension of the central claim.

    Authors: We agree that the finite-temperature section requires additional methodological detail to fully substantiate the MLIP-based results. In the revised manuscript we will expand the Methods to specify the training-set composition (DFT calculations on all 57 HDPs plus a range of distorted supercells), the MLIP architecture and hyperparameters, and quantitative validation metrics including force and energy MAEs. We will also report cross-validation performance on soft-mode forces and demonstrate that residuals show no systematic trend with tolerance factor or lone-pair character. These additions will confirm the absence of bias that could affect the reported transition temperatures and 350 K phonon trends. revision: yes

  2. Referee: Results on correlations (near the discussion of lone-pair vs. t effects): The manuscript states that the lone-pair trend largely reflects shifts in t and cites several lone-pair-free compounds with strong tilting, but provides no quantitative disentanglement such as partial correlation coefficients, multivariate regression, or a table isolating the variance explained by t after controlling for lone-pair presence. This leaves the 'disentangling' claim qualitative and load-bearing for the paper's title and abstract.

    Authors: Our disentanglement rests on the clear, monotonic correlation of tilt angles and stabilization energies with t across the entire 57-compound set, reinforced by the existence of multiple lone-pair-free compounds that nevertheless exhibit large tilts. These observations already indicate that lone-pair activity is neither necessary nor sufficient. To make the separation more quantitative, the revised manuscript will include partial correlation coefficients between tilt metrics and t while controlling for lone-pair presence, together with a short multivariate regression summary that reports the fraction of variance attributable to t after the control. This will provide a statistical measure without changing the central conclusions. revision: yes

Circularity Check

0 steps flagged

No significant circularity: primary trends derived from independent DFT calculations correlated to established external tolerance factor

full rationale

The paper computes 0 K tilt angles and phase energies (presumably via direct DFT) across 57 compounds, then correlates both magnitude and stabilization energy against the pre-existing Goldschmidt tolerance factor t, an external geometric descriptor independent of the present calculations. The secondary role of lone-pair cations is supported by explicit observation of strong tilting in multiple non-lone-pair compounds whose ionic radii shift t away from unity. Finite-temperature extension via MLIPs trained on the DFT data constitutes an independent simulation step rather than a re-derivation of the 0 K inputs; no equation or result is shown to equal its own training data or a self-citation by construction. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; tolerance factor is a standard geometric descriptor from prior literature rather than a new invention. No free parameters or invented entities are explicitly introduced in the summary.

axioms (1)
  • domain assumption Goldschmidt tolerance factor serves as a reliable primary descriptor for octahedral tilting and phase stability in halide double perovskites
    Invoked throughout the abstract to explain main trends in tilt angles and energies.

pith-pipeline@v0.9.0 · 5821 in / 1357 out tokens · 50789 ms · 2026-05-20T04:50:06.602108+00:00 · methodology

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