Pith. sign in

REVIEW 2 major objections 7 minor 71 references

Unveiling the Optoelectronic Potential of Vacancy-Ordered Double Perovskites: A Computational Deep Dive

T0 review · 2 major / 7 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A computational study of twelve lead-free Rb2BX6 vacancy-ordered double perovskites predicts tunable direct band gaps from 0.56 to 6.12 eV, strong infrared-to-ultraviolet absorption, and identifies Rb2SnI6 as the most promising…

desk verdict A useful but overclaimed computational screening of Rb2BX6 perovskites where the paper's own phonon data undercut its headline stability claim, since half the family, including the top PV candidate, is dynamically unstable at T=0 K. read the letter →

arxiv 2411.08528 v1 pith:3MZHRRZ2 submitted 2024-11-13 cond-mat.mtrl-sci

Surajit Adhikari , Ayan Chakravorty , Priya Johari This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords vacancy-ordereddoubleperovskiteslead-freeRb2SnI6G0W0bandgapsBethe-Salpeterexcitonspolaronmobilityphotovoltaicabsorberfirst-principlesDFT
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 seeks to establish that the twelve lead-free vacancy-ordered double perovskites Rb2BX6 (B = Si, Ge, Sn, Pt; X = Cl, Br, I) form a family of stable, tunable optoelectronic materials. Using first-principles methods, the authors compute mostly direct band gaps between 0.56 and 6.12 eV, strong infrared-to-ultraviolet absorption, low to moderate exciton binding energies, and electron polaron mobilities up to 85.11 cm2V−1s−1. They single out Rb2SnI6 with a direct G0W0 gap of 1.16 eV as the most suitable photovoltaic absorber, placing it near the ideal range for solar cells. The broader point is that Rb-based vacancy-ordered double perovskites could serve as non-toxic alternatives to lead halide perovskites across a wide spectral range.

What carries the argument

The structural platform is the vacancy-ordered double perovskite lattice (space group Fm-3m), where the B cation sits inside isolated [BX6] octahedra and Rb atoms occupy the 12-coordinate sites between them, so that the electronic states near the band edges are shaped by B-s and halogen-p hybridization. The property predictions rest on a computational chain: G0W0@PBE quasiparticle calculations for band gaps and band structures, Bethe-Salpeter equation on top of G0W0 for optical and excitonic quantities, density functional perturbation theory for phonons and the ionic dielectric response, and the Feynman and Hellwarth Fröhlich polaron models for polaron energies and mobilities. The chain converts a list of twelve compositions into concrete predictions of gaps, absorption edges, exciton binding energies, and carrier mobilities.

What would settle it

Compute temperature-dependent or anharmonic phonon spectra for the six compounds that show imaginary modes at T = 0 K: if the imaginary modes persist, the stability half of the central claim collapses for those materials. Alternatively, grow a Rb2SnI6 crystal and measure the optical absorption edge and its direct or indirect character; a gap significantly above about 1.16 eV or an indirect onset would contradict the paper's headline prediction.

Watch

Extended reading notes

Core claim

On its own terms, the paper claims that the Rb2BX6 family are viable, mostly direct-gap semiconductors whose properties can be tuned by swapping the B-site cation and the halogen. The calculated G0W0@PBE gaps run from 0.56 eV (Rb2GeI6) to 6.12 eV (Rb2SiCl6); Rb2SnI6 has a direct gap of 1.16 eV, close to the experimental 1.32 eV, placing it in the optimal range for single-junction solar cells. Exciton binding energies after phonon screening lie between 0.065 and 0.407 eV, absorption edges span 0.31 to 5.58 eV, and electron polaron mobilities reach 3.33 to 85.11 cm2V−1s−1, exceeding previously reported Cs-based vacancy-ordered double perovskites. The paper also reports that six of the twelve configurations are not dynamically stable at T = 0 K, but proceeds on the basis of mechanical and thermodynamic stability.

Load-bearing premise

The paper's conclusion that the whole Rb2BX6 series is stable rests on the assumption that the six compounds with imaginary phonon modes at T = 0 K (Rb2SiI6, Rb2GeI6, Rb2SnCl6, Rb2SnBr6, Rb2SnI6, and Rb2PtI6) can still be treated as viable optoelectronic materials, either because mechanical and thermodynamic stability alone are sufficient or because finite-temperature effects would stabilize them, and neither rescue is demonstrated.

Editorial extensions

If this is right

  • Rb2SnI6 emerges as the prime candidate for a lead-free perovskite solar absorber and should be prioritized for experimental device testing.
  • The halogen trend (chlorine > bromine > iodine in band gap) gives a simple composition handle for tuning absorption from ultraviolet to infrared.
  • Electron mobilities dominate hole mobilities in every compound, so the family is predicted to behave as n-type semiconductors with efficient electron transport.
  • Iodine-containing compounds combine smaller band gaps with higher polaron mobility and longer exciton lifetimes, making them the most promising subset for photovoltaics.
  • The exciton binding energies of 0.065 to 0.407 eV imply that many of these materials will operate in an intermediate exciton and free-carrier regime, relevant for device design.

Reading between the lines

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

  • A natural next step not taken in the paper is to test whether epitaxial strain or finite-temperature anharmonicity removes the imaginary phonon modes in the six compounds that are dynamically unstable at T = 0 K; if so, the viable set could expand beyond the six that are stable at absolute zero.
  • The paper's mobility comparison against Cs-based vacancy-ordered double perovskites suggests that rubidium's smaller cation size may be the systematic factor behind the higher electron mobilities, a hypothesis that could be tested by computing the same polaron properties for mixed Rb/Cs compositions.
  • Because Rb2GeI6 shows the highest electron mobility (85.11 cm2V−1s−1) but also a very small gap (0.56 eV), it may be more useful as an infrared detector or low-gap material than as a solar absorber, a distinction the paper does not draw.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 7 minor

Summary. The paper reports first-principles calculations for a family of twelve vacancy-ordered double perovskites Rb2BX6 (B = Si, Ge, Sn, Pt; X = Cl, Br, I). Using DFT (PBE and HSE06), G0W0@PBE, BSE@G0W0, DFPT, and Feynman-Hellwarth polaron models, the authors compute structural stability, band structures and gaps, optical absorption, exciton binding energies, and polaron mobilities. They conclude that the materials form a stable series with tunable direct bandgaps from 0.56 to 6.12 eV, strong infrared-to-ultraviolet absorption, low-to-moderate exciton binding energies, and high electron polaron mobility, and they single out Rb2SnI6 (G0W0 gap 1.16 eV) as the most promising photovoltaic absorber.

Significance. If correct, the study would provide a useful computational screen of lead-free vacancy-ordered double perovskites, with a particularly valuable comparison of many-body techniques across a chemically systematic series. The methods are standard and several benchmark values agree with prior theory or experiment (e.g., Rb2SnI6 G0W0 gap 1.16 eV versus the reported experimental optical gap of 1.32 eV). The main significance is limited, however, because the paper's own phonon calculations show that six of the twelve compounds, including the headline candidate Rb2SnI6, are dynamically unstable at T=0 K, and this fact is not integrated into the conclusions.

major comments (2)
  1. [III.A.2 (Dynamical Stability)] The phonon results in Sec. III.A.2 state that only Rb2SiCl6, Rb2GeCl6, Rb2PtCl6, Rb2SiBr6, Rb2GeBr6, and Rb2PtBr6 have no imaginary modes, while the remaining six configurations, including Rb2SnI6, are not dynamically stable at T=0 K. Nevertheless, all subsequent band-gap, BSE, exciton, and polaron results for those six compounds are computed on the cubic Fm-3m phase, and the paper's central conclusion presents the full Rb2BX6 series as stable candidates. Negative formation energies (Table I) and the mechanical stability criteria (Sec. III.A.3) do not establish that a structure with imaginary phonon modes is a viable phase. The load-bearing premise that the instabilities are removed by finite-temperature or anharmonic effects is never demonstrated. To support the central claim, the authors should provide explicit evidence (e.g., finite-temperature phonon calculations, ab initio molecular dynamics, or an analysis of metastability), or they should re-scope all stability and property claims to the six dynamically stable compounds.
  2. [Abstract and Section IV (Conclusions)] The abstract states that these materials 'exhibit high stability' and the conclusions describe 'phase stability of these systems' without qualification, yet Sec. III.A.2 reports that six of the twelve configurations are dynamically unstable at T=0 K. This is an internal inconsistency in the manuscript's main claim. In particular, the paper's singled-out photovoltaic candidate, Rb2SnI6, is one of the dynamically unstable compounds, so the overstatement is not a peripheral caveat. The abstract and conclusions should clearly distinguish the six dynamically stable compounds from the six unstable ones, or provide the missing evidence of finite-temperature stabilization.
minor comments (7)
  1. [II (Computational Details)] There is a typo 'Aditionally' near the end of the section; also the valence configuration for Pt is written as '5d 96s1' with a missing space.
  2. [III.D (Excitonic Properties)] The phrase 'for details, for details' appears twice in the paragraph discussing exciton lifetime; one instance should be removed.
  3. [Figure 3 and Section III.B] The text in Sec. II says band structures were calculated with PBE including SOC, while Fig. 3 and the text in Sec. III.B say the band structures were computed using G0W0@PBE. Please clarify which method produced the plotted bands and the effective masses in Table III.
  4. [Tables I and II] The footnotes (a), (b), (c) are used differently in Table I (experimental/theoretical) and Table II (PBE/HSE06/TB-mBJ); use distinct symbols or explicitly restate the meanings in each caption.
  5. [Table II] For Rb2GeI6, the HSE06 gap column appears to be empty; if the HSE06 value was not computed or is not reported, this should be stated explicitly rather than left as a blank.
  6. [Eq. (4)] The expression for the phonon-screening correction ΔE_B^{ph} appears to have a prefactor that, as written, may be dimensionally inconsistent with the reported values in eV in Table IV; please verify the formula against Ref. [63] and clarify the intended units.
  7. [Table III] The parenthetical values for Rb2PtBr6 and Rb2PtI6 are not explained in the caption; the caption should state that these are the effective masses at the lowest direct band edge.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: all headline quantities are computed from independent first-principles inputs, and the single self-citation is introductory and not load-bearing.

full rationale

The paper's central results—G0W0 band gaps, BSE absorption edges, exciton binding energies, polaron energies, and polaron mobilities—are each obtained from independent first-principles inputs: band structures from G0W0@PBE, dielectric constants from DFPT and BSE, effective masses from band-dispersion curvature, and optical-phonon frequencies from the Hellwarth spectral-averaging scheme. The Wannier-Mott exciton formula and the Feynman/Hellwarth polaron mobility expression are standard external formulas whose parameters are not fitted to the claimed outputs. No equation defines a predicted quantity in terms of itself, and no parameter is fitted to a subset of the data and then repackaged as a prediction. The only self-citation (Ref. [4], an earlier work by two of the authors on Cs2MSbX6) appears in the introduction as background and is not used to justify any load-bearing step. The dynamical-stability caveat in Sec. III.A.2—that six configurations, including Rb2SnI6, have imaginary phonon modes at T=0 K—is a correctness or stability concern, not a circularity, because the electronic, excitonic, and polaronic calculations are not derived from the phonon calculation. Standalone benchmarks, including experimental band-gap comparisons for Rb2SnI6, provide external support. Therefore no circular step can be exhibited, and the appropriate finding is a non-finding with score 0.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No free parameters were fitted to experimental target properties. The central claim depends on domain assumptions about the applicability of DFT-based quasiparticle methods, the hydrogenic exciton model, and the Fröhlich/Hellwarth polaron formalism to vacancy-ordered double perovskites. The most consequential assumption is that the cubic PBE-relaxed phase is representative even for the six compounds that show imaginary phonon modes at T=0 K.

assumptions (5)
  • domain assumption PBE, G0W0@PBE, HSE06, and GW-BSE approximations accurately describe the electronic and optical properties of these Rb2BX6 compounds.
    No experimental band structure or optical spectra are provided for most compounds; accuracy rests on prior validation of these methods on similar halide perovskites.
  • domain assumption The hydrogenic Wannier-Mott exciton model with parabolic bands and a single reduced mass applies to these systems.
    Used for exciton binding energy, radius, and wavefunction overlap via Eqs. (2), (5), and (6); ignores band non-parabolicity and valley degeneracies.
  • domain assumption The Fröhlich model and the Hellwarth polaron mobility formula with a single spectral-averaged LO phonon frequency capture polaron physics in these materials.
    Used in Eqs. (7) to (13); assumes weak to intermediate coupling, isotropic parabolic dispersion, and a well-defined omega_LO.
  • domain assumption The PBE-relaxed cubic Fm-3m phase is the relevant structure for all twelve compounds; no lower-symmetry distortions, octahedral tilts, or defect-mediated stabilization are considered.
    All properties are computed on this phase. The dynamic instability of six compounds suggests this assumption may fail for them.
  • domain assumption The phonon screening correction formula from Ref. [63] with omega_LO from the Hellwarth athermal B scheme is valid for these materials.
    Used to compute the phonon screening correction DeltaE_B^ph in Eq. (4).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Unveiling the Optoelectronic Potential of Vacancy-Ordered Double Perovskites: A Computational Deep Dive." pith.science (2026). https://pith.science/paper/3MZHRRZ2

@misc{pith2026241108528,
  author       = {Pith},
  title        = {Pith review of: Unveiling the Optoelectronic Potential of Vacancy-Ordered Double Perovskites: A Computational Deep Dive},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3MZHRRZ2}},
  note         = {Machine review of arXiv:2411.08528}
}
abstract

Lead-free perovskite materials have emerged as key players in optoelectronics, showcasing exceptional optical and electronic properties, alongside being environmentally friendly and non-toxic elements. Recently, among studied perovskite materials, vacancy-ordered double perovskites (VODPs) stand out as a promising alternative. In this study, we captured the electronic, optical, excitonic, and polaronic properties of a series of VODPs with the chemical formula Rb$_{2}$BX$_{6}$ (B = Si, Ge, Sn, Pt; X = Cl, Br, I) using first-principles calculations. Our results indicate these materials exhibit high stability and notable electronic and optical properties. The calculated G$_{0}$W$_{0}$ bandgap values of these perovskites fall within the range of 0.56 to 6.12 eV. Optical properties indicate strong infra-red to ultraviolet light absorption across most of the systems. Additionally, an analysis of excitonic properties reveals low to moderate exciton-binding energies and variable exciton lifetimes, implying higher quantum yield and conversion efficiency. Furthermore, utilizing the Feynman polaron model, polaronic parameters are evaluated, and for the majority of systems, charge-separated polaronic states are less stable than bound excitons. Finally, an investigation of Polaronic mobility reveals high polaron mobility for electrons (3.33-85.11 cm$^{2}$V$^{-1}$s$^{-1}$) compared to previously reported Cs-based VODP materials. Overall, these findings highlight Rb-based VODPs as promising candidates for future optoelectronic applications.

Figures

Figures reproduced from arXiv: 2411.08528 by the authors.

Figure 1
Figure 1. (a) Crystal structure of Rb2BX6 (B = Si, Ge, Sn, Pt; X = Cl, Br, I) VODPs, and phonon dispersion curves of (b) Rb2SiCl6, (c) Rb2GeCl6, (d) Rb2PtCl6, (e) Rb2SiBr6, (f) Rb2GeBr6, and (g) Rb2PtBr6 VODP, respectively, calculated with the DFPT method. Table I provides an overview of the optimized lattice parameters of the analyzed VODPs. We find that our computed lattice parameters match well with the earlier theoretical… view at source ↗
Figure 2
Figure 2. Calculated electronic total density of states (TDOS) and partial density of states (PDOS) of (a-c) Rb [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Calculated electronic band structures of (a-c) Rb [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Imaginary [Im(ε)] part of the dielectric function of (a) Rb2SiX6, (b) Rb2GeX6, (c) Rb2SnX6, and (d) Rb2PtX6 VODPs, where X = Cl, Br, and I, respectively, obtained using the BSE@G0W0@PBE method. The computed imaginary parts of the dielectric function are plotted in [PI…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

71 extracted references · 57 canonical work pages

  1. [1]

    This configuration is similar to insufficient B-site ABX3 perovskite materials that have discrete [BX6] clusters

    Crystal Structure: TheRb 2BX6 doubleperovskites, havingelements Rb, Si, Ge, Sn, Pt, Cl, Br, and I,showcasean orderlyface-centered cubic crystal structure designated by the space group Fm¯3m (225). This configuration is similar to insufficient B-site ABX3 perovskite materials that have discrete [BX6] clusters. In this configuration, 12 halogen ions surroun...

    work page

  2. [2]

    The dynamical stability of a material is a key factor in determining its overall stability as it is closely related to the characteristics of its phonon modes

    Dynamical Stability: We employed the DFPT[43] approach to thoroughly assess the dynamical stability of the Rb2BX6 (B = Si, Ge, Sn, Pt; X = Cl, Br, I) VODPs. The dynamical stability of a material is a key factor in determining its overall stability as it is closely related to the characteristics of its phonon modes. In the case of Rb2BX6, there are 27 phon...

    work page

  3. [3]

    Mechanical Stability and Elastic Properties: Stability is one of the crucial aspects to consider when choosing a material for its future research applications. Therefore, to acquire a more comprehensive understanding, the mechanical stability and elastic properties of Rb2BX6 compounds are also investigated alongside the crystallographic and dynamical stab...

    work page

  4. [4]

    Here, l, m, n refers to the number of atoms (l=2, m=1, n=6)

    Thermodynamical Stability: In assessing the thermodynamic stability of the compounds, the formation energy (Ef) is calculated using the following formula: Ef = ERblBmXn−lERb−mEB−nEX (l +m +n) (1) where ERblBmXn represents the total energy of investigated compounds andERb, EB, and EX are the energies of individual Rb, B-site (Si, Ge, Sn, Pt) and halogen (C...

    work page

  5. [5]

    Table III

    The heavier hole masses, indicating Rb2BX6 VODPs are more suitable forn-type semiconductors. Table III. Carrier’s effective mass, and reduced mass (µ∗) of Rb2BX6 (B = Si, Ge, Sn, Pt; X = Cl, Br, I) VODPs calculated using G0W0@PBE method. Here, me and mh represents electron and hole effective mass (wheremo is the rest mass of the electron), respectively. T...

    work page

  6. [6]

    Hussain, M

    M. Hussain, M. Rashid, A. Ali, M. F. Bhopal, and A. Bhatti, Ceram. Int.46, 21378 (2020)

    work page 2020

  7. [7]

    K. A. Bush, A. F. Palmstrom, Z. J. Yu, M. Boccard, R. Cheacharoen, J. P. Mailoa, D. P. McMeekin, R. L. Z. Hoye, C. D. Bailie, T. Leijtens, I. M. Peters, M. C. Minichetti, N. Rolston, R. Prasanna, S. Sofia, D. Harwood, W. Ma, F. Moghadam, H. J. Snaith, T. Buonassisi, Z. C. Holman, S. F. Bent, and M. D. McGehee, Nat. Energy2, 17009 (2017)

    work page 2017

  8. [8]

    M. K. Jana, S. M. Janke, D. J. Dirkes, S. Dovletgeldi, C. Liu, X. Qin, K. Gundogdu, W. You, V. Blum, and D. B. Mitzi, J. Am. Chem. Soc.141, 7955 (2019), pMID: 31017429, https://doi.org/10.1021/jacs.9b02909

    work page doi:10.1021/jacs.9b02909 2019

Show all 71 references
  1. [9]

    Adhikari and P

    S. Adhikari and P. Johari, Phys. Rev. Mater.7, 075401 (2023)

    2023

  2. [10]

    Nazir, S

    S. Nazir, S. Maqsood, N. Noor, S. Mumtaz, and I. M. Moussa, Polyhedron256, 117003 (2024)

    2024

  3. [11]

    Zhang, G

    W. Zhang, G. E. Eperon, and H. J. Snaith, Nat. Energys1, 16048 (2016)

    2016

  4. [12]

    26,4653(2014),https://onlinelibrary.wiley.com/doi/pdf/10.1002/adma.201306281

    W.-J.Yin, T.Shi,andY.Yan,Adv.Mater. 26,4653(2014),https://onlinelibrary.wiley.com/doi/pdf/10.1002/adma.201306281

    2014 doi

  5. [13]

    A. A. Dotsenko, V. I. Vovna, V. V. Korochentsev, A. G. Mirochnik, O. L. Shcheka, T. V. Sedakova, and V. I. Sergienko, Inorg. Chem. 58, 6796 (2019), https://doi.org/10.1021/acs.inorgchem.9b00250

    2019 doi

  6. [14]

    A. E. Maughan, A. M. Ganose, M. M. Bordelon, E. M. Miller, D. O. Scanlon, and J. R. Neilson, J. Am. Chem. Soc.138, 8453 (2016), pMID: 27284638, https://doi.org/10.1021/jacs.6b03207

    2016 doi

  7. [15]

    M. M. S. Karim, A. M. Ganose, L. Pieters, W. W. Winnie Leung, J. Wade, L. Zhang, D. O. Scanlon, and R. G. Palgrave, Chem. Mater. 31, 9430 (2019), pMID: 32116409, https://doi.org/10.1021/acs.chemmater.9b03267

    2019 doi

  8. [16]

    Travis, E

    W. Travis, E. N. K. Glover, H. Bronstein, D. O. Scanlon, and R. G. Palgrave, Chem. Sci.7, 4548 (2016)

    2016

  9. [17]

    Faizan, J

    M. Faizan, J. Xie, G. Murtaza, C. Echeverría-Arrondo, T. Alshahrani, K. C. Bhamu, A. Laref, I. Mora-Seró, and S. Haidar Khan, Phys. Chem. Chem. Phys.23, 4646 (2021)

    2021

  10. [18]

    Faizan, K

    M. Faizan, K. C. Bhamu, G. Murtaza, X. He, N. Kulhari, M. M. AL-Anazy, and S. H. Khan, Sci. Rep.11, 6965 (2021)

    2021

  11. [19]

    Zhao, X.-N

    X.-H. Zhao, X.-N. Wei, T.-Y. Tang, L.-K. Gao, Q. Xie, L.-M. Lu, and Y.-L. Tang, Opt. Mater.114, 110952 (2021)

    2021

  12. [20]

    Huang, Z.-Y

    H.-M. Huang, Z.-Y. Jiang, and S.-J. Luo, Chin. Phys. B26, 096301 (2017)

    2017

  13. [21]

    B. Lee, C. C. Stoumpos, N. Zhou, F. Hao, C. Malliakas, C.-Y. Yeh, T. J. Marks, M. G. Kanatzidis, and R. P. H. Chang, J. Am. Chem. Soc.136, 15379 (2014), pMID: 25299304, https://doi.org/10.1021/ja508464w

    2014 doi

  14. [22]

    M.-G. Ju, M. Chen, Y. Zhou, H. F. Garces, J. Dai, L. Ma, N. P. Padture, and X. C. Zeng, ACS Energy Lett.3, 297 (2018), https://doi.org/10.1021/acsenergylett.7b01167. 14

    2018 doi

  15. [23]

    Y. Cai, W. Xie, H. Ding, Y. Chen, K. Thirumal, L. H. Wong, N. Mathews, S. G. Mhaisalkar, M. Sherburne, and M. Asta, Chem. Mater. 29, 7740 (2017), https://doi.org/10.1021/acs.chemmater.7b02013

    2017 doi

  16. [24]

    Zhou, J.-F

    L. Zhou, J.-F. Liao, Z.-G. Huang, X.-D. Wang, Y.-F. Xu, H.-Y. Chen, D.-B. Kuang, and C.-Y. Su, ACS Energy Lett.3, 2613 (2018), https://doi.org/10.1021/acsenergylett.8b01770

    2018 doi

  17. [25]

    M. C. Folgueras, J. Jin, M. Gao, L. N. Quan, J. A. Steele, S. Srivastava, M. B. Ross, R. Zhang, F. Seeler, K. Schierle-Arndt, M. Asta, and P. Yang, J. Phys. Chem. C125, 25126 (2021), https://doi.org/10.1021/acs.jpcc.1c08332

    2021 doi

  18. [26]

    H. Wan, F. Jia, F. Dinic, M. Imran, B. Rehl, Y. Liu, W. Paritmongkol, P. Xia, Y.-K. Wang, Y. Liu, S. Wang, Q. Lyu, G. F. Cotella, P. Chun, O. Voznyy, S. Hoogland, and E. H. Sargent, Chem. Mater. 35, 948 (2023), https://doi.org/10.1021/acs.chemmater.2c02673

    2023 doi

  19. [27]

    Glockzin, M

    B. Glockzin, M. S. Oakley, A. Karmakar, A. Pominov, A. A. Mitchell, X. Ma, M. Klobukowski, and V. K. Michaelis, J. Phys. Chem. C127, 7284 (2023), https://doi.org/10.1021/acs.jpcc.2c08073

    2023 doi

  20. [28]

    X. Qiu, B. Cao, S. Yuan, X. Chen, Z. Qiu, Y. Jiang, Q. Ye, H. Wang, H. Zeng, J. Liu, and M. Kanatzidis, Sol. Energy Mater. Sol. Cells159, 227 (2017), publisher Copyright:© 2016 Elsevier B.V

    2017

  21. [30]

    J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003), https://pubs.aip.org/aip/jcp/article- pdf/118/18/8207/10847843/8207_1_online.pdf

    2003

  22. [32]

    Kresse and J

    G. Kresse and J. Furthmüller, Phys. Rev. B54, 11169 (1996)

    1996

  23. [33]

    Kresse and J

    G. Kresse and J. Furthmüller, Comput. Mater. Sci.6, 15 (1996)

    1996

  24. [34]

    J. J. Mortensen, L. B. Hansen, and K. W. Jacobsen, Phys. Rev. B71, 035109 (2005)

    2005

  25. [35]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett.77, 3865 (1996)

    1996

  26. [36]

    Hedin, Phys

    L. Hedin, Phys. Rev.139, A796 (1965)

    1965

  27. [37]

    M. S. Hybertsen and S. G. Louie, Phys. Rev. Lett.55, 1418 (1985)

    1985

  28. [38]

    Albrecht, L

    S. Albrecht, L. Reining, R. Del Sole, and G. Onida, Phys. Rev. Lett.80, 4510 (1998)

    1998

  29. [39]

    Rohlfing and S

    M. Rohlfing and S. G. Louie, Phys. Rev. Lett.81, 2312 (1998)

    1998

  30. [40]

    Gajdoš, K

    M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, and F. Bechstedt, Phys. Rev. B73, 045112 (2006)

    2006

  31. [41]

    Thiele, C

    G. Thiele, C. Mrozek, D. Kämmerer, and K. Wittmann, , Z. Naturforsch. 38b38, 905 (1983)

    1983

  32. [42]

    D. I. Torres, J. D. Freire, and R. S. Katiyar, Phys. Rev. B56, 7763 (1997)

    1997

  33. [43]

    Ketelaar, A

    J. Ketelaar, A. Rietdijk, and C. Van Staveren, Recl. Trav. Chim. Pays-Bas56, 907 (1937)

    1937

  34. [44]

    Werker, Recl

    W. Werker, Recl. Trav. Chim. Pays-Bas58, 257 (1939)

    1939

  35. [45]

    Engel, Z

    G. Engel, Z. Kristallogr Cryst. Mater.90, 341 (1935)

    1935

  36. [46]

    Mahmood, M

    Q. Mahmood, M. Hassan, T. H. Flemban, B. Ul Haq, S. AlFaify, N. A. Kattan, and A. Laref, J. Phys. Chem. Solids148, 109665 (2021)

    2021

  37. [47]

    Suzuki and M

    S. Suzuki and M. Tsuyama, Opt. Mater.119, 111323 (2021)

    2021

  38. [48]

    de Gironcoli, Phys

    S. de Gironcoli, Phys. Rev. B51, 6773 (1995)

    1995

  39. [49]

    Mouhat and F

    F. Mouhat and F. m. c.-X. Coudert, Phys. Rev. B90, 224104 (2014)

    2014

  40. [50]

    V. Wang, N. Xu, J.-C. Liu, G. Tang, and W.-T. Geng, Comput. Phys. Commun.267, 108033 (2021)

    2021

  41. [51]

    Wu, E.-j

    Z.-j. Wu, E.-j. Zhao, H.-p. Xiang, X.-f. Hao, X.-j. Liu, and J. Meng, Phys. Rev. B76, 054115 (2007)

    2007

  42. [52]

    Hill, Proc

    R. Hill, Proc. Phys. Soc. A65, 349 (1952)

    1952

  43. [53]

    S. Pugh, S. Pugh45, 823 (1954), https://doi.org/10.1080/14786440808520496

    1954 doi

  44. [54]

    Huang, Y.-H

    B. Huang, Y.-H. Duan, W.-C. Hu, Y. Sun, and S. Chen, Ceram. Int.41, 6831 (2015)

    2015

  45. [55]

    Zhang, Y

    J.-M. Zhang, Y. Zhang, K.-W. Xu, and V. Ji, J. Phys. Chem. Solids68, 503 (2007)

    2007

  46. [56]

    S. I. Ranganathan and M. Ostoja-Starzewski, Phys. Rev. Lett.101, 055504 (2008)

    2008

  47. [57]

    M.-G. Ju, J. Dai, L. Ma, and X. C. Zeng, Adv. Energy Mater. 7, 1700216 (2017), https://onlinelibrary.wiley.com/doi/pdf/10.1002/aenm.201700216

    2017 doi

  48. [58]

    Q. Li, L. Zhou, Y. Ge, Y. Ren, J. Zhao, W. Wan, K. Zhang, and Y. Liu, arXiv preprint arXiv:1908.02187 (2019), arXiv:1908.02187 [physics.app-ph]

    2019 arXiv

  49. [59]

    T. I. Al-Muhimeed, A. Shafique, A. A. AlObaid, M. Morsi, G. Nazir, M. m. AL-Anazy, and Q. Mahmood, Int. J. Energy Res. 45, 19645 (2021), https://onlinelibrary.wiley.com/doi/pdf/10.1002/er.7022

    2021 doi

  50. [60]

    Chadli, A

    S. Chadli, A. Bekhti Siad, M. Baira, M. Siad, A. Allouche, and A. Reguig, Solid State Commun.342, 114633 (2022)

    2022

  51. [61]

    S. A. Qamar, T.-W. Lin, Y.-T. Tsai, and C. C. Lin, ACS Appl. Nano Mater. 5, 7580 (2022), https://doi.org/10.1021/acsanm.2c01647

    2022 doi

  52. [62]

    A. E. Maughan, A. M. Ganose, M. A. Almaker, D. O. Scanlon, and J. R. Neilson, Chem. Mater. 30, 3909 (2018), https://doi.org/10.1021/acs.chemmater.8b01549

    2018 doi

  53. [63]

    Hemidi, T

    D. Hemidi, T. Seddik, T. Benmessabih, M. Batouche, W. Ouerghui, H. B. Abdallah, G. Surucu, and S. Ahmad, Appl. Phys. A: Mater. Sci. Process.129, 762 (2023)

    2023

  54. [64]

    Kumar, A

    M. Kumar, A. Singh, D. Gill, and S. Bhattacharya, J. Phys. Chem. Lett. 12, 5301 (2021), pMID: 34061540, https://doi.org/10.1021/acs.jpclett.1c01034

    2021 doi

  55. [65]

    Bokdam, T

    M. Bokdam, T. Sander, A. Stroppa, S. Picozzi, D. D. Sarma, C. Franchini, and G. Kresse, Sci. Rep.6, 28618 (2016)

    2016

  56. [66]

    X. Wang, W. Meng, and Y. Yan, J. Appl. Phys.122, 10.1063/1.4991913 (2017), https://pubs.aip.org/aip/jap/article- pdf/doi/10.1063/1.4991913/15201223/085104_1_online.pdf

    2017 doi

  57. [67]

    Ferreira, A

    F. Ferreira, A. J. Chaves, N. M. R. Peres, and R. M. Ribeiro, J. Opt. Soc. Am. B36, 674 (2019)

    2019

  58. [68]

    M. R. Filip, J. B. Haber, and J. B. Neaton, Phys. Rev. Lett.127, 067401 (2021)

    2021

  59. [69]

    R. W. Hellwarth and I. Biaggio, Phys. Rev. B60, 299 (1999). 15

    1999

  60. [70]

    J. M. Frost, Phys. Rev. B96, 195202 (2017)

    2017

  61. [71]

    Franchini, M

    C. Franchini, M. Reticcioli, M. Setvin, and U. Diebold, Nat. Rev. Mater.6, 560 (2021)

    2021

  62. [72]

    R. P. Feynman, Phys. Rev.97, 660 (1955)

    1955

  63. [73]

    Bhumla, M

    P. Bhumla, M. Jain, S. Sheoran, and S. Bhattacharya, J. Phys. Chem. Lett. 13, 11655 (2022), pMID: 36503226, https://doi.org/10.1021/acs.jpclett.2c02852

    2022 doi

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.