Vacancy-Ordered Halide Perovskites as High Entropy Semiconductors

Slides for my talk on vacancy-ordered halide perovskites as high entropy semiconductors (theoretical modelling and experiments) at MRS Spring 2024, Seattle.

YouTube video recording: https://youtu.be/lLFkX7mW1r4

References:
Ultra-Strong Excitons in Vacancy-Ordered Halide Perovskites: https://doi.org/10.1021/acs.jpclett.2c02436
Mixed-Cation Vacancy-Ordered Halide Perovskites: https://pubs.acs.org/doi/10.1021/acs.jpcc.3c05204

Questions welcome! For other computational photovoltaics, defects and disorder talks, have a look at my YouTube channel!
https://www.youtube.com/SeanRKavanagh
For other research articles see:
https://bit.ly/3pBMxOG

Abstract:
Due to their quasi-0D / molecular-aggregate type crystal structure, vacancy-ordered double perovskites (VODPs) with the chemical formula A2BX6, exhibit unusual material properties associated with both zero-dimensional and three-dimensional materials.1–4 These include low thermal conductivity, high compressibility, and strong exciton binding despite relatively small semiconducting band gaps, making them potential candidates for a range of alternative applications, such as thermoelectrics, white-light emitters/phosphors, photocatalysts, non-linear optics and more. In this study, we report a combined experimental and computational investigation on the mixing behavior of cations in this system. Remarkably, we find ultra-low enthalpic costs to cation mixing, resulting in entropy dominance and ideal mixing behavior. This facilitates the room-temperature and low-temperature synthesis of high-entropy materials (high-entropy semiconductors) from these compounds, as demonstrated experimentally by Folgueras et al in Nature, 2023.5 We elucidate the underlying structural and electronic origins of this facile cation miscibility in these systems, and analyze the resulting optical, thermodynamic and structural changes upon cation mixing. Our work demonstrates that vacancy-ordered perovskites present an exciting new class of high-entropy semiconductors, synthesisable at much milder conditions than typical high-entropy materials. Moreover, we elucidate the origins of this behavior, allowing the extraction of general design rules for high-entropy semiconductors with tailored properties.

Transcript

1. 2 28/05/2024 skavanagh@seas.harvard.edu Vacancy-Ordered Halide Perovskites for High Entropy Semiconductors Seán R. Kavanagh, Shanti M. Liga, Gerasimos Konstantatos, David O. Scanlon & Aron Walsh
2. High Entropy Semiconductors? • Major growth in research on high entropy (metallic) alloys & ceramics/oxides in recent years. • However, discovery & design of high entropy semiconductors has been sparse. • Lower melting/decomposition temperatures • Typically more covalent bonding • A key challenge is the high synthesis temperatures (>1000 ℃) required to achieve mixing, as well as complex synthesis processes (e.g. hot rolling). 3
3. High Entropy Semiconductors? • Major growth in research on high entropy (metallic) alloys & ceramics/oxides in recent years. • However, discovery & design of high entropy semiconductors has been sparse. • Lower melting/decomposition temperatures • Typically more covalent bonding • A key challenge is the high synthesis temperatures (>1000 ℃) required to achieve mixing, as well as complex synthesis processes (e.g. hot rolling). 4
4. How can we reduce Tsynthesis ? ➡ Need to reduce mixing enthalpies Gmix = Hmix - TSmix Target Properties: • Soft / easily-distorted lattice, to accommodate ionic radii variations • Non-directional (i.e. ionic) bonding, yielding high structural uniformity, flexibility and ion solubility 5
5. 6 1. A. E. Maughan, A. M. Ganose, D. O. Scanlon, J. R. Neilson, Chem. Mater. 2019, 31 (4), 1184–1195 2. Y.-T. Huang, S. R. Kavanagh, D. O. Scanlon, A. Walsh and R. L. Z. Hoye, Nanotechnology, (2021), 32, 132004. 3. M. Chen, M.-G. Ju, A. D. Carl, Y. Zong, R. L. Grimm, J. Gu, X. C. Zeng, Y. Zhou and N. P. Padture, Joule, (2018), 2, 558–570. A2 MX6 ≋ A(0/M)X3 Vacancy-Ordered Double Perovskites
6. 7 1. A. E. Maughan, A. M. Ganose, D. O. Scanlon, J. R. Neilson, Chem. Mater. 2019, 31 (4), 1184–1195 2. Y.-T. Huang, S. R. Kavanagh, D. O. Scanlon, A. Walsh and R. L. Z. Hoye, Nanotechnology, (2021), 32, 132004. 3. M. Chen, M.-G. Ju, A. D. Carl, Y. Zong, R. L. Grimm, J. Gu, X. C. Zeng, Y. Zhou and N. P. Padture, Joule, (2018), 2, 558–570. AI 2 MIVX6 ≋ A(00/MIV)X3 Vacancy-Ordered Halide Double Perovskites • Photovoltaics • Photocatalysts • White-light emission / phosphors • Thermoelectrics • Photo detectors • Non-linear optics (THG active) • … • High entropy semiconductors?
7. 8 A+: Spectator ion (Cs+, Rb+, K+, MA+…) M4+: Sn4+, Te4+, Ge4+, Ti4+, Zr4+, Hf4+, Pt4+, Pd4+, Re4+… X -: Halide ion (I -, Br -, Cl -, F -) • Isolated MX6 octahedra • Fully-oxidised cations ➡ ionic M-X bonds • Solution synthesis (nanocrystals, thin films and single crystals) 1. Y.-T. Huang, S. R. Kavanagh, D. O. Scanlon, A. Walsh and R. L. Z. Hoye, Nanotechnology, (2021), 32, 132004. 2. M. Chen, M.-G. Ju, A. D. Carl, Y. Zong, R. L. Grimm, J. Gu, X. C. Zeng, Y. Zhou and N. P. Padture, Joule, (2018), 2, 558–570. AI 2 MIVX6 Vacancy-Ordered Halide Double Perovskites
8. 9 AI 2 MIVX6 Vacancy-Ordered Halide Double Perovskites Key Properties: • Weak orbital hybridization between octahedra • Significant van der Waals attraction between octahedra (~10% volume contraction)1 Consequences: • Effective “zero-dimensional” / molecular salt behaviour • Ionic and vdW bonding, negligible covalent contributions • Ultra-strong excitonic effects, despite relatively low band gaps1,2 1. Kavanagh et al. J. Phys. Chem. Lett. 2022 2. Cucco et al. Mater. Lett. 2023
9. How can we reduce Tsynthesis ? ➡ Need to reduce mixing enthalpies Gmix = Hmix - TSmix Target Properties: • Soft / easily-distorted lattice, to accommodate ionic radii variations • Non-directional (i.e. ionic) bonding, yielding high structural uniformity and cation solubility 10
10. How can we reduce Tsynthesis ? ➡ Need to reduce mixing enthalpies Gmix = Hmix - TSmix Target Properties: • Soft / easily-distorted lattice, to accommodate ionic radii variations ✅ (inter-octahedral voids, significant vdW effects) • Non-directional (i.e. ionic) bonding, yielding high structural uniformity and cation solubility ✅ (negligible covalency) 11
11. Special Quasirandom Structures (SQS) with hybrid DFT including spin-orbit coupling. 12 A2 {M}X6 : Mixing Energetics “Quasirandom” radial distribution function g(r) g(r)supercell ≃ g(r)random
12. 13 A2 {M}X6 : Mixing Energetics Liga‡ & Kavanagh‡ et al. J. Phys. Chem. C 2023
13. 14 d(Ti – X) in Cs2 (Snx Ti1-x )X6 ≃ d(Ti – X) in Cs2 TiX6 d(Sn – X) in Cs2 (Snx Ti1-x )X6 ≃ d(Sn – X) in Cs2 SnX6 Consistent behaviour across all X = I, Br, Cl HSE06+SOC+vdW A2 {M}X6 : Mixing Energetics
14. 15 A2 {M}X6 : Facile Mixing in Solution Liga‡ & Kavanagh‡ et al. J. Phys. Chem. C 2023
15. 16 Room (20℃) & low (80℃) temperature synthesis of single crystals in solution
16. 17 A2 {M}X6 : Optical Properties Negligible orbital hybridization ➡ Additive type behaviour: ⍺(A2 {M}X6 ) ≃ x1 *⍺(A2 M1X6 ) + x2 *⍺(A2 M2X6 ) + …
17. 18 A2 {B}X6 : Stability? ➡ Again, additive type behaviour: ΔH(A2 {M}X6 ) ≃ x1 *ΔH(A2 M1X6 ) + x2 *ΔH(A2 M2X6 ) + … • A2MIVX6 thermodynamically stable in inert atmospheres • O2 decomposition to MIVO2 thermodynamically favoured (except X = Cl), but kinetically inhibited. • Hygroscopic; decomposition accelerated in aqueous environments. • Stability increases as X -> I, Br, Cl, F. • vdW interactions contribute significantly to stability. Liga‡ & Kavanagh‡ et al. J. Phys. Chem. C 2023
18. Takeaways Isolated MX6 octahedra yield: Dominant ionic & vdW bonding, with flexible crystal structure due to vacant space between octahedra. ➡ Ultra-low mixing enthalpies ➡ Low-temperature solution synthesis of mixed compositions Novel class of easily-synthesized, low-gap, excitonic high-entropy semiconductors! Liga‡ & Kavanagh‡ et al. J. Phys. Chem. C 2023 Folgueras et al. Nature 2023
19. Final Notes Modelling Considerations: • vdW interactions crucial! (Volume, electronic properties, stability…) • Strong excitonic behaviour (DFT unsuitable for electronic properties) 1. Padelkar et al. Phys. Rev. Appl. 2024 Halide mixing also relatively facile!1 High-entropy mixed-cation mixed-anion semiconductors?
20. Acknowledgements Shanti Liga & Prof G. Konstantatos Profs Aron Walsh & David O. Scanlon @Kavanagh_Sean_ skavanagh@seas.harvard.edu Kavanagh et al. ‘Frenkel Excitons in Vacancy- Ordered Titanium Halide Perovskites (Cs2TiX6)’ J. Phys. Chem. Lett. 2022, 13, 10965–10975 Liga‡ & Kavanagh‡ et al. ‘Mixed-Cation Vacancy- Ordered Perovskites (Cs2 Ti1–x Snx X6 )’ J. Phys. Chem. C. 2023, 43, 21399–21409 Paper Links:
21. Cs2 SnX6 = Mostly stable under air, thermal, water & photo stresses. X = I (Cs2 SnI6 ) shows some very slow decomposition in air. X = Br, Cl ➡ Stable in (humid) air. 22 Cs2 MX6 – Stability Saporov et al. Chem Mater 2016
22. Cs 2 TiX 6 : X = I: Unstable in air. X = Br: Stable under heat and light. Stability in air? • 1Chen et al. Joule 2018 ➡ Thin films, stable in humid air • 2Kong et al. J. Mater. Chem. C 2019 ➡ Powder, slight decomposition in humid air • 3Euvrard et al. J. Mater. Chem. A 2020 ➡ Powder, decomposition in humid air (~20h) • 4Grandhi et al. Nanomaterials 2021 ➡ Nanocrystal films, slow decomposition in air (~1 wk) X = Cl: Very slow decomposition in air (~1-2% over 2 weeks).2,4 23 Cs2 MX6 – Stability Cs 2 TiBr 6 Cs 2 TiI 6
23. Intrinsic Thermodynamic Stability Cs 2 SnI 6 Cs 2 SnBr 6 Cs 2 SnCl 6 Cs 2 TiI 6 Cs 2 TiBr 6 Cs 2 TiCl 6 Hybrid DFT + vdW Decomposition Energy (eV) +56 meV +129 meV +174 meV +75 meV +120 meV +162 meV 24 • Positive decompositions energies ➡ Thermodynamically stable in each case, as witnessed experimentally (stable in inert atmospheres) • Van der Waal’s dispersion interactions found to be significant in stabilizing Cs2MX6: Cs 2 SnI 6 Cs 2 TiI 6 Hybrid DFT Decomposition Energy (eV) +14 meV +51 meV Hybrid DFT + vdW Decomposition Energy (eV) +56 meV +75 meV Increasing stability as X: I -> Br -> Cl
24. External Decomposition in Oxygen/Water • O2 decomposition significantly more favourable for M = Ti as expected (strong stability of TiO2 ) • O2 decomposition less favoured as X -> I, Br, Cl. Note: Reaction kinetics ignored here. Reactants Products ΔH (eV) Cs2SnI6 + O2 SnO2 + 2CsI + 4I(s) -2.43 Cs2SnBr6 + O2 SnO2 + 2CsBr + 2Br2(l) -0.10 Cs2SnCl6 + O2 SnO2 + 2CsCl + 2Cl2(g) +0.82 Reactants Products ΔH (eV) Cs2TiI6 + O2 TiO2 + 2CsI3 + 4I(s) -4.90 Cs2TiBr6 + O2 TiO2 + 2CsBr + 2Br2(l) -1.70 Cs2TiCl6 + O2 TiO2 + 2CsCl + 2Cl2(g) -0.38 Aqueous Decomposition: Cs2 MX6 + H2 O ➡ MO2 + 2 CsX + 4HX(g) Gaseous product (4HX(g)) means reaction energy ΔE is a function of pHX (i.e. environment-dependent)
25. • Experimentally, Cs2MX6 found to be hygroscopic and to exhibit accelerated decomposition under humid oxygen atmospheres. • Calculations find aqueous decomposition to be thermodynamically favoured under certain HX(g) partial pressure ranges. • Additionally, potential kinetic/catalytic effect from surface hydration. O 2 /H 2 O Decomposition 26 Humid Air Dessicated Air E.G: Cs2(Ti0.4Sn0.6)Br6
26. Cs2 MX6 Stability: Conclusions • Cs 2 SnX 6 far more stable than Cs 2 TiX 6 in ambient atmospheres. • However Cs 2 TiX 6 is interesting because: • Ultra-strong Frenkel excitons ➡ Playground to study associated physical phenomena • Initially, promising photovoltaic performance (diminished by identification of strong excitons however) • Non-linear optics: Only known third-harmonic generation (THG) active lead- free perovskite, thanks to centrosymmetric crystal structure.1 • Can we alloy Sn/Ti to tune stability and optical/electronic properties? 27 1Grandhi et al. Nanomaterials 2021
27. Energy-lowering reconstructions prevalent in a wide & diverse range of materials/defects. 32 Importance of Defect Structure Searching! More details in Thursday morning’s talk: EL04.05.02: Symmetry-Breaking and Reconstruction at Point Defects in Perovskites April 13, 9-9.15 AM shakenbreak.readthedocs.io 1. Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* npj Comp Mater 2023 2. Mannodi-Kanakkithodi Nature Physics 2023 3. Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* J. Open Source Software 2022 4. Mosquera-Lois & Kavanagh*, Matter 2021 5. Kavanagh, Walsh, Scanlon ACS Energy Lett 2021 6. Kavanagh*, Scanlon, Walsh, Freysoldt; Faraday Discussions 2022 Cs2 TiI6 : Large energy lowering of ΔE: -0.4 – -2.5 eV for many native defects: • VTi 0, VTi -1, VTi -2, VTi -3, VTi -4 (all VTi charge states) • Ii 0, Ii -1 • ICs 0, ICs -1, ICs -2 • TiCs 0, TiCs +1, TiCs +2, TiCs +3 • ITi 0, ITi -1 • TiI +2, TiI +5 • Csi +1
28. V Ti -4 – Fully-ionised Titanium Vacancy Unperturbed; Slightly contracted octahedron ShakeNBreak: Iodine trimer; ΔE = -0.8 eV
29. V Ti -1 Unperturbed; distorted contracted octahedron ShakeNBreak: double Iodine trimer; ΔE = -1.1 eV
30. V Ti -1 Unperturbed; distorted contracted octahedron ShakeNBreak: double Iodine trimer; ΔE = -1.1 eV
31. Ti Cs +3 – Fully-ionised Titanium-on-Caesium Unperturbed; Ti-Ti bond within Iodine octahedron ShakeNBreak: Ti split, one goes to vacant octahedral site near missing caesium -> ΔE = -2.5 eV
32. Energy-lowering reconstructions prevalent in a wide & diverse range of materials/defects. 41 Importance of Defect Structure Searching! More details in Thursday morning’s talk: EL04.05.02: Symmetry-Breaking and Reconstruction at Point Defects in Perovskites April 13, 9-9.15 AM shakenbreak.readthedocs.io 1. Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* npj Comp Mater 2023 2. Mannodi-Kanakkithodi Nature Physics 2023 3. Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* J. Open Source Software 2022 4. Mosquera-Lois & Kavanagh*, Matter 2021 5. Kavanagh, Walsh, Scanlon ACS Energy Lett 2021 6. Kavanagh*, Scanlon, Walsh, Freysoldt; Faraday Discussions 2022 Cs2 TiI6 : Large energy lowering of ΔE: -0.4 – -2.5 eV for many native defects, due to: • Multinary composition • Reduced crystal symmetry • Space to distort / ‘open’ crystal structure • Presence of ionic & covalent bonding