On the thermal expansion of the tetragonal phase of MAPbI₃ and MAPbBr₃

Abstract

Based on previously published research, the structural response of the tetragonal hybrid perovskite crystal structure of MAPbX₃ [MA: [CH₃NH₃]⁺, methylammonium; X = I, Br] to thermal expansion is reviewed here. From an averaged crystal structure perspective, the tetragonal perovskite structure of MAPbI₃ and MAPbBr₃, based on diffraction data, shows apparent Pb-X bond length shortening and apparent shrinkage of the [PbX₆] octahedra with increasing temperature. At the same time, these apparent observations, and hence the thermal expansion, are related to the progressive phase transformation towards the cubic structure, as the lattice parameters respond to a shear stress that couples to the order parameters, and this coupling is predicted by group theory and thus aims to explain precisely the apparent negative thermal expansion-like effects. A different picture emerges for the thermal expansion when considering the very localized structure, since neither a shortening of the Pb-X bond lengths nor a shrinking of the [PbX₆] octahedra is observed with pair distribution function analysis, and the presence of orthorhombic short-range order in the tetragonal and cubic perovskite structures is assumed in published studies. The compared extended X-ray absorption fine structure studies, which also map the local structure and provide the “true” bond distance, show no lead-halide bond length shortening with temperature. The perpendicular mean square relative displacement has been determined. Therefore, a comparison of the tension and bond expansion effects in both perovskites can be made. In the orthorhombic phase of MAPbI₃ and MAPbBr₃, positive expansion and negative tension of the lead-halide bond are almost balanced. After transitioning to the tetragonal phase, the equilibrium shifts toward negative tension. This suggests that both hybrid perovskites have tighter lead-halide bonds and less rigid [PbX₆] octahedra in the tetragonal phase than in the low temperature perovskite crystal structure.

Keywords

Hybrid perovskites / thermal expansion / local structure / pair distribution function (PDF) analysis / extended X-ray absorption fine structure (EXAFS) / tension effect

References

[1] Chouhan L,Subrahmanyam C,Biju V.Synthesis, optoelectronic properties and applications of halide perovskites.Chem Soc Rev2020;49:2869-85

[2] Pérez-Fidalgo L,Charles BL.Anomalous electron-phonon coupling in cesium-substituted methylammonium lead iodide perovskites.J Phys Chem C2023;127:22817-26

[3] Spera EL,Gau DL,Marotti RE.Excitonic optical properties of CH₃NH₃PbI₃ perovskite and its dependence with temperature.MRS Adv2024;9:39-44

[4] Jošt M,Korte L.Monolithic perovskite tandem solar cells: a review of the present status and advanced characterization methods toward 30% efficiency.Adv Energy Mater2020;10:1904102

[5] Duan L,Chang N.Stability challenges for the commercialization of perovskite-silicon tandem solar cells.Nat Rev Mater2023;8:261-81

[6] Schuck G,Wallacher D,Tien TS.Temperature-dependent EXAFS measurements of the Pb L3-edge allow quantification of the anharmonicity of the lead-halide bond of chlorine-substituted methylammonium (MA) lead triiodide.J Phys Chem C2022;126:5388-402

[7] Weadock NJ,Qin X.Thermal contributions to the local and long-range structural disorder in CH₃NH₃PbBr₃.PRX Energy2023;2:033004

[8] Schuck G,Ollivier J,Schorr S.Influence of chloride substitution on the rotational dynamics of methylammonium in MAPbI_3-xCl_x perovskites.J Phys Chem C2019;123:11436-46

[9] Miyata K,Zhu XY.Lead halide perovskites: crystal-liquid duality, phonon glass electron crystals, and large polaron formation.Sci Adv2017;3:e1701469 PMCID:PMC5640380

[10] Tailor NK.Crystalline-liquid duality of specific heat in halide perovskite semiconductor.Scr Mater2023;223:115061

[11] Adams DJ.Classification of perovskite structural types with dynamical octahedral tilting.IUCrJ2023;10:309-20 PMCID:PMC10161773

[12] Liang X,Baldwin WJ,Csányi G.Structural dynamics descriptors for metal halide perovskites.J Phys Chem C Nanomater Interfaces2023;127:19141-51 PMCID:PMC10544022

[13] Weadock NJ,Vigil JA.The nature of dynamic local order in CH₃NH₃PbI₃ and CH₃NH₃PbBr₃.Joule2023;7:1051-66

[14] Beecher AN,Skelton JM.Direct observation of dynamic symmetry breaking above room temperature in methylammonium lead iodide perovskite.ACS Energy Lett2016;1:880-7

[15] Page K,Quadrelli P.Short-range order of methylammonium and persistence of distortion at the local scale in MAPbBr₃ hybrid perovskite.Angew Chem Int Ed2016;55:14320-4

[16] Bernasconi A.Direct evidence of permanent octahedra distortion in MAPbBr₃ hybrid perovskite.ACS Energy Lett2017;2:863-8

[17] Bird TA,Songvilay M. Large dynamic scissoring mode displacements coupled to band gap opening in hybrid perovskites. arXiv 2021. Available from: https://arxiv.org/abs/2108.05751 [Last accessed on 7 Aug 2024]

[18] Simenas M,Banys J.Phase transitions and dynamics in mixed three- and low-dimensional lead halide perovskites.Chem Rev2024;124:2281-326 PMCID:PMC10941198

[19] Kutes Y,Zhou Y,Huey BD.Direct observation of ferroelectric domains in solution-processed CH₃NH₃PbI₃ perovskite thin films.J Phys Chem Lett2014;5:3335-9

[20] Bari M,Ye Z.Ferroelastic domains and phase transitions in organic-inorganic hybrid perovskite CH₃NH₃PbBr₃.J Mater Chem C2021;9:3096-107

[21] Bari M,Leach GW.Ferroelastic domains and effects of spontaneous strain in lead halide perovskite CsPbBr₃.Chem Mater2023;35:6659-70

[22] Wilson JN,Wallace SK.Dielectric and ferroic properties of metal halide perovskites.APL Mater2019;7:010901

[23] Breternitz J.The “ferros” of MAPbI₃: ferroelectricity, ferroelasticity and its crystallographic foundations in hybrid halide perovskites.Cryst Mater2022;237:135-40

[24] Ambrosio F,Goñi AR.The ferroelectric-ferroelastic debate about metal halide perovskites.J Phys Chem Lett2022;13:7731-40 PMCID:PMC9421894

[25] Zheng W,Zhang X.Emerging halide perovskite ferroelectrics.Adv Mater2023;35:e2205410

[26] Haeger T,Riedl T.Thermal properties of metal-halide perovskites.J Mater Chem C2020;8:14289-311

[27] Jacobsson TJ,Ottosson M,Edvinsson T.Determination of thermal expansion coefficients and locating the temperature-induced phase transition in methylammonium lead perovskites using X-ray diffraction.Inorg Chem2015;54:10678-85

[28] Bozec Y, Kaang S, Hine P, Ward I. The thermal-expansion behaviour of hot-compacted polypropylene and polyethylene composites.Composit Sci Technol2000;60:333-44

[29] Becker P,Siegert H.The lattice parameter of highly pure silicon single crystals.Z Physik B Condens Matter1982;48:17-21

[30] Ge C,Wu P.Ultralow thermal conductivity and ultrahigh thermal expansion of single-crystal organic-inorganic hybrid perovskite CH₃NH₃PbX₃ (X = Cl, Br, I).J Phys Chem C2018;122:15973-8

[31] Zhou Y,Qaid SMH,Zhou Y.Strain engineering toward high-performance formamidinium-based perovskite solar cells.Solar RRL2023;7:2300438

[32] Katan C,Even J.Entropy in halide perovskites.Nat Mater2018;17:377-9

[33] Fornasini P.On EXAFS debye-waller factor and recent advances.J Synchrotron Rad2015;22:1242-57

[34] Sanson A.EXAFS spectroscopy: a powerful tool for the study of local vibrational dynamics.Microstructures2021;1:2021004

[35] Schuck G,Koch-müller M,Schorr S.Infrared spectroscopic study of vibrational modes across the orthorhombic-tetragonal phase transition in methylammonium lead halide single crystals.J Phys Chem C2018;122:5227-37

[36] Whitfield PS,Guise WE.Structures, phase transitions and tricritical behavior of the hybrid perovskite methyl ammonium lead iodide.Sci Rep2016;6:35685 PMCID:PMC5073364

[37] Franz A,Schorr S.Interaction between cation orientation, octahedra tilting and hydrogen bonding in methylammonium lead triiodide.Cryst Res Technol2016;51:534-40

[38] Stoumpos CC,Kanatzidis MG.Semiconducting tin and lead iodide perovskites with organic cations: phase transitions, high mobilities, and near-infrared photoluminescent properties.Inorg Chem2013;52:9019-38

[39] Celeste A.Hybrid perovskites under pressure: present and future directions.J Appl Phys2022;132:220903

[40] Szafrański M.Mechanism of pressure-induced phase transitions, amorphization, and absorption-edge shift in photovoltaic methylammonium lead iodide.J Phys Chem Lett2016;7:3458-66

[41] Gil-González E,Sánchez-Jiménez PE.Paving the way to establish protocols: modeling and predicting mechanochemical reactions.J Phys Chem Lett2021;12:5540-6 PMCID:PMC8280717

[42] Whitfield PS,Guise WE.Correction: Corrigendum: structures, phase transitions and tricritical behavior of the hybrid perovskite methyl ammonium lead iodide.Sci Rep2017;7:42831 PMCID:PMC5318896

[43] Schorr S.Low-temperature thermal expansion in sphalerite-type and chalcopyrite-type multinary semiconductors.J Phys Condens Matter2008;20:104245

[44] Haussühl S. Kristallphysik; Weinheim, Germany: Physic-Verlag; 1983.

[45] Feng J.Mechanical properties of hybrid organic-inorganic CH₃NH₃BX₃ (B = Sn, Pb; X = Br, I) perovskites for solar cell absorbers.APL Mater2014;2:081801

[46] Campbell BJ,Tanner DE.ISODISPLACE: a web-based tool for exploring structural distortions.J Appl Cryst2006;39:607-14

[47] Liu J,Phillips AE,Keen DA.Neutron powder diffraction study of the phase transitions in deuterated methylammonium lead iodide.J Phys Condens Matter2022;34:145401

[48] Egami T. Underneath the bragg peaks: structural analysis of complex materials; Oxford: Elsevier; 2003.

[49] Billinge SJ.Nanoscale structural order from the atomic pair distribution function (PDF): there’s plenty of room in the middle.J Solid State Chem2008;181:1695-700

[50] Bird TA,Senn MS.Symmetry-adapted pair distribution function analysis (SAPA): a novel approach to evaluating lattice dynamics and local distortions from total scattering data.J Appl Cryst2021;54:1514-20 PMCID:PMC8493621

[51] Bird TA,Hu L.Anharmonicity and scissoring modes in the negative thermal expansion materials ScF₃ and CaZrF₆.Phys Rev B2020;101:064306

[52] Ravel B.ATHENA, ARTEMIS, HEPHAESTUS: data analysis for X-ray absorption spectroscopy using IFEFFIT.J Synchrotron Rad2005;12:537-41

[53] Bunker G.Application of the ratio method of EXAFS analysis to disordered systems.Nucl Instrum Methods Phys Res1983;207:437-44

[54] Bunker G. Introduction to EXAFS; Cambridge: Cambridge University Press; 2010.

[55] Fornasini P,Dalba G.Extended X-ray-absorption fine-structure measurements of copper: local dynamics, anharmonicity, and thermal expansion.Phys Rev B2004;70:174301

[56] Fornasini P.The coefficient of bond thermal expansion measured by extended X-ray absorption fine structure.J Chem Phys2014;141:164503

[57] Fornasini P.Vibrational anisotropy. In: Schnohr CS, Ridgway MC, editors. X-ray absorption spectroscopy of semiconductors. Berlin: Springer; 2015. pp. 127-42.

[58] Attfield JP.Mechanisms and materials for NTE.Front Chem2018;6:371 PMCID:PMC6113360

[59] Dove MT.Negative thermal expansion and associated anomalous physical properties: review of the lattice dynamics theoretical foundation.Rep Prog Phys2016;79:066503

[60] Dalba G,Fornasini P.An EXAFS study of thermal disorder in GaAs.J Phys Condens Matter1994;6:3599-608

[61] Dalba G,Kuzmin A,Rocca F.X-ray absorption spectroscopy study of ReO₃ lattice dynamics.J Phys Condens Matter1995;7:1199-213

[62] Talit K.Stress effects on vibrational spectra of a cubic hybrid perovskite: a probe of local strain.J Phys Chem C2020;124:27287-99

[63] Gava V,Perottoni CA.First-principles mode Gruneisen parameters and negative thermal expansion in α-ZrW₂O₈.Phys Rev Lett2012;109:195503

[64] Boldyrev KN,Semenova OI.Infrared spectra of the CH₃NH₃PbI₃ hybrid perovskite: signatures of phase transitions and of organic cation dynamics.J Phys Chem C2020;124:23307-16

[65] Železný V,Kamba S,Kundu S.Infrared and terahertz studies of phase transitions in the CH₃NH₃PbBr₃ perovskite.Phys Rev B2023;107:174113