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Structural Evolution in Methylammonium Lead Iodide CH3NH3PbI3 Khuong P. Ong,*,† Teck Wee Goh,‡ Qiang Xu,‡ and Alfred Huan† †

Institute of High Performance Computing, Agency of Science, Technology and Research (A*STAR), 1 Fusionopolis Way, 138632 Singapore ‡ Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore S Supporting Information *

ABSTRACT: The organic−inorganic hybrid perovskite, in particular, methylammonium lead iodide (MAPbI3), is currently a subject of intense study due to its desirability in making efficient photovoltaic devices economically. It is known that MAPbI3 undergoes structural phase transitions from orthorhombic Pnma to tetragonal I4/mcm at ∼170 K and then to cubic Pm3̅m at ∼330 K. A tetragonal P4mm phase is also reported at 400 K considering total cation disorder is not appealing due to its hydrogen-bonding capabilities. Resolving this ambiguity of phase transition necessitates the study of the structural evolution across these phases in our work using ab initio methods. In this work, we show that the structural phase evolves from Pnma to I4/mcm to P4mm to Pm3̅m with increasing volume. The P4mm phase is a quasi-cubic one with slight distortion in one direction from cubic Pm3̅m due to the rotation of MA cations. Biaxial strain on MAPbI3 reveals that only the Pnma and P4mm phases are energetically stable at a < 9.14 Å and a > 9.14 Å, respectively. The Pnma, I4/mcm, P4mm, and Pm3̅m phases can be stable under various uniaxial strain conditions. Our study provides a clear understanding of the structural phase transitions that occur in MAPbI3 and provides a guide for the epitaxial growth of specific phases under various strain conditions.

T

cation resides within the network of corner-sharing PbI6 cuboctahedral cage having different tilting characteristics at various structural phases of the material. It was found through powdered X-ray diffraction (XRD)14 that the methylammonium lead iodide (MAPbI3) perovskite exists in the cubic Pm3̅m phase at high temperature above 330 K, below which it undergoes a phase transition to the tetragonal I4/mcm phase and then to the orthorhombic Pnma phase below 170 K; however, in single-crystal XRD it was reported that the phase transition from I4/mcm phase15 at high temperature tends to 15,17 both the cubic16 Pm3m P4mm space groups. ̅ and tetragonal The P4 mm space group was also proposed considering that total disorder of cation orientation is not ideal due to their hydrogen-bonding capabilities with PbI6 cuboctahedral cage. A slight ambiguity is present in the nature of crystal structure of this material at high temperatures. The physical origin leading to the existence of these MAPbI3 phases is not well understood, and thus a careful re-examination of the crystallographic properties in this material is required. Despite initial theoretical work performed in recent years to elucidate properties of OIHP pertaining to doping and interfaces, the fundamental understanding is still premature to explore such more complex aspects of this material. Some of these fundamental understanding derived from theoretical calculations include characterization of defects,18−21 the

he organic−inorganic hybrid perovskite (OIHP) has been a popular material of research for its potential in efficient and economical photovoltaic technology. Currently the most efficient laboratory solar cells fabricated from this material, having exceeded 19%,1 are comparable to the performance of existing solar cell technologies. The pace of research to reach this stage is also impressive considering only 5 years have passed since the first report2 on perovskite photovoltaics, whose progress has surpassed that of other types of solar cell in photovoltaic research. Even with the impressive application of OIHP in solar cells, fundamental research in understanding its physical properties is lacking, and only recently some of these properties have been illuminated despite the older papers on this material. These properties include the material’s long carrier diffusion length,3−6 low exciton binding energy,7,8 large dielectric constant,9 large absorption coefficient,10 and ferroelectricity.11 Despite concerted efforts in the fundamental research of OIHP, much work remains to be done to understand the material from a theoretical viewpoint to illustrate the important chemical properties that make it desirable for its application. Perovskite is a general class of materials, which has the chemical formula ABX3, where in this intensely studied OIHP A represents the methylammonium (MA+), formamidinium (FA+), or guanidinium12 (GA+) cation, B represents the lead (Pb2+), tin (Sn2+), or germanium (Ge2+) cation and X represents the iodide (I−) cation, which can be substituted with the other halide13 (Br−, Cl−) anions. Structurally, the MA © 2015 American Chemical Society

Received: October 9, 2015 Published: October 13, 2015 11033

DOI: 10.1021/acs.jpca.5b09884 J. Phys. Chem. A 2015, 119, 11033−11038

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The Journal of Physical Chemistry A

Figure 1. Analysis of chemical bonds between I atoms and H atoms within different structures: P4mm with a = b = 6.375 Å and c = 6.253 Å; Pm3m ̅ with a = b = c = 6.455 Å; and Pnma and I4/mcm with a = 8.98 Å and c = 12.57 (I4/mcm) and 12.30 Å (Pnma).

presence of dispersive forces,22 optical properties23 and Rashba effect.24 Other notable theoretical works in this area include charge screening by the cation,25 interfacial phenomena,26,27 hysteresis effect,28 ion transport,29 role of chlorine in mixedhalide perovskites,30 and the role of MA cation orientation toward the perovskites’ band structure;31 however, understanding of fundamental properties in OIHP is paramount before studying its more complex properties. Recently, the role of tetragonal lattice parameters (c/a) ratio toward the Pnma to I4/mcm phase transition has been elucidated.32 This strain effect, facilitated by the hydrogen-bonding interaction between the MA cation and the surrounding PbI6 cuboctahedral cage, could open up the possibility of inducing structural phase transitions through other means apart from a change in temperature. Experimental realization of this phenomenon could open up a new area of solar cell optimization by suitably inducing specific structural phases in devices. We discuss the interplay between the various MA orientations in different phases of MAPbI3 and cubic cell volume to simulate how volume change reorients the MA cations and invokes structural phase transitions. The structural evolution of MAPbI3 under different epitaxial conditions, namely, biaxial and uniaxial constraints, with the verified orientations of MA in structural phases of MAPbI3 is investigated to predict the conditions for the existence of various phases. The existence and phase transition of a distinct P4mm structure to Pm3̅m is confirmed.

Throughout the paper, unless specified otherwise, the ratio of lattice constants c against a (c/a) for the cubic Pm3̅m and tetragonal P4mm structures will be referenced to the cubic/ pseudocubic unit cell, which is made up of one MAPbI3 formula unit, whereas those for the tetragonal I4/mcm and Pnma will be referenced to the tetragonal unit cell, which is the √2 × √2 × 2 transformation of the cubic/pseudocubic structure. (See the Supporting Information.) MA cation orientations will always be referred to with respect to the cubic/pseudocubic cells for easy comparison. Comparison of cell volume across all structural phases of MAPbI3 is done with respect with the cubic/pseudocubic cell volume. All energies in our calculation are normalized to the most stable Pnma structure, E = E − EPnma. The change in cell volume by varying its lattice constants results in different structural phase transitions. The chemical bonding between MA cations and the PbI6 cuboctahedral cage dictates the orientation of MA cations in MAPbI3 and plays a key role in the structural phase transitions. Experimentally through nuclear magnetic resonance (NMR)33 it was found that the MA cations reorient themselves in the cubic phase on the order of picoseconds, approaching that of a freely rotating motion that increasingly gets arrested at low temperatures. The orientation and movement of MA cations in MAPbI3 were first predicted to be influenced by the c/a ratios and the H−I bonds32 in the I4/mcm and Pnma phases. This theoretical analysis reveals that the NH3 components of MA are strongly 11034


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The Journal of Physical Chemistry A bonded to the I atoms compared with those of CH3, which results in the MA cations precessing about the NH3 component instead of a completely free rotation. This is an almost general feature of the OHIP class, which is understood to be due to hydrogen bonding 12,34 between the H atoms in NH 3 components with their surrounding I atoms. Within our simulations the orientations of MA components in MAPbI3 are carefully studied in different directions35 depicted in Figure 1. This work reveals the existence of several metastable MA orientations in the cubic Pm3̅m and tetragonal P4mm structures, where the MA cations do not preferentially rotate toward other directions, even though that may not be the globally stable one. The origin relates to the strong and weak bonds between NH3 and CH3 components toward their surrounding I atoms, respectively. These metastable orientations are identified as following: (1) The MA cations orient along the direction: If atom H1 in the NH3 component bonds to I6 or I5, H3 bonds to I9, and H2 bonds to I1, then MA cation will orient along the [010] direction in Figure 1a; if H1 bonds to I9 or I10, H2 bonds to I12, and H3 bonds to I10, then the MA cation will orient along the [001] direction; if H1 bonds to I6 or I7, H2 bonds to I2, and H3 bonds to I10, then the MA cation will orient along [100] direction. (2) The MA cations orient along [111]: H atoms from NH3 component mainly bond to I atoms at the corners such as H1 bonds to I9, H2 bonds to I5, and H3 bond to I12 shown in Figure 1b. (3) The MA cations orient along [110], [011], and [101], which happens in two different ways: (1) H2 and H3 instead of bonding to I1 and I9 in case (i) will bond to I4 and I12, respectively, as shown in Figure 1c. (2) H2 and H3 instead of bonding to I1 and I9 in case (i) will bond to I5 and (I9, I10, I12), respectively, shown in Figure 1d. These orientations strongly distort the rotations of PbI6 octahedra from no tilting in cubic Pm3̅m or in-phase tilting in tetragonal P4mm to antiphase tilting in the orthorhombic Pnma and tetragonal I4/ mcm structures. To understand the interplay between MA cation orientations with phase transitions, we first need to determine the dependence of the respective phases with respect to volume change. The variation of energy with cubic/pseudocubic cell volume for the various phases is shown in Figure 2. Our results show that the transition from cubic Pm3̅m to tetragonal I4/ mcm is not direct as originally believed. Instead, a tetragonal P4mm phase is established between I4/mcm and Pm3̅m. The P4mm phase is indeed a quasi-cubic phase with slight distortion in one direction having small energy difference between two phases. This tendency is vice versa with transitions in MAPbBr3 with cubic Pm3̅m (T > 237 K) to tetragonal I4/mcm (155 < T < 237 K) then to tetragonal P4/mmm (149.5 < T < 155 K) and to orthorhombic Pna21 at low temperature (T < 144.5 K).36 Our study on the P4mm phase shows that c/a is greater than 1 at small volumes with the MA cation oriented along [001] direction. This c/a ratio decreases with an increase in volume with the most stable P4mm phase achieved at c/a ≈ 1. At larger volume the c/a ratio is 1 is not stable in comparison with that of the I4/mcm (c/a(I4/mcm) > 1). The result shows that during the phase transition from P4mm to I4/mcm the MA cations rotate from in-plane [010] direction toward the out-ofplane c direction. Such rotations of the MA cations cause an antiphase tilt in the PbI6 octahedra, which is stabilized by I4/ mcm symmetry. The √2 × √2 × 2 cell of the I4/mcm structure is derived from either Pm3̅m or P4mm structure by rotating the cubic or pseudocubic cell of Pm3̅m or P4mm structure, respectively, by 45° and doubling the unit cell along the c direction; therefore, the [010] direction in the P4mm structure corresponds to [110] direction in I4/mcm structure. The orientations of MA cations along the [111] direction for I4/mcm structure are equivalent to the rotations of MA components in [010] direction out-of-plane to the c direction in P4mm structure. The transition between the tetragonal I4/ mcm and orthorhombic Pnma phases was well studied.32 Figure 2 shows that the real stable I4/mcm structure (at B, see Figure 2) is not with the most stable I4/mcm structure (at A, see Figure 2). The calculation shows that the I4/mcm lattice parameters at B are in better agreement with experimental reports. (See Table 1.) Experimental reports14,15 show that at low temperatures MAPbI3 perovskite has the Pnma orthorhombic phase and undergoes a phase transition to the I4/mcm tetragonal phase at higher temperatures from 161.4 K. At T > 330 K, the MAPbI3 is stabilized with cubic Pm3m ̅ phase. A different tetragonal P4mm space group, which can be considered as pseudocubic having lattice difference of 0.005 Å between its in-plane and out-ofplane lattice constants, was also reported17 at 400 K in single 11035


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The Journal of Physical Chemistry A Table 1. Lattice Constants of I4/mcm and P4mm Structure a (Å) cubic I4/mcm exp

6.194 6.222 6.258

P4mm exp

6.320 6.312

b (Å) tetra

cubic

V (Å3)

c (Å) tetra

cubic

8.76 6.194 8.76 8.8 6.222 8.8 8.85 6.258 8.85 cubic/tetra = cubic/tetra representation: aT/bT = aC/bC 6.320 6.312

6.255 6.34 6.22 × √2; cT = cC × 6.310 6.316

tetra 12.51 12.68 12.44 2; VT = VC × 4

cubic

tetra

240.2 245.48 243.58

960.8 981.9415 974.3314

252 251.6017

aI4/mcm > 9.14 Å, while the Pnma phase is stabilized at aI4/mcm < 9.14 Å under biaxial strain. In contrast with introducing biaxial strain, the influence of uniaxial constraint along [001] direction on the phase transitions of MAPbI3 reveals the possibility of obtaining multiple structural phases. The Pnma phase is stable at low strain with a phase transition to the I4/mcm tetragonal phase32 at cI4/mcm ≈ 12.42 Å. The MA cations reorient themselves from [110] in Pnma structure to [011] in I4/mcm structure, as shown in Figure 1. At larger c, the I4/mcm is unstable and transforms to tetragonal P4mm at cI4/mcm = 12.74 Å − 12.78 Å (cP4mm = c/2 = 6.37 − 6.39 Å), as shown in Figure 4, as the MA

crystals; however, the transition from tetragonal to cubic is widely believed to be from the I4/mcm phase to the Pm3m ̅ phase. The physical origin of the P4mm phase and how it comes into the picture of phase transition is not well understood. Strain engineering of materials through epitaxial growth has been a particularly effective approach for realizing novel properties. We therefore study the existence of these possible phases in MAPbI3 by strain engineering with different biaxial and uniaxial constraints. The influence of biaxial constraint on the (001) MAPbI3 thin films is shown in Figure 3. The results show that under biaxial

Figure 4. Influence of uniaxial constraint along [001] direction on the phase transitions of MAPbI3 thin film. The lattice constants c of P4mm and Pm3m ̅ structures are doubled to make a reasonable comparison to I4/mcm and Pnma structures.

Figure 3. Influence of biaxial constraint on the (001) MAPbI3 thin film. To make a reasonable comparison with I4/mcm and Pnma structures, we multiplied the in-plane lattice constant a of P4mm and Pm3m ̅ by √2.

constraint the Pnma phase is stabilized up to aI4/mcm = bI4/mcm ≈ 9.14 Å. At higher tensile constraint aI4/mcm > 9.14 Å, the tetragonal P4mm is stabilized (aP4mm = aI4/mcm/√2, following the stated convention) instead. The cubic Pm3m ̅ and tetragonal I4/mcm phases are not stable under biaxial constraint on the (001) MAPbI3 thin films. At larger in-plane lattice constant a, the out-of-plane lattice constant c, is less than √2a (cI4/mcm < √2aI4/mcm). The structural transition from orthorhombic Pnma to tetragonal P4mm is simply the rotation of MA cations from [110] direction to [100] or [010] direction and the tilt of PbI6 octahedral changes from antiphase tilt a−b−c+ to in-phase tilt in P4mm. As reported, the Pnma phase is stable at high (c/a)I4/mcm ratio (c/a > 1.45). When the in-plane lattice constants increase, (c/a)I4/mcm decreases and thus Pnma phase becomes unstable. On the contrary, the P4mm is stabilized at low (c/a)I4/mcm ratio. As a result, when the lattice constant aI4/mcm increases, the MA cations are forced to rotate from [110] direction to the [100] or [010] directions, that is, transform from Pnma structure to P4mm structure. Therefore, the P4mm structure is stabilized at

cations rotate from [011] direction in I4/mcm to the [001] direction in the P4mm structure. At c from 12.78 to 12.95 Å (cPm3̅m,P4mm = 6.39 − 6.495 Å), the Pm3̅m structure is more stable than the P4mm structure but the energy difference between these two structures is very small, shown in the Figure 4 inset, implying the coexistence of these two phases. At c larger than 12.95 Å (cP4mm = 6.495 Å), the P4mm is stabilized with a discontinuity at c = 12.95 Å (cP4mm = 6.495 Å). This discontinuity is due to the change in chemical bonding between I atoms and H atoms from CH3 components. For P4mm structure, increasing lattice constant c results in decrease in lattice constant a. This brings the I atoms I5, I6, I7, and I8 closer to CH3 component, making bonds H5−I7, H5−I8, H6− I6, and H4−I5 being comparable to chemical bonds H5−I3, H4−I4, and H6−I2 shown in Figure 1. These additional bonds between CH3 components to I5, I6, I7, and I8 further stabilize the P4mm structure at high tensile strain along the [001] direction. The lattice constants at which the various phase transitions occur are summarized in Table 1. 11036


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The Journal of Physical Chemistry A In conclusion, we have studied the evolution of structural phases in MAPbI3 and obtaining them under biaxial and uniaxial strain conditions. We show the existence of P4mm structure, which is distorted along one direction from the Pm3m ̅ by rotations of MA cations. Toward larger crystal volume, MAPbI3 transforms from tetragonal I4/mcm to tetragonal P4mm and not directly to the cubic Pm3̅m as commonly believed. The cubic Pm3̅m phase is also more stable at larger volume when MAPbI3 transforms from P4mm to Pm3̅m. The increase in crystal volume causes the MA cations to rotate from [110] direction (Pnma phase) → [011] direction (I4/mcm phase) → [001] direction (P4mm phase) → [111] direction (Pm3m ̅ phase). The influence of strain on the epitaxial growth of MAPbI3 reveals that the biaxial constraint helps to stabilize the P4mm structure at a > 9.14 Å (aP4mm > 6.46 Å), while the Pnma phase is stable at a < 9.14 Å. The uniaxial constraint along the c direction reveals that all structural phases could be obtained and shows an ambiguity in the phase transition from I4/mcm to P4mm and Pm3̅m with c from 12.74 to12.95 Å. We show the actual origin for the structural evolution of MAPbI3 from orthorhombic Pnma → tetragonal I4/mcm → tetragonal P4mm and to cubic Pm3̅m of large single crystals, which can now be grown by methods such as antisolvent vapor-assisted crystallization6 and top-seeded solution growth5 or solution-based hot-casting technique37 in the case of practical solar cell applications. Our study guides the solar cell community to explore conditions for the existence of these different structural phases in MAPbI3 to utilize beneficial properties in each of them to optimize better devices. For the electronic structures of MAPbI3 calculations, we use the all-electron-like projector-augmented wave (PAW) method38 with the Perdew−Burke−Ernzerhof (PBE)39 and PBE revised for solids (PBEsol)40 exchange correlation potential, as implemented in the VASP code.41 The cutoff energy for the plane wave expansion of the wave functions is 500 eV, and all atoms in the unit cell are fully relaxed until the Hellman− Feynman forces are 175 μm in SolutionGrown CH3NH3PbI3 Single Crystals. Science 2015, 347, 967−970. (6) Shi, D.; Adinolfi, V.; Comin, R.; Yuan, M.; Alarousu, E.; Buin, A.; Chen, Y.; Hoogland, S.; Rothenberger, A.; Katsiev, K. others, Low Trap-State Density and Long Carrier Diffusion in Organolead Trihalide Perovskite Single Crystals. Science 2015, 347, 519−522. (7) Sun, S.; Salim, T.; Mathews, N.; Duchamp, M.; Boothroyd, C.; Xing, G.; Sum, T. C.; Lam, Y. M. The Origin of High Efficiency in Low-Temperature Solution-Processable Bilayer Organometal Halide Hybrid Solar Cells. Energy Environ. Sci. 2014, 7, 399. (8) D’Innocenzo, V.; Grancini, G.; Alcocer, M. J. P.; Kandada, A. R. S.; Stranks, S. D.; Lee, M. M.; Lanzani, G.; Snaith, H. J.; Petrozza, A. Excitons Versus Free Charges in Organo-Lead Tri-Halide Perovskites. Nat. Commun. 2014, 5, 3586. (9) Juarez-Perez, E. J.; Sanchez, R. S.; Badia, L.; Garcia-Belmonte, G.; Kang, Y. S.; Mora-Sero, I.; Bisquert, J. Photoinduced Giant Dielectric Constant in Lead Halide Perovskite Solar Cells. J. Phys. Chem. Lett. 2014, 5, 2390−2394. (10) Singh, S. P.; Nagarjuna, P. Organometal Halide Perovskites as Useful Materials in Sensitized Solar Cells. Dalton Trans. 2014, 43, 5247. (11) Frost, J. M.; Butler, K. T.; Brivio, F.; Hendon, C. H.; van Schilfgaarde, M.; Walsh, A. Atomistic Origins of High-Performance in Hybrid Halide Perovskite Solar Cells. Nano Lett. 2014, 14, 2584− 2590. (12) Giorgi, G.; Fujisawa, J.-I.; Segawa, H.; Yamashita, K. OrganicInorganic Hybrid Lead Iodide Perovskite Featuring Zero Dipole Moment Guanidinium Cations: A Theoretical Analysis. J. Phys. Chem. C 2015, 119, 4694−4701. (13) Mosconi, E.; Amat, A.; Nazeeruddin, M. K.; Gratzel, M.; De Angelis, F. First-Principles Modeling of Mixed Halide Organometal

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b09884. Structural transformations in methylammonium lead iodide CH3NH3PbI3. Transformation from cubic/ pseudocubic structure (orange color) to tetragonal (I4/ 11037


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