Phase Diagram and Dielectric Properties of MA1âxFAxPbI3 | ACS

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Phase Diagram and Dielectric Properties of MA FAPbI

Ashutosh Mohanty, Diptikanta Swain, Sharada Govinda, Tayur N. Guru Row, and D. D. Sarma ACS Energy Lett., Just Accepted Manuscript • DOI: 10.1021/acsenergylett.9b01291 • Publication Date (Web): 30 Jul 2019 Downloaded from pubs.acs.org on July 31, 2019

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Phase Diagram and Dielectric Properties of MA1-xFAxPbI3 Ashutosh Mohanty, Diptikanta Swain, Sharada Govinda, Tayur N. Guru Row and D. D. Sarma* Solid State and Structural Chemistry Unit, Indian Institute of Science, Bengaluru - 560012, India

Corresponding Author: *[email protected]

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Abstract

With the help of 10 different compositions (x) between 0.0 and 0.4 for MA1-xFAxPbI3 and about 20 temperature points between 15 and 310 K for each composition, we establish a rich temperature-composition phase diagram in terms of structural variations determined by powder and single-crystal x-ray diffraction. Four crystallographic phases are found to exist for this solid solution series namely, cubic (Pm-3m), tetragonal (P4/mcm), orthorhombic (Pnma) and largecell cubic (I-m). Variable temperature dielectric measurement reveals qualitative changes in dielectric properties of these materials driven by the observed structural phase transitions; it establishes that with an increasing FA content, the high temperature dominant Curie-like behavior in dielectric constant of MAPbI3 gets suppressed and an unusually prominent glassy behavior evolves in direct correlation with the structural evolution. This reveals a strong structure-property correlation existing in these solid solutions, qualitatively modifying properties of MAPbI3 with FA substitution.


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Methyl ammonium lead iodide (MAPbI3) shot into fame following reports of solar cells made with it as the active material exhibiting power conversion efficiencies beyond 10%.1-2 With an unprecedented level of excitement and activities involving a large number of groups from across the world, the efficiency has been pushed beyond 23%.3-4 The early concern and criticisms arising from the rather unstable nature of this and related compounds are being adequately addressed by enormous global efforts, formulating chemical and structural variations of the active material to achieve greater stability. The most important progresses in delivering high power conversion efficiency together with long device operational life-times have been achieved by partially replacing the A-site methyl ammonium (MA) cation with other organic moieties, most notably formamidinium (FA), defining a solid solution of MAPbI3 and FAPbI3 to form MA1-xFAxPbI3.5

The crystal structures of MAPbI3 and FAPbI3 have already been discussed extensively in the literature. After some early disagreement of various space groups reported for different phases,63 ACS Paragon Plus Environment


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it is now generally agreed11-12 that MAPbI3 has a high temperature cubic (C) phase with the

space group Pm-3m, which transforms to a tetragonal (T) phase below 331 K with the space group I4/mcm and to an orthorhombic (O) phase below 162 K with the space group Pnma. FAPbI3 exhibits possibly an even richer variety of crystal structures depending on the temperature and on post-synthesis methods adopted.13 For example, Stoumpos et al. refined9 the structure of α-FAPbI3 at 293 K to be trigonal with the space group P3m1 from a single crystal Xray diffraction study, while Weller et al.14 using high resolution neutron powder diffraction experiments and Zhumekenov et al.15 from single crystal X-ray diffraction studies suggested the structure of α-FAPbI3 to be cubic with the space group Pm-3m at 298 K. Further, FAPbI3 is also known to exist in a non-perovskite polymorphic δ-phase at the room temperature with the hexagonal space group P63mc.16 It is important to note that this hexagonal phase, though stable at the room temperature, is not a good absorber of the solar spectrum because of a large band gap; in addition, its chain like structure hinders electron transfer. This example of electron movement through chain like backbone underlines the importance of structure-property relationship in this class of materials for their selection in photovoltaic applications. α-FAPbI3 (room temperature phase) transforms into a tetragonal phase with the space group P4/mbm below 285 K and to another tetragonal phase below 140 K, attributed to the same space group.17 This low temperature structure below 140 K has also been refined to a new tetragonal phase with space group P4bm by Chen et al. from their neutron and powder x-ray diffraction data.13 Some of these structural phase transitions are also known to impact dielectric properties of these materials profoundly with qualitatively and quantitatively different behaviours as a function of the temperature.18-19 Interestingly, the FA and the MA analogues have been shown to have drastically different dielectric properties, around the room temperature.19 Noting the relevance of


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the dielectric constant, controlling the excitonic binding energy, charge transport and screening of defect potentials, it is surprising to note that very little is known about the structural phase diagram or the inter-related dielectric properties of the solid solutions, MA1-xFAxPbI3, for various values of x between 0 and 1, though such compositions are being routinely explored in attempts to achieve highly efficient photovoltaic devices with greatly enhanced stabilities. Only few reports exist in the literature on the crystal structure of solid solution MA1-xFAxPbI3. In the only temperature dependent investigation,20 Weber et al. reported temperature dependent powder XRD of MA1-xFAxPbI3, for x = 0.0 – 1.0 with a step size of 0.1 and analysed the structures from room temperature to 150 K. This limitation of the lowest temperature and the coarse graining of the composition leads to missing the richness of the crystallographic phase diagram of this system, as will be shown in the Results and Discussion section. Moreover, there is no dielectric property reported in the literature for these mixed compositions so far. Therefore, we have investigated the structural phase diagram of the solid-solution with the help of powder XRD from 295 K to 15 K with more than 180 independent measurements at various compositiontemperature points and more than 10 temperature dependent single crystal XRD measurements down to 95 K. In addition, we also measured dielectric properties of each composition over wide temperature and frequency ranges, allowing us to make evident a strong and universal correlation between the structure and the dielectric properties of the solid solution with a probable clue to the microscopic origin of the enhanced stability of FA-doped systems.



We have carried out temperature dependent X-ray diffraction measurements on MA1-xFAxPbI3 with x = 0.05, 0.075, 0.1, 0.125, 0.5, 0.75, 0.2, 0.3 and 0.4. Profile fittings of these data reveal a very rich structural phase diagram for this solid solution. We show a typical example of a powder XRD and the results of its profile fitting for x = 0.1 at 130 K in Fig. 1a. The pattern (a)

(b)

AA

AA

Figure 1. (a) Profile fitting of powder XRD pattern for MA0.9FA0.1PbI3 at 130 K and (b) Powder XRD pattern for MA0.875FA0.125PbI3 at representative temperatures. could be fitted with a cubic structure having I-3m space group with profile R-factor less than 10% and χ2 of value 1.35 indicating a good fitting. Similar results for all compositions at various characteristic temperatures are shown in the Supporting Information (SI) Figs. S1 – S9. The results of the profile fitting in terms of lattice parameters for characteristic temperatures of each composition have been presented in Tables S1 – S9 in the SI. All compositions show evidence of structural phase transitions with temperature, as illustrated in Fig. 1b for the x = 0.125 composition. The XRD shows emergence of new peaks with changing temperatures, allowing us to identify as many as four different crystallographic phases, namely cubic (C), tetragonal (T), 6 ACS Paragon Plus Environment

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large cell cubic (LC) and orthorhombic (O) crystal structures. The highest temperature phase (C) has only one peak at about 28.1 within the range of angles 26-29, at 310 K displayed in Fig. 1b with the profile fit suggesting a cubic structure (shown in Fig. S4(a)). This XRD pattern persists down to about 295 K and our single crystal diffraction data suggests Pm-3m space group for this part of the phase diagram. However, single crystal data cannot fix the orientations of the organic moieties due to dynamic and static disorder, as shown in Fig. 2a. At temperatures below 290 K, x = 0.125 sample shows a splitting of the cubic peak at 28.1 into a doublet appearing at 27.9 and 28.3 (see Fig. 1b for T = 250 K), indicating a tetragonal distortion. This phase exists down to about 160 K and the single crystal data refines in a tetragonal space group I4/mcm with disordered FA/MA entities, as shown in Fig. 2b. With a further lowering of the temperature, the powder XRD pattern shows the emergence of new peaks, at 26.5 and 28.5 as shown for 150 K in Fig. 1b, along-with the peaks of the tetragonal phase, indicating the existence of mixed phases. It is noteworthy that this mixed phase region exists for only a narrow temperature range. Accordingly, the peaks due to the tetragonal phase disappear below 140 K, as illustrated for T = 120 K in Fig. 1b, with the suggestion of a super cell formation with doubling of the unit cell axis

(a)

(b)

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AA



(c)

(d)

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Figure 2. Single crystal XRD showing crystal structures of (a) cubic, (b) tetragonal, (c) largecell cubic and (d) orthorhombic phases for x = 0.125 with cation disorder at different temperatures. for the cubic system. The single crystal data of this phase suggests Im-3 space group for this large cubic cell, shown in Fig. 2c. While the organic units are still disordered, the number of orientations possible in this low temperature phase is reduced to 4 in contrast to 24 equivalent positions available in the higher temperature, smaller cubic cell (Fig. 2a). We believe that this reduction is probably responsible for the super cell formation at this temperature region. Finally, the diffraction pattern of x = 0.125 composition shows the formation of the ground state orthorhombic phase below 90 K, as shown at T = 15 K in Fig. 1b, through a narrow range of mixed large-cell cubic and orthorhombic phases, illustrated by the T = 100 K diffraction pattern


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in Fig. 1b. The lowest temperature orthorhombic phase has the Pnma space group and its unit cell is shown in Fig. 2d. Based on extensive powder diffraction investigations on a dense grid of composition-temperature phase space, we have constructed the phase diagram of MA1-xFAxPbI3 as a function of x and T; this phase diagram is shown as Fig. 3. We have marked each point on the phase space analyzed

Figure 3. Temperature-Composition Phase Diagram for MA1-xFAxPbI3 system showing distinct Cubic (C), tetragonal (T), large-cell cubic (LC) and orthorhombic (O) phases separated by phase boundary shown in red, blue, green and orange colour. Three mixed phases namely, T+O, T+LC and O+LC also exist between pure phases. by us with a cyan dot, so that the accuracy of determining the phase transition lines in this diagram is self-evident. The lines separate the regions of pure crystallographic phases from one another as well as from the mixed phase regions, with the cubic (Pm-3m), tetragonal (I4/mcm), large cell cubic (Im-3) and orthorhombic (Pnma) phases denoted as C, T, LC and O,



respectively. This diagram makes it clear that the MA-rich end with x ≤ 0.075 retains essentially the same sequence of crystallographic transitions as pure MAPbI3 of C→T→O with a decrease in the temperature; however, both cubic to tetragonal and tetragonal to orthorhombic transition temperatures are found to decrease with an increasing x. These decreases in the transition temperatures with an increasing x become a lot more rapid for x > 0.075 with an additional largecell cubic phase appearing for this higher x-range. Thus, the crystallographic phase transitions with a decreasing temperature successively go through cubic, tetragonal, large cell cubic and orthorhombic phases for 0.075 < x ≤ 0.15. For x > 0.15, the ground state orthorhombic phase is entirely suppressed, making the large cell cubic phase as the ground state. Thus, for the range 0.15 < x ≤ 0.2, we find only the sequence of phase transitions as C→T→ LC. For x > 0.2, the large cell cubic phase dominates the phase space with the cubic phase existing only at increasingly higher temperatures and with a complete absence of the tetragonal and the orthorhombic phases. This is an interesting observation in view of the fact that properties of MAPbI3 have been discussed in the literature almost exclusively in terms of the tetragonal phase, dominating our thinking about these systems. However, our results show that this tetragonal phase is unstable with respect to doping of the A-site and for any level of FA doping beyond 10%, the tetragonal phase does not exist at the room temperature and above. Therefore, properties of such doped systems, known to be essential for high efficiency together with stability, will have to be understood in terms of the cubic and the large cell cubic structures. We have provided the lattice parameters of all compositions at representative temperatures in the SI. Next we show that this shift of the crystal structure has profound effects on physical properties, probed here in terms of temperature dependent dielectric properties changing qualitatively with changes in the underlying crystal structure.


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The structure-property relationship is best illustrated by the compilation of the real part of the dielectric constant as a function of the temperature for all compositions, measured at a fixed frequency of 1 MHz in Fig. 4, with the frequency dependent dielectric properties discussed later. Clearly, the dielectric constant changes rapidly as a function of both compositions and the temperature. Most of the compositions are characterized by a peak in the dielectric constant at a temperature that depends non-monotonically on the composition. With an increasing FA content, denoted by an increasing x-value, the peak temperature shifts to lower values for 0.0 ≤ x ≤ 0.075 in Fig. 4, following the phase line separating the tetragonal and orthorhombic phases (see Fig. 3).

Figure 4. The comparative plot shows the real part of dielectric constant at 1 MHz frequency for different compositions of MA1-xFAxPbI3. Interestingly, the peak temperature shifts to higher values for x > 0.075 (see Fig. 4), reflecting the increasing temperature at which the tetragonal - large-cell cubic phase transition takes place with an increasing x beyond 0.075, as seen in Fig. 3. Clearly, the cubic - tetragonal phase transition observed for x ≤ 0.175 in Fig. 3 has little or no effect on the dielectric property as can 11 ACS Paragon Plus Environment


be seen from Fig. 4, with the dielectric constant smoothly varying across the phase transition temperature. However, the cubic - large-cell cubic phase transition observed for x ≥ 0.2 in Fig. 3 influences the dielectric constant (see the plot of x = 0.2 in Fig. 4) in a manner closely resembling the impact of tetragonal - large-cell cubic phase transition observed for x ≤ 0.175. In other words, the cubic and tetragonal phases are not distinguished by any perceivable changes in the dielectric constant in these solid solutions; this observation is consistent with reported results on pure end-member compounds, MAPbX3.18-19, 21 In sharp, contrast, the large cell cubic phase represents a qualitatively different dielectric property. In order to understand the dielectric properties in greater details and to make its connection to the structural variations observed in this solid-solution evident, the dielectric constants of MA1xFAxPbI3

for a selected set of x-values, namely 0.05, 0.075, 0.1, 0.125, 0.15, 0.175, 0.2, 0.3 and

0.4, are shown as a function of temperature in Fig. 5 (a) - (i) for a few representative frequencies. The low frequency dielectric constants in most cases show an up-turn with an increasing temperature near the high temperature end; this has been ascribed to extrinsic effects19 and not discussed further here. Clearly the dielectric constant exhibits interesting dependency on both temperature and composition, closely following the crystal structure variations shown in Fig. 3 in the form of the phase diagram. To make this close interplay between the structure and the dielectric property evident, we have marked with vertical lines the temperature ranges for specific crystallographic phases observed in each composition in various panels of Fig. 5 (a) - (i).


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Figure 5. (a) - (i) Temperature dependent dielectric constant (real part) at selected frequencies for the solid solution MA1-xFAxPbI3 (where x = 0.05, 0.075, 0.10, 0.125, 0.15, 0.175, 0.2, 0.3 and 0.4). Vertical red lines in each figure separate different crystallographic phases e.g. cubic (C), tetragonal (T), orthorhombic (O), large-cell cubic (LC) and their mixed phases. Fig. 5 (a) shows the dielectric constant of the x = 0.05 sample, appearing very similar to that of the pure MAPbI3 reported earlier.18 It shows a rapid increase of the dielectric constant with a decreasing temperature over the range of temperatures for which the tetragonal phase is stable, namely down to 150 K. This is followed by a precipitously rapid drop in the dielectric constant 13 ACS Paragon Plus Environment


over a relatively narrow temparature 150 K – 120 K; this is the temparature range over which we find the evidence for the coexistence of the tetragonal and the orthorhombic phases. Below 120 K, the dielectric constant is relatively less dependent on the temparature in its orthorhombic phase. The rapid increase in the dielectric constant with a decrease in the temperature within the tetragonal phase and a relatively temperature independent dielectric constant in the orthorhombic phase in Fig. 5a are attributed to nearly freely rotating MA+ dipoles and an ordered dipolar arrangement at the high and the low temparature phases, respectively, in analogy to the case of MAPbI3.18 With an increasing FA content, however, distinct differences begin to appear between the solid solution and the pure MAPbI3 dielectric properties. Specifically, the appearance of the cubic phase with the large unit cell (the LC phase) in the intermediate temperature range between the high temperature tetragonal phase and the low temperature orthorhombic phase for FA content, x ≥ 0.1 gives rise to a prominent frequency dependent dielectric constant, unlike any of the other phases. This frequency dependent dielectric property, suggestive of a dipolar glassy state,22 becomes increasingly more prominent with increasing FA content as shown in Figs. 5 (c) – (i), with the thermal stability of the LC phase steadily increasing with the FA content, as shown in Fig. 3. This clearly establishes that the LC phase is characterised by a prominent and unique dipolar glassy state with large frequency dependencies below typically about 160 K, unlike in any other phases of this solid solution, that have essentially frequency independent dielectric properties. In order to understand this phenomenon, we first note that the dielectric constant of the end-members, namely MAPbX3 and FAPbX3 in their higher temperature phases are distinctly different,19 with MAPbX3 showing the characteristic 1/T dependency of the dielectric constant characteristic of the freely rotating MA+ dipoles; these are also seen in Fig. 4 for the compositions with lower dopings. The absence of this characteristic 1/T dependency of the


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dielectric constant of FAPbX3 in contrast was earlier taken19 as an indication of the FA dipoles not being free to rotate. We note here that this need not be the explanation in view of the fact that the dipole moment of FA+ is approximately an order of magnitude smaller than that of MA+ ion.17, 23-24 As discussed in Reference 18, the paraelectric contribution of a free to rotate dipole to the dielectric constant is given by Debye theory as

(𝐶𝑇)1 +1𝜔 𝜏

2 2

where the constant C is given by

𝐶=

𝑁𝜇2𝜂 3𝑘𝜀0

with N being the number of dipoles per unit volume, η = (ε∞+2)/3, k the Boltzman constant, and ε0 the permitivitty of free space. It is important to note here that this contribution depends on the square of the dipole moment, 𝜇. The dipole moment of FA+ ion is 0.21 D and that of MA+ is 2.29 D, as given in Reference 23, thereby suppressing the 1/T contribution arising from any dipole on rotating FA+ ions by about two orders of magnitude compared to the contribution from dipoles on MA+ ions in corresponding hybrid perovskites. In other words, the dipole moment of FA+ ion is too small to have any perceptible influence on the dielectric properties of FAPbX3 compounds. In passing, we note that NMR studies of FAPbX3 suggests that the FA+ ions rotate nearly as freely as MA+ ions in corresponding MAPbX3 compounds,25 validating the reinterpretation of the dielectric properties of FAPbX3 compounds, suggested here. The above discussion, together with results presented in Fig. 4, suggests that the high temperature cubic and tetragonal phases of this solid solution are dominated by the paraelectric contributions from the freely rotating MA+ ions in view of its large dipole moment, whereas the 15 ACS Paragon Plus Environment


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FA+ ions do not significantly contribute to the dielectric constant, due to the small value of the dipole moment on FA+ ions. Consequently, the dielectric constant of the solid solution steadily decreases on an average with an increasing FA content (see Fig. 4). The most interesting dielectric property is observed for the large-cell cubic phase, where a glassy dipolar phase is established by the presence of a prominent frequency dependency of the dielectric constant (Figs. 5(c) - (i)). This phase extends over the widest temperature range for large x values or FA content, as seen in Fig. 3. This phase is intriguing since none of the pure end-members in the general family of APbX3 with A = MA or FA and X = Cl, Br or I exhibits such a prominently glassy dielectric property; also, the large-cell cubic crystal structure is unique to the solid solution. Such a glassy state can only arise if the MA+ and FA+ ions are frozen into locked states with random orientations. It is known that the rotations of MA+ are aided by the local structural distortions in the accompanying PbX3-1 units that follow the rotation dynamically.18,

26-27

In the pure end-

member, say MAPbI3, this is possible with neighboring PbI3 units giving rise to dynamic octahedral rotational distortions in a correlated manner in response to the rotation of the MA units in ps time-scale.18, 27 However, the local lattice distortions required to aid the rotation of FA+ units are likely to be different in comparison to those required for MA+ rotation. This provides the most likely interpretation for the presence of the large-cell cubic phase with the glassy dielectric properties, where the free rotations of the MA+ and FA+ dipoles are significantly hindered due to the presence of the other type of dipoles in the neighboring unit cells. The suppression of the dipolar rotation removes the dominant contribution to the dielectric constant arising from the dipolar rotations which is strongly temperature dependent, as already discussed. This leads to relatively temperature independent dielectric constant in the vicinity of the room temperature for the solid solution with a large FA content and stabilizing the large-cell cubic


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structure. In this scenario, it is also conceivable that the structural response over a ps time-scale observed following the photoexcitation of an electron-hole pair in MAPbI3 will be strongly influenced by the formation of the solid solution due to the underlying disorder frustrating any correlated structural response of the PbI6 units.28

In summary, we have established a rich structural phase diagram of MA1-xFAxPbI3 in the composition (x)-temperature (T) space. It is seen that a large cubic unit cell, corresponding to a 2 x 2 x 2 primitive cell, dominates much of the phase space for this solid solution. Interestingly, the dielectric properties of the solid solution within this phase is shown to be unique with a highly prominent glassy dielectric behaviour, pointing to a random freezing of the organic moieties in different orientations. This is suggestive of a suppression of the structural fluidity that appears in the pure end-members as a consequence of the correlated octahedral rotational response of PbI6 units following the rotational degrees of freedom of the organic units in the ps time-scale.

ASSOCIATED CONTENT: Supporting Information Available

Sample synthesis, dielectric characterization details, temperature dependent XRD results, refinement of XRD pattern for each phase AUTHOR INFORMATION: Corresponding Author 17 ACS Paragon Plus Environment


*[email protected] ACKNOWLEDGEMENTS: AM acknowledges University Grant Commission for a student fellowship. DS and TNG thanks Department of Science and Technology, Government of India for providing low temperature powder XRD facility in IISc. AM thanks Bhusan P. Kore for useful discussions. DDS thanks Jamsetji Tata Trust for support. REFERENCES: (1)

Lee, M. M.; Teuscher, J.; Miyasaka, T.; Murakami, T. N.; Snaith, H. J. Efficient Hybrid

Solar Cells Based on Meso-Superstructured Organometal Halide Perovskites. Science 2012, 338 (6107), 643. (2)

Burschka, J.; Pellet, N.; Moon, S.-J.; Humphry-Baker, R.; Gao, P.; Nazeeruddin, M. K.;

Grätzel, M. Sequential deposition as a route to high-performance perovskite-sensitized solar cells. Nature 2013, 499, 316. (3)

Zhao, D.; Wang, C.; Song, Z.; Yu, Y.; Chen, C.; Zhao, X.; Zhu, K.; Yan, Y. Four-

Terminal All-Perovskite Tandem Solar Cells Achieving Power Conversion Efficiencies Exceeding 23%. ACS Energy Lett. 2018, 3 (2), 305-306. (4)

Jeon, N. J.; Na, H.; Jung, E. H.; Yang, T.-Y.; Lee, Y. G.; Kim, G.; Shin, H.-W.; Il Seok,

S.; Lee, J.; Seo, J. A fluorene-terminated hole-transporting material for highly efficient and stable perovskite solar cells. Nature Energy 2018, 3 (8), 682-689. (5)

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Stable Quasi-Cubic FAxMA1–xPbI3 Perovskite Structure for Solar Cells with Efficiency beyond 20%. ACS Energy Lett. 2017, 2 (4), 802-806. 18 ACS Paragon Plus Environment

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(6)

Kawamura, Y.; Mashiyama, H.; Hasebe, K. Structural Study on Cubic–Tetragonal

Transition of CH3NH3PbI3. J. Phys. Soc. Jpn. 2002, 71 (7), 1694-1697. (7)

Baikie, T.; Fang, Y.; Kadro, J. M.; Schreyer, M.; Wei, F.; Mhaisalkar, S. G.; Graetzel,

M.; White, T. J. Synthesis and crystal chemistry of the hybrid perovskite (CH3NH3)PbI3 for solid-state sensitised solar cell applications. J. Mater. Chem. A 2013, 1 (18), 5628-5641. (8)

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crystal growth of hybrid perovskite material CH3NH3PbI3. CrystEngComm 2015, 17 (3), 665670. (9)

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