Hidden polymorphism of FAPbI 3 discovered by Raman spectroscopy †

Formamidinium lead iodide (FAPbI 3 ) can be used in its cubic, black form as a light absorber material in single-junction solar cells. It has a band-gap (1.5 eV) close to the maximum of the Shockley–Queisser limit, and reveals a high absorption coefficient. Its high thermal stability up to 320 1 C has also a down-side, which is the instability of the photo-active form at room temperature (RT). Thus, the black a -phase transforms at RT with time into a yellow non-photo-active d -phase. The black phase can be recovered by annealing of the yellow state. In this work, a polymorphism of the a -phase at room temperature was found: as-synthesized ( a i ), degraded ( a d ) and thermally recovered ( a rec ). They differ in the Raman spectra and PL signal, but not in the XRD patterns. Using temperature-dependent Raman spectroscopy, we identified a structural change in the a i -polymorph at ca. 110 1 C. Above 110 1 C, the FAPbI 3 structure has undoubtedly cubic Pm % 3 m symmetry (high-temperature phase: a HT ). Below that temperature, the a i -phase was suggested to have a distorted perovskite structure with Im % 3 symmetry. Thermally recovered FAPbI 3 ( a rec ) also demonstrated the structural transition to a HT at the same temperature ( ca. 110 1 C) during its heating. The understanding of hybrid perovskites may bring additional assets in the development of new and stable structures.


Introduction
Hybrid perovskites have drawn genuine attention of scientists in the past several years. Along with the studies on their applications as prospective semiconductors, particular attention was paid to understanding the phenomenon of so-called defect tolerance and stability issues. 1 The dynamics of the relatively rigid network of PbI 6 octahedra as well as the rotational activity of the organic cation can give basic answers to those questions. 2,3 The formamidinium cation (FA + = NH 2 -C-NH 2 + ) has replaced the methylammonium cation (MA + = CH 3 NH 3 + ) in hybrid perovskite semiconductors used in the study of solar cells. 4 FAPbI 3 has a narrower bandgap than MAPbI 3 (1.5 eV vs. 1.59 eV), closer to the Shockley-Queisser limit. Furthermore, FAPbI 3 decomposes at a much higher temperature (320 1C vs. 275 1C). [5][6][7][8] There are two known polymorphs of FAPbI 3 at room temperature (RT = 20 1C): photo-active (black) a and non-photo-active (yellow) d. The first one crystallizes from g-butyrolactone (GBL) solution at 110 1C, remaining stable in the GBL-solution at temperatures above 60 1C. 9,10 At RT, the a-form transforms into the d-form due to the structural instability attributed to internal stress. 1 This transformation occurs in about 1 day when single crystals are stored in ambient air with a relative humidity of 55-57% and up to 10 days when they are stored in a vacuum or inert gas. 7,9 Polycrystal a-FAPbI 3 can be recovered from the d crystal via annealing, which in turn retards the ad phase-transition up to 20 to 30 days. [10][11][12][13][14] Differential scanning calorimetry performed on d-FAPbI 3 showed an endothermic peak at 160 1C for the powder and at 185 1C for single crystals, which is attributed to the reverse da phase-transition. 7,15 Chemical decomposition of d-FAPbI 3 single crystals takes place at higher temperatures: HI decomposes around 320-360 1C, while FA + around 375-420 1C. 7 The structure of the d-phase is accepted as hexagonal P6 3 mc. 10 On the contrary, the structure of the a-phase is still a matter of scientific debate in the literature.
Recent studies based on X-ray diffraction (XRD) and powder neutron diffraction define thermally recovered FAPbI 3 (a-phase) as a cubic perovskite with Pm% 3m symmetry, 12,16 refuting the structure previously assigned as trigonal P3. 10 The discussion arises when the structural instability of the a-phase and the structure of the molecular cation are considered. Other characteristics that lack explanation if the cubic Pm% 3m symmetry is considered are listed in the following. First, the Goldschmidt tolerance factor of FAPbI 3 is equal to 1.008, which predicts structural stability for perovskites. Also, the combination with cubic Pm% 3m FAPbBr 3 presents an instability region from 30 to 50% of FAPbBr 3 , which is unexpected in a mixture of materials possessing the same space group. 17 Density functional theory (DFT) calculations give a band-gap energy 0.2 eV lower than that experimentally observed if cubic Pm% 3m is considered. 18 A more precise result (+0.05) is obtained for a relaxed tetragonal structure with head-to-tail cation organization. Carignano et al. studied octahedral distortions in FAPbI 3 using molecular dynamics simulations and group theory. 19,20 These results showed that the cubic Pm% 3m structure adequately represents the material at 177 1C due to the harmonicity of the vibrations, but at 27 1C the distortion of the structure can be better described by the cubic symmetry Im% 3. In this case, the body centered cell is eight-times larger than the primitive one.
As presented above, such distorted cubic structures as Im% 3 are considered in the literature as relevant for FAPbI 3 ; 19 however, there is no direct experimental proof yet. Additionally, the fresh-synthesized material and the thermally recovered one are not usually differentiated, even though there is a clear disparity in their structural stability. We also point out that the structural instability has not been explored in terms of distortion of the FAPbI 3 structure.
In this work, we expand the knowledge about the polymorphism of FAPbI 3 at RT. For this, we characterized single crystals by Raman spectroscopy and supported our findings with XRD and photoluminescence (PL). We identify 4 polymorphs: 3 photo-active a (fresh-synthesized, degraded, and thermally recovered) and one non-photo-active d (degraded). To support these analyses, time or temporally dependent XRD and Raman-spectroscopy measurements were undertaken to characterise the transition from the fresh-synthesized state (RT) to the high temperature state (200 1C), then the transition from the fresh-synthesized state to the degraded state (after 1 day), and the recovery of the degraded state (RT) via sequential annealing up to 180 1C.

Sample preparation
Single crystals (SCs) of the FAPbI 3 compound were synthesized following the modified inverse temperature crystallization method reported by Saidaminov et al. 9 1 M of precursors FAI (DyeSol) and PbI 2 (99.99% TCI) was dissolved in 1 ml of GBL at room temperature (RT = 20 1C) in a controlled N 2 atmosphere (H 2 O o 1 ppm, O 2 o 10 ppm). The solubility was increased by placing the vials over a preheated hot plate at 60 1C for at least 1 h. The solution was then filtered through a 0.2 mm polytetrafluoroethylene syringe filter, poured into a 10 ml vial and placed over a preheated hot plate at 90 1C. The temperature was elevated in steps of 5 1C h À1 up to 115 1C and kept for 3 h to increase the crystal size. After that, the crystals were wiped with filter paper and dried with N 2 gas flux. Powder samples were obtained by grinding of single crystals in an agate mortar.

Experimental methods
Raman spectroscopy was performed on a high-resolution Lab-RAM HR800 spectrometer (Horiba). The equipment has an ultra-low frequency (ULF) unit that allows measuring from 10 cm À1 for an excitation wavelength of 633 nm. Spectra were recorded with a mesh of 600 and 1800 lines per mm. The laser beam was focused using 50Â/0.75 and 100Â/0.90 microscope objectives. The power was maintained within a range of 70 to 90 mW, considering a restriction of 1 mW for the selected wavelength to avoid degradation by the laser. 3 The reproducibility of the measurements was probed through the analysis of several samples, whose normalized Raman spectra are presented in Fig. S1 (ESI †). The Raman spectra of the polymorphs are invariant in terms of the position of the Raman modes, supporting our attribution. The difference in intensity is related to the instrument adjustment. The spectrum of PbI 2 resulting from measuring FAPbI 3 with a power higher than 1 mW is presented in Fig. S2 (ESI †). Supportive PL measurements are presented in Fig. S3-S5 (ESI †). XRD patterns were acquired using Cu Ka radiation on a D8 Discover diffractometer from Bruker. A high resolution model of the LYNXEYE XE-T detector in combination with 2.51 axial parallel-slit collimators and 0.6 mm slits from the primary and secondary beam sides was used. Measurements were performed in a Bragg-Brentano geometry with a 0.021 step size and 2 s step time. Differently annealed thin films, powder and small assynthesized single crystals (ca. 0.5 mm) were measured in ambient air. These measurements were done immediately after the preparation of the samples to avoid any visible ad phase transition. The fastest transition was visually observed for the as-prepared FAPbI 3 films crystallized at 80 1C and took 2 hours, but even in this case the XRD experiment proceeded faster. XRD patterns were fitted using the software TOPAS program using the Pawley method.

Temperature dependent measurements
Temperature-dependent Raman spectroscopy measurements were performed in a module THMS600 from Linkam Scientific. The chamber of the heating module was open during the measurements to avoid water condensation over the sample. FAPbI 3 was heated from 20 to 200 1C and measured in temperature steps of 30 1C, maintaining the selected temperature for 10 min for the sample to reach thermal equilibrium with the heating stage. After identifying a transition between 80 1C and 110 1C, additional measurements were done at 90 1C, 95 1C and 100 1C. PL measurements were performed in the same way, with temperature steps of 10 1C and an integration time of 1 s. Temperature-dependent XRD measurements were conducted in ambient air as described above using the high-temperature chamber TC-DOME with Be-walls from Anton Paar. XRD patterns were recorded for several selected temperatures in the range from 30 1C to 180 1C. Each pattern was recorded in a 2y scan from 51 to 701 with a step size of 0.011 and an integration time of 1.2 s per step.

Methodology
The SCs remain in the as-synthesized state for less than 24 h in air after synthesizing, degrading heterogeneously. Within this time, the appearance of the FAPbI 3 samples became yellow by eye. The recovered samples were obtained by heating the degraded samples to 180 1C for 2 min on a hot plate and cooling down to RT. 7 The as-synthesized and the recovered samples were measured immediately after preparation and the degraded one after 24 h exposure in air. The spectra of the degraded samples were obtained using micro-Raman maps with a spacing of 5 mm to scope the heterogeneous surface. The preferable sample positions to measure the as-synthesized samples were located at the crystal borders or side planes, where the PL signal is lowered enough to disclose the lowfrequency zone (o200 cm À1 ).

Results and discussion
In this section, we describe and distinguish the structural polymorphism of FAPbI 3 at RT: 1 -as synthesized or initial a i , 2 -degraded d and a d , and 3 -thermally recovered a rec and PbI 2 . The alpha phase at high temperature is distinguished as a HT . The attribution of the corresponding structures was supported by following the phase-transitions as presented in Table 1: (a) temperature-driven phase transition a ia HT , (b) time-driven phase transition a ia d + d, and (c) temperaturedriven phase transition a d + da HTa rec + PbI 2 .

As synthesized a i -FAPbI 3
Thin film a i -samples are analyzed through XRD, with a mean value of the lattice constant of a = 6.372 Å considering the cubic Pm% 3m symmetry 12 (see Fig. S7, ESI †). As noted above, it is probably inconsistent to attribute to the a i -structure the cubic Pm% 3m symmetry. In fact, states with different structural instability cannot possess the same structure. As agreed in the literature, the a HT -phase, which is stable at 180 1C, has a primitive cubic cell. Furthermore, group theory dictates that cubic Pm% 3m Pb-based hybrid perovskites present only active Raman modes for low-coupled and strictly molecular vibrations, 21 which are over 200 cm À1 for FA + . This is experimentally supported in the case of a-MAPbI 3 . 2,22 Following this reasoning, we performed a thermal analysis of the sample from RT to 200 1C to identify the structural differences between the two boundary states. Temperature-dependent Raman spectra are shown in Fig. 1, while supporting PL and XRD measurements are presented in Fig. S5a and S6 (ESI †).
The Raman spectrum at RT shows the expected 4 Raman modes in the low frequency region: mode 1 -octahedral distortion (M1 at 43 cm À1 ), mode 2 -molecular in-plane rotation around a corner H (M2 at 63 cm À1 ), mode 3 -molecular out-ofplane rotation around the N-N axis (M3 at 96 cm À1 ), and mode 4 -molecular translation (M4 at 114 cm À1 ). 3 In the range from 20 1C to 100 1C, these 4 modes slightly broaden and red-shift. Beyond 100 1C only M4 remains, broadening and blue-shifting.
A stepwise conjugated change of the full width at half maximum and Raman shift with temperature may indicate a phase transition in perovskites. 23 Thus, we deal with some structural reorganization in a i -FAPbI 3 at 100-110 1C. Following the quantification of the temperature range for the phase transition from the a i to the a HT phase, we next focus on the properties of the FAPbI 3 structure before this transition.
Basically, phase transitions in perovskites can be caused by changes in the motion of the organic cation and its interaction with the lattice. 24,25 At temperatures below 100 1C, the I À atoms displace within a characteristic time of 10 ps 19 and cannot rearrange as fast as FA + groups rotate (2 ps), 12 breaking the lattice centrosymmetry. This leads to the activation of Raman modes in the a i -phase. At temperatures higher than 110 1C, the Raman modes are suppressed due to the spherical rotation of the FA cations and the faster response of I ions. If the molecule rotates spherically with almost statistical symmetry, the structure can be considered as centrosymmetric. This means that the vibrational modes do not change the polarizability of the structure at the equilibrium position of the ideal cubic perovskite. As a consequence, the Raman modes become inactive. 21,22 The inactivation of modes in the thermally restructured a HT -polymorph can be explained as follows. By definition, an asymmetric vibration in a symmetric system should be Raman inactive. This is the case of M1. In the case of M2 and M3, the center of charge is almost static: M2 constrains the vibration in Table 1 Scheme of the phase-transitions: high temperature structure (a HT ), as-synthesized (a i ), thermally-recovered (a rec ), and degraded (a d the plane where FA + is located, and in M3 the center of charge is kept within the rotation axis. M4 is the last remaining active mode after the transition since it involves the displacement of the molecular cation and consequentially I ions. Finally, this conjugated displacement results in a shift of the charge center. The mode gets broader when the amplitude of polarization reduces since the cation translation loses its preferential direction. According to MD calculations, there is a weak anharmonicity of I À displacement existing in FAPbI 3 below 97 1C, diverting the structure from the ideal configuration. 20 Several experimental details match this idea. These include the optimum temperature for single crystal growth in the range of 100-125 1C, 9 longterm stability of FAPbI 3 crystals at 87 1C inside the mother liquor 10 and the phase-transition of FAI into the cubic form at 113 1C. 26 In this work, we discovered a slope variation of the wavelength shift in the PL curve (Fig. S5a, ESI †). Along with this change, the lattice constant of FAPbI 3 shrinks on heating from 80 to 120 1C ( Fig. S6 and Table S1, ESI †).
Therefore, it is clear that the structure a i has highly displaced I À atoms and low molecular rotation. As noticed above, MD calculations suggested for FAPbI 3 a cubic body centered cell with Im% 3 symmetry at RT. 19 Our XRD investigation does not reveal any peak characteristic of this symmetry, for instance at 22.51 and 26.51 (see Fig. S7b, ESI †). However, modelling XRD patterns in the VESTA program discloses that this method is: (i) insensitive to the position and/or ordering of organic cations; and (ii) insensitive to the dynamics of the PbI 6 -network if its average disposition remains the same. Therefore, the already known head-to-tail organization of the FA + molecules 10,18 associated with the I À displacements at RT can be attributed to the difference between the a i and a HT phases observed in Raman/ PL spectra.
To summarize, the as-prepared FAPbI 3 appears in a distorted cubic form with Im% 3 symmetry due to the anharmonicity of iodine displacements. When heated up to 100-110 1C, it transforms into the ideal perovskite with Pm% 3m symmetry. At higher temperature, the active rotation of FA + ions results in geometrical sphericity, which provides higher crystal symmetry.

Degraded a d + d-FAPbI 3
The yellow polymorph of FAPbI 3 is usually obtained at RT from the a i -phase with time and remains stable for more than 10 weeks storage in a vacuum. This is a result of the structural instability of the a i -phase due to internal stresses. 1 The analysis of the XRD patterns of degraded thin films reveals the coexistence of two phases: Pm% 3m (20.99%) and P6 3 mc (79.01%). The cubic phase presents a lattice constant of 6.361 Å (see Fig. S7 and S8, ESI †).
Visually yellow SCs demonstrate under the microscope three different zones: yellow needles, a dark matrix and an intermediate zone of small yellow round crystals of approx. 1 mm. We analyzed each zone using Raman spectroscopy (see Fig. 2).
The dark matrix (denoted as a d ) presents a similar Raman spectrum to the a i -phase. The main difference is a red-shift of 15 cm À1 of the Raman spectrum of a d compared to a i . This is related to a variation of the Pb-I bond direction and consequentially a distortion of the unit cell. It is also visible in the blue shift of the PL signal, which has a wavelength around 100 nm shorter than the a i -phase (see Fig. S2, ESI †).  The small round yellow crystals show different Raman spectra, as presented in brown in Fig. 2. These spectra possess two distinctive qualities: a red-shift of M1 and M4 around 13 cm À1 with respect to the a i -spectrum and sharpening and degeneration of M2 and M3. We identified these characteristics with the partial merging of the octahedra corresponding to the intermediate states of the transition a id.
The yellow needles appear in the Raman spectrum as pure d-phase. The Raman spectrum shows six peaks in the lowfrequency range (o200 cm À1 ). M1 and M4 are kept at the same position as a d , while M2 is split into two peaks at 44 and 51 cm À1 , and M3 into two peaks at 66 and 72 cm À1 . This variation from the a i -spectrum coveys the structural change. In the case of the hexagonal P6 3 mc lattice, the octahedra merge in a 2-fold disposition and interconnect by faces along the h001i directions. 10 The red shift with respect to the a i -spectrum is a consequence of longer Pb-I bonds. According to the XRD analysis on degraded thin films, the cell parameters of the hexagonal lattice are a = 8.682 Å and c = 7.929 Å. This means Pb-I bond lengths of 3.20 Å and 3.25 Å, longer than the 3.19 Å presented in the a i thin films (see Fig. S7 and S8, ESI †). Additionally, two FA + ions of the elementary cell affect via molecular reorientation three double-merged octahedral units and vice versa. This results in the splitting and sharpening of coupled modes.
With the information from Raman spectroscopy, we can interpret the temporal transition a i to d as follows. Initially, the distortion of the FAPbI 3 cubic structure leads to the nucleation of the d-phase at the most defective sites of the a i -matrix. Then, some octahedra expand and merge together, encircling two organic cations per unit cell. This starts the growth of a second phase as different crystals. The octahedra continue merging in the vicinities, leading to the consolidation of the hexagonal structure. Thus, the yellow needles of a pure d-phase grow.

Thermally recovered a rec -FAPbI 3 + PbI 2
The transition from degraded to recovered was followed by in situ powder XRD, as presented in Fig. 3.
The following changes can be noticed: the hexagonal lattice turns into a cubic one during heating from RT to 100 1C. Between 100 1C and 140 1C, the XRD patterns can be described by the superposition of two phases with hexagonal and cubic space groups. The main transition occurs between 140 1C and 180 1C, where the d-phase fully disappears. This fact is supported in the literature by an endothermic peak around 160 1C detected by differential scanning calorimetry. 15 After cooling, the sample contains cubic FAPbI 3 (a rec ) and PbI 2 . Recovered thin films show on average 25% of PbI 2 (see Fig. S7 and S8, ESI †). The presence of this non-photoactive PbI 2 works as superficial traps, decreasing the amplitude of the PL signal about tenfold as compared to a i under the same illumination conditions.
A thermally recovered SC was analyzed by Raman spectroscopy and compared to the other polymorphs of FAPbI 3 at RT, as shown in Fig. 4. From an initial inspection, all polymorphs differ one from another.
The Raman spectrum of the a rec -sample shows the same 4 modes of a i with 3 distinctions: (i) a red-shift of 9 cm À1 , (ii) an increase in the intensity ratio between M2 and M3 from 0.22 (a i ) to 1.84 (a rec ), and (iii) the appearance of an additional mode at 311 cm À1 .
The first variation is analogous to the case of a d . The redshift of the Raman spectrum suggests a weakening of the Pb-I bond, which is a consequence of a variation either in the bond length or angle. As extracted from our XRD on thin films, a i and a rec have similar lattice constants. Thus, a change of the Pb-I bond direction is involved. This distortion is lower than the one of a d , as evidenced by the lower magnitude of the red-shift and the lesser shift of the PL signal position (see Fig. S3, ESI †).
For the second change, different FAPbI 3 polymorphs at RT are compared in terms of the IM2/IM3 ratio and stability in Table 2. We can deduce a direct impact of the M3 relative intensity on the perovskite stability. This mode represents the out-of-plane rotation of FA + around the N-N axis and solely causes volumetric changes since all other modes are active in a molecular plane. The data on doped Cs 0.1 FA 0.9 PbI 3 and Cs 0.1 FA 0.9 PbI 2.6 Br 0.4 compounds also support this finding. 3 The third characteristic is the peak at 311 cm À1 of the a rec -spectrum, which also appears in the d-phase at 243 and 314 cm À1 . These correspond to the modes ''symmetric and asymmetric out-of-plane bending of FA + ''. 3 In the spectra of a i and a d , the absence of this mode could be either veiled due to luminescence or inactive. In the last case, it may be the result of static hydrogen atoms, which govern these modes.
It is worth noticing that the transition temperature from a rec to a HT coincides with the transition a i to a HT according to the temperature dependant shift of the PL position (Fig. S5, ESI †).
It can be concluded that higher stability of the a d -phase in the degraded sample is interconnected with the constriction of volumetric displacement of FA + . The latter is expressed as a hindering of the mode ''out-of-plane rotation around the N-N axis''. Both constituent phases, d and a d , have similar density: 4.10 g cm À3 (ref. 10) and 4.00 g cm À3 (ref. 12), respectively. Moreover, the lattice constant in the SC remains almost unchanged in the a i to a d transition, discarding the possibility of stress release.
The even higher stability of the a rec -phase in the recovered sample can be explained by stress release, which is known to improve the stability of hybrid perovskites. 1 The observed expanded lattice of the a rec -phase (see Fig. S9, ESI †) corresponds to release of isotropic compressive stress. This may be bound exactly with the formation of PbI 2 , which is appreciably denser: 5.36 g cm À3 . In turn, lead iodide has the same structural fragments as the delta-phase (face shared PbI 6 -octahedra), which gives rise to PbI 2 formation in a compressive environment during heating. Moreover, the fact that the mixture of the a d /d phases undergoes a solid phase transformation causes multiphase interfaces facilitating nucleation of PbI 2 . A remarkable suppression of the ''out-of-plane rotation around the N-N axis'' mode is also observed in the a rec c-phase, becoming almost inactive as in the case of the isolated molecule. This points to a larger unoccupied volume for the free rotation of the molecule, uncoupling from the surrounding octahedra.

Conclusions
We distinguished in our experiments three polymorphs of photo-active a-FAPbI 3 existing at RT: as-synthesized (a i ), degraded (a d ) and thermally recovered (a rec ). They mostly differ in the level of distortion, the product of a secondary phase: d for the degraded sample and PbI 2 for the thermally recovered one. The Raman spectrum of the a i -phase points at the highest activity of the Raman mode ''molecular rotation around the N-N axis'', which is likely a main factor in the structural instability.
We proposed the a i -FAPbI 3 crystals to have a cubic Im% 3 structure at RT. Herewith, the FA + molecules are organized in a head-to-tail fashion and the displacement of I À ions proceeds slower than the FA + displacement. Raman spectroscopy disclosed a transition of this distorted phase into the ideal Table 2 Correlation between the FAPbI 3 phase stability in ambient air and intensity ratio of Raman modes M2 and M3. The spectrum and synthesis of a d are presented in Fig. S4 (ESI). The data on doped FAPbI 3 compounds are taken from our previous work. 3 The term ''stable'' considers the invariability of the Raman spectrum for more than 10 weeks

Conflicts of interest
There are no conflicts to declare.