Reassigning the Pressure-Induced Phase Transitions of Methylammonium Lead Bromide Perovskite

The high-pressure crystal structure evolution of CH3NH3PbBr3 (MAPbBr3) perovskite has been investigated by single-crystal X-ray diffraction and synchrotron-based powder X-ray diffraction. Single-crystal X-ray diffraction reveals that the crystal structure of MAPbBr3 undergoes two phase transitions following the space-group sequence: Pm3̅m → Im3̅ → Pmn21, unveiling the occurrence of a nonpolar/polar transition (Im3̅ → Pmn21). The transitions take place at around 0.8 and 1.8 GPa, respectively. This result contradicts the previously reported phase transition sequence: Pm3̅m → Im3̅ →Pnma. In this work, the crystal structures of each of the three phases are determined from single-crystal X-ray diffraction analysis, which is later supported by Rietveld refinement of powder X-ray diffraction patterns. The pressure dependence of the crystal lattice parameters and unit-cell volumes are determined from the two aforementioned techniques, as well as the bulk moduli for each phase. The bandgap behavior of MAPbBr3 has been studied up to around 4 GPa, by means of single-crystal optical absorption experiments. The evolution of the bandgap has been well explained using the pressure dependence of the Pb–Br bond distance and Pb–Br–Pb angles as determined from single-crystal X-ray diffraction experiments.


Ⅰ. INTRODUCTION
Metal halide perovskites form a group of materials with the simple configuration ABX3 where A, B, and X are, respectively, organic parts (usually CH3NH3 + (MA) or NH2CH=NH2 + (FA)), metal cations, and halide anions (Cl -, Br -etc.).Amongst these materials, MAPbBr3 and MAPbI3 have been found to efficiently sensitize TiO2 for visible-light conversion in photoelectron chemical cells, increasing the power conversion efficiency by 3.13% and 3.81%, respectively. 1After these results, both materials have attracted a great amount of attention.The efforts made by different research groups to study metal halide perovskites, the photovoltaic efficiency of perovskite solar cells have been soared to around 25% in 2021. 2 The tunability of bandgap energy for perovskite semiconductors is a requirement to optimize their optical properties for specific applications.For example, multi-junction perovskite solar cells, where narrow-bandgap (1.1 to 1.2 eV) and wide-bandgap (1.7 to 1.8 eV) perovskites are combined, are expected to perform with an efficiency as high as 39%. 3,4By simply varying the ratio of I and Br in MAPb(IxBr1-x) compounds, the bandgap of hybrid perovskites can be tuned in the range of 1.6 to 2.3 eV, 5 however, this can generate instabilities due to the halide segregation. 68][9] Pressure usually shortens bond distances, changing and distorting the crystal structure, and can even induce phase transitions, thereby having a significant influence on the electronic band structure.
Although several studies have been performed on the pressure-induced structural phase transitions of MAPbBr3, there is still much controversy in the literature as we summarize in Figure 1.In 2007, Swainson et al. 10 investigated the pressure-induced crystal structural change of MAPbBr3 with neutron diffraction up to around 3 GPa at room temperature and down to around 80 K.They reported that the crystal structure transforms from the space group 3 �  to 3 � , a cubic-to-cubic phase transition, at 0.87 -1.01 GPa.They also found that MAPbBr3 amorphized at around 2.8 GPa.In these experiments, 2-Propanol-d8 (perdeuterated isopropanol) was used as pressure transition medium (PTM).In 2015, Wang et al. 7 studied the crystal structure and electronic band structure of MAPbBr3 under high pressure up to 34 GPa at room temperature, by powder X-ray diffraction (PXRD) in a synchrotron light source.No PTM was used in their study.Two phase transitions were observed, from 3 �  to 3 � at 0.4 GPa, and from 3 � to Pnma at 1.8 GPa.In addition, amorphization was reported to take place at 4 GPa.The transition pressure was strongly affected by non-hydrostatic effects in this experiment.In addition, the assignment of the space group Pnma was not obtained by mean of indexation followed by a full-structure solution, but based on a Rietveld refinement of PXRD patterns assuming results of density-functional theory (DFT) calculations reported by Swainson et al. 10 However, such structure has not been experimentally found by Swainson et al. 10 at room temperature and high-pressure, being only observed at a temperature lower than 148 K at room pressure by using single-crystal X-ray diffraction (SCXRD). 11On the other hand, PXRD results reported by Jaffe et al. 12 also contradict the existence of a high-pressure Pnma structure.These studies were performed using helium as PTM, which provides hydrostatic conditions up to 12 GPa. 13In particular, Jaffe et al, 12 observed the phase transition from 3 �  to 3 � at 0.9 GPa and the onset of amorphization at 2.7 GPa.The crystal structures of those two cubic phases were determined by SCXRD at ambient conditions and 1.7 GPa, as well as by the Rietveld refinement of the PXRD patterns from both phases.The first phase transition and amorphization pressures are consistent with that report by Swainson et al 10 Four other high-pressure studies can be found in the literature.Kong et al. carried out studies only up to 1 GPa. 14They only reported the phase transition from 3 �  to 3 � at around 0.5 GPa.In their case, silicone oil was the PTM.On the other hand, the first phase transition was observed at 0.75 GPa by Szafrański et al. 8 In their work the 3 � phase coexisted with an unknown phase (named Phase Ⅶ in their work) in the pressure range 2.1-2.7 GPa.These authors correlate changes in the crystal structure with changes in the bandgap.They propose that the bandgap energy of MAPbBr3 may have a linear relationship with the Pb-Br bond length.The pressureinduced crystal structure phase transition has been also investigated by Zhang et al.   with three different quasi-hydrostatic conditions (Helium, Argon, and no PTM). 15In the experiment where helium was used as the PTM, SCXRD was used to characterize the crystal structure, the pressure-induced phase transition from space group 3 �  to 3 � have been observed at 0.85 GPa, followed by an isostructural phase transition at 2.7 GPa, which was accompanied by a unit cell volume collapse of around 4.4 Å 3 .In the second experiment where argon was used as PTM, the first phase transition was observed at 1 GPa, after that the 3 � phase coexisted with the Pnma phase up to the highest pressure in their work (11.9 GPa).The reason used to justify the phase coexistence was the solidification of argon at around 1.4 GPa and room temperature. 13he experiment where no PTM was used, the first phase transition was observed at the lowest pressure of 0.4 GPa, in agreement with the transition pressure reported in the work from Wang et al. 7 followed by another pressure-induced phase transition from 3 � to Pnma was found at 1.5 GPa.Finally, in the PXRD experiment of Yin et al, 16 the first phase transition (3 �  to 3 � ), second phase transition (3 �  to Pnma) and amorphization were located at 0.99 GPa, 2.41 GPa and 4.06 GPa, respectively, however the use of PTM is not reported in this work.
In summary, the use of different pressure transmitting media could affect the structural sequence and phase transition pressures observed in MAPbBr3.The crystal structures of the two low pressure cubic phases have been unambiguously characterized by neutron diffraction, PXRD, and SCXRD and there is an agreement about this fact in the literature.However, the second pressure-induced phase transition, from space group 3 � to Pnma, has only been observed in three papers, 7,15,16 and the crystal structure used to perform Rietveld refinements on PXRD patterns was not properly solved because it was adopted from the phase observed at low temperature and ambient pressure.Wang et al, 7 Jaffe et al, 12 Kong et al, 14 Szafrański et al, 8 Zhang et al, 15 Yin et al, 16 and this work.The different crystal structures with different space groups are shown in different colors.The diffraction method, single-crystal Xray diffraction (SCXRD), powder X-ray diffraction (PXRD) and pressure transition medium (PTM) used in the studies are shown on the right-hand side.
In this work, the pressure-induced crystal structure phase transitions of MAPbBr3 have been re-examined by SCXRD up to 5 GPa.The crystal structures have been well established up to 3 GPa, the pressure-induced phase transitions have been further confirmed by the Rietveld refinement on PXRD phases and changes in bandgap energies have been investigated and explained.Two pressure-induced crystal structure phase transitions were founded both in SCXRD, PXRD, and optical experiments.The detailed crystal structure information of the three phases obtained from SCXRD will be reported, as well as the pressure-induced change in the lattice parameters and equations of state.The pressure-induced amorphization has been also observed in both SCXRD and PXRD.

A. Sample preparation
Lead bromide (PbBr2, 98% purity, purchased from Fisher Chemical), Methylammonium bromide (MABr, 98% purity, purchased from Ossila), and Dimethylformamide (DMF, 99.8% purity, purchased from Sigma Aldrich) were used as the starting materials.Lead bromide and methylammonium bromide were dissolved in DMF (1 M).The solution was stirred at ambient conditions until the precursors were completely dissolved.The solution was then filtered with 0.2 mm pore size filter, kept in a closed vial of 20 cm 3 , and heated up to 80 ºC in an oil bath.The temperature ramp was set to 20 ºC/h until 60 ºC.Then, the solution is heated until 80 ºC with a temperature ramp of 10 ºC/h.Finally, it was kept at 80 ºC for 24 hours.Reproducible size crystals are obtained with this method.The fine powder sample was obtained from grounding the single-crystal sample.

B. X-ray diffraction
1. High-pressure single-crystal X-ray diffraction SCXRD has advantages over the PXRD approach because it decouples the fitting of lattice and structural parameters, leading thus to higher resolution.In this study, SCXRD measurements were performed at room temperature using a Rigaku SuperNOVA diffractometer equipped with an EOS charge-coupled device (CCD) detector and a molybdenum radiation micro-source (λ = 0.71073 Å).All measurements were processed with the CrysAlisPro software. 17Numerical absorption corrections based on Gaussian integration over a multifaceted crystal model were applied using the ABSORB-7 program. 18For HP measurements, a Mini-Bragg diamond-anvil cell with an opening angle of 85° and anvil culets of 500 μm diameter was used to generate the high-pressure environment.A stainless-steel gasket with a centered hole of 200 μm diameter and 75 μm depth was used as the gasket.Silicone oil was used as pressuretransmitting medium (PTM). 13The sample was placed on one of the diamond anvils (diffracting side), together with a small ruby sphere used as a pressure sensor. 19The crystal structure was refined for each pressure, using previous results as starting points, against F 2 by full-matrix least-squares refinement implemented in the SHELXL program. 20

High-pressure powder X-ray diffraction
In situ PXRD experiments were performed at the BL04-MSPD beamline of ALBA-CELLS synchrotron. 21A membrane LeToullec-type diamond anvil cell (DAC), with a culet of 400 μm in diameter, was used to generate the high-pressure environment.
A hole with a diameter of 200 μm drilled in the center of a pre-indented stainless-steel gasket served as the sample chamber.As in SCXRD experiments, silicone oil was used as the PTM, and the ruby fluorescence method was used for pressure determination. 19e wavelength of the monochromatic X-ray beam was 0.4642 Å, and the spot size of the X-ray was 20 × 20 μm (full width at half maximum).A Rayonix SX165 CCD image plate was used to collect the diffraction patterns, and the sample-to-detector distance was calibrated using a LaB6 standard.The collected two-dimensional diffraction images were reduced to conventional XRD patterns using DIOPTAS. 22The FullProf 23 suit was used to perform Rietveld refinements. 24

C. High-pressure optical absorption
A membrane-type DAC was used to generate the high-pressure environment, the culet of the diamond was 400 μm.A stainless-steel gasket was first pre-indented to a thickness of 40 μm, then a 200 μm in diameter hole was drilled in the center and served as sample chamber.A single-crystal sample, together with silicone oil (PTM) and a ruby sphere (pressure gauge), were loaded in the sample chamber.The sample-in and sample-out method was used to acquire the optical absorption spectra in a home-built optical setup, consisting of a tungsten lamp, fused silica lenses, reflecting optics objectives (15×), and a visible-near infrared spectrometer (Ocean Optics Maya 2000 pro).The light transmitted through the sample [I(ω)] was normalized by the intensity of the light transmitted through the PTM [I(ω0)].[27] Ⅲ. RESULTS AND DISCUSSION Information.CIF files can be obtained from Cambridge Crystallographic Data Centre (deposit numbers 2194528-30).At ambient conditions, MAPbBr3 crystallized in the cubic structure, described by the space group 3 � .The crystal structure determined here at ambient conditions is in agreement with that reported in all the previous works, 7,8,10,12,[14][15][16] and it schematically represented in Figure 2.Here we name it as Phase Ⅰ.In this structure Pb atoms are bonded with six Br atoms forming a regular octahedron.The six Pb-Br bonds have a length of 2.9642 ± 0.0011 Å.The PbBr6 octahedra are bridged by corner sharing Br atoms.The Pb-Br-Pb angle is 180º forming PbBr6 octahedra in a linear chain.The organic molecule is located at the center of the cubic structure with an important positional disorder.The SCXRD pattern collected at 1.1 GPa is different from that collected at ambient conditions (Figure 2b), we also found change in the PXRD experiment at a similar pressure as we show later in this section.Both results support that a pressure-induced structural phase transition has taken place.Here we name the second phase as Phase Ⅱ, the phase transition pressure (Phase Ⅰ to Phase Ⅱ) we found in SCXRD experiment is 0.81 GPa, in agreement with the phase transitions pressure reported in Ref. 8,10,12,15,16 where Helium or perdeuterated isopropanol were used as PTM (Figure 1).The crystal structure of Phase Ⅱ determined from our SCXRD data can be described by the space group 3 � .It is consistent with the results reported in Ref. 7,8,10,12,[14][15][16] determined from neutron diffraction, SCXRD or PXRD.In Phase Ⅱ (Figure 2e), the PbBr6 octahedron remain regular, the six Pb-Br bonds are equal in length, and the bond distance is 2.9304 ± 0.0012 Å at 1.1 GPa.
However, the Pb-Br-Pb bonds are not straight anymore, the angle of Pb-Br-Pb is 161.4 ± 0.3 °.A second pressure-induced phase transition was observed at 1.8 GPa in our SCXRD experiment, diffraction data at 2.3 GPa are shown in Figure 2c.The crystal structure determined is orthorhombic (Figure 2f) and the space group is Pmn21 (No.

31
).Here we name the third phase as Phase Ⅲ.The crystal structure determined here from SCXRD is different from the previous results (space group Pnma), 7,15,16   PXRD patterns of MAPbBr3 at selected pressures are shown in Figure 3a.At pressures lower than 0.9 GPa, they can be well refined by the ambient-pressure cubic crystal structure (Phase Ⅰ, space group: 3 � , Rp=1.05 and Rwp=1.97)obtained from SCXRD experiment.As an example, we provide in Figure 3b the Rietveld refinement at 0.1 GPa.At 1.4 GPa, there are two additional peaks located between 6 and 8 degrees (marked by black diamonds in Figure 3a and pink diamonds in Figure 3c).Notably, the same extra peaks also have been observed in the PXRD patterns reported in Ref. 7,15,16 .Another additional peak can be observed at 1.4 GPa at around 12 degrees.This peak is too weak to be observed in Figure 3a, but it can be identified in Figure 3c.The emergence of the new peaks indicates a pressure-induced phase transition.Furthermore, the Rietveld refinement of the PXRD pattern at 1.4 GPa (Figures 3b and   3c) shows that all peaks can be explained by the cubic crystal structure described by the space group 3 � as we determined for the Phase Ⅱ in SCXRD experiment (Rp=0.60 and Rwp=1.17).At pressures above 1.8 GPa, two extra peaks appear on either side of the peak located at around 8.2 degrees (marked by a black heart in Figure 3a and pink hearts in Figure 3d), indicating another pressure-induced phase transition.These extra peaks have also been observed in Ref. 16 , but in that work the space group of the third phase has been assigned to Pnma following the assignment made in Ref. 7 .
However, the structural solution made in Ref. 7 raises some doubt since there is a peak at low angles not explained by the proposed structure and there are peaks predicted by the Pnma structure not observed in the experiments.In contrast, as the Rietveld refinement of the PXRD collected at 2.6 GPa (Figures 3b and 3d) shows (Rp=0.61 and Rwp=1.13), the PXRD pattern can be satisfactorily explained by the crystal structure with a space group Pmn21 (No. 31) determined from our SCXRD experiments for Phase Ⅲ.In all our experiments, the new peaks (which are the sign of pressure-induced phase transitions, both Phase Ⅰ → Phase Ⅱ and Phase Ⅱ → Phase Ⅲ) are properly indexed by the crystal structure determined from SCXRD in this work (Figures 3c and 3d).
Therefore, the Rietveld refinements of the PXRD patterns confirm the crystal structure determined from SCXRD.With increasing pressure beyond 3.4 GPa, the intensity of the diffraction peaks is reduced, most peaks become broader and most peaks for values of 2θ higher than 11° disappear (as the purple PXRD patterns show in Figure 3a).This might be caused by a gradual disordering of the crystal structure related with the partial amorphization of MAPbBr3 which was proposed to occur based on previous PXRD experiments. 7,12,15,16The most likely picture is the disorder of MA within an ordered inorganic PbBr6 framework which is preserved.Furthermore, the pressure-induced structural changes in MAPbBr3 are totally reversible, as shown by the PXRD pattern collected after the pressure was released to ambient pressure (see the topmost spectra in Figure 3a).This is consistent with the reversibility found in works. 7,15,16e lattice parameter and the unit-cell volume per formula unit as a function of pressure obtained from our experiments are plotted in Figure 4 and the data can be found in Tables S5 and S6 in the Supplementary Information.From the structure information of the three phases summarized in Table.S1 in the Supplementary Information, it can be seen that lattice parameters from Phases Ⅱ and Ⅲ nearly doubled the lattice parameter from phase I, and consequently the unit-cell volume becomes approximately 8 times that of Phase Ⅰ.Then, for a better comparison in Figure 4, the lattice parameters from Phases Ⅱ and Ⅲ are divided by 2 and the unit-cell volume per formula is represented.There is no observable discontinuity in the unit-cell volume at the phase transitions (Figure 4b).On the other hand, at the second transition the crystal structure is elongated in one direction (b axis) and shortened in other (c axis), while the third direction remains unmodified (a axis).In the figure it is shown that the lattice parameters obtained from PXRD and SCXRD show a good agreement with each other.The unit-cell volumes per formula unit for each phase are have been fitted separately by second-order Birch-Murnaghan equations of state (BM-EOS) (Figure 4b). 29,30The obtained bulk modulus and its pressure derivatives are summarized in Table Ⅰ, together with the value reported in the previous works by using different experiment methods and PTM.In this work, the bulk moduli for Phases Ⅰ and Ⅱ obtained by fitting the unit-cell volume per formula unit (according to SCXRD) as functions of pressure, are in agreement with the values reported in Ref. 10 , where neutron diffraction was used to measure the unit-cell volume, and isopropanol was used as PTM, also in agreement with the value reported in Ref. 15 , in which the unit-cell volume of MAPbBr3 is determined from SCXRD experiment with helium as PTM.However, we did not find any sign of the pressure-induced isostructural alleged phase transition at around 2.7 GPa in Ref. 15 and the accompanied ~4.4 Å 3 drop in the volume.The bulk modulus for Phase Ⅰ from the PXRD experiment in this work is similar to the data reported in Ref. 12 , where the probing method is PXRD and helium was used as the PTM.
Unfortunately, the bulk modulus in phase Ⅱ obtained from the PXRD in this work only contain two data, and it is higher than any reported values in the literature.There is no reported experimental bulk modulus of Phase Ⅲ, which is described by space group Pnma in previous work 7,15,16 but unambiguously by Pmn21 in this work.It is 13.0 GPa and 19.1 GPa calculated from the SCXRD and PXRD experiment, respectively.There is a discrepancy in the bulk modulus determined From SCXRD and PXRD in this work, the same phenomenon has also been observed in previous works which show a larger bulk modulus in PXRD than that determined from SCXRD experiment when using helium as PTM. 12,15Therefore, the differences cannot be related to deviatoric stresses induced by non-hydrostaticity.Similar differences have been observed in other compounds, Like FeVO4, PbCrO4, and BiMnO3 [31][32][33] being related to the existence of grain-grain stresses in powder XRD experiments.It should be noted here that the three phases are highly compressible with values of the bulk modulus comparable to that of metal-organic frameworks. 34 also fitted the lattice parameters a, b and c obtained from our SCXRD experiment (Figure 4a) in Phase Ⅲ with a similar modified Birch's EOS 35 as following: where a0 is the lattice parameter of MAPbBr3 at normal conditions, Ba is the linear moduli in a axis, Ba' is the pressure derivative.As in the second-order BM-EOS, here   Two independent high-pressure optical-absorption experiments were performed to investigate the bandgap of MAPbBr3.The optical-absorption spectra from the first experiment (exp 1) at selected pressure are shown in Figure 5a, and the optical image of the loading at selected pressures can be found in Figure S1 in the Supplementary Information during both the compression and decompression process.The absorption edge first shows a red-shift from room pressure up to around 0.7 GPa, after that the absorption edge exhibits a blue-shift under compression up to 3.8 GPa.We did not conduct any theoretical calculation on the electronic band structure of MAPbBr3, because of the partial occupations in Phase I, but according to the previous calculations, 7,36 the bandgap shows a direct nature.Therefore, the Tauc plot for direct bandgap materials was used to obtain the bandgap energy from the optical-absorption spectra at each pressure, 37 by extrapolating the linear fit of the high-energy part of the (αhν) 2 vs hν plot to zero, where α, h and ν are absorption coefficient, Plank constant, and photon frequency, respectively.The bandgap derived from the two opticalabsorption experiments (exp 1 and exp 2) are in a good agreement (Figure 5b).The bandgap decreases with the increasing pressure in Phase Ⅰ and increases in Phases Ⅱ and Ⅲ with a different slope.The pressure-induced bandgap change is totally reversible, as the bandgap collected at the decompression process of the first experiment shows (Figure 5b).According to the previous theoretical calculations, the valence band maximum (VBM) is dominated by the Br-4p orbitals, whilst the conduction band minimum (CBM) is dominated by the Pb-6p orbital. 7Therefore, the bandgap of MAPbBr3 is strongly affected by the bond distance of Pb-Br and Pb-Br-Pb angle 25 .
Furthermore, the positive linear relationship between the Pb-Br bond distance and bandgap energy of MAPbBr3 and MAPbI3 have been established in ref. 8 .On the other hand, the decrease of Pb-Br-Pb angle causes the opening of the bandgap energy in

Ⅳ. CONCLUSION
In this work, we have reported the results of single-crystal X-ray diffraction The crystal structure in the third phase (Pmn21) is different from that determined in previous works (Pnma) 7,15,16 where only PXRD was used and a full structural determination was not performed.

Figure. 1 .
Figure. 1. Summary of the pressure-induced phase transitions observed in MAPbBr3 reported in the literature.Including the results reported by Swainson et al,10 Wang et al,7 Jaffe et al,12 Kong et al,14 Szafrański et al,8 Zhang et al,15 Yin et al,16 and this work.The different crystal structures with different space groups are shown in different colors.The diffraction method, single-crystal Xray diffraction (SCXRD), powder X-ray diffraction (PXRD) and pressure transition medium (PTM)

Figure. 2 .
Figure. 2. Results of high pressure SCXRD experiments on MAPbBr3.(Top) Reconstructed reciprocal-space precession-images for the (hk0) plane at (a) ambient conditions, (b) 1.1 GPa, and (c) 2.3 GPa.They correspond to phases I, II, and III.In phases I and II the order of rotational symmetry is 4. In phase III it is 2. (Bottom) (d)-(e) show the crystal structure of MAPbBr3 obtained from the SCXRD data shown above.The space group (SG) of each crystal structure is shown at the bottom.The atoms are shown in different colors as indicated in the figure.
and it is confirmed by the Rietveld refinements of our PXRD patterns as shown later.For the crystal structure of Phase Ⅲ collected at 2.3 GPa (Figure2f), the PbBr6 octahedra are not regular anymore, Pb are located at two different Wyckoff positions and Br are located at eight different Wyckoff positions.The Pb-Br bond distances range from 2.859 ± 0.015 Å to 3.034 ± 0.015 Å, wherein the Pb-Br-Pb angle varies in the range of 142.0 ± 0.5 to 172.1 ± 0.5 degrees.At pressures higher than 3 GPa in the SCXRD experiment, the quality of the diffraction data quickly decreases, probably due to degradation of the monocrystal, and it becomes impossible to resolve the structure.A possible reason for this is the introduction of disorder in the crystal structure as a precursor of the pressure-induced amorphization of the sample.28

Figure. 3 .
Figure. 3. Results of high pressure PXRD experiments on MAPbBr3.(a) PXRD patterns at selected pressures, patterns from different phases are shown in different colors.Phases Ⅰ, Ⅱ, and Ⅲ are shown in blue, red, and green, respectively.The patterns in purple show signs of a pressureinduced gradual of loss long-range order.Pressures are given in GPa.The black diamond and heart symbols identify the appearance of new reflections.(b) Typical Rietveld refinement at 0.1 GPa (Phase Ⅰ), 1.4 GPa (Phase Ⅱ), and 2.6 GPa (Phase Ⅲ).(c) and (d) Enlarged images of the areas marked by red boxes in (b) for experiments collected at 1.4 GPa and 2.6 GPa, respectively.The

Figure. 4 .
Figure. 4. Pressure dependence of the lattice parameters and unit-cell volume of MAPbBr3.(a).Crystal lattice parameters obtained from PXRD (solid symbols) and SCXRD (empty symbols) as a function of pressure.The lattice parameters in Phase Ⅱ and Ⅲ have been divided by 2 to better

we fixed Ba' in a value of 4 . 3 ± 2 .
The ambient-condition lattice parameter and moduli are obtained from the fitting.The moduli of the crystal structure in axis a, b and c are 13.93 GPa, 5.3 ± 0.9 GPa and 21.3 ± 1.0 GPa, respectively.The crystal structure in Phase Ⅲ shows an anisotropic behavior under compression and b axis is the most compressible axis.

Figure. 5 .
Figure. 5. Pressure dependence of bandgap of MAPbBr3.(a).Optical-absorption spectra of MAPbBr3 at selected pressures from the first experiment (exp 1).(b).Bandgap energy of MAPbBr3 as a function of pressure, the bandgap here at each pressure was derived from the optical absorption spectra shown in (a) by means of a Tauc plot.(c).Pressure dependence of Pb-Br-Pb angles and (d) Pb-Br bond distance obtained from SCXRD experiments.The vertical dash line indicates the phase transition pressure.In figures (c) and (d), the average Pb-Br-Pb angles and Pb-Br bond distance of phase Ⅲ are shown in solid green lines.
pressure-induced bandgap change of MAPbBr3 can be explained by the pressure dependence of Pb-Br bond distance and Pb-Br-Pb angle as shown in Figures 5c and 5d, which is obtained from SCXRD experiments.In phase Ⅰ, both Pb and Br atoms are located at only one Wyckoff position (each of them), all the Pb-Br bonds are identical and shortening with increasing pressure, and there is no pressure-induced titling of the PbBr6 octahedra.Therefore, the pressure-induced narrowing of the bandgap energy is caused by the shortening of the Pb-Br bond distance under compression, which favors an increase of atomic hybridization.In Phase Ⅱ, the Pb-Br bond distance show an independent behavior of pressure, the Pb-Br-Pb angle dramatically bends from 180 o to around 165 o and further decreases with increasing pressure, so the bandgap starts to broaden under compression.In phase Ⅲ, Pb is located at two Wyckoff positions and Br is located at eight Wyckoff positions, so there are 12 different Pb-Br bond distances and 4 different Pb-Br-Pb angles.We have calculated the average Pb-Br bond distance and Pb-Br-Pb angles as shown in Figures 5c and 5d.The average Pb-Br slightly decrease with increasing pressure, as well as the average Pb-Br-Pb angles.Those two effects compete under compression, caused a slight increase of the bandgap energy under compression.

(
SCXRD), synchrotron-based powder X-ray diffraction (PXRD), and opticalabsorption experiments performed on MAPbBr3 perovskite under high pressure.Two pressure-induced phase transition have been independently observed through the three different diagnostics.The crystal structures of each of three MAPbBr3 phases have been determined from high-pressure SCXRD, the transition sequence is 3 � →3 � →Pmn21, and the phase transitions occurred at 0.8 and 1.8 GPa according to both the SCXRD and PXRD data.The crystal structure determined from SCXRD has been used to perform Rietveld refinements on our PXRD patterns, explaining very well the experiments and supporting the crystal structure determined from SCXRD.

For
each of the three phases, the pressure dependence of the lattice parameters obtained from SCXRD and PXRD, as well as the unit-cell volume per formula unit have been given.The bulk moduli have been calculated by fitting the unit-cell volume data with a second-order Birch-Murnaghan equation of state, the results have been compared with previous works.The bandgap change has been derived from opticalabsorption experiments, it shows a narrowing behavior with increasing pressure in Phase Ⅰ (3 � ), while a widening behavior in Phases Ⅱ (3 � ) and Ⅲ (Pmn21), but with a different pressure dependence.There are two effects competing under compression, which results in a nonlinear pressure dependence of the bandgap energy.The pressure-induced shortening of Pb-Br bond distances causes the narrowing of the bandgap energy, while the decrease of the Pb-Br-Pb angles causes the opening of the bandgap energy.The pressure dependence of the Pb-Br bond distance and Pb-Br-Pb angles obtained from SCXRD experiments have been used to explain the bandgap energy change of MAPbBr3 under compression.All the changes found in those three techniques are totally reversible.

TABLE Ⅰ .
Summary of the bulk moduli (B0) for different phases of MAPbBr3."ND" means neutron diffraction, "PXRD" powder X-ray diffraction, "SCXRD" single-crystal X-ray diffraction and "DFT" computer simulations using density-functional theory.Other information, like pressure transition medium (PTM) used in experiment, the order of Birch-Murnaghan equation of state (BM-EOS), zero-pressure volume per formula (V0/Z) are also included in this table.
a .This work.