High‐Resolution In‐Situ Synchrotron X‐Ray Studies of Inorganic Perovskite CsPbBr3: New Symmetry Assignments and Structural Phase Transitions

Abstract Perovskite photovoltaic ABX3 systems are being studied due to their high energy‐conversion efficiencies with current emphasis placed on pure inorganic systems. In this work, synchrotron single‐crystal diffraction measurements combined with second harmonic generation measurements reveal the absence of inversion symmetry below room temperature in CsPbBr3. Local structural analysis by pair distribution function and X‐ray absorption fine structure methods are performed to ascertain the local ordering, atomic pair correlations, and phase evolution in a broad range of temperatures. The currently accepted space group assignments for CsPbBr3 are found to be incorrect in a manner that profoundly impacts physical properties. New assignments are obtained for the bulk structure: Im3¯ (above ≈410 K), P21/m (between ≈300 K and ≈410 K), and the polar group Pm (below ≈300 K), respectively. The newly observed structural distortions exist in the bulk structure consistent with the expectation of previous photoluminescence and Raman measurements. High‐pressure measurements reveal multiple low‐pressure phases, one of which exists as a metastable phase at ambient pressure. This work should help guide research in the perovskite photovoltaic community to better control the structure under operational conditions and further improve transport and optical properties.

2 PbBr2 (1.83 g, 5 mmol) and CH3NH3Br (560 mg, 5 mmol) were dissolved in 50 ml of dimethylformamide. The solution was heated slightly to obtain a transparent solution. This solution was further filtered through a compacted Celite column and the filtrate was collected. Two milliliters of this solution was transferred into an inner vial (5 ml in total vial volume) that was placed in a larger outer vial (25 ml in total volume) with 5 ml of toluene inside. Finally, the outer vial was carefully sealed. The diffusion of toluene from the outer vial into the inner vial was slow, and the crystallization process was maintained in a dark and undisturbed environment for at least three days. Orange block-shaped single crystals were obtained and characterized by X-ray diffraction. For powder sample derived experiments, crystals samples were crushed and sieved to obtain ~ 400 mesh powders. All measurements are based on crystal derived materials.
Differential scanning calorimetry measurements were conducted under flowing N2 gas using a Perkin Elmer DSC 6000. Measurements were made at a cooling/heating rate of 2 K/min. The rotational anisotropy second harmonic generation (RA-SHG) measurements were performed with the geometry shown in Fig.4(a) and spectrum of the incident beam shown in Fig. 4 (b). The reflected SHG intensity was recorded as a function of the azimuthal angle ϕ, while selecting either Sin-Sout or Sin-Pout polarization channels. In this experiment, the incident ultrafast light source was of 50 fs pulse duration and 200 kHz repetition rate, and was focused down to a 20 µm diameter spot on the sample and at a power of 0.7 mW, corresponding to a fluence of ~ 1 mJ/cm 2 . The intensity of the reflected SHG was measured with a single photon counting detector.
Severe laser-induced lattice dynamics is not observed in our measurements on CsPbBr3. RA-SHG patterns from the same sample at 290 K and the Sin-Sout channel, taken under different optical fluence 1.1 and 2.3 mJ/cm 2 , remain unchanged within the uncertainty level of the measurements. This indicates minimal lattice perturbation from the laser. Furthermore, the pulsed fs-laser source used in the RA-SHG experiments is of a 200 kHz repetition rate, corresponding to 5 s separations between adjacent pulses. It is unlikely that the photoexcited lattice change/dynamics, if any, have a recovery timescale of microseconds making it detected by subsequent pulses. Ambient pressure temperature-dependent Raman Spectra were measured with an excitation wavelength of 780 nm in backscattering geometry using a Thermo Scientific DXR Raman Microscope. A 50× objective was used with the laser power set at 15 mW. The sample was found to be stable under this laser power after tests were done on a range of laser power values (0.1 to 15 mW). Each temperature data set is comprised of one hundred 0.2-second scans. A Linkam Scientific THMS600 stage was used to measure the temperature-dependent Raman spectra. Only warming data are shown. Samples return to the original phase after heating up to the maximum temperature of 830 K used in the experiments. These measurements were conducted at the NJIT York Center.
High-pressure Raman measurements were conducted at the National Synchrotron Light Source II (NSLS II) beamline 22-IR-1 National. Measurements were conducted in a symmetric cylindrical diamond cell with (100) oriented diamonds. The diamond culet size was 500 m, and tungsten gaskets were used.
The pressure medium utilized was methanol:ethanol: water in a 16:3:1 ratio by volume. Pressure calibration was conducted using ruby fluorescence mainline shifts [1]. Pressure calibration measurements were made before and after each Raman spectrum was collected. In addition, calibration measurements as a function of position at multiple points (in the sample region of the gasket) at the highest pressure showed a high level of hydrostatic behavior of the pressure medium. Typical pressure errors are ± 0.10 GPa for pressures below ~ 4 GPa and ~ ±0.20 GPa for pressures above ~4 GPa. For this experiment, the custom micro-Raman system at beamline 22-IR-1 consisted of a 646 nm solid-state laser, a Princeton Instruments liquid-nitrogen cooled PyloN CCD detector, a PI Acton SpectraPro SP-2556 Imaging Spectrograph, and a 20× objective.
For all Raman measurements, no change in the spectra was observed over time at a given pressure. Each pressure data set is comprised of sixty 10-second scans.
Diffraction measurements on ~50 m edge length crystals (cube-like shape) were conducted at the Advanced Photon Source (APS) beamline 15-ID-D (NSF's ChemMatCARS) at Argonne National Laboratory using a wavelength of 0.41328 Å (30 keV). The data were collected with a PILATUS 1M CdTe detector (by DECTRIS, maximum count rate = 10 7 cps/pixel, counter depth =20 bit) between 100 K and 4 450 K in steps of 10 K (data are for increasing temperature). The data were processed using APEX3 (Bruker, 2016) 2 . The experimental reciprocal space precession images were generated using the same software. The simulated reciprocal space images were obtained using SingleCrystal 4.1.2 (CrystalMaker). The solution and refinement of the data were done using the program Olex2 [3]  We note that the NSF ChemMatCARS beamline 15-ID-D beamline was operated at 30 keV for these measurements. It is an undulator beamline. An undulator source does not output a continuous x-ray spectrum but a sharply peaked spectrum centered at the set energy, which is 30 keV in this case. In addition, the beamline utilized a Si (111) double crystal monochromator. The Si (222) Bragg reflection is forbidden.
More importantly, the beamline has a harmonic rejection mirror to suppress the photons with energies above 30 keV. Hence the combination of tuned undulator energy, the use of a Si (111) monochromator, and a harmonic rejection mirror make Bragg peaks due to the /2 (60 keV) contamination impossible. To determine force constants and phonon DOS for CsPbBr3, density functional calculations in the projector augmented wave approach were carried out utilizing the VASP code [ 6 ]. Full structural optimization was conducted for both lattice parameters and atomic positions. The LDA exchange functional (Ceperly and Alder as parameterized by Perdew and Zunger [7]) was used to obtain the relaxed structure.
The ground-state structure was optimized so that forces on each atom were below 2 x 10 -5 eV/Å. The optimized cell was found to be orthorhombic with volume = 8.3876 Å x 11.5197 Å x 7.5612 Å utilized ((4,4,4) gamma centered grid). Calculations for a 2×2×2 supercell with a gamma centered k-space grid were. The force constants were calculated in the frozen phonon approximation. The code Phonopy was utilized to determine the phonon density of states and phonon displacement modes from the force constants (Fig. S3, and Table S1) [8]. Gaussian broadening with full-width at half maximum of 7.1 cm -1 was applied to each phonon DOS spectrum shown in Fig. S3(a).
To determine the low-temperature space group by modeling methods (DFT based on VASP), we initiated a structural optimization starting from the 120 K XRD Pm solution (~2 × 2 × 2 cell, ((4,4,4) gamma centered k-space grid)). In the first runs, the positions of the Pb atoms were fixed. The positions of all Br and Cs atoms were allowed to move, and the unit cell was free to adjust its shape to reduce the forces on all atoms to be less than 2.5 x 10 -5 eV/Å. A second optimization cycle was conducted will all atoms and lattice parameters were free to adjust until the forces on atoms were minimized (again to less than 2.5 x 10 -5 eV/Å). The structural optimization resulted in a monoclinic Pm cell with a = 11.293 Å, b= 11.518 Å, c=11.293 Å and b = 95.91°. We found the energy per CsPbBr3 per formula unit (f.u.) to be lower (E=-18.019 eV/f.u.) for this cell than that derived from fully optimizing a cell ((8,8,4) gamma centered k-space grid)) with dimension ~ √2 × √2 × 2 (E=-17.944 eV/f.u.). These smaller cells result in a Pnma structure after optimization. Note that these calculations generate the zero temperature structure.
Molecular dynamics (MD) simulations were also conducted with the VASP code and projectoraugmented wave (PAW) potentials [3]. The simulations were conducted as done in Ref.
[9] for MAPbI3 and used a 400 eV energy cutoff. A 2×2×2 orthorhombic supercell (based on the optimized structure 6 obtained above with 160 atoms) was utilized. For separate MD simulations, the system temperature was set at 100, 250, and 500 K utilizing the NVT ensemble. MD time steps of 1 fs were used, with ~2500 time step for each simulation.
Br K-edge XAFS spectra were collected at APS beamline 20-BM at Argonne National Laboratory on single crystals (~2 mm x 3 mm x 0.5 mm) in fluorescence mode (20 K to 125 K). Higher temperature measurements were done in fluorescence mode with powders at beamline at NSLS-II beamline 7 BM (120 K to 300 K). Data were corrected for self-absorption. Reduction of the x-ray absorption fine-structure (XAFS) data was performed using standard procedures [10]. In the XAFS refinements, to treat the atomic distribution functions on equal footing, the Br K-edge spectra were modeled in R-space by optimizing the integral of the product of the radial distribution functions and theoretical spectra with respect to the measured spectra. Specifically, the experimental spectrum is modeled by, 2 ( ) ( , ) 4 ( ) k k r r g r dr th th  is the theoretical spectrum and g(r) is the real space radial distribution function based on a sum of Gaussian functions ((k) is the measured spectrum) [11] at each temperature (as in Ref. [12]). For each shell fit, the coordination number (N) was held at the crystallographic value, but the position (R) and Gaussian width () was fit to the data. the k-range 1.16 < k < 11.1 Å -1 and the R-range 1.96 < R < 4.00 Å were utilized. Coordination numbers for the atomic shells were fixed to the crystallographic values. The Gaussian widths and positions were fit for each component Two independent Pair distribution function (PDF) data sets (140 to 500 K (run 1) and 10 to 200 K (run 2)) were collected at NSLS-II beamline 28-ID-2 (XPD) beamline at Brookhaven National Laboratory using a wavelength  = 0.1877 Å (run 1) and  = 0.1872 (run 2). Measurements utilized Perkin Elmer Area detectors with a sample to detector distance of ~200 mm. Exact detector to sample distances were derived by fits to Ni powder calibration standards. The Ni standard was also used to determine set-up specific parameters (Qdamp and Qbroad), which were held fixed for these samples. The range Qmim = 1.2 Å -1 and Qmax = 24.5 Å -1 (run 1) was used in data reduction. (For run 2 the range was Qmim = 1.2 Å -1 and Qmax = 22.5 Å -1 used.) All samples were measured in 1 mm Kapton capillaries with 50 micron thick walls. Scans 7 were collected with blank capillaries to determine the background scattering. This background was subtracted from all datasets. The methods utilized for analysis of the PDF data are described in detail in Refs. [13]. For the fits in R-space, the range 2.0 < r < 30 Å was utilized. The time interval between temperature points was ~2 minutes. Combined with the small temperature steps, the approach kept the samples from being in a quenched state. For the PDF curves in Fig thick rhenium gasket pre-indented to ~42 m (with 200 m hole) was used as the sample chamber. Neon was used as the pressure transmitting medium and Ruby balls and gold balls were placed near the pressed powder samples. Small pressure steps were enabled with the use of a gas membrane apparatus. At each pressure, 1-second exposures were conducted to acquire images. The sample was measured up to ~18 GPa and then released and remeasured. The ambient pattern was recovered on pressure release. Dioptas [15] 8 were utilized to integrate the two-dimensional diffraction images (powder rings) to generate the intensity vs 2 curves.       Table S1) indicating the motion of Cs (green), Br (red), and Pb (black) atoms.   systematic violations must also be examined (Table S2). (c) The R1 based on the space groups in the literature. The unite cell for Pnma is ~√2 × √2 × 2 , P4/mbm is ~√2 × √2 × , and ~× × for Pm-3m space group.    K. The (h k l) grid corresponds to the previously reported Pm-3m space group with a lattice constant a = 5.87 Å. Diffraction spots with half-integer values are observed, indicating that the correct lattice constant should be doubled. The simulated powder diffraction patterns of the Pm-3m and the newly proposed Im-3 space group based on the solved structure from single-crystal diffraction refinement are given in panels (b) and (c), respectively. (d) Single-crystal X-ray diffraction reciprocal space images of the (h k l) planes of CsPbBr3 at 360 K. The grid corresponds to the previously reported P4/mbm space group with unit cell dimension: √2 × √2 × . Note the presence of half-integer peaks. The simulated powder diffraction patterns of P4/mbm and the newly proposed P21/m space group based on the solution of the single-crystal diffraction refinement are given in panels (e) and (f), respectively. The wavelength for the simulated powder diffraction patterns is 1.54059 Å (Cu-Kα). Powder diffraction measurements are not adequate to distinguish between the P4/mbm and P21/m space groups in the 360 K data and between the Pm-3m and Im-3 space groups in the 450 K data. We also note that above 360 K, the Im-3m and Im-3 space groups have similar R1 parameters. However, the Cs ADPs of Im-3m are highly anomalous (dramatically reduced in size with temperature increase). The anomalous behavior is due to the presence of distortions in CsPbBr3 not supported by the high symmetry Im-3m space group.  The intensity (y-axis) is displayed on a log scale. The additional features in the spectra are indicated with asterisks (*) symbols corresponds to the halfinteger peaks in reciprocal lattice shown in panel (a). In the reciprocal space images, an examination of the intensities of halfinteger reflections, (-1.5 k 0) is shown in panel (d), and the integer reflections, (h -1 0) is in panel (e), reveals the intensity of halfinteger peaks are ~10 2 times weaker than the integer peak intensity but ~10 times stronger than the intensity of the background. Returning to the powder diffraction simulations [panel (c)], it is observed that the weak peaks (*) are of the same level relative to the main peaks as what is seen in the reciprocal space images (d) for the single-crystal measurements. Hence fitting powder data to the Pm-3m structure will not be strongly influenced by the exclusion of these additional peaks. Consequently, powder diffraction can not be used to ascertain the space group. A plot of |Fo| (observed) vs. |Fc| (calculated) parameters at 450 K for the strong (eveninteger) and the weak satellite (odd-integer) reflections in Im-3 space group with a linear fit (black line). The inset is the same plot with data for the odd-integer reflections. (g) Experimental reciprocal space image at 450 K for the (h k 0) plane compared with the simulated pattern (h) for the Im-3 structure (2 × 2 × 2 ). In the calculation, the high-intensity peaks are in the red region of the color spectrum and the low-intensity peaks are on the blue end of the spectrum. The size of the peaks shown also indicates their intensities.    S9. The completeness as a function of d spacing is given for both the previously reported models and new models. Reflections are binned in d space using 20 bins for all models. This gives a representative sample of the density of reflections. Note that not all reflections are captured on this coarse grid. The reciprocal lattice precession images are also present to better clarify where are the additional reflections occur in the raw data. The (h k l) grids in these images are based on the old unit cell dimensions. The shell completeness of the old model is presented as the solid red square symbols and the new model as open square symbols. Note that, for the old models, mainly strong reflections (integer reflections) in the full data set are utilized. While for the new model, all the reflections (both integer and half-integer reflections) are captured and utilized in the structural refinement. The half-integer reflections are not fitted in the old models. In panel (c), it's not surprising that some weak reflections appear at low temperatures which are difficult to be captured completely. In our structural solutions, the overall completeness for the P21/m and Pm solution is >97% while for Im-3 is >99%. The completeness of old models is >99% since they require only a subset (dominant reflections only) of the measured reflections.  (c). We found that these reflections are weak (~ 10 times the background intensity). Careful considerations showed that all these previously unfitted weak reflections can indeed be indexed on a primitive monoclinic supercell with a =11.6126(6) Å, b =11.7344(6) Å, c =11.6156(5) Å, and β =89.1610(10). Considering all observed reflections, the space group can no longer be taken as Pnma space group. The true space group is Pm with unit cell dimensions ~ 2 × 2 × 2 .