High pressure crystal structure of CsPbBr3
From high pressure SXD data, we found that the CsPbBr3 crystal underwent a phase transition from orthorhombic structure (space group Pnma, #62) to a more distorted monoclinic structure (space group P21/c, #14) at 2 GPa (Fig. 1). In this process, the unit cell expands to include six times more atoms whereas the density of the crystal increased by ~8% from 5.23 g/cm3 to 5.64 g/cm3 (Fig. 2). We have observed that for the high pressure P21/c phase, two of the Pb sites (Pb01 and Pb07) changes from 6-coordinated to 7-coordinated (Fig. 1). Although the β angle of the high pressure P21/c phase is very close to 90° (90.110–90.134°), in the structure we can’t find either three perpendicular 2-fold axes, or one 2-fold axis and two mirror planes. We have also attempted to solve the crystal structure with an orthorhombic starting model, yet the structure solution/refinement didn’t converge, so we conclude that the crystal system of the high pressure phase has to be monoclinic.Fig. 1: Single crystal structures of the low-pressure (left) and high-pressure (right) phases of CsPbBr3.The red boundaries indicate the unit-cell of each phase. 7-coordinated Pb sites (Pb01 and Pb07) in the high pressure phase are highlighted with the grey polyhedra.Fig. 2: Density of CsPbBr3 as a function of pressure.Curves in the figure indicate the best-fit BM2-EoS, with the best-fit bulk modulus K0 labeled next to each EoS.We also determined the density and equations of states of the low pressure and high pressure phases of CsPbBr3 and compared them with published data. At pressures below 2 GPa, our results is consistent with published powder diffraction measurements8. It has been suggested that the Pnma structured CsPbBr3 will undergo an isostructural transition at 1.2 GPa8, in which the crystal maintains the same space group but the bulk modulus K0 increases from 18.1 GPa to 37.3 GPa when fitting the P-V data with a second-order Birch-Murnaghan equation of states (BM2-EoS): \(P\left(V\right)=\,\frac{3{K}_{0}}{2}\left[{\left(\frac{{V}_{0}}{V}\right)}^{7/3}-{\left(\frac{{V}_{0}}{V}\right)}^{5/3}\right]\), where V0 is the unit cell volume at 0 GPa. Our data show the same kink in pressure-density relationship below and above 1.2 GPa (Fig. 2). When fitting our measured P-V data below 1.2 GPa (usually referred to as the phase-I, and phase-II refers to the structure between 1.2 and 2 GPa2,8) with BM2-EoS, the best-fit bulk modulus K0 of phase-I is 18.0 ± 0.8 GPa, consistent with powder X-ray diffraction results (18.1 GPa)8. The P-V relationship of the high pressure P21/c phase is also fitted with a BM2-EoS, and the best fit K0 is 22.1 ± 1.8 GPa, which lies between the K0 of phase-I and phase-II. The best-fit V0 for the P21/c phase is 4437 ± 32 A3. The V0 for the Pnma phase is 793 ± 5 A3. Considering that one unit cell in the P21/c phase corresponds to six unit cells in the Pnma phase, at zero pressure, the density of the Pnma phase is ~7% smaller than the P21/c phase.We notice that, the bulk modulus K0 for Pnma Phase-I (0–1 GPa) is 18.0 GPa, K0 for Pnma phase-II (1–2 GPa) is 37.3 GPa, and K0 for P21/c phase (>2 GPa) is 22.1 GPa. K0 for Pnma phase-II is significantly higher than the other two. We suspect that this phenomenon indicates that the Pnma-P21/c transition has a martensitic-like nature. Martensitic transition16 involves rotation of polyhedra within the crystal structure, and has been observed in other perovskite-structured materials17. It is also known that pressure induced martensitic transition has significant effect on the bulk moduli of materials18, so we suspect that the abrupt change in the bulk moduli before and after the Pnma-P21/c transition indicates its martensitic-like nature.Electronic band structure at high pressuresDuring our measurement, we monitor the evolution of sample color at various pressures. The sample starts as a brown colored translucent crystal. When the phase transition occurs at 2 GPa, the color of the crystal changes from brown to light yellow in back-reflection light (Fig. 3), which has been observed by multiple studies before2,8,19. The change of the sample color from brown to transparent is an indicator that the sample no longer absorbs green light near ~530 nm, which coincides with the observations from optical absorption spectroscopy2,8,20. On release of the pressure after decompression, the sample’s color changes back to brown, and the diffraction images switched back to the Pnma diffraction pattern as well (Fig. 3), showing that the pressure-induced Pnma-P21/c transition is reversible.Fig. 3: Optical images (top) and corresponding merged diffraction images (bottom) of CsPbBr3 at various pressures.Sample is located at the center of the Re-gasket hole and a small piece of ruby sphere is located close to the sample as pressure marker. A&D): 0.27 GPa (right after gas loading). B&E): 2.08 GPa (right after the structural transition). C&F): 1 bar after decompression.The change of sample’s color is strongly related to the electronic band structure evolution in the sample. In order to examine the association of the electronic band structure as a function of pressure, we have carried out DFT calculations based on the high pressure crystal structure we resolved with SXD (Fig. 4). Below the structural transition pressure at 2 GPa, the band gap of the low pressure Pnma phase gradually decreases from 2.09 eV at 1 bar to a minimum of 2.05 eV at 1.5 GPa, then increases to 2.07 eV at 2 GPa, and the same pressure dependence of band gap has been observed in multiple experimental2,8,20 and DFT2,7,8,21 studies before. This non-monotonic pressure dependence of the band gap has been interpreted as the result of competition between isotropic volume deformation and structural relaxation22.Fig. 4: Electronic band structure and projected density of states (PDOS) of CsPbBr3.Calculations at A) 1 bar (Pnma) and B) 2.08 GPa (P21/c). C zoomed-in band structure at the top of valence band at 2.08 GPa, highlighting the high electronic energy near the Z-point (0, 0.5, 0). Since the bottom of the conduction band is around the Γ-point (0, 0, 0), we conclude that there is an emergent indirect bandgap in the P21/c phase CsPbBr3 at 2.08 GPa.After the Pnma-P21/c structural transition, our calculations have demonstrated that the valence band maximum shifted from Γ-point (0, 0, 0) to around Z-point (0, 0.5, 0) (Fig. 4C), whereas the conduction band minimum stays at the Γ-point (Fig. 4B), which indicates the emergence of an indirect bandgap in the high pressure P21/c phase, consistent with experimental observations2. Our calculations also show that the high pressure phase has a bigger band gap than the low pressure phase (Fig. 5). At the Pnma-P21/c transition, the band gap of CsPbBr3 jumps from 2.07 eV to 2.38 eV, and similar band gap jumps have been experimentally observed across the 2 GPa phase transition boundary in both nano-crystalline20 (0.25 eV) and single crystal2 CsPbBr3 (0.23 eV) (Fig. 5, inset). We note here that the experimental band gaps are measured using the Tauc method2,8,20. High pressure optical absorption spectra were measured between 250 and 1100 nm. Experimental band gap was then calculated by extrapolating the linear part of (αdhν)2-hν curve. The 0.31 eV band gap jump shifts the optical absorbance edge from ~540 nm to ~475 nm, and hence leads to the change in sample color from brown to light yellow (Fig. 3). The band gap of the high pressure P21/c phase also has a negative slope as a function of pressure, which is consistent with published experimental measurements on single crystal CsPbBr32, where a negative band gap-pressure slope were observed between 5 and 40 GPa in a compression run, and between 1 and 30 GPa in a decompression run. At pressures above 3.5 GPa, we notice that the band gap of CsPbBr3 becomes direct again (Fig. S1), which is similar to the predicted P21/m high pressure metastable phase2. In conclusion, our DFT calculations have demonstrated that the Pnma-P21/c structural transition can explain the experimental optical measurements on CsPbBr3 at high pressures. Our results highlights the necessity of using in-situ crystal structure in the calculation of electronic band structures of halide perovskites.Fig. 5: Experimentally determined and DFT computed electronic band gap of CsPbBr3 as functions of pressure.Plus-signs and dashed curves: results from DFT calculations. Multiply-signs and solid curves: results from experimental measurements. Blue circles: band gap determined from this study using experimentally determined crystal structure as the initial structure for DFT calculations (Supplementary Table S1). Note the band gap from DFT (right axis) is shifted by 0.2 eV up relative to the band gap measured by experiments (left axis) to highlight the consistency between different studies, because DFT calculations tend to systematically underestimate the band gap39. The value of 0.2 eV was chosen so that the experimental and DFT bandgaps in Gong et al.2 and Zhang et al.8 at 1 bar would be aligned in the same figure. References: Z20178, G202020, G20222, S20227, Y202021. Inset: Comparison between the band gap jump across the transition boundary in this study (blue) and two experimental measurements (red: G20222; cyan: G202020).Our study also demonstrates the importance of pressure medium in high pressure DAC experiments. It has been pointed out by Szafrański and Katrusiak23 and Zhang et al.24 that the hydrostaticity of the pressure medium used in the DAC could control the kinetics and even the resultant phase of the pressure-induced phase transition. We notice that in the two experiments (G202020 and G20222) that used silicone oil as the pressure medium, the bandgap jump right after the transition around 2 GPa was smaller (0.25 eV for G2020 and 0.23 eV for G2022) than our value (0.31 eV). Meanwhile, in both G202020 and G20222, the bandgap continues to increase over the range of 1–3 GPa by an additional 0.05 eV after the transition, and then decrease with pressure2, yet in our study the bandgap decreases with pressure right after the Pnma-P21/c transition (Fig. 5). We suspect that this phenomenon indicates that the pressure-induced transition in CsPbBr3 is slow in non-hydrostatic silicone oil pressure medium, and similar kinetics has been observed in MAPbCl3 perovskite23. The bandgap of MAPbCl3 increased by 0.05 eV at the same pressure over 280 h23, which is close to the offset between our reported value and G2020 (0.31 eV vs. 0.25 eV). In the meantime, for the compression and decompression runs in G20222, the bandgap of CsPbBr3 is distinct at around 2 GPa (Fig. 5). In G2022, for the compression run, at ~2 GPa, the band gap was ~2.3 eV, while for the decompression run, at ~2 GPa, the band gap was ~3.1 eV. Besides, the decompression run seems to have a discontinuity around the ambient pressure in G2022: the band gap dropped abruptly from ~3.1 eV at 0.03 GPa to 2.3 eV at 1 bar. We believe that this slow kinetics is a result of the non-hydrostatic pressure medium. On the other hand, we used neon pressure medium25, which is hydrostatic up to 4.8 GPa. We conclude that the hydrostatic pressure environment is beneficial for a sharp phase transition boundary because of less deviatoric stress and pressure gradient26.
Pressure induced structural and electronic band transition in CsPbBr3
