## Introduction

Organic-inorganic hybrid perovskites (OIHPs) have attracted great research interests as promising materials for the next generation photovoltaic energy harvesting1,2, electro-optic detection3,4 and all-optical conversion5,6. Their remarkable properties are underpinned by atomic structures of hybrid perovskites7, ABX3, with organic species such as CH3NH3+ (MA+) and CH(NH2)2+ (FA+) occupying A-site and inorganic Pb2+ in B-site surrounded by X-octahedron formed by halogen elements like I and Br. In particular, the corner-sharing [PbI6]4− octahedron is believed to be beneficial for carrier diffusion8,9, while its distortion under chemical strain10 makes the band gap tunable, ideal for photovoltaic conversion. Moreover, the organic cations as well as the hydrogen bonding may lead to spontaneous polarization and ferroelectricity11, which promotes the separation of photoexcited electron-hole pairs, and thus reduces the recombination and improves the carrier lifetime12. These characteristics are responsible for the promising optoelectronic properties including high carrier mobility, long charge diffusion length and superior power conversion efficiency13. Nevertheless, the exact atomic structure of OIHPs is still unsettled, with two possible space groups, polar I4cm and nonpolar I4/mcm still hotly debated depending on the orientations of polar ions such as MA+14. While many perovskite oxides are polar with strong ferroelectricity, the polarity of OIHPs has yet to be firmly established15.

The lack of detailed understanding on atomic structure of OIHPs is largely due to the incapability to image OIHPs at the atomic scale16,17. It is well known that OIHPs are quite unstable and prone to decomposition under electron beam irradiation18,19,20,21. While much progress has been made in transmission electron microscopy (TEM) characterizations of OIHPs, direct visualization of atomic structure remains to be elusive. Initial TEM studies at low doses are mainly observing the morphology evolutions18 and structure transitions by reciprocal-space electron diffraction (ED) techniques19,20, and many of the earlier studies mislabeled the decomposition product PbI2 as MAPbI322,23,24. With the help of direct-detection electron-counting (DDEC) camera, high-resolution TEM (HRTEM) image of CH3NH3PbBr3 has been successfully obtained, which is much more stable than MAPbI3, though the observed off-centered MA+ with different orientations has not been well substantiated16. Recently, low-dose scanning transmission electron microscopy (STEM) technique provides atomic-scale insights into crystalline defects of CH(NH2)2PbI3 (FAPbI3), though the obtained atomic structures have already been damaged due to the large doses involved (53–221 e Å−2)25. Cryo-HRTEM has been used to image MAPbI3 at 100 e Å−2, yet the corresponding fast Fourier transform (FFT) pattern lacks (002) reflection, indicating substantial beam damage26. Furthermore, Li et al. found that superstructure reflections, a sign of structural transition due to beam damage, have already appeared at a dose as low as 7.6 e Å−2 (Ref. 27), and under Cryo-TEM, rapid amorphization has also been observed18,28. Indeed, the damage-free pristine structure of MAPbI3 has not been imaged at the atomic scale, and the corresponding real-space degradation pathway is yet to be established, thus motivating this study.

It is well known that STEM imaging introduces comparably larger dose and damage than low-dose HRTEM, while the contrast of HRTEM is sensitive to imaging condition, making it difficult to identify the specific atomic columns of MAPbI329. To overcome these difficulties, we adopted DDEC camera combined with an imaging technique using a negative value of the spherical-aberration coefficient30, and we have successfully captured the atomic structure of MAPbI3 in real space at a dose as low as 0.7 e Å−2, ensuring minimum beam damage if any. We further observed a two-step degradation pathway at the atomic scale, initiated with the loss of MA+ to form a superstructure MA0.5PbI3 with ordered MA+ vacancies ($${{{\mbox{V}}}}_{{{\mbox{MA}}}}^{-}$$), followed by the diffusion of I and Pb2+ to form the decomposed 6H-PbI2, with the corresponding critical doses also identified. During the process, C–N bonds can be destroyed under irradiation, releasing NH3 and HI and leaving hydrocarbons. The continuous structure transformations result in gradually increased bandgap, which is confirmed by scanning electron microscope cathodoluminescence (SEM-CL) experiments and validated by density functional theory (DFT) calculations. The direct visualization of the structure and degradation process at the atomic scale provides valuable sights into understanding the properties and stability of OIHPs. Furthermore, the emergence of superstructure before the collapse of perovskite framework also points toward a strategy for stabilizing the materials during the degradation.

## Results

### Identification of damage-free threshold dose

MAPbI3 nanocrystals with 10–20 nm size and good crystalline (Supplementary Fig. 1) are chosen for low-dose imaging. Using DDEC camera, HRTEM images of MAPbI3 can be acquired at low doses as shown in Fig. 1. It is noted that sufficient dose (Supplementary Fig. 2) is needed to obtain images with good quality and superstructure diffraction reflections appear due to the generation of intermediate phases when the dose is larger than 2.7 e Å−2 (Fig. 1b, g). Judging from the corresponding FFT patterns, the [001] MAPbI3 with intermediate phases gradually transforms at 13.6 e Å−2, and finally decomposes into [$$\bar{4}$$41] or [48$$\bar{1}$$] 6H-PbI2 (Supplementary Fig. 3) at 272.0 e Å−2. Such a 6H-PbI2 product has also been observed during the degradation of polycrystal MAPbI321. Thus the threshold dose for MAPbI3 without forming superstructures is determined to be 2.7 e Å−2 while 272.0 e Å−2 for the complete decomposition into PbI2. These determined doses can guide the future TEM characterizations of MAPbI3, especially for in situ ones such as under heat, electric field etc, for which the effect of electron beam irradiation is generally more significant due to the larger dose.

### Atomic-imaging of MAPbI3 structure and the intermediate phase

We then investigate the atomic structure via an imaging technique using a negative value of the spherical-aberration coefficient (Cs), which has enabled the successful observation of both light and heavy elements in oxide perovskite30. Figure 2a is the HRTEM image acquired at a negative Cs with an overfocus, wherein the brightest ‘I’ column, second brightest ‘II’ column and the darkest ‘III’ column can be distinguished. By comparing the atomic structure features of MAPbI3 (Fig. 2b) and HRTEM simulations (Supplementary Fig. 4), ‘I’, ‘II’ and ‘III’ columns are identified to be Pb2+-I, I and MA+, respectively. With increased dose, the intensity of MA+ is decreased at 10.5 e Å−2 as shown in Fig. 2c. The quantitative intensity analysis (Fig. 2d) further verifies that the intensity of MA+ progressively decreases within the initial 10.5 e Å−2, and then remains stable until 28.0 e Å−2 before subsequent gradual increase (Supplementary Fig. 5). The decreased intensity is caused by the formation of $${{{\mbox{V}}}}_{{{\mbox{MA}}}}^{-}$$31 while the unchanged intensity is likely resulted from a relatively stable intermediate phase with the preserved perovskite framework. The subsequently increased intensity is resulted from the diffusion of I and Pb2+, as discussed in the following. Figure 2e and Supplementary Fig. 6 further show $${{{\mbox{V}}}}_{{{\mbox{MA}}}}^{-}$$ appears at every other ‘III’ column, as illustrated in Fig. 2f. Such a cation-vacancy-ordered structure with superstructure reflections (Supplementary Fig. 7) corresponds to MA0.5PbI3, whose stability is verified by molecular dynamic simulation (Supplementary Fig. 8). Accordingly, it is concluded that the loss of MA+ starts even at 1.0 e Å−2 and reaches a balanced state between ~10.5 and 28.0 e Å−2 to form ordered $${{{\mbox{V}}}}_{{{\mbox{MA}}}}^{-}$$, wherein the perovskite structure framework is preserved.

### Evolution of the electronic structure and chemical bonding

The effect of ordered $${{{\mbox{V}}}}_{{{\mbox{MA}}}}^{-}$$ on its electronic structure is further investigated. Figure 3a, b show the calculated band structure of MAPbI3 and MA0.5PbI3. The band gap of MAPbI3 is 1.56 eV while it is 1.69 eV for MA0.5PbI3. The increased band gap is caused by the enhanced hybridization between I-5p and Pb2+-6p atomic orbitals and the conduct band minimum shifting about 0.1 eV to the high energy level, as explained in Supplementary Fig. 9. To confirm this analysis, we also carried out SEM CL experiments. Supplementary Fig. 10 shows the initial CL emission with a single excitonic peak at the photon energy of ~1.58 eV. Time-series CL emissions in Fig. 3c show that the observed peaks gradually become broader and shift to higher energy (2.05 eV) with the excitonic peak intensity decreasing. Such blue-shift is associated with the electron-beam-induced phase transformations32, i.e., forming the intermediate phases and decomposing into 6H-PbI2, considering that the calculated bandgaps of MAPbI3, MA0.5PbI3 and 6H-PbI2 are 1.56, 1.69, and 2.15 eV (Supplementary Fig. 11), respectively, in good agreement with the experimental observation.

### Atomic-scale observation of I− and Pb2+ diffusion

Based on above study, we further investigate the atomic-scale decomposition pathway of MAPbI3. Figure 4a is the structure of perovskite with $${{{\mbox{V}}}}_{{{\mbox{MA}}}}^{-}$$, as illustrated in Fig. 4e. With increased doses, it is observed that the intensities of these three columns gradually change (Fig. 4b–d). A quantitative analysis of the intensity changes (Supplementary Fig. 13) shows that the intensities of ‘I’ columns initially increase and then gradually decrease while the intensities of ‘II’ columns continuously increase and the intensities of ‘III’ columns initially decrease and then gradually increase. Finally, intensities of all three type columns converge, indicating the formation of PbI2. The initial intensity decrease of MA+ column results from the formation of $${{{\mbox{V}}}}_{{{\mbox{MA}}}}^{-}$$, while the following increased intensity of MA+ column and decreased intensity of Pb2+-I column are believed to be caused by two kinds of I and Pb2+ diffusion as illustrated in Fig. 4f. One is the diffusion of I and Pb2+ into $${{{\mbox{V}}}}_{{{\mbox{MA}}}}^{-}$$ (Supplementary Fig. 14) while the other is caused by the [PbI6]4− octahedron slipping from corner sharing to edge sharing. Finally, the structure gradually evolves to PbI2. Figure 4e–g illustrate the atomic-scale structural evolution and the related ion migration during the decomposition from MAPbI3, MA0.5PbI3, to the final PbI2, mainly involving two processes, forming $${{{\mbox{V}}}}_{{{\mbox{MA}}}}^{-}\,$$and the collapse of perovskite structure via the diffusion of Pb2+ and I. While previous literature21 proposed a two-step transformation of polycrystalline MAPbI3: Pb-related defects form at grain boundary and then phase transforms into PbI2, here we have observed an intermediate phase with locally ordered MA+ vacancies and revealed the atomic-scale decomposition pathway from MAPbI3 into PbI2, which enhances our understanding on the OHIPs’ degradation.

## Discussion

The extreme beam sensitivity of OIHPs hinders atomic-resolution imaging and thus the detailed investigations on their structure-property relationships. By DDEC camera, we have determined that the threshold dose for superstructure formation is about 2.7 e Å−2, and perovskite collapses into PbI2 within 272.0 e Å−2, both of which are smaller than those measured by ED19. This is mainly because ED pattern is obtained from a comparably larger region and represents the average information. These threshold conditions can guide future TEM characterizations and encourage more atomic-scale investigations about OIHPs.

Atomic-scale imaging of MAPbI3 and its degradation pathway allows us to better understand properties of OIHPs. For example, the observed off-center displacements (up to ~30 pm) between different atom columns likely indicate the polar nature of this material40, although further studies are needed to fully clarify this point, including determining MA+ configuration15 and quantifying the effects from possible mistilt and residual aberrations41. Furthermore, from the energetic point of view, the electron beam can transfer energy to the materials, enable ions to overcome the diffusion barrier and thus induce structure transformations, which is similar to heat- or light-induced phase transformations and degradation. For example, the decomposition of MAPbI3 into PbI2 with the release of NH3 and HI38 has also been observed under light illumination42 and moisture atmosphere39. In addition, the increase of bandgap during the degradation has also been observed under illumination43,44. Therefore, our investigation of electron beam-induced decomposition pathway can also help understand how the devices fail in practical working conditions. Besides, the superstructure phase with additional reflections has been previously reported to be likely related with octahedra tilts18 or ordered iodine vacancies19 based on reciprocal-space ED analysis, our atomic-resolution imaging, however, has suggested that cation-ordered vacancies are more likely. Such an intermediate phase (MA0.5PbI3) with locally ordered vacancies can stably exist before perovskite collapses, suggesting the degraded structure with partial formation of $${{{\mbox{V}}}}_{{{\mbox{MA}}}}^{-}$$ may be recovered. This likely sheds light into reversible photoinduced structural changes without forming PbI245. Such self-healing behavior under illumination has also been observed in MAPbI3-based solar cells46. In addition, the loss of MA+ causes the increase of bandgap, which provides a potentially new strategy to tune the bandgap in constructing tandem solar cells47. Also, the increased bandgap facilitates multiwave electroluminescence emission, adjusting various color luminescence under increasing bias voltage4,48.

Ion migration in OIHP-based electronic device is regarded as one of the most important processes, which contributes to the phase segregation, hysteresis in J-V curves and device degradation49. Previous studies about ion migration are either based on calculations or macro-measurements49 like time of flight secondary ion mass spectroscopy50, conductive atomic force microscopy51, and energy-dispersive X-ray mappings52,53, all without achieving the atomic-scale resolution in real space. Our atomic-resolution imaging provides direct evidence for the diffusion of MA+, I, and Pb2+ under electron beam irradiation, thus providing some insights into understanding ion-migration-induced phase transformations and degradation, and consequently the optimization of device performance. For example, since the gentle irradiation under illumination likely only causes the reversible formation of $${{{\mbox{V}}}}_{{{\mbox{MA}}}}^{-}$$ with perovskite structure preserved, accordingly the device efficiency can be fully recovered at early degradation stages54. However, longer irradiation brings in I and Pb2+ diffusion to induce an irreversible transformation into PbI2, thus bringing in an irreversible device performance degradation. The irreversible performance decline has also been observed under elevated temperature55,56 and large bias57 due to the irreversible ion migration and structure degradation.

In summary, we have acquired the atomic structure of MAPbI3, determined the threshold doses during TEM characterizations, and clarified the atomic-scale ion migration during its degradation into PbI2. The degradation pathway is proposed to be a two-step, initialed by the loss of MA+ and followed by the diffusion of I and Pb2+ to form PbI2, during which C–N bonds can be destroyed under irradiation, releasing NH3 and HI and leaving hydrocarbons. Such degradation process leads to the gradual increase of bandgap. These findings can be used to guide the future TEM characterizations, enrich the understandings of the degradation mechanism and optimization strategies, and provide atomic-scale insights into understanding its fundamental properties.

## Methods

### MAPbI3 synthesis

MAPbI3 nanocrystals were bought from Xiamen Luman Technology Co., Ltd. Micro MAPbI3 was synthesized as previously reported58. Specifically, PbI2 and MAI were prepared in γ-butyrolactone (GBL) with molar ratio 1:1 and the concentration of 1.3 mol L−1. Then they were stirred at 70 °C for 12 h to obtain the precursor solution. After, the  precursor solution was filtered using polytetrafluoroethylene (PTFE) filter with 0.22 μm pore size. Two pieces of fluorine-doped tin oxide (FTO)/TiO2 substrates were clamped together and vertically and partially soaked in MAPbI3 precursor solution (10 ml) at 120 °C. Then the precursor solution was added twice one day in the nitrogen glove box. After several days, the substrates with single-crystal MAPbI3 film were brought out, and dried at 120 °C for 10 min in nitrogen.

### Characterization and image analysis

ED patterns and HRTEM images were acquired at an aberration corrected FEI electron microscope (Titan Cubed Themis G2) operated at 300 kV. The Cs value is ~6.8 μm. Before acquiring images, the illumination range was set to be ~3 μm in diameter. To shorten the exposure time to electron beam, we adjusted the defocus and the astigmatism well in one ~3-μm region, then blanked beam, and moved to another ~3-μm region to acquire the HRTEM image. HRTEM images were acquired at a magnification of 77,000 by DDEC camera in electron-counting mode with the dose fractionation function. The correction of drift was achieved by using the DigitalMicrograph software by cross-correlation. The original image contains 40 subframes in 4 s and every 2 subframes were summed to enhance the contrast for a more accurate estimation of drift. Hanning window and Bandpass filters were combined to improve the accuracy of the cross correlation. HRTEM images in Figs. 12e, and 4, and Supplementary Figs. 2, 6, and 7 have been ABSF-filtered. HRTEM images in Fig. 2a, c have been first ABSF-filtered and then averaged from multiple regions using a home-made MATLAB code to reduce noise.

The morphology was characterized by SEM (FEI Quanta 200 F) and CL spectrum was acquired using Rainbow-CL of Beijing Goldenscope Technology Co., Ltd at 5 kV, spotsize 4. Each single CL spectrum was acquired using 4 s. Vibrational spectra characterizations were obtained under 30 kV using Nion U-HERMES200 electron microscope. Each spectrum was stacked from 200 single spectrum, obtained using 800 ms, and the processing details were shown in Supplementary Fig. 12. The simulated ED patterns were obtained by the SingleCrystal (Crystalmaker) software. Structural models were acquired using Vesta software.

### DFT calculation

Our first-principles calculations were performed within the framework of DFT as implemented in the Vienna ab initio simulation package59,60. The ion-electron interaction was depicted by projector augmented-wave method61. The electron exchange correlation was treated by the generalized gradient approximation with Perdew–Bruke–Ernzerhof functional62. A kinetic cutoff energy was set as 500 eV for the Kohn–Sham orbitals being expanded in the plane-wave basis. The atomic positions were fully optimized with a conjugate gradient algorithm until the Hellman–Feynman force on each atom are less than 0.01 eV/Å63. The Monkhorst-Pack k- point meshes was sampled as 9 × 9 × 764.

### Ab initio molecular dynamics simulation

We performed the ab initio molecular dynamic (AIMD) simulation. The plane-wave cutoff was set as 500 eV and the Brillouin zone is sampled at the Γ point. The AIMD was performed in the canonical ensemble at 300 K.