Total X-ray Scattering and Big-Box Modeling of Pressure-Induced Local Disorder and Partial Amorphization in CsPbBr3

Total X-ray Scattering and Big-Box Modeling of Pressure-Induced Local Disorder and Partial Amorphization in CsPbBr3 | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Total X-ray Scattering and Big-Box Modeling of Pressure-Induced Local Disorder and Partial Amorphization in CsPbBr3 Anna Celeste, Samuel Girdzis, Bernadette Cladek, Christina Deschene, and 6 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6087274/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract The mechanisms governing pressure-induced amorphization and its reversibility in halide perovskites remain poorly understood, particularly the role of local disorder in this process. We performed high-pressure synchrotron total X-ray scattering and reverse Monte Carlo (RMC) big-box modeling using CsPbBr₃ as a model system to investigate short-range structural evolution in both the ordered and partially amorphous phases. While X-ray diffraction (XRD) indicates that long-range order persists up to 2 GPa, pair distribution function (PDF) analysis reveals the emergence of significant local distortions, including PbBr₆ octahedral tilting and Cs displacement, which directly influence the bandgap through a complex interplay between bond compression and angular tilting. Beyond 2 GPa, CsPbBr₃ undergoes partial amorphization, with significant disordering of Cs and Br, while the Pb sublattice remains preserved, allowing for reversible pressure-induced amorphization upon decompression. Unraveling the short-range mechanisms behind this reversibility could provide key insights into phase stability and disorder recovery, paving the way for new strategies to stabilize metastable phases in halide perovskites. These results demonstrate that the approach proposed here, which accounts for both short- and long-range structural evolution through RMC modeling, successfully captures the role of disorder in the structural response of halide perovskites to pressure. Physical sciences/Materials science/Materials for energy and catalysis/Solar cells Physical sciences/Materials science/Condensed-matter physics/Phase transitions and critical phenomena Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 INTRODUCTION Halide perovskites have emerged as a leading class of materials in optoelectronic applications, particularly in photovoltaic cells. 1 Since the development of the first perovskite-based solar cells in 2009 with a modest 3.8% power conversion efficiency (PCE), subsequent advancements have not only pushed efficiencies over 33% in tandem cells 2 but also expanded their use into light-emitting diodes, photodetectors, lasers, and transistors. 3 – 5 Their remarkable success is due to their exceptional properties such as strong light absorption, long charge-carrier lifetimes, and low-cost synthesis. The ability to chemically tune their structure through replacing one or more chemical species allowed the synthesis of a wide variety of systems, fully inorganic or hybrid organic-inorganic, with tailored optoelectronic properties. Additionally, external factors like temperature and pressure can modulate their structures and properties. Multiple studies have investigated the behavior of halide perovskites under high pressure 6 – 10 , reporting a range of structural and electronic/optical phenomena, including crystalline phase transitions 11 , 12 , metallization 13 and enhanced photoluminescence. 14 A common behavior observed in halide perovskites is the transition to a partially amorphous phase under pressure, with the onset of this transition varying across different systems. 10 Halide perovskites often exhibit the ability to recover their original structure upon decompression, highlighting the reversibility of their structural changes under pressure. While reversible pressure-induced amorphization is a known phenomenon, the fundamental mechanisms driving this structural recovery remain unclear. To address this, new methods beyond the conventional analysis of X-ray diffraction patterns are required. A promising approach lies in focusing on the short-range structure and examining the material’s evolution on a more localized scale. While X-ray diffraction primarily provides information on the average crystal structure, local structural behavior, i.e. on Angstrom scale, can differ significantly. Indeed, this approach has proven particularly effective in uncovering local disorder in halide perovskites. For instance, in CsSnBr 3 , local off-centering of the Sn atoms, undetectable by conventional crystallography, has been identified as causing asymmetries in the cubic phase. 15 Similarly, studying the system locally in (MHy)PbBr 3 (MHy + = methylhydrazinium) has revealed how lone pair activity drives structural distortions, enhances electron-phonon interactions, and influences bandgap behavior and charge dynamics. 16 The pair distribution function (PDF), or G(r), is a powerful tool to study the local atomic structure of materials, as it captures the probability of finding pair of atoms separated by a specific distance in real space. 17 By revealing local density variations and atoms arrangements, the PDF provides valuable insights into both local (short-range) and average (long-range) atomic structure. 18 Performing total X-ray scattering experiments makes it possible to extract the PDF and construct atomistic structural models which describes the local atomic environment at the unit-cell scale, known as ‘small-box’ approach. This method has proven effective in our previous work on Cs 2 AgBiBr 6 at high pressure, where it revealed that a lower-symmetry model better describes the system on the local scale compared to symmetry observed through X-ray diffraction. 19 A more complex approach involves the use of a supercell built on the unit cell of the material studied which allows for more sophisticated models of the structure. Big-box modeling is usually coupled with the Reverse Monte Carlo (RMC) method where a randomly selected atom is displaced by a random distance to improve the agreement between the modeled and experimental data. 20 It was initially developed to study liquid and amorphous phases, 21 however, this approach is also suitable to study correlated disorder in crystalline materials since it provides a detailed representation of the disordered crystal structure, incorporating local correlations consistent with the measured total scattering data while simultaneously reproducing the average structure seen in the Bragg profile. 22 This approach produces a ‘snapshot’ of the structure capturing both static and dynamic disordering processes, making it ideal to study pressure-induced modification and amorphization processes. 23 Here, we employ total X-ray scattering combined with RMC big-box modeling to study the high-pressure behavior of CsPbBr 3 , an archetypal three-dimensional (3D) halide perovskite. 24 Indeed, the simplest halide perovskite structure is the 3D perovskite, with the formula ABX 3 where A is a monovalent cation (either an atom or an organic molecule), B is a divalent metal cation and X is a halogen anion. CsPbBr 3 exemplifies this structure, combining a relatively simple inorganic composition with exceptional optical properties. 25 Such characteristics make CsPbBr 3 an ideal candidate for studying the effects of pressure on 3D halide perovskites, particularly regarding phenomena like reversible amorphization and the evolution of local disorder upon compression. Previous studies have noted a pressure-induced bandgap shift from red to blue around 1 GPa and subsequent partial amorphization at 2.4 GPa, with explanations ranging from isostructural phase transitions at 1 GPa to changes in Rashba splitting. 26 – 28 First-principle calculations indicate that the nonmonotonic pressure dependence of the bandgap results from competing effects of bond shrinkage and octahedral distortion, suggesting complex underlying mechanisms beyond straightforward structural changes. 29 Our study focuses on the evolution of local disorder under compression, employing a novel methodological approach that provides both detailed insights into the role of disorder within the crystalline phase and information about the amorphization process and its reversibility. To the best of our knowledge, this is the first experimental study to perform structural modeling of the high-pressure partially amorphous phase of a 3D halide perovskite. We propose that the bandgap behavior under pressure is mainly driven by disorder effects and the reversibility of the amorphization stems from the preserved Pb sublattice, despite significant distortion of the PbBr 6 octahedra and Cs atoms off-centering. Our study proves the critical importance of understanding both the local and average structural dynamics in halide perovskites to get a more accurate picture of the structure–property relationships. RESULTS AND DISCUSSION High-pressure powder XRD of CsPbBr 3 (Fig. 1 a) and the atomic PDFs (Fig. 1 b), derived from total X-ray scattering data collected at a shorter sample-to-detector distance, were collected in a diamond anvil cell up to 5 GPa. We used silicone oil as the pressure transmitting medium which remains quasi-hydrostatic up to 3 GPa, with pressure variations across the sample chamber being less than 0.2 GPa at 5 GPa. 30 At ambient pressure, the diffraction pattern exhibits Bragg reflections characteristic of the Pbnm space group, as previously reported. 31 We performed Rietveld refinement on the XRD data up to 1.6 GPa to extract the lattice parameters (see Figure S3). Above 2 GPa, most peaks, particularly those above 4.5°, start to vanish or significantly broaden, signaling the onset of amorphization. Despite this, a few reflections remain sharp and detectable up to 5 GPa, indicating that partial long-range order is preserved in the structure up to this pressure value. This coexistence of amorphous and crystalline regions makes Rietveld refinement unsuitable beyond 2 GPa. Consequently, we switched to Le Bail fitting while maintaining the ambient pressure space group. We also attempted to fit the data using the recently proposed triclinic space group for CsPbBr 3 at 2 GPa, 27 but at this pressure, the diffraction pattern is already too broadened for a meaningful distinction between low-symmetry space groups, and any could be fit using Le Bail refinement. The discrepancy with that study likely stems from differences in hydrostatic conditions and sample types (powder vs. single crystal). Focusing on the PDFs, we observe short-range structural modifications even below 1.6 GPa, particularly in the 3.5 and 5.5 Å range, where primary contributions arise from the Br-Cs, Br-Br, and Pb-Cs first-neighbor distances. These changes reflect pressure-induced effects on the local structure that are not apparent in the average structure captured by XRD. Above 2 GPa, we detect significant alterations in both the shape and intensity of the peaks, consistent with the transition to a more disordered phase, as observed in the XRD patterns. The diminished periodicity of the structure can clearly be seen in the flattened G(r) at higher values of r. Upon releasing pressure, CsPbBr 3 recovers its original crystalline structure, as highlighted by the comparison of the XRD data at ambient pressure before and after pressure release (Figure S4). The lattice parameters obtained through Rietveld refinement are almost identical to the ones of the sample before increasing pressure (Table S1 ). While this recovery demonstrates that pressure-induced transition to the partially amorphous phase is mainly reversible, minor deviations from the initial pattern are still apparent. These include slight broadening and shifts in some Bragg peaks, suggesting residual strain within the crystal lattice. These subtle changes are also mirrored in the PDF comparison between the initial and post-release data (Figure S6), although the overall G(r) regains its original shape, differences in peak intensities and positions are evident, particularly in the 3.0-5.5 Å range. Such alterations highlight that, while the crystalline structure largely recovers, the local environment within the crystal lattice retains modifications induced by high-pressure conditions. We analyzed X-ray PDFs using a Pbnm model in PDFgui, as shown in Figure S7. 18 However, since Pbnm is already a relatively low-symmetry space group, this approach provided limited insight. Additionally, the refined lattice parameters became unstable and unphysical at higher pressures. Moreover, the single-unit cell model in PDFgui is likely too small to account for the increasing disorder beyond approximately 2 GPa. To address these challenges, we shifted to RMC simulations using RMCProfile. 21 We built a 6x6x4 supercell containing 2880 atoms allowing for significantly greater variation in the atomic arrangements. We started the RMC simulation by applying the distance windows constraint alongside the polyhedral constraint, which allow atoms to move as groups or units within a specified range. Given that CsPbBr 3 adopts a perovskite structure at ambient conditions, we used the polyhedral restraint to fix the PbBr 6 octahedra. Simultaneously, we fit XRD data using the parameters obtained from the Rietveld refinement, such as peak shape and scale factor. This method provided good fitting results for both the XRD and the PDF data up to 1.2 GPa. However, at 1.6 GPa, RMCProfile failed to fit the diffractogram, causing the PDF fit to fail as well. By excluding the average structure data from the fitting procedure, we successfully obtained a good fit for the local structure at this pressure. Beyond 2 GPa, the polyhedral constraint failed, suggesting bond breaking as pressure increased. In response, we tested alternative approaches for data above this pressure, such as constraining only the Pb-Pb distances. This method yielded acceptable chi 2 values for the total G(r) fit. However, further inspection of the partial PDFs showed that the Br-Cs and Br-Br distance distributions assumed unphysical shapes, with distances increasingly compressed to their lower limits at higher pressures. These unusual shapes suggest atomic arrangements with bond lengths that are too short to be physically meaningful. The preliminary tests briefly discussed are detailed in the Supplementary Information. To overcome these challenges, we adopted bond valence sum constraints, which account for interatomic distances and atomic coordination. 32 This approach effectively fits the PDFs up to 5 GPa, providing physically consistent results. It is worth noting that above 2 GPa, we used the parameters obtained from the Le Bail refinement to fit the Bragg data in RMCProfile. Since the Le Bail refinement does not provide a scale factor, which is required by RMCProfile, we estimated it by considering the scale factor obtained at 1.6 GPa and performing a least-squares fit between the observed and the theoretical peak intensities of the first main reflection detected, i.e. , (110), for the diffractograms up to 5 GPa. To ensure accurate fitting, we first subtracted the background from experimental data using a Chebyshev function. Further on, all the results reported and discussed were obtained using bond valence sum constraints for Cs, Pb, and Br. The total and the partial PDFs at 0.0 GPa, obtained through big-box modeling, are shown in Fig. 2 (a). The experimental PDF (black open circles) and the calculated PDF (red solid line) are in excellent agreement across the full r-range, demonstrating the suitability of the big-box approach for modeling the structural configuration at ambient conditions. The partial PDFs, representing contributions from specific atomic pairs (Pb-Pb, Pb-Br, Br-Br, Br-Cs, Pb-Cs, and Cs-Cs), display well-defined peaks corresponding to distinct interatomic distances, extending up to 23 Å. Focusing on the 3.3–5.6 Å range, the main contributions to the total PDF at these distances arise from the Br-Cs, Br-Br, and Pb-Cs first-neighbor interactions. Figure 2 (b–e) illustrates the evolution of these partial PDFs with increasing pressure, specifically at 0.0 GPa (b), 0.4 GPa (c), 0.8 GPa (d), and 1.2 GPa (e). With increasing pressure, the most significant changes are observed in the Br-Br peak (green curve), which broadens and shifts, indicating that pressure induces local distortions within the octahedra. Notably, the shape and intensity of the first peak in the G(r), primarily from the Pb-Br contribution, remain relatively unchanged up to 1.6 GPa (see Fig. 1 b). This suggests that the PbBr 6 framework is not significantly impacted within this pressure range. However, the Br-Cs and Pb-Cs partial contributions exhibit gradual broadening as pressure increases, reflecting enhanced disorder in the Cs local coordination environment. At ambient pressure, CsPbBr 3 exhibits nominal bond angles of 90° and 180° for the intra-octahedral Br–Pb–Br bonds, and approximately 160° for the inter-octahedral Pb–Br–Pb angles. These values are reflected in the angle distributions derived from the big-box modeled structure at 0.0 GPa, as shown in panels f and g of Fig. 2 . Upon applying pressure up to 0.8 GPa, the intra-octahedral angle distributions broaden, indicating increased local distortion within the octahedra. Simultaneously, the distribution of inter-octahedral angles shifts toward 180°, suggesting a reduction in octahedral tilting. At 1.2 GPa, the inter-octahedral angle distribution shifts back toward 160° and broadens further, indicating the onset of more significant local disorder. This dynamic evolution of octahedral tilting correlates directly with the non-monotonic bandgap behavior previously observed 26 , 28 and is further confirmed by our absorption spectroscopy measurement, which we performed and analyzed under pressure (see Figure S23). Our measurements reveal a distinct trend: the bandgap narrows (red-shifts) up to ~ 1 GPa, then reverses and widens (blue-shifts) beyond 1.2 GPa. A previous experimental study attributed this behavior to an isostructural phase transition. 26 Shortening of the Pb–Br bond under pressure and reduced octahedral tilting (angles approaching 180°) enhances orbital overlap, leading to a bandgap reduction. 8 , 29 Beyond 1 GPa, the reintroduction of tilting (angles shifting back to \(\:\sim\) 160°) reduces orbital overlap, causing the bandgap to widen. Our analysis of XRD data and PDFs reveals no evidence of a structural phase transition between 0 and 1.6 GPa, which would be expected in a true isostructural phase transition. Instead, we observe increasing local disorder, reflected in the broadening and shifting of both intra- and inter-octahedral angle distributions. The evolution of inter-octahedral angles, shifting toward 180° up to 0.8 GPa and returning to \(\:\sim\) 160° at 1.2 GPa, closely mirrors the observed bandgap changes. This suggests that the bandgap behavior may be driven by the cumulative effects of local distortions within the PbBr 6 framework, rather than by a sharp phase transition. At 1.6 GPa, both the partial PDFs, indicative of the bong lengths, and the angle distributions, broaden and shift, indicating a significant increase in disorder with pressure. As previously discussed, a much more pronounced change in the experimental data occurs at 2.0 GPa, indicating the onset of the amorphization. This transition, clearly observed in the XRD data (see Fig. 1 ), is also reflected in the big-box configurations, represented in Fig. 3 as snapshots of the 6x6x4 supercells for selected pressures along the c -axis. In the ideal structure (the first snapshot in the sequence), the atoms are well-aligned, and the crystal symmetry is clearly evident. The configuration modeled with RMCProfile based on our experimental PDF at ambient pressure already exhibits some atomic displacements, primarily due to thermal effects. As pressure increases, the disorder becomes progressively more pronounced. Up to 1.6 GPa, it is still possible to discern the underlying crystal symmetry despite the noticeable distortions. However, at 2.0 GPa and beyond (3.4 and 5.0 GPa), the snapshots reveal severe deviations from the initial positions, particularly around Cs atoms, which are significantly off-centered. These changes mark the transition to a highly disordered, amorphous-like state. To gain deeper insights into the transition, we analyze the distributions of key bond lengths and inter- and intra-octahedral angles at pressures above 2.0 GPa. Figure 4 compares the partial PDFs for selected atomic pairs and the angular distributions for octahedral bond angles at pressures beyond the onset of amorphization. To better capture the structural evolution, we also include the distributions at 0 GPa, as a reference, and at 1.6 GPa, just before the amorphization begins, highlighting the changes leading to the disordered state. The Pb-Pb PDF shifts to a shorter distance between 0 and 1.6 GPa, consistent with lattice shrinkage induced by pressure, and exhibits significant broadening and intensity reduction above 2.0 GPa. At higher pressures, the partial PDF develops a tail below the main peak, suggesting that Pb atoms occupy a broader range of positions due to lattice distortions and local strain. However, since RMCProfile does not enforce interatomic potentials, it is necessary to impose a limit on the shortest allowable atomic pair distances to prevent unphysical configurations. 21 For Pb-Pb, this limit was set at 5.1 Å at 0 GPa, based on the orthorhombic unit cell at ambient conditions, and reduced to 4.8 Å above 2 GPa to account for compressions effects, in line with the 4.6 Å Pb-Pb distance previously calculated for MAPbI 3 at 6 GPa. 33 This constraint may influence the development of the tail. Interestingly, the position of the main Pb-Pb peak does not shift further after 2.0 GPa. In contrast, the Pb-Br PDF (Fig. 4 b) remains sharp, despite a reduction in intensity when the amorphization begins at 2.0 GPa. On the other hand, the Br-Br distance distribution shows significant broadening and peak shifts (Fig. 4 d), reflecting increasing distortions within and between the octahedra under compression. These observations suggest that while the PbBr 6 octahedra are highly distorted, although partially preserved, the Pb sublattice is relatively stable up to 5 GPa, as shown in the supercell snapshots in Figure S25 where only the Pb atoms are displayed. The octahedra distortions are further reflected in the Br-Pb-Br (intra-octahedral) and Pb-Br-Pb (inter-octahedral) angular distributions (Fig. 4 e and f, respectively). At ambient pressure, the intra-octahedral bond angles (e) exhibit peaks at 90° and 180°, corresponding to the nominal angles within the PbBr 6 ​ octahedra, while the inter-octahedral bond angles (f) are centered around 160°, indicating the tilting between the octahedra. As pressure increases above 1.6 GPa, both angle distributions broaden, highlighting local deformations. Notably, the Br-Pb-Br distribution peaks shift to lower angles, while the Pb-Br-Pb develops a tail extending down to 100 °, signaling severe tilting of the PbBr 6 ​ octahedra and significant lattice disorder. Regarding the Cs cations, we observe that increasing pressure induces significant broadening and intensity reduction in both the Pb–Cs (Fig. 4 c) and Br–Cs (Figure S24f) partial PDFs, reflecting growing disorder in the Cs coordination environment, especially beyond 1.6 GPa. This suggests that Cs atoms are displaced from their ideal positions as pressure increases, contributing to the overall loss of crystallinity in the lattice. Another way to visualize the evolution of the system under compression, as obtained through RMC simulations, is to pack the supercell back into a single unit cell containing all atoms. Figure 5 shows the unit cells for pressures of 0, 0.8, 2, and 5 GPa, while the configurations at remaining pressures are reported in Figure S26. These pressures were selected to represent key stages of the structural evolution along compression: the starting system at ambient pressure (0 GPa, Fig. 4 a), the system under compression while still preserving long-range order (0.8 GPa, panel b), the onset of the amorphization (2.0 GPa, panel c) and the highest pressure measured (5.0 GPa, panel d). At 0.0 GPa, the configuration shows atoms of each species overlapping, which indicates a highly ordered crystalline lattice where the structural symmetry of CsPbBr 3 is recognizable. The distribution of atomic positions is due to thermal motion. At 0.8 GPa, we observe small but noticeable movements from the ideal sites, particularly among Cs and Br atoms, while the overall long-range order remains preserved. This intermediate state reflects the initial structural response to compression, with increased density as pressure is applied. By 2.0 GPa, significant atomic displacements become more evident, marking the transition to an amorphous-like phase. In particular, the Cs atoms are displaced from their ideal positions, and disorder in the vertices of the octahedra, i.e. , the Br atoms, is also evident. These changes correspond to the broadening and shifting observed in the partial PDFs and angular distributions, highlighting the local disorder which starts to arise at this pressure. At 5.0 GPa, the system exhibits a highly disordered structure, with substantial overlap and dispersion of atomic positions, particularly among the Cs and Br atoms. However, the Pb atoms still appear to occupy the original sites, although they are statistically more dispersed. As previously mentioned, a few Bragg reflections remain detectable in the XRD patterns (see Fig. 1 ), indicating that the long-range order is not completely lost. These reflections can be indexed to the hkl planes associated with the Pb atoms (see Figure S26), suggesting that the Pb sublattice retains partial order even as the surrounding atoms are displaced. Upon releasing pressure, we observed the recovery of the initial phase, albeit with minor differences already discussed. This reversibility is a well-documented phenomenon in other halide perovskite materials, even when compressed to pressures exceeding 60 GPa. 13 Although we did not collect data at intermediate pressures, RMC simulations were conducted starting from the configuration obtained at 5 GPa. This approach enabled the successful recovery of more ordered configurations, beginning with the most disordered state observed at 5 GPa. Simulations conducted on the experimental data collected after the pressure release provides a large-box configuration that displays well-aligned atoms, with the structural symmetry clearly reestablished (Figures S27-29). Further analysis on the octahedral bond lengths and tilting shows a return to values consistent with those at ambient conditions. However, the intra- and inter-octahedral bond angle distributions obtained for the recovered system are slightly broader than the initial ones (Figure S30), suggesting that the pressure-induced local disorder is not entirely eliminated after pressure release. This is underscored by the inability of RMCProfile to perfectly fit the XRD data, as demonstrated in Figure S31. The ability to fit the data after pressure release backtracking from the 5 GPa data demonstrates that the model is capable of accurately capturing the reversibility of the structural transition, effectively simulating the recovery process from a partially amorphous phase back to a more crystalline state. CONCLUSIONS This study highlights the capability of combining total X-ray scattering with RMC big-box modeling to uncover the complex interplay between local structural distortions and long-range crystalline behavior in CsPbBr 3 , a prototype three-dimensional halide perovskite, on compression. Our approach reveals that pressure-induced distortions in the PbBr 6 octahedra and Cs coordination environment precede the onset of the amorphization at 2 GPa, providing critical insights into structural dynamics that cannot be captured by traditional XRD. By examining both short-range and long-range structural correlations through PDF analysis, we elucidate how local disorder impacts optical properties within the crystalline phase and gain information about the mechanisms underlying pressure-induced amorphization and reversibility upon pressure release. Specifically, the nonmonotonic bandgap evolution observed below 2 GPa, transitioning from a red to a blue shift, is directly linked to the interplay between bond compression and octahedral tilting. Beyond this pressure threshold, while the Pb sublattice retains partial order, significant disorder emerges, particularly in the Cs and Br coordination environments, resulting in a partially amorphous structure. Upon pressure release, the recovery of the crystalline phase is facilitated by the stability of the Pb sublattice, although residual strain and subtle local distortions persist. The reversible amorphization highlights the dynamic interplay between long-range and local structural behavior under pressure. These findings underscore the value of large-box modeling as a powerful tool to probe the structural drivers of both the crystalline and amorphous phases, enhancing our understanding of pressure-induced phenomena in halide perovskites. This integrated approach paves the way for designing materials with tailored properties for optoelectronic applications under extreme conditions. MATERIALS AND METHODS Sample synthesis and characterization All chemicals were used as received from commercial vendors. To synthesize CsPbBr 3 powder, 400 mg of PbBr 2 and 232 mg of CsBr were dissolved in 4 mL and 12 mL of dry dimethylsulfoxide, respectively. The two solutions were combined and then added to 100 mL of dry acetonitrile. An orange powder slowly precipitated after 5 minutes of stirring. The CsPbBr 3 powder was isolated by filtration and dried under reduced pressure. A milling jar was filled with toluene, 360 mg of the perovskite powder, and zirconia balls (ca. 5 g). The sample was ball milled at 500 rpm with 8 cycles of 30 minutes of milling and 30 minutes of rest. The sample was further dried under reduced pressure and stored in desiccant to avoid decomposition from moisture exposure. The crystal structure of CsPbBr 3 was verified by both laboratory and synchrotron X-ray powder diffraction (PXRD) at ambient conditions. A high-resolution PXRD diffractogram of the sample was collected in a capillary at the 11-ID-B beamline of the Advanced Photon Source synchrotron and is shown in Figure S1 together with the corresponding Rietveld refinement. High-pressure Total X-Ray Scattering Measurements Ball-milled CsPbBr 3 powder was loaded into a short symmetric diamond anvil cell with 300-µm culets. The gasket was stainless steel and silicone oil served as the pressure transmitting medium. 30 The diamond-seat-cell combination had large ca. 90° aperture angles to access a large Q range. Pressure was measured within 0.1 GPa using the ruby fluorescence method. 31 High-pressure total X-ray scattering data were collected at beamline 11-ID-B at the Advanced Photon Source at Argonne National Laboratory using an energy of 86.7 keV (0.143 A°). 32 The 2-D scattering patterns were masked to remove diamond reflections and integrated using Fit2d software. 34 The PDFgetX2 software program was used to extract the structure factor S(Q) up to Q = 18 °A − 1 . 35 Scattering data collected using the empty diamond anvil cell, with the gasket pre-indented and drilled, was used for background subtraction when extracting the pair distribution functions (PDFs). 36 PDFgetX2 was used to transform S(Q) to the real-space PDF G(r) for initial analysis. Subsequent analysis of the PDFs using RMC simulations involved transforming S(Q) internally, normalizing to an absolute scale using StoG within the RMCProfile program. 19 A Fourier filter and Lorch window function were used in the Fourier transform. We also collected powder XRD (PXRD) data at a longer sample-to-detector distance for average structure analysis. Reverse Monte Carlo (RMC) simulations Reverse Monte Carlo (RMC) simulations were conducted using RMCProfile to analyze the experimental data. 19 A 6x6x4 supercell containing 2880 atoms was constructed, with initial atomic positions derived from the experimental crystallographic structure obtained through Rietveld refinement. The simulation aimed to fit the experimental real-space PDF, particularly focusing on the G(r) function which is defined as: $$\:G\left(r\right)=\frac{1}{({2\pi\:)}^{3}{\rho\:}_{0}}{\int\:}_{0}^{\infty\:}{Q}^{2}F\left(Q\right)\frac{\text{sin}\left(Qr\right)}{Qr}\text{d}Q$$ Where \(\:F\left(Q\right)\) is the total scattering structure factor, given by: $$\:F\left(Q\right)={\rho\:}_{0}{\int\:}_{0}^{\infty\:}4\pi\:{r}^{2}G\left(r\right)\frac{\text{sin}\left(Qr\right)}{Qr}\text{d}r$$ With \(\:{\rho\:}_{0}=N/V\) represents the average atom number density on atoms Å −3 . The G(r) represents the probability of finding a pair of atoms separated by a specific distance in real space, providing information on local density variations due to the arrangement of atoms. This method helps in understanding the local atomic arrangements beyond what is observable from Bragg peaks alone, including distortions and short-range order in the material. For a more detailed explanation of the formalism, we refer to the papers by Keen 37 and Peterson et al . 17 In order to prevent unphysical atomic configurations, several approaches have been used. In an initial test at low pressures, polyhedral restraints were applied to maintain the integrity of BX 6 octahedra. In this case, the “distance-window” restraint was implemented to define a minimum and maximum allowed value for the distance r ij between a pair of neighboring atoms, where i and j denote the species of atoms in the pair. Also, a bond valence sum restraint was employed on the whole dataset to limit bond distances and further ensure chemically reasonable configurations. RMCProfile was also used to fit the Bragg data. The RMCProfile simulations were run between approximately 12 and 30 hours each, which correspond to between 1 and 3 million accepted moves. An example of the evolution of χ 2 is shown in Figure S32. High-pressure Visible Absorption Measurements Optical absorption measurements were collected at beamline 22-IR-1 of the National Synchrotron Light Source II (NSLS-II) at Brookhaven National Laboratory (BNL). Visible absorption measurements between 400 and 1000 nm were performed using a customized visible microscope system equipped with an IsoPlane SCT-320 Imaging Spectrograph, a PyLon CCD detector (Princeton Instruments) and a tungsten light source. A symmetric DAC with type IIas diamond anvils of 500 µm culets was used for the absorption measurements. The sample chamber, a 200 µm hole drilled in a pre-indented stainless-steel gasket, was filled with KBr as the pressure transmitting medium. 38 A thin pellet of the sample, a few microns thick, was placed to occupy half of the chamber area. At each pressure point, a reference transmission spectrum was collected through KBr before measuring the sample transmission under the same beam conditions (e.g., energy range and aperture size). The spectra were analyzed using the Tauc-plot method to determine the bandgap evolution as a function of pressure. Declarations ACKNOWLEDGEMENTS This work was supported by the Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DE-AC02-76SF00515. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under contract no. DE-AC02-06CH11357. C.R.D acknowledges a Stanford Center for Molecular Analysis and Design fellowship and N.R.W. acknowledges a Stanford Interdisciplinary Graduate Fellowship. The authors thank Olaf Borkiewicz and Leighanne Gallington for assistance with PDF measurements. The mail-in program at Beamline 11-ID-B contributed to the data. The authors thank Dr. Zhenxian Liu for experimental assistance with high-pressure optical absorption measurements. High-pressure absorption measurements used beamline 22-IR-1 of the National Synchrotron Light Source II, a U.S.DOE Office of Science User Facility operated by the Brookhaven National Laboratory (DE-SC0012704) and supported by COMPRES, the Consortium for Materials Properties Research in Earth Sciences, under the NSF cooperative agreement EAR-1606856, and DOE-NNSA cooperative agreement DE-NA0003975 (CDAC). References Jena, A. K.; Kulkarni, A.; Miyasaka, T. Halide Perovskite Photovoltaics: Background, Status, and Future Prospects. Chem. Rev. 2019 , 119 (5), 3036–3103. https://doi.org/10.1021/acs.chemrev.8b00539. Liu, J.; He, Y.; Ding, L.; Zhang, H.; Li, Q.; Jia, L.; Yu, J.; Lau, T. W.; Li, M.; Qin, Y.; Gu, X.; Zhang, F.; Li, Q.; Yang, Y.; Zhao, S.; Wu, X.; Liu, J.; Liu, T.; Gao, Y.; Wang, Y.; Dong, X.; Chen, H.; Li, P.; Zhou, T.; Yang, M.; Ru, X.; Peng, F.; Yin, S.; Qu, M.; Zhao, D.; Zhao, Z.; Li, M.; Guo, P.; Yan, H.; Xiao, C.; Xiao, P.; Yin, J.; Zhang, X.; Li, Z.; He, B.; Xu, X. 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Pressure-Induced Indirect-Direct Bandgap Transition of CsPbBr3 Single Crystal and Its Effect on Photoluminescence Quantum Yield. Adv. Sci. 2022 , 9 (29), 2201554. https://doi.org/10.1002/advs.202201554. Chen, Z.; Teng, G.; Wei, S.-H. Origin of the Nonmonotonic Pressure Dependence of the Band Gap in the Orthorhombic Perovskite CsPbBr3. J. Phys. Chem. Lett. 2024 , 15 (6), 1652–1657. https://doi.org/10.1021/acs.jpclett.4c00020. Klotz, S.; Chervin, J.-C.; Munsch, P.; Marchand, G. L. Hydrostatic Limits of 11 Pressure Transmitting Media. J. Phys. Appl. Phys. 2009 , 42 (7), 075413. https://doi.org/10.1088/0022-3727/42/7/075413. Rodová, M.; Brožek, J.; Knížek, K.; Nitsch, K. Phase Transitions in Ternary Caesium Lead Bromide. J. Therm. Anal. Calorim. 2003 , 71 (2), 667–673. https://doi.org/10.1023/A:1022836800820. Norberg, S. T.; Tucker, M. G.; Hull, S. Bond Valence Sum: A New Soft Chemical Constraint for RMCProfile. J. Appl. Crystallogr. 2009 , 42 (2), 179–184. https://doi.org/10.1107/S0021889809004981. Lee, J.-H.; Jaffe, A.; Lin, Y.; Karunadasa, H. I.; Neaton, J. B. Origins of the Pressure-Induced Phase Transition and Metallization in the Halide Perovskite (CH3NH3)PbI3. ACS Energy Lett. 2020 , 5 (7), 2174–2181. https://doi.org/10.1021/acsenergylett.0c00772. Hammersley, A. P. FIT2D: A Multi-Purpose Data Reduction, Analysis and Visualization Program. J. Appl. Crystallogr. 2016 , 49 (2), 646–652. https://doi.org/10.1107/S1600576716000455. Qiu, X.; Thompson, J. W.; Billinge, S. J. L. PDFgetX2: A GUI-Driven Program to Obtain the Pair Distribution Function from X-Ray Powder Diffraction Data. J. Appl. Crystallogr. 2004 , 37 (4), 678–678. https://doi.org/10.1107/S0021889804011744. Chapman, K. W.; Chupas, P. J.; Halder, G. J.; Hriljac, J. A.; Kurtz, C.; Greve, B. K.; Ruschman, C. J.; Wilkinson, A. P. Optimizing High-Pressure Pair Distribution Function Measurements in Diamond Anvil Cells. J. Appl. Crystallogr. 2010 , 43 (2), 297–307. https://doi.org/10.1107/S0021889810002050. Keen, D. A. A Comparison of Various Commonly Used Correlation Functions for Describing Total Scattering. J. Appl. Crystallogr. 2001 , 34 (2), 172–177. https://doi.org/10.1107/S0021889800019993. Celeste, A.; Borondics, F.; Capitani, F. Hydrostaticity of Pressure-Transmitting Media for High Pressure Infrared Spectroscopy. High Press. Res. 2019 , 39 (4), 608–618. https://doi.org/10.1080/08957959.2019.1666844. Additional Declarations There is NO Competing Interest. Supplementary Files CsPbBr3RMCSIfinal.docx Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6087274","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":430416020,"identity":"80d6a1d2-a651-493b-80dd-a122b10c2c65","order_by":0,"name":"Anna Celeste","email":"","orcid":"https://orcid.org/0000-0001-6728-8449","institution":"Stanford University","correspondingAuthor":false,"prefix":"","firstName":"Anna","middleName":"","lastName":"Celeste","suffix":""},{"id":430416021,"identity":"c9ecf221-bc45-4a55-b986-801d19ba597f","order_by":1,"name":"Samuel Girdzis","email":"","orcid":"","institution":"Stanford University","correspondingAuthor":false,"prefix":"","firstName":"Samuel","middleName":"","lastName":"Girdzis","suffix":""},{"id":430416022,"identity":"9bc8d29a-6360-4d31-a88b-e0fdcd154144","order_by":2,"name":"Bernadette Cladek","email":"","orcid":"https://orcid.org/0000-0001-8538-6827","institution":"University of Tennessee","correspondingAuthor":false,"prefix":"","firstName":"Bernadette","middleName":"","lastName":"Cladek","suffix":""},{"id":430416023,"identity":"29f703f6-6ad6-4794-accc-e937896edc40","order_by":3,"name":"Christina Deschene","email":"","orcid":"","institution":"Stanford University","correspondingAuthor":false,"prefix":"","firstName":"Christina","middleName":"","lastName":"Deschene","suffix":""},{"id":430416024,"identity":"6e996095-855f-4792-9c83-2b176de28360","order_by":4,"name":"Nathan Wolf","email":"","orcid":"https://orcid.org/0000-0001-5718-4283","institution":"Stanford University","correspondingAuthor":false,"prefix":"","firstName":"Nathan","middleName":"","lastName":"Wolf","suffix":""},{"id":430416025,"identity":"e6116ed0-6b6e-4ff9-992b-531d1cf51cf9","order_by":5,"name":"Karena Chapman","email":"","orcid":"https://orcid.org/0000-0002-8725-5633","institution":"Stony Brook University","correspondingAuthor":false,"prefix":"","firstName":"Karena","middleName":"","lastName":"Chapman","suffix":""},{"id":430416026,"identity":"c2809845-3077-4527-b14e-10354cb72102","order_by":6,"name":"Hemamala Karunadasa","email":"","orcid":"https://orcid.org/0000-0003-4949-8068","institution":"Stanford University","correspondingAuthor":false,"prefix":"","firstName":"Hemamala","middleName":"","lastName":"Karunadasa","suffix":""},{"id":430416027,"identity":"cdad9e3c-63c8-449a-ba09-58f6b76f2b2b","order_by":7,"name":"Matthew Tucker","email":"","orcid":"https://orcid.org/0000-0002-2891-7086","institution":"Oak Ridge National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Matthew","middleName":"","lastName":"Tucker","suffix":""},{"id":430416028,"identity":"4f484086-cc2a-4b28-acc2-ba0009d88c99","order_by":8,"name":"Wendy Mao","email":"","orcid":"https://orcid.org/0000-0003-0595-7760","institution":"Stanford University","correspondingAuthor":false,"prefix":"","firstName":"Wendy","middleName":"","lastName":"Mao","suffix":""},{"id":430416019,"identity":"a6ab6d6c-3ad8-4587-96f1-1eb033f55d44","order_by":9,"name":"Yu Lin","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA50lEQVRIie3NMYvCMBTA8Vce5JZc45jQLxEpFMR+mECgqzc6SKkcuHb1wA+TEtBFcC24KF1vE+RAEGvdHKJuwuUPyQshPwLg871hIQS77sC6PW2XAeAuQgDldXJRYDuyV4g0TxOug2Y8zvN4s6kOXyodhQarLXUT7K/Xlie1xmiussGPIXroJqOlmM5MSxCizz8rpaFJ9OAXIqbnnMelxRNVV8KOT5ACuQRNohuhxE1og/1iacW81smQqkwKS+LBwkHYhw72xSRnrKyaLVWpDFff+/rXQaCn7m/Q9bz7xjx64fP5fP++C7ftQ+e8tWqCAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0001-5174-9546","institution":"SLAC National Accelerator Laboratory","correspondingAuthor":true,"prefix":"","firstName":"Yu","middleName":"","lastName":"Lin","suffix":""}],"badges":[],"createdAt":"2025-02-22 20:20:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6087274/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6087274/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":78825863,"identity":"e057c2b1-52e8-4068-ba8b-c69a2ced354d","added_by":"auto","created_at":"2025-03-19 12:30:51","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":74631,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental powder XRD patterns (a) and X-ray PDF data (b) of CsPbBr\u003csub\u003e3\u003c/sub\u003e under pressure. Patterns are stacked vertically for clarity. Patterns collected after releasing pressure are shown in orange.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6087274/v1/65b120a037dd9c882bc3ac27.png"},{"id":78825864,"identity":"8112ead6-0fd0-46f0-a312-746d26c2cb06","added_by":"auto","created_at":"2025-03-19 12:30:51","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":316403,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental PDF (open black circles) and calculated PDF from big-box RMC modeling (solid red line) of CsPbBr\u003csub\u003e3\u003c/sub\u003e are compared over the full r-range at (a) 0.0 GPa, with a focus on the short-range PDF region (3.3-5.6 Å) shown for (b) 0.0 GPa, (c) 0.4 GPa, (d) 0.8 GPa, and (e) 1.2 GPa. Partial atomic pair contributions (Pb-Pb, Pb-Br, Br-Br, Br-Cs, Pb-Cs, and Cs-Cs) are reported as well in distinguished colors. PbBr\u003csub\u003e6\u003c/sub\u003e intra-octahedral (f) and inter-octahedral (g) angle distributions at selected pressures. Data was normalized by sin(θ).\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-6087274/v1/d40386b280d8f94e1a103348.png"},{"id":78825867,"identity":"1b492d73-e868-4515-99f4-6a550f912c84","added_by":"auto","created_at":"2025-03-19 12:30:51","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1714236,"visible":true,"origin":"","legend":"\u003cp\u003eSnapshots of the 6x6x4 supercells representing the atomic configurations obtained through RMCProfile of CsPbBr\u003csub\u003e3\u003c/sub\u003e along the c-axis at different pressures: the ideal structure (\"Initial\"), 0.0 GPa, 0.8 GPa, 1.2 GPa, 1.6 GPa, 2.0 GPa, 3.4 GPa, and 5.0 GPa. Cs atoms are shown in green, Br in deep red, and Pb in gray.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-6087274/v1/f4a697f72967e3eb01dd05fb.png"},{"id":78825866,"identity":"2ddb55d4-d159-4f87-a348-a4c240a2ae21","added_by":"auto","created_at":"2025-03-19 12:30:51","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":90784,"visible":true,"origin":"","legend":"\u003cp\u003eCsPbBr\u003csub\u003e3\u003c/sub\u003e partial PDFs for Pb–Pb (a), Pb–Br (b), Pb–Cs (c), and Br–Br (d) atomic pairs at 0.0 GPa, 1.6 GPa, 2.0 GPa, 3.4 GPa, and 5.0 GPa. Angular distributions for Br–Pb–Br (e) and Pb–Br–Pb (f) bond angles at the same pressures.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6087274/v1/50e271cf3f8b08a8c2cf0305.png"},{"id":78825868,"identity":"ca9485ee-804b-41e0-8edb-e55377cf4e60","added_by":"auto","created_at":"2025-03-19 12:30:51","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":672630,"visible":true,"origin":"","legend":"\u003cp\u003eAtomic positions in the CsPbBr\u003csub\u003e3\u003c/sub\u003e unit cell obtained through RMCProfile modeling of the PDF function at (a) 0, (b) 0.8, (c) 2.0 GPa and (d) 5.0 GPa. The large-box configurations are collapsed back to a single unit cell. Cs atoms are depicted in green, Br in deep red, and Pb in gray.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-6087274/v1/dc496e0db1542bb1122aa222.png"},{"id":79104466,"identity":"91dd63ab-b1b9-4917-804a-bfec789c8b92","added_by":"auto","created_at":"2025-03-24 12:54:20","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3374780,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6087274/v1/fa3a2506-c6fa-4d21-8c8f-a42bcb201734.pdf"},{"id":78825879,"identity":"da359428-c545-4d1d-802c-30d321a90235","added_by":"auto","created_at":"2025-03-19 12:30:51","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":4068763,"visible":true,"origin":"","legend":"","description":"","filename":"CsPbBr3RMCSIfinal.docx","url":"https://assets-eu.researchsquare.com/files/rs-6087274/v1/208563ba87b0bb722ef32748.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Total X-ray Scattering and Big-Box Modeling of Pressure-Induced Local Disorder and Partial Amorphization in CsPbBr3","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eHalide perovskites have emerged as a leading class of materials in optoelectronic applications, particularly in photovoltaic cells.\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e Since the development of the first perovskite-based solar cells in 2009 with a modest 3.8% power conversion efficiency (PCE), subsequent advancements have not only pushed efficiencies over 33% in tandem cells\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e but also expanded their use into light-emitting diodes, photodetectors, lasers, and transistors.\u003csup\u003e\u003cspan additionalcitationids=\"CR4\" citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e Their remarkable success is due to their exceptional properties such as strong light absorption, long charge-carrier lifetimes, and low-cost synthesis. The ability to chemically tune their structure through replacing one or more chemical species allowed the synthesis of a wide variety of systems, fully inorganic or hybrid organic-inorganic, with tailored optoelectronic properties. Additionally, external factors like temperature and pressure can modulate their structures and properties. Multiple studies have investigated the behavior of halide perovskites under high pressure\u003csup\u003e\u003cspan additionalcitationids=\"CR7 CR8 CR9\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e, reporting a range of structural and electronic/optical phenomena, including crystalline phase transitions\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e,\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e, metallization\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e and enhanced photoluminescence.\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e A common behavior observed in halide perovskites is the transition to a partially amorphous phase under pressure, with the onset of this transition varying across different systems.\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e Halide perovskites often exhibit the ability to recover their original structure upon decompression, highlighting the reversibility of their structural changes under pressure. While reversible pressure-induced amorphization is a known phenomenon, the fundamental mechanisms driving this structural recovery remain unclear. To address this, new methods beyond the conventional analysis of X-ray diffraction patterns are required. A promising approach lies in focusing on the short-range structure and examining the material\u0026rsquo;s evolution on a more localized scale. While X-ray diffraction primarily provides information on the average crystal structure, local structural behavior, i.e. on Angstrom scale, can differ significantly. Indeed, this approach has proven particularly effective in uncovering local disorder in halide perovskites. For instance, in CsSnBr\u003csub\u003e3\u003c/sub\u003e, local off-centering of the Sn atoms, undetectable by conventional crystallography, has been identified as causing asymmetries in the cubic phase.\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e Similarly, studying the system locally in (MHy)PbBr\u003csub\u003e3\u003c/sub\u003e (MHy\u003csup\u003e+\u003c/sup\u003e = methylhydrazinium) has revealed how lone pair activity drives structural distortions, enhances electron-phonon interactions, and influences bandgap behavior and charge dynamics.\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eThe pair distribution function (PDF), or G(r), is a powerful tool to study the local atomic structure of materials, as it captures the probability of finding pair of atoms separated by a specific distance in real space.\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e By revealing local density variations and atoms arrangements, the PDF provides valuable insights into both local (short-range) and average (long-range) atomic structure.\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e Performing total X-ray scattering experiments makes it possible to extract the PDF and construct atomistic structural models which describes the local atomic environment at the unit-cell scale, known as \u0026lsquo;small-box\u0026rsquo; approach. This method has proven effective in our previous work on Cs\u003csub\u003e2\u003c/sub\u003eAgBiBr\u003csub\u003e6\u003c/sub\u003e at high pressure, where it revealed that a lower-symmetry model better describes the system on the local scale compared to symmetry observed through X-ray diffraction.\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e A more complex approach involves the use of a supercell built on the unit cell of the material studied which allows for more sophisticated models of the structure. Big-box modeling is usually coupled with the Reverse Monte Carlo (RMC) method where a randomly selected atom is displaced by a random distance to improve the agreement between the modeled and experimental data.\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e It was initially developed to study liquid and amorphous phases,\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e however, this approach is also suitable to study correlated disorder in crystalline materials since it provides a detailed representation of the disordered crystal structure, incorporating local correlations consistent with the measured total scattering data while simultaneously reproducing the average structure seen in the Bragg profile.\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e This approach produces a \u0026lsquo;snapshot\u0026rsquo; of the structure capturing both static and dynamic disordering processes, making it ideal to study pressure-induced modification and amorphization processes.\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eHere, we employ total X-ray scattering combined with RMC big-box modeling to study the high-pressure behavior of CsPbBr\u003csub\u003e3\u003c/sub\u003e, an archetypal three-dimensional (3D) halide perovskite.\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e Indeed, the simplest halide perovskite structure is the 3D perovskite, with the formula ABX\u003csub\u003e3\u003c/sub\u003e where A is a monovalent cation (either an atom or an organic molecule), B is a divalent metal cation and X is a halogen anion. CsPbBr\u003csub\u003e3\u003c/sub\u003e exemplifies this structure, combining a relatively simple inorganic composition with exceptional optical properties.\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e Such characteristics make CsPbBr\u003csub\u003e3\u003c/sub\u003e an ideal candidate for studying the effects of pressure on 3D halide perovskites, particularly regarding phenomena like reversible amorphization and the evolution of local disorder upon compression. Previous studies have noted a pressure-induced bandgap shift from red to blue around 1 GPa and subsequent partial amorphization at 2.4 GPa, with explanations ranging from isostructural phase transitions at 1 GPa to changes in Rashba splitting.\u003csup\u003e\u003cspan additionalcitationids=\"CR27\" citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e First-principle calculations indicate that the nonmonotonic pressure dependence of the bandgap results from competing effects of bond shrinkage and octahedral distortion, suggesting complex underlying mechanisms beyond straightforward structural changes.\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e Our study focuses on the evolution of local disorder under compression, employing a novel methodological approach that provides both detailed insights into the role of disorder within the crystalline phase and information about the amorphization process and its reversibility. To the best of our knowledge, this is the first experimental study to perform structural modeling of the high-pressure partially amorphous phase of a 3D halide perovskite. We propose that the bandgap behavior under pressure is mainly driven by disorder effects and the reversibility of the amorphization stems from the preserved Pb sublattice, despite significant distortion of the PbBr\u003csub\u003e6\u003c/sub\u003e octahedra and Cs atoms off-centering. Our study proves the critical importance of understanding both the local and average structural dynamics in halide perovskites to get a more accurate picture of the structure\u0026ndash;property relationships.\u003c/p\u003e"},{"header":"RESULTS AND DISCUSSION","content":"\u003cp\u003eHigh-pressure powder XRD of CsPbBr\u003csub\u003e3\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea) and the atomic PDFs (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb), derived from total X-ray scattering data collected at a shorter sample-to-detector distance, were collected in a diamond anvil cell up to 5 GPa. We used silicone oil as the pressure transmitting medium which remains quasi-hydrostatic up to 3 GPa, with pressure variations across the sample chamber being less than 0.2 GPa at 5 GPa.\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e At ambient pressure, the diffraction pattern exhibits Bragg reflections characteristic of the \u003cem\u003ePbnm\u003c/em\u003e space group, as previously reported.\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e We performed Rietveld refinement on the XRD data up to 1.6 GPa to extract the lattice parameters (see Figure S3). Above 2 GPa, most peaks, particularly those above 4.5\u0026deg;, start to vanish or significantly broaden, signaling the onset of amorphization. Despite this, a few reflections remain sharp and detectable up to 5 GPa, indicating that partial long-range order is preserved in the structure up to this pressure value. This coexistence of amorphous and crystalline regions makes Rietveld refinement unsuitable beyond 2 GPa. Consequently, we switched to Le Bail fitting while maintaining the ambient pressure space group. We also attempted to fit the data using the recently proposed triclinic space group for CsPbBr\u003csub\u003e3\u003c/sub\u003e at 2 GPa,\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e but at this pressure, the diffraction pattern is already too broadened for a meaningful distinction between low-symmetry space groups, and any could be fit using Le Bail refinement. The discrepancy with that study likely stems from differences in hydrostatic conditions and sample types (powder vs. single crystal). Focusing on the PDFs, we observe short-range structural modifications even below 1.6 GPa, particularly in the 3.5 and 5.5 \u0026Aring; range, where primary contributions arise from the Br-Cs, Br-Br, and Pb-Cs first-neighbor distances. These changes reflect pressure-induced effects on the local structure that are not apparent in the average structure captured by XRD. Above 2 GPa, we detect significant alterations in both the shape and intensity of the peaks, consistent with the transition to a more disordered phase, as observed in the XRD patterns. The diminished periodicity of the structure can clearly be seen in the flattened G(r) at higher values of r.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eUpon releasing pressure, CsPbBr\u003csub\u003e3\u003c/sub\u003e recovers its original crystalline structure, as highlighted by the comparison of the XRD data at ambient pressure before and after pressure release (Figure S4). The lattice parameters obtained through Rietveld refinement are almost identical to the ones of the sample before increasing pressure (Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e). While this recovery demonstrates that pressure-induced transition to the partially amorphous phase is mainly reversible, minor deviations from the initial pattern are still apparent. These include slight broadening and shifts in some Bragg peaks, suggesting residual strain within the crystal lattice. These subtle changes are also mirrored in the PDF comparison between the initial and post-release data (Figure S6), although the overall G(r) regains its original shape, differences in peak intensities and positions are evident, particularly in the 3.0-5.5 \u0026Aring; range. Such alterations highlight that, while the crystalline structure largely recovers, the local environment within the crystal lattice retains modifications induced by high-pressure conditions.\u003c/p\u003e \u003cp\u003eWe analyzed X-ray PDFs using a \u003cem\u003ePbnm\u003c/em\u003e model in PDFgui, as shown in Figure S7.\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e However, since \u003cem\u003ePbnm\u003c/em\u003e is already a relatively low-symmetry space group, this approach provided limited insight. Additionally, the refined lattice parameters became unstable and unphysical at higher pressures. Moreover, the single-unit cell model in PDFgui is likely too small to account for the increasing disorder beyond approximately 2 GPa. To address these challenges, we shifted to RMC simulations using RMCProfile.\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e We built a 6x6x4 supercell containing 2880 atoms allowing for significantly greater variation in the atomic arrangements.\u003c/p\u003e \u003cp\u003eWe started the RMC simulation by applying the distance windows constraint alongside the polyhedral constraint, which allow atoms to move as groups or units within a specified range. Given that CsPbBr\u003csub\u003e3\u003c/sub\u003e adopts a perovskite structure at ambient conditions, we used the polyhedral restraint to fix the PbBr\u003csub\u003e6\u003c/sub\u003e octahedra. Simultaneously, we fit XRD data using the parameters obtained from the Rietveld refinement, such as peak shape and scale factor. This method provided good fitting results for both the XRD and the PDF data up to 1.2 GPa. However, at 1.6 GPa, RMCProfile failed to fit the diffractogram, causing the PDF fit to fail as well. By excluding the average structure data from the fitting procedure, we successfully obtained a good fit for the local structure at this pressure. Beyond 2 GPa, the polyhedral constraint failed, suggesting bond breaking as pressure increased. In response, we tested alternative approaches for data above this pressure, such as constraining only the Pb-Pb distances. This method yielded acceptable chi\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e values for the total G(r) fit. However, further inspection of the partial PDFs showed that the Br-Cs and Br-Br distance distributions assumed unphysical shapes, with distances increasingly compressed to their lower limits at higher pressures. These unusual shapes suggest atomic arrangements with bond lengths that are too short to be physically meaningful. The preliminary tests briefly discussed are detailed in the Supplementary Information. To overcome these challenges, we adopted bond valence sum constraints, which account for interatomic distances and atomic coordination.\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e This approach effectively fits the PDFs up to 5 GPa, providing physically consistent results. It is worth noting that above 2 GPa, we used the parameters obtained from the Le Bail refinement to fit the Bragg data in RMCProfile. Since the Le Bail refinement does not provide a scale factor, which is required by RMCProfile, we estimated it by considering the scale factor obtained at 1.6 GPa and performing a least-squares fit between the observed and the theoretical peak intensities of the first main reflection detected, \u003cem\u003ei.e.\u003c/em\u003e, (110), for the diffractograms up to 5 GPa. To ensure accurate fitting, we first subtracted the background from experimental data using a Chebyshev function. Further on, all the results reported and discussed were obtained using bond valence sum constraints for Cs, Pb, and Br.\u003c/p\u003e \u003cp\u003eThe total and the partial PDFs at 0.0 GPa, obtained through big-box modeling, are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a). The experimental PDF (black open circles) and the calculated PDF (red solid line) are in excellent agreement across the full r-range, demonstrating the suitability of the big-box approach for modeling the structural configuration at ambient conditions. The partial PDFs, representing contributions from specific atomic pairs (Pb-Pb, Pb-Br, Br-Br, Br-Cs, Pb-Cs, and Cs-Cs), display well-defined peaks corresponding to distinct interatomic distances, extending up to 23 \u0026Aring;. Focusing on the 3.3\u0026ndash;5.6 \u0026Aring; range, the main contributions to the total PDF at these distances arise from the Br-Cs, Br-Br, and Pb-Cs first-neighbor interactions. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (b\u0026ndash;e) illustrates the evolution of these partial PDFs with increasing pressure, specifically at 0.0 GPa (b), 0.4 GPa (c), 0.8 GPa (d), and 1.2 GPa (e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWith increasing pressure, the most significant changes are observed in the Br-Br peak (green curve), which broadens and shifts, indicating that pressure induces local distortions within the octahedra. Notably, the shape and intensity of the first peak in the G(r), primarily from the Pb-Br contribution, remain relatively unchanged up to 1.6 GPa (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb). This suggests that the PbBr\u003csub\u003e6\u003c/sub\u003e framework is not significantly impacted within this pressure range. However, the Br-Cs and Pb-Cs partial contributions exhibit gradual broadening as pressure increases, reflecting enhanced disorder in the Cs local coordination environment.\u003c/p\u003e \u003cp\u003eAt ambient pressure, CsPbBr\u003csub\u003e3\u003c/sub\u003e exhibits nominal bond angles of 90\u0026deg; and 180\u0026deg; for the intra-octahedral Br\u0026ndash;Pb\u0026ndash;Br bonds, and approximately 160\u0026deg; for the inter-octahedral Pb\u0026ndash;Br\u0026ndash;Pb angles. These values are reflected in the angle distributions derived from the big-box modeled structure at 0.0 GPa, as shown in panels f and g of Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Upon applying pressure up to 0.8 GPa, the intra-octahedral angle distributions broaden, indicating increased local distortion within the octahedra. Simultaneously, the distribution of inter-octahedral angles shifts toward 180\u0026deg;, suggesting a reduction in octahedral tilting. At 1.2 GPa, the inter-octahedral angle distribution shifts back toward 160\u0026deg; and broadens further, indicating the onset of more significant local disorder. This dynamic evolution of octahedral tilting correlates directly with the non-monotonic bandgap behavior previously observed\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e,\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e and is further confirmed by our absorption spectroscopy measurement, which we performed and analyzed under pressure (see Figure S23). Our measurements reveal a distinct trend: the bandgap narrows (red-shifts) up to ~\u0026thinsp;1 GPa, then reverses and widens (blue-shifts) beyond 1.2 GPa. A previous experimental study attributed this behavior to an isostructural phase transition.\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e Shortening of the Pb\u0026ndash;Br bond under pressure and reduced octahedral tilting (angles approaching 180\u0026deg;) enhances orbital overlap, leading to a bandgap reduction.\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e,\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e Beyond 1 GPa, the reintroduction of tilting (angles shifting back to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sim\\)\u003c/span\u003e\u003c/span\u003e160\u0026deg;) reduces orbital overlap, causing the bandgap to widen.\u003c/p\u003e \u003cp\u003eOur analysis of XRD data and PDFs reveals no evidence of a structural phase transition between 0 and 1.6 GPa, which would be expected in a true isostructural phase transition. Instead, we observe increasing local disorder, reflected in the broadening and shifting of both intra- and inter-octahedral angle distributions. The evolution of inter-octahedral angles, shifting toward 180\u0026deg; up to 0.8 GPa and returning to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sim\\)\u003c/span\u003e\u003c/span\u003e160\u0026deg; at 1.2 GPa, closely mirrors the observed bandgap changes. This suggests that the bandgap behavior may be driven by the cumulative effects of local distortions within the PbBr\u003csub\u003e6\u003c/sub\u003e framework, rather than by a sharp phase transition.\u003c/p\u003e \u003cp\u003eAt 1.6 GPa, both the partial PDFs, indicative of the bong lengths, and the angle distributions, broaden and shift, indicating a significant increase in disorder with pressure. As previously discussed, a much more pronounced change in the experimental data occurs at 2.0 GPa, indicating the onset of the amorphization. This transition, clearly observed in the XRD data (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), is also reflected in the big-box configurations, represented in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e as snapshots of the 6x6x4 supercells for selected pressures along the \u003cem\u003ec\u003c/em\u003e-axis. In the ideal structure (the first snapshot in the sequence), the atoms are well-aligned, and the crystal symmetry is clearly evident. The configuration modeled with RMCProfile based on our experimental PDF at ambient pressure already exhibits some atomic displacements, primarily due to thermal effects. As pressure increases, the disorder becomes progressively more pronounced. Up to 1.6 GPa, it is still possible to discern the underlying crystal symmetry despite the noticeable distortions. However, at 2.0 GPa and beyond (3.4 and 5.0 GPa), the snapshots reveal severe deviations from the initial positions, particularly around Cs atoms, which are significantly off-centered. These changes mark the transition to a highly disordered, amorphous-like state.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo gain deeper insights into the transition, we analyze the distributions of key bond lengths and inter- and intra-octahedral angles at pressures above 2.0 GPa. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e compares the partial PDFs for selected atomic pairs and the angular distributions for octahedral bond angles at pressures beyond the onset of amorphization. To better capture the structural evolution, we also include the distributions at 0 GPa, as a reference, and at 1.6 GPa, just before the amorphization begins, highlighting the changes leading to the disordered state.\u003c/p\u003e \u003cp\u003eThe Pb-Pb PDF shifts to a shorter distance between 0 and 1.6 GPa, consistent with lattice shrinkage induced by pressure, and exhibits significant broadening and intensity reduction above 2.0 GPa. At higher pressures, the partial PDF develops a tail below the main peak, suggesting that Pb atoms occupy a broader range of positions due to lattice distortions and local strain. However, since RMCProfile does not enforce interatomic potentials, it is necessary to impose a limit on the shortest allowable atomic pair distances to prevent unphysical configurations.\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e For Pb-Pb, this limit was set at 5.1 \u0026Aring; at 0 GPa, based on the orthorhombic unit cell at ambient conditions, and reduced to 4.8 \u0026Aring; above 2 GPa to account for compressions effects, in line with the 4.6 \u0026Aring; Pb-Pb distance previously calculated for MAPbI\u003csub\u003e3\u003c/sub\u003e at 6 GPa.\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e This constraint may influence the development of the tail. Interestingly, the position of the main Pb-Pb peak does not shift further after 2.0 GPa. In contrast, the Pb-Br PDF (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb) remains sharp, despite a reduction in intensity when the amorphization begins at 2.0 GPa. On the other hand, the Br-Br distance distribution shows significant broadening and peak shifts (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed), reflecting increasing distortions within and between the octahedra under compression. These observations suggest that while the PbBr\u003csub\u003e6\u003c/sub\u003e octahedra are highly distorted, although partially preserved, the Pb sublattice is relatively stable up to 5 GPa, as shown in the supercell snapshots in Figure S25 where only the Pb atoms are displayed.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe octahedra distortions are further reflected in the Br-Pb-Br (intra-octahedral) and Pb-Br-Pb (inter-octahedral) angular distributions (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee and f, respectively). At ambient pressure, the intra-octahedral bond angles (e) exhibit peaks at 90\u0026deg; and 180\u0026deg;, corresponding to the nominal angles within the PbBr\u003csub\u003e6\u003c/sub\u003e​ octahedra, while the inter-octahedral bond angles (f) are centered around 160\u0026deg;, indicating the tilting between the octahedra. As pressure increases above 1.6 GPa, both angle distributions broaden, highlighting local deformations. Notably, the Br-Pb-Br distribution peaks shift to lower angles, while the Pb-Br-Pb develops a tail extending down to 100 \u0026deg;, signaling severe tilting of the PbBr\u003csub\u003e6\u003c/sub\u003e​ octahedra and significant lattice disorder.\u003c/p\u003e \u003cp\u003eRegarding the Cs cations, we observe that increasing pressure induces significant broadening and intensity reduction in both the Pb\u0026ndash;Cs (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec) and Br\u0026ndash;Cs (Figure S24f) partial PDFs, reflecting growing disorder in the Cs coordination environment, especially beyond 1.6 GPa. This suggests that Cs atoms are displaced from their ideal positions as pressure increases, contributing to the overall loss of crystallinity in the lattice.\u003c/p\u003e \u003cp\u003eAnother way to visualize the evolution of the system under compression, as obtained through RMC simulations, is to pack the supercell back into a single unit cell containing all atoms. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the unit cells for pressures of 0, 0.8, 2, and 5 GPa, while the configurations at remaining pressures are reported in Figure S26. These pressures were selected to represent key stages of the structural evolution along compression: the starting system at ambient pressure (0 GPa, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea), the system under compression while still preserving long-range order (0.8 GPa, panel b), the onset of the amorphization (2.0 GPa, panel c) and the highest pressure measured (5.0 GPa, panel d).\u003c/p\u003e \u003cp\u003eAt 0.0 GPa, the configuration shows atoms of each species overlapping, which indicates a highly ordered crystalline lattice where the structural symmetry of CsPbBr\u003csub\u003e3\u003c/sub\u003e is recognizable. The distribution of atomic positions is due to thermal motion. At 0.8 GPa, we observe small but noticeable movements from the ideal sites, particularly among Cs and Br atoms, while the overall long-range order remains preserved. This intermediate state reflects the initial structural response to compression, with increased density as pressure is applied. By 2.0 GPa, significant atomic displacements become more evident, marking the transition to an amorphous-like phase. In particular, the Cs atoms are displaced from their ideal positions, and disorder in the vertices of the octahedra, \u003cem\u003ei.e.\u003c/em\u003e, the Br atoms, is also evident. These changes correspond to the broadening and shifting observed in the partial PDFs and angular distributions, highlighting the local disorder which starts to arise at this pressure. At 5.0 GPa, the system exhibits a highly disordered structure, with substantial overlap and dispersion of atomic positions, particularly among the Cs and Br atoms. However, the Pb atoms still appear to occupy the original sites, although they are statistically more dispersed. As previously mentioned, a few Bragg reflections remain detectable in the XRD patterns (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), indicating that the long-range order is not completely lost. These reflections can be indexed to the hkl planes associated with the Pb atoms (see Figure S26), suggesting that the Pb sublattice retains partial order even as the surrounding atoms are displaced.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eUpon releasing pressure, we observed the recovery of the initial phase, albeit with minor differences already discussed. This reversibility is a well-documented phenomenon in other halide perovskite materials, even when compressed to pressures exceeding 60 GPa.\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e Although we did not collect data at intermediate pressures, RMC simulations were conducted starting from the configuration obtained at 5 GPa. This approach enabled the successful recovery of more ordered configurations, beginning with the most disordered state observed at 5 GPa. Simulations conducted on the experimental data collected after the pressure release provides a large-box configuration that displays well-aligned atoms, with the structural symmetry clearly reestablished (Figures S27-29). Further analysis on the octahedral bond lengths and tilting shows a return to values consistent with those at ambient conditions. However, the intra- and inter-octahedral bond angle distributions obtained for the recovered system are slightly broader than the initial ones (Figure S30), suggesting that the pressure-induced local disorder is not entirely eliminated after pressure release. This is underscored by the inability of RMCProfile to perfectly fit the XRD data, as demonstrated in Figure S31. The ability to fit the data after pressure release backtracking from the 5 GPa data demonstrates that the model is capable of accurately capturing the reversibility of the structural transition, effectively simulating the recovery process from a partially amorphous phase back to a more crystalline state.\u003c/p\u003e"},{"header":"CONCLUSIONS","content":"\u003cp\u003eThis study highlights the capability of combining total X-ray scattering with RMC big-box modeling to uncover the complex interplay between local structural distortions and long-range crystalline behavior in CsPbBr\u003csub\u003e3\u003c/sub\u003e, a prototype three-dimensional halide perovskite, on compression. Our approach reveals that pressure-induced distortions in the PbBr\u003csub\u003e6\u003c/sub\u003e octahedra and Cs coordination environment precede the onset of the amorphization at 2 GPa, providing critical insights into structural dynamics that cannot be captured by traditional XRD. By examining both short-range and long-range structural correlations through PDF analysis, we elucidate how local disorder impacts optical properties within the crystalline phase and gain information about the mechanisms underlying pressure-induced amorphization and reversibility upon pressure release. Specifically, the nonmonotonic bandgap evolution observed below 2 GPa, transitioning from a red to a blue shift, is directly linked to the interplay between bond compression and octahedral tilting. Beyond this pressure threshold, while the Pb sublattice retains partial order, significant disorder emerges, particularly in the Cs and Br coordination environments, resulting in a partially amorphous structure. Upon pressure release, the recovery of the crystalline phase is facilitated by the stability of the Pb sublattice, although residual strain and subtle local distortions persist. The reversible amorphization highlights the dynamic interplay between long-range and local structural behavior under pressure. These findings underscore the value of large-box modeling as a powerful tool to probe the structural drivers of both the crystalline and amorphous phases, enhancing our understanding of pressure-induced phenomena in halide perovskites. This integrated approach paves the way for designing materials with tailored properties for optoelectronic applications under extreme conditions.\u003c/p\u003e"},{"header":"MATERIALS AND METHODS","content":"\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eSample synthesis and characterization\u003c/h2\u003e \u003cp\u003eAll chemicals were used as received from commercial vendors. To synthesize CsPbBr\u003csub\u003e3\u003c/sub\u003e powder, 400 mg of PbBr\u003csub\u003e2\u003c/sub\u003e and 232 mg of CsBr were dissolved in 4 mL and 12 mL of dry dimethylsulfoxide, respectively. The two solutions were combined and then added to 100 mL of dry acetonitrile. An orange powder slowly precipitated after 5 minutes of stirring. The CsPbBr\u003csub\u003e3\u003c/sub\u003e powder was isolated by filtration and dried under reduced pressure. A milling jar was filled with toluene, 360 mg of the perovskite powder, and zirconia balls (ca. 5 g). The sample was ball milled at 500 rpm with 8 cycles of 30 minutes of milling and 30 minutes of rest. The sample was further dried under reduced pressure and stored in desiccant to avoid decomposition from moisture exposure. The crystal structure of CsPbBr\u003csub\u003e3\u003c/sub\u003e was verified by both laboratory and synchrotron X-ray powder diffraction (PXRD) at ambient conditions. A high-resolution PXRD diffractogram of the sample was collected in a capillary at the 11-ID-B beamline of the Advanced Photon Source synchrotron and is shown in Figure \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e together with the corresponding Rietveld refinement.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eHigh-pressure Total X-Ray Scattering Measurements\u003c/h3\u003e\n\u003cp\u003eBall-milled CsPbBr\u003csub\u003e3\u003c/sub\u003e powder was loaded into a short symmetric diamond anvil cell with 300-\u0026micro;m culets. The gasket was stainless steel and silicone oil served as the pressure transmitting medium.\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e The diamond-seat-cell combination had large ca. 90\u0026deg; aperture angles to access a large Q range. Pressure was measured within 0.1 GPa using the ruby fluorescence method.\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e High-pressure total X-ray scattering data were collected at beamline 11-ID-B at the Advanced Photon Source at Argonne National Laboratory using an energy of 86.7 keV (0.143 A\u0026deg;).\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e The 2-D scattering patterns were masked to remove diamond reflections and integrated using Fit2d software.\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e The PDFgetX2 software program was used to extract the structure factor S(Q) up to Q\u0026thinsp;=\u0026thinsp;18 \u0026deg;A\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e.\u003csup\u003e35\u003c/sup\u003e Scattering data collected using the empty diamond anvil cell, with the gasket pre-indented and drilled, was used for background subtraction when extracting the pair distribution functions (PDFs).\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e PDFgetX2 was used to transform S(Q) to the real-space PDF G(r) for initial analysis. Subsequent analysis of the PDFs using RMC simulations involved transforming S(Q) internally, normalizing to an absolute scale using StoG within the RMCProfile program.\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e A Fourier filter and Lorch window function were used in the Fourier transform. We also collected powder XRD (PXRD) data at a longer sample-to-detector distance for average structure analysis.\u003c/p\u003e\n\u003ch3\u003eReverse Monte Carlo (RMC) simulations\u003c/h3\u003e\n\u003cp\u003eReverse Monte Carlo (RMC) simulations were conducted using RMCProfile to analyze the experimental data.\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e A 6x6x4 supercell containing 2880 atoms was constructed, with initial atomic positions derived from the experimental crystallographic structure obtained through Rietveld refinement. The simulation aimed to fit the experimental real-space PDF, particularly focusing on the G(r) function which is defined as:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:G\\left(r\\right)=\\frac{1}{({2\\pi\\:)}^{3}{\\rho\\:}_{0}}{\\int\\:}_{0}^{\\infty\\:}{Q}^{2}F\\left(Q\\right)\\frac{\\text{sin}\\left(Qr\\right)}{Qr}\\text{d}Q$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:F\\left(Q\\right)\\)\u003c/span\u003e\u003c/span\u003e is the total scattering structure factor, given by:\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:F\\left(Q\\right)={\\rho\\:}_{0}{\\int\\:}_{0}^{\\infty\\:}4\\pi\\:{r}^{2}G\\left(r\\right)\\frac{\\text{sin}\\left(Qr\\right)}{Qr}\\text{d}r$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWith \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\rho\\:}_{0}=N/V\\)\u003c/span\u003e\u003c/span\u003e represents the average atom number density on atoms \u0026Aring;\u003csup\u003e\u0026minus;3\u003c/sup\u003e. The G(r) represents the probability of finding a pair of atoms separated by a specific distance in real space, providing information on local density variations due to the arrangement of atoms. This method helps in understanding the local atomic arrangements beyond what is observable from Bragg peaks alone, including distortions and short-range order in the material. For a more detailed explanation of the formalism, we refer to the papers by Keen\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e and Peterson \u003cem\u003eet al\u003c/em\u003e.\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eIn order to prevent unphysical atomic configurations, several approaches have been used. In an initial test at low pressures, polyhedral restraints were applied to maintain the integrity of BX\u003csub\u003e6\u003c/sub\u003e octahedra. In this case, the \u0026ldquo;distance-window\u0026rdquo; restraint was implemented to define a minimum and maximum allowed value for the distance r\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e between a pair of neighboring atoms, where \u003cem\u003ei\u003c/em\u003e and \u003cem\u003ej\u003c/em\u003e denote the species of atoms in the pair. Also, a bond valence sum restraint was employed on the whole dataset to limit bond distances and further ensure chemically reasonable configurations. RMCProfile was also used to fit the Bragg data. The RMCProfile simulations were run between approximately 12 and 30 hours each, which correspond to between 1 and 3\u0026nbsp;million accepted moves. An example of the evolution of χ\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e is shown in Figure S32.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eHigh-pressure Visible Absorption Measurements\u003c/h2\u003e \u003cp\u003eOptical absorption measurements were collected at beamline 22-IR-1 of the National Synchrotron Light Source II (NSLS-II) at Brookhaven National Laboratory (BNL). Visible absorption measurements between 400 and 1000 nm were performed using a customized visible microscope system equipped with an IsoPlane SCT-320 Imaging Spectrograph, a PyLon CCD detector (Princeton Instruments) and a tungsten light source. A symmetric DAC with type IIas diamond anvils of 500 \u0026micro;m culets was used for the absorption measurements. The sample chamber, a 200 \u0026micro;m hole drilled in a pre-indented stainless-steel gasket, was filled with KBr as the pressure transmitting medium.\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e A thin pellet of the sample, a few microns thick, was placed to occupy half of the chamber area. At each pressure point, a reference transmission spectrum was collected through KBr before measuring the sample transmission under the same beam conditions (e.g., energy range and aperture size). The spectra were analyzed using the Tauc-plot method to determine the bandgap evolution as a function of pressure.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003eACKNOWLEDGEMENTS\u003c/p\u003e\n\u003cp\u003eThis work was supported by the Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DE-AC02-76SF00515. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under contract no. DE-AC02-06CH11357. C.R.D acknowledges a Stanford Center for Molecular Analysis and Design fellowship and N.R.W. acknowledges a Stanford Interdisciplinary Graduate Fellowship. The authors thank Olaf Borkiewicz and Leighanne Gallington for assistance with PDF measurements. The mail-in program at Beamline 11-ID-B contributed to the data. The authors thank Dr. Zhenxian Liu for experimental assistance with high-pressure optical absorption measurements. High-pressure absorption measurements used beamline 22-IR-1 of the National Synchrotron Light Source II, a U.S.DOE Office of Science User Facility operated by the Brookhaven National Laboratory (DE-SC0012704) and supported by COMPRES, the Consortium for Materials Properties Research in Earth Sciences, under the NSF cooperative agreement EAR-1606856, and DOE-NNSA cooperative agreement DE-NA0003975 (CDAC). \u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eJena, A. K.; Kulkarni, A.; Miyasaka, T. Halide Perovskite Photovoltaics: Background, Status, and Future Prospects. \u003cem\u003eChem. Rev.\u003c/em\u003e \u003cstrong\u003e2019\u003c/strong\u003e, \u003cem\u003e119\u003c/em\u003e (5), 3036\u0026ndash;3103. https://doi.org/10.1021/acs.chemrev.8b00539.\u003c/li\u003e\n\u003cli\u003eLiu, J.; He, Y.; Ding, L.; Zhang, H.; Li, Q.; Jia, L.; Yu, J.; Lau, T. 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Res.\u003c/em\u003e \u003cstrong\u003e2019\u003c/strong\u003e, \u003cem\u003e39\u003c/em\u003e (4), 608\u0026ndash;618. https://doi.org/10.1080/08957959.2019.1666844.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-6087274/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6087274/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe mechanisms governing pressure-induced amorphization and its reversibility in halide perovskites remain poorly understood, particularly the role of local disorder in this process. We performed high-pressure synchrotron total X-ray scattering and reverse Monte Carlo (RMC) big-box modeling using CsPbBr₃ as a model system to investigate short-range structural evolution in both the ordered and partially amorphous phases. While X-ray diffraction (XRD) indicates that long-range order persists up to 2 GPa, pair distribution function (PDF) analysis reveals the emergence of significant local distortions, including PbBr₆ octahedral tilting and Cs displacement, which directly influence the bandgap through a complex interplay between bond compression and angular tilting. Beyond 2 GPa, CsPbBr₃ undergoes partial amorphization, with significant disordering of Cs and Br, while the Pb sublattice remains preserved, allowing for reversible pressure-induced amorphization upon decompression. Unraveling the short-range mechanisms behind this reversibility could provide key insights into phase stability and disorder recovery, paving the way for new strategies to stabilize metastable phases in halide perovskites. These results demonstrate that the approach proposed here, which accounts for both short- and long-range structural evolution through RMC modeling, successfully captures the role of disorder in the structural response of halide perovskites to pressure.\u003c/p\u003e","manuscriptTitle":"Total X-ray Scattering and Big-Box Modeling of Pressure-Induced Local Disorder and Partial Amorphization in CsPbBr3","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-19 12:30:46","doi":"10.21203/rs.3.rs-6087274/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"0637a2bd-ec9f-4ed8-901e-3cc0372b6416","owner":[],"postedDate":"March 19th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":45841231,"name":"Physical sciences/Materials science/Materials for energy and catalysis/Solar cells"},{"id":45841232,"name":"Physical sciences/Materials science/Condensed-matter physics/Phase transitions and critical phenomena"}],"tags":[],"updatedAt":"2025-07-31T11:15:32+00:00","versionOfRecord":[],"versionCreatedAt":"2025-03-19 12:30:46","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6087274","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6087274","identity":"rs-6087274","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}