Introduction

The fundamental understanding of electron-beam radiation damage mechanisms serves as the cornerstone for driving technical innovations in electron microscopy (EM). These innovations are dedicated to enhancing the control of electron-beam illumination and associated radiation damage to the specimen so as to offer precise and high-resolution nanopatterning for non-destructive structural elucidation for EM. Within the realm of radiation-induced phenomena, classical beam damage mechanisms and descriptive models play a prominent role in explaining diverse effects. These mechanisms encompass knock-on displacement and radiolysis (ionization) as the primary damage mechanisms. Additionally, electrostatic charging, electron-beam heating, and other secondary or ternary events such as diffusion, contamination, and segregation further contribute to the overall understanding of radiation-induced phenomena1. These widely acknowledged mechanisms and models collectively provide a comprehensive framework for comprehending and characterizing the intricate effects of radiation.

Knock-on displacement arises from high-angle elastic scattering between primary electrons and screened nuclei of atoms with kinetic energy and momentum conserved, which results in the atomic displacement at a lattice site and sputtering at a surface site by overcoming their respective binding energies and associated energy transfer thresholds, termed displacement energy (Ed)2,3. The Ed values are site-specific and may vary from tens of eV at lattice sites, to a few eV at pore walls, boundaries and defects, or even lower than 1 eV for lateral motion of surface adatoms3,4,5. The analytical form of knock-on cross-section (σK) is derived by integrating the differential elastic cross-section (σe) over high scattering angles. This integration incorporates single exponential terms (i.e., Wentzel atom model) or summed exponential terms considering screening effects, as well as a probability term accounting for effective energy transfer that introduces atomic displacement6,7,8. As a result, the analytical σK model exhibits a step-edge shape, manifesting an intense onset at the energy threshold and a slightly diminishing tail at higher energy side. In contrast to knock-on displacement that dominates radiation damage in conducting materials, radiolysis usually dominates in non-conducting materials and arises from inelastic scattering of primary and secondary electrons that create long-lived electronic excitations (τ > 1 ps) to drive atomic displacements towards permanent breakage and reformation of chemical bonds3,9,10. Such energy–momentum conversion can be readily achieved by thermal vibration, local Coulomb repulsion, or in most cases the combination of both, which leads to temperature-dependent radiolytic structural damage8. The radiolysis cross-section can be approximately estimated based on the Bethe ionization cross-section model11 by summing up corresponding terms for individual electron shells considering the efficiency of radiolytic damage transferred from ionization events12,13. Generally, the validation of classical beam damage mechanisms relies on limited tools for the measurement of diverse symptoms induced by radiation damage. The symptoms are usually directly measurable and dictate the collective properties of structural dynamics. For example, the fading of Bragg spots and diffuse scattering rings arising from radiation-induced amorphization of crystalline materials can be measured by electron diffraction (ED) series14,15. The compositional variation or mass loss induced by sputtering can be tracked by energy-dispersive X-ray spectra series16. Moreover, electron energy-loss spectra series allow the monitoring of characteristic energy band evolutions that dictate the electronic structure alteration induced by radiation damage17. Practically, individual classical beam damage mechanisms are usually oversimplified and fail to explain many intricate damage phenomena. The current understanding of radiation-induced structural alterations and associated beam damage mechanisms lacks the dynamic and precise depiction that an evolutionary and synergistic perspective can provide. To address this gap, it is crucial to employ real-space visualization techniques with high spatial and temporal resolutions, enabling a comprehensive exploration of the structural dynamics under beam radiation.

A pioneer work conducted by Kaiser et al. quantitatively measure the knock-on displacement of single-layer graphene by directly counting the ejected atoms under radiation in high-resolution transmission electron microscopy (HRTEM) images, which enables the explicit identification of damage mechanism and accurate modeling of knock-on cross sections including lattice vibration effects18. The emerging low-dose EM offers opportunities for real-space imaging of radiation-induced structural dynamics even in beam-sensitive materials, while maintaining high spatial resolution19,20,21,22,23,24,25,26,27. The technique has enabled the structural elucidation of beam-sensitive materials like metal-organic frameworks (MOFs)19,21,28,29, covalent-organic frameworks30,31, organic-inorganic hybrid materials32,33, 2D materials34,35, and zeolites36. Imaging radiation damage at the atomic or molecular level unravels mechanistic insights that: (i) enrich the theoretical framework of radiation damage beyond classical mechanisms, (ii) inspire mechanism-specific damage circumventing techniques in EM, such as cryogenic and low-kV conditions to mitigate radiolysis and knock-on damage, respectively, and (iii) eliminate beam damage-induced artifacts, ensuring accurate structural elucidation of beam-sensitive materials.

As a unique class of crystalline porous materials featuring tunable topologies, large specific surface areas, and adjustable chemical compositions, MOFs are promising candidates for catalysis37,38, gas storage and separation39, energy storage and conversion40, chemical sensing41, water adsorption42,43, and lithium-ion storage44. The precise structural elucidation of MOFs by traditional EM is, however, challenging because they are extremely beam-sensitive and predominantly subjected to radiolytic damage27,29,45. For instance, MIL-101(Cr) was reported to withstand an electron dose of ~16 e− Å−2 46. The high-order reflection of UiO-66(Zr) starts to fade when the cumulative dose reaches about 17 e− Å−2 19, while the crystallinity of ZIF-8(Zn) quickly lost at a dose as low as 25 e− Å−2 47. To directly visualize the radiation damage of MOFs, we present an investigation into the radiation-induced structural dynamics of UiO-66(Hf) by low-dose EM, aiming to uncover the largely unexplored beam damage mechanisms that underlie the radiation behavior of such an open-framework material. We comprehensively investigate potential mechanisms occurring in MOFs upon beam radiation, examining morphological, lattice, and molecular levels. Our findings encompass the following aspects:

(i) We uncover the radiation-induced anisotropic volumetric shrinkage of polyhedral MOF crystals, which arises from the formation of stripe-like amorphized domains. These domains exhibit collapsed structures and diminished porosity compared to the remaining crystalline domains.

(ii) We introduce a nonclassical reversible radiolysis mechanism that deviates from the traditional understanding of radiolysis. This mechanism involves cascade self-repairing process, entailing the dynamic crystalline-to-amorphous interconversion events. While adhering to the first-order kinetic model of structural degradation, the nonclassical mechanism embraces a direct dose-rate effect. We furthermore propose a regulation strategy for this mechanism by introducing gas atmosphere in electron microscope and monitoring the structural dynamics.

(iii) Furthermore, we observe that the anisotropic lattice strain resulting from radiolytic structural degradation facilitates site-specific ligand knockout events. This observation indicates a nonclassical radiolysis-enhanced knock-on displacement mechanism.

Results and discussion

In light of the disparity in evaluating the level of radiation damage of MOFs in relation to the electron dose, quantitative structural damage measurement can be achieved by ED dose series based on the fading of diffraction spots, which arises from the loss of different degrees of structural order48,49. The radiolytic damage basically follows first-order kinetics, and similar to the half-life of radioactive decay, a critical dose (Dc) that dictates the vulnerability of the materials can be derived by fitting the exponential decay of ED intensities3,49,50,51. Despite these considerations, relying solely on Dc as a direct and universal quantitative indicator for the radiolytic structural vulnerability of MOFs is insufficient due to the following reasons: (i) The illumination conditions applied to these materials are often poorly defined, leading to potential dose-rate effects. (ii) The fading of diffraction spots at various spatial frequencies indicates a decrease in structural order but does not necessarily correlate with specific types of structural damage or distortion in real space. (iii) Discerning more complex forms of radiation damage beyond amorphization becomes challenging. We hereby enable by integrating direct detection devices and low-dose EM the real-space visualization of radiation damage and associated structural dynamics of a model MOF material UiO-66(Hf), which provides insights into the nonclassical beam damage mechanisms that account for complicated beam induced structural dynamics visualized.

Integrating both classical and nonclassical damage events occurring in UiO-66(Hf), different stages of radiation damage mechanisms and their logical relations are summarized in Fig. 1. These radiation damage events spanning different time scales encompass primary knock-on displacement and radiolysis based on electron-nucleus elastic scattering and electron-electron inelastic scattering respectively. Primary knock-on displacement events occur at very short time scale, which constitutes atomic displacement steps including cascade interatomic collisions (~0.1 ps), energy dissipation for defect stabilization (~10 ps), and thermal migration of point defects (>10 ps) that precede instantaneous electron-nucleus energy transfer at 10−21 s52,53. Primary radiolysis originates from electronic excitations at a very short time scale (~0.1 fs) followed by immediate bond dissociation (~fs) but requires momentum transfer and long-lived core-hole excitation states (>1 ps) to drive mechanical displacement of molecular ligand groups and structural damage of MOFs through coupling with vibrations (~0.1 to ~1 ps) and/or Coulomb interactions (~0.01 ps)8,52,54,55. As a nonclassical competitive mechanism proposed in this work, cascade self-repairing events that sequentially relink the displaced molecular ligand groups take place within the ~ps time scale and heal the broken coordinate bonds arising from radiolytic damage of MOFs. These two competitive mechanisms involve dynamic crystalline-to-amorphous interconversion events and direct dose-rate effect. Considering both primary and secondary damage events via damage cross-section and stopping power for knock-on and radiolysis7, i.e., knock-on events by displaced groups and further ionization by generated secondary electrons respectively, radiolysis has been reported to predominate in non-conducting materials like MOFs56. In addition to the classical secondary events, the anisotropic lattice deformation of UiO-66(Hf) resulting from radiolytic amorphization (~μs to ~s) gives rise to amplified knock-on effects and site-specific ligand knockout events. These phenomena collectively constitute a nonclassical radiolysis-enhanced knock-on displacement mechanism.

Fig. 1: The schematic illustration of radiation damage events and their time scales for MOFs UiO-66(Hf).
figure 1

(i) The primary damage events including radiolytic damage (fs~ns) and knock-on displacement (ps~μs)68. The atomic motion arising from radiolytic damage is achieved by energy–momentum conversion through thermal vibration and/or local Coulomb repulsion effects. (ii) Nonclassical reversible radiolysis triggers cascade self-repairing events within the ps range, demonstrated by a simplified representation of UiO-66 structural model based on AIMD simulations. In this representation, blue dots refer to Hf6O4(OH)4 nodes, while red and green lines refer to broken and intact Hf–O bonds formed between BDC linkers and Hf6O4(OH)4 nodes respectively. The yellow arrows point to relinked Hf–O bonds in cascade self-repairing events. The yellow and green domains in the upper right part refer to dynamic crystalline-to-amorphous interconversion caused by nonclassical reversible radiolysis. (iii) The secondary and multistage damage events, including radiolysis-enhanced knock-on displacement events that account for the anisotropic lattice contraction and associated site-specific ligand knockout processes.

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In pursuit of a thorough understanding of the complex radiation damage phenomena described above, a comprehensive investigation of the underlying nonclassical damage mechanisms and their physical origins has been undertaken. Through a comprehensive elucidation of structural dynamics encompassing multiple scales, including morphological, lattice, and molecular levels, a profound understanding has been achieved by real-space imaging. UiO-66 belongs to an important MOF family that adopts an fcu topology and is composed of 12-connected M6O4(OH)4 (M = Zr or Hf) octahedral nodes bridged by 1,4-benzene-dicarboxylate (BDC) linkers with a density of 1.21(Zr) and 1.62(Hf) g cm−3, respectively. The crystalline structure and octahedral crystal shape of UiO-66(Hf) have been confirmed by powder X-ray diffraction and TEM images as shown in Supplementary Figs. 1 and 2. By utilizing low-dose EM imaging along the [1\(\bar{1}\)0] projection, as exemplified in Supplementary Fig. 3, the crystal structure can be visually depicted at the molecular level. This visualization reveals the presence of rhombic-shaped dark contrasts, representing two pairs of Hf atomic columns positioned at the corners, alongside BDC linkers situated along the edges and short diagonals.

By inspecting the radiation-induced structural dynamics at morphological level, an immediate outcome of homogeneous illumination of the electron beam is a large and continuous contraction of a UiO-66(Hf) octahedral crystal oriented along the [1\(\bar{1}\)0] projection. It is observed that the crystal contraction is approximately anisotropic, with a contraction rate of 12.5% along the [001] direction and 10.4% along the [110] direction (Supplementary Fig. 4). Upon reaching higher accumulative doses, the crystal contraction ceases, and the morphology remains unaltered. By employing ED dose series, the progressive changes in the crystal structure can be examined. During this process, the Bragg spots exhibit a continuous fading, with the exception of the low spatial frequency spots that remain constant even at higher accumulative doses (Fig. 2a). The Dc value can be quantitatively measured by fitting the exponential decay of radially averaged ED intensities (Fig. 2b, c). Actually, it has been widely observed that the radiation damage causes crystal contraction in open-framework materials49,57,58, while the explicit physical origin of such structural deformation remains elusive. In order to precisely understand and resolve the ambiguity surrounding radiation-induced structural dynamics, it becomes imperative to investigate these phenomena at the lattice level using low-dose HRTEM imaging. This approach not only enables direct visualization of both crystalline and local structural features but also offers a precise elucidation of damage events, such as amorphization and defect formation, thereby addressing the intricacies involved. The structural deformations that dictate the overall crystal contraction upon radiation originate from two effects, the intragranular and intergranular contractions. Figure 3a illustrates the precise decoupling of the above-mentioned two effects from the lattice contrast in the dose-dependent images. The intragranular contraction arises from the deformations of crystal lattice and can be quantitatively evaluated by geometric phase analysis (GPA) using the pristine UiO-66(Hf) crystal lattice as reference in Fig. 3d, Supplementary Figs. 5 and 6. The GPA results (i.e., εxx, εyy, and εxy components for \(\vec{{{\bf{x}}}}\) = [110] and \(\vec{{{\bf{y}}}}\) = [001] axes) suggest that there is no considerable crystal lattice contraction before an electron dose as high as 64.7 e− Å−2 is reached, beyond which significant lattice contraction along the long axis (i.e., [001] axis) of the octahedral crystal together with considerable deformations at the (001) equatorial plane (i.e., [110] axis) are observed. Evidently, the significant contraction of crystals observed during the early stages of electron-beam radiation cannot be attributed to deformations within the crystal lattice, as the possibilities for stretching and contraction of chemical bonds are inherently limited. Instead, the crystal contraction actually originates from the formation of intergranular amorphous domains that exhibit greatly reduced volume and elevated packing density. The ab initio molecular dynamics (AIMD) simulation is based on spontaneous and post-ionization structural dynamics, which account for the amorphization-induced volumetric contraction. We have proved by AIMD simulations that an equilibrated supercell UiO-66(Hf) model with massive broken bonds exhibits significant volumetric shrinkage and elevated density (from 1.62 to 2.09 g cm−3) due to the collapsed porous network (Supplementary Fig. 7). Moreover, the dynamic evolutions of intergranular amorphous domains can be explicitly visualized by negative masking of Bragg-filtered crystalline domains in the serial HRTEM images under different electron dose (Fig. 3d). A stunning observation is that, instead of the continuous growth of amorphous domains upon beam radiation as expected, a large expanse of amorphized region with a size of 76.6 × 37.5 nm at the early stage of radiation is considerably diminished at a dose of 24.3 e− Å−2, which then reemerges and gradually turns into intermittent and mobile stripe-like domains distributed along the [110] direction. This striking observation strongly suggests the presence of dynamic crystalline-to-amorphous interconversion, likely stemming from the self-repair events that address radiolytic structural damage. A notable characteristic of these events is their inclination towards in-plane rather than out-of-plane self-repairing, specifically with a preference for the (001) equatorial plane of the UiO-66(Hf) octahedral crystal. This intriguing phenomenon gives rise to the formation of well-defined stripe-like amorphous domains and highlights the intricate interplay between crystalline and amorphous phases. In order to further explore the process of crystal-amorphous interconversion, by an in situ low-dose HRTEM imaging technique, we successfully acquired a molecular-resolution HRTEM image dose series of a crystalline ___domain in a UiO-66(Hf) MOF crystal along the [1\(\bar{1}\)0] projection and near Scherzer defocus. This approach enables us to directly observe the molecular-level structural dynamics associated with the recrystallization of UiO-66(Hf) MOFs while approximately preserving the ordered framework (Fig. 4). Overall, the crystal lattice of UiO-66(Hf) MOFs exhibits rhombic-shaped dark contrasts, characterized by dark dot-like contrasts at the corners of the rhombi corresponding to projected Hf6O4(OH)4 nodes, and dark rod-like contrasts along the edges and short diagonals for the BDC linkers. The serial imaging results enable us to visualize the radiolytic bond breaking and relinkage within the UiO-66(Hf) framework, as evidenced by the appearance and disappearance of dark rod-like contrasts between the dark dot contrasts representing the metal nodes. Magnified views of the regions of interest (ROIs) marked by white, yellow, blue, and green dashed rectangles in Fig. 4a are presented in Fig. 4b–e, accompanied by schematic illustrations of the structural models. The molecular-level recrystallization process dictates the sequential appearance, disappearance, and reappearance of contrasts for BDC linkers under beam radiation. This behavior arises from the partial dissociation of metal-linker bonds and the detachment of BDC linkers from one end to the metal nodes. Although the partially detached and displaced BDC linkers exhibit negligible contrast, they become visible again when they approach and reconnect to the metal nodes. Above an accumulated electron dose of 48 e− Å−2, by carefully inspecting these image contrasts, the bridging BDC linkers at the short diagonals of the rhombi are more frequently subject to radiolytic damage and most of them disappear permanently when the cumulative dose approaching 64 e− Å−2. On the other side, accurately quantifying intergranular contraction in the UiO-66(Hf) octahedral crystal poses a challenge due to its composite nature, comprising a blend of crystalline and amorphous domains. We hereby developed a coarse-grained strain analysis (CG-SA) method, to effectively quantify the dose-dependent deformations of the crystal. Our method entails tracking the relative displacements among multiple crystalline ROIs using our previously elaborated registration algorithm for noisy images59, which are collected at noncollinear sites and serve as coarse-grained representations (Fig. 3b and see Supplementary Methods section 1.2.2). Provided that the intragranular deformations are negligible before an accumulated dose of 64.7 e− Å−2, the relative intergranular displacements are then converted into a deformation vector that is partitioned into two orthogonal basis vectors (i.e., ux and uy) to calculate the compressive, tensile, and shear deformation components (i.e., εxx = \(\frac{\partial {{{u}}}_{{{\rm{x}}}}}{\partial {{x}}}\), εyy = \(\frac{\partial {{{u}}}_{{{\rm{y}}}}}{\partial {{y}}}\) and εxy = \(\frac{1}{2}\) (\(\frac{\partial {{{u}}}_{{{\rm{x}}}}}{\partial {{y}}}\) + \(\frac{\partial {{{u}}}_{{{\rm{y}}}}}{\partial {{x}}}\))) of the overall crystal. Besides a moderate fluctuation of shear deformation εxy, an enhanced contraction εyy up to 9.5% is observed along the [001] direction (Fig. 3c), in contrast to the 3.5% contraction εxx along [110] direction. The observed results affirm that the radiation damage behavior of UiO-66(Hf) MOF adheres to the radiolytic damage kinetics with negligible energy threshold. However, nonclassical self-repairing events compete the radiolytic damage and result in the dynamic crystalline-to-amorphous interconversion. These dynamic self-repairing events under “dark” condition can be reproduced by AIMD simulations using a UiO-66(Hf) supercell model with multiple broken Hf–O bonds and displaced BDC ligands with one end detached (Fig. 5a and Supplementary Fig. 8). The supercell model closely resembles the scenario of radiolytic damage that ionizes the chemical bonds and displaces the molecular groups through vibration and/or Coulomb repulsion. As an intriguing observation, these detached BDC linkers with broken bonds are subject to cascade self-repairing events and serial relinkage to the original coordination unsaturated metal sites in the UiO-66 framework. Based on the serial snapshots of the simulated dynamic process by sampling the canonical ensemble at 298.15 K (Supplementary Fig. 9), sequential reattachment and bonding of displaced BDC ligands takes place from 0.6 to 11 ps by concurrent ligand wagging and approaching to the target undercoordinated metal sites of the Hf6O4(OH)4 node, which is guided by the continuous decrease of overall potential energy as shown in Supplementary Fig. 10. The time scale (~ps) of these self-repairing events is comparable with the lifetime of excitation (>ps) required to achieve energy–momentum conversion and mechanical displacement of atoms or molecular groups, which entails the fact that radiolytic damage and self-repairing are two competitive reactions. More importantly, it is observed that the (001) in-plane structural recovery steps (e.g., steps at 0.6, 1.2, 1.9, and 2.3 ps) are generally faster than those out-of-plane ones (e.g., steps at 3.7, 4.8, and 5.3 ps), likely arising from the collective geometric interaction among neighboring unit cells at (001) plane and structural restoration reinforced self-repairing reactions (Fig. 5d and Supplementary Fig. 11). This point is further validated by calculating the serial partial pair distribution functions (pPDFs) of Hf–O bonds among supercell trajectories collected during the simulated self-repairing process. It is observed that the (001) in-plane pPDF profile becomes more intensive and sharper prior to the pPDF profile of the long axis (i.e., [001] axis) in the octahedral crystal structure, which confirms the faster restoration of in-plane structural order of the UiO-66 framework (Fig. 5b). The total pPDFs profile from 0 to 11 ps is shown in Supplementary Fig. 12. Taken together, combined molecular-level experimental observation and theoretical simulation have elaborated a nonclassical reversible radiolysis mechanism that is dictated by the concurrent structural damage and healing events as mutually reversible reactions. These phenomena involve the spontaneous self-repairing events of partially detached and displaced BDC linkers, which further explain the observed dynamic crystalline-to-amorphous interconversion. The forward and reverse reactions both conform to first-order kinetics, thereby maintaining the classical exponential decay model of radiolysis kinetics. This model effectively describes the changes in trackable features, such as the intensities of Bragg spots in ED patterns (Fig. 2a, b). Based on these kinetic aspects, the self-repairing reactions, dictated by the diminished amorphous domains, are observable at an elevated dose (e.g., ~Dc) because the rate of structural healing only becomes considerable when the fraction of damaged structure is substantial. Moreover, the anisotropic structural healing rate entails the faster (001) in-plane structural recovery and thus the appearance of intermittent and mobile stripe-like amorphous domains in the HRTEM image series (Fig. 3d and Supplementary Fig. 13).

Fig. 2: The elucidation of dose-rate effects from electron diffraction and kinetic model of nonclassical reversible radiolysis.
figure 2

a Serial electron diffraction patterns collected over a [1\(\bar{1}\)0] projected UiO-66(Hf) crystal and under a dose rate of 1.0 e− Å−2 s−1. b Radially averaged electron diffraction patterns and their projections spanning along accumulated electron dose. Red rectangular region refers to the profiled Bragg reflection at Q = 2.8 nm−1. c The exponential fitting of diffraction intensity decay curve as a function of accumulated electron dose. d Dose-rate effect calculated based on the kinetic model of nonclassical reversible radiolysis, which is plotted by dimensionless parameters for critical dose (\(\widetilde{m}\)) versus dose rate (\(\widetilde{n}\)), respectively. α refers to a dimensionless factor for the damage-to-repair ratio at unitary dose rate. The \(\widetilde{m}\) value scales the critical dose for classical radiolysis while the \(\widetilde{n}\) value scales the unitary dose rate.

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Fig. 3: Decoupling intergranular and intragranular deformations based on CG-SA and GPA methods.
figure 3

a Schematic illustration of intergranular and intragranular deformations of an octahedral UiO-66(Hf) crystal under electron-beam radiation. b Demonstration of CG-SA method used for evaluating intergranular deformations, where rectangular ROIs are marked for measuring their relative displacements. Red and blue solid rectangles refer to original and displaced two crystalline ROIs connected by a predefined basis vector (solid red arrow). The displacement vectors are denoted by solid blue arrows. The auxiliary ROI and vectors are denoted by dashed rectangle and arrows to form a vector triangle that allows the determination of the deformation vector (solid yellow arrow). The predefined orthogonal x and y basis vectors are based on [110] and [001] axes respectively. c The evolutions of εxx [110], εyy [001], and εxy strain components for anisotropic deformation of UiO-66(Hf) crystals under different accumulated electron dose derived by CG-SA. d The evolution of εyy [001] strain component for intragranular deformations in UiO-66(Hf) crystals derived by GPA and rendered in temperature color code. The reference region for GPA analysis is marked by a white square.

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Fig. 4: Direct observation of molecular-level recrystallization process.
figure 4

a Serial HRTEM images of UiO-66(Hf) crystals along the [1\(\bar{1}\)0] projection, after correcting CTF effects, under increasing accumulated electron dose in vacuum. b–e Magnified views of ROIs marked by white, yellow, blue, and green dashed rectangles in (a), accompanied by schematic illustrations of the structural models. The HRTEM images are rendered in a black-body false-color code. Blue represents the Hf6O4(OH)4 nodes, red indicates BDC linkers with broken bonds, and yellow indicates pristine BDC linkers.

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Fig. 5: Simulated cascade self-repairing steps dictated by nonclassical reversible radiolysis based on AIMD method.
figure 5

a The simplified representation of structural models with multiple broken Hf–O bonds between BDC linkers and Hf6O4(OH)4 nodes and viewed along the [001] projection. The red rectangles refer to broken BDC linkers that undergo cascade self-repairing steps, the rest BDC linkers are denoted as yellow rectangles, and the blue square refers to Hf6O4(OH)4 nodes. b Time-dependent evolution of pPDFs for Hf–O pairs in serial trajectories simulated by AIMD. (left panel) pPDF profiles at (001) equatorial plane; (right panel) pPDF profiles along [001] direction. c The evolution of critical dose with different dose rates. The error bars are standard deviations. d The serial trajectories evolved during cascade self-repairing process. The recovery sequence of BDC linkers is numbered.

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The classical and nonclassical radiolysis mechanisms and their associated kinetic models can be explicitly compared. A quantitative expression for the irreversible damage model that dictates the classical radiolysis can be deduced as follows:

$${{{r}}}_{{{\rm{c}}}}=-\frac{{{\rm{d}}}{{{N}}}_{{{\rm{c}}}}}{{{\rm{d}}}{{t}}}={{{k}}}_{{{\rm{D}}}}{{{N}}}_{{{\rm{c}}}}$$
(1)
$${{{k}}}_{{{\rm{D}}}}{{t}}={\mathrm{ln}}\left(\frac{{{{I}}}_{0}}{{{{I}}}_{{{\rm{t}}}}}\right)$$
(2)

where rc, kD, and Nc refer to reaction rate, rate constant of structural damage, and number density of remnant crystalline domains. The Dc value is obtained by the point at which the intensity (It) of a specific Bragg spot diminishes to \(1/{{{e}}}^{-}\) (\({{{e}}}^{-}\) is the electronic charge) of its original intensity (I0). The kD dictates the rate of radiolytic damage events and equals to the damage cross-section for radiolysis (σr) times the beam flux (Φd), and is thus monotonic to the dose rate (Rd).

$${k}_{D}={\sigma }_{r}{\Phi }_{d}=\frac{{\sigma }_{r}{R}_{d}}{{e}^{-}}$$
(3)

Accordingly, the Dc for classical radiolytic damage that adopts irreversible first-order kinetic model can be properly expressed as \({{{\rm{e}}}}^{-}/{{{\rm{\sigma }}}}_{{{\rm{r}}}}\)1 and validates the linear dose-rate effect. In contrast, the nonclassical reversible radiolysis mechanism operates according to reversible first-order kinetics, with the net damage being influenced by the cumulative effect of structural damage surpassing the repair processes. The rate constants for structural damage (kD) and repair (kR) play a critical role in determining the overall outcome. By including the reverse reaction term (i.e., self-repairing events) and the number density of amorphized domains (Na), we will then have

$${{{r}}}_{{{\rm{c}}}}=-\frac{{{\rm{d}}}{{{N}}}_{{{\rm{c}}}}}{{{\rm{d}}}{{t}}}={{{k}}}_{{{\rm{D}}}}{{{N}}}_{{{\rm{c}}}}-{{{k}}}_{{{\rm{R}}}}{{{N}}}_{{{\rm{a}}}}$$
(4)
$$({{k}}_{{{\rm{D}}}}+{{{k}}}_{{{\rm{R}}}}){{t}}={\mathrm{ln}}\left(\frac{{{{I}}}_{0}-{{{I}}}_{{{\rm{e}}}}}{{{{I}}}_{{{\rm{t}}}}-{{{I}}}_{{{\rm{e}}}}}\right)$$
(5)

where a steady-state intensity of Bragg spot (Ie) and ED pattern arising from the remnant crystalline domains at equilibrium are expected. The fraction of steady-state crystalline domains (i.e., Nc/(Na + Nc) \(\propto\) Ie), can be evaluated based on the following equation,

$$\frac{{{{k}}}_{{{\rm{D}}}}}{{{{k}}}_{{{\rm{R}}}}}=\frac{{{{N}}}_{{{\rm{a}}}}}{{{{N}}}_{{{\rm{c}}}}}=\frac{{{{I}}}_{0}-{{{I}}}_{{{\rm{e}}}}}{{{{I}}}_{{{\rm{e}}}}}$$
(6)

and a lower fraction of crystalline domains is anticipated at an elevated dose rate (i.e., \({{{k}}}_{{{\rm{D}}}}\propto \,{{{R}}}_{{{\rm{d}}}}\)). The establishment of a steady state arises from the delicate balance between structural damage and self-repairing processes, constrained within specific temporal and spatial domains corresponding to the degree of structural damage. Achieving complete structural recovery in MOFs through self-repair processes necessitates the presence of well-preserved scaffolds that facilitate the precise reconnection of displaced linkers or nodes. Conversely, higher levels of structural damage often result in molecular misalignment and erroneous linkages, deviating from the ideal crystal structures. Similar phenomena can be observed in the radiolytic cross-linking of polymers under electron-beam radiation60. By defining the damage rate constant and damage-to-repair ratio at unitary dose rate (R0 = Rd/\(\widetilde{n}\), \(\widetilde{n}\) is a dimensionless scale factor for dose rate) as \({{{k}}}_{{{\rm{D}}}}^{{\prime} }\) and \(\alpha\), we will have \({{{k}}}_{{{\rm{D}}}}=\widetilde{n}{{{k}}}_{{{\rm{D}}}}^{{\prime} }\) and \(\alpha={k}_{D}^{{\prime} }/{{{k}}}_{{{\rm{R}}}}\). The critical dose for nonclassical reversible radiolysis (\({{{D}}}_{{{\rm{c}}}}^{{\prime} }\)) dictated by a dimensionless factor of \(\widetilde{m}\) scaled from that of classical irreversible radiolysis (i.e., \({{{D}}}_{{{\rm{c}}}}^{{\prime} }=\widetilde{m}{{{D}}}_{{{\rm{c}}}}\)), can be measured under the \({{{I}}}_{{{\rm{t}}}}={{{I}}}_{0}/{{{e}}}^{-}\) condition of a high-order Bragg spot as well but based on the following equation considering the self-repairing events.

$${\widetilde{{\rm{m}}}}={{\mathrm{ln}}}{\left(\frac{{\rm{e}}}{1-\frac{{{\rm{e}}}-1} { {{\alpha}} {\tilde{{\rm{n}}}}}} \right)}^{\frac{1}{ {1}+\frac{1}{ {\alpha} \tilde{{\rm{n}}}}}}$$
(7)

Where e is a natural logarithm (e ≈ 2.718). Accordingly, we are able to quantify the dose-rate effects of nonclassical reversible radiolysis with respect to different damage-to-repair ratios based on these dimensionless parameters (Fig. 2d). It is thus predicted that reversible radiolysis adopts a direct dose-rate effect and elevated critical dose than that of classical radiolysis (i.e., \(\widetilde{m}\) > 1). Intuitively, enhanced self-repairing rate leads to decreased α and increased \(\widetilde{m}\) values, indicating elevated beam resistance against radiolytic damage. For materials with significantly high structural recovery rate (i.e., a small α value), a dose-rate threshold may appear as shown in Fig. 2d, below which the net radiolytic damage becomes negligible. This nonclassical reversible radiolysis model offers an alternative interpretation for the existence of a dose-rate threshold, distinct from the induced electric field model proposed for metal oxides8.

Based on these kinetic considerations, there are two major discrepancies between classical and nonclassical radiolysis models that can be experimentally validated. Firstly, classical radiolysis mechanism follows irreversible first-order kinetics with the critical dose or damage per dose independent of dose rate (i.e., a linear dose-rate effect). On the contrary, the nonclassical reversible radiolysis features a direct dose-rate effect albeit the adherence of first-order kinetics as well. As a result, the critical dose decreases and damage per dose increases as the dose rate elevates. We indeed observe this direct dose-rate effect by measuring the dose rate dependent Dc values on UiO-66(Hf) crystals (Fig. 5c and Supplementary Fig. 14), which decreases from 81.7 to 20.5 e− Å−2 when the dose rate increases from 0.2 to 2.0 e− Å−2 s−1. Secondly, unlike the classical radiolysis model, the reversible kinetics for nonclassical radiolysis would eventually reach a steady state dictated by the presence of fractional crystalline domains that are measurable by ED. Based on Eq. (7), increased dose rate is expected to result in higher kD and lower fraction of remnant crystalline MOFs at steady state. To validate this point, we conducted observations of distinct steady-state crystal diffraction patterns for UiO-66(Hf) crystals that are exposed to varying dose rates. Lower dose rate results in greater fraction of remnant crystalline matters at equilibrium state and leads to better preservation of Bragg spots in ED patterns (Supplementary Fig. 15). We further conduct in situ low-dose HRTEM imaging to investigate the structural dynamics associated with recrystallization under a programmed dose rate procedure. A UiO-66(Hf) MOF crystal is initially radiated by electron beam at a dose rate of 3 e− Å−2 s−1 for 20 s, followed by a lower dose rate of 1 e− Å−2 s−1 for 32 s. Serial Bragg-filtered HRTEM images, as shown in Supplementary Fig. 16, reveal that a local crystalline ___domain becomes fractionally amorphized once the accumulated electron dose exceeds the critical dose of 30.3 e− Å−. The size, shape, and spatial distribution of the amorphous domains vary with radiation, indicating an ongoing dynamic recrystallization process. Notably, we observed a significant acceleration in the recrystallization rate immediately after switching the dose rate from 3 to 1 e− Å−2 s−1. This acceleration results from the marked reduction in damage rate corresponding to the decreased dose rate, facilitating a more rapid structural recovery of the amorphized domains alongside the reemergence of crystalline regions. After an accumulated dose of 92 e− Å−2 under continuous low-dose-rate beam radiation, a substantial fraction of the amorphized domains fully recrystallized, as illustrated in Supplementary Fig. 16. Generally, the nonclassical radiolysis mechanism elaborated here features reformation of metal-ligand chemical bonds broken by ionization under “dark” condition. A similar phenomenon has been observed in the radiolysis of polymers, where cross-linking occurs instead of self-repairing after bond breakage60. The disparity in bond reformation observed between these two types of materials can be attributed to the presence or absence of geometric constraints offered by a crystalline framework, as seen in MOFs instead of in polymers.

An intriguing approach to control the bond reformation, so as to regulate the MOFs recrystallization process, can be achieved by introducing hydrogen atmosphere in an environmental transmission electron microscope (ETEM) as shown in Fig. 6a. By further integrating low-dose EM, we can simultaneously monitor structural dynamics in response to beam radiation and the gas environment. Hydrogen molecules, as a well-known radical scavenger61, effectively terminate the dangling bonds generated by bond ionization, significantly inhibiting self-repairing processes and bond reformation as shown in Fig. 6b. Consequently, the damage-to-repair ratio of reversible radiolysis is markedly increased, resulting in a reduced critical dose for UiO-66(Hf) crystals in a hydrogen environment at different pressures compared to vacuum (i.e., decreasing from 30.3 e− Å−2 in vacuum to 19.8 e− Å−2 at 5 mbar and 16.4 e− Å−2 at 10 mbar of hydrogen, as shown in Supplementary Fig. 17). We conducted in situ low-dose HRTEM imaging of the structural dynamics of MOF crystals in response to the hydrogen atmosphere. The series of HRTEM images reveal that crystalline-to-amorphous interconversion process under a hydrogen atmosphere is dramatically altered compared to that in vacuum (Fig. 6c, Supplementary Figs. 13 and 18). This phenomenon is clearly visualized through the evolution of the spatial distribution of crystalline domains in the HRTEM images. In contrast to the intermittent and mobile stripe-like amorphous domains generated by anisotropic structural recovery in vacuum (Supplementary Fig. 13), the inhibition of self-repairing processes in the hydrogen environment leads to widespread localized amorphous domains that grow rapidly and interconnect under continuous illumination (Fig. 6c and Supplementary Fig. 18). These observations correspond to a reduced crystalline-to-amorphous interconversion in hydrogen, resulting in modified kinetics that favor more irreversible structural damage. This ultimately leads to a steady-state structure characterized by a smaller quantity of remnant crystalline domains and further degraded Bragg spots compared to those observed in vacuum (Supplementary Fig. 19). To further unravel the mechanism of recrystallization process under hydrogen atmosphere, we conducted AIMD simulations of UiO-66(Hf) structures with hydrogen molecules loaded in the unit cell (Supplementary Fig. 20). The dynamic process reached equilibrium, as indicated by the evolution of the potential energy profile shown in Supplementary Fig. 21. Serial snapshots of the trajectories reveal that the introduction of hydrogen molecules as radical scavengers significantly retards the recrystallization processes of UiO-66(Hf) by terminating broken bonds before they can reform. The trajectories involving geometries with hydrogen-terminated and detached BDC linkers are clearly visualized in Supplementary Fig. 22. The dynamic structural evolution can be quantitatively described by the pPDFs of O–H and Hf–O pairs among the trajectories collected during the recrystallization process (Supplementary Fig. 23a, b). Comparing snapshots at 0 and 11 ps, we observe the emergence of a correlation peak centered at ~1.0 Å for H–O pairs, indicating the formation of H–O bonds, while the weakened correlation peak at around 2.2 Å for Hf–O pairs suggests inhibited formation of Hf–O bonds and decreased structural order. These observations stem from the hydrogen termination of partially detached BDC linkers and the enhanced structural distortion due to inhibited reformation of metal-linker bonds. Taken together, the findings not only validate the proposed nonclassical mechanism and its associated kinetic model but also introduce a regulatory strategy based on a previously unexplored physical parameter.

Fig. 6: Regulation of nonclassical reversible radiolysis by introducing hydrogen atmosphere in environmental transmission electron microscope.
figure 6

a The schematic of a dedicated ETEM equipped with a differential pumping vacuum system. b The schematic illustration of bond ionization followed by either inhibited or facilitated self-repairing events in hydrogen environment and vacuum respectively. The R* radical refers to O (red color) radical. c The dose series HRTEM images of the UiO-66(Hf) crystal in hydrogen atmosphere with a pressure of 5 mbar. The lattice contrast is enhanced by Bragg filtering. The crystalline-to-amorphous domains are rendered in a purple-blue-green false-color code.

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Another notable radiation damage beyond amorphization lies in the enhanced lattice deformation of crystalline domains at elevated electron dose of 64.7 e− Å−2 according to the strain analysis (Fig. 3d). By analyzing an enlarged view of serial HRTEM images collected from a local crystalline ___domain and correcting for contrast inversion effects (Fig. 7), we observed the disappearance of dark contrast at the short diagonals of the rhombic-shaped lattice in the UiO-66(Hf) crystal at an accumulated dose exceeding 64.7 e− Å−2 (Fig. 7a, c). This observation aligns with results obtained from molecular-resolution imaging (Fig. 4). This observation is attributed to the site-specific absence of the bridging BDC linker at the short diagonal site of the rhombic-shaped lattice projection, while linkers at other symmetry-equivalent sites remain intact (Fig. 7b, d). This symmetry-breaking behavior is discernible through real-space imaging rather than diffraction and likely results from anisotropic strain evolution, as revealed by GPA analysis (Fig. 3d). However, the site-specific linker absence does not correlate with radiolytic damage, as anisotropic strain alone would not induce site-specific bond ionization within the UiO-66(Hf) framework. This is supported by evaluating the evolution of the highest occupied molecular orbital (HOMO), which is closely related to bond ionization probability and susceptibility to radiolytic damage, under both strained and unstrained conditions (Fig. 8a and Supplementary Fig. 24). Specifically, the HOMO frontier states, which are primarily composed of Hf–O bonded states localized at the Hf6O4(OH)4 nodes and characterized by overlapping Hf 3d and O 2p states (Fig. 8c, d and Supplementary Fig. 25), show minimal impact from anisotropic lattice contraction, as illustrated in Supplementary Fig. 24. This suggests that the Hf–O covalent bonds within the Hf6O4(OH)4 node may also be susceptible to radiolytic breakage, contributing to structural deformation and amorphization upon beam radiation, as validated by AIMD simulation and pPDFs analysis (Supplementary Fig. 26). Instead, such an anisotropic [001] lattice contraction would however induce lattice expansion at the (001) equatorial plane of the octahedral crystal due to the inherent positive Poisson’s ratio of the UiO-66(Hf) structure (Fig. 8b and Supplementary Table 1). This effect further contributes to the radiation-induced anisotropic lattice deformation of UiO-66(Hf), and more importantly, significantly weakens the chemical bonding of bridging BDC linker at the diagonal site to the rhombic-shaped lattice of projected UiO-66(Hf) framework. The evolution of binding energy for the bridging BDC linker at (001) equatorial plane of the UiO-66 structure can be quantitatively evaluated, which decreases monotonically as the magnitude of [001] lattice contraction increases and bond length of local Hf–O moieties at (001) equatorial plane increases from 2.18 to 2.40 Å (Fig. 8e). Such structural evolution may be directly linked to the knock-on displacement or surface sputtering events, because the binding energy is related with the displacement threshold of atoms and thus the cross-section of knock-on damage62. The probabilities for knock-on damage arising from events such as generation of Frenkel pairs, vacancy-enhanced displacement and surface sputtering63,64,65, can be quantitatively evaluated by integrating the Mott cross-section for an elastic collision (see Supplementary Methods section 1.2.2).

Fig. 7: Real-space visualization of site-specific ligand knockout events in UiO-66(Hf).
figure 7

a, c Serial HRTEM images (upper) and enlarged regions (bottom) after correcting contrast inversion effects and taken under increasing accumulated electron dose over a UiO-66(Hf) crystal along the [1\(\bar{1}\)0] projection. The green circles denote the presence and absence of a BDC linker at an identical linker site under an electron dose of 8.0 e− Å−2 and 64.7 e− Å−2. b, d The structural models (left panels) and simulated projected potentials (right panels) for pristine and defective UiO-66(Hf) structures projected along the [1\(\bar{1}\)0] projection. The insets refer to corresponding contrast-corrected experimental HRTEM image motifs rendered in black-body color code.

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Fig. 8: Theoretical calculation of strain-dependent electronic structures and binding energies for radiolysis-enhanced knock-on displacement in UiO-66(Hf).
figure 8

a The visualization of model-embedded HOMO orbitals for both unstrained and −15% strained UiO-66(Hf) structures along the [001] direction. b The relationship between Poisson’s ratio and magnitude of lattice expansion at the (001) equatorial plane. The calculated PDOS profiles of BDC linkers and Hf–O bonding sites between BDC linkers and Hf6O4(OH)4 nodes for c unstrained and d strained UiO-66(Hf) structures (i.e., −5%, −10%, and −15% strain along [001] direction). e The strain-dependent Hf–O binding energy of a BDC linker at the bridging site of a UiO-66(Hf) structure. f The calculated knock-on cross-section for O sites of BDC linkers bonded to the Hf6O4(OH)4 nodes, as a function of incident-electron energy under different Ed values.

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The incidence energy dependent cross sections of knock-on damage for both O and Hf atoms are presented in Fig. 8f and Supplementary Fig. 27. The threshold incidence energy (\({{{E}}}_{{\rm{Th}}}\)), defined by the critical incidence energy that initiates knock-on displacement, increases monotonically both with the atomic mass and Ed value as shown in Supplementary Fig. 28. As a result, the \({{{E}}}_{{\rm{Th}}}\) value increases from 17 keV to over 150 keV as the atomic mass goes up from O to Hf atoms. The calculated cross-section of knock-on damage σK reaches maximum near the threshold incidence energy region and increases dramatically as the Ed value decreases (Fig. 8f and Supplementary Table 2). Accordingly, the introduction of specific binding energy at atomic sites by anisotropic lattice contraction entails rather different Ed and thus σK values for these sites. As a result, the probability of knock-on damage at the O site of bridging BDC linker bonded to the Hf site of Hf6O4(OH)4 node increases significantly as the binding energy of the bridging linker decreases from 7.77 to 2.43 eV at a larger [001] lattice contraction of 5%, which results in lowered Ed values and increased σK from 117 to 958 barn. The enhanced displacement of O sites easily breaks the node-linker Hf–O bonds and results in the observed site-specific knockout of bridging BDC linkers while maintaining the overall crystallinity of the UiO-66 framework. Taken together, the generation of site-specific missing linker defects can be attributed to secondary beam damage events, which can be attributed by nature the knock-on displacement mechanism but more properly defined as a secondary damage mechanism namely radiolysis-enhanced knock-on displacement (Fig. 1). Such a nonclassical damage mechanism deviates from primary damage mechanisms like radiolysis or knock-on displacement, and instead represents a combined effect resulting from the interplay between these mechanisms, mediated by structural deformations. The mechanism can be further validated by evaluating the temperature-dependent beam damage behaviors of UiO-66(Hf), as radiolysis and knock-on displacement exhibit distinct temperature dependence20,66. Figure 9a, b illustrates the cryogenic electron microscopy (cryo-EM) imaging processes and cryogenic transfer method. Imaging beam-sensitive materials (e.g., MOFs) under low temperature down to cryogenic condition using cryo-EM has been widely acknowledged to minimize radiolysis due to the diminished thermal vibration that converts long-lived electronic excitations to momentum. However, the measured Dc value for UiO-66(Hf) at a dose rate of 1.0 e− Å−2 s−1 does not increase monotonically as the temperature decreases (Fig. 9f and Supplementary Fig. 29), which varies from 30.3 to 77.8 e− Å−2 and a maximum Dc value is reached at −50 °C instead of LN2 temperature. This allows the imaging of UiO-66(Hf) framework at an elevated electron dose with structural integrity through well-developed low-dose imaging methodology21,48. Imaging at −50 °C and under an electron dose of 77.8 e− Å−2 well preserves the crystal lattice of UiO-66(Hf) in contrast to images taken at either higher or lower temperature (Fig. 9e), but with most bridging BDC linkers knocked out as viewed along the [1\(\bar{1}\)0] projection. It is well conceivable that the structural integrity of UiO-66(Hf) should be maintained under an electron dose below Dc at −50 °C, provided radiolysis dominates the beam damage. Notwithstanding this, the knock-on displacement mechanism remains largely unaffected by temperature67. It already exhibits significance in the site-specific sputtering of bridging BDC linkers in UiO-66(Hf), as demonstrated by room temperature imaging results, under an electron dose of 64.7 e− Å−2, as depicted in Fig. 9c, d. Accordingly, the site-specific formation of missing linker defects in UiO-66(Hf) under electron-beam radiation has been proved to follow the nonclassical radiolysis-enhanced knock-on displacement mechanism.

Fig. 9: Low-dose cryogenic HRTEM imaging and low-temperature radiation damage in UiO-66(Hf).
figure 9

Schematic illustrations of a the electron optical system in an electron microscope. b cryogenic specimen transfer and imaging process for beam-sensitive materials at multiple temperature points by employing a custom-designed ultra-stable double-tilt cryo-transfer TEM holder. The structural models (left) and the contrast-corrected HRTEM image motifs (right) for c pristine and d defective UiO-66(Hf) structures. e Contrast-corrected HRTEM images of UiO-66(Hf) taken along the [1\(\bar{1}\)0] projection and at −196 °C, −50 °C, and 25 °C. Insets denote corresponding FFT patterns with their respective information transfer marked. f The measured critical doses at different temperatures under a dose rate of 1.0 e− Å−2 s−1. The error bars are standard deviations.

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In this study, we utilized low-dose EM to uncover the nonclassical mechanisms of electron-beam radiation damage in open-framework materials. Through real-space visualization, we observed radiation-induced structural dynamics at the morphological, lattice, and molecular levels within a MOF structure. In addition to the classical beam damage mechanisms, we propose the existence of reversible radiolysis and radiolysis-enhanced knock-on displacement as secondary damage mechanisms. By developing physical, kinetic models and regulation strategy associated with these nonclassical mechanisms, we were able to accurately identify and predict exotic beam damage events and phenomena. These include the direct dose-rate effect, crystalline-to-amorphous interconversion, and site-specific ligand knockout. These insights significantly enhance our fundamental understanding of the underlying physics of electron-matter interactions, the chemistry of radiation-induced structural dynamics, and the unbiased interpretation of pristine structural information independent of beam effects. Moreover, our findings have the potential to inspire the development of new methodologies and techniques in the fields of electron-beam lithography and EM. These areas often require precise and logic-based control of radiation damage across diverse materials.

Methods

Low-dose (cryogenic) TEM imaging and data processing

The low-dose HRTEM image stacks were acquired using an objective aberration-corrected TFS Themis ETEM equipped with Gatan K3 direct detection camera. The specific experimental setup is as follows: an acceleration voltage of 300 KV and a maximum frame rate of 400 fps at an extremely low electron dose rate (usually below 1 e− Å−2 s−1). Before acquisition, the specimens were searched, tilted to zone axis for optimal crystal structure information retrieval using our reported low-dose imaging procedures19 with a minimal dose consumption below 1 e− Å−2. Following the image stack acquisition, the dataset was subject to a motion correction procedure to fully restore high-frequency information. The motion-corrected image stack was then subject to a contrast-transfer-function (CTF) correction procedure19 to achieve chemically interpretable image. Low-dose cryo-EM was conducted by a Gatan custom-designed double-tilt ultra-stable cryo-transfer holder to investigate the low-temperature effects on radiation damage behaviors. To better distinguish crystalline and amorphous domains, the lattice contrast of the serial HRTEM images is enhanced by Bragg filtering through masking the Bragg spots. Amplification of these high-frequency components relative to the rest of the information has been conducted to better visualize the spatial distribution of crystalline domains.

Electron diffraction acquisition and data processing

ED patterns and dose series were acquired in diffraction mode by using Gatan OneView camera on a TFS ETEM. The acquisition parameters were adjusted upon required cumulative dose and dose rate.

The dataset of ED dose series can be transformed to visualize the fading dynamics of Bragg spots and mapped onto the axes for cumulative dose and reciprocal vector, respectively, through the following steps: (i) the acquisition of the ED dose series; (ii) the correction of drift in the stack; (iii) the radial averaging of diffraction patterns within the stack; and (iv) the creation of a 1D projection of the diffraction pattern, spanning along the stack direction to accumulate the electron dose. The fading dynamics of a specific Bragg spot can be profiled and then fitted by the exponential decay function to derive the Dc value.

Theoretical calculations

The details of DFT calculations and AIMD simulation methods were provided in Supplementary Methods section 1.3.