Introduction

Symmetry in crystalline solids plays a critical role in determining their physical properties. Breaking of symmetry has been shown to impart exotic properties in inorganic materials, like increased ferroelectricity1, unconventional superconductivity2, and ultralow thermal conductivity3. Most symmetry-breaking events reported in literature are spontaneous, whereby an initially symmetric system becomes asymmetric during a spontaneous process like crystallization4 or a phase transition5. The other possibility, where the asymmetry is introduced explicitly through electric fields, optical excitations or mechanical strain, is more challenging to adapt6. Hence, to date, the potential implications of symmetry breaking, particularly in the context of molecular materials, remain poorly investigated.

Organic molecular crystals offer unique advantages like easy solution processing, long-range order, extensive functionalization possibilities and generally good biocompatibility, but their utility in devices is currently very limited as they are frequently prone to vertical stress-induced mechanical failure, cracks and abrupt reduction in performance at times7. Imparting self-healing ability can be a promising way to improve the mechanical robustness of molecular crystals, as this can help in repairing any eventual mechanical damage8. However, currently there is a lack of understanding of the underlying mechanisms and the factors that promote self-healing in crystalline materials, making it extremely challenging to design this property in building sustainable devices. Currently known self-healing approaches rely primarily on some form of external stimuli such as local heating9, aqueous media10, light11, compressive forces12 or combinations of them13 to trigger the healing process. This greatly limits their use, particularly in applications where external intervention is undesirable or impossible. To enable autonomous self-healing, typical strategies utilized in polymers, hydrogels and composites make use of either cross-linking14 or healing agents which are released in a controlled manner15,16 to repair the damaged areas. Such techniques prove inadequate for employing in crystalline materials, where reestablishing the complete long-range order at the molecular level is imperative for maintaining structural integrity. Most research on crystalline hard materials has been confined to the healing of minute cracks at the nanoscale17,18. A few molecular crystals relying on mechanical softness and dynamic bonding have also been reported in recent years to show self-repairing capability12,19,20,21. Certain non-centrosymmetric crystals possessing polar structures and inherent piezoelectricity are reported to self-heal via electrostatic surface charge-based actuation22,23. Given the immense potential of molecular materials in various miniaturized devices24, there is an urgent need to identify the inherent mechanisms that promote self-healing, so that this exotic phenomenon can be better understood and designed to a much broader set of crystals, not restricted by symmetry considerations.

Herein, we report a centrosymmetric crystal that exhibits reversible, mechanically induced symmetry-breaking, leading to ultrafast self-healing of large cracks (Supplementary Table 1 and Supplementary Note 1). The molecular crystal of 2-methyl-4-nitroimidazole (MNI), featuring a layered architecture analogous to 2D van der Waals materials1, develops macro-cracks parallel to its layers that undergo instantaneous autonomous self-healing (Supplementary Video 1). The self-healing crystals have an elastic modulus of 13.3 ± 0.5 GPa on their major face, overcoming the trade-off between healing ability and inherent stiffness (Supplementary Table 2). Successful self-repair is characterized by high-resolution scanning electron microscopy (SEM), atomic force microscopy (AFM) and single-crystal X-ray diffraction experiments, indicating an excellent efficiency with respect to crystallinity. Raman spectroscopic mapping and second-harmonic (SH) imaging techniques unambiguously confirm that mechanical stress can lead to local symmetry breaking, indicating its role in subsequent self-healing. In-depth analysis from the lens of fracture mechanics provides some fundamental understanding of the mechanism of crack propagation and its arrest, which is correlated with the underlying crystal structure. Our study elucidates a correlation between strain, structure and symmetry (Supplementary Fig. 1), demonstrating that the paths to self-healing are many and are yet to be discovered.

Results

Evaluation of fast self-healing under mechanical stress

Single crystals of MNI grown as large plates ( ~ 5 mm × ~2 mm × ~100 µm size; Supplementary Fig. 2) were investigated for their self-healing behavior by application of vertical as well as lateral loads and their real-time responses recorded under a stereomicroscope, integrated with a high-speed imaging capability (see Supplementary Videos 2 and 3 and Supplementary Fig. 3). A vertical mechanical stress on the (010) crystal face using a metal pin initiates a hairline fracture propagating from the point of stress, hereafter the defect point. From a defect point, the crack propagates in the form of a linear elliptical crack under external stress (Fig.1a–c). When the applied force is removed, the crack growth halts and begins to close autonomously via reverse propagation towards the defect point, leading to a rapid self-healing event (Fig. 1c). No external compression is required to facilitate the healing process. For instance, a crack of length ≈336 µm could repair itself autonomously in an ultrafast timescale of four milliseconds (Supplementary Fig. 3), which is impressive considering that the crack spreads approximately 90% of the entire width of the crystal. The cracks generated under lateral loads on the (01\(\overline{1}\)) face of MNI crystals using a metal tweezer also heal in a similar fashion upon withdrawal of the external stress (Supplementary Fig. 4 and Supplementary Video 3).

Fig. 1: Demonstration of self-healing behavior in MNI.
Fig. 1: Demonstration of self-healing behavior in MNI.
Full size image

a A batch of single crystals of MNI. The inset shows the molecular structure of MNI. b Schematic of autonomous self-healing of an MNI single crystal. c Video grabs of a self-healing event under vertical stress applied with a metal needle on the (010) face of a crystal. The arrow indicates the position of an applied vertical stress that initiates a crack. d SEM image of the same self-healed crystal demonstrates no sign of remnant cracks. The inset shows the fracture event of the crystal used for SEM. e Repeated healing cycles of an MNI single crystal at the same damaged site are shown along with the time required for each healing event. The black circle denotes the defect point, used as a reference for identifying the area of interest. See Supplementary Videos 1–4.

The self-repair of micron-sized cracks is examined using cross-polarized optical microscopy (Supplementary Fig. 4), SEM (Fig.1d and Supplementary Fig. 5) and AFM (Supplementary Fig. 6), which demonstrate only surface features devoid of any scars after healing. Such crack closure could be observed repeatably under cyclic loading at the same damaged area (Supplementary Video 4). Figure1e shows seven consecutive cycles of crack formation and subsequent self-repair in a single MNI crystal, where each healing cycle takes ≈4 ms. Examination of a healed region using single-crystal X-Ray diffraction (SCXRD) produces sharp diffraction spots, confirming single-crystalline nature in the healed region (Supplementary Fig. 7). The diffraction profile remains similar to that of an undeformed (hereafter, pristine) crystal (see Supplementary Tables 3 and 4). We note that the value of mosaicity from the pristine crystal is 0.63 and that from the healed crystal is 0.85, which might be due to partial loss of intensity, indicating that the crystal healed with minimal structural degradation. Retaining a high level of crystallinity in healed regions is highly challenging, and our system with respect to these parameters is on par with the best self-healing crystals reported in literature17,18,19,20,21,22,23.

Excessive stress resulting in the propagation of cracks to either end of the crystal generally leads to permanent cracks (hereafter, fractured crystals). Such crystals with visible crack lines, show sharp but doubly split diffraction peaks (Supplementary Fig. 8). To further confirm the true nature of the cracks (gaps that extend deep into the bulk material), we experimentally examined them using AFM (Supplementary Fig. 9). The AFM topography profile of vertically strained crystals shows linearly oriented cracks that are approximately 1.5 µm in depth and 3 µm in width. Furthermore, the MNI crystals were examined using X-ray microtomography (XMT) imaging (see “Methods” and Supplementary Fig. 10). The reconstructed modeling of the three-dimensional spatial distribution of voids in the XMT image confirmed a deep visible fissure, whereas no such fissure lines can be seen in pristine and healed regions of the crystals (Supplementary Note 2).

To quantify the threshold stress for observing self-healing of cracks in our MNI crystals, we fixed a pristine sample to a support at one end and applied a uniaxial stress using a commercially available force sensor (see “Methods”). As shown in Supplementary Fig. 11, a crystal, having a thickness of 97 µm and a width of 2 mm, could self-heal from cracks formed by an external load of up to 45 mN. We also tested the crystals by mounting them on specially designed push-to-pull chips and applied a three-point bending load (see “Methods”) in a commercial indenter, Intraspect 90. Samples of thickness ranging from approximately 50 µm to 150 µm showed the ability to withstand a stress of 11.5 to 13.5 MPa before their first fracture event (see Supplementary Fig. 12). Subsequently, we quantified the self-healing efficiency (Fsh) from these mechanical tests by defining it as Fsh =  F/F0 × 100, where F0 and F represent the fracture stress of the pristine crystal and that of the healed crystal, respectively. The fracture behavior of pristine and healed samples under controlled mechanical loading is summarized in Supplementary Fig. 13, demonstrating a healing efficiency of ≈ 40% for a sample of thickness approximately 100 µm. This is impressive considering that these crystals maintain excellent crystallinity at the fractured region after the self-healing process. It is to be noted that the healing efficiency observed here is with respect to the mechanical strength of the crystals. However, these self-healing crystals maintain a higher level of crystallinity than crystals of other classes following diffusion or twinning-based healing mechanisms (see Supplementary Note 3).

Healing mechanisms observed in structural materials often involve toughening to arrest the crack propagation25. Moreover, stress dissipation in such materials occurs via crack deflection and/or crack branching26 and sometimes, the healing of microcracks is accompanied by subsequent crack resumption along a different path17. This behavior contrasts sharply with that of our MNI system, where the induced cracks propagate along a well-defined direction, usually without any deflection or branching (Supplementary Video 5 and Supplementary Fig. 14). Furthermore, healing of a crack does not subsequently lead to new cracks in a different direction. When fresh block-shaped crystals are fragmented into pieces by applying a three-point bending stress, they show a mild recombination tendency via attraction behavior (Supplementary Video 6 and Supplementary Fig. 15). Understandably, the actuation in these crystals is not as prominent as in the case of non-centrosymmetric piezoelectric crystals22,23,27. Hence, we can’t directly adapt the mechanisms proposed for the piezoelectric crystals22 or those with mechanical softness8, reported recently.

Correlation of fracture mechanics with crystal symmetry

According to Griffith’s theory, a crack or hairline fracture is defined as “a localized breakdown of bonds in any material initiated by a stress concentration”28. Fracture and eventual failure of a material follow three basic stages: crack initiation, crack propagation and eventual rupture (see Supplementary Note 4). To prevent rupture and enable efficient self-healing, the crack propagation has to be terminated in Stage II itself25. To investigate the fracture mechanics of the MNI system, high-resolution SEM was employed (Fig. 2a–f). Herein, application of an external compressive force using a metal pin of diameter ≈10 µm creates a defect point on the surface (Fig. 2a), essentially a highly localized stressed point28. In Stage II, the local strain manifests as ductile micro-tearing events and provides opportunity for further propagation, while the crack tip bears the ultimate strain gradient26. In most known cases, the crack will propagate with increasing widths (Fig. 2b) to cause ultimate rupture of the crystal (Fig. 2c). Perfectly sharp cracks imply infinite stress concentration, meaning a minute crack formed by any chance in an ideal brittle material will propagate infinitely, causing total rupture28. However, perfectly sharp cracks are rarely formed due to some amount of plastic deformation at the crack tip, causing blunting25. As evident from Fig. 2d–f, local yielding (plastic deformation) and stress dissipation occur at the crack tip, which arrests crack propagation in this material. Once the external load is withdrawn, the self-repairing process begins. The presence of a combination of dispersive and hydrogen-bonding interaction regions in the crystal structure of MNI seems to provide a degree of plasticity, which allows for elasto-plastic deformation at the crack tips marked by crack arrest, which is further confirmed from AFM imaging of the crack tips (Supplementary Fig. 9).

Fig. 2: Correlation of fracture mechanics with underlying microstructure in MNI crystals.
Fig. 2: Correlation of fracture mechanics with underlying microstructure in MNI crystals.
Full size image

a–f Experimental (SEM) analysis of fracture mechanics on the (010) face of a single crystal. a Application of a vertical mechanical stress on a pristine crystal using a metal pin creates a defect point, from where a microcrack is initiated. This is known as Stage I in fracture mechanics. In Stage II, there is a gradual extension of crack propagation leading to divergent cracks (b), which, if left uncontrolled, lead to catastrophic rupture (c). However, if crack propagation adapts a steady state growth (d), an elliptically shaped crack tip emerges (e), which leads to crack arrest via crack-tip plasticity (e) and consequent self-healing in MNI crystals (f). g–j Investigation of the crystal structure of MNI. g The MNI is a polar molecule with a net dipole moment, but it forms a homodimer via C(sp2)–H···O hydrogen bonding with an inversion center (yellow circle). h The MNI molecules form a 1-D chain via strong N–H···N hydrogen bonds (d/Å; θ/°: 2.07 Å, 159°). i The adjacent 1D tapes are connected on both sides by C(sp2)–H···O hydrogen bonds (2.45 Å, 155°) to form a 2D sheet. j These sheets are further stacked over one another in a ladder-like fashion by relatively weaker C(sp3)–H···O hydrogen bonds (2.52 Å, 174°), forming a hierarchical structure closely resembling a van der Waals material. The weakest bonds, which connect the molecular layers, act as sacrificial bonds whose disruption during force application leads to the generation of a crack.

To find the structural origin of the well-defined crack propagation followed by self-repair in this material, we examined the crystal structure obtained using SCXRD, which depicts a monoclinic space group P21/n (see “Methods”). The structure consists of polar imidazole molecules forming centrosymmetric dimers via C(sp2)–H···O hydrogen bonds, which are further connected by N–H···N bonds to form an extended 2D sheet (Fig. 2g–i). These 2D sheets are connected by relatively weaker C(sp3)–H···O hydrogen bonds along the (10-1) plane of the crystal (Fig. 2j). The hydrogen

bonding interactions of varying strengths constitute a 3D crystal with layered packing framework (Supplementary Fig. 16). The layers are stacked with inversion symmetry, similar to van der Waals materials like graphene or h-BN1. The layered organization of the structure is further highlighted from the total intermolecular interaction energies calculated by B3LYP DFT functional using CrystalExplorer (see “Methods” and Supplementary Fig. 17). Interestingly, the crack propagation direction in the single crystals is parallel to the 2D layers, as confirmed from crystal face indexing and Bravais–Friedel–Donnay–Harker (BFDH) morphology deduction (Supplementary Fig. 18).

To correlate the structure-property relationship of this material, we performed nanoindentation experiments on the (010) major face of MNI using a diamond probe of 150 nm radius (see “Methods” and Supplementary Fig. 19). Upon applying 3 mN load on the (010) face, microcracks appear from the edges of the indent impression (Supplementary Fig. 20a). Direction of these cracks is parallel to the 2D layers in the crystal, consistent with the cracks observed in qualitative tests. Furthermore, when the crystal is rotated by 90 degrees, the corresponding fissures and pile-up at the indent impressions also rotate by 90 degrees (Supplementary Fig. 20b). These observations confirm that the uniaxial stress generates cracks along a specific direction, i.e., parallel to the (10-1) cleavage planes, irrespective of the orientation of the tip or stress direction. The inversion center lies in between these obliquely aligned layers, forming the (10-1) plane as confirmed from crystal structure analysis (Fig. 2j). Hence, physical separation of the layers upon application of vertical stress causes interlayer bonds to be broken at the fracture interface. However, the subsurface layers immediately beneath the fracture surface will have “broken symmetry” with some distortions in the noncovalent interactions as compared to the pristine layers. Since the crack in this particular case follows an elliptical shape, there might be elastic strain too in the slightly curved surface, prompting the layers to spring back to normal, helping the self-healing. The newly created surfaces can raise the potential energy of the system, which can act as an additional driving force for crack closure, similar to the healing of enamel nanocrystals29.

Activation of new Raman modes by symmetry breaking

Theoretical Raman mode assignment reports Cs symmetry of the MNI molecule, consisting of 45 fundamental vibrations, active in both infrared (IR) and Raman spectroscopy30. Experimental Raman spectra were collected from pristine as well as fractured regions of an MNI crystal and compared to reveal distinct differences (see “Methods”). Pristine crystal has two prominent peaks centered at 820 cm-1 and 703 cm-1 (Fig. 3a). Traversing via a line-profile from pristine—crack—pristine area along [100] reveals emergence of two new modes at 826 cm-1 and 696 cm-1 adjacent to their corresponding parent peaks (Fig. 3b). The additional Raman modes observed from fractured zones are absent from the adjoining undeformed areas (full Raman spectra in Supplementary Fig. 21). To reveal the differences across strained vs unstrained regions on the crystal, we performed Raman spectral mapping on the tip of a vertically induced crack by selecting 120 x–y points in the form of an area map (Fig. 3c–g). Figure 3d, f shows the spatial variation of 696 cm-1 and 826 cm-1 modes, respectively, in and around the position of the crack tip. These additional modes are restricted only to the deformed regions, with the highest intensity being at the center of the crack. Crack tips, irrespective of the symmetry of the system, are known to bear the ultimate strain gradients that a material can withstand31. A similar Raman map over the same crack tip for the 703 cm-1 and 820 cm-1 peaks (Fig. 3e,g) reveals saturated intensities at all x–y positions, confirming the uniform distribution of the parent modes both in and around the fractured zones (Supplementary Figs. 22–25).

Fig. 3: Probing symmetry breaking using Raman micro-spectrometry.
Fig. 3: Probing symmetry breaking using Raman micro-spectrometry.
Full size image

a The Raman spectra of interest from 650 cm-1 to 850 cm-1 collected from the pristine surface (blue curve) overlayed on that of the fractured surface (pink curve), depicting two additional modes at 696 cm-1 and 826 cm-1, which are absent in the pristine region. b Line-profile Raman spectra obtained by traversing across a crack junction (inset) show a gradual evolution of the additional modes on approaching the crack, which gradually diminish on moving away from the crack. c–g Normalized spatially resolved Raman mapping on a crack tip (c). Raman map of the new modes d at 696 cm-1 and f at 826 cm-1 shows distinct differences in spatial intensity from their corresponding parent peaks e at 703 cm-1 and g at 820 cm-1, respectively. While the whole area in and around the crack tip is populated with the parent modes, the new modes under normalization appear restricted only up to the crack tips.

The new modes appearing in the fractured regions (Supplementary Fig. 26) are indicative of local strain arising out of vertical mechanical stress on the crystal lattice, which is absent in surrounding pristine regions32. Emergence of new Raman modes is widely reported to give direct evidence for the breaking of centrosymmetry in 2D layered structures like graphene33 and MoTe234, where the presence of an inversion center in the layer leads to in-plane shear modes being Raman inactive; however, when the crystal structure does not hold inversion symmetry, these modes become both Raman and IR active and begin to surface in Raman spectroscopy (Supplementary Note 5)34.

Role of symmetry breaking in self-healing

The symmetry-breaking effect and its role in the subsequent self-healing event were further probed by studying the non-linear susceptibilities of pristine, fractured, and healed crystals (see “Methods” and Supplementary Fig. 27 for experimental setup). Optical second harmonic (SH) generation is the final word on tracing any point-symmetry violation through micron-scale variations in SH intensity35,36,37. Figure 4a shows the schematic of the SH generation experiment, where an input femtosecond-pulsed laser centered at 800 nm is incident over a 250 × 250 μm area on the (010) crystal surface. SCXRD experiments undisputedly show the presence of a center of inversion in between the stacked layers in bulk MNI crystals (Fig.4b). Under the influence of mechanical stress, local interlayer interactions predominantly disrupt, leading to dangling bonds and the inversion symmetry lying in between them gets broken (Fig.4b). However, the intra-layer interactions, which are relatively stronger, remain intact, which prevents the overall crystal structure from collapsing. This is essential for allowing bonds to reform and for beginning the healing process.

Fig. 4: Local inversion symmetry breaking in parent centrosymmetric MNI crystal.
Fig. 4: Local inversion symmetry breaking in parent centrosymmetric MNI crystal.
Full size image

a Experimental setup of SH generation. b Schematic depiction of an elliptical crack generated from locally perturbed crystal layers. The color scheme represents features of pristine crystals as blue and fractured crystals as pink. Application of a vertical force on the major (010) face of a single-crystal potentially ruptures the weakest interaction in the structure, causing elastic straining of crystal layers. c Spatially resolved SH mapping of a pristine region and d fractured region of MNI crystal. The double-sided arrow indicates the orientation of incident polarization. e SH generation polar plots obtained from a pristine region (blue, isotropic) are compared to those from the center of a crack (pink, anisotropic). Varying the linear polarization of the excitation pulse relative to the [001] axis causes the emergent lobes in the SH pattern to develop a clear polarization-dependent asymmetry. f The SH signal increases approximately 6-fold in intensity (pink bar) on multiple samples as compared to pristine, undeformed samples (blue bar). g Power dependence plot shows a slope of ~1.85 in a log plot of the SH signal versus input power, confirming the quadratic nature of the SH process.

To test our hypothesis, we first collected SH signal maps at 400 nm from pristine regions (Fig.4c) and then from mechanically strained regions (Fig.4d). The dramatic difference in non-linear optical response is further highlighted in Supplementary Figs. 28 and 29. The undeformed regions show a negligible SH signal, as expected, since this frequency-doubling phenomenon is not allowed in centrosymmetric media38,39,40. In contrast, bright oblique features are observed from a fractured region, demonstrating significant enhancement in SH intensity. One typical feature of these enhanced SH signals is that they come out in the form of an elliptical shape, which corroborates that the entire SH signal emanates only from the distortion of locally perturbed crystal layers.

Polarization-dependent SH generation (PSH) measurements were conducted by rotating the incident light polarization direction and collecting both parallel and perpendicular components, measured with respect to the laboratory axis (Fig.4e). The polar plot of the PSH response in the fractured region exhibits a two-fold symmetry, while the pristine region shows a nearly circular polar plot (Fig.4e). This difference arises due to different crystal symmetry of the interface layer of pristine area as compared to deformed area41. By repeating the experiments over multiple samples, PSH data over fractured regions are shown to exhibit almost 6 times higher intensity compared to pristine region (Fig.4f). From the SH experiments, the highest intensity is observed at the center of the crack, consistent with the highest intensity of the new modes found in Raman spectroscopy (Supplementary Fig. 29). Figure4g shows the SH efficiency which is linearly proportional to the intensity of the input beam, further verifying that the signal emanating from the perturbed region is a non-linear optical process. Furthermore, we recorded the SH signal after a successful self-healing event, demonstrating a clear loss in SH intensity comparable to that of a pristine surface (Supplementary Fig. 30 and Supplementary Note 6). These results reveal that the self-healing process is indeed associated with a symmetry-breaking pathway, indicating that the energy penalty associated with healing arises from this temporary loss of symmetry.

Discussion

Application of vertical force on the (010) face of MNI probes the structure parallel to the pristine stacked layers, which are supported by weak van der Waals and C–H···O interactions and related by inversion symmetry. The mechanical stress parallel to these layers leads to a crack formation, causing symmetry breaking in the subsurface layers of the fracture surfaces. We hypothesize that when the crack is formed, the interactions among the strained surface layers result in transient surface charges, thus leading to attraction between the fractured shards and making them behave like what we reported earlier in non-centrosymmetric crystals22,23. Since the symmetry of the pristine state is broken, the induced polarization helps in the reorganization of the interlayer interactions, enabling rapid self-healing. Like non-centrosymmetric crystals where self-healing is shown to occur due to charge imbalance by broken polar bonds, herein, a similar electrostatically driven mechanism is perhaps followed after the structure becomes locally non-centrosymmetric42. Unlike the non-centrosymmetric crystals, the opposite polarity of the broken surfaces could not be confirmed by Kelvin Probe Force Microscopy (KPFM) measurements, as the charges here are much smaller and short-lived, but the evidence of instantaneous attraction between broken shards (Supplementary Video 6) supports our above hypothesis. Further, the formation of cracks in an elliptical shape under external vertical stress results in curved fractured surfaces that impart elastic strain, which, upon withdrawal of the external stress, favors the closure of the formed cracks in the fractured crystals, leading to self-healing. The presence of methyl groups in the MNI molecule lends some softness to the layered crystal structure, along with sufficient directional bonds, which may be optimal for fast, diffusionless self-healing. We hypothesize that the above factors play a role in the self-healing observed here, which is distinct from that of other reported crystals. The mechanism proposed here is valuable for expanding the scope of self-healing to a large set of organic crystals. For instance, piezoelectric-based self-healing requires that the crystal structure be non-centrosymmetric22,23. Other reported mechanisms of self-healing involve either ferroelastic detwinning12 or temperature-induced phase transitions (during heating-cooling cycles)17 or diffusion-based mechanisms20. Diffusionless self-healing in centrosymmetric crystals needs further investigation to shed more light on the mechanism involved, and reports along these lines are scarce43. A recent report demonstrating self-healing in conjunction with macroscopic elasticity and thermal twisting44 indicates that more examples are needed to draw connections among various behaviors of crystals from the perspective of structure-property correlation.

In summary, our study highlights three key findings. First, this molecular material exhibits autonomous self-healing of mechanically induced cracks on an ultrafast timescale. Secondly, the fracture mechanics governing different types of crack propagation have been experimentally determined using AFM, SEM, and correlated to the underlying structure through single-crystal XRD. Third, detailed analyses using micro-Raman spectroscopy and second-harmonic generation experiments confirm local symmetry-breaking in the fractured regions, which plays a critical role in subsequent self-healing. We have developed a framework that integrates these experimental observations to propose a coherent mechanism for microstructural-level crack arrest and self-repair. The methodology outlined in this paper offers a foundation for designing advanced self-healing strategies in a wide range of smart materials.

Methods

Sample preparation

The compound 2-methyl-5-nitroimidazole (MNI) was purchased from Sigma-Aldrich and used as-received without further purification. 50 mg of the compound was added to 5 mL of methanol in a clean conical flask with a flat base, warmed at 35 °C for 10 min and kept undisturbed to induce crystallization by slow evaporation. Macroscopically large plate-shaped crystals (a few millimeters in size) grew in one week’s time from the solution. Crystallization can also be performed from a water or ethanol solution. The single crystals of MNI typically exhibit spindle-shaped or open-book-shaped morphology, which is a result of growth twinning in the lattice, as shown in Supplementary Fig. 2.

Single-crystal X-ray diffraction

SCXRD data for the MNI crystal were collected at room temperature (R.T.) on a Bruker Quest D8 diffractometer using Mo Kα (λ = 0.71073) radiation having a 110 µm beam size. Using Olex2 (version 1.5)45, the structure was solved with the SHELXT structure solution program and refined with the SHELXL refinement package. Displacement parameters of all non-hydrogen atoms were refined anisotropically. All the crystal packing diagrams were prepared using Mercury (2022.3.0 version) and Chimera (1.16 version) software. Crystallographic refinement details can be found in Supplementary Note 7.

Characterization of self-healing

As-grown “pristine” crystals were subjected to vertical stresses under a Leica (M205 FCA) polarized optical microscope equipped with a Fastcam Mini high-speed camera. The magnification used was in the range of 4–8× while the videos were recorded at 250–1000 frames per second (fps) and a resolution of 1280 × 1024. Analysis of the videos was done using Fastcam software to visualize the healing in slow motion and real-time, and to quantify the time required for healing. On application of a vertical stress, typically, the crystals begin to crack from the point of stress application, termed as the defect point. Elliptically shaped cracks propagate on both sides of the defect point until the stress is applied. As soon as the force is withdrawn, the crack propagation stops, and the crack begins to heal. The efficiently healed crystals with no visible crack line when viewed under a polarized microscope are termed “healed” crystals. Whereas the crystals where the crack is unable to close perfectly show thin cracks termed as “fractured crystals”. Using excessive force, pristine crystals can be broken into pieces and separated apart, which are termed as “fragmented crystals”.

For characterizing self-healing using a scanning electron microscope (SEM), the images were obtained using a Zeiss DSM 950 and FEI QUANTA 200 3D microscope operating at 10 kV using a tungsten filament as the electron S4 source. Before the imaging, the healed samples were sputtered with gold (nano-sized film) using an SCD 040 Balzers Union sputterer to avoid charging during SEM analyses.

For characterizing self-healing using atomic force microscopy (AFM), a single MNI crystal was subjected to vertical stress under a microscope, allowed to heal, and the healed region was imaged under a commercial AFM Asylum Research Cypher ES using an AC240TS-R3 probe with a spring constant of ≈2 N/m and tip radius of ≈ 7 nm.

For characterizing self-healing using SCXRD, a healed single crystal of MNI at room temperature (RT) was carefully mounted on the diffractometer, and the incident X-ray beam was centered on the healed region of the crystal. The complete dataset obtained from a healed crystal was compared against that of a pristine crystal to characterize the self-healing (see Supplementary Tables 3 and 4). The structural models of both the pristine and neatly healed crystals exhibited comparable statistical refinement parameters, such as GooF and R1 (Supplementary Table 3). The hydrogen-bonding parameters (distances and angles) obtained for both pristine and healed crystals were consistent, confirming their identical crystalline phase before and after healing (Supplementary Table 4). The mosaicity value of the pristine crystal is 0.63, and that of the healed crystal is 0.85, which might be attributed to stress-induced local defects following the fracture and subsequent self-healing, leading to a reduction in the number of measurable reflections.

Computerized microtomography

Crystals were imaged using X-ray microtomography (Xradia 510 Versa X-ray Microscope, Zeiss X-ray Microscopy, Pleasanton, CA, USA) to obtain information from the bulk of any solid material via 3D reconstructed modeling. Crystals were loaded onto the sample holder and kept between the X-ray source and the detector assembly. Detector assembly consisted of a scintillator, 20× optics and a CCD camera. The X-ray source was ramped up to 80 kV and 7 W. The tomographic image acquisitions were completed by acquiring 3201 projections over 360° of rotation with a pixel size of approximately 0.7 microns for a field of view of approximately 0.7 × 0.7 × 0.7 mm3. Each projection was recorded with a 2 seconds exposure time. The filtered back-projection algorithm was used for the reconstruction of the projections to generate two-dimensional (2D) virtual cross-sections of the specimens. Segmentation and further processing were performed using Dragonfly Pro software (Version 3.6, Object Research Systems, Montreal, Canada). 2D images were trimmed down to a sub-volume (approximately 300 × 600 × 700 microns) and filtered to remove noise. During the image segmentation process, the voxels pertaining to crystals and voids in the grayscale histogram were differentiated with the aid of an OTSU-mediated threshold selection program. The resultant 3D reconstructed model was used to visualize the spatial distribution of voids inside the crystals.

Energy frameworks calculations

Energy frameworks analysis was performed by CrystalExplorer using the B3LYP hybrid function with A6–31 G(d,p) basis set46. Energy frameworks calculations help to understand the energies among molecules at play in the lattice. The interaction energy among the layers of MNI was calculated by using energy frameworks analysis, where the thickness of blue bars represents the strength of interaction energies.

Nanoindentation

Nanoindentation experiments have been performed on MNI single crystals using TI Premier from Hysitron, Minneapolis, USA, equipped with an in-situ Scanning Probe Microscope (SPM). A Berkovich probe (three-sided pyramidal tip with a total included plane-edge angle of 142.3°) of radius ~150 nm was used to obtain the load–depth (P–h) curves, which were analyzed using the standard Oliver–Pharr method to determine the hardness (H) and elastic modulus (E) of the crystals47,48. The indent impressions were captured immediately after unloading using the Berkovich probe and were analyzed to draw structure-property correlations (Supplementary Figs. 19 and 20).

Quantitative analysis of healing events

To quantify the load responsible for self-healing, MNI crystals were mounted with a small amount of glue on a glass slide with the major portion of the crystal projected outwards. Then the stage having the crystals was translated towards the tip of a force sensor (accuracy of ±1 %) with a minimum count of 1 mN, having a tip diameter of ~190 µm23. It is to be noted that the load values obtained from the instrument are directly reported here (Supplementary Fig. 11).

The in-situ fracture tests were performed with a PicoIndenter IntraSpect 90 coupled to a stereomicroscope integrated with a camera (M205 FCA). Crystals of different thicknesses were mounted on custom-designed push-to-pull chips in three-point bending geometry. A diamond flat punch tip of diameter 500 µm was driven in displacement mode with a rate of 4000 nm s-1. During the mechanical testing, load (F) and displacement (D) were recorded in real-time. The load versus displacement curves were obtained dynamically and converted to stress-strain curves using the following equations49.

$${{\rm{Stress}}}\,{{\rm{at}}}\,{{\rm{any}}}\,{{\rm{point}}}({{\sigma }})=\frac{3{{{\rm{Fg}}}}}{2{{\rm{wd}}}^{2}}$$
(1)
$${{\rm{Strain}}}\; {{\rm{at}}}\; {{\rm{any}}}\; {{\rm{point}}}({{\rm{\varepsilon }}})=\frac{6d}{g^{2}}\times {{\rm{D}}}$$
(2)

Where,

F is the load at a given point of time

g is the length of the crystal between supports

w is the thickness of the crystal

d is the width/breadth of the crystal

D is the loading arm displacement

Quantitative tests were performed on a pristine sample, a fractured sample and a healed sample. To quantify the healing efficiency, a pristine crystal and a healed crystal of two different thicknesses – one of 100 µm and another of 136 µm were chosen (see Supplementary Figs. 12 and 13).

Raman spectroscopy

Raman spectroscopy measurements were carried out using a Horiba-JobinYovn LABRAM HR spectrometer using 632 nm excitation and 100% laser power using 1800 grooves for an acquisition time of 5 s. Raman microscopy has been performed on the pristine and fractured zones of the same MNI crystal and used for further comparison. The full spectra were recorded from 200 cm-1 to 3300 cm-1. The typical approximate width of the crack, assessed from the 100× objective lens, is ~0.5 micrometer, which decreases as one approaches the crack tip. The appearance and disappearance of new modes can be ascertained as one moves across the crack (i.e. along the white line in the optical image, Fig. 3a) by looking at the spectra color coded as blue (pristine) and pink (fractured). Raman mapping was performed on the selected area in the green box (Supplementary Fig. 26). Raman mapping was recorded by selecting 120 x–y points in the form of an area map. The selected area, as shown in the optical image under a 100× objective lens, comprises both fractured and pristine regions of the crack tip. Mapping of the 696, 703, 820, and 826 cm-1 peaks has been done to obtain a 2-D Raman map and plotted by color contrast after normalization. Overall, the Raman maps confirm the appearance of new modes along the crack. For detailed experimental discussions, see Supplementary Note 5.

Second-harmonic generation microscopy

The polarization-dependent second-harmonic imaging of the organic crystal was performed using a standard non-linear optical microscopy imaging setup50. The system consists of a femtosecond pump laser source (Fidelity HP) at 1040 nm wavelength with a pulse width of 140 fs and repetition rate of 80 MHz, pumping an optical parametric oscillator (Levante-IR) tuned to generate a signal at 1600 nm wavelength with a pulse width of ~ 200 fs pulse width and repetition rate of 80 MHz. The output laser from the OPO is then fed into a Harmonic generator (APE HarmoniXX SHG) to generate a harmonic signal at 800 nm wavelength, which is used as an input laser source for the SH measurement. The organic crystal sample, glued on a glass slide, is then mounted over an XY motorized stage of the Olympus inverted microscope in an inverted position. The laser source with an average input power of 14.5 mW is focused on the sample using a 20x/0.75 NA Olympus objective. The same objective is used to collect the backward SH emission and then separated from the input laser using a dichroic beam-splitter. The SH signal is further spectrally filtered using a bandpass (400  ±  20 nm) and short-pass filters (550 nm cut-off) and detected using a photomultiplier tube (PMT). The set of bandpass and short-pass filters ensured effective rejection of the fundamental excitation, thus ensuring detection of only the SH signal. A pair of galvo-scanning mirrors is used to scan the incident laser beam over the sample to acquire two-dimensional SH images over a field of view of 150–200 µm mapped into a 256 × 256 pixels by mapping the PMT signal for each pixel. For the polarization-dependent SH studies, the input polarization was rotated from 0° to 180° in 5° steps using a half-wave plate to acquire SH generation images for each angle. An analyzer parallel to the laboratory horizontal axis is placed in front of the PMT to selectively detect the parallel-oriented SH emission from the sample with respect to the laboratory horizontal axis. For more experimental details, refer to Supplementary Note 6.