Spontaneous crack healing in calcite reveals the influence of dynamic strain evolution and surface chemistry

Domain: biology
Published: 2026-04-01
Editorial outcome: major_revision

Abstract
The mechanics of fracture healing in calcite remain poorly constrained yet are fundamental to managing fluid transport in geothermal reservoirs and hydrocarbon systems. Here, we apply microfocused synchrotron Laue X-ray diffraction and infrared spectroscopy to investigate subcritical crack healing in a 1 mm-thick calcite crystal subjected to controlled loading in a double-torsion device. Over a 44-hour period following load removal, we map the evolution of residual strain fields surrounding the crack tip and observe a progressive increase in compressive strain perpendicular to the crack plane accompanied by infrared spectroscopic signatures that reveal enhanced accumulation of water at the healed interface. The correlation between strain evolution and surface chemistry suggests that spontaneous crack healing in calcite is driven by dynamic anelastic relaxation coupled with irreversible fluid-mineral interactions. These findings offer insight into time-dependent crack closure processes in carbonates and highlight the role of chemically-mediated plasticity in subsurface fracture evolution.

Introduction
Subcritical crack growth (SCG) and spontaneous crack healing (SCH) are governed by a complex interplay of stress corrosion, dissolution-precipitation, ion exchange, microplasticity, and residual strain, requiring multi-scale and multi-modal approaches to decipher their evolution. While the crack mechanics of ductile and metallic systems are well-characterized, where microstructural damage ahead of the crack tip competes with shielding processes behind (1, 2), the corresponding behavior in macroscopically brittle geologic materials, those which deform brittlely but may accommodate some crystal plasticity at the grain scale, remains poorly resolved and the influence of crystal plasticity, residual stress, and environment-driven anelasticity on crack closure is only beginning to be explored.

The deformation and fracture behavior of calcite (CaCO₃) and calcite-rich rocks such as marble have been investigated experimentally for over a century (3-6), owing to the mineral’s abundance in the Earth’s crust and its ability to deform readily under low confining pressures.

Calcite remains relevant due to its prevalence in hydrocarbon basins and geothermal reservoirs, in crustal fault zones, as well as its ubiquity and influence on the mechanical properties of engineered materials like concrete (7-12). Fluid transport in energy-rich hydrocarbon basins and geothermal reservoirs is governed by the competing processes of crack propagation and crack healing in the reservoir’s rock formations (13). The connectivity of fracture networks to the wellbore, either inherent to the rock formation or artificially created through reservoir stimulation, determine the delivery rate and overall economic recovery of the reservoir (14-16). Permeability of the formation changes over time due to continuous fluid-rock interactions and mineral precipitation, such as crack sealing processes where secondary minerals from distant sources precipitate onto the fracture surfaces, potentially occluding the fracture and requiring stimulation to improve reservoir permeability (17-19). Crack healing, the process in which the fracture surface is eliminated and the lattice is repaired via mass transport operations like diffusion, is usually aided by factors such as heat, time, and confining pressure (17, 18, 20). Distortion, displacement, and contamination of the fracture surface can prevent strong bonds from forming between the two surfaces and reduce the strength of re-healing (21). A perfectly healed crack would demonstrate strength equivalent to its pre-crack state (21). SCG, the time-dependent propagation of cracks at stress intensities below the critical threshold (22), has been identified as a key driver of carbonate sediment compaction, fracture size and spacing, and fracture propagation velocity which can affect reservoir permeability, and crustal fault zone stability (e.g. 9, 22-26). Conversely, SCH, whereby cracks gradually close and mechanical properties partially recover once the driving force of propagation is removed, remains less well understood despite its potential to significantly alter permeability and seismic stability (20, 27).

Understanding the mechanisms driving SCG and SCH is essential for maintaining production performance of energy-rich reservoirs, and predicting the mechanical stability of fault-zone carbonate-rich rock formations.

To address this, we apply a time-resolved, synchrotron-based approach to directly observe strain evolution during crack healing in a single crystal of calcite. Using a double-torsion apparatus, we propagated a controlled Mode I crack in a calcite slide, then monitored the real-time redistribution of deviatoric strain over the course of the 44 hours following load removal using microfocused synchrotron Laue X-ray diffraction at the Advanced Light Source (ALS) beamline 12.3.2. This technique enables high-resolution mapping of elastic strain within bulk samples, as previously demonstrated with metallic thin films (28), rolled titanium (29), and polycrystalline geologic materials (30), offers a unique window into the post-fracture relaxation processes operating at the micro-scale. Infrared spectroscopy of the crack plane after load removal was used to assess chemical alteration of the crack plane, capturing irreversible surface reactions.

This work sheds light on the physical and chemical drivers of fracture closure in a common reservoir mineral. The results reveal how mechanical and environmental interactions co-evolve in fractured carbonates and underscore the importance of dynamic residual stress and surface chemistry in governing porosity and permeability evolution across a range of geologic settings.

Results
Stress evolution measured with Laue microdiffraction

A pre-notched, rectangular slice of calcite measuring 30 mm × 10 mm × 1 mm was used in this experiment. A custom double-torsion device was used to propagate a Mode I crack parallel to the (10-14) cleavage plane using a small ball-bearing placed at the tip of a cup-tipped set screw, which applied a controlled 3-point bending force directly over the notch (Fig. 1a, 1b). This design held the calcite slice perpendicular to the incident beam (Supplementary Fig. 1a) and maintained constant load which enabled precise control over crack growth under Mode I loading conditions. The sample was then partially unloaded and elastic strain maps around the crack were collected by translating the sample stage around the X and Y coordinates in a stepwise manner and capturing a Laue diffraction image at each step. The step sizes, or the length of translational stage displacement, varied depending on the purpose of each scan. A shadow from the device can be observed on the right-most panels of the detector (Supplementary Fig. 1b). Details on the experimental set up and beamline geometry are provided in Section 5.

Prior to crack propagation, a control scan (1.5 mm × 2 mm) was collected to establish a baseline strain field (control, Fig. 2). The purpose of the control scan was to collect baseline strain values of the sample prior to crack propagation and was intended to overlap with the path of crack propagation. However, the control scan was misplaced and was collected slightly above the ultimate location of the crack plane due to inability to predict its propagation path. The sample was then manually loaded using the ball-bearing-tipped actuator, propagating a fresh tensile crack ~15 mm in length along the (10-14) plane. From here on, the “crack tip” refers to the optically visible leading edge of crack plane. For follow-up scans, permanent ink fiducial markers were applied to the sample surface to mark the location of the crack tip under load; it’s approximate location relative to the cracktip_unloaded scan dimensions is visualized in Figure 2. The load was then reduced. Upon partial unloading, spontaneous crack closure was observed: the crack tip retreated along the plane to the left towards the pre-notched edge of the sample, and the former location of the crack tip became optically indistinguishable from the surrounding crystal, indicating a self-healing response. To investigate the evolution of strain during this healing process, three high-resolution Laue microdiffraction scans (cracktip_unloaded 1, 2, 3; Fig. 2) of the former location of the crack tip were collected. During data collection, the crack tip was located to the left the cracktip_unloaded scans and was not included in the scan area. Each cracktip_unloaded scan measured ~0.17 mm × 1.4 mm, with a reduced vertical range in cracktip_unloaded 3 (shortened by 50 μm) to accommodate time constraints. The approximate location of the crack tip (while under load) relative to the cracktip_unloaded scans 1, 2, and 3 is visualized in Figure 2.

The step size, or stage displacement lengths between diffraction images collected, varied depending on the purpose of the scan. The control scans used large step sizes (10 μm) to cover a larger region at lower resolution. In contrast, the cracktip_unloaded scans used fine step spacing (2 μm) to generate high-resolution strain maps around the former location of the crack tip. Due to the small step size, these datasets were time-intensive: cracktip_unloaded 1 and 2 each collected ~59,000 diffraction images over ~16 hours, and unloaded 3 collected ~45,000 patterns in 12 hours. As such, each scan should be considered a temporally distributed dataset, with several hours elapsing between the first and last diffraction image collected within each map. Scan measurements were not corrected for temporal artifacts as time-dependent slip system activity could not be resolved and strain rates could not be quantified.

Deviatoric strain tensors were used to quantify the elastic strain fields from each Laue diffraction image using the XMAS software package (31). For more details on how strain is calculated, the reader is referred to (29, 31, 32). Following crystallographic indexing of diffraction peaks, the local deviatoric strain tensor was calculated by comparing observed peak positions with those expected for an ideal, unstrained calcite lattice. Because deviatoric strain quantifies relative changes in shape of the unit cell, the sign convention assigned is arbitrary. In this study, positive values are associated with strain values indicating an extension, and negative values are associated with strain values indicating a contraction as compared to an ideal, unstrained calcite lattice. An Eigen decomposition converts the deviatoric strain tensor from a coordinate system attached to the unit cell into the coordinate system of the sample (ε).

The corresponding stress tensor (σ) was then derived by applying Hooke’s law (σ = ε·C), using the stiffness tensor for calcite (C) (33). In addition, von Mises stress was computed to represent a scalar equivalent stress magnitude incorporating both normal and shear components (Eq. 1) (34).

(Eq. 1) 𝜎 = √ (𝜎11−𝜎22)2+(𝜎22−𝜎33)2+(𝜎33−𝜎11)2+6(𝜎122+𝜎232+𝜎312) 𝑣𝑚 2

To isolate the effects of crack propagation and healing and remove any inherent strain in the slide, all strain and stress data were baseline-corrected by subtracting the minimum value measured in the pre-crack control scan for each field (Supplementary Table 1).

Upon unloading, spatially diffuse negative strain in the Y-direction (ε ), perpendicular to the crack plane, was initially observed in scan 1, but intensified and became more localized along the crack plane in scans 2 and 3 (Fig. 3a). This progressive increase in negative strain in the Y-direction (ε ) was accompanied by the accumulation of positive strain in the Z-direction (ε ), parallel to the X-ray beam path and along the thickness of the sample. The coherent, uniform pattern of strain in the Z-direction indicates limited dilatational strain, which means the negative strain in the Y-direction can be interpreted as compression. Strain in the X-direction (ε ), parallel with the path of crack propagation remained minimal and largely invariant throughout the post-unloading scans. These trends suggest the development of a dynamic strain field in the region of the former crack tip after the load had been removed that effectively closes the fracture.

Quantitatively, the minimum compressive strain perpendicular to the crack (ε ) became increasingly more negative over time, decreasing from –2.428 millistrain in scan 1 to –3.041 millistrain in scan 3. Concurrently, the maximum strain value perpendicular to the crack (ε ) became less negative, increasing from –1.033 to 0.2790 millistrain between scans 2 and 3 (Table 1). This reflects the time-dependent accumulation of strain along the crack plane and simultaneous relaxation in the surrounding material. A similar trend was observed for ε : the maximum tensile strain values increased from 3.417 millistrain in scan 1 to 3.796 millistrain in scan 3, while the minimum strain values decreased from 1.464 to 0.076 millistrain, suggesting both accumulation and redistribution of tensile strain along the crack plane.

Von Mises stress, which provides a scalar representation of the overall stress state, also increased along the crack plane during the post-unloading period. Maximum values rose from 174 MPa in scan 1 to 258 MPa in scan 3, while minimum values declined from 50 MPa to near zero, indicating stress accumulation around the former region of the crack tip (prior to unloading) and concurrent relaxation in the surrounding material (Fig. 3b).

Localized plasticity measured using diffraction peak width

Dislocation density and lattice defect accumulation was evaluated using Laue diffraction peak broadening (35). To isolate peak broadening caused by plastic deformation from that caused by variation in X-ray beam intensity, the peak broadening due to X-ray beam intensity was subtracted from the average peak width value of each diffraction image. Trendlines correlating the measured average peak width value from each diffraction image to X-ray beam intensity, which varied over the course of each scan due to decreasing accelerator conditions during scans 2 and 3, were used to calculate the contribution of peak width caused by the variable X-ray beam intensity (Supplementary Fig. 2). The residual value between the calculated and measured average peak width value for each diffraction image was plotted (Fig. 3c) and used to observe the evolution of plastic strain around the crack. An increase in peak width is observed in a two-lobed pattern around the crack plane in scan 1. A planar feature of lesser average peak width coincident with the crack plane can be observed. This feature widens in the Y-direction and becomes more obvious in scan 2. By scan 3, the area of increased average peak width has shrunk to the immediate crack surroundings.

Dislocation activity along four common slip systems in calcite–r-slip {10-14}⟨–2021⟩ and {10-14}⟨1-210⟩, and f-slip {01-12}⟨0-111⟩ and {01-12}⟨–2021⟩–was evaluated using the dislocation study tool of PYXIS software (36-39). Elongation of diffraction peak profiles reflects dislocation activity because lattice distortions caused by dislocations introduce anisotropic strain fields which broaden and elongate the intensity distribution of the peak in the direction of the active slip system (39). The diffraction image from the same stage coordinate position near the crack plane of unloaded scans 1, 2, and 3 was used to compare slip system activity during crystal healing (Fig. 4a). Because the control scan area ultimately did not overlap with the crack tip scan area, a diffraction image from the control scan was used with the same X-stage coordinate but with a Y-coordinate 3 mm above the crack. The orientation of the long axis of the diffraction peak is compared against the expected orientation for the selected slip system (Fig. 4b, c, d). Only slip systems with a long axis orientation variance (Δ°) of less than 10° were included in our analysis.

Results show that the common four slip systems were active during unloading, and slip system activity across scans 1, 2, and 3 appears to be consistent with time elapsed since unloading (Table 2). Peak shape evolution is most prominent between the control scan and the first cracktip unloaded scan (Fig. 5). Systematic variations in peak shape occur during cracktip unloaded scans 1, 2 and 3; most notably peak elongation in the vertical direction decreases with increased time post load removal; however, variation is minor within the resolution of the diffraction image. Only one diffraction image was analyzed using PYXIS due to the time required for the analysis. For this reason, the spatial distribution of slip system activity across the scan was not evaluated.

Additionally, a dominant deformation process for the experiment could not be determined from this analysis due to the limited number of slip systems, peaks, and number of diffraction images used in the analysis. Generally, slip systems with lower critical resolved shear stress are more easily activated. Slip systems that were identified as active for more than one scan suggest they could be a more dominant deformation mechanism than others, however in the diffraction image analyzed only four possible slip systems were studied, and neither the r- or f- systems were observed as significantly more active than the other (Table 2), thus a dominant deformation mechanism for the system cannot be identified. Further study into a larger population of peaks and slip systems across multiple diffraction images could yield greater insight into the deformation process during spontaneous healing.

Water identified around crack plane using IR spectroscopy

Infrared spectroscopy, performed after X-ray diffraction data collection and removal of the calcite slide from the double-torsion device, revealed a persistent, localized accumulation of water along the healed crack interface. As water was not added to the experiment, its presence is attributed to ambient humidity. To assess the spatial distribution of water, we conducted FTIR hyperspectral imaging and generated semi-quantitative maps of water content by integrating the absorption intensity of the O–H bending mode centered at ~1620 cm⁻¹ or at a wavelength of ~6.2 µm (Fig. 3d). This vibrational mode is a reliable proxy for molecular water (40) and enables spatially resolved, diffraction-limited imaging of hydration state using the Beer-Lambert law, which relates absorption intensity to concentration through known optical parameters.

Notably, the water signal was not uniformly distributed across the sample surface but was instead tightly localized to a narrow, 15 μm-wide band centered along the location of the crack tip and plane, which were visible prior to unloading. The signal extended approximately 7 μm into the bulk from the crack interface. This spatial pattern indicates that water accumulation is not limited to the crack surface, but reflects chemical modification of the subsurface region below the crack surface, albeit limited by the IR attenuation depth on the order of several micrometers. With 14-16 hours elapsed between the first and last diffraction image collected for each scan, interpretation of the asymmetric shape of the water halo above and below the crack plane, which mimics the shape of the deviatoric strain (Fig. 3a), is limited to possibly an artefact due to this temporal distortion. The persistence of the water signal—despite prior scanning electron microscopy (SEM) under high vacuum and prolonged ambient storage—suggests that the water is strongly retained, either via chemisorption or incorporation into defect structures. Prior studies have shown that molecular water can remain bound to calcite surfaces, particularly the (10-14) cleavage plane, even under high-vacuum conditions (41,42), and that one such water layer was measured to be 5-6 nm thick (43), an order of magnitude thinner than the water signal measured in this study, supporting the hypothesis that water has migrated into the bulk of the material.

If the observed water distribution does indeed result from diffusion, the calculated apparent diffusivity would exceed expected values for room-temperature diffusion in pristine calcite (44), implying either enhanced transport along dislocation networks (45) or fast pathways created by microstructural damage (46). Additional experimental work is needed to identify the mechanism of water emplacement, whether adsorption, absorption, or diffusion. Because the fracture zone follows crack front geometry and may transect the thickness of the sample (Supp. Fig. 3), water adsorption along the microcrack surfaces would be expected to be present throughout the entire thickness of the sample so long as the microcrack network is connected to the crack-air interface. Due to the shallow depth sensitivity of the IR method used in this study, surface adsorption and condensation along the crack surface followed by mass transport along microcracks, or areas of high free energy such as defect sites are the most plausible mechanisms (47). In either case, the persistent presence of water reflects a permanent chemical alteration of the fracture zone potentially linked to the observed residual strain and plastic deformation (Fig. 6).

Moreover, the retention of water in the healed region despite the apparent optical closure of the crack suggests an irreversible change in the local hydration state of the crystal. This bound water may contribute to the strain anomalies observed near the crack, as water incorporation into defect-rich regions can locally swell the lattice or modify surface energy. Importantly, such chemically modified zones may remain mechanically weaker than the pristine crystal, thereby impeding full recovery of tensile strength and stiffness (48, 49). The combination of residual water, persistent plasticity, and strain gradients indicates that spontaneous crack closure does not equate to mechanical restoration, and that water plays a critical role in modulating both surface reactivity and fracture mechanics in calcite.

Methods
Sample Preparation

A rectangular slice of calcite measuring 30 mm × 10 mm × 1 mm was prepared from an optical-grade natural single crystal of Brazilian provenance (sourced and cut by Crystran, Ltd., UK). The crystallographic orientation of the slice relative to the three primary cleavage planes is shown in Figure 1a. A pre-notch was introduced to control crack initiation and propagation direction. The sample was then mounted in a custom-designed double-torsion device to initiate crack propagation. The slice was oriented such that the induced crack would propagate along the long axis of the sample, parallel to the (10-14) cleavage plane (Fig. 1b). Crack initiation was achieved by a small ball-bearing placed at the tip of a cup-tipped set screw, which applied a controlled 3-point bending force directly over the notch. This design enabled precise control over crack growth under Mode I loading conditions. The double-torsion device was modified to hold the sample perpendicular to the X-ray beam (Supplementary Fig. 1).

Laue Microdiffraction

The experiment was conducted at ALS beamline 12.3.2 using a polychromatic beam with a spot size of 1 μm and an energy range of 5–24 keV. The beamline was configured in transmission geometry and calibrated using a YAG (Y Al O ) crystal mounted on a glass substrate. A 90° angle of incidence was used to uniformly sample the crack plane across the scanned area. After defining the 2D scan area with beamline control software, the stage advanced in discrete steps, collecting one Laue diffraction image at each position, using a DECTRIS Pilatus 1M placed directly above the sample, with an exposure time of 1s per frame.

Prior to crack propagation, a control scan (1.5 mm × 2 mm) was misplaced and collected slightly above the anticipated crack plane due to inability to predict crack propagation path. This control scan was used to establish a baseline strain field (control, Fig. 2). The sample was then manually loaded using the ball-bearing-tipped actuator, propagating a fresh tensile crack ~15 mm in length along the (10-14) plane. Permanent ink fiducial markers were applied to the sample surface to mark the location of the crack tip while under load. The load was then gradually reduced. Upon partial unloading, spontaneous crack closure was observed: the crack tip retreated left toward the ball bearing and the area that previously displayed the crack while under load became optically indistinguishable from the surrounding crystal, indicating a self-healing response. To investigate the evolution of strain during this healing process, three high-resolution scans were collected in the area of the former crack tip (cracktip_unloaded 1, 2, 3; Fig. 2). Each scan measured ~0.17 mm × 1.4 mm, with a reduced vertical range in cracktip_unloaded 3 (shortened by 50 μm) to accommodate time constraints. The approximate location of the former crack tip relative to the cracktip_unloaded scans 1, 2, and 3 is visualized in Fig. 2.

Step sizes, or the distance of stage translation between collected diffraction images, varied depending on scan purpose. The control scan used large step sizes (10 μm) to cover a broader region at lower resolution. In contrast, the cracktip_unloaded scans used fine step spacing (2 μm) to generate high-resolution strain maps of the former crack tip area. Due to the small step size and extended scan area, these datasets were time-intensive: cracktip_unloaded scans 1 and 2 each collected ~59,000 diffraction images over ~16 hours, and scan 3 collected ~45,000 patterns in 12 hours. As such, each scan should be considered a temporally distributed dataset, with several hours elapsing between the first and last diffraction image collected within each map.

Infrared Spectroscopy

The infrared hyperspectral imaging was performed using a Fourier Transform Infrared (FTIR) microscope (Cary 620 FTIR microscope and Cary 670 Spectrometer, Agilent Technologies) equipped with a liquid-nitrogen-cooled focal-plane array (FPA) detector at ALS beamline 2.4. This configuration enables acquisition of spatially resolved spectral data with a diffraction-limited spatial resolution of approximately 4 µm under a 25X objective (N.A. = 0.81), providing fine-scale chemical imaging of the sample. Spectra were collected by co-adding 100 individual scans to enhance the signal-to-noise ratio, covering the mid-infrared spectral range from 700 cm⁻¹ to 4000 cm⁻¹. This range encompasses key vibrational modes, including the carbonate symmetric stretching mode characteristic of calcite (~1450 cm⁻¹), the O-H bending mode of molecular water (~1620 cm⁻¹), and the broad O-H stretching band (~3200 cm⁻¹). These spectral features enable simultaneous mapping of mineralogical and fluid phases within the sample. The spatial distribution of water was reconstructed by integrating the absorption intensity of the O-H bending mode at ~1620 cm⁻¹, which provides a quantitative proxy for local water content based on the Beer-Lambert law.

Dislocation Analysis

A dislocation analysis was performed using PYXIS software (39) to evaluate activity along four common slip systems in calcite: r-slip (10-14)[–2021] and (10-14)[1-210], and f-slip (01-12)[0-111] and (01-12)[–2021]. The analysis compared slip system activity over the duration of the experiment. The diffraction image was collected at the same stage coordinates for the three unloaded scans, taken from the center of the crack plane. Only peaks with complete and well-defined intensity profiles were considered; any partial or truncated peaks were excluded. Peaks for which a satisfactory fit could not be obtained were discarded from further analysis. To ensure robust identification of slip system activation, only peaks with angular deviations of less than 10° between the measured elongation axis and the predicted slip direction were included. This filtering step helped isolate those peaks most reliably associated with specific crystallographic slip systems.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Dear editor,\nI have reviewed the manuscript titled “Spontaneous Crack Healing in Calcite: Insights from Synchrotron Laue\nMicrodiffraction and Infrared Spectroscopy.” This study presents a detailed investigation into the mechanisms of subcritical\ncrack growth and healing in calcite, using advanced synchrotron-based techniques and infrared spectroscopy. The authors\ndocument the progressive intensification of compressive strain perpendicular to the crack plane (εyy) and the accumulation\nof tensile strain parallel to the crack (εzz) over a 44-hour period. This provides direct evidence of mechanically driven crack\nclosure under ambient conditions. The results are noteworthy as they challenge the traditional view that crack healing in\nbrittle minerals like calcite requires elevated temperatures or fluid saturation.\nThe article is very well written, providing a clear flow between the explanation of the methodology (experimental design,\nnovelty, complexity), the results and their impact. This work is worthy of publication in Nature Communications because:\n- this work shed light on the mechanisms of spontaneous crack healing (SCH) under ambient conditions by demonstrating\nthat dislocation-mediated plasticity and water accumulation can drive fracture closure without external stimuli in calcite. The\nresults align with recent studies on dislocation recovery in calcite and extend these findings to ambient conditions, which is\na significant advancement;\n- the study offers a physical basis for understanding permeability reductions during shut-in periods and the mechanical\nstability of carbonate-rich fault zones;\n- the findings provide critical insights into permeability evolution in geothermal and hydrocarbon reservoirs, where fracture\nhealing can significantly impact fluid transport and reservoir performance.\nResults and conclusions are well-supported by the data, and reproducibility is possible.\nUpon reviewing this article, I only noted five points for clarification for me.\n1) A main reference (e.g.) to Laue (micro)diffraction is missing.\n2) In Table 1, it is unclear what the standard deviations are for: min, max, non presented average Von Mises values? At the\nmoment, one could read that the min values could be negative which is not possible by definition.\n3) One area that could benefit from further clarification is the interpretation of water distribution. The authors suggest that\nwater accumulation may result from diffusion or adsorption along microcracks. While the data support the presence of water,\nthe exact mechanism (diffusion vs. adsorption) could be explored further, possibly through additional modeling or\nexperimental validation.\n4) As each scan took several hours to complete, how did the temporal artifacts were accounted for in the analysis?\n5) Do certain slip systems dominate the process, or is their activity uniformly distributed?\nThank you for the opportunity to review this manuscript.", "reviewer_2": "Dear authors, dear editor,\nThe manuscript entitled “Spontaneous crack healing in calcite revealed: Strain evolution, dislocation dynamics and surface\nchemistry” by Michelle Devoe and co-workers presents results from high resolution mapping of the strain field surrounding a\nhealing crack in a calcite crystal. Using state of the art synchrotron technology, the authors demonstrate that cracks in calcite\ncan heal significantly at nominally ambient conditions driven by a combination of dislocation motion and water-mediated\nchemical interactions.\nThe manuscript is well written and engaging. The methods are at the forefront of the field, and the results challenge the\nprevailing view that crack healing in calcite requires elevated temperature or pressure. My only reservation concerns the\nintroduction, which I found somewhat limited in its review of the current state of knowledge on crack healing (see my line-by-\nline comments). I recommend publication after minor revisions.\nBest regards,\nGabriel Meyer\nLine by line comments:\nL52: Here, I must kindly disagree with the use of “brittle geologic materials” in this sentence. In the rock mechanics literature,\n“brittle” refers to materials in which no crystal plasticity occurs. A comprehensive description of the nomenclature generally\nfollowed in the field can be found in Rutter et al., 1986.\nL56: I suggest adding Fredrich et al., 1989 to the references, as it is widely regarded as a seminal study on marble\ndeformation.\nL60: Could you give a reference for a geo-reservoir hosted in calcitic rocks here? I only see those for cements and faults.\nL61: What is meant by fault healing here? The cited reference studies calcite sealing which I believe is quite different from\nthe process that is the subject of the manuscript.\nL71: The connection to the opening of this paragraph on crack healing and sealing is not sufficiently developed. Where does\nspontaneous crack healing fit within the broader range of crack-healing processes? How does it differ from sealing? Under\nwhat conditions can SCH be expected? Further clarification would strengthen this section.\nL73. From reading the abstract, citation 19 does not appear to support the point being made here as it refers to SCG and not\nSCH. For SCH impact on mechanical and seismic properties in calcitic rocks, I would suggest Schubnel et al., 2005 or\nMeyer et al., 2021. The latter, in particular, shows crack healing in calcite at ambient temperature and humidity, which might\nbe of interest to you.\nL89: Overall, the introduction does not provide a sufficient state-of-the-art overview of crack self-healing. Several seminal\nstudies already exist and should be acknowledged, including Smith et al. (1984), Evans et al. (1977), and Hickman et al.\n(1987).\nL117: Is there a reason why the control scan is not acquired where the crack will eventually propagate?\nL126: I believe the scan map in supplementary should be part of the main text. I personally found hard to visualize the\nposition of the different scans from the text only.\n129: Maybe specify “displacement steps” for clarity.\nL212: First reference to “north” in text. I would suggest homogenizing. I believe earlier the control position was referred to as\n“above” the crack.\nL261: Where is this water originally from? Is it just room humidity?\nL276: The shape of the water halo as well as that of the deviatoric strain on figure 5 appears asymmetrical — being wider\nabove the healed crack. Is this an artefact? Could you comment?\nL277-282: Citation needed to support these statements.\nReferences:\nEvans, A. G. and Charles, E. A. (1977). Strength recovery by diffusive crack healing. Acta Metallurgica, 25(8):919–927.\nFredrich, J. T., Evans, B., & Wong, T. F. (1989). Micromechanics of the brittle to plastic transition in Carrara marble. Journal\nof Geophysical Research: Solid Earth, 94(B4), 4129-4145.\nHickman, S. H. and Evans, B. (1987). Influence of geometry upon crack healing rate in calcite. Physics and Chemistry of\nMinerals, 15(1):91–102.\nMeyer, G. G., Brantut, N., Mitchell, T. M., Meredith, P. G., and Pl¨umper, O. (2021). Time dependent mechanical crack closure\nas a potential rapid source of post-seismic wave speed recovery: Insights from experiments in Carrara Marble. Journal of\nGeophysical Research: Solid Earth, 126(4):e2020JB021301.\nRutter, E. H. (1986). On the nomenclature of mode of failure transitions in rocks. Tectonophysics, 122(3-4), 381-387.\nSchubnel, A., Fortin, J., Burlini, L., and Gueguen, Y. (2005). Damage and recovery of calcite rocks deformed in the\ncataclastic regime. Geological Society, London, Special Publications, 245(1):203–221.\nSmith, D. L. and Evans, B. (1984). Diffusional crack healing in quartz. Journal of Geophysical Research: Solid Earth,\n89(B6):4125–4135.351", "reviewer_3": "Review of 634938_0 submitted to Nature Communications:\nSummary:\nThe manuscript entitled “Spontaneous crack healing in calcite revealed: Strain evolution, dislocation dynamics and surface\nchemistry” by Michelle Devoe, Harrison Lisabeth, Seiji Nakagawa, Zhao Hao, Nobumichi Tamura, and Hans-Rudolf Wenk\npresents experimental measurements of crack healing based on time-resolved synchrotron Laue X-ray diffraction, optical\nmeasurements of crack opening, and scanning infrared spectroscopy. The main result that negative axial strains develop\nnear the crack surface upon unloading, accompanied by increased plastic activity and localized water migration, suggesting\na chemically-driven healing mechanism.\nEvaluation:\nThe study is original and supported by a rich experimental dataset. It has significant potential to advance our understanding\nof fracture and healing processes in reservoir rocks. The manuscript is generally well written. However, the definition of the\ncrack tip (a key concept for interpreting the measurements) is ambiguous and leads to confusion. In addition, while crack\nhealing is mentioned, it is not (mechanically) assessed. I recommend publication in Nature Communications after major\nrevisions\nThe authors will find below detailed comments on the manuscript.\nDetailed comments:\n• Introduction – The introduction is well-written. The motivation and broader relevance of the study are clearly stated. The\nresults are likely to interest a wide audience across geomechanics, geophysics, and (to some extent) mechanical and civil\nengineering.\n• Section 2 “Results”\nRemark 2.1: The dimensions of the sample could be added to the main text, even if they are reported in the methods section.\nRemark 2.2: I expect that the diffraction pattern obtained from transmission Laue measurements represents an average\nresponse through the sample thickness (if the energy is high enough), whereas both the optical observations of crack\nopening and the infrared spectroscopy data correspond to surface measurements. However, during a double-torsion test, the\ncrack front is curved, as shown by the authors in Figure 1. Is the curvature negligible with respect to the dimension of\nscanned area? If it is not the case, how can the authors reconcile bulk-averaged (Laue) and surface (optical and IR)\nmeasurements? Specify whether the surface measurements are performed on the side of shorter or longer crack length?\nRemark 2.3: The notion of the crack tip is not clearly defined throughout the manuscript. At line 125, the authors refer to “the\nformer crack tip after unloading”, which I understand as the right end of the optically visible crack opening prior to unloading.\nLater, at line 131, they mention “high-resolution strain maps around the healed crack tip”. It is unclear whether this refers to\nthe same position as the “former crack tip” or to a distinct location. In Figure 2a/b/c, the “crack plane” is indicated by a white\nline, but since the line has finite length, its right edge could also be interpreted as a (former/new/healed?) crack tip. Figure 5\nshows a visible and a healed crack. I recommend clarifying this definition early in the manuscript and keep the same\nterminology.\nRemark 2.4: Assuming plane stress conditions, I would expect ε_zz to be a fraction of ε_yy (assuming negligible ε_xx), i.e. |\nε_zz| < |ε_yy|. The opposite signs are correct. Yet, |ε_zz| > |ε_yy|. Can the authors comment on that? Is it an artifact\nintroduced by substracting the baseline strain?\nRemark 2.5: In Figures 3a and 4a, the caption mentions diffraction peaks boxed in red and white, but there is no such thing\nin the figure.\nRemark 2.6: The IR spectroscopy measurements are performed on the surface of the specimen. Do the authors expect the\nsame signal near the crack surface within the material (in the z direction)?\n• Section 3 “Discussion”\nRemark 3.1: If the crack indeed healed, the force required to propagate upon reloading should exceed that previously\nneeded to reach the initial crack length before unloading. I understand that in situ force measurements were not possible\nduring the synchrotron experiments due to technical constraints. However, do the authors have any supporting evidence for\ncrack healing from complementary tests conducted outside the synchrotron, where the setup was instrumented with a force\nsensor?\nRemark 3.2: In Figure 2, the region of axial strain goes behind the white line, which I identify as the visible crack tip after\nunloading. Does this mean that the crack healed in an opened region? Did the authors observe a decrease of crack opening\nin that region, as it would be expected during healing? I do not know how to interpret this without a clear answer to my\nprevious remark 2.2\nRemark 3.3: Traditional healing cohesive-zone models include a minimum opening, below which healing process are\nactivated. Do these measurements provide way to validate such models?\nMinor comments:\n• the notations SCG and SCH of line 67 and 71 are already defined at line 47.\n• in figure 3, numbering of the subfigures are in capital letters instead of lowercase.\n• at line 290 and 291, the symbol epsilon is not consistent with that used in section 2 and Figures 2 and 5."}, "author_response": "Nature Communications\nManuscript #NCOMMS-25-56737\nResponse to Reviewers’ Comments\nJanuary 15, 2026\nPlease note that the line references the Authors provide in this document correspond to the Track Changes\n“All Markup Visible” version of the Word document.\nRESPONSE TO REVIEWER COMMENTS\nReviewer #1 (Remarks to the Author):\nUpon reviewing this article, I only noted five points for clarification for me.\n1) A main reference (e.g.) to Laue (micro)diffraction is missing.\nReferences to previous studies that used Laue diffraction to study the elastic strain in bulk samples have\nbeen added: Spolenak et al. (2016), Devoe et al. (2023), and Chen et al. (2016) (lines 92-95). References\non how elastic strain is measured from Laue diffraction patterns have been added: Tamura (2014), Wenk\net al. (2020), Devoe et al. (2023) (line 174-175).\n2) In Table 1, it is unclear what the standard deviations are for: min, max, non presented average\nVon Mises values? At the moment, one could read that the min values could be negative which is\nnot possible by definition.\nAverage values have been added to Table 1 (line 217). The Table 1 caption has also been modified to\nclarify that the strain values presented in the table are the corrected values. A few strain values in the table\nerroneously reported the uncorrected data values and have been replaced with the corrected strain values,\nand the text was also modified to reflect these changes.\n3) One area that could benefit from further clarification is the interpretation of water distribution.\nThe authors suggest that water accumulation may result from diffusion or adsorption along\nmicrocracks. While the data support the presence of water, the exact mechanism (diffusion vs.\nadsorption) could be explored further, possibly through additional modeling or experimental\nvalidation.\nWe agree additional experimental work is needed to identify the mechanism. A response addressing this\nand the reasoning for our presumed mechanism has been added to lines 352-359.\n4) As each scan took several hours to complete, how did the temporal artifacts were accounted for\nin the analysis?\nScans were not corrected for temporal artifacts as strain rates could not be quantified and time-dependent\nslip system activities could not be resolved. Clarifying language addressing this has been added to lines\n170-172, and lines 330-333.\n5) Do certain slip systems dominate the process, or is their activity uniformly distributed?\nIn regards to identifying the dominant deformation process present in the experiment, only a small subset\nof possible slip systems was studied on a limited number of peaks on one diffraction pattern due to time\nconstraints, so no dominant slip system to describe the deformation process could be determined with\ncertainty. In regards to the PYXIS analysis performed, neither slip system (r or f) was significantly more\nactive than the other, so out of the four slip systems investigated, neither could be determined as more\ndominant. In regards to spatial distribution, only one diffraction pattern was analyzed for this experiment\ndue to the amount of time required to perform the analysis, so no differences in slip system activity across\nthe scan area were determined. Additionally, PYXIS analyses on more diffraction patterns across the scan\narea could reveal more insights into the dominant deformation processes and their spatial distribution.\nSentences addressing this have been added to lines 275-286.\nReviewer #2 (Remarks to the Author):\nL52: Here, I must kindly disagree with the use of “brittle geologic materials” in this sentence. In the\nrock mechanics literature, “brittle” refers to materials in which no crystal plasticity occurs. A\ncomprehensive description of the nomenclature generally followed in the field can be found in\nRutter et al., 1986.\nThe Authors thank the Reviewer for raising this point. We, however, diverge and suggest crystal plasticity\ncan occur even in materials that fail in a macroscopically brittle manner. In rock mechanics, the terms\n“brittle” and “ductile” are typically used to distinguish macroscopic post-failure behavior, with brittle\nmaterials showing strain softening and ductile materials exhibiting strain-neutral or strain-hardening\nbehavior prior to softening. These classifications do not imply the absence of micro-scale plasticity, and\nrocks commonly express mixed micromechanical processes that vary with pressure, temperature, and\nchemistry. Our original use of the term “brittle” was intended to contrast calcite-rich geomaterials with\nmetals, whose mechanical response at ambient conditions is dominated by crystal plasticity. Calcite-\nbearing rocks at low pressure and temperature are generally understood to behave macroscopically brittle,\ndespite accommodating some crystal plasticity at the grain scale. To avoid any ambiguity, we have\nrevised the text to use the term “macroscopically brittle” in place of “brittle,” and an explanation which\nmore precisely conveys the intended meaning and avoids implying the absence of plasticity (lines 53-54,\n507).\nL56: I suggest adding Fredrich et al., 1989 to the references, as it is widely regarded as a seminal\nstudy on marble deformation.\nA reference to Fredrich et al. (1989) has been added to the statement of historic calcite deformation\nstudies (line 58).\nL60: Could you give a reference for a geo-reservoir hosted in calcitic rocks here? I only see those\nfor cements and faults.\nA reference to the Ekofisk Field, a chalk hydrocarbon reservoir, has been added (Agarwal et al. 2000),\nand a reference to the common occurrence of calcite, deposited as scale within a geothermal reservoir, in\nthis case Miravalles in Costa Rica, has been added (Vaca et al. 1989) (line 62).\nL61: What is meant by fault healing here? The cited reference studies calcite sealing which I believe\nis quite different from the process that is the subject of the manuscript.\nThe Authors thank the Reviewer for this comment, however cannot find mention of fault healing at line\n61 of the original, submitted manuscript or in the Introduction section. Could it be possible that this\ncomment is in reference to the mention of “fault zone stability” (line 79), with references to Carpenter et\nal. (2025), Olsen et al. (1993), and Orlecka-Sikora & Cielesta (2020)? These references refer to the\ndeformation response of calcitic-rocks under shear stress, subcritical crack growth, and subcritical rupture\nprocesses, which are integral to fault zone mechanical stability. Indeed, crack sealing is much different\nfrom spontaneous crack healing. An explanation of the differences and supporting references have been\nadded and are addressed in the following comment/response.\nL71: The connection to the opening of this paragraph on crack healing and sealing is not\nsufficiently developed. Where does spontaneous crack healing fit within the broader range of crack-\nhealing processes? How does it differ from sealing? Under what conditions can SCH be expected?\nFurther clarification would strengthen this section.\nAn explanation of crack sealing (lines 68-71) and how it differs from crack healing (lines 71-76) has been\nadded. Spontaneous crack healing can occur upon removal of the driving force of crack propagation, and\nthis clarifying point has been added (line 81-82).\nL73. From reading the abstract, citation 19 does not appear to support the point being made here\nas it refers to SCG and not SCH. For SCH impact on mechanical and seismic properties in calcitic\nrocks, I would suggest. The latter, in particular, shows crack healing in calcite at ambient\ntemperature and humidity, which might be of interest to you.\nThe Authors thank the Reviewer for contributing these supportive citations demonstrating the influence of\ncrack healing on seismic wave velocities. The citation to the reference previously numbered #19\n(Orlecka-Sikora & Cielesta, 2020) has been removed and replaced with citations to Schnubel et al. 2005\nand Meyer et al. 2021 (line 83).\nL89: Overall, the introduction does not provide a sufficient state-of-the-art overview of crack self-\nhealing. Several seminal studies already exist and should be acknowledged, including Smith et al.\n(1984), Evans et al. (1977), and Hickman et al. (1987).\nAdditional background information and references to the seminal studies on crack healing and\nmechanisms responsible have been added (lines 68-80).\nL117: Is there a reason why the control scan is not acquired where the crack will eventually\npropagate?\nA sentence has been added clarifying that the control scan coordinates were intended to but ultimately did\nnot overlap with the scan area due to the Authors’ inability to predict crack propagation path (lines 140-\n144; lines 573-574). Language has been added to clarify the purpose of the control scan (lines 140-142).\nL126: I believe the scan map in supplementary should be part of the main text. I personally found\nhard to visualize the position of the different scans from the text only.\nSupplementary Figure 2 from the original manuscript, showing the relative scan positions, has been\nmoved from Supplementary Materials into the main text as the new Figure 2 (line 133) and the\nsubsequent figures in the Manuscript and Supplementary Materials have been renumbered accordingly.\n129: Maybe specify “displacement steps” for clarity.\nClarifying language that “step size” refers to the length of stage displacement has been added to lines\n116-118 and line 588.\nL212: First reference to “north” in text. I would suggest homogenizing. I believe earlier the control\nposition was referred to as “above” the crack.\n“North” has been changed to “above” (line 266).\nL261: Where is this water originally from? Is it just room humidity?\nThe presence of water is attributed to ambient humidity. A clarifying sentence has been added (lines 316-\n317).\nL276: The shape of the water halo as well as that of the deviatoric strain on figure 5 appears\nasymmetrical — being wider above the healed crack. Is this an artefact? Could you comment?\nIndeed, the asymmetry of the halo above and below the crack is an intriguing feature. Due to the temporal\ndistortion of the scan, with ~14-16 hours difference between the collection of the first and last diffraction\nimages of each scan, it is possible that this asymmetry is a temporal artefact and therefore the Authors\nrefrain from overinterpretation of this feature. A clarifying sentence has been added (lines 330-333).\nL277-282: Citation needed to support these statements.\nBecause this paragraph, which provided discussion on the interpretation of the water signal and its\nmechanism of placement, is redundant with the paragraph that followed, this paragraph has been deleted\n(lines 341-348), and language on the explanation of the interpretation of the water signal and possible\nwater emplacement mechanisms, and supporting references, have been added to lines 337-340, and lines\n349-359.\nReferences:\nEvans, A. G. and Charles, E. A. (1977). Strength recovery by diffusive crack healing. Acta Metallurgica,\n25(8):919–927.\nFredrich, J. T., Evans, B., & Wong, T. F. (1989). Micromechanics of the brittle to plastic transition in\nCarrara marble. Journal of Geophysical Research: Solid Earth, 94(B4), 4129-4145.\nHickman, S. H. and Evans, B. (1987). Influence of geometry upon crack healing rate in calcite. Physics\nand Chemistry of Minerals, 15(1):91–102.\nMeyer, G. G., Brantut, N., Mitchell, T. M., Meredith, P. G., and Pl¨umper, O. (2021). Time dependent\nmechanical crack closure as a potential rapid source of post-seismic wave speed recovery: Insights from\nexperiments in Carrara Marble. Journal of Geophysical Research: Solid Earth, 126(4):e2020JB021301.\nRutter, E. H. (1986). On the nomenclature of mode of failure transitions in rocks. Tectonophysics, 122(3-\n4), 381-387.\nSchubnel, A., Fortin, J., Burlini, L., and Gueguen, Y. (2005). Damage and recovery of calcite rocks\ndeformed in the cataclastic regime. Geological Society, London, Special Publications, 245(1):203–221.\nSmith, D. L. and Evans, B. (1984). Diffusional crack healing in quartz. Journal of Geophysical Research:\nSolid Earth, 89(B6):4125–4135.351\nReviewer #3 (Remarks to the Author):\nEvaluation:\nThe study is original and supported by a rich experimental dataset. It has significant potential to\nadvance our understanding of fracture and healing processes in reservoir rocks. The manuscript is\ngenerally well written. However, the definition of the crack tip (a key concept for interpreting the\nmeasurements) is ambiguous and leads to confusion. In addition, while crack healing is mentioned,\nit is not (mechanically) assessed. I recommend publication in Nature Communications after major\nrevisions\nThe authors will find below detailed comments on the manuscript.\nDetailed comments:\n• Introduction – The introduction is well-written. The motivation and broader relevance of the\nstudy are clearly stated. The results are likely to interest a wide audience across geomechanics,\ngeophysics, and (to some extent) mechanical and civil engineering.\nThe Authors thank the Reviewer for this feedback.\n• Section 2 “Results”\nRemark 2.1: The dimensions of the sample could be added to the main text, even if they are\nreported in the methods section.\nThe dimensions of the sample have been added to section 2.1 (line 108).\nRemark 2.2: I expect that the diffraction pattern obtained from transmission Laue measurements\nrepresents an average response through the sample thickness (if the energy is high enough),\nwhereas both the optical observations of crack opening and the infrared spectroscopy data\ncorrespond to surface measurements. However, during a double-torsion test, the crack front is\ncurved, as shown by the authors in Figure 1. Is the curvature negligible with respect to the\ndimension of scanned area? If it is not the case, how can the authors reconcile bulk-averaged (Laue)\nand surface (optical and IR) measurements? Specify whether the surface measurements are\nperformed on the side of shorter or longer crack length?\nAs the Reviewer points out, Laue X-ray diffraction measurements, optical, and IR measurements do not\nexamine the same sample volume in our experiment; Laue X-ray diffraction probes the entire thickness of\nthe sample due to the high energy X-ray beam and produces a bulk-averaged strain measurement, whereas\ninfrared (IR) measurements probe only several micrometers into the surface of the sample. Optical\nmeasurements were limited to crack position and optically-observed healing. Both optical imaging and IR\nimaging were conducted on the tensile side (long-crack side) of the sample. Additional language\nclarifying the surficial-nature of the IR measurements has been added to the manuscript (lines 327-330).\nThe curved crack front of a double torsion experiment produces a depth-dependent strain field, and while\ndepth-resolved Laue diffraction has been done at other synchrotrons, the technique is not available at\nAdvanced Light Source beamline 12.3.2. Although we currently do not have an established method for\nevaluating and correcting for this discrepancy, we will describe below how the “uncorrected” strain data\nshould be understood and considered when compared to other surface-based measurements. In the\nSupplementary Materials section, we added the new Supplementary Figure 3 as a supporting visual,\nwhich is also provided below.\nIn our experiment, the incident X-ray beam contains high-energy wavelengths (>20 keV) that can\npenetrate through the entire sample thickness. Therefore, diffraction can originate at any point along the\nX-ray beam path through the sample thickness. For this reason, each Laue diffraction image contains the\nbulk-averaged signal of the sample at that sample stage coordinate position (i.e. 2D positions within the\nscan area). Double torsion experiments typically produce a curved crack front that intersects the tensile\nside of the sample surface at a high angle. The crack front rapidly changes slope on the order of the\nsample thickness, then asymptotically becomes parallel to the sample surface (e.g. Nakagawa et al. 2023).\nThe highly concentrated stress around the crack front creates a localized damage zone (“process zone”)\ncontaining microcracks and plastic deformation including dislocations. Because plastic deformation is\ngenerated mostly within the narrow process zone along the crack front, once the crack front moves on and\nthe crack is fully propagated, we can think that plastic deformation is distributed evenly along the crack\nsurface at any given sample depth (or crack height). However, unfortunately, the rotation of the strain\nfield along the curved crack front does not allow us to have a simple relationship between the crack height\n(along a beam path) and the averaging effect.\nBecause the strain measured by Laue X-ray diffraction is a measure of average strain along the beam path\nthrough the thickness of the sample, the measured strain can vary depending on the location of the X-ray\nbeam path relative to the crack front geometry. In our experiment, conducted after crack healing, the\ncrack front retreated following unloading and remained outside of the X-ray diffraction scan area.\nSupplementary Figure 3c shows how Path A intersects a larger volume of distorted lattice than Path B;\nand therefore, diffraction patterns collected along Path A will have greater strain than those collected\nalong Path B. This variation in strain magnitude can be seen most clearly in the ε strain tensor\nyy\ncomponent (Fig. 3a); strain magnitude increases to the left, towards the notch. In lines 384-396, we\nprovided an explanation on the cumulative nature of Laue diffraction patterns, the asymmetry of the crack\nfront, and the difference in strain magnitude due to the curvature of the crack front, which we have\ndiscussed in the above.\nRemark 2.3: The notion of the crack tip is not clearly defined throughout the manuscript. At line\n125, the authors refer to “the former crack tip after unloading”, which I understand as the right\nend of the optically visible crack opening prior to unloading. Later, at line 131, they mention “high-\nresolution strain maps around the healed crack tip”. It is unclear whether this refers to the same\nposition as the “former crack tip” or to a distinct location. In Figure 2a/b/c, the “crack plane” is\nindicated by a white line, but since the line has finite length, its right edge could also be interpreted\nas a (former/new/healed?) crack tip. Figure 5 shows a visible and a healed crack. I recommend\nclarifying this definition early in the manuscript and keep the same terminology.\nThe Authors agree that the language used to describe the location of the scans is not consistent and can\ncause confusion. A definition of the “crack tip” has been added to line 146.\nFollowing partial unloading, the crack tip retreated toward the notch, and was located outside and to the\nleft of cracktip_unloaded scans 1, 2, and 3. Language clarifying the crack tip location while the sample\nwas loaded (lines 147-148), following unloading and during the cracktip_unloaded scans has been added\n(lines 150-152, 154-155, 159-161, 580-581, 586-587).\nThe coordinates of scans 1, 2, and 3 surround the crack tip location while the sample was under load, as\ntracked using permanent ink fiducial markers (added lines 146-147, 578-579), but which became optically\nindistinguishable from the bulk sample following partial unloading. Because the data was collected\nfollowing partial unloading of the sample and the retreat of the crack tip toward to notch-end side of the\nsample, clarifying language has been added to references to the “crack tip” to aid in the reader’s\nunderstanding, such as “former location” and/or “prior to unloading” (lines 151-152, 154-155, 166, 202-\n203, 216-217, 223, 234, 325-326, 375-376, 591).\nThe figure caption for Figure 3 (Figure 2 in the original manuscript) has been modified to clarify that the\nwhite line overlay in the maps for scans 1, 2, and 3 is a visual aid and its length is arbitrary (lines 230-\n231).\nThe text in Figure 6 (Figure 5 in the original manuscript) and its figure caption have been modified to\nclarify crack location terminology (lines 441-447).\nRemark 2.4: Assuming plane stress conditions, I would expect ε_zz to be a fraction of ε_yy\n(assuming negligible ε_xx), i.e. |ε_zz| < |ε_yy|. The opposite signs are correct. Yet, |ε_zz| > |ε_yy|.\nCan the authors comment on that? Is it an artifact introduced by substracting the baseline strain?\nLaue diffraction cannot calculate the full strain tensor (dilatational strain tensor + deviatoric strain tensor)\nas absolute unit cell lengths cannot be determined when a white X-ray beam is used. For this reason, only\nthe deviatoric strain tensor can be calculated which describes the relative change in shape of the unit cell,\nand as such, the signage convention (whether positive or negative) is arbitrary. In this study, the Authors\nhave assigned positive values to strain which demonstrates an extension, and negative to strain values that\ndemonstrate a contraction as compared to an ideal, unstrained calcite unit cell. Language clarifying this\nhas been added to lines 178-181. Additional language on the calculation of strain was also added for\nclarification(lines 181-183).\nRemark 2.5: In Figures 3a and 4a, the caption mentions diffraction peaks boxed in red and white,\nbut there is no such thing in the figure.\nReferences to red and white boxes in captions for Figures 3a (now 4a) and 4a (now 5a) have been\nreplaced with references to yellow boxes to reflect what is displayed in the figure (lines 290-291, 307-\n308).\nRemark 2.6: The IR spectroscopy measurements are performed on the surface of the specimen. Do\nthe authors expect the same signal near the crack surface within the material (in the z direction)?\nAs mentioned by the Reviewer, IR measurements only probe the surface of the specimen. However, the\nmechanism for water attachment is likely via adsorption along microcracks and defect structures\noriginating from the surfaces of the crack. Because these microcracks are formed due to the movement of\nthe process zone through the material during crack propagation, they are expected to be distributed\nthroughout the thickness of the material following crack front geometry (Supplementary Figure 2). Thus,\nwater distribution would be expected to be distributed through the thickness of the sample following the\nresultant microcrack network so long as the microcracks are connected to the crack-air interface. Lines\naddressing this comment have been added (lines 352-359).\n• Section 3 “Discussion”\nRemark 3.1: If the crack indeed healed, the force required to propagate upon reloading should\nexceed that previously needed to reach the initial crack length before unloading. I understand that\nin situ force measurements were not possible during the synchrotron experiments due to technical\nconstraints. However, do the authors have any supporting evidence for crack healing from\ncomplementary tests conducted outside the synchrotron, where the setup was instrumented with a\nforce sensor?\nYes, we have observed strength recovery in calcite slides in the double-torsion geometry using offline\ntests, however the results of such are being used in another manuscript currently in preparation for\nsubmission and therefore cannot be included here. An explanation about this offline data and a citation to\nwork done by Wan et al. 1990 on successful healing and partial recovery of strength in mica has been\nadded to the manuscript (lines 430-435).\nRemark 3.2: In Figure 2, the region of axial strain goes behind the white line, which I identify as the\nvisible crack tip after unloading. Does this mean that the crack healed in an opened region? Did the\nauthors observe a decrease of crack opening in that region, as it would be expected during healing?\nI do not know how to interpret this without a clear answer to my previous remark 2.2\nThe white line in Figure 2 (current Figure 3) is just a visual aid. The location of the crack tip after\nunloading is outside of the scan dimensions. Clarifying language on the crack tip location during the\nscans, and the purpose of the white lines in Figure 3 (Figure 2 in the original manuscript) have been added\nto lines 155-156, and lines 230-231, respectively.\nRemark 3.3: Traditional healing cohesive-zone models include a minimum opening, below which\nhealing process are activated. Do these measurements provide way to validate such models?\nThe Authors thank the Reviewer for this thought-provoking question. The microdiffraction measurements\npresented here do not directly resolve crack opening displacements at the scale required to define a\nprecise healing threshold in terms of separation distance. However, they do provide indirect but\nphysically relevant constraints on such models. Specifically, the measurements resolve spatial and\ntemporal evolution of elastic strain, lattice rotation, and stress redistribution associated with crack closure\nand interfacial contact during healing. These observables reflect the re-establishment of load-bearing\npathways across previously damaged regions, even when absolute crack apertures cannot be measured\ndirectly. In this sense, our results can be viewed as constraining the mechanical consequences of healing,\nnamely, the recovery of stiffness and stress transmission, rather than the geometric criterion (minimum\nopening) itself.\nMinor comments:\n• the notations SCG and SCH of line 67 and 71 are already defined at line 47.\nDuplicate definitions of SCG and SCH have been removed (lines 76, 80).\n• in figure 3, numbering of the subfigures are in capital letters instead of lowercase.\nThe subfigures in Figure 4 (Figure 3 in the original manuscript) are labeled in lowercase letters which is\nconsistent with the rest of the manuscript, however the subfigure labels in the figure caption have been\nchanged from capital letters to lowercase (lines 289-292).\n• at line 290 and 291, the symbol epsilon is not consistent with that used in section 2 and Figures 2\nand 5.\nThe epsilon symbol present in original Lines 290 and 291 (now line 378) have been replaced with the\nepsilon symbol used in the rest of the manuscript to maintain consistency (ε).\nOther minor edits have been made by the Authors to improve reading comprehension\nand/or grammar, and do not affect the results or conclusions of this study:\nLine 2: The title was changed to remove punctuation and replaced with “Spontaneous crack\nhealing in calcite reveals the influence of dynamic strain evolution and surface chemistry”\nLine 33: a comma was removed\nLine 47: “Introduction” capitalized and heading number removed\nLine 48: “subcritical” was replaced with “spontaneous”\nLine 95: “offering” was changed to “offers”\nLine 96: “micron scale” was replaced with “micro-scale”\nLine 99-100: “uses in-situ Laue microdiffraction to investigate the time-dependent healing of\ncracks in calcite” was removed due to redundancy, and “shedding” was changed to “sheds”.\nLine 106: “Results” capitalized and heading number removed\nLine 107: Subheading number removed\nLine 108-109: “in a pre-notched piece of calcite” was removed as “A pre-notched, rectangular\nslice of calcite” was added to the prior sentence.\nLine 114: “The sample was then partially unloaded and” was added\nLine 116, 168, 170, 174, 245, 251, 275, 289, 314, 579, 601, 604: “pattern(s)” was replaced with\n“image(s)” for consistency\nLine 133: The color of the line representing the crack in Figure 2 was changed from purple to red\nfor better visibility and the figure caption was updated accordingly\nLine 158: “cracktip_unloaded” was added\nLine 193: “y-direction” was replaced with “Y-direction” for consistency\nLine 195-196: “in the Y-direction” was added for clarity\nLine 196: “z-direction” was replaced with “Z-direction” for consistency\nLine 197: \"parallel to the X-ray beam path and along the thickness of the sample” was added\nLine 198: “z-direction” was replaced with “Z-direction”, “dilational” was replaced with\n“dilatational”\nLine 199: “y-direction” was replaced with “Y-direction”\nLine 200: “x-direction” was replaced with “X-direction”, and “parallel with the path of crack\npropagation” was added\nLine 204: “minimum” was added\nLine 206: “(ε )” was added\nyy\nLine 208-209: “This reflects the time-dependent accumulation of strain along the crack plane and\nsimultaneous” was added\nLine 210 and 211: “values” was added\nLine 214: “the baseline-corrected” was added for clarity\nLine 217: “0.0279” was corrected to “0.2790”\nLine 223: “focusing” was replaced with “accumulation”\nLines 237-238: Words to clarify the (X,Y,Z) sample coordinate system and their orthogonality\nwere added.\nLine 239: “Horizontal and vertical scales are equivalent.” was added\nLine 241: Subheading number removed\nLine 245-246: “Trendlines correlated the measured average peak width value from each\ndiffraction pattern to X-ray beam” was added\nLine 247: “decreased” was changed to “decreasing”\nLines 248-249: “and the average peak width of each diffraction image was” was removed and\nreplaced with “were used to calculate the contribution of peak width caused by the variable”\nLine 255: “vertical” was removed\nLine 261-262: “of the peak” and a reference to Kou et al. (2024) were added\nLine 264: “ultimately” was added\nLine 291: “Miller indices” was added\nLine 294-295: “Intensity ranges from minimum (blue) to maximum (red).” was added\nLine 300: “directions” was moved after “planes”\nLine 301 (Table 2): “hkl” was added after “Peak” and “hkil” was added after “Slip system”\nLine 307-308: “Select diffraction” and “(hkl)” were added\nLine 309: Closing double apostrophes replaced the colon following “c”.\nLine 310: “Intensity ranges from minimum (blue) to maximum (red).” was added\nLine 313: Subheading number removed\nLine 313: “mechanical testing” was removed and “X-ray diffraction data collection and removal\nof the calcite slide from the double-torsion device,” was added\nLine 319-320: “or at a wavelength of ~6.2 um”, a reference to Seki et al. 2020, and “diffraction-\nlimited” were added\nLine 333: “the water” replaced “this”\nLine 360” “persistent” was added\nLine 368: References to Wan et al. 1990 and Wang et al. 2023 were added.\nLine 373: “Discussion” capitalized and heading number removed\nLine 376: “that became optically indistinguishable from the bulk following load removal” was\nadded\nLine 377: “In particular” was replaced with “Over time”\nLine 378-379: “increased over time” and “became more pronounced” were removed and\n“increased in magnitude and localized closer to the location of the crack-air interface” was added\nLines 397-416: The paragraphs beginning with “Increases in diffraction peak width” and the\nfollowing one starting with “Diffraction peak shape analysis identified” were moved up to\nimprove flow\nLines 417-423: Due to formatting requirements, the Conclusions section was removed. Relevant\nand non-redundant information has been moved into the Discussion section, including paragraph\nstarting with “Scanning infrared spectroscopy….”\nLines 497-507: Due to formatting requirements, the Conclusions section was removed. Relevant\nand non-redundant information has been moved into the Discussion section, including paragraph\nstarting with “These findings indicate that the stress imparted”.\nLine 551: Heading number and “Materials and” removed. “METHODS” capitalized to\ndistinguish from subheadings.\nLine 552: Subheading unitalicized, bolded, and colon removed\nLine 554: The sample’s provenance and supplier was added: “of Brazilian provenance (sourced\nand”\nLine 565: Subheading unitalicized, bolded, and colon removed\nLine 573: “misplaced and” was added\nLine 574-575: “due to inability to predict crack propagation path. This control scan was used”\nwas added\nLine 589: “and loaded” was removed\nLine 590: “a” was added and “regions” was made singular\nLine 593: “scans” was added\nLine 594: “scan” was added and “unloaded” was removed\nLine 598: Subheading unitalicized and bolded\nLine 601: “at the ALS beamline 2.4” was added\nLine 614: Subheading unitalicized and bolded\nLine 626: “Data availability” capitalized and colon removed\nLine 628: “Supplementary” was replaced with “Source”\nLine 629: “from the authors” was added\nLine 631: “References” capitalized\nLine 898: “Acknowledgements” capitalized\nLine 919: “Author Contributions” capitalized, colon removed\nLine 928: “Competing interests” capitalized\nMinor changes were made to the Source Data File that do not change the results or\noutcomes of this study:\n● Tab names were updated to correspond to the revised figure numbers in the Manuscript\nand Supplementary Materials.\n● “Table 1” was added to the name of tabs 1 and 2 to indicate the location of the data used\nto generate Table 1.\n● A new tab (“Suppl. Table 1”) was added with the control scan source data used to\ngenerate Supplementary Table 1."}, {"round": 2, "reviewer_comments": {"reviewer_2": "Dear Editor, dear Authors,\nThis is the second time I have reviewed the manuscript entitled “Spontaneous crack healing in calcite reveals the influence\nof dynamic strain evolution and surface chemistry”, by Michelle Devoe, Harrison Lisabeth, Seiji Nakagawa, Zhao Hao,\nNobumichi Tamura and Hans-Rudolph Wenk.\nIn my initial review, most of my concerns related to the introduction and the supporting literature. I am happy to report that\nthese points have now been satisfactorily addressed.\nI believe the manuscript is now suitable for publication in Nature Communications.\nBest regards,\nGabriel Meyer", "reviewer_3": "The authors have carefully addressed all points raised in my first review. The notion of crack tip is clearer, and makes the\nmanuscript easier to read. The experiments are carefully conducted, and were cleverly designed to reconcile surface and\ndepth-averaged multi-field measurements, which is no small feat. I am therefore happy to recommend the manuscript for\npublication."}, "author_response": ""}]

Decision letter