Molecularly resolved mapping of heterogeneous ice nucleation and crystallization pathways using in-situ cryo-TEM

Domain: earth_science
Published: 2025-08-09
Editorial outcome: minor_revision

Abstract
Crystallization plays a fundamental role in diverse fields such as glaciology, geology, biology, and materials science. Among various crystallizing systems, the formation of ice remains elusive, despite decades of intensive investigation. In this study, we integrate in-situ cryogenic transmission electron microscopy with molecular dynamics simulations to develop a molecular-resolution mapping and thermodynamic framework for deposition freezing under low-temperature, low-pressure conditions. Our results demonstrate that ice formation on rapidly cooled substrates, representing far-from-equilibrium states, proceeds via an adsorption-mediated, barrierless pathway of heterogeneous ice nucleation, followed by progression toward thermodynamic equilibrium. This process is unveiled to involve a series of distinct yet interconnected steps, including amorphous ice adsorption, spontaneous nucleation and growth of ice Ih, Ostwald ripening, Wulff construction, oriented coalescence, and aggregation, all governed by interfacial free energy minima. Our findings offer direct molecular-level insight into the mechanisms of heterogeneous ice nucleation, enrich current understanding of non-classical nucleation pathways, and emphasize the critical role of interfacial energetics in shaping ice crystal morphology and quality.

Introduction
The assembly of water molecules on foreign substrates, forming precipitation such as rain and snow, is a ubiquitous phenomenon that influences Earth’s ecosystems and environments. Despite broad and intense research interests, the scenario of these heterogeneous nucleation and growth process remains far from well-understood. In the well-established ice phase diagram that present stable forms of ice at varied conditions, hexagonal ice, labeled as ‘ice Ih’ as the first discovered form, exhibits a hexagonal close-packed structure with rippled hexagons, where water molecules construct a tetrahedral arrangement through hydrogen bonding1–3. This form of ice is acknowledged as a final precipitation product and is commonly found in natural environments, exhibiting hexagonal symmetry. Despite its common occurrence, the water phase transition process, whereby water molecules assemble from the vapor or liquid phases into the hexagonal ice due to shifts in the environment conditions, remains a longstanding and fugitive focus in research4–8.

In particular, the intricate microscopic details of ice formation remain elusive due to temporal and spatial challenges inherent in experiments5,6,9–11. Most crystallographic research methods, such as X-ray diffraction and neutron scattering, with the highest spatial resolution, are nonetheless prone to detecting homogeneous, uniform bulk structures due to their limited detection sensitivity. As a result, these methods lack dynamic information about the nucleation and growth processes that occur across length scales from microscopic to macroscopic. Environmental scanning electron microscopy offers a feasible approach for identifying active sites involved in heterogeneous ice formation12,13, while water freezing assays enable direct observation of ice nucleation behavior in micrometer-sized single droplet and particles14–18. However, both techniques lack the spatial resolution required to capture the embryonic stages of ice nucleation at the molecular scale.

To bridge this gap, molecular dynamics (MD) simulations employing atomistic19,20 and coarse-grained water models21,22 have been widely employed to probe the microscopic mechanisms of ice formation. Among these, the monoatomic water (mW) model23 has been extensively applied due to its computational efficiency and ability to reproduce key thermodynamic and structural properties of water, such as the melting point and local tetrahedrality21,22,24,25, despite its limitations in representing hydrogen atoms and electrostatic interactions. Nevertheless, a comprehensive understanding of the microscopic crystallization pathway throughout the entire icing process, spanning from embryonic nucleation to the establishment of a thermodynamically stable phase, remains elusive. Whether the process follows a one-step classical nucleation theory26,27, involves metastable intermediates as proposed in non-classical nucleation mechanisms28, or proceeds via an adsorption-mediated nucleation pathway as recently suggested29–31, remains an open question.

Here, by employing in-situ cryogenic transmission electron microscopy (cryo-TEM) with millisecond temporal resolution and picometer spatial resolution, we demonstrate a feasible experimental approach to directly map the microscopic crystallization pathways of ice I from nucleation to equilibrium states. These observations are further corroborated by MD simulations, demonstrating an amorphous ice adsorption-facilitated spontaneous nucleation and growth of polymorphic ice I during the vapor deposition process.

Results
Heterogeneous ice nucleation and growth
By the in-situ cryo-TEM equipped with high-resolution real-time and real-space imaging (see “Methods”), we investigated the micro-dynamics of ice I formation from vapor deposition on translucent graphene substrates under non-equilibrium conditions, with a temperature of 102 K and a pressure of 10−6 Pa. Figure 1 represents the process of crowded nucleation and growth, where multiple nuclei emerge within a relatively small region (Supplementary Movie 1).

During the initial stages of vapor deposition (0–1 s), clusters of amorphous solid water32,33 formed on the cryogenic graphene substrate, serving as an adsorption layer (Fig. 1a, b, f, g). This observation is consistent with the hypothesized adsorption nucleation theory for heterogeneous freezing in deposition mode30.

Subsequently, two isolated hexagonal ice (ice Ih) nuclei, ≈5 nm in size and designated as Ih1 and Ih2, evidenced from the sequential TEM images and the respective corresponding fast Fourier transform (FFT) data (Fig. 1c–e, h–j). From FFT, the diffraction peak corresponding to amorphous ice and estimated from the halo pattern was observed at 3.9 Å. This coincides with the position of the {100} Bragg peak of ice Ih with lattice constants of a = 4.5 Å and c = 7.3 Å. Both ice nuclei Ih1 and Ih2 were oriented in the 〈001〉 crystallography direction without lattice registry with the graphene substrate. The deposits during the initial nucleation process deduced from the real-time TEM images were not sharp-faceted and exhibited convex shapes.

While the ice Ih2 nucleus gradually diminished and eventually disappeared, the nearby ice Ih1 nucleus continued to grow (Fig. 1k, l), suggesting that either the larger size of the Ih1 nucleus exceeds the critical size required for sustained growth, or that larger nuclei grow at the expense of smaller ones due to the Ostwald ripening process34. Meanwhile, a third hexagonal ice nucleus (Ih3), a cubic-ice35,36 twin nucleus (Ic1), and a single-crystalline cubic ice nucleus (Ic2) formed around ice Ih1 nucleus (Fig. 1k–t). The corresponding FFT analysis of these sequential TEM images indicated that nucleus Ih3 shared the same orientation as Ih1 along the 〈001〉 crystallographic direction. In contrast, both Ic1 and Ic2 nuclei were oriented along the 〈110〉 axis, with {111} plane d-spacing of 2.3 Å, consistent with a face-centered cubic lattice constant of 6.4 Å. The competitive heterogeneous nucleation, growth, and aggregation of these ice deposits produced an evolving botryoidal shape, revealing surface instability driven by the diffusion of water molecules.

Both nuclei Ic1 and Ic2 first grew to a dozen nanometers in size in tens of seconds and then dissolved or sublimed finally without a notable solid-state phase transition (Fig. 1u–ad, Suppl. Figs. 1 and 2). As a corollary, we can declare that the transient ice Ic that observed during the crowded ice nucleation and growth process acted simply as a competitor for ice Ih. In parallel, ice Ih nuclei aggregated and grew to tens of nanometers (see more examples in Suppl. Figs. 3 and 4). This dynamic behavior indicated that a surface energy-minima driven ripening process was predominant, which might explain why the smaller-sized ice Ih2 nucleus disappeared as the larger nuclei grew. In the following growth process, the randomly spread out ice clusters intuitively evolved towards the edge of the ice Ih1 island and aggregated (Fig. 1u–x). Finally, the initial convex ice Ih1 crystallite transformed into a 50-nm-sized well-formed euhedral crystallite in about an hour after the crowded growth, exhibiting a mature plate-like stout hexagonal prism (Fig. 1y).

Moreover, the corresponding FFT (Fig. 1ad) of the high-resolution TEM image of the ice crystallite clearly demonstrate the six prism facets of ice Ih, implying that Wulff’s construction37 in related to surface free energy was valid for the equilibrium crystal shape of ice Ih at microscopic size, consistent with the six-sided hexagonal crystal habit of ice I at macroscopic level.

Surface structure
The surface structure of the fully-grown ice Ih crystallite resulting from the crowded growth process was further carefully examined. Intriguingly, the exposed prism facets of the equilibrium ice Ih crystallite were partially coated with a thin layer of cubic ice, hinting at ice Ic nucleation occurred on this stable base (Fig. 2). Figure 2a shows the low-magnification TEM image of the faceted ice Ih crystallite. We sorted and numbered 12 typical ice crystallite areas in the micrograph. The corresponding TEM images of the respective regions were magnified and measured using the associated FFT (Fig. 2b).

Using the micro-domain lattice structure scanning analysis, we derived the planar spatial configuration of ice Ih crystallite, indicating that both the bulk and the upper sides of the hexagon (1–5) exhibited the structure of ice Ih oriented along the 〈001〉 crystallographic zone axis. Intriguingly, the other prism surfaces (6–12) featured an in-plane lattice epitaxial shell of 〈111〉 zone axis-oriented cubic ice measuring ≤1.5 nm in width, as evidenced by both micrographs and, notably, the corresponding FFT. In the FFT, the disappearance of diffraction spots exclusively corresponding to {100} planes of ice Ih indicated a deviation of the structure in the shell from the bulk, leaving only spots representing {220} planes for ice Ic, which were loosely distributed with a d-spacing of 2.3 Å (Fig. 2b, Suppl. Fig. 5). Accordingly, the observed mature crystallite displayed an intriguing in-plane Ih/Ic heterogeneous structure, as illustrated schematically in Fig. 2c.

Real-time images revealed the nucleation and growth of cubic ice on the prism surface of ice Ih crystallite during its faceting process. In contrast to the well-faceted mature ice Ih crystallite, the rounded ice Ih formed during the early stages of growth exhibited no signs of cubic ice on its surface (Suppl. Fig. 6). This suggests that the probabilistic nucleation of ice Ic under current conditions does not transition to the thermodynamically stable ice Ih, indicating that it is not an intermediate phase in the nucleation and growth pathway of ice Ih. More intriguingly, the region where the cubic ice shell was discovered corresponded to the lower portion of ice Ih, where previous observations have noted the nucleation and dissolution of ice Ic crystallites. In stark difference, the cubic ice shell was oriented in 〈111〉 direction that is distinct from the 〈110〉 orientation for the initial Ic crystallites. It is noteworthy that the {112̅} planes of 〈111〉-oriented ice Ic aligned with the {100} planes of 〈001〉-oriented ice Ih, demonstrating an unexampled in-plane coherent heterostructure. Thus, these observed coincidences suggest that the unusual cubic shell forming on the ice Ih structure might have resulted from growth driven by interfacial free energy minima.

Oriented aggregation
It is evident that the interplay between nuclei polytype, interface orientation, nuclei size, and nuclei spacing resulted in varied growth patterns of ice crystallites in the present conditions.

Further observations suggested that when concomitant polymorphic ice nuclei were spaced slightly farther apart and grew independently, cubic ice achieved sizes similar to those of equilibrium ice Ih via a comparable process of nucleation, aggregation, and faceting (Suppl. Figs. 7 and 8). More intriguingly, when the sizes of polymorphic ice nuclei were similar, and the distance between them was within the nanometer range (Fig. 3), the orientation-aligned polymorphs, albeit occasionally happening, tended to form a coherent interface as they grew and attached. This further supports the critical role of interfacial free energy minima-driven oriented aggregation in dictating ice growth. Figure 3a, b shows that a 〈001〉 zone axis-oriented ice Ih nuclei first formed in the amorphous ice matrix and then grew to several nanometers on a graphene substrate. Later on, the growth of this ice Ih nuclei was followed by the nucleation and growth of a 〈111〉 zone axis-oriented ice Ic crystallite (Fig. 3c–l).

Analysis of the FFTs corresponding to sequential micrographs showed that the two polymorphic nuclei aligned in the layer-stacking direction orientation from the embryonic nucleation stage (Fig. 3e–h, m–p). Moreover, the basal {110} plane of the 〈001〉 crystallography direction-oriented ice Ih nucleus and the {22̅0} plane for the 〈111〉 crystallography direction-oriented ice Ic were found to be parallel. Consequently, when the two polymorphic nuclei grew and attached, the resulting fused hexagons once again formed an in-plane coherent heterojunction (Fig. 3k). It seems that this in-plane heterogeneous configuration has been overshadowed by the out-of-plane heterostructures found in ice Isd, which have drawn more attention in previous discussions7,38. However, the growth dynamics revealed here suggest that it is plausible for both types of heterostructure to form during ice growth driven by coherent interfaces.

The oriented assembly and faceting phenomena observed in the present study are consistent with growth processes reported in other systems, such as mesocrystals and inorganic crystals39. This reaffirms the significance of interface engineering in crystal assembly within the context of ice formation. The concept of oriented interface-driven aggregation might reveal why macro-sized snowflakes consistently exhibit a sixfold rotational symmetrical self-similar fractal structure that aligns with their microscopic symmetry, despite the assembly of numerous branches during the growth process.

Spontaneous nucleation
While the microscopic ice growth data support the validity of thermodynamic criteria based on free energy minima, the complex polymorphism resulting from the probabilistic presence of metastable cubic ice observed here is challenging to explain, warranting a detailed study into the critical nucleation stages. The CNT indicates that the nuclei directly enter the stable phase when they exceed the critical size as to overcome the free energy barrier27. Recent investigations on kinetics in biomineralizations demonstrated that the crystallization passes through less stable states to finally reach the most stable crystalline state, i.e., following the Ostwald’s law of phases40. The anomaly of the observed ice nucleation pathway in the present study thus suggests that ice Ic could have been only a transient intermediate phase in previously established models based on the fact that ice Ic is considered metastable compared to ice Ih32. The consistently observed ice Ic either nucleates and grows independently or nucleates over on mature Ih crystallites, suggesting that the process for polymorphic ice nucleation is a stochastic selection other than a thermodynamic preference dictated by the free-energy landscape under the current conditions as illustrated in Fig. 4a.

To gain a deeper understanding of the nucleation process, we conducted a statistical analysis of heterogeneous ice nucleation and growth rates under the present conditions by tracking a large number of individually ice nuclei as they formed. The entire process, from the embryonic to the equilibrium state of over 100 groups of isolated nucleated nuclei, was meticulously recorded. The corresponding large-scale nucleation and growth processes were charted. Several sequential TEM imaging recording examples are depicted in Suppl. Fig. 9. Figure 4b presents scattered plots of growth rates against the radius size of nuclei throughout the entire growth process. Instantaneous growth rates were calculated based on raw experimental data because the nucleation and growth rates measured in our system rapidly decay over time and reach various plateaus (Fig. 4c, d). In contrast to the classical nucleation scenario where nuclei smaller than a critical size tend to shrink, it is evident that there was a consistent statistical increase in the sizes of ice nuclei observed in the present study.

Additionally, the net growth probabilities for ice nuclei throughout the overall growth process were consistently positive (Fig. 4e). This observation suggests the absence of a critical nucleus size, rc, which lies within the range where the net probability changes from negative to positive, as predicted by CNT. Alternatively, this implies a zero free-energy barrier within the framework of CNT, leading to spontaneous ice nucleation in the current conditions.

The initial average growth rate was estimated to be G_ = 4.7 × 10−2 nm s−1, while the nucleation rate was N_ = 4.6 × 107 cm−2 s−1 (see “Methods”), surpassing previous studies in heterogeneous nucleation for the supercooled water regime around 250 K in the atmosphere by at least three to four orders of magnitude4. Given the significant differences between the current and atmospheric conditions, the absence of empirical parameters within this gap presents considerable challenges when extrapolating heterogeneous ice nucleation models from the atmosphere to this extreme environment.

We extended CNT, which is based on atmospheric parameters, to low-temperature environments for the analysis of heterogeneous nucleation in extremely supercooled conditions, identifying free energy barriers despite limitations such as the lack of microscopic description and the failure of capillarity approximation in early and strong supercooling stages (see “Methods”). Nonetheless, CNT offers qualitative insights into the thermodynamics and kinetics across various systems, extending its applicability from gas-liquid to gas-solid transitions, including heterogeneous nucleation4,9. Assessing the nucleation free energy barrier across temperatures ranging from mild to deeply strong supercooling states relative to the melting temperature of 269 K, the observed energy barrier in the mild supercooling state aligned with previously reported values41, confirming the reliability of the parameters used in the study (see “Methods”, Suppl. Fig. 10).

Consequently, the determined energy barrier was approximately 0.22 kT under the present supercooled vapor deposition conditions. With this barrier lower than 1 kT, ice nucleation became spontaneous as thermal perturbation aided in overcoming the barrier, consistent with experimental statistical data. This spontaneous nucleation behavior of randomly-oriented, polymorphic ice I was also observed on hBN and amorphous carbon substrates (Suppl. Figs. 11 and 12), implying that under deeply supercooled conditions, which are characterized by reduced kinetic energy and dominant hydrogen-bonding interactions, heterogeneous ice nucleation proceeds via a similar mechanism regardless of the specific substrate. In other words, both experimental and computational data suggest that the current state of deep supercooling will lead to energy-barrier-free heterogeneous nucleation of cubic and hexagonal phases. This, in turn, results in the formation of various polymorphs and heterojunction structures through subsequent growth processes, driven by the lowest interface energy.

Non-classical growth
MD simulations were conducted to further evaluate the free energy profile for the nuclei growth pathways observed in the experiments, including discrete growth, oriented aggregation, and Ostwald ripening, as shown in Fig. 5 (see “Methods”, Supplementary Fig. 13). Specifically, we investigated the growth and ripening of three typical ice nuclei with Ih 〈001〉, Ic 〈111〉, and Ic 〈110〉 orientations exposed to the substrate, which are the predominant ice structures observed experimentally and exhibit the lowest potential energy in MD simulations (Suppl. Fig. 14). Figure 5a presents the MD snapshots and the corresponding free energy profile for the growth of ice Ic and Ih nuclei growth through monomer attachment, demonstrating a rapid decrease in free energy that indicates a preference for discrete growth in the initial stages. Figure 5b–e illustrates the typical merging process of nuclei during growth. Ice Ic along the 〈110〉 orientation tends to form twin boundaries on the {111} stacking planes, resulting in varied twin crystals, while ice Ih undergoes oriented aggregation upon contact, highlighting the interfacial-driven growth process. This behavior is also observed in the merging of polymorphic nuclei as shown in Fig. 5e, where larger ice Ih tend to consume smaller ice Ic nuclei, indicating a ripening process. Additionally, larger ice Ih can also consume smaller ice Ih as well. When nuclei of comparable sizes come into contact, the resulting heterostructure of ice Ic and ice Ih with a coherent interface exhibit a metastable state to a single-phase crystal.

The overall free energy evolution pathway for the competitive growth of ice Ic and ice Ih nuclei was further examined. Figure 5f presents a plausible pathway that illustrates discrete growth through monomer attachment during the initial stages. Upon contact between two or more nuclei, the interfacial-driven merging process causes a reduction in free energy, resulting in the formation of stable crystalline phases. It is noteworthy that the interfacial-driven coalesce scenario demonstrates lower free energy and greater efficient compared to discrete growth, providing mechanistic support for the experimentally observed post-nucleation phenomena.

In the future, further studies on ice crystallization dynamics under varying environmental conditions are crucial to fully reveal the microscopic kinetic nucleation pathways underling the thermodynamic phase diagram, as well as to gain a deeper understanding of the phase transitions and critical phenomena in ice. Moreover, experimentally examining the microscopic mechanisms serves to furnish empirical parameters that are essential for a foundational understanding in harmony with theoretical concepts of nucleation kinetics and thermodynamics. This symbiotic relationship between empirical and theoretical research facilitates a more profound understanding of the prevalent crystallization process, holding promise for guiding crystal design and optimizing performance.

Methods
In-situ cryogenic TEM characterization
An ultra-low dose in-situ cryogenic TEM imaging technique36 was employed to visualize the formation and growth process of individual ice I crystallites on monolayer graphene substrates at molecular resolution. Residual water vapor in the high vacuum (≈10−6 Pa) of a TEM column served as the precursor source while the temperature gradually cooled from room temperature to ≈100 K over the course of 30 min. Solid state water deposition was initiated in low-pressure conditions when the temperature dropped to 110 K, which was consistent with previous observations.

Data fitting
Individual ice nuclei were monitored in real time to observe the nucleation and growth processes. The time-dependent behavior of ice nucleation and growth was elucidated using the Avrami equation42, which describes transition kinetics from one phase to another via random formation of nuclei in the parent phase43. We fitted the following equations to the experimental nucleation density n(t) and nuclei size r(t) data by modifying the original Avrami equation:

dn/dt = N_ e−(t/t1)3 (1)

dr/dt = G_ e−(t/t2)3 (2)

The exponential decay over t3 arises from the finite volume effect on a two-dimensional plane, while the nucleation rate N_ and growth rate G_ represent the maximum rates at the initial time.

We first performed such fitting for each individual data curve to smoothen the fitted results and then plotted the average smoothed n(t) and r(t) over all samples. Next, we extracted the initial nucleation and growth rates from the smoothed n(t) and r(t) using the finite-difference method.

Second-order corrections included ΔG estimation
Second-order corrections to thermodynamic parameters were introduced into the computation of Gibbs free energy to better capture the thermodynamics of water-ice transition44. The equation for ΔG is given by

ΔG = 16πT2v2 / 3(ΔH sl)2(ΔT)2 * (γ3 - ΔCγ3 / 3ΔH * ΔT) (3)

where vm is the molecular volume of ice (3.65 × 10−29 m3), ΔC is the difference in isobaric heat capacity between water and ice (40.1 J mol−1 K−1), ΔH is the enthalpy of fusion (6.017 kJ mol−1), and ΔT is the supercooling (269 K). Experimental data for ΔC suggest values around 40.1 J mol−1 K−1 (ref. 45), while calculations for TIP4P/2005 yielded a value close to 41.8 J mol−1 K−1 (ref. 47). Enthalpy data for ice and water at various temperatures provide a value of 39.4 J mol−1 K−1 (ref. 44). Surface tension is estimated at 26.2 mJ m−1 (ref. 44): a value between 30.88 mJ m−1 for Ih/water and 23.65 mJ m−1 for Ic/water46.

The estimated barriers were in good agreement with the findings by Niu et al.41 and Wang et al.44 in mild supercooling conditions. This method also serves as a useful test for CNT in strong supercooling conditions.

Two sets of parameters were employed to describe the nucleation barrier from vapor to ice in strong supercooling conditions. In the more precise set of parameters, ΔH sv was calculated as the sum of ΔH lv at 273 K and ΔH sl at 273 K, resulting in (6.017 + 45.064) kJ mol−1 = 51.081 kJ mol−1 (ref. 48). Additionally, a numerical fit of ice enthalpy and vapor enthalpy in mild supercooling conditions was used to extrapolate ΔH sv during strong supercooling. Specifically, the extrapolated ΔH sv was found to be 51.344 kJ mol−1 at the experimental temperature of 102 K and remained relatively stable (0.6% change) within the range of 98–273.15 K.

Regarding ΔCp, a significant variation was observed in the reported estimates of isobaric heat capacity for water, with reported values of 75.730 J mol−1 K−1 (273.15 K)49, 76.023 J mol−1 K−1 (273.15 K)48, 99 J mol−1 K−1 (273.15 K)44, and 117.152 J mol−1 K−1 (235 K)49. The values for ice were 13.141 J mol−1 K−1 (102 K)48, 37.97 J mol−1 K−1 (273.15 K)48, to 59.6 J mol−1 K−1 (273.15 K)44. In addition, a value of 16.033 J mol−1 K−1 at 100 K has been reported for vapor48.

Conversely, surface tension is challenging to measure, with reported values of 10 and 44 mJ m−2 at the melting temperature50. Typically, it can only be determined indirectly using the Young’s equation, which involves known contact angles of liquid on solid and known surface tensions51. In the present calculations, 59.6 J mol−1 K−1 was directly utilized as ΔCp and 75.7 mJ m−2 as the surface tension. The following liquid-like values were adopted in the alternate set of parameters: 23.65 mJ m−2 for the surface tension46, 5.01 kJ mol−1 for the enthalpy change46, 59.6 J mol−1 K−1 for the change in isobaric heat capacity44, and 269 K for the melting temperature46.

Ice saturation ratio included ΔG estimation
Using saturation ratio52 is another method to estimate ΔG, such that

ΔG = 16πT2v2 / 3(kT ln S)2 * γ3 (4)

The molecular volume of ice and surface tension remain the same as described above. The ice saturation ratio (S) is defined as the ratio between the vapor pressures of supercooled vapor and ice. Our experimental vapor pressure (10−6 Pa) was utilized in the present study and the parameterizations for the vapor pressure of ice were employed according to the following equations described by Murphy and Koop52

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This study explores the heterogeneous nucleation and crystallization pathways of ice on graphene substrates at 102K under\nultra-high vacuum (10⁻⁶ Pa). By combining in-situ cryo-TEM imaging with molecular dynamics (MD) simulations, the authors\ntrack how water molecules assemble, nucleate, and grow into ice under extreme supercooling conditions.\nA key finding is that ice nucleates and crystallizes rapidly at 102K, despite expectations that diffusion should be extremely\nslow at such low temperatures. The study suggests that graphene significantly lowers the energy barrier for nucleation,\nallowing ice formation to proceed without the usual reliance on molecular diffusion. The work also provides insight into\npolymorphic ice formation, showing how hexagonal ice (Ih) and transient cubic ice (Ic) emerge and interact through different\ngrowth mechanisms, including Ostwald ripening, oriented coalescence, and aggregation.\nI find the work and manuscript well-executed and valuable. However, I have a few questions\nthat may help guide the reader and address some points of curiosity:\n- Does graphene act as a template for ice nucleation, influencing the orientation and structure of the forming ice? Are there\nspecific substrate-water interactions (e.g., van der Waals forces, hydrogen bonding) that could explain the observed\nnucleation dynamics?\n- Is there any observation of bilayer ice, similar to what has been seen in previous MD simulations? Has the height of the ice\nnuclei been measured, and does it match expected bilayer thicknesses?\n- The study states that nucleation occurs without a significant energy barrier (~0.22 kBT). Do the MD simulations predict the\nsame barrier, or are there discrepancies between experimental and computational results?\n- Would similar nucleation behavior be expected on other substrates? If so, which types of surfaces might facilitate\nnucleation in a way similar to graphene?", "reviewer_2": "The manuscript titled “Molecular-resolution mapping of heterogeneous ice nucleation and crystallization pathways”\npresented by Wang. et. al. describes a significant methodological innovation in experimental investigation of ice nucleation\nusing in-situ cryogenic transmission electron microscopy through a case study that unravels the freezing pathways of\ndeposition ice nucleation observed at 102 K on a graphitic surface. The results are supported by coarse grained molecular\ndynamics simulations. The method presented in the manuscript is clearly revolutionary and, to my knowledge, goes beyond\nthe temporal and spatial resolution of any experimental technique that has so far been used for observing ice nucleation at\nmicroscopic scales. The result are promising and tend to align with well known theoretical foundations of\nice nucleation science. It has the potential to revolutionize our understanding of this process\nand help to significantly improve its representation in climate models for instance, where the lack of detailed theoretical understanding of ice nucleation\naccounts for a significant fraction of the model uncertainties. Therefore, I believe that the manuscript is of interest for an\nextended community and should be considered for publication after the following comments are addressed.\nMajor comments\nThe introduction covers basics of ice nucleation science. However, despite of the paper presenting a methodological\ninnovation/novel approach it somewhat flies through the description of existing methods to observe ice formation, such as E-\nSEM, freezing assays or MD simulations. I am particularly missing an at least semi-quantitative comparison of the above,\npointing out why innovation is needed (eg. spatial resolution, costs etc.) It would really make it much easier for the reader to\nput the new method into context if this information was added in the manuscript. In general references to the abundant\namount of previous literature could be added at many points, some of which are highlighted in this review.\nIn line 49-51 of the introduction, the authors state: “So far, achieving a comprehensive understanding of the microscopic 48\ncrystallization pathway throughout the entire icing process, spanning from nucleation to the establishment of 49 a\nthermodynamically stable phase, whether it adheres to the one-step classical nucleation and growth12,13 50 scenario or the\nmetastable phase-involved non-classical nucleation and growth14 scenario remains elusive.” I would like to point out that\nthe invalidity of the single step classical nucleation behavior exactly of deposition ice nucleation has been hypothesized by\nthe Adsorption Nucleation Theory (Laaksonen et. al. 2020, https://doi.org/10.5194/acp-20-13579-2020). Lately molecular\nsimulations for instance by Lbadaoui-Darvas et. al. 2023 (https://doi.org/10.5194/acp-23-10057-2023) and Roudsari et. al.\n2024 (https://doi.org/10.1039/D3EA00140G) have also demonstrated that a mechanism obeying the classical nucleation\ntheory is impossible in the case of deposition freezing as it always passes through the adsorption of supercooled water\nnanodroplets (which are also observed in your experiments).\nThe molecular simulations presented use a standard approach to studying ice nucleation however the technical choice raise\na series of questions.\nTo my understanding the authors placed already existing ice slabs on their substrate and simulated heating cooling cycles.\nNeither the length of the entire simulation nor the rate of the temperature change are reported, without which it is hard to\njudge how far out of equilibrium the simulated heating-cooling cycle is. Without this information the interpretation of the\nobtained structures is somewhat arbitrary, so these data should be added to the methods section. The total length of the\nsimulation is important because relaxation and the formation of the real equilibrium structures is known to be largely limited\nby the hindered thermal motion at extreme low temperatures. Please also report a measure of relaxation (i.e. the stabilization\nof the slowest changing variable in the system) for the equilibration of the structures.\nIt appears to me that the authors use an amourphous surface consisting of Lennard-Jones spheres as the model of graphite,\nwith this neglecting lattice match between graphite and water. Please repeat the simulations with an actual graphite\nmultilayer.\nFurthermore, the authors should report the source of the Lennard-Jones parameters that they use, and clarify if the values\nreported are pairwise LJ parameters of between the carbon and the oxygen atom or atomistic ones of the carbon only. In the\nformer case the values should also be carefully revised, as more commonly epsilon values of 1.3 kcal/mol/nm and sigma\nvalues of 0.32 nm are reported for the pairwise LJ parameters between the carbon and the oxygen atom (see for instance\nhttps://doi.org/10.1063/1.4895543).\nFinally, it is not a simple task to find the optimal configuration of ice nanostructures at a solid surface. Given the stochasticity\nof the ice nucleation process, these structures can vary greatly and should be selected by a careful optimization method for\ninstance as presented by Pedevilla et. al. (https://doi.org/10.1063/1.5029336) Alternatively MD simulations themselves can\nbe used to grow real thermodynamically stable ice grains on solid surface using for instance GCMC/MD\n(https://doi.org/10.5194/acp-23-10057-2023). One of these methods should be adapted when preparing new geometries for\nthe simulations in order to ensure that real equilibrium structures and not metastable ones are used.\nHow do your results align with the existance of stacking disordered ice (Ih + Ic) which is expected to form in a patchy\nstructure at the initial steps of freezing, after which it converts into a layered metastable structure with a long lifetime, that\nfinally reaches the thermodynamically stable hexagonal state. Does any of your experimental data indicate that such\nprocess occurs?\nMinor comments\nIn line 38 tetrahedron alignment should be tetrahedral\nIn the FFT signal how do you differentiate amorphous ice and very strongly supercooled water, is it possible that the two are\nindistinguishable?\nIn line 69-70 the authors state “While the ice Ih2 nucleus gradually diminished and eventually disappeared, the nearby ice\nIh1 nucleus 69 continued to grow (Fig. 1 k, l), suggesting that either the larger size of the Ih1 nucleus exceeds the critical size\n70 required for sustained growth, in line with classical nucleation theory (CNT)” . Previously they mention the presence\nof amorphous droplets before freezing onset, which cannot be in-line with the classical nucleation theory which treats ice\nnucleation from the vapor phase a single step processes with no intermediate states between the crystalline ice and the\nvapor. Please clarify this.\nLine 128 nanometer rang should be nanometer range."}, "author_response": "Point-to-Point Response to Referee Reports\nReferee #1\nThis study explores the heterogeneous nucleation and crystallization pathways of ice on\ngraphene substrates at 102K under ultra-high vacuum (10⁻⁶ Pa). By combining in-situ cryo-\nTEM imaging with molecular dynamics (MD) simulations, the authors track how water\nmolecules assemble, nucleate, and grow into ice under extreme supercooling conditions.\nA key finding is that ice nucleates and crystallizes rapidly at 102K, despite expectations that\ndiffusion should be extremely slow at such low temperatures. The study suggests that graphene\nsignificantly lowers the energy barrier for nucleation, allowing ice formation to proceed\nwithout the usual reliance on molecular diffusion. The work also provides insight into\npolymorphic ice formation, showing how hexagonal ice (Ih) and transient cubic ice (Ic) emerge\nand interact through different growth mechanisms, including Ostwald ripening, oriented\ncoalescence, and aggregation.\nI find the work and manuscript well-executed and valuable. However, I have a few questions\nthat may help guide the reader and address some points of curiosity:\nReply: We thank the referee for the positive comments and valuable suggestions for further\nimproving our manuscript. The recognition and improvement of our present study is greatly\nappreciated.\n1. Does graphene act as a template for ice nucleation, influencing the orientation and structure\nof the forming ice? Are there specific substrate-water interactions (e.g., van der Waals forces,\nhydrogen bonding) that could explain the observed nucleation dynamics?\nReply: We thank the reviewer for this insightful question regarding the potential epitaxial role\nof graphene substrate in ice nucleation. While it is plausible that a crystalline substrate such as\ngraphene, with hexagonal symmetry and hydrophobic honeycomb lattice, could promote\nepitaxial growth, our cryo-TEM analysis (Fig. R1) of individual ice crystallites formed via\nvapor deposition on graphene shows no evidence of lattice registry or preferential orientational\nalignment with the substrate. The observed Ice I crystallites exhibit random orientations and\npronounced polymorphism, suggesting that graphene does not serve as a template for ice\nnucleation under the conditions studied. This analysis is included in the revised manuscript as\nSupplementary Fig. S11.\nTo further examine substrate effects, we conducted comparative experiments on monolayer\nhBN and amorphous carbon. As shown in Fig. R2 below, similar nucleation and growth\nbehavior was observed across all substrates, indicating a substrate-independent crystallization\nmechanism. Under deep supercooling, we conclude that the nucleation barrier is significantly\nreduced and the process is dominated by hydrogen bonding rather than epitaxial or kinetic\nconstraints.\nFig. R1. Polymorphic and randomly oriented ice crystallites grown via vapor deposition on\ngraphene. The low-magnification micrograph shows ice-deposited region on a cooling\ngraphene substrate. The high-magnification images and corresponding diffractogram patterns\nof the distinct areas in low-magnification image, highlighting individual crystallites, reveal the\ncoexistence of ice Ih and Ic with no preferential orientation. The random orientations and\npolymorphism indicate the absence of epitaxial alignment between the ice and the underlying\ngraphene lattice.\nFig. R2. Evolution of nucleus size over time on different cooling substrates. Time-dependent\ngrowth curves of ice nuclei formed via vapor deposition on graphene, monolayer hBN, and\namorphous carbon substrates under identical high vacuum and cryogenic conditions. All cases\nexhibit spontaneous growth of polymorphic ice, highlighting a substrate-independent\ncrystallization mechanism.\n2: Is there any observation of bilayer ice, similar to what has been seen in previous MD\nsimulations? Has the height of the ice nuclei been measured, and does it match expected bilayer\nthicknesses?\nReply: We thank the referee for this important question. In our experiments, we did not observe\nany discernible bilayer ice structures. The detectable height of ice nuclei in our cryo-TEM\nmeasurement is generally greater than 2 nm, as low-dose electron beam imaging requires\nsufficient specimen volume to generate measurable contrast. In comparison, bilayer ice—\ntypically ~2.5 Å in thickness–lies well below the detection threshold of conventional TEM,\nparticularly when its signal is embedded within the combined electron transmission from\ngraphene, amorphous ice, and ice nuclei.\nBilayer ice has been reported in simulations of confined water (Physical Review Letters 79,\n5262–5265, 1997)) and in STM/AFM studies of water adsorbed on Au (111) surfaces (Nature\n577, 60–63, 2020). However, such structures typically form under specific conditions,\nincluding confinement or highly ordered metal substrates, which differ substantially from the\nopen cryogenic environments used in our experiments. Additionally, the low pressure and\ntemperature conditions employed here may not favor the formation or stabilization of bilayer\nphases at the initial interface.\nWe agree that bilayer ice remains an intriguing target for future structural investigation, and\nemerging techniques such as liquid-cell TEM with advanced temperature control could provide\nfurther insight. However, such methods are beyond the scope of the present study.\n3: The study states that nucleation occurs without a significant energy barrier (~0.22 k T). Do\nB\nthe MD simulations predict the same barrier, or are there discrepancies between experimental\nand computational results?\nReply: The MD simulation using the coarse-grained mW water model is not ab initio and\ntherefore lacks the precision required to accurately predict the nucleation energy barrier.\nHowever, we can still make an estimation of the energy barrier using the mW potential model.\nThe energy barrier is estimated based on Equation.3 of the manuscript as\n2 2 3 2 2 3\n16𝜋𝜋𝑇𝑇𝑚𝑚𝑣𝑣𝑖𝑖𝑖𝑖𝑖𝑖𝛾𝛾𝑠𝑠𝑠𝑠 8𝜋𝜋𝑇𝑇𝑚𝑚𝑣𝑣𝑖𝑖𝑖𝑖𝑖𝑖∆𝐶𝐶𝛾𝛾𝑠𝑠𝑠𝑠\n∆𝐺𝐺 = 2 2 − 3\n3(∆𝐻𝐻𝑚𝑚) (∆𝑇𝑇) 3(∆𝐻𝐻𝑚𝑚) ∆𝑇𝑇\nFor the mW model, some of corresponding parameters for cubic ice Ic (hexagonal ice Ih) were\ndocumented in prior studies [J. Phys. Chem. B 113, 4008 (2009), J. Chem. Theory Comput. 11,\n5613, (2015)] as follows:\nmelting temperature: ,\nsurface tension: 𝑇𝑇𝑚𝑚 = 269.0 (274.7) K ,\n2\nenthalpy change: 𝛾𝛾𝑠𝑠𝑠𝑠 = 23.65 (30.88 ) mJ/m\n.\n∆𝐻𝐻𝑚𝑚 = ∆𝐻𝐻 solid−liquid +∆𝐻𝐻 liquid−vapor\nT h e r e s t o f t h e p a r a m e t e r c a n = be5 .d0i1re (c5tl.y2 9o)b tkaJi/nmedo flr+om4 4M.5D6 skiJm/mulaotlio=ns4 a9s.5 f7o l(lo4w9.s9: 5 ) kJ/mol\nmolecular volume of ice ,\n−29 3\nsupercooling temperature 𝑣𝑣𝑖𝑖𝑖𝑖𝑖𝑖 = 3.01 (3.00)×10 m\n,\n∆𝑇𝑇 = 𝑇𝑇𝑚𝑚 −𝑇𝑇\n= 269.0 (274.7) K−102.0K = 167.0(172.7)K\ndifference in heat capacity\n∆𝐶𝐶 = 𝐶𝐶liquid−𝐶𝐶solid\n= 30.06J/(mol∙K)−25.7. 6 (25.31)J/(mol∙K)\n= 4.30 (4.71) J/(mol∙K)\n4: Would similar nucleation behavior be expected on other substrates? If so, which types of\nsurfaces might facilitate nucleation in a way similar to graphene?\nReply: We thank the referee for this insightful question. Due to the experimental constraints--\nnamely the ultra-high vacuum environment, liquid-nitrogen cryo-temperatures, and the need\nfor electron-conducting and electron-transparent substrates compatible with TEM imaging—\nthe range of applicable substrates is limited. Nonetheless, to assess substrate dependence, we\nconducted additional experiments using monolayer hBN and ultrathin amorphous carbon as\nalternative supports for vapor-deposited water.\nAs shown Fig. R2 (now included as Supplementary Fig. 12 in the revised manuscript), both\nsubstrates exhibit spontaneous nucleation and growth dynamics comparable to those observed\non graphene. These consistent results indicate that under deeply supercooled conditions, where\nkinetic energy is substantially reduced and the potential energy landscape is dominated by\nhydrogen bonding, the nucleation pathway becomes largely substrate-independent.\nWe have revised the manuscript to include the following clarifying sentence:\n“This spontaneous nucleation behavior was also observed on hBN and amorphous carbon\nsubstrates (Supplementary Fig. 12), implying that under deeply supercooled conditions, which\nare characterized by reduced kinetic energy and dominant hydrogen-bonding interactions,\nheterogeneous ice nucleation proceeds via a similar mechanism regardless of the specific\nsubstrate.”\nReferee #2:\nThe manuscript titled “Molecular-resolution mapping of heterogeneous ice nucleation and\ncrystallization pathways” presented by Wang. et. al. describes a significant methodological\ninnovation in experimental investigation of ice nucleation using in-situ cryogenic transmission\nelectron microscopy through a case study that unravels the freezing pathways of deposition ice\nnucleation observed at 102 K on a graphitic surface. The results are supported by coarse grained\nmolecular dynamics simulations. The method presented in the manuscript is clearly\nrevolutionary and, to my knowledge, goes beyond the temporal and spatial resolution of any\nexperimental technique that has so far been used for observing ice nucleation at microscopic\nscales. The result are promising and tend to align with well known theoretical foundations of\nice nucleation science. It has the potential to revolutionize our understanding of this process\nand help to significantly improve its representation in climate models for instance, where the\nlack of detailed theoretical understanding of ice nucleation accounts for a significant fraction\nof the model uncertainties. Therefore, I believe that the manuscript is of interest for an extended\ncommunity and should be considered for publication after the following comments are\naddressed.\nWe thank the referee for their recognition and encouraging endorsement of our work. We\nsincerely appreciate the thoughtful feedback and have carefully addressed all suggestions to\nimprove the manuscript. Detailed responses to each point are provided below.\n1: The introduction covers basics of ice nucleation science. However, despite of the paper\npresenting a methodological innovation/novel approach it somewhat flies through the\ndescription of existing methods to observe ice formation, such as E-SEM, freezing assays or\nMD simulations. I am particularly missing an at least semi-quantitative comparison of the\nabove, pointing out why innovation is needed (eg. spatial resolution, costs etc.) It would really\nmake it much easier for the reader to put the new method into context if this information was\nadded in the manuscript. In general references to the abundant amount of previous literature\ncould be added at many points, some of which are highlighted in this review.\nReply: We thank the referee for this helpful suggestion. To better contextualize our approach,\nwe have added a comparative discussion of existing experimental and computational methods\nin the revised Introduction, highlighting their respective limitations in spatial resolution and\ntemporal access. The revised text reads:\n“Environmental scanning electron microscopy provides a feasible means to identify active sites\ninvolved in heterogeneous ice formation12,13, while water freezing assays enable direct\nobservation of ice nucleation behavior in micrometer-sized single droplet and particles14-18.\nHowever, both techniques lack the spatial resolution required to capture the embryonic stages\nof ice nucleation at the molecular scale.\nFully atomistic molecular dynamics (MD) simulations offer mechanistic insights but are\nlimited by computational cost, with spontaneous ice nucleation observed in only a single\nreported case¹⁹ ”.\nAdditional citations have been added where appropriate throughout the revised manuscript, in\nline with the referee’s recommendation.\n2: In line 49-51 of the introduction, the authors state: “So far, achieving a comprehensive\nunderstanding of the microscopic 48 crystallization pathway throughout the entire icing process,\nspanning from nucleation to the establishment of 49 a thermodynamically stable phase, whether\nit adheres to the one-step classical nucleation and growth12,13 50 scenario or the metastable\nphase-involved non-classical nucleation and growth14 scenario remains elusive.” I would like\nto point out that the invalidity of the single step classical nucleation behavior exactly of\ndeposition ice nucleation has been hypothesized by the Adsorption Nucleation Theory\n(Laaksonen et. al. 2020,https://doi.org/10.5194/acp-20-13579-2020). Lately molecular\nsimulations for instance by Lbadaoui-Darvas et. al. 2023 (https://doi.org/10.5194/acp-23-\n10057-2023) and Roudsari et. al. 2024 (https://doi.org/10.1039/D3EA00140G) have also\ndemonstrated that a mechanism obeying the classical nucleation theory is impossible in the\ncase of deposition freezing as it always passes through the adsorption of supercooled water\nnanodroplets (which are also observed in your experiments).\nReply: We thank the referee for this important observation and the relevant literature\nsuggestions. We have revised the sentence in the Introduction to acknowledge recent advances,\nincluding adsorption-mediated pathways observed in both simulations and experiments. The\nrevised sentence now reads:\n“So far, achieving a comprehensive understanding of the microscopic crystallization pathway\nthroughout the entire icing process, spanning from embryonic nucleation to the establishment\nof a thermodynamically stable phase, remains elusive, whether the process follows the one-step\nclassical nucleation theory20,21, involves metastable intermediates as in non-classical\nnucleation mechanisms22, or proceeds via an adsorption-mediated nucleation pathway as\nrecently proposed23-25.”\n3: The molecular simulations presented use a standard approach to studying ice nucleation\nhowever the technical choice raise a series of questions. To my understanding the authors\nplaced already existing ice slabs on their substrate and simulated heating cooling cycles.\nNeither the length of the entire simulation nor the rate of the temperature change are reported,\nwithout which it is hard to judge how far out of equilibrium the simulated heating-cooling cycle\nis. Without this information the interpretation of the obtained structures is somewhat arbitrary,\nso these data should be added to the methods section. The total length of the simulation is\nimportant because relaxation and the formation of the real equilibrium structures is known to\nbe largely limited by the hindered thermal motion at extreme low temperatures. Please also\nreport a measure of relaxation (i.e. the stabilization of the slowest changing variable in the\nsystem) for the equilibration of the structures.\nReply: We thank the reviewer for raising these important points regarding the simulation\nprotocol. Our MD simulations presented in Fig. 5 focus on the post-nucleation regime,\nspecifically the growth and coalescence of pre-existing ice nuclei. To efficiently sample the\nintermediate and final configurations along these growth pathways, we initialized\nrepresentative ice nuclei on the substrate and applied repeated heating-cooling cycles. This\nthermocycling protocol has been widely adopted to overcome kinetic barriers and accelerate\nrelaxation in non-equilibrium systems [Acta Mater. 213, 116952 (2021)]. The simulated growth\nbehaviors were consistent with our experimental observations. In addition, we mapped the free\nenergy surfaces associated with the growth process, which helped to reveal the underlying non-\nclassical crystallization pathways.\nTo address the reviewer’s concern regarding simulation timescales and equilibration, we have\nnow provided detailed temperature profiles and convergence analyses (Fig. R3a–c). As a\nrepresentative case, for the coalescence of Ih <001> and Ic <110> nuclei, the system was first\nequilibrated at 100 K for 1 ns. Each subsequent cycle consisted of heating from 100 K to 230 K\nover 0.1 ns (corresponding to a heating rate of ~1.3 × 10¹² K/s similar with previous works\n[Acta Mater. 213, 116952 (2021)]), holding at 230 K for 0.5 ns, cooling back to 100 K over\n0.1 ns, and holding at 100 K for 0.3 ns. A total of 44 such cycles were conducted, resulting in a\n45 ns simulation (Fig. R3b).\nWe monitored structural relaxation by tracking the system’s potential energy (PE) as a function\nof time (Fig. R3c). The PE exhibited regular oscillations aligned with the thermal cycles and\nshowed a gradual decline before stabilizing around t=35 ns. Corresponding snapshots of the\nice structures (Fig. R3d–m) reveal the dynamic reorganization of the Ic (red) and Ih (blue)\nnuclei during early cycles (d–j), followed by structural stability in later stages (k–m). These\nresults confirm convergence of both energy and structure variables. Similar convergence\nbehavior was observed across all other simulated trajectories, with PE and ice configurations\nremaining stable for at least 10 cycles (10ns) before termination.\nTo clarify these settings in the manuscript, we have revised the Methods section to read:\n“Ice nuclei were thermally cycled between 100 K and 230 K, with heating and cooling\ndurations of 0.6 ps and 0.4 ps, respectively (see Supplementary Fig. S15 for the full temperature\nprotocol). Potential energy and ice configurations were monitored during the cycles to ensure\nconvergence of both structure and energy for at least 10 cycles prior to the end of the\nsimulation.”\nThe newly added supplementary figure (Fig. S15) illustrates the thermal cycling protocol and\nconfirms equilibration across the simulation.\nFig.R3. Thermocycling protocol and structural equilibration in MD simulations of ice\ncoalescence. a–c, Temporal evolution of the temperature (a, b) and potential energy (c) during\nthe coalescence of ice Ih <001> and Ic <110> nuclei on the substrate. The system undergoes\nrepeated heating–cooling cycles between 100 K and 230 K. The potential energy exhibits\nperiodic fluctuations synchronized with thermal cycling, followed by gradual stabilization after\n~35 ns, indicating structural relaxation. d–m, Time-lapse snapshots of the ice nuclei\ncorresponding to the green markers in c, capturing representative configurations throughout\nthe simulation. Blue, red, and white spheres denote Ih, Ic, and amorphous water molecules,\nrespectively. Dynamic rearrangements and merging of nuclei are evident in early cycles (d–j),\nfollowed by structural stabilization (k–m), confirming convergence of the system’s structural\nand energetic state.\nPoint 4: It appears to me that the authors use an amorphous surface consisting of Lennard-\nJones spheres as the model of graphite, with this neglecting lattice match between graphite and\nwater. Please repeat the simulations with an actual graphite multilayer. Furthermore, the authors\nshould report the source of the Lennard-Jones parameters that they use, and clarify if the values\nreported are pairwise LJ parameters of between the carbon and the oxygen atom or atomistic\nones of the carbon only. In the former case the values should also be carefully revised, as more\ncommonly epsilon values of 1.3 kcal/mol/nm and sigma values of 0.32 nm are reported for the\npairwise LJ parameters between the carbon and the oxygen atom (see for\ninstance https://doi.org/10.1063/1.4895543).\nReply: We thank the reviewer for raising this important point regarding the choice of substrate\nmodel and the Lennard-Jones (LJ) parameters used in our simulations. In the main text, the\ngraphene substrate is modeled as a structureless flat wall, interacting with water molecules via\na 9–3 LJ potential:\n9 3\n2 𝜎𝜎 𝜎𝜎\n𝑈𝑈(𝑟𝑟) = 𝜖𝜖   −  , 𝑟𝑟 < 𝑟𝑟𝑖𝑖,\nwith parameter σ = 0.356 nm and ε = 1.7 kcal/mol. These values were adopted from previous\n15 𝑟𝑟 𝑟𝑟\nstudies [J. Chem. Phys. 141, 18C508 (2014)] and have been shown to reproduce a water contact\nangle of around 80° on graphitic surfaces. This structureless wall model has also been widely\nused in the literature to study water–graphite interactions [e.g., J. Am. Chem. Soc. 143, 8177\n(2021); Nat. Commun. 14, 4110 (2023)].\nIn response to the referee’s suggestion, we have performed additional simulation using an\nexplicit atomistic multilayer graphene substrate, consistent with experimental setups. The\ngraphene sheets were modeled as fixed layers, and the water–carbon interaction was described\nusing a two body Stillinger-Weber potential with σ = 0.32 nm and ε = 0.13 kcal/mol, following\nRef. [J. Chem. Phys. 141, 18C508 (2014)]. These parameters are widely used to represent\npairwise water-carbon interactions and yield comparable wetting behavior.\nAs shown in the newly added Supplementary Fig. S13, we compared the nucleation and\ncoalescence of Ih <001> and Ic <110> ice nuclei using (i) the structureless 9–3 LJ wall (main\ntext, Fig. 5d, reproduced as Fig. R4a) and (ii) the explicit atomic graphene model (Fig. R4b).\nWhile some quantitative differences in morphology and free energy profiles are observed, both\nmodels consistently predict that nucleation proceeds preferentially along the Ih pathway. This\nconfirms that the sampled 9-3 LJ wall model captures the essential interfacial physics and does\nnot alter the qualitative conclusions of our study.\nAccordingly, we have revised the Methods section to clarify both models and parameter\nchoices:\n“The graphene substrate is modeled as either (1) a structureless flat wall interacting with water\nvia a 9-3 Lennard-Jones (LJ) potential with and 39, or\n(ii) an atomistic multilayer graphene slab, where water–carbon interactions are described by\n𝜀𝜀𝑠𝑠𝑠𝑠𝑠𝑠 = 1.7𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘/𝑚𝑚𝑚𝑚𝑘𝑘 𝜎𝜎𝑠𝑠𝑠𝑠𝑠𝑠 = 0.356𝑛𝑛𝑚𝑚\na two body Stillinger-Weber potential with σ = 0.32 nm and ε = 0.13 kcal/mol consistent with\nprevious work39. The cutoff radius was set to . These values yield water contact\nangles consistent with those measured on graphitic surfaces (~80°). The carbon atoms in the\n𝑟𝑟𝑖𝑖 = 2.5𝜎𝜎𝑠𝑠𝑠𝑠𝑠𝑠\ngraphene slabs were kept frozen during the simulations, and therefore no intralayer carbon–\ncarbon potential was applied.\"\nWe have added the simulation results for the atomic graphene (Fig.R4b) simulations to the\nSupplementary Information (Fig. S13), which demonstrate the robustness of our main\nconclusions across both substrate models.\nFig. R4. Comparison of substrate models for ice nucleation and transformation. a\nStructureless 9-3 LJ wall. b Atomistic graphene surface. In both models, the Ic <110> nuclei\nare consumed by growing Ih <111> nuclei, consistent with experimental observations.\n5: Finally, it is not a simple task to find the optimal configuration of ice nanostructures at a\nsolid surface. Given the stochasticity of the ice nucleation process, these structures can vary\ngreatly and should be selected by a careful optimization method for instance as presented by\nPedevilla et. al. (https://doi.org/10.1063/1.5029336) Alternatively MD simulations themselves\ncan be used to grow real thermodynamically stable ice grains on solid surface using for instance\nGCMC/MD (https://doi.org/10.5194/acp-23-10057-2023). One of these methods should be\nadapted when preparing new geometries for the simulations in order to ensure that real\nequilibrium structures and not metastable ones are used.\nReply: We thank the referee for this constructive suggestion. In our molecular dynamic\nsimulations, we focused on three representative ice configurations—Ih<001>, Ic<111> and\nIc<110>— exposed to the substrate. These structures are the predominant ice phases observed\nexperimentally via TEM.\nFollowing the referee’s advice, we applied the structural optimization method proposed by\nPedevilla et. al. [J. Chem. Phys. 149, 072327 (2018)] to verify the thermodynamically stability\nof these ice seeds on graphene. Using the Heterogeneous SEEDing (HSEED) approach, we\ncompared the potential energy per water molecule of five different ice seeds on two graphene\nsubstrate models: (i) a structureless flat surface with a 9-3 LJ potential [see Fig.R5b], and (\nii) an explicit atomistic graphene layer [see Fig.R5d]. In both cases, Ih <001>, Ic <111>, and Ic\n<110> appeared to be the most stable seeds with the lowest potential energies.\nWe then performed MD simulations at 100K—consistent with the TEM experiments—on these\noptimized seeds. As shown in Fig.R5b, d, the Ih <001>, Ic <111>, and Ic <110> configurations\nremain stable after 5 ns of simulation, whereas the Ic <100> and Ih <221> seeds show less\nstability and structural distortion. These results confirm that the ice structures investigated in\nour study correspond to real equilibrium configurations.\nIn the revised manuscript, we have added a clarifying statement in the first paragraph of the\nNon-classical Growth section:\n“Specifically, we investigated the growth and ripening of three typical ice nuclei with Ih<001>,\nIc<111>, and Ic<110> orientations exposed to the substrate, which are the predominant ice\nstructures observed experimentally and exhibit the lowest potential energies in MD simulations\n(Supplementary Fig. 14).”\nThis guides readers to the newly added Supplementary Figure S14 (derived from Fig. R5)\ndetailing the structural optimization.\nWe also appreciate the referee’s suggestion regarding the GCMC/MD method for growing ice\ngrains. While effective at ~200K where crystallization rates for mW water are rapid [Atmos.\nChem. Phys. 23, 10057–10074 (2023); PNAS 116, 8184 (2019); Phys. Chem. Chem. Phys. 12,\n4124 (2010)], this method is computationally challenging at the lower temperature of 100 K\nand the high vacuum (10-6 Pa) conditions in our system due to significantly slower\ncrystallization kinetics. Developing efficient computational techniques for simulating ice\ncrystallization at such low temperatures is an important avenue for future work.\nFig.R5. Structural optimization of ice seeds on graphene substrates. a, c Potential energy per\nwater molecule for five distinct ice seeds after energy minimization. b, d Ice morphologies\nbefore ((top) and after (bottom) 5 ns of MD simulation at 100K. Two different graphene\nsubstrate models are considered: a structureless 9-3 LJ wall (a, b) and an atomistic graphene\nsurface (c, d). Both models yield consistent results, identifying Ih <001>, Ic <111>, and Ic <110>\nas the most stable configurations.\n6: How do your results align with the existance of stacking disordered ice (Ih + Ic) which is\nexpected to form in a patchy structure at the initial steps of freezing, after which it converts\ninto a layered metastable structure with a long lifetime, that finally reaches the\nthermodynamically stable hexagonal state. Does any of your experimental data indicate that\nsuch process occurs?\nReply: We thank the referee for highlighting this important aspect of ice nucleation. The\nformation and evolution of stacking-disordered ice (Isd) — comprising mixed Ih and Ic\nsequences — is indeed a fascinating topic that has been widely discussed in the literature.\nIn our current cryo-TEM experiments, the electron beam is aligned along the top-view (plan-\nview) direction, which enables the identification of distinct, randomly oriented ice polymorphs.\nHowever, when the stacking direction of the crystal is parallel to the beam, the contrast between\nIh and Ic becomes indistinguishable in this geometry. As such, our current imaging\nconfiguration is not sensitive to stacking sequences along the beam axis, and does not allow\ndirect identification of stacking disorder or its temporal evolution.\nTherefore, while our data clearly resolve individual domains of Ih and Ic, they do not provide\ndefinitive evidence for or against the transient formation of stacking-disordered ice. Addressing\nthis question would require a dedicated experimental setup, such as tilt-series imaging or cryo-\nelectron tomography, which is beyond the scope of the present study but represents a promising\ndirection for future work.\n7: In line 38 tetrahedron alignment should be tetrahedral\nReply: The typo has been corrected to “tetrahedral” in the revised manuscript.\n8: In the FFT signal how do you differentiate amorphous ice and very strongly supercooled\nwater, is it possible that the two are indistinguishable?\nReply: In the FFT signal, the Bragg peaks of the graphene substrate was used as a reference.\nthe diffraction halo corresponding to the deposition was identified at the {001} Bragg peak of\nice Ih. This observation is consistent with previously reported X-ray diffraction results of\namorphous ice (Nature 188, 1144-1148, 1960 [ref. 26], Nature 206, 806-807, 1965 [ref. 27]).\nHowever, deeply supercooled liquid water exhibits short-range order comparable to that of\namorphous ice, making it indistinguishable from amorphous ice based on a single diffraction\npattern alone. Nevertheless, throughout the sequential TEM imaging, the deposited material\ndid not display any fluid-like characteristics typically observed in aqueous solutions.\nFurthermore, the deposition exhibited robust structural stability, persisting between the\nsubstrate and mature crystalline ice over the course of all experimental hours. This behavior\ncontradicts the expected transient nature of deeply supercooled water, which resists\ncrystallization, thereby supporting the identification of the deposition as amorphous ice serving\nas an adsorption layer.\nWe acknowledge the importance and complexity of phase transitions in water prior to\ncrystallization. Accurately capturing the behavior of strongly supercooled water, however,\nwould require enhanced environmental control and significantly higher temporal resolution—\nchallenges that merit further technological development in future studies.\n9: In line 69-70 the authors state “While the ice Ih2 nucleus gradually diminished and\neventually disappeared, the nearby ice Ih1 nucleus 69 continued to grow (Fig. 1 k, l), suggesting\nthat either the larger size of the Ih1 nucleus exceeds the critical size 70 required for sustained\ngrowth, in line with classical nucleation theory (CNT)” . Previously they mention the presence\nof amorphous droplets before freezing onset, which cannot be in-line with the classical\nnucleation theory which treats ice nucleation from the vapor phase a single step processes with\nno intermediate states between the crystalline ice and the\nvapor. Please clarify this.\nReply: We appreciate the referee’s valuable comment. The sentence in question treated each\nnucleation step separately in a way that lacks scientific rigor. We have revised the text\naccordingly and removed the misleading wording in the revised manuscript.\n11: Line 128 nanometer rang should be nanometer range.\nReply: The typo has been corrected in the revised manuscript.\nOnce again, we sincerely thank the referee for their constructive and insightful comments and\nsuggestions, which have significantly contributed to improving the quality of our manuscript."}, {"round": 2, "reviewer_comments": {"reviewer_1": "- In the introduction, line 52, I would like to raise two points:\nIt is unclear why the discussion focuses on spontaneous ice formation in atomistic simulations if the main goal of the paper\nis to address heterogeneous nucleation. While studies of homogeneous nucleation are important, many previous works\nusing both atomistic and coarse-grained models have successfully simulated heterogeneous ice nucleation without the\nneed for external bias, capturing spontaneous ice embryo formation at interfaces. Please clarify the relevance of\nhomogeneous nucleation in this context.\nIt would be valuable to include a brief discussion on the strengths and limitations of using coarse-grained models to study\nice embryo formation.", "reviewer_2": "I thank the authors for carefully addressing all the points raised in my review. I recommend the paper to be accepted for\npublication."}, "author_response": "Response to Review Comments\nReviewer #1 (Remarks to the Author):\n- In the introduction, line 52, I would like to raise two points:\nIt is unclear why the discussion focuses on spontaneous ice formation in atomistic simulations if the main goal\nof the paper is to address heterogeneous nucleation. While studies of homogeneous nucleation are important,\nmany previous works using both atomistic and coarse-grained models have successfully simulated\nheterogeneous ice nucleation without the need for external bias, capturing spontaneous ice embryo formation\nat interfaces. Please clarify the relevance of homogeneous nucleation in this context.\nReply: We appreciate the referee’s time and effort in reviewing our manuscript. We are also grateful for the\nvaluable suggestions to better improve our manuscript. The discussion primarily focused on heterogeneous\nnucleation. We have reorganized the introduction as follows for better clarify:\nTo bridge this gap, molecular dynamics (MD) simulations employing atomistic19,20 and coarse-grained water\nmodels21,22 have been widely employed to probe the microscopic mechanisms of ice formation.\nIt would be valuable to include a brief discussion on the strengths and limitations of using coarse-grained\nmodels to study ice embryo formation.\nReply: We apricate the valuable suggestion. The discussion has been incorporated into the revised manuscript\nas follows:\nTo bridge this gap, molecular dynamics (MD) simulations employing atomistic19,20 and coarse-grained water\nmodels21,22 have been widely employed to probe the microscopic mechanisms of ice formation. Among these,\nthe monoatomic water (mW) model23 has been extensively applied due to its computational efficiency and\nability to reproduce key thermodynamic and structural properties of water, such as the melting point and local\ntetrahedrality21,22,24,25, despite its limitations in representing hydrogen atoms and electrostatic interactions.\nReviewer #2 (Remarks to the Author):\nI thank the authors for carefully addressing all the points raised in my review. I recommend the paper to be\naccepted for publication.\nReply: We appreciate the referee’s valuable suggestions to improve the quality of our manuscript. We are also\ngrateful for the time and effort devoted to reviewing our work."}]

Decision letter