Rapid synthesis of micron-thick flexible graphite films via non-equilibrium carbon flux engineering

Domain: physics
Published: 2026-02-28
Editorial outcome: minor_revision

Abstract
The scalable synthesis of high-quality graphite materials remains a formidable challenge due to the inherent trade-off between crystalline perfection and manufacturing efficiency. Existing forms of graphite, such as highly oriented pyrolytic graphite (HOPG) and Kish graphite, suffer from sluggish pyrolytic processes, limited carbon diffusion rates and energy-intensive protocols, often requiring several days for production. Here, we report a pulsed Joule heating-induced carburization (PJHIC) strategy that exploits transient non-equilibrium states to enable rapid carbon diffusion and segregation in metal substrates. By applying instantaneous thermal shocks (>1300 °C, >300 °C/s heating rate) to solid carbon precursor-coated nickel and cobalt foils, we demonstrate the rapid carbon transport in bulk metals and achieve a vertical graphite growth rate of 730 nm/min, which is an order of magnitude faster than conventional methods. Cyclic temperature pulses further enable the synthesis of 1–5 μm-thick ABA-stacked graphite films with millimeter-scale grain sizes. The resulting rapid epitaxially grown graphite films exhibit a highly ordered crystalline structure and exceptional thermal conductivity (1314 Wm–1 K–1), comparable to high-quality HOPG and Kish graphite. This work establishes a non-equilibrium synthesis paradigm for high-quality layered materials, bridging atomic-scale precision with industrial-scale manufacturing.

Introduction
Graphite, a cornerstone material in both industrial engineering and fundamental physics, has garnered enduring acclaim for its exceptional thermal conductivity (>1500 Wm–1 K–1) and extraordinary high-temperature stability (>3000 °C sublimation point)1,2. Its layered van der Waals architecture has also enabled groundbreaking discoveries in band structure engineering and quantum Hall effect research3–5. Moreover, graphite thinned to micron dimensions (<10 μm) gains mechanical compliance while sustaining crystallinity, positioning it as an ideal candidate for next-generation flexible thermal spreaders, electrothermal actuators, EUV manufacturing shielder, and conformal electronics skins6–12.

However, the scalable synthesis of high-quality graphite materials remains constrained by an irreconcilable trade-off between crystalline quality and production efficiency. Conventional approaches face fundamental limitations. For instance, highly oriented pyrolytic graphite (HOPG) synthesis suffers from slow pyrolysis process (~0.1 μm/h deposition rate, >24h cycle time), sustained high temperature and pressure (2500–3000 °C, 30 MPa), and limited size (<10 cm2)1,2,13. The Kish graphite generates micron-sized grains (1–5 μm) through rapid melt solidification, necessitating 2000 °C post-annealing to reduce porosity (>30%) and metal impurities (500–1000 ppm Fe)2,14. Polymer-derived graphitization struggles with energy-intensive processing (3000 °C for days), poor crystallinity, and difficulty in thickness control below 10 μm2,15.

Transition metal (e.g., Ni, Co) catalyzed epitaxy offers a promising alternative by enabling continuous graphene layer segregation at reduced graphitization temperatures (1000~1300 °C)16–21. These metal (foil) substrates also act as templates to form graphite films. However, current approaches remain limited by the amount of dissolved carbon and insufficient carbon diffusion during continuous epitaxy, resulting in either submicron thickness or prohibitively long processing times (over days)20–30.

The diffusion of carbon species in metals is governed by two driving forces: (1) concentration gradient-driven diffusion under isothermal conditions, and (2) forced segregation caused by cooling-induced reductions in carbon solubility. The latter provides significantly stronger driving forces and faster carbon transport. Capitalizing on this, we propose a non-equilibrium diffusion strategy leveraging rapid thermal cycling. Using pulsed Joule heating technique31–33 to achieve rapid temperature ramping and cooling, we revealed the accelerated carbon diffusion during the forced segregation process (>4.5 μm/s), enabling the rapid synthesis of high-quality, micron-thick graphite films with a vertical growth rate of 730 nm/min on Ni, which is an order of magnitude faster than conventional methods. Cyclic temperature pulses further overcome solubility limits, producing 1–5 μm-thick ABA-stacked graphite films with millimeter-sized grains. The resulting films exhibit a highly ordered crystalline structure, with interlayer spacings (3.355 Å) and thermal conductivity (1314 Wm–1 K–1) comparable to those of high-quality HOPG and Kish graphite. This work establishes non-equilibrium carbon-flux engineering as a general paradigm for layered-material synthesis.

Results
Figure 1a illustrates the pulsed Joule heating-induced carburization (PJHIC) strategy for rapid synthesis of graphite films. Polymethyl methacrylate (PMMA) serves as solid-state carbon source, coated on a nickel foil (50 μm-thick) and in a sealed reaction chamber. Application of pulsed current through graphite electrodes generates instantaneous Joule heating, elevating the system to 1300 °C with heating rate exceeding 300 °C/s (Fig. 1b and Supplementary Fig. 1). This heating enables thermal decomposition of PMMA, releasing carbon species that diffuse into the nickel matrix. Subsequent annealing promotes carbon diffusion under concentration gradients, while controlled cooling (~70 °C/s via water-cooling) triggers forced segregation through reduced solubility of nickel, forming high-quality graphite films (Fig. 1c). Figure 1d, e show as-synthesized graphite films transferred onto Si/SiO2 and flexible polyethylene terephthalate (PET) substrates, demonstrating micron-scale thickness and flexibility with continuous, crack-free coverage on curved PET.

To investigate the growth rate limit of graphite segregation through Ni foil, PJHIC experiments with varying annealing time were performed (Fig. 1f). A three-stage pulsed current protocol (240 A→320 A→280 A) mitigated thermal overshoot, maintaining ideal thermal plateau with consistent ramp/cool rates. Given that 1000 °C is the conventional growth temperature for graphene17,24, the effective growth durations in our experiments are defined as the period above 1000 °C, which are calculated to be 11 s, 42 s, 51 s, 61 s, 72 s, 102 s, and 132 s, respectively. Figure 1g (Details please see in Supplementary Figs. 2 and 3) shows the resulting film thickness evolution, in which graphite nucleated within 11 s, thickened progressively, and saturated at ~800 nm beyond 72 s. The rapid nucleation indicates non-equilibrium carbon diffusion through nickel bulk, consisting with Fickian diffusion models (Supplementary Note 1)34. With a growth duration of 61 s, a maximum vertical growth rate was calculated to be 730 nm/min (Supplementary Note 2), outperforming state-of-art methods that rely on prolonged thermal treatments (<100 nm/min) (Fig. 1h). Notably, considering that graphite segregation occurs predominantly during the rapid cooling stage (from 1300 °C to 1000 °C within 4~5 seconds), the corresponding instantaneous segregation rate is calculated to be ~12,000 nm/min (Supplementary Fig. 4). The PJHIC strategy enables micron-thick, uniform graphite films with growth rates over an order of magnitude higher than previous reports15,20–29,35–42.

Raman spectroscopy of as-synthesized graphite films with different growth time (Fig. 1i and j) revealed prominent G (~1580 cm-1) and 2D (~2670 cm-1) bands with negligible D-band intensity, indicating low defect density. Deconvolution of the 2D band into asymmetric Lorentzian components centered at 2680 cm-1 (2D1) and 2718 cm-1 (2D2) confirms AB stacking order of the graphene layers43,44. Spatial mapping across an 80×80 μm2 area, coupled with statistical analysis of >10,000 spectra (Fig. 1k and Supplementary Fig. 5) yields an average ID/IG ratio of ~0.03 and G-band full width at half maximum (FWHM) of 13 cm-1, quantitatively validate the exceptional crystallinity of the as-synthesized graphite films45.

To gain deeper insights into the spatial evolution of carbon distribution, time-of-flight secondary ion mass spectrometry (ToF-SIMS) characterizations along with depth-resolved analysis46,47 were conducted on pristine Ni foil and PJHIC-samples with different growth durations of 10, 12, and 72 s. The 3D distributions of carbon and Ni elements were reconstructed by detecting the secondary ions of C− and Ni−, respectively. The pristine Ni sample shows negligible carbon signals (Fig. 2a, b), while the 10-second-grown sample exhibits homogeneous C⁻ signal enhancement throughout the Ni matrix (Fig. 2c, d), confirming bulk carbon dissolution prior to segregation onset. Crucially, a graphite layer emerged at 12-second-grown sample (Fig. 2e, f), directly evidencing that carbon segregation initiates within the critical 10-12 s window and revealing rapid phase transformation kinetics. Prolonged growth to 72 s yields continuous graphite films averaging ~800 nm thickness (Fig. 2g and Supplementary Fig. 3d). Strikingly, the reconstructed 3D map revealed localized thickening specifically within Ni grain boundary grooves (Fig. 2h), contrasting with the 800 nm baseline in adjacent regions. This boundary-confined enhancement demonstrates accelerated carbon migration along grain defects, where the reduced atomic packing density lowers the diffusion barriers, the defects enable preferential nucleation and growth.

Notably, at graphite/Ni interfaces, the pseudomorphic nickel enrichment signature results from increased secondary Ni– yields due to altered electronic states at imperfectly bonded interfaces (Fig. 2e–h and Supplementary Fig. 6). Cross-sectional transmission electron microscopy (TEM) combined with energy-dispersive X-ray spectroscopy (EDS) analysis independently validated the clear graphene/Ni interface structure on the 72-second growth sample, where C signals terminate coincidently with Ni signal onset within <5 nm interfacial width (Supplementary Fig. 7). The multiscale analysis conclusively establishes that non-equilibrium thermal shocks drive explosive segregation rates by synergizing bulk carbon super-saturation with boundary-mediated rapid nucleation.

The rapid non-equilibrium segregation growth process comprises two distinct yet interconnected stages (Supplementary Note 3). In Stage I (Solute depletion-driven carbon precipitation), the rapid cooling from 1300 °C to 1000 °C within 4~5 seconds creates a massive carbon supersaturation (ΔC ≈ 0.28 wt.%) due to the drastic reduction in equilibrium solubility dictated by the Ni-C phase diagram34. This corresponds to a chemical potential difference of Δμ ≈ 0.08 eV/atom. In Stage II, the accumulated carbon overcomes a drastically reduced nucleation barrier and forms graphite layers. Classical nucleation theory indicates that the high Δμ lowers both the critical nucleation radius r* and energy barrier ΔG*, facilitating the observed high-density nucleation and rapid graphite layer formation48,49. Quantitatively, the carbon atomic flux in PJHIC reaches F ≈ 2.1 × 1022 atoms·m-2·s-1, surpassing state-of-the-art CVD graphene growth by two orders of magnitude (F ≈ 3.1 × 1020 atoms·m-2·s-1)50,51. This fundamental difference in mass transport efficiency underscore the paradigm-shifting nature of the non-equilibrium forced segregation mechanism compared to diffusion-limited processes.

To transcend the sub-micrometer thickness constraint of single-step graphite growth, we engineered a cyclic heating–cooling strategy harnessing carbon segregation kinetics (Fig. 3a) with upgraded carbon source and extended metal substrates. Theoretical modeling established a maximum segregation thickness of 1.17 μm (Supplementary Note 1), while experimental optimization of PMMA volume (0.2–0.8 mL) yielded 1.07 ± 0.03 μm at 0.6 mL (Supplementary Fig. 8). Although the 7.42% carbon loss happens due to PMMA decomposition into gaseous byproducts (Supplementary Note 4 and Supplementary Table 1), the decomposed gaseous carbon source favors a rapid and massive carbon influx into the Ni substrate, potentially creating a higher initial supersaturation. The cyclic process (Fig. 3a) enforced continuous chemical potential gradients through precisely controlled thermal pulses: each cycle consisted of 120 s of high-current heating for dissolving carbon, followed by 30 s of forced cooling for triggering the segregation (Supplementary Fig. 9).

This approach achieved programmable thickness control (1-5 μm) on both Ni and Co foils through 1-50 cycles (Fig. 3b). Figure 3c shows the step edges of the graphite layers grown on the Ni surface, characterized by white light interferometry (WLI), which allow the measurement of the graphite film thickness (Fig. 3d). Furthermore, we statistically analyzed the thickness of graphite layers segregated from the surfaces of Ni and Co foil (Supplementary Fig. 10), revealing a linear growth relationship between thickness and the number of cycles (Fig. 3e, f). Notably, the vertical growth rate of ~0.1 μm per cycle (150 s) was lower than the single-step process due to partial redissolution of low-crystallinity layers during reheating. Nevertheless, a 5 μm-thick film requires only ~2 h total processing, demonstrating a several times throughput increase over conventional CVD, and demonstrating the strong capability for the rapid synthesis of microscale-thick graphite films.

The crystallographic orientation and domain size of the as-obtained graphite films were investigated by electron backscatter diffraction (EBSD) characterizations (Fig. 4a, b and Supplementary Fig. 11). The inverse pole figure (IPF) map in the out-of-plane (Z) exhibits a globally uniform red intensity, confirming consistent (0001) stacking orientation across the film. The in-plane (Y) IPF mapping reveals >1.2 mm domain size with >95% blue area signifying dominant single in-plane orientation, while cyan-to-green grains (<5%) indicate minor misoriented grains with grain boundaries. This domain size substantially exceeds that of the underlying Ni substrate (100–200 μm, Supplementary Fig. 11a), suggesting graphene’s rapid epitaxial propagation across substrate grain boundaries during segregation. The in-plane alignment of the graphite films was predominantly governed by intrinsic graphene layer orientation rather than the Ni lattice. The black vein-like regions observed in the inverse pole figures correspond to wrinkle structures, where three-dimensional distortion led to the loss of Kikuchi diffraction signals. It is noteworthy that although films synthesized on single-crystalline Ni(111) foils exhibited a single crystallographic orientation, their thickness was reduced due to the absence of grain boundary acceleration effects; the unresolved EBSD area is even more due to the stronger graphite-Ni(111) interaction and thus resulting wrinkles (Supplementary Fig. 11e–h). Owing to the large domain size and high continuity, the electrical conductivity reaches 6.73 × 105 S·m–1 with high uniformity (Supplementary Fig. 12).

The graphitization degree was evaluated by using X-ray diffraction (XRD) (Fig. 4c). The as-obtained PJHIC-graphite film exhibits (0002) peak at 26.543°, with a full width at half maximum (FWHM) of 0.169°. This peak position was compared with those of several commercially available graphite: HOPG (26.511°, FWHM=0.173°), natural graphite (26.562°, FWHM=0.167°), and Kish graphite (26.553°, FWHM=0.165°). According to the Bragg’s law, the interlayer spacing of the PJHIC-graphite film is calculated as 3.355 Å, closely matching that of HOPG (3.360 Å), natural graphite (3.354 Å) and Kish graphite (3.355 Å).

Atomic-scale characterization via scanning tunneling microscopy (STM) reveals continuous hexagonal lattices (Fig. 4d). TEM combined with selected area electron diffraction (SAED) characterizations show hexagonal symmetric patterns, and the intensity ratios I1-210/I0-10 and I2110/I-1010 is about 4, indicative of ABA-stacking structure (Fig. 4e)52. Angular dark-field (ADF) scanning transmission electron microscopy (STEM) image and corresponding Fast Fourier transform (FFT) patterns also match the simulated ABA-stacked registry (Fig. 4f and Supplementary Fig. 13). Cross-sectional HRTEM confirmed that the basal-plane C-C bonds of 0.246 nm and c-axis periodicity of 0.68 nm (Fig. 4g, h).

In-plane (Ʌ//) and cross-plane (Ʌ⊥) thermal conductivity were measured via time-domain thermoreflectance (TDTR) technique53–55, yielding 1314 Wm–1 K–1 and 7.51 Wm–1 K–1, respectively (Fig. 4i, j). These values are comparable to high-quality HOPG (Ʌ// = 1480 Wm–1 K–1, Ʌ⊥ = 8.5 Wm–1 K–1) and Kish graphite (Ʌ// = 1362 Wm–1 K–1, Ʌ⊥ = 8.57 Wm–1 K–1), and substantially exceed natural graphite (Ʌ// = 904 Wm–1 K–1, Ʌ⊥ = 8 Wm–1 K–1), (Fig. 4k and Supplementary Figs. 14–15). These results demonstrate that fast-epitaxially grown-graphite films by the PJHIC process exhibit structural characteristics matching those of ideal graphite and achieve exceptional crystallinity.

In summary, this work demonstrates a pulsed Joule-heating-induced carburization method that enables rapid synthesis of high-quality, micron-thick graphite films by leveraging transient non-equilibrium thermal states. Scientifically, we reveal an exceptionally high rate of carbon transport (>4.5 μm/s) within bulk metals during cooling-driven segregation, for which the driving force is significantly greater than that of steady-state diffusion. We achieved a record vertical growth rate of 730 nm/min for ABA-stacked graphite films, which exhibit millimeter-scale domain size and excellent thermal conductivity of 1314 Wm–1 K–1, rivaling commercial HOPG and Kish graphite. This approach marks a substantial advance in synthesis speed, but the crystalline perfection of the resulting films still falls short of single-crystal standards, as the rapid non-equilibrium process introduces grain boundaries, point defects, and wrinkles. Our insights into segregation dynamics suggest that further optimization of kinetic control could reconcile both speed and quality. The PJHIC method also shows good scalability, as demonstrated by a large-area graphite film with a size of 12 cm × 5 cm (Supplementary Fig. 16). We anticipate that non-equilibrium carbon flux engineering will provide a generalizable pathway for the high-throughput synthesis of other layered materials requiring precise atomic control and industrial-scale viability.

Methods
PJHIC growth
High-purity nickel foil (purity 99.9%, thickness 50 μm) and cobalt foil (purity 99.9%, thickness 50 μm) were commercially obtained from Beijing Gaoke New Materials Technology Co., Ltd. Poly(methyl methacrylate) (PMMA, Mw ≈ 950 kDa) was supplied by KAYAKU Advanced Materials, Inc. (model: PMMA 950KA4, spin-coating speed 4000 rpm).

The Ni/Co foils were cut into 21 mm × 21 mm pieces. Subsequently, approximately 0.6 mL of PMMA solution was spin-coated onto the surface of the foils. Based on a systematic evaluation of decomposition kinetics and comparative experiments with alternative sources (e.g., graphite paper, carbon black powder, and PI film), PMMA is chosen as the carbon source suitable for the rapid PJHIC process. In the cyclic growth experiments, the PMMA carbon source was coated only once at the initial stage and the PMMA-coated sample was directly placed on graphite paper for the subsequent cyclic graphitization process. The coated samples were then cured at 170 °C for 10 min and placed inside a Joule heating chamber (JH3.3-P type, Hefei In Situ Technology Co., Ltd.). Prior to heating, the chamber was purged three times with argon gas, each cycle consisting of pressurization to 0.3 MPa followed by evacuation. Synthesis was conducted under a constant argon flow with a pressure of approximately 0.1 MPa and a flow rate of 2000 sccm. The samples were rapidly heated to 1300 °C under a three-stage current program: 240 A for initial rapid heating, 320 A to reach the peak temperature of 1300 °C, and 280 A for isothermal holding at 1300 °C throughout the growth period. After growth. For the cyclic process, a current of 320–325 A was applied to the graphite plate for 120 s to rapidly achieve 1250–1280 °C, ensuring sufficient dissolution and minimizing heat accumulation during repeated cycling. The cooling stage was set to be 30 s to promote effective carbon segregation.

Transfer of graphite films
The experimentally obtained graphite/nickel films were cut into samples measuring 20 mm × 20 mm. Subsequently, the nickel substrate was removed by wet chemical etching: the samples were immersed in an aqueous ferric chloride (FeCl₃) solution (1 mol/L concentration) for more than 10 h to obtain self-supporting graphite films. The etched films were repeatedly rinsed with deionized water (3-4 times) to remove residual metal ions adsorbed on the surface. Finally, the graphene films were transferred onto silicon dioxide/poly(ethylene terephthalate) (SiO₂/PET) substrates and dried at room temperature to eliminate residual moisture between the film and the substrate, preparing them for subsequent characterization.

ToF-SIMS measurements
Time-of-flight secondary ion mass spectrometry (ToF-SIMS) analysis of freshly isolated trilayer graphene island samples was performed using an ION ToF-SIMS 5 instrument (Germany). Surface sputter depth profiling was initially conducted with a 2 keV Cs1⁺ primary ion beam, followed by compositional imaging using a 30 keV Bi1⁺ primary ion beam. Imaging areas of 50 × 50 μm2 were acquired with an image resolution set to 128 × 128 pixels. Under these conditions, the spatial resolution in the XY plane—defined as the distance over which the signal intensity at the graphene domain boundary rises from 25% to 75%—was approximately 0.2 μm, while the depth resolution was approximately 1 nm. The entire analysis was carried out under a chamber-based vacuum of approximately 10-8 mbar. Final data processing, including characteristic peak identification and image reconstruction, was performed using the instrument’s proprietary SurfaceLab 7.0 software (ION-TOF).

STEM Characterizations
STEM characterization was performed using an aberration-corrected JEOL GRAND ARM 2 microscope operated at 200 kV. ADF-STEM image was acquired with a beam convergence semi-angle of 32 mrad and a collection semi-angle range of 36–147 mrad. The image was subsequently denoised using an average background-subtracted filter.

Thermal conductivity measured by TDTR
TDTR is a non-contact optical method for characterizing the thermal transport properties of various materials. In the methodology, an ultrafast femtosecond laser source (785 nm, 80 MHz repetition rate, linearly polarized) was split into pump and probe beams using a polarizing beam splitter. The pump beam was modulated at radio frequencies via an Electro-Optical Modulator to induce periodic thermal oscillations at the sample surface. Concurrently, the probe beam—modulated at 200 Hz with a mechanical chopper—detected temperature-dependent reflectance variations. The 600 mm delay stage can control the time difference between the pump beam and the probe beam reaching the sample. Prior to measurements, an Aluminum layer (109 nm thickness, deposited by magnetron sputtering; thickness determined by picoacoustics) was applied to the sample surface as transducer, when the pump beam is directed onto the Aluminum, a fraction of its energy is absorbed by the film, causing the surface temperature to rise. Consequently, the reflected probe-beam intensity varies directly with the temperature change. The photodetector converts an optical signal into an electrical signal. Acquired signals were demodulated relative to the pump-probe delay time using lock-in amplifiers.

By employing objective lens configurations with selective sensitivity to the direction of heat transport (a 5× objective provide greater sensitivity to the cross-plane thermal conductivity, Ʌ⊥, whereas a 20× objective is more sensitive to the in-plane thermal conductivity, Ʌ//) and conducting measurements at the same location and under an identical pump modulation frequency of 10.1 MHz, the independent thermal conductivity components were successfully separated and obtained. In this work, the measured HOPG is from Tipsnano Co., Ltd. (ZYB grade). Although premium HOPG (e.g., SPI Co., Ltd., with 0.8°±0.2° mosaic spread) achieves higher Ʌ// (2010 Wm–1 K–1) and Ʌ⊥ (13.4 Wm–1 K–1), the measured Tipsnano HOPG properties align with its specified structural parameters55.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript presents a highly compelling and timely study on the ultrafast synthesis of high-quality, micron-thick graphite films via a pulsed Joule heating-induced carburization strategy. This work addresses a critical challenge in graphite synthesis (the trade-off between crystalline quality and manufacturing efficiency) by leveraging non-equilibrium carbon flux engineering. The authors demonstrate that transient thermal shocks enable exceptionally rapid carbon diffusion and segregation in Ni substrates, achieving a record vertical growth rate of 730 nm/min. The insights into ultrafast carbon transport offer valuable inspiration for cost-effective industrial-scale manufacturing. The work is scientifically rigorous, methodologically innovative, and well-presented, with clear potential for industrial applications. I believe it meets the high standards of Nature Communications and recommend its publication after revisions.\n1. The authors demonstrated the synthesis of graphite films on centimeter-size Ni and Co foils. To further underscore the scalability and general applicability of the PJHIC method, it would be beneficial to include data on larger substrate sizes, which would help readers better assess the potential for industrial-scale production.\n2. In the cyclic heating-cooling process for thickness control, it is unclear whether the same PMMA is reused across multiple cycles or recoated after each cycle. Clarifying this point in the Methods or Results section would help readers understand the carbon source consumption and the reproducibility of the cyclic growth process.\n3. Although the supplementary information provides a diffusion model based on Fick's laws, a more detailed analysis incorporating the Ni–C phase diagram would strengthen the theoretical foundation. Quantitative comparisons between predicted and experimental segregation thicknesses, along with a discussion of any discrepancies (e.g., due to kinetic limitations or carbon loss), would provide deeper insight into the non-equilibrium segregation mechanism.\n4. The in-plane thermal conductivity of the PJHIC-graphite film (1314 Wm-1K-1) is notable, but not the highest among reported graphite materials. The authors are encouraged to include a more detailed analysis linking the defect density (e.g., via Raman ID/IG ratio) and grain boundary structure (from EBSD) to the thermal conductivity. A discussion on how further defect reduction or grain orientation optimization could enhance thermal performance would be valuable for readers interested in high-thermal-conductivity applications.", "reviewer_2": "This manuscript presents a work on the ultrafast synthesis of high-quality graphite films using a pulsed Joule heating approach. The concept of \"non-equilibrium carbon flux engineering\" is introduced and investigated through a series of experiments characterizing growth kinetics, structural properties, and thermal performance. The study demonstrates rapid film growth rates and the ability to control film thickness. However, several aspects require further clarification:\nQ1: The core concept revolves around a \"non-equilibrium\" process, primarily defined by fast heating/cooling rates (>300 oC/s). Beyond the kinetic rates, what are the key physical parameters (e.g., carbon supersaturation at the interface, phase transformation driving force) that quantitatively define this non-equilibrium state? Could the authors provide a quantitative comparison (even a model-based estimation) of the carbon flux or segregation driving force against a traditional isothermal CVD process with a similar effective growth duration (e.g., ~60 s)? This would more forcefully demonstrate the unique advantage of the method beyond simply being \"faster.\"\nQ2: The choice of an extremely fast cooling rate (>50 °C/s) and the specific durations for the heating (120 s) and cooling (30 s) intervals in the cyclic process are critical to the method's success. However, the rationale behind selecting these specific parameters is not clearly explained. Were these values optimized empirically, or are they based on a theoretical consideration (e.g., a characteristic time for carbon diffusion vs. segregation)? Please clarify the reasoning behind these key process choices.\nQ3: The comparison in Figure 1h is excellent, but it primarily includes works prior to 2023. Please clearly articulate the fundamental distinctions between your work and very recent (or contemporary) studies also focusing on rapid synthesis of high-quality graphite films, such as Zhang et al. Nat. Commun. 16, 7180 (2025) (Ref. 21). Given that Ref. 21 also reports considerable growth rate (6.2 layers/s) and high thermal conductivity, what is the definitive advantage of your method in terms of growth speed, energy consumption, or process simplicity?\nQ4: The \"effective growth time\" is defined as the duration above 1000°C, leading to a vertical growth rate of 730 nm/min. However, the manuscript correctly identifies the cooling phase as the primary period for forced segregation. Does this \"effective growth time\" accurately represent the actual time window for segregation? If segregation occurs predominantly during the few seconds of cooling from 1300°C to 1000°C, the instantaneous segregation rate would be extraordinarily high. This point requires clarification.\nQ5: The use of PMMA as a solid-state carbon source is a key experimental detail. What is the specific advantage of using a polymer precursor like PMMA over others carbon sources (e.g., Graphite plate) in this particular PJHIC process? Does its decomposition kinetics at ultra-high heating rates favor a rapid and massive carbon influx into the Ni substrate, potentially creating a higher initial supersaturation? A brief justification for this choice would be helpful.\nQ6: The rapid thermal shocks and the associated large thermal stress could potentially introduce more wrinkles and defects into the graphite films. The conclusion states that \"the crystalline perfection of the resulting films still falls short of single-crystal standards.\" While this responsible statement is appreciated, it seems somewhat contradictory to the data presented (millimeter-scale grains, excellent Raman signals, ABA stacking). Please specify in what aspects it \"falls short.\" Is it a larger mosaic spread? Or the presence of some stacking faults?\nThe color bar of Raman map in Supplementary Fig. 4 represents the ID/IG ratio, ranging from 0 to 2, which convincingly shows the overall high quality. However, to honestly reveal and discuss any potential micro-scale heterogeneity or defect populations introduced by the process, would it be more informative to use a narrower color scalefor this mapping? The current scale might be masking subtle variations."}, "author_response": "Point-by-point response to editor and reviewers’ comments\nNCOMMS-25-71011-T\nEditor\nWe sincerely appreciate the editor and reviewers' careful reading and constructive\nsuggestions. We have thoroughly revised the manuscript according to the comments,\nand detailed corrections are as follows:\nResponse to the Reviewer #1\nThis manuscript presents a highly compelling and timely study on the ultrafast synthesis\nof high-quality, micron-thick graphite films via a pulsed Joule heating-induced\ncarburization strategy. This work addresses a critical challenge in graphite synthesis\n(the trade-off between crystalline quality and manufacturing efficiency) by leveraging\nnon-equilibrium carbon flux engineering. The authors demonstrate that transient\nthermal shocks enable exceptionally rapid carbon diffusion and segregation in Ni\nsubstrates, achieving a record vertical growth rate of 730 nm/min. The insights into\nultrafast carbon transport offer valuable inspiration for cost-effective industrial-scale\nmanufacturing. The work is scientifically rigorous, methodologically innovative, and\nwell-presented, with clear potential for industrial applications. I believe it meets the\nhigh standards of Nature Communications and recommend its publication after\nrevisions.\nAuthors’ response:\nWe greatly appreciate the constructive comments provided by the reviewer 1.\nComment 1:\nThe authors demonstrated the synthesis of graphite films on centimeter-size Ni and Co\nfoils. To further underscore the scalability and general applicability of the PJHIC\nmethod, it would be beneficial to include data on larger substrate sizes, which would\nhelp readers better assess the potential for industrial-scale production.\nAuthors’ response:\nWe appreciate your attention to the scalability of the method and agree with your\nsuggestion. As a preliminary exploration, we have added the demonstration of a larger\ngraphite film with the size of 12 cm × 5 cm (Fig. R1-1).\nFig. R1-1(Revised Supplementary Fig. 16) | Synthesis of 12 cm × 5 cm graphite\nfilm grown on a Ni foil. (a) Optical image. (b) Typical optical microscopy image of\nthe film. (c) Raman spectra of the graphite film.\nThe results indicate that continuous graphite films without macroscopic cracks\nwere successfully fabricated on the substrate with a size of 5 cm × 12 cm. Optical\nmicroscopy observations, together with Raman spectroscopy measurements at multiple\nrepresentative points across the large-area film, confirmed good uniformity. Naturally,\nachieving even larger-scale films with high quality and uniformity will require further\nrefinement and optimization of the synthesis conditions, which will be the focus of our\nfuture work. Nevertheless, the successful synthesis on the 12 cm × 5 cm Ni foil\ndemonstrates the significant scalability and potential for upscaling of the PJHIC method.\nAccordingly, we add this figure to Supplementary Fig. 16. The corresponding\nrevised content in the main text (in Conclusion part) is as follow:\n“In summary, … The PJHIC method also shows good scalability, as demonstrated by\na large-area graphite film with a size of 12 cm × 5 cm (Supplementary Fig. 16). We\nanticipate that non-equilibrium carbon flux engineering will provide a generalizable\npathway for the high-throughput synthesis of other layered materials requiring precise\natomic control and industrial-scale viability”\nComment 2:\nIn the cyclic heating-cooling process for thickness control, it is unclear whether the\nsame PMMA is reused across multiple cycles or recoated after each cycle. Clarifying\nthis point in the Methods or Results section would help readers understand the carbon\nsource consumption and the reproducibility of the cyclic growth process.\nAuthors’ response:\nWe appreciate the reviewer’s comments regarding the lack of clarity in our\nprevious description. In the cyclic growth experiments, PMMA was applied as the\ncarbon source only once at the initial stage and was subsequently reused in all following\ncycles without any re-coating. Specifically, the PMMA-coated sample was directly\nplaced onto a graphite paper support for the subsequent treatments. During multiple\nrounds of carburization and carbon precipitation, the PMMA was progressively\nconsumed; therefore, the effective carbon supply originated not only from the PMMA\nbut also from the underlying graphite paper.\nWe have added this crucial experimental detail to the Methods section of the\nrevised manuscript under “PJHIC Growth” and highlighted it accordingly:\n“The Ni/Co foils were cut into 21 mm × 21 mm pieces.… PMMA is chosen as the\ncarbon source suitable for the ultrafast PJHIC process. In the cyclic growth experiments,\nthe PMMA carbon source was coated only once at the initial stage and the PMMA-\ncoated sample was directly placed on graphite paper for the subsequent cyclic\ngraphitization process. …”\nComment 3:\nAlthough the supplementary information provides a diffusion model based on Fick's\nlaws, a more detailed analysis incorporating the Ni–C phase diagram would strengthen\nthe theoretical foundation. Quantitative comparisons between predicted and\nexperimental segregation thicknesses, along with a discussion of any discrepancies\n(e.g., due to kinetic limitations or carbon loss), would provide deeper insight into the\nnon-equilibrium segregation mechanism.\nAuthors’ response:\nWe sincerely appreciate the reviewer’s insightful question regarding the\nquantitative definition of our non-equilibrium process. As rightly pointed out, fast\nheating/cooling rates are the experimental manifestation, while the underlying physics\nis rooted in enhanced thermodynamic driving forces. To address this, we have\ndeveloped a two-stage model that quantitatively describes the non-equilibrium\nsegregation process, emphasizing the roles of interfacial carbon supersaturation (ΔC)\nand phase transformation driving force (Δμ), as well as compared the carbon flux\nagainst a traditional isothermal CVD process.\nStage I: Solute depletion-driven carbon segregation to the interface\nThe PJHIC process initiates with rapid cooling from a starting high temperature\n(T , 1300°C) to a lower segregation temperature (1000°C < T < 1300°C). This creates\n0\na massive transient supersaturation at the metal-graphite interface. According to the Ni–\nC phase diagram (Fig. R2-1) and the empirical relationship proposed by Lander &\nMarshall [J. Appl. Phys. 1952, 23 (12), 1305]:\n4880\nln𝑆 = 2.480−\n𝑇\nwhere S denotes weight-percent carbon solubility (wt %, grams C per 100 grams Ni).\nFor small values of S, the dimensionless mass fraction C can be directly calculated by:\n𝑆 𝑆 1 4880\n𝐶 = ≈ = exp (2.480− )\n100+𝑆 100 100 𝑇\nFor just 4.0 ~ 4.7 s of cooling time (see comment 4), the equilibrium carbon solubility\ndrops from C (1300°C) = 0.536 wt.% to C (1000°C) = 0.259 wt.%. The ultrafast\n0 1\ncooling rate contributes great interfacial supersaturation ΔC = C (1300°C) – C (1000°C)\n0 1\n= 0.277 wt.%, and thus drives a chemical potential difference Δμ. The molar Gibbs free\nenergy (𝜇) is expressed as:\n𝜇(𝐶,𝑇) = 𝜇0(𝑇)+𝑘 𝑇ln(𝐶)\n𝐵\nwhere 𝜇0(𝑇) is the standard (reference-state) chemical potential of carbon in Ni at\ntemperature 𝑇, 𝑘 is the Boltzmann constant. We assume that the carbon has been\n𝐵\nsolved in Ni bulk at T = 1300 °C with an equilibrium carbon solubility C (1300°C) =\n0 0\n0.536 wt.%. When the temperature drops, the excess chemical potential that drives\nsegregation to the surface at temperature 𝑇 is:\n𝐶\n0\n∆𝜇 = 𝜇(𝐶 ,𝑇)−𝜇(𝐶(𝑇),𝑇) = 𝑘 𝑇ln\n0 𝐵 𝐶(𝑇)\nFor T = 1000°C = 1273 K, ∆𝜇 ≈ 7.73×103𝐽⁄𝑚𝑜𝑙(≈ 0.080 𝑒𝑉/𝑚𝑜𝑙) . The\n1\nsignificantly high ΔC and Δμ promote the subsequent phase transformation from carbon\natoms to graphite layers.\n[Figure Redacted]\nStage II: Supersaturation-driven graphite layer formation\nThe supersaturated carbon at the interface must overcome the nucleation barrier to\nform graphite layers. In classical nucleation theory, graphene nucleation on metal\nsurfaces is an activated process in which a stable nucleus forms once it surpasses a\ncritical size, balancing the energetic competition between creating a new interface\n(surface energy cost) and forming a new phase (volumetric energy gain from\nsupersaturation). A new phase (graphene nucleus) forms via discrete nucleation events\nrather than continuous transformation. Nuclei are assumed circular (2D disc-shaped)\nand energetically isotropic. Interface properties (line energy 𝜆) and driving force (Δ𝜇)\nare considered constant and uniform during nucleation. Nucleation is\nthermodynamically driven and kinetically activated, involving the random fluctuation-\ndriven formation of critical-sized clusters [Acta Chim. Sin. 2014, 72, 345-358; J. Am.\nChem. Soc. 2011, 133 (13), 5009-5015].\nThe Gibbs free energy for forming a circular graphene nucleus of radius r is:\n∆𝐺(𝑟) = 2𝜋𝑟𝜆−𝜋𝑟2𝜌 Δ𝜇\n𝑔\nWhere 𝜆 ≈ 1 eV/nm is the graphene-Ni line energy [Nano lett. 2011, 11, 518-522],\n𝜌 = 3.82×1019 𝑎𝑡𝑜𝑚 𝑚−2 is the areal atomic density, and ∆𝜇 is the areal\n𝑔\nthermodynamic driving force. The critical nucleation radius 𝑟∗ and barriers ∆𝐺∗ follow\nfrom 𝜕∆𝐺⁄𝜕𝑟 = 0:\n𝜆 𝜋λ2\n𝑟∗ = , Δ𝐺∗ =\n𝜌 Δ𝜇 𝜌 Δ𝜇\n𝑔 𝑔\nWe can find that the 𝑟∗ and ∆𝐺∗ both are inversely proportional to Δμ. The high\nΔμ in our PJHIC process significantly lowers ΔG*, facilitating high nucleation\ndensity and rapid layer formation (Fig. 1g,h). For nucleation of subsequent layers\n(2nd layer, 3rd layer,…) beneath the first layer, the same theoretical framework applies,\nthough with a generally lower interfacial line energy 𝜆 due to spatial confinement and\n2\nweaker coupling to metal substrate. Graphene thickening proceeds once the interfacial\ncarbon activity sufficiently reduces Δ𝐺∗ small enough.\nComparisons between predicted and experimental thicknesses\nOur theoretical analysis is based on the Ni–C phase diagram. At the heating\ntemperature of 1300 °C, the bulk Ni foil (50 μm thick) can reach the equilibrium carbon\nsolubility corresponding to this temperature, which is approximately 0.536 at.%\n(equivalent to 0.536 wt.%). According to the principle of mass conservation, we assume\nthat all the dissolved carbon atoms segregate completely to both surfaces of the Ni foil\nduring the subsequent forced cooling process to form graphite films. This allows us to\ntheoretically predict the maximum total film thickness achievable in a single PJHIC\npulse. The calculation indicates that the theoretical maximum segregation thickness on\none side is approximately 1.17 μm.\nA quantitative comparison between this theoretical prediction and the\nexperimentally measured saturation thickness obtained from single-pulse experiments\n(average value: 1.07 μm, see Fig. R1-3) shows that the experimental result approaches\nthe theoretical limit of carbon solubility–driven segregation, being only about 8.5%\nlower. This close agreement strongly supports the high carbon-utilization efficiency of\nthe PJHIC process.\nWe further analyzed the ~8.5% deviation and attribute it primarily to carbon loss\nduring polymer pyrolysis. A portion of the PMMA precursor decomposes into gaseous\nbyproducts (e.g., CH₄, CO₂, etc.), which are swept away by the high-speed inert gas\nflow before sufficient dissolution into the Ni matrix occurs. To explore the practical\nlimit of single-pulse segregation, we precisely controlled the PMMA coating volume\nusing a micropipette. The relevant experimental parameters and measured results are\nsummarized in Table R1.\nFig. R1-3 | Thickness characterization of graphite edges.\nTable R1 | Mass change under different PMMA coating amounts.\nThe The\nThe carbon\nNumber mNi/g VPMMA/mL mPMMA/Ni/g ∆mPMMA （g） mGr/Ni/g ∆mGr/g\nloss rate/%\nthe average/ error/\n% %\n1 0.1839 0.2000 0.1941 0.0102 0.1852 0.0013 12.75%\n2 0.1801 0.4000 0.1994 0.0193 0.1822 0.0021 10.88%\n3 0.1855 0.6000 0.2177 0.0322 0.1874 0.0019 5.90% 7.42% 3.73%\n4 0.1836 0.8000 0.2232 0.0396 0.1849 0.0013 3.28%\n5 0.1778 1.0000 0.2289 0.0511 0.1800 0.0022 4.31%\nAccordingly, we have revised the manuscript by adding a paragraph at the end of\nthe section “Pulsed Joule heating activated ultrafast carbon diffusion and\nsegregation” :\nThe rapid non-equilibrium segregation growth process comprises two distinct yet\ninterconnected stages (Supplementary Note 3). In Stage I (Solute depletion-driven\ncarbon precipitation), the rapid cooling from 1300 °C to 1000 °C within 4 ~ 5 seconds\ncreates a massive carbon supersaturation (ΔC ≈ 0.28 wt.%) due to the drastic reduction\nin equilibrium solubility dictated by the Ni-C phase diagram34. This corresponds to a\nchemical potential difference of Δμ ≈ 0.08 eV/atom. In Stage II, the accumulated\ncarbon overcomes a drastically reduced nucleation barrier and form graphite layers.\nClassical nucleation theory indicates that the high Δμ lowers both the critical nucleation\nradius r* and energy barrier ΔG*, facilitating the observed high-density nucleation and\nrapid graphite layer formation48,49. Quantitatively, the carbon atomic flux in PJHIC\nreaches F ≈ 2.1×1022 atoms·m-2·s-1, surpassing state-of-the-art CVD graphene\nPJHIC\ngrowth by two orders of magnitude (F ≈ 3.1×1020 atoms·m-2·s-1)50,51. This\nCVD\nfundamental difference in mass transport efficiency underscores the paradigm-shifting\nnature of the non-equilibrium forced segregation mechanism compared to diffusion-\nlimited processes.\nThe Supplementary Information has also been revised by adding “Supplementary\nNote 3” and “Supplementary Note 4”:\nSupplementary Note 3. two-stage model for non-equilibrium segregation process\nA two-stage model that quantitatively describes the non-equilibrium segregation process,\nemphasizing the roles of interfacial carbon supersaturation (ΔC) and phase transformation driving\nforce (Δμ).\nStage I: Solute depletion-driven carbon segregation to the interface\nThe PJHIC process initiates with rapid cooling from a starting high temperature (T , 1300°C)\n0\nto a lower segregation temperature (1000°C < T < 1300°C). This creates a massive transient\nsupersaturation at the metal-graphite interface. According to the Ni–C phase diagram and the\nempirical relationship (Equation 7) proposed by Lander & Marshall1, The rapid cooling time within\n4.0~4.7 seconds contributes great interfacial supersaturation ΔC = C (1300°C) – C (1000°C) =\n0 1\n0.277 wt.%. Note that, for small values of S, the dimensionless mass fraction C can be directly\n𝑆 𝑆 1 4880\ncalculated by 𝐶 = ≈ = exp (2.480− ).\n100+𝑆 100 100 𝑇\nThe ΔC drives a chemical potential difference Δμ. The molar Gibbs free energy (𝜇) is expressed\nas:\n𝜇(𝐶,𝑇)=𝜇0(𝑇)+𝑘 𝑇ln(𝐶) (10)\n𝐵\nwhere 𝜇0(𝑇) is the standard (reference-state) chemical potential of carbon in Ni at temperature 𝑇,\n𝑘 is the Boltzmann constant. We assume that the carbon has been solved in Ni bulk at T = 1300 °C\n𝐵 0\nwith an equilibrium carbon solubility C (1300°C) = 0.536 wt.%. When the temperature drops, the\n0\nexcess chemical potential that drives segregation to the surface at temperature 𝑇 is:\n∆𝜇 =𝜇(𝐶 ,𝑇)−𝜇(𝐶(𝑇),𝑇)=𝑘 𝑇ln\n𝐶0\n(11)\n0 𝐵\n𝐶(𝑇)\nFor T = 1000°C = 1273 K, ∆𝜇 ≈7.73×103𝐽⁄𝑚𝑜𝑙(≈0.080 𝑒𝑉/𝑚𝑜𝑙). The significantly high ΔC\n1\nand Δμ promote the subsequent phase transformation from carbon atoms to graphite layers.\nStage II: Supersaturation-driven graphite layer formation\nThe supersaturated carbon at the interface must overcome the nucleation barrier to form\ngraphite layers. In classical nucleation theory, graphene nucleation on metal surfaces is an activated\nprocess in which a stable nucleus forms once it surpasses a critical size, balancing the energetic\ncompetition between creating a new interface (surface energy cost) and forming a new phase\n(volumetric energy gain from supersaturation). A new phase (graphene nucleus) forms via discrete\nnucleation events rather than continuous transformation. Nuclei are assumed circular (2D disc-\nshaped) and energetically isotropic. Interface properties (line energy 𝜆) and driving force (Δ𝜇) are\nconsidered constant and uniform during nucleation. Nucleation is thermodynamically driven and\nkinetically activated, involving the random fluctuation-driven formation of critical-sized clusters2,3.\nThe Gibbs free energy for forming a circular graphene nucleus of radius r is:\n∆𝐺(𝑟)=2𝜋𝑟𝜆−𝜋𝑟2𝜌 Δ𝜇 (12)\n𝑔\nWhere 𝜆 ≈1 eV/nm is the graphene-Ni line energy4, 𝜌 =3.82×1019 𝑎𝑡𝑜𝑚 𝑚−2 is the areal\n𝑔\natomic density, and ∆𝜇 is the areal thermodynamic driving force. The critical nucleation radius 𝑟∗\nand barriers ∆𝐺∗ follow from 𝜕∆𝐺⁄𝜕𝑟 =0:\n𝑟∗ = 𝜆 , Δ𝐺∗ = 𝜋λ2 (13)\n𝜌𝑔Δ𝜇 𝜌𝑔Δ𝜇\nWe can find that the 𝑟∗ and ∆𝐺∗ both are inversely proportional to Δμ. The high Δμ in our\nPJHIC process significantly lowers ΔG*, facilitating high nucleation density and rapid layer\nformation (Fig. 1g,h). For nucleation of subsequent layers (2nd layer, 3rd layer,…) beneath the first\nlayer, the same theoretical framework applies, though with a generally lower interfacial line energy\n𝜆 due to spatial confinement and weaker coupling to metal substrate. Graphene thickening\n2\nproceeds once the interfacial carbon activity sufficiently reduces Δ𝐺∗ small enough.\nComparison between PJHIC and conventional isothermal CVD\nIn conventional isothermal CVD at 1000 °C, supersaturation is limited and originates not from\nbulk solubility changes, but from the surface decomposition of hydrocarbon precursors (e.g.,\nmethane, acetylene). These precursors adsorb and dissociate to form active carbon species, which\nthen migrate to create localized supersaturation. Given this fundamental difference in mechanism,\ncarbon atomic flux (F) provides a more direct and quantitative parameter for comparing the mass\ntransport behaviors of CVD and PJHIC processes.\nFor the PJHIC process, the effective growth duration is within 4s ~ 4.7s, and the vertical growth\nrate is calculated as 11,162.8 nm min-1 (see Response to Comment 4). The carbon flux is calculated\nas:\n𝐹 = 2.1×1022 𝑎𝑡𝑜𝑚𝑠/(𝑚2∙𝑠) (14)\n𝑃𝐽𝐻𝐼𝐶\nThe local concentration of active carbon species in CVD has not been experimentally\nquantified. So we estimated the effective flux (for lattice incorporation) using data from two\nbenchmark CVD studies: I) the current growth record-holder5, II) a high-speed process on CuNi\nalloy6.\n𝐹 = 3.06×1020𝑎𝑡𝑜𝑚𝑠/(𝑚2∙𝑠) (15)\nI\n𝐹 = 1.27×1017𝑎𝑡𝑜𝑚𝑠/(𝑚2∙𝑠) (16)\nII\nThe calculation results clearly demonstrate that the carbon atomic flux of the\nPJHIC process (2.11 × 1022 atoms m-2 s-1) exceeds that of conventional isothermal CVD\nprocesses (3.06×1020 atoms m-2s-1) by at least two orders of magnitude, highlighting the\nexceptional mass transport efficiency and high segregation driving force enabled by the\nnon-equilibrium forced segregation mechanism.\nSupplementary Note 4. The single segregation limit of graphite films\nBy systematically increasing the PMMA coating volume (0.2-0.8 mL) and\nextending the annealing time to 5 minutes, a maximum experimental thickness of 1.067\n± 0.032 μm was achieved at a coating volume of 0.6 mL. The relationship between film\nthickness and PMMA dosage exhibited a non-monotonic trend, first increasing and then\ndecreasing. This behavior was attributed to excessive PMMA decomposition, which\ngenerated gaseous byproducts (CH , C H , CO, etc.), resulting in substantial carbon\n4 2 4\nloss and thus limiting further thickness growth. Details regarding carbon loss of PMMA\nplease see in Supplementary Table 1.\nComment 4:\nThe in-plane thermal conductivity of the PJHIC-graphite film (1314 Wm-1K-1) is\nnotable, but not the highest among reported graphite materials. The authors are\nencouraged to include a more detailed analysis linking the defect density (e.g., via\nRaman ID/IG ratio) and grain boundary structure (from EBSD) to the thermal\nconductivity. A discussion on how further defect reduction or grain orientation\noptimization could enhance thermal performance would be valuable for readers\ninterested in high-thermal-conductivity applications.\nAuthors’ response:\nWe sincerely thank the reviewer for this insightful comment. We fully agree that a\ndetailed analysis linking defect density is critical to elucidating the in-plane heat\ntransport mechanisms in our PJHIC- graphite films.\nThe PJHIC-graphite film exhibits an ID/IG ratio of 0.03 in its Raman spectrum.\nUsing the empirical equation proposed by Pimenta and Dresselhaus et al. for in-plane\ncrystallite size calculation [Phys. Chem. Chem. Phys. 9, 1276-1290 (2007)]:\n1\nI \nL (nm)(2.41010)4  D \na laser I\n \nG\nwhere λ (532 nm) is the laser wavelength, we calculate the in-plane crystallite\nlaser\nsize L of 650 nm. To correlate this with thermal conductivity, we compared our\na\nexperimental thermal conductivity (1314 W·m⁻¹·K⁻¹) with Fugallo et al.’s first-\nprinciples calculations2, which depict Λ as a function of the effective thermal\ncharacteristic length (Fig. R1-4). Fugallo et al.’s curve shows a significant decrease\nin Λ when the characteristic length is below 10 μm. Specifically, their calculation\npredicts Λ of 1220 W·m⁻¹·K⁻¹ for a characteristic length of 650 nm. The good\nagreement between our experimental results and first-principles calculations (within\nexpected experimental uncertainties) shows that finite crystallite size is a primary factor\nlimiting further thermal conductivity improvements.\nWe concur with the reviewer that reducing defects and optimizing grain orientation\nhave substantial potential to further enhance in-plane thermal conductivity. In future\nsample fabrication efforts, we will target two key strategies: (1) Reducing defect density\nand increasing crystallite size by optimizing heating/cooling protocols (e.g., slower\nheating rates to promote grain growth and rapid quenching to suppress defect formation)\nand refining carbon dissolution-segregation processes; (2) Improving grain orientation\nuniformity via enhanced texture control during film formation, which will minimize\nphonon scattering at grain boundaries. These modifications are expected to\npush thermal conductivity closer to the theoretical limit, making the material more\ncompetitive for high-thermal-conductivity applications.\nFig. R1-4 | In-plane thermal conductivity of graphite as a function of grain\nsize (L ). TDTR measurement of Λ at 300 K (black squares) and Fugallo et al.\na ∥\n(orange dashed dot lines) are presented [Nano Lett. 14, 6109-6114 (2014)].\nAccordingly, we have revised the manuscript in the conclusion part:\n“In summary, …This approach marks a substantial advance in synthesis speed,\nbut the crystalline perfection of the resulting films still falls short of single-crystal\nstandards, as the rapid non-equilibrium process introduces grain boundaries, point\ndefects, and wrinkles. Our insights into segregation dynamics suggest that further\noptimization of kinetic control could reconcile both speed and quality.”\nResponse to the Reviewer #2\nThis manuscript presents a work on the ultrafast synthesis of high-quality graphite\nfilms using a pulsed Joule heating approach. The concept of \"non-equilibrium carbon\nflux engineering\" is introduced and investigated through a series of experiments\ncharacterizing growth kinetics, structural properties, and thermal performance. The\nstudy demonstrates rapid film growth rates and the ability to control film thickness.\nHowever, several aspects require further clarification:\nAuthors’ response:\nWe thank the reviewer for the positive assessment of our work and the insightful\ncomments. We have carefully addressed all points raised, with special attention to\nclarifying the mechanistic aspects of non-equilibrium carbon transport and segregation.\nOur point-by-point responses are provided below.\nComment 1:\nThe core concept revolves around a \"non-equilibrium\" process, primarily defined\nby fast heating/cooling rates (>300 °C/s). Beyond the kinetic rates, what are the key\nphysical parameters (e.g., carbon supersaturation at the interface, phase\ntransformation driving force) that quantitatively define this non-equilibrium state?\nCould the authors provide a quantitative comparison (even a model-based estimation)\nof the carbon flux or segregation driving force against a traditional isothermal CVD\nprocess with a similar effective growth duration (e.g., ~60 s)? This would more\nforcefully demonstrate the unique advantage of the method beyond simply being\n\"faster.\"\nAuthors’ response:\nWe sincerely appreciate the reviewer’s insightful question regarding the\nquantitative definition of our non-equilibrium process. As rightly pointed out, fast\nheating/cooling rates are the experimental manifestation, while the underlying physics\nis rooted in enhanced thermodynamic driving forces. To address this, we have\ndeveloped a two-stage model that quantitatively describes the non-equilibrium\nsegregation process, emphasizing the roles of interfacial carbon supersaturation (ΔC)\nand phase transformation driving force (Δμ), as well as compared the carbon flux\nagainst a traditional isothermal CVD process.\nStage I: Solute depletion-driven carbon segregation to the interface\nThe PJHIC process initiates with rapid cooling from a starting high temperature\n(T , 1300°C) to a lower segregation temperature (1000°C < T < 1300°C). This creates\n0\na massive transient supersaturation at the metal-graphite interface. According to the Ni–\nC phase diagram (Fig. R2-1) and the empirical relationship proposed by Lander &\nMarshall [J. Appl. Phys. 1952, 23 (12), 1305]:\n4880\nln𝑆 = 2.480−\n𝑇\nwhere S denotes weight-percent carbon solubility (wt %, grams C per 100 grams Ni).\nFor small values of S, the dimensionless mass fraction C can be directly calculated by:\n𝑆 𝑆 1 4880\n𝐶 = ≈ = exp (2.480− )\n100+𝑆 100 100 𝑇\nFor just 4.0 ~ 4.7 s of cooling time (see comment 4), the equilibrium carbon solubility\ndrops from C (1300°C) = 0.536 wt.% to C (1000°C) = 0.259 wt.%. The ultrafast\n0 1\ncooling rate contributes great interfacial supersaturation ΔC = C (1300°C) – C (1000°C)\n0 1\n= 0.277 wt.%, and thus drives a chemical potential difference Δμ. The molar Gibbs free\nenergy (𝜇) is expressed as:\n𝜇(𝐶,𝑇) = 𝜇0(𝑇)+𝑘 𝑇ln(𝐶)\n𝐵\nwhere 𝜇0(𝑇) is the standard (reference-state) chemical potential of carbon in Ni at\ntemperature 𝑇, 𝑘 is the Boltzmann constant. We assume that the carbon has been\n𝐵\nsolved in Ni bulk at T = 1300 °C with an equilibrium carbon solubility C (1300°C) =\n0 0\n0.536 wt.%. When the temperature drops, the excess chemical potential that drives\nsegregation to the surface at temperature 𝑇 is:\n𝐶\n0\n∆𝜇 = 𝜇(𝐶 ,𝑇)−𝜇(𝐶(𝑇),𝑇) = 𝑘 𝑇ln\n0 𝐵 𝐶(𝑇)\nFor T = 1000°C = 1273 K, ∆𝜇 ≈ 7.73×103𝐽⁄𝑚𝑜𝑙(≈ 0.080 𝑒𝑉/𝑚𝑜𝑙) . The\n1\nsignificantly high ΔC and Δμ promote the subsequent phase transformation from carbon\natoms to graphite layers.\n[Figure Redacted]\nStage II: Supersaturation-driven graphite layer formation\nThe supersaturated carbon at the interface must overcome the nucleation barrier to\nform graphite layers. In classical nucleation theory, graphene nucleation on metal\nsurfaces is an activated process in which a stable nucleus forms once it surpasses a\ncritical size, balancing the energetic competition between creating a new interface\n(surface energy cost) and forming a new phase (volumetric energy gain from\nsupersaturation). A new phase (graphene nucleus) forms via discrete nucleation events\nrather than continuous transformation. Nuclei are assumed circular (2D disc-shaped)\nand energetically isotropic. Interface properties (line energy 𝜆) and driving force (Δ𝜇)\nare considered constant and uniform during nucleation. Nucleation is\nthermodynamically driven and kinetically activated, involving the random fluctuation-\ndriven formation of critical-sized clusters [Acta Chim. Sin. 2014, 72, 345-358; J. Am.\nChem. Soc. 2011, 133 (13), 5009-5015].\nThe Gibbs free energy for forming a circular graphene nucleus of radius r is:\n∆𝐺(𝑟) = 2𝜋𝑟𝜆−𝜋𝑟2𝜌 Δ𝜇\n𝑔\nWhere 𝜆 ≈ 1 eV/nm is the graphene-Ni line energy [Nano lett. 2011, 11, 518-522],\n𝜌 = 3.82×1019 𝑎𝑡𝑜𝑚 𝑚−2 is the areal atomic density, and ∆𝜇 is the areal\n𝑔\nthermodynamic driving force. The critical nucleation radius 𝑟∗ and barriers ∆𝐺∗ follow\nfrom 𝜕∆𝐺⁄𝜕𝑟 = 0:\n𝜆 𝜋λ2\n𝑟∗ = , Δ𝐺∗ =\n𝜌 Δ𝜇 𝜌 Δ𝜇\n𝑔 𝑔\nWe can find that the 𝑟∗ and ∆𝐺∗ both are inversely proportional to Δμ. The high\nΔμ in our PJHIC process significantly lowers ΔG*, facilitating high nucleation\ndensity and rapid layer formation (Fig. 1g,h). For nucleation of subsequent layers\n(2nd layer, 3rd layer,…) beneath the first layer, the same theoretical framework applies,\nthough with a generally lower interfacial line energy 𝜆 due to spatial confinement and\n2\nweaker coupling to metal substrate. Graphene thickening proceeds once the interfacial\ncarbon activity sufficiently reduces Δ𝐺∗ small enough.\nQuantitative comparison between PJHIC and conventional CVD\nAs the reviewer’s suggestion, we compare the driving force and carbon flux\nbetween PJHIC and traditional isothermal CVD process with a similar effective growth\nduration of 5 s.\nFor the PJHIC process, the effective growth duration is within 4s ~ 4.7s, and the\nvertical growth rate is calculated as 11,162.8 nm min-1 (see Response to Comment 4).\nThe carbon flux is calculated as:\n𝐹 = 2.1×1022 𝑎𝑡𝑜𝑚𝑠/(𝑚2 ∙𝑠)\n𝑃𝐽𝐻𝐼𝐶\nIn conventional isothermal CVD at 1000°C, supersaturation is limited and\noriginates not from bulk solubility changes, but from the surface decomposition of\nhydrocarbon precursors (e.g., methane, acetylene). These precursors adsorb and\ndissociate to form active carbon species, which then migrate to create localized\nsupersaturation. The local concentration of active carbon species in CVD has not been\nexperimentally quantified. So we estimated the effective flux (for lattice incorporation)\nusing data from two benchmark CVD studies: the current growth record-holder (Nat.\nChem. 2019, 11 (8), 730-736) and a high-speed process on CuNi alloy (ACS Nano 2018,\n12 (6), 6117-6127).\nFor the literature Nat. Chem. 2019, 11 (8), 730-736, taking the typical data of Fig\n1b-d as an example, the substrate area where flux occurs\n𝐴 = 1.96 × 10−8m2\n𝑠𝑢𝑏\nthe growth rate of graphene island (area)\nd𝐴 𝐴 7.854 × 10−7m2\n𝑔𝑟𝑎𝑝ℎ𝑒𝑛𝑒 = 𝑔𝑟𝑎𝑝ℎ𝑒𝑛𝑒 = = 1.5708 × 10−7m2/s\nd𝑡 𝑡 5 𝑠\nthe carbon atom deposition rate\nd𝐴\n𝑅 = 𝜌 𝐺𝑟𝑎𝑝ℎ𝑒𝑛𝑒 = 6 ×1012 𝑎𝑡𝑜𝑚𝑠/𝑠\n𝑐𝑎𝑟𝑏𝑜𝑛 𝑎𝑡𝑜𝑚𝑠 d𝑡\nWhere ρ = 3.82 × 1019 atoms/m2 is surface atomic density of graphene. Hence, the\ncarbon flux can be calculated as:\n𝑅\n𝐹 = 𝑐𝑎𝑟𝑏𝑜𝑛 𝑎𝑡𝑜𝑚𝑠 = 3.06×1020𝑎𝑡𝑜𝑚𝑠/(𝑚2 ∙𝑠)\n𝑁𝑎𝑡.𝐶ℎ𝑒𝑚. 𝐴\n𝑠𝑢𝑏\nSimilarly, for the ACS Nano 2018, 12 (6), 6117-6127,\nd𝐴\n𝐹 = 𝜌× 𝑔𝑟𝑎𝑝ℎ𝑒𝑛𝑒 ≈ 1.27×1017𝑎𝑡𝑜𝑚𝑠/(𝑚2 ∙𝑠)\n𝐴𝐶𝑆 𝑁𝑎𝑛𝑜 d𝑡 𝐴\n𝑠𝑢𝑏\nAll calculations were conducted using the following standard physicochemical\nparameters: Graphite density (𝜌 = 2.26 𝑔/𝑐𝑚3 ); Molar mass of carbon ( 𝑀 =\n12.01 𝑔/𝑚𝑜𝑙 ); Avogadro’s number (𝑁 = 6.022×1023 /𝑚𝑜𝑙 ); C–C bond length\na\n(𝑑 = 0.142 𝑛𝑚); Single-layer graphene thickness (0.34 nm); Lattice constant (𝑎 =\n𝑐−𝑐\n√3×𝑑 ≈ 0.246 𝑛𝑚 ); Unit cell area ( 𝐴 = √3 ×𝑎2 ≈ 5.246×10−20𝑚2 );\n𝑐−𝑐 𝑐𝑒𝑙𝑙\n𝑉\n𝐴𝑐𝑒𝑙𝑙\nthe carbon atomic density.\nThe calculation results clearly demonstrate that the carbon atomic flux of the\nPJHIC process (2.11 × 1022 atoms m-2 s-1) exceeds that of conventional isothermal CVD\nprocesses (3.06×1020 atoms m-2s-1) by two orders of magnitude, highlighting the\nexceptional mass transport efficiency and high segregation driving force enabled by the\nnon-equilibrium forced segregation mechanism.\nAccordingly, we have revised the manuscript by adding a paragraph at the end of\nthe section “Pulsed Joule heating activated ultrafast carbon diffusion and\nsegregation” :\nThe rapid non-equilibrium segregation growth process comprises two distinct yet\ninterconnected stages (Supplementary Note 3). In Stage I (Solute depletion-driven\ncarbon precipitation), the rapid cooling from 1300 °C to 1000 °C within 4 ~ 5 seconds\ncreates a massive carbon supersaturation (ΔC ≈ 0.28 wt.%) due to the drastic reduction\nin equilibrium solubility dictated by the Ni-C phase diagram34. This corresponds to a\nchemical potential difference of Δμ ≈ 0.08 eV/atom. In Stage II, the accumulated\ncarbon overcomes a drastically reduced nucleation barrier and form graphite layers.\nClassical nucleation theory indicates that the high Δμ lowers both the critical nucleation\nradius r* and energy barrier ΔG*, facilitating the observed high-density nucleation and\nrapid graphite layer formation48,49. Quantitatively, the carbon atomic flux in PJHIC\nreaches F ≈ 2.1×1022 atoms·m-2·s-1, surpassing state-of-the-art CVD graphene\nPJHIC\ngrowth by two orders of magnitude (F ≈ 3.1×1020 atoms·m-2·s-1)50,51. This\nCVD\nfundamental difference in mass transport efficiency underscores the paradigm-shifting\nnature of the non-equilibrium forced segregation mechanism compared to diffusion-\nlimited processes.\nThe Supplementary Information has also been revised by adding “Supplementary\nNote 3”:\nSupplementary Note 3. two-stage model for non-equilibrium segregation process\nA two-stage model that quantitatively describes the non-equilibrium segregation process,\nemphasizing the roles of interfacial carbon supersaturation (ΔC) and phase transformation driving\nforce (Δμ).\nStage I: Solute depletion-driven carbon segregation to the interface\nThe PJHIC process initiates with rapid cooling from a starting high temperature (T , 1300°C)\n0\nto a lower segregation temperature (1000°C < T < 1300°C). This creates a massive transient\nsupersaturation at the metal-graphite interface. According to the Ni–C phase diagram and the\nempirical relationship (Equation 7) proposed by Lander & Marshall1, The rapid cooling time within\n4.0~4.7 seconds contributes great interfacial supersaturation ΔC = C (1300°C) – C (1000°C) =\n0 1\n0.277 wt.%. Note that, for small values of S, the dimensionless mass fraction C can be directly\n𝑆 𝑆 1 4880\ncalculated by 𝐶 = ≈ = exp (2.480− ).\n100+𝑆 100 100 𝑇\nThe ΔC drives a chemical potential difference Δμ. The molar Gibbs free energy (𝜇) is expressed\nas:\n𝜇(𝐶,𝑇)=𝜇0(𝑇)+𝑘 𝑇ln(𝐶) (10)\n𝐵\nwhere 𝜇0(𝑇) is the standard (reference-state) chemical potential of carbon in Ni at temperature 𝑇,\n𝑘 is the Boltzmann constant. We assume that the carbon has been solved in Ni bulk at T = 1300 °C\n𝐵 0\nwith an equilibrium carbon solubility C (1300°C) = 0.536 wt.%. When the temperature drops, the\n0\nexcess chemical potential that drives segregation to the surface at temperature 𝑇 is:\n∆𝜇 =𝜇(𝐶 ,𝑇)−𝜇(𝐶(𝑇),𝑇)=𝑘 𝑇ln\n𝐶0\n(11)\n0 𝐵\n𝐶(𝑇)\nFor T = 1000°C = 1273 K, ∆𝜇 ≈7.73×103𝐽⁄𝑚𝑜𝑙(≈0.080 𝑒𝑉/𝑚𝑜𝑙). The significantly high ΔC\n1\nand Δμ promote the subsequent phase transformation from carbon atoms to graphite layers.\nStage II: Supersaturation-driven graphite layer formation\nThe supersaturated carbon at the interface must overcome the nucleation barrier to form\ngraphite layers. In classical nucleation theory, graphene nucleation on metal surfaces is an activated\nprocess in which a stable nucleus forms once it surpasses a critical size, balancing the energetic\ncompetition between creating a new interface (surface energy cost) and forming a new phase\n(volumetric energy gain from supersaturation). A new phase (graphene nucleus) forms via discrete\nnucleation events rather than continuous transformation. Nuclei are assumed circular (2D disc-\nshaped) and energetically isotropic. Interface properties (line energy 𝜆) and driving force (Δ𝜇) are\nconsidered constant and uniform during nucleation. Nucleation is thermodynamically driven and\nkinetically activated, involving the random fluctuation-driven formation of critical-sized clusters2,3.\nThe Gibbs free energy for forming a circular graphene nucleus of radius r is:\n∆𝐺(𝑟)=2𝜋𝑟𝜆−𝜋𝑟2𝜌 Δ𝜇 (12)\n𝑔\nWhere 𝜆 ≈1 eV/nm is the graphene-Ni line energy4, 𝜌 =3.82×1019 𝑎𝑡𝑜𝑚 𝑚−2 is the areal\n𝑔\natomic density, and ∆𝜇 is the areal thermodynamic driving force. The critical nucleation radius 𝑟∗\nand barriers ∆𝐺∗ follow from 𝜕∆𝐺⁄𝜕𝑟 =0:\n𝑟∗ = 𝜆 , Δ𝐺∗ = 𝜋λ2 (13)\n𝜌𝑔Δ𝜇 𝜌𝑔Δ𝜇\nWe can find that the 𝑟∗ and ∆𝐺∗ both are inversely proportional to Δμ. The high Δμ in our\nPJHIC process significantly lowers ΔG*, facilitating high nucleation density and rapid layer\nformation (Fig. 1g,h). For nucleation of subsequent layers (2nd layer, 3rd layer,…) beneath the first\nlayer, the same theoretical framework applies, though with a generally lower interfacial line energy\n𝜆 due to spatial confinement and weaker coupling to metal substrate. Graphene thickening\n2\nproceeds once the interfacial carbon activity sufficiently reduces Δ𝐺∗ small enough.\nComparison between PJHIC and conventional isothermal CVD\nIn conventional isothermal CVD at 1000 °C, supersaturation is limited and originates not from\nbulk solubility changes, but from the surface decomposition of hydrocarbon precursors (e.g.,\nmethane, acetylene). These precursors adsorb and dissociate to form active carbon species, which\nthen migrate to create localized supersaturation. Given this fundamental difference in mechanism,\ncarbon atomic flux (F) provides a more direct and quantitative parameter for comparing the mass\ntransport behaviors of CVD and PJHIC processes.\nFor the PJHIC process, the effective growth duration is within 4s ~ 4.7s, and the vertical growth\nrate is calculated as 11,162.8 nm min-1 (see Response to Comment 4). The carbon flux is calculated\nas:\n𝐹 = 2.1×1022 𝑎𝑡𝑜𝑚𝑠/(𝑚2∙𝑠) (14)\n𝑃𝐽𝐻𝐼𝐶\nThe local concentration of active carbon species in CVD has not been experimentally\nquantified. So we estimated the effective flux (for lattice incorporation) using data from two\nbenchmark CVD studies: I) the current growth record-holder5, II) a high-speed process on CuNi\nalloy6.\n𝐹 = 3.06×1020𝑎𝑡𝑜𝑚𝑠/(𝑚2∙𝑠) (15)\nI\n𝐹 = 1.27×1017𝑎𝑡𝑜𝑚𝑠/(𝑚2∙𝑠) (16)\nII\nThe calculation results clearly demonstrate that the carbon atomic flux of the\nPJHIC process (2.11 × 1022 atoms m-2 s-1) exceeds that of conventional isothermal CVD\nprocesses (3.06×1020 atoms m-2s-1) by at least two orders of magnitude, highlighting the\nexceptional mass transport efficiency and high segregation driving force enabled by the\nnon-equilibrium forced segregation mechanism.\nComment 2:\nThe choice of an extremely fast cooling rate (>50 °C/s) and the specific durations for\nthe heating (120 s) and cooling (30 s) intervals in the cyclic process are critical to the\nmethod's success. However, the rationale behind selecting these specific parameters is\nnot clearly explained. Were these values optimized empirically, or are they based on a\ntheoretical consideration (e.g., a characteristic time for carbon diffusion vs.\nsegregation)? Please clarify the reasoning behind these key process choices.\nAuthors’ response:\nWe sincerely appreciate the reviewer’s insightful question concerning the key\nprocess parameters. The selection of the specific conditions 120 s for heating and 30 s\nfor cooling was determined through a combination of theoretical considerations,\nequipment capability, and experimental validation.\n1. Heating stage (120 s): Ensuring bulk-phase carbon saturation\nThe duration of the heating stage was determined by combining the theoretical\ndiffusion requirement of carbon in Ni with experimental observations.\nAccording to our Supplementary Note 1, at the growth temperature T = 1573 K,\nthe diffusion coefficient D was calculated to be 6.571 × 10-6 cm2 · s-1, and the diffusion\ntime t through a 50 μm-thick nickel foil was determined to be approximately 3.8 s. Our\nToF-SIMS experiments also revealed that the diffusion time is about 11 seconds.\nHowever, for the cyclic process, we should ensure sufficient dissolution of carbon\natoms, thereby achieving a maximized supersaturation state and subsequent forced\nsegregation. According to our experiment in Figure 1 g (Fig. R2-5), the thickness of the\ngraphite film gets saturated after 80 s (by applying 1300 °C).\nFig. R2-5 (Figure 1g) | Graphite thickness as a function of growth time.\nIn another hand, for the cyclic process, the growth temperature was set to 1250-\n1280 °C rather than 1300 °C in order to avoid heat accumulation during repeated\ncycling. Experimentally, we confirmed this phenomenon that the peak temperature of\nthe system would gradually increase with the number of cycles, potentially causing\nmelting or structural degradation of the Ni foil (Fig. R2-3). Therefore, the applied\ncurrent was appropriately reduced to balance the Joule heating effect with the system’s\nheat accumulation behavior.\nFig. R2-3 | Optical image of the Ni foil obtained after the 1300 °C cyclic growth\nprocess.\nTherefore, during the heating stage, a current of 320-325 A was applied to the\ngraphite plate and maintained for 120 s, enabling the system to rapidly reach 1250-\n1280 °C.\nFig. R2-2 (Supplementary Fig. 9) | The curve of current and temperature\nvarying with time during the cyclic heating and cooling process.\n2. Cooling stage (30 s): Balancing forced segregation and system capability\nThe selection of the cooling time represents a balance between process\nrequirements and system limitations. Process requirement: The cooling stage serves as\nthe critical window during which “forced segregation” occurs. The system must be\nrapidly cooled to a temperature where the solubility of carbon in nickel becomes\nextremely low (well below 1000 °C), in order to induce a strong segregation driving\nforce.\nSystem capability: In our water-cooled system, a 30 s duration corresponds to the\ntypical time required for the temperature to naturally decrease from 1250-1280 °C to\nbelow 800 °C after power shutdown. This cooling window has been experimentally\nverified to be sufficient for completing the main segregation process within a single\ncycle.\nAccordingly, we have revised the manuscript by adding sentences in Methods\nsection as follow:\n“The Ni/Co foils were cut into 21 mm × 21 mm pieces… For the cyclic process, a\ncurrent of 320-325 A was applied to the graphite plate for 120 s to rapidly achieve 1250-\n1280 °C, ensuring sufficient dissolution and minimizing heat accumulation during\nrepeated cycling. The cooling stage was set to be 30 s to promote effective carbon\nsegregation.”\nComment 3:\nThe comparison in Figure 1h is excellent, but it primarily includes works prior to 2023.\nPlease clearly articulate the fundamental distinctions between your work and very\nrecent (or contemporary) studies also focusing on rapid synthesis of high-quality\ngraphite films, such as Zhang et al. Nat. Commun. 16, 7180 (2025) (Ref. 21). Given\nthat Ref. 21 also reports considerable growth rate (6.2 layers/s) and high thermal\nconductivity, what is the definitive advantage of your method in terms of growth speed,\nenergy consumption, or process simplicity?\nAuthors’ response:\nWe appreciate the reviewer’s suggestion to include a comparison with this recent\nand important work. We fully acknowledge the significant progress achieved by Zhang\net al. (Ref. 21) in the fabrication of high-quality graphite films. It should be noted,\nhowever, that the PJHIC approach developed in this study differs fundamentally from\ntheir “isothermal carbon diffusion/lamination-graphitization” pathway in terms of core\nmechanism, process design, and product morphology. The PJHIC method demonstrates\nclear advantages in the preparation efficiency, energy consumption, and procedural\nsimplicity for micrometer-thick films.\nTo enable a fair and quantitative comparison, the layer growth rate reported in Ref.\n21 (6.2 layers s-1) was converted to the vertical growth rate used in this work. Assuming\na single graphene layer thickness of 0.335 nm, the equivalent vertical growth rate is\napproximately 126 nm min-1. In contrast, the PJHIC process developed here achieves a\nvertical growth rate of 730 nm min-1, which is about 5.8 times higher.\nFig. R2-6 (Revised Fig. 1 h) | Comparative analysis of the growth time and\ngrowth rate of graphite films reported in this work and in literatures.\nEfficiency and speed advantages for thick-film fabrication: For the preparation of\nmicrometer-scale graphite films (e.g., 5 μm), the layer-by-layer growth and subsequent\nprocessing reported in Ref. 21 require a relatively long total time. In contrast, the PJHIC\nmethod enables rapid thickening at the bulk-material level, allowing a 5 μm-thick film\nto be obtained directly within approximately 2 h, thus demonstrating a clear advantage\nin overall time efficiency.\nLow energy consumption and procedural simplicity: The PJHIC approach avoids\nthe high energy consumption associated with conventional CVD processes and long-\nduration high-temperature graphitization furnaces. Moreover, it integrates the\ntraditionally multi-step processes into a single-step synthesis, significantly reducing\nboth equipment requirements and procedural complexity.\nTherefore, this work not only provides a faster route for graphite film synthesis,\nbut more importantly, it establishes an innovative pathway for high-throughput, low-\nenergy, single-step preparation of micrometer-thick, high-quality graphite films,\ncomplementing the precise layer-by-layer epitaxial growth techniques.\nIn the revised manuscript, Figure 1 has been updated.\nFig. 1 | Ultrafast growth of graphite films via the PJHIC process.\na-c Schematic of the PJHIC system (a), the thermal shock generated by pulsed current\napplication (b), and carbon diffusion–graphite segregation process (c). d,e Optical\nimages of the as-synthesized graphite film transferred on Si/SiO (d) and flexible PET\n2\n(e) substrate, respectively. f Current–time and temperature–time profiles corresponding\nto different growth durations. g Graphite thickness as a function of growth time. Inset:\nAFM image at side of a typical graphite sheet grown with 72s. h Comparative analysis\nof the growth time and growth rate of graphite films reported in this work and in\nliteratures15,20-29,35-42. i Raman spectra acquired at as-synthesized graphite films with\ndifferent growth time. j Deconvolution of a typical 2D Raman band into two Lorentzian\ncomponents. k The statistical distribution of I /I ratio and FWHM of the G band over\nD G\nan 80 × 80 μm² region.\nComment 4:\nThe \"effective growth time\" is defined as the duration above 1000°C, however,\nthe manuscript correctly identifies the cooling phase as the primary period for forced\nsegregation. Does this \"effective growth time\" accurately represent the actual time window for segregation? If segregation occurs predominantly during the few seconds of cooling from 1300°C to 1000°C, the instantaneous segregation rate would be extraordinarily high. This point requires clarification.\nAuthors’ response:\nWe sincerely thank the reviewer for this insightful comment and important\nsuggestion. The primary driving force for the forced segregation process is indeed\nconcentrated within the short cooling window from 1300 °C to 1000 °C. Accordingly,\nwe have re-evaluated the instantaneous segregation rate specifically during this critical\nperiod.\nThe recalculated cooling durations for the series of experiments (corresponding to\nFigure 1f, g and Supplementary Fig. 2-3) are presented in Fig. R2-7. The instantaneous\nsegregation rates during this cooling phase are calculated as follows:\nFor the sample under 11 s growth time, the cooling time t = 4.7 s, the instantaneous\n1\nsegregation rate\n62 𝑛𝑚\nv = = 13.2 𝑛𝑚/𝑠 = 792 𝑛𝑚/𝑚𝑖𝑛\n1 4.7𝑠\nFor the sample under 42 s growth time, the cooling time t = 4.6 s, the\n2\ninstantaneous segregation rate\n487 𝑛𝑚\nv = = 105.9 𝑛𝑚/𝑠 = 6,354 𝑛𝑚/𝑚𝑖𝑛\n2 4.6 𝑠\nFor the sample under 51 s growth time, the cooling time t = 4.3 s, the\n3\ninstantaneous segregation rate\n608 𝑛𝑚\nv = = 141.4 𝑛𝑚/𝑠 = 8,484 𝑛𝑚/𝑚𝑖𝑛\n3 4.3 𝑠\nFor the sample under 61 s growth time, the cooling time t = 4.5 s, the\n4\ninstantaneous segregation rate\n743 𝑛𝑚\nv = = 165.1 𝑛𝑚/𝑠 = 9,906 𝑛𝑚/𝑚𝑖𝑛\n4 4.5 𝑠\nFor the sample under 72 s growth time, the cooling time t = 4.0 s, the\n5\ninstantaneous segregation rate\n811 𝑛𝑚\nv = = 202.8 𝑛𝑚/𝑠 = 12,168 𝑛𝑚/𝑚𝑖𝑛\n5 4.0 𝑠\nFor the sample under 102 s growth time, the cooling time t = 4.2 s, the\n6\ninstantaneous segregation rate\n834 𝑛𝑚\nv = = 198.6 𝑛𝑚/𝑠 = 11,916 𝑛𝑚/𝑚𝑖𝑛\n6 4.2 𝑠\nFor the sample under 132 s growth time, the cooling time t = 4.1 s, the\n7\ninstantaneous segregation rate\n842 𝑛𝑚\nv = = 205.4 𝑛𝑚/𝑠 = 12,324 𝑛𝑚/𝑚𝑖𝑛\n7 4.1 𝑠\nFig. R2-7 (Revised Supplementary Fig. 4) | Analysis of cooling duration and\ncorresponding instantaneous segregation rates. The specific cooling time windows\n(from 1300 °C to 1000 °C) associated with the temperature profiles in Fig. 1f are\ndelineated.\nAs these calculations demonstrate, the instantaneous segregation rate during the\n4-5 seconds of cooling is extraordinarily high, reaching up to ~12,000 nm/min.\nHowever, the complete graphite formation process in the PJHIC strategy comprises two\nessential stages: (1) the heating/dissolution stage for carbon source decomposition and\ncarbon influx into the metal bulk, and (2) the cooling/segregation stage for graphite\nformation. The \"effective growth time\" (duration above 1000 °C) encompasses both\nstages and represents the total processing time from the system's perspective. Therefore,\nthe average vertical growth rate of 730 nm/min (calculated based on the total\neffective time) remains a meaningful and conservative metric for comparing the overall\nsynthesis efficiency against other methods in the literature.\nTo provide a comprehensive picture, we have now clarified this distinction in the\nrevised manuscript. We report both the average growth rate (for cross-method\ncomparison) and the instantaneous segregation rate (to highlights the exceptional\nkinetics of the non-equilibrium forced segregation), as reflected in the added sentences\nin the main text:\n“To investigate the growth rate limit of graphite segregation through Ni foil……\nNotably, considering that graphite segregation occurs predominantly during the rapid\ncooling stage (from 1300 °C to 1000 °C within 4 ~ 5 seconds), the corresponding\ninstantaneous segregation rate is calculated to be ~12,000 nm/min (Supplementary Fig.\n4). The PJHIC strategy enables micron-thick, uniform graphite films with growth rates\nover an order of magnitude higher than previous reports15,20-29,35-42.”\nAccordingly, we revised the Supplementary Information by adding Supplementary\nFig. 4:\nSupplementary Fig. 1 | Analysis of cooling duration and corresponding\ninstantaneous segregation rates. The specific cooling time windows (from 1300 °C\nto 1000 °C) associated with the temperature profiles in Fig. 1f are delineated. the\ninstantaneous segregation rates are calculated to be: v = 792 nm/min, v = 6,354\n1 2\nnm/min, v = 8,484 nm/min, v = 9,906 nm/min, v = 12,168 nm/min, v = 11,916\n3 4 5 6\nnm/min, and v = 12,324 nm/min.\nThe use of PMMA as a solid-state carbon source is a key experimental detail. What is\nthe specific advantage of using a polymer precursor like PMMA over others carbon\nsources (e.g., Graphite plate) in this particular PJHIC process? Does its decomposition\nkinetics at ultra-high heating rates favor a rapid and massive carbon influx into the Ni\nsubstrate, potentially creating a higher initial supersaturation? A brief justification for\nthis choice would be helpful.\nAuthors’ response:\nWe sincerely appreciate the reviewer’s insightful question regarding the choice of\ncarbon source. The selection of PMMA was made after systematic experimental\ncomparison and careful mechanistic consideration. The key advantage of PMMA lies\nin its decomposition kinetics, which are well matched to the ultrafast heating profile\nemployed in the PJHIC process. This compatibility enables the rapid release of a\nsufficient amount of carbon atoms within an extremely short time window, thereby\nproviding the necessary conditions for achieving high interfacial carbon supersaturation.\nTo comprehensively evaluate the influence of different carbon sources, we\nconducted a series of comparative experiments involving five solid carbon precursors:\ngraphite paper, carbon black powder, polyimide (PI) film, and PMMA. The\nmacroscopic results (Fig. R2-8) clearly demonstrate that among all tested precursors,\nonly PMMA produced a complete, continuous, and uniform graphite film on the Ni foil\nsurface. In contrast, the other carbon sources yielded only discontinuous and patchy\ngraphite domains, failing to achieve full substrate coverage.\nFig. R2-8 | Optical images of samples obtained from different carbon sources. a,\ngraphite paper. b, carbon black powder. c, PI film. d, PMMA.\nPMMA exhibits a relatively low onset temperature for pyrolysis (approximately\n400 °C) and undergoes rapid, continuous decomposition during heating up to the peak\ntemperature (1300 °C), generating a large quantity of reactive carbon species. Such a\nprecursor-type decomposition behavior is highly compatible with the ultrafast heating\nrate adopted in PJHIC. Consequently, carbon atoms can be released and dissolved\nrapidly around the catalytic graphitization temperature of Ni foil. As suggested by the\nreviewer, this process facilitates the rapid establishment of a high carbon\nsupersaturation within the metal substrate, thereby providing sufficient driving force\nfor the subsequent non-equilibrium enforced segregation.\nGraphite paper and carbon black are both thermodynamically stable allotropes of\ncarbon, where carbon atoms can only enter the metallic bulk through a sublimation\nmechanism. This process proceeds extremely slowly at 1300 °C and cannot supply\nsufficient carbon flux within the second-to-minute timescale of PJHIC. As a result, only\nsparse and discontinuous graphite islands are formed.\nAlthough PI film is also a polymeric precursor, it possesses higher thermal stability\nand graphitization temperature. Its decomposition kinetics are slower compared to\nPMMA, leading to an insufficient rate and amount of carbon release under ultrafast\nheating conditions. This limitation prevents homogeneous nucleation and continuous\ngrowth across the entire substrate.\nTherefore, the selection of PMMA is not arbitrary, but rather dictated by its ability\nto meet the key requirement of PJHIC for an extremely high initial carbon flux. Its rapid\ndecomposition kinetics ensure the instantaneous and abundant release of carbon, which\nserves as the prerequisite for establishing a high initial supersaturation and achieving\nultrafast, uniform graphite growth under non-equilibrium conditions.\nAccordingly, we have revised the manuscript at the Section of “Cyclic saturation\nengineering for thickness control” and Methods section:\n“Cyclic saturation engineering for thickness control\nTo transcend the sub-micrometer……Although the 7.42% carbon loss happens due to\nPMMA decomposition into gaseous byproducts (Supplementary Note 3 and\nSupplementary Table 1), the decomposed gaseous carbon source favors a rapid and\nmassive carbon influx into the Ni substrate, potentially creating a higher initial\nsupersaturation….30 s of forced cooling for triggering the segregation (Supplementary\nFig. 9).”\nRevised Methods section, PJHIC growth:\n“The Ni/Co foils were cut into 21 mm × 21 mm pieces. Subsequently,\napproximately 0.6 mL of PMMA solution was spin-coated onto the surface of the foils.\nBased on a systematic evaluation of decomposition kinetics and comparative\nexperiments with alternative sources (e.g., graphite paper, carbon black powder, and PI\nfilm), PMMA is chosen as the carbon source suitable for the ultrafast PJHIC process. …”\nComment 6:\nThe rapid thermal shocks and the associated large thermal stress could potentially\nintroduce more wrinkles and defects into the graphite films. The conclusion states that\n\"the crystalline perfection of the resulting films still falls short of single-crystal\nstandards.\" While this responsible statement is appreciated, it seems somewhat\ncontradictory to the data presented (millimeter-scale grains, excellent Raman signals,\nABA stacking). Please specify in what aspects it \"falls short.\" Is it a larger mosaic\nspread? Or the presence of some stacking faults?\nThe color bar of Raman map in Supplementary Fig. 4 represents the ID/IG ratio,\nranging from 0 to 2, which convincingly shows the overall high quality. However, to\nhonestly reveal and discuss any potential micro-scale heterogeneity or defect populations introduced by the process, would it be more informative to use a narrower color scalefor this mapping? The current scale might be masking subtle variations.\nAuthors’ response:\nWe sincerely thank the reviewer for the insightful comments and constructive\nsuggestions. The reviewer has astutely identified the nuanced structural characteristics\nof our PJHIC-synthesized graphite films. We appreciate the opportunity to clarify in\nwhat specific aspects the crystalline perfection falls short of single-crystal standards.\nIndeed, while our films exhibit excellent macroscopic crystallinity (millimeter-\nscale grains, high-quality Raman signals, ABA stacking), the ultrafast non-equilibrium\ngrowth process inherently introduces specific microstructural imperfections that\nprevent them from achieving true single-crystal perfection. The primary limitations are\nas follows:\n1) Point defects from rapid kinetics: The extremely rapid segregation and\ncooling process intrinsically limits the time for carbon atoms to anneal into the most\nstable lattice positions. This results in a low, yet non-negligible, density of point defects,\nas consistently reflected in our Raman statistical analysis (average I /I ≈ 0.03, Figure\nD G\n1k, Figure R2-9 and Revised Supplementary Fig 5).\n2) Wrinkles induced by thermal stress: The large thermal shocks and associated\nmismatch stress during rapid cooling cannot be fully relieved, leading to the formation\nof wrinkles. These are visible in optical micrographs (Figure 1d), SEM images\n(Supplementary Fig 11f), and the revised Raman mapping data (Revised\nSupplementary Fig.5). These are a direct consequence of the non-equilibrium process\nconditions.\n3) Polycrystallinity and grain boundaries: The graphite films are synthesized\non polycrystalline Ni foils. Consequently, the segregated films are inherently\npolycrystalline as well, albeit with very large grain sizes (millimeter-scale) (Figure 4a,b,\nSupplementary Fig. 11 and Fig. R2-10). The presence of these grain boundaries\ninevitably introduces additional scattering centers for phonons, which is a key factor\nlimiting the in-plane thermal conductivity of our films (1314 W m-1 K-1) from reaching\nthe values of the highest-grade single-crystal HOPG (>2000 W m-1 K-1).\n4) Presence of stacking faults: Regarding stacking faults, while a detailed\nstatistical analysis of their density is beyond the scope of this current work and will be\na focus of future studies, the high quality of our XRD data (Figure 4c) showing an\ninterlayer spacing (3.355 Å) and a sharp (0002) peak (FWHM = 0.169°) comparable to\nthose of high-quality HOPG and Kish graphite—indicates that the overall stacking\norder is predominantly the thermodynamically stable ABA type.\nFollowing the reviewer's valuable suggestion, we have revised the Raman\nmapping in Supplementary Fig. 4 by narrowing the I /I color scale from 0–2 to 0–0.5.\nD G\nThis adjustment, as shown in the updated figure below, effectively reveals the\npreviously masked micro-scale heterogeneity. It now clearly demonstrates that: 1) The\nbasal plane of the large grains exhibits very low defect levels (I /I ≈ 0.03),\nD G\ncorresponding to the point defect density mentioned above; 2) The defect ratio increases\nsignificantly (> 0.1, locally > 0.2) precisely along the wrinkle lines, directly validating\nthe spatial correlation between these structural features and enhanced defect formation.\nFig. R2-9 (Revised Supplementary Fig. 5) | Raman characterization of graphite\nfilms. (a) Typical Raman spectra of the graphite film at 6 random positions. (b-d)\nRaman mapping of the graphite film showing I /I (b), FWHM of the G band (c), and\nD G\npeak position of 2D (d).\nalong the Z-direction and Y-direction of graphite films grown by segregation on the\nsurface of ordinary commercial nickel foils.\nAccordingly, we have revised the manuscript in the conclusion part by specify the\n“fall short” aspects:\n“In summary, … This approach marks a substantial advance in synthesis speed,\nbut the crystalline perfection of the resulting films still falls short of single-crystal\nstandards, as the rapid non-equilibrium process introduces grain boundaries, point\ndefects, and wrinkles. Our insights into segregation dynamics suggest that further\noptimization of kinetic control could reconcile both speed and quality...”\nIn all, we appreciate having highly constructive remarks from all reviewers. With\nall their comments addressed in the text, we are looking forward to the publication of\nour manuscript in Nature communication.\nThank you for your consideration.\nSincerely yours,\nZhongfan Liu and Luzhao Sun\nList of changes\n1. Enhanced theoretical foundation: A comprehensive two-stage model for the non-\nequilibrium segregation process has been developed and added to the manuscript\n(end of section \"Pulsed Joule heating activated ultrafast carbon diffusion and\nsegregation\") and the Supplementary Information (as Supplementary Note 3).\n2. Clarification of process parameters: The rationale behind key experimental\nparameters, including the selection of heating (120 s) and cooling (30 s) durations\nin the cyclic process, has been clarified in the Methods section. A justification for\nchoosing PMMA as the carbon source, based on its decomposition kinetics and\ncomparative experiments with other sources (graphite paper, carbon black, PI film),\nhas been added to the \"Cyclic saturation engineering\" section and the Methods\nsection.\n3. Demonstration of scalability: Data demonstrating the synthesis of a larger-area\ngraphite film (12 cm × 5 cm) has been added as Revised Supplementary Fig. 16.\n4. Refined growth rate analysis: The concept and calculation of the instantaneous\nsegregation rate (reaching up to ~12,000 nm/min during the rapid cooling phase)\nhave been introduced. This analysis, along with the corresponding cooling time\nwindows, is now presented in the main text and as Revised Supplementary Fig. 4.\n5. In-depth analysis of material quality: A more detailed discussion linking defect\ndensity (via Raman I /I ratio and crystallite size calculation) and grain boundary\nD G\nstructure to the measured thermal conductivity has been added. The Raman I\nD\n/I\nG\nmapping color scale has been narrowed (0–0.5) in Revised Supplementary Fig. 5\nto better reveal micro-scale heterogeneity.\n6. The Figure number in main text and supplementary information have been updated.\n7. Considering the contribution regarding the theoretical discussions on the\nsegregation model, we have added two authors, Xiongzhi Zeng and Zhenyu Li."}]

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