# Kinetically trapped amorphous states and AB pairing in rGO: an in-situ XRD study of process-structure map

Nicolò Galvani, Jasper Plaisier, Cosimo Anichini, Alicia Moya, Paolo Samorì, Andrea Liscio, Fabiola Liscio

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Nicolò Galvani, Jasper Plaisier, Cosimo Anichini, Alicia Moya, Paolo Samorì, et al. Kinetically trapped amorphous states and AB pairing in rGO: an in-situ XRD study of process-structure map. Carbon, 2026, 249, pp.121247. 10.1016/j.carbon.2026.121247. hal-05459809

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# Kinetically trapped amorphous states and AB pairing in rGO: an in-situ XRD study of process-structure map

Nicolò Galvani<sup>a,†</sup>, Jasper R. Plaisier<sup>b</sup>, Cosimo Anichini<sup>c,1</sup>, Alicia Moya<sup>d,‡</sup>, Paolo Samorì<sup>c</sup>, Andrea Liscio<sup>e,∗</sup>, Fabiola Liscio<sup>a,∗∗</sup>

## ARTICLE INFO

### Keywords:

- Graphene oxide

- Reduced graphene oxide

- In situ X-ray diffraction

- Stacking order

- In-plane strain

- Amorphous graphene

## ABSTRACT

Understanding and controlling the evolution of the graphene oxide (GO) structure during thermal reduction is critical for tailoring the reduced GO (rGO) properties for applications in energy storage and generation, electronics, and membrane. While previous in-situ diffraction studies have largely focused on interlayer collapse along the (00*') direction, the fate of the in-plane lattice and stacking registry has remained elusive. Here, we use synchrotron powder X-ray diffraction, complemented by in-/out-of-plane laboratory measurements on films, to monitor the (100)/(101) region of GO during reduction. Applying the Basic Structural Components (BSC) model, we quantitatively track turbostratic single layers, AB-paired bilayers, and short Bernal ABA sequences, alongside the evolving in-plane lattice parameter. We uncover a transient, rate-selected amorphous-like regime (140–190 °C) where the (100) intensity nearly vanishes, followed by divergent kinetic pathways: fast ramps trap AB-enriched but ABA-deficient states even at 900 °C, whereas slow ramps (≤0.5 °C/min) below ~240 °C enable progressive AB ordering and the emergence of short-range ABA. These results establish a process-structure map linking thermal history to stacking registry and in-plane strain. Beyond elucidating the reduction mechanism, our work outlines kinetic guidelines to deliberately trap amorphous-like 2D carbon or promote AB/ABA order, providing a controllable pathway to engineer interlayer coupling in rGO.

## 1. Introduction

Graphene oxide (GO) is arguably the least universal “graphene”: unlike crystalline graphene, its stoichiometry and microstructure are not fixed but vary significantly depending on the synthesis history and processing conditions. As a result, GO's properties can be extremely diverse. Recent efforts to classify and standardize GO, including surveys of commercial materials, document the breadth of variability, calling for protocols that bind chemistry to structure, properties and performance [1–5].

This variability matters for applications because transport, mechanics and surface reactivity in GO-derived materials are governed by its microstructure. Three structural factors are central for charge

transport: (i) the connectivity and lateral size $L_a$ of sp² domains; (ii) the topology and density of defects (for example vacancies, 5–7 rings, dislocations) that corrugate the lattice and impose in-plane strain; and (iii) the interlayer registry, from turbostratic to AB or ABA, which controls interlayer coupling and hopping pathways [6,7]. In reduced GO (rGO), charge transport at low–moderate temperature (typically ≈ –50 to +80 °C) is dominated by variable-range hopping between sp² nano-domains. As films become thicker upon layers stacking, the emergence of interlayer hopping is observed with the transport exhibiting thickness-dependent crossovers [8–11]. As the interlayer electronic coupling depends on stacking sequence, the realized registry directly impacts device-level resistance. Insights from high-quality few-layer graphene with very low disorder highlight this sensitivity to stacking:

<footnote><sup>a</sup> Istituto per lo Studio Dei Materiali Nanostrutturati (ISMN), Consiglio Nazionale Delle Ricerche (CNR), Via P. Gobetti 101, Bologna, 40129, Italy</footnote>

<footnote><sup>b</sup> Elettra – Sincrotrone Trieste S.C.p.A., Strada Statale 14, km 163,5 Basovizza, Trieste, 34149, Italy</footnote>

<footnote><sup>c</sup> University of Strasbourg, CNRS, ISIS UMR 7006, 8 Allée Gaspard Monge, Strasbourg, F-67000, France</footnote>

<footnote><sup>d</sup> Universidad Autónoma de Madrid, Applied Physical Chemistry Departament, 28049, Madrid, Spain</footnote>

<footnote><sup>e</sup> Istituto per la Microelettronica e Microsistemi (IMM) Consiglio Nazionale Delle Ricerche, Via Del Fosso Del Cavaliere 100, 00133, Roma, Italy</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>** Corresponding author.</footnote>

<footnote>E-mail addresses: andrea.liscio@cnr.it (A. Liscio), fabiola.liscio@cnr.it (F. Liscio).</footnote>

<footnote n="1">¹ Current address: BeDimensional S.p.A., Via Lungotorrente Secca 30 R, 16163, Genoa, Italy.</footnote>
AB (Bernal) bilayers develop an electric-field-induced gap [12], whereas trilayers exhibit stacking-dependent responses, i.e. ABC becomes gapped, ABA remains semimetallic [13–15]. If stacking alone reshapes bands in pristine systems, then in defective graphenic carbons the relative fractions of A/AB/ABA components should likewise control interlayer coupling and device performance.

Diffraction offers a way to read stacking directly. In powder, the pattern in the (100)/(101) region, sensitive to the in-plane hexagonal network and to interlayer registry via the (101) contribution, can be described by the Basic Structural Components (BSCs) model. The pattern is represented as superposition of turbostratic single layers (A), AB paired bilayers, and short Bernal sequences such as ABA, each with a characteristic line shape and intensity ratio [16,17]. This framework assigns physical meaning to the in-plane peaks and enables quantitative tracking of stacking evolution.

Most in-situ XRD studies, however, have focused on the out-of-plane (002) reflection. These works established that thermal reduction collapses the interlayer spacing through a transient disordered intermediate, the prominence of which depends on heating rate [18]. Yet, (002) intensity alone cannot reveal whether the graphene sheets themselves preserve or lose sixfold symmetry, because it is insensitive to the in-plane lattice. The logical next step is to examine the (100) family to follow the fate of the hexagonal lattice while the interlayer registry collapses and reforms.

Atomic-scale studies provide the mechanism that links these observations. Experiments and simulations show that reduction removes oxygen groups in stages and leaves behind vacancies, Stone–Wales rotations and other non-hexagonal rings that distort local geometry. Graphitic motifs can nucleate before complete deoxygenation, but defect fields and corrugation persist and generate in-plane strain [6,7,14,19,20]. These fields frustrate extended Bernal registry: gradual relaxation favors AB pairs and short-range ABA, whereas rapid high-temperature reduction creates additional defects that bias AB but suppress longer sequences.

Despite this progress, in-situ diffraction has largely privileged the [00*] axis, leaving the evolution of the in-plane hexagonal lattice comparatively underexplored. A recent in-plane synchrotron XRD study up to ~700 °C began filling this gap, reporting lattice contraction and defect-mediated reorganization during GO reduction [21]. What is still lacking is a process-structure map that connects ramp rate and isothermal holds with the distribution of BSC components (A/AB/ABA) and with in-plane strain. These very levers matter for through-film transport and reproducible performance.

The broader context of amorphous two-dimensional carbon strengthens the motivation. Free-standing monolayer amorphous carbon has been realized, which proves that a one-atom-thick random network is attainable and mechanically robust [22,23]. Ultrathin amorphous carbon dielectrics at wafer scale show high breakdown strength and low leakage, underscoring device relevance [24]. Theory and microscopy chart pathways from point defects in graphene to two-dimensional amorphous carbon and discuss the metastability of such networks [25–27]. GO reduction is therefore a natural top-down route to approach two-dimensional amorphous carbon. Ultrafast or pulsed heating can drive GO into highly disordered, amorphous-like configurations that only partially re-order during dwell, which suggests kinetic recipes to trap such states before AB registry develops [28].

Here, we combine in-situ XRD on GO powders and films, explicitly tracking both the in-plane (100) and out-of-plane (002) channels. The analysis reveals a kinetic map: fast thermal ramps drive a transient amorphous-like state and yield a turbostratic matrix with AB pairs; slower ramps up to 240 °C allow AB together with short-range ABA; a contraction of $d_{100}$ persists to 900 °C, consistent with defect-induced strain reported at the atomic scale. Expressed in the BSCs framework, these outcomes provide a structural basis for interpreting interlayer coupling and transport in rGO stacks.

Because GO is non-universal, processing is more faithfully defined in

kinetic terms than by final temperature. By selecting ramp rate and dwell, rGO can be steered into distinct structural basins, from AB-enriched defective stacks to more extended ABA correlations, or even towards amorphous-like states. This process-structure map rationalizes batch-to-batch variability and outlines a kinetic pathway to two-dimensional amorphous-carbon-like films.

## 2. Experimental

### 2.1. Materials and sample preparation

Commercial GO powder (Layer One, Abalonix lot) was used as received. Powders and films were prepared from the same batch to ensure consistency. Thin films (~100 nm) were fabricated by spray coating GO dispersions onto Si wafers with thermally grown SiO$_2$. After deposition the films were gently dried before thermal treatments described below.

### 2.2. In-situ PXRD

Synchrotron powder X-ray diffraction (PXRD) was carried out at ELETTRA (MCX beamline [29]) in transmission using glass capillaries under $N_2$ flow. Heating was provided by a hot-air blower with programmable profiles up to 900 °C. Data were collected at 10 keV and 15 keV beam energies, corresponding to wavelengths $\lambda \approx 1.240$ Å and $\lambda \approx 0.827$ Å, by a point detector. Two classes of thermal histories were used: (i) fast ramps at $\beta \sim 8-9$ °C/min to 240 °C and to 900 °C, and (ii) slow ramps to 240 °C at 0.38, 0.50, or 0.70 °C/min run with interleaved stabilization rests at preselected temperatures 10, 3 and 1 min respectively, each followed by an isothermal hold. Frames were normalized by acquisition time and monitor counts, background-subtracted, and aligned on a common q-grid.

### 2.3. In-plane and out-of-plane XRD on films

Film measurements were performed on a Rigaku SmartLab diffractometer equipped with a rotating-anode Cu source. Samples were mounted in a home-built cell with a heated stage under $N_2$ flow. Two geometries were used: (i) in-situ out-of-plane (specular $\theta-2\theta$) scans acquired during stepwise annealing, and (ii) ex-situ in-plane scans collected at room temperature after each anneal at an incidence angle of 0.19°. The annealing series spanned 110–210 °C in 10 °C increments; the heating ramp was $\beta \sim 7$ °C/min. At each step the sample was heated to the target temperature, held for ~1 h under $N_2$ and monitored by out-of-plane XRD, then cooled to room temperature for the in-plane measurement. Before every in-plane scan the optics were switched to the in-plane configuration and the sample was re-aligned; after the scan the optics were returned to the out-of-plane configuration, the sample was re-aligned, and the next temperature step was executed. Alignment was verified before each acquisition.

### 2.4. Data processing and fitting

PXRD raw data measured in $\theta$ are converted into q space according to the known wavelength. For each scan, the baseline is evaluated through the erPLS algorithm [30], with the smoothing parameter in the range 8–15 $\cdot 10^3$. Focusing on the (100) family of planes, we determine from the corrected scans the corresponding peak height and area, taking for the signal uncertainty the standard deviation of the residual between the measured profile and a smoothed curve. In parallel, we perform non-linear least-square minimization to fit a superposition of the characteristic peak functions of the three Bernal stacked configurations. We model the domains as having a common value for graphene domain $L_a$ and the lattice parameter $a$. In practice, for each pattern we refine a single effective in-plane lattice parameter $a$ and a single lateral coherence length domain $L_b$, and we use these common values for all A, AB
and ABA components in the BSC decomposition. The out-of-plane lattice parameter *c* and the ABA coherence length *L*<sub>c</sub> are constrained independently from the (002) reflection, with *L*<sub>c</sub> restricted to short stacks (≤ 2 nm, i.e., ≤ 5–6 layers) to reflect the limited Bernal registry expected after fast ramps and to prevent overfitting of weak asymmetries. The scans of a given experiment are processed in sequence, injecting the fitted parameters of the preceding measurement as a starting point for the following; further details of the procedure are provided in the Supporting Information. We emphasize that the BSC line shapes were originally developed for graphitic carbons with higher crystallinity than GO. In the present work they are used as a phenomenological basis to describe the contribution of graphenic nanodomains to the (100)/(101) region in GO/rGO. The extracted A/AB/ABA fractions should therefore be interpreted as relative contributions of different local stacking motifs within the graphenic fraction, rather than as absolute phase fractions of the entire GO matrix, which also contains highly oxidized and amorphous regions.

## 2.5. Raman spectroscopy

Raman measurements were performed ex situ at room temperature on GO and rGO films prepared under selected thermal protocols. Spray coated films on Si/SiO₂ were annealed using the same slow ramp applied in the in-situ XRD experiments and were measured after cooling from four representative temperatures (140, 180, 240, and 900 °C). Spin coated films were instead subjected to a fast ramp to 900 °C, quenched to room temperature, and, in selected cases, further annealed at intermediate temperatures prior to Raman analysis. For each condition, spectra were collected at multiple positions and averaged to obtain a representative response.

Raman spectra of spin coated films were acquired using a Renishaw InVia spectrometer, whereas spray coated film by LabRAM Soleil Horiba Raman microspectrometer (laser wavelength λ = 532 nm, laser power below 5.7 mW on the sample (which we confirmed to be sufficiently low to avoid damage in the sample by the laser), spectral resolution ≈ 1 cm⁻¹, using an integration time of 1 s and accumulating 2 scans per spectrum.). The D (~1350 cm⁻¹), G (~1580 cm⁻¹) and 2D (~2700 cm⁻¹) bands were fitted using Lorentzian or pseudo-Voigt line shapes. Defect density and defect type were extracted through quantitative analysis of peak areas following the correlation method of Eckmann et al. [31] As these measurements are performed ex situ after cooling, they reflect the final microstructures produced by each thermal protocol rather than the transient kinetic states captured in situ by XRD at high temperature.

## 2.6. AFM measurements

Atomic Force Microscopy (AFM) and Kelvin Probe Force Microscopy (KPFM) were performed in air using a Multimode 8 microscope (Bruker) equipped with probe cantilevers model RTESPA-300 (material: 0.01–0.025 Ωcm Sb (n) -doped Si, f₀: 300 kHz, k: 40 N/m, from Bruker) working in the tapping mode. AFM topography was acquired in tapping mode on isolated GO and rGO flakes drop-cast onto Si/SiO₂ substrates and dried in ambient conditions. Typical scan areas ranged from 5 to 2500 µm², allowing the analysis of both individual flakes and small aggregates. KPFM measurements were carried out on the same areas by rescanning the previously acquired AFM topographic line using amplitude-modulation (AM) mode in lift mode, with a lift height of 20 nm. This ensured a direct correlation between local surface potential contrast and nanoscale morphological features. Raw AFM and KPFM datasets were processed using histogram-flattening procedures [32] to remove piezo-scanner artefacts and background curvature without altering the intrinsic flake morphology. Height profiles extracted across isolated flakes were used to estimate the apparent thickness before and after thermal reduction. Because AFM-derived thickness values may be influenced by tip-sample convolution, surface adsorbates and intrinsic

flake corrugation, they are interpreted qualitatively and not as direct quantitative estimates of interlayer spacing.

# 3. Results and discussion

## 3.1. *High-rate thermal history reveals an amorphous window*

Fig. 1a reports the in situ PXRD experiments performed on GO powders at **high heating rates** (β ~8–9 °C/min) under inert gas with sequential ramps to 240 °C and 900 °C, each followed by an isothermal hold at the target temperature. The horizontal axis is q scattering vector, whereas, horizontal features correspond to the evolution of diffraction peaks with temperature and time.

After the rapid ramp to 240 °C, the out-of-plane (002) reflection showed a significant reduction in intensity or near disappearance, consistent with the collapse of the interlayer spacing and rapid desorption of water and labile oxygen-containing groups. Due to the experimental setup (capillary scattering effects), the exact position of the (002) peak was difficult to quantify during the ramp; however, an approximate spacing of 3.9 Å was observed ($q_{002}(240\,^\circ\text{C}) = 1.6\,^\circ\text{A}^{-1}$) during isothermal annealing at 240 °C, indicative of partial deoxygenation and interlayer contraction (Fig. S3).

At the same time, the in-plane (100) peak, although strongly attenuated immediately after the rapid heating, remained detectable as a weak bump (see Fig. 1b). This confirms that short-range hexagonal order survives the thermal shock. Importantly, the (100) position shifted to higher *q* (lower *d*), evidencing an in-plane lattice contraction that persisted during the isothermal hold ($q_{100}(\text{RT}) = 2.95\,^\circ\text{A}^{-1}$, $q_{100}(240\,^\circ\text{C}) = 3\,^\circ\text{A}^{-1}$, strain $\Delta d_{100}/d_{100} = 1.9\%$). The same behavior was observed for the other in-plane (2-10) peak (Fig. 1c). During the 240 °C hold, both (002) and (100) regained intensity with time, pointing out recrystallization out-of-plane and partial restoration of in-plane order. The (100) line-shape evolved from a single broadened bump to a profile with a weak asymmetry/shoulder consistent with the onset of (101) intensity. In the framework of BSCs, this evolution is naturally interpreted as the nucleation of local AB-paired bilayers with short ABA segments within a turbostratic matrix [16].

A second rapid ramp to 900 °C produced a further contraction of the interlayer spacing to $d_{002} \approx 3.48\,^\circ\text{A}$ ($q_{002}(900\,^\circ\text{C}) = 1.8\,^\circ\text{A}^{-1}$), close to the graphite value. During the 900 °C hold, the (002) intensity rose steadily, indicating progressive restacking. The (100) reflection also strengthened, confirming partial healing of the in-plane lattice. Its shape, however, remained more consistent with AB-pair-dominated stacking than with extended ABA correlations, suggesting that defect formation and out-of-plane corrugation at high temperature limit the coherence required for long Bernal sequences [7,18].

## 3.2. Quantification by BSC: fast-ramp outcomes at 240 °C and 900 °C

The PXRD intensity around (100)/(101) reflection was fitted with the **BSCs** basis. Bounds, initialization, and the diffraction profiles superimposed with the fit are given in the Supporting Information (Fig. S1 and S2), following the procedure of Puech and co-workers [16].

A preliminary remark is essential. Immediately after each fast ramp, both at 240 °C and at 900 °C, the in-plane (100) intensity is very low. This is the transient amorphous-like state identified in Section 3.1. In this regime the BSC decomposition trivially returns an A-dominated pattern, because the lineshape is featureless and the signal-to-noise is poor. That outcome is expected and should not be over-interpreted structurally. For this reason, the quantitative discussion below refers to the isothermal recovery phase, once the (100) signal has re-emerged above a reliability threshold.

As detailed in the Supporting Information (Section 1), the BSC fits are performed sequentially in time with constraints on the allowed frame-to-frame variation of the phase fractions and are only retained for quantitative analysis when the coefficient of determination exceeds R²
<figure><img src="image_3.png" /><figcaption>Fig. 1. a) In-situ 2D intensity map of PXRD scans collected for GO powder before, after a fast ramp to 240°C (β = 8 °C/min), during 180 min of isothermal holding, after a second rapid ramp to 900°C (β = 9 °C/min), after 240 min of isothermal annealing, and after cooling to room temperature. Dashed lines mark the peak positions of (002)RT, (002)900, (100)RT, (100)900, (2-10)RT, (2-10)900. Zoom of PXRD scans collected for GO powder around b) (100) and c) (2-10) during the 240 °C hold showing recovery, slight right-shift, and a weak (101) shoulder.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 2. BSC fractions extracted from (100)/(101) fits under fast-ramp histories. (a) 240 °C hold after an 8 °C/min ramp. (b) 900 °C hold after a 9.4 °C/min ramp.</figcaption></figure>
≥ 0.9. For scans with very low signal-to-noise ratio, the fit is still used to initialize the following frame but the instantaneous A/AB/ABA values are not assigned physical meaning. In other words, the absolute fractions near the amorphous-like window should be regarded as semi-quantitative, whereas the kinetic trends discussed below are extracted from scans with well-defined (100) profiles and robust fits.

During the 240°C hold, the structure remains **A-dominated** while AB and ABA emerge as **minor components** that increase slowly with time, each reaching ~18 percent by the end of the 180 min dwell (Fig. 2a). At the same time, the (100) profile evolves from a single broadened maximum toward a weak high-q asymmetry that the AB and ABA bases capture as the onset of (101) intensity. The fits require few-nanometer lateral domains, consistent with the large (100) width. The simultaneous shift of (100) to higher q (smaller $d_{100}$, Section 3.1) points to persistent in-plane strain, which coexists with the small domain size.

After the second fast ramp to 900 °C, the BSC fractions remain essentially constant during the 240 min hold, with no variation beyond the uncertainty for any component (Fig. 2b). The turbostratic contribution continues to dominate the (100)/(101) region, accounting for ≈60–80 % of the total intensity throughout the anneal.

Raman spectroscopy performed ex situ on representative thermal states (Fig. S11) confirms the strong increase in defect-related D-band intensity in samples that traverse the amorphous-like regime. In particular, rGO obtained after fast ramps and quenched from high temperature exhibits a broadened D band and higher $A_D/A_G$ ratios, consistent with the severe in-plane disorder and turbostratic character captured by in-situ XRD during the intensity collapse.

### 3.3. Isothermal kinetics of the (100) peak

Isothermal holds after fast ramps were analysed through the normalized (100) peak height, $H/H_0$, where $H_0$ is the value at the start of the hold (values are plotted in Fig. 3).

The data are well described by logarithmic law, $H/H_0 = 1 + C\ln[(t+t_0)/t_0]$ with $t_0 = 1$ min. In this normalization by construction the kinetic content resides in the slope C. At 240 °C the fit yields $C = 2.63 \pm 0.08$, which corresponds to a per-decade gain $C \ln 10 = 6.06 \pm 0.18$ in the chosen units. At 900 °C the recovery follows the same form with a smaller coefficient, $C = 0.61 \pm 0.04$, that translates into $C \ln 10 = 1.40 \pm 0.09$, per time decade. The reduction of C indicates slower growth of diffracting in-plane domains per logarithmic time unit after

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Normalized height $H/H_0$ vs time. Dotted lines indicate the fitting curve for thermal annealing at 240°C ($\beta = 8$ °C/min) and at 900°C ($\beta = 9.4$ °C/min). Estimated errors are within marker size.</figcaption></figure>

the fast excursion to high temperature.

A logarithmic time dependence is indicative of a **broad distribution of activation barriers and pinning energies**, such that successive decades in time contribute comparably to re-ordering, a hallmark of glassy relaxations in disordered solids [33,34]. Two non-exclusive mechanisms can account for this behaviour in rGO. First, a diffusion-limited coarsening scenario: at early times defects are numerous and mobile, enabling rapid reorganization and a steep initial rise of $H/H_0$; as these defects are consumed or coalesce, further growth requires increasingly collective moves and the rate diminishes, approaching a logarithmic law. Second, heterogeneous kinetics: spatial variations in local environment (oxygen content, thickness, pre-strain, curvature) produce a wide spectrum of local relaxation times; the superposition of many exponentials with broadly distributed time constants yields an apparent logarithmic trend at the ensemble level [35].

The smaller coefficient at 900 °C has a clear physical origin: the fast jump to high temperature removes most oxygen but simultaneously generates vacancies and Stone–Wales–type rotations that corrugate the lattice and strengthen pinning fields; healing these defects requires carbon mass transport and local flattening, which are slow under $N_2$. As a result, the dwell at 900 °C samples the slow tail of the relaxation and the logarithmic slope is reduced, consistent with atomic-scale observations and simulations of persistent defect networks at high temperature [7,19,20].

Consistent with this picture, the integrated (100) area increases noticeably during the 240 °C holds while the peak height changes more modestly, which points to coarsening of AB-correlated regions at approximately fixed maximum intensity; at 900 °C the growth is weaker per time decade, in line with stronger pinning. These kinetic trends are coherent with the BSC analysis reported for powders: below 240 °C AB appears with short-range ABA as ordering progresses, whereas after a fast ramp to 900 °C the structure relaxes into a turbostratic-dominant matrix (≈60 %), and within the ordered fraction AB exceeds ABA, but extended Bernal coherence remains limited.

### 3.4. Slower ramps resolve the sub-240 °C transition

Slow heating ($\beta = 0.38–0.70$ °C/min) resolves the structural transition below 240 °C into three reproducible regimes, which are already visible in the evolution of the raw (100) peak height and area without invoking any specific line-shape model. Fig. 4a and b shows the raw (100) profiles collected during two representative slow ramps, $\beta = 0.38$ and $\beta = 0.50$ °C/min (all profiles are reported in Fig. S4); Fig. 4c and d report, for the same runs, the normalized integrated area $Area/Area_{RT}$ and the normalized height $Height/Height_{RT}$ as a function of temperature. A third series at $\beta = 0.70$ °C/min exhibits the same phenomenology and is provided in the Supporting Information (Fig. S5).

In Regime I (from RT to ≈140 °C) area and height evolve gradually, whereas Bragg peak profiles, reported in Fig. 4a and b, show a small right-shift of (100) maximum consistent with a slight in-plane lattice contraction; the quantitative $d_{100}(T)$ trends are reported in SI, Fig. S6a and are consistent with the expected early-stage structural adjustments in GO/rGO systems [7,36]. In Regime II (≈140–190 °C) the height collapses by a factor ≈3–4 while the area displays a pronounced minimum; the temperature of this minimum shifts with $\beta$, evidencing kinetic control. This identifies a transient disordered stage during reduction, in agreement with the in-situ out-of-plane XRD observations that GO passes through a disordered intermediate before restacking [18]. In Regime III (≈190–240 °C) the height remains nearly constant while the area increases, indicating a line-shape change rather than a simple intensity gain. The evolution, including a weak (101) shoulder when visible, is naturally attributed to the onset of an AB-paired bilayer contribution superposed on a broadened turbostratic background, consistent with the BSC interpretation of the (100) region [16,36]. This interpretation is corroborated by the BSC decomposition (Fig. 5a–c), which translates the observed changes in the (100)/(101) line shape into
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** (a,b) In-plane (100) diffraction profiles during heating to 240 °C at β = 0.38 °C/min (10 min rests) and β = 0.50 °C/min (3 min rests) under N₂. Curves are colored by temperature, for each β the last 4 curves belong to the annealing stage at 240 °C. Fitting curves are reported in dark. (c,d) Area/Area<sub>RT</sub> and Height/Height<sub>RT</sub> of the (100) peak versus temperature (integration window q ≈ 2.8–3.3 Å<sup>-1</sup>). Vertical bands mark Regime I (RT-140 °C), Regime II (140–190 °C), and Regime III (190–240 °C).</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** BSC fractions extracted from (100) fits under slow-ramp histories. (a–b) β = 0.38 °C/min with 10min rests; (c–d) β = 0.50 °C/min with 3min rests. Evolution during the (a–c) ramp and the (b–d) annealing at T = 240 °C are shown.</figcaption></figure>

variations of A, AB and short-range ABA stacking under the constraints described in Section 2.4. In other words, the three kinetic regimes are revealed already from model-independent (100) peak metrics, and the BSC analysis is used only to express these regimes in terms of stacking motifs within the graphenic fraction. In Regime II (≈160 °C) additional components become discernible and the A fraction decreases from 100 % to ≈85 %. At β = 0.38 °C/min the first emerging signal corresponds to the ABA stack, which grows to ≈10 %, whereas at β = 0.50 °C/min the

AB pair dominates, reaching ≈20 %. In Regime III the trend continues, with A progressively supplanted by AB, leading to final fractions of ≈45 % A, ≈35 % AB, and the remainder ABA. The β = 0.70 °C/min dataset follows the same trend (Fig. S5d).

Consistently with the gradual reorganization observed in XRD, Raman spectra of films processed using slow ramps display a reduction of A<sub>D</sub>/A<sub>G</sub> and narrower D/G bands compared to the amorphous counterpart (Fig. S12). These trends corroborate the formation of larger sp²
domains and partial registry during the slow recovery stage.

### 3.5. Kinetic selection at 240 °C: AB-pair-dominated re-ordering with short-range ABA

At 240 °C, the BSC decomposition shows that the subsequent annealing dynamics depend on the heating rate (Fig. 5b–d).

For $\beta = 0.38$ °C/min, the A fraction converts rapidly into AB during the hold: AB rises from ≈35 % to ≈70 % within 270 min, while ABA remains approximately constant at ≈12 %. By contrast, for $\beta = 0.50$ °C/min the early stage of the anneal shows no change larger than the uncertainty and the overall conversion is slower, with AB increasing from ≈35 % to ≈58 % over 240 min. Thus, slower ramps allow structural relaxation during the ascent and drive a faster, time-dependent growth of AB during isothermal annealing, whereas faster ramps carry the sample through the 140–190 °C disordered stage with limited structural relaxation and only partial AB development. Throughout the slow-ramp series, the (100) maximum remains shifted to higher q relative to pristine graphene, evidencing a persistent in-plane lattice contraction. This behaviour is consistent with defect-induced strain and mild corrugation in reduced GO, as observed by atomic-resolution studies reporting 5–7 ring clusters and related distortions [7]. Considering together the Regime III line-shape change (area increase at nearly constant height), the onset of (101) intensity, and the annealing evolution of the BSC fractions, the data indicate that AB-paired bilayers are the dominant low-temperature re-ordering pathway, whereas extended Bernal sequences remain limited.

### 3.6. Films: out-of-plane collapse, persistent in-plane strain, and local stacking

GO films on Si/SiO$_2$ were measured in out-of-plane and grazing-incidence in-plane geometries. The strong preferred orientation (basal planes parallel to the substrate) means that in the in-plane configuration only the (100) family is sampled, so BSC deconvolution is not applicable. The thermal protocol for films uses fast ramps (≈7 °C/min) followed by long rests (up to ~1 h).

Out-of-plane XRD scans of the (002) reflection show a stepwise interlayer contraction under N$_2$ (details in Supporting Information). An initial decrease from $d_{002}$ ≈ 8.27 Å to 7.41 Å is attributed to water desorption, followed by further contraction to ≈6.69 Å as reduction proceeds. Subsequent steps between ~120 and 210 °C yield additional gradual tightening; upon rehydration the spacing recovers only partially, indicating permanent removal of oxygen functionalities and partial stacking.

From in-plane scans (Fig. 6a), the (100) position has been extracted and reporting a shift to higher q along the series, giving a monotonic decrease of $d_{100}(T)$ (Fig. 6b) and a persistent negative in-plane strain after cooling. This confirms that the graphene network contracts in films as it does in powders, despite the different pristine microstructure and texture. The absence of an in-plane “collapse” or amorphous signature in the film data is attributed to kinetics and measurement timing: because fast ramps are followed by long rests and the in-plane patterns are collected after cooling, the transient amorphous stage prominent in continuous fast-ramp powders is bypassed, consistent with a kinetically

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** (a) In-plane GIXRD scans recorded on GO film after annealing at different temperatures, identified by color; d100 (b), width (c) and Area normalized by the initial value (d) extracted from 100 reflection vs temperature. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>
selected amorphization regime.

Peak-width estimates from laboratory GIXRD (Fig. 6c) carry large uncertainties in this GI geometry, dominated by the low counting statistics. The error on the (100) FWHM is comparable to, or larger than, the apparent variations across the series. For this reason, no quantitative FWHM trend is reported and the width is not used to extract microstrain or La values [21]. Conversely, the integrated (100) area, evaluated within a fixed q-window and reported with its uncertainty, exhibits a non-monotonic evolution with temperature: an initial decrease consistent with disordering and peak broadening, followed by recovery during the long dwell periods, which indicates partial re-ordering at fixed temperature. Overall, the film measurements (i) corroborate a persistent in-plane contraction during reduction, (ii) show that coupling fast ramps with long rests suppresses the appearance of the amorphous window in ex-situ in-plane scans, and (iii) remain consistent, despite the lack of BSC analysis, with the AB-biased re-ordering inferred from the powder experiments.

### 3.7. Discussion: kinetic control of defects, stacking, and amorphization

Results obtained from powders and films show that the structural pathway of GO during thermal reduction is selected by kinetics rather than by the final temperature. In continuous high-rate ramps the powder passes through a transient amorphous-like window between ~140 and 190 °C, captured in-situ by the collapse of the (100) height and the minimum in area. In slow ramps below 240 °C the same interval resolves into a rate-dependent sequence: mild evolution (Regime I), disordering (Regime II), and recovery with the onset of an AB-pair contribution (Regime III). BSC fits at 240 °C quantify the rate selection: gentle ramps yield higher AB and short-range ABA, whereas faster ramps leave a more turbostratic state at the same temperature. After a fast ramp to 900 °C, the structure is turbostratic-dominant, with a minor AB component larger than ABA and limited Bernal coherence.

This rate dependence is consistent with the defect landscape expected along the reduction pathway. In-situ TEM/EELS shows that oxygen loss proceeds in stages (physisorbed water <100 °C; carboxyls ~150–200 °C; epoxides >200 °C) and that graphitic islands can nucleate before complete deoxygenation; defects persist well into the high-temperature regime [20]. Atomistic simulations predict that removal of epoxides and hydroxyls creates vacancies, holes, and Stone–Wales rotations that do not heal without extensive carbon mobility [19]. Mild anneals favor progressive restoration of sp² networks [6]. Our observations map onto this picture. Under slow ramps up to 240 °C, partial deoxygenation and reduced corrugation allow local planarity, therefore, AB nucleates and short-range ABA develops. After a fast ramp to 900 °C, the structure remains turbostratic-dominant (≈60 % by BSC); during the dwell the ordered fraction increases only modestly, with AB exceeding ABA, but Bernal coherence and lateral correlation lengths stay limited. The vacancy-rich, corrugated sheets bias bilayer-like registry (AB pairs) while frustrating the extended periodicity required for ABA, consistent with the pinning-limited, heterogeneous kinetics quantified in section 3.3.

Films reinforce the kinetic interpretation. Although their ramps are fast, the long rests (up to ~1 h) allow re-ordering before in-plane scans are recorded ex-situ at room temperature. As a result, the in-plane signal never collapses, yet the (100) right-shift reveals the same persistent lattice contraction seen in powders, in line with strain-based analyses of GIXRD in GO/rGO films [21]. The large and uncertain FWHM in GI geometry prevents a quantitative microstrain trend, but the integrated area still reports disordering followed by re-ordering during the stepwise protocol. The contrast between powders (continuous ramps, measured in-situ) and films (fast ramps plus long dwell, measured ex-situ) shows that amorphization is a kinetic state that appears along fast paths and is suppressed when time is provided for relaxation.

These structural fingerprints are strongly correlated to transport properties. Reduced GO generally conducts via variable-range hopping

across a heterogeneous sp² network, where interlayer pathways are strengthened by AB pairing and weakened by turbostratic misalignment and corrugation. States prepared by slow ramps at 240 °C, which contain AB plus short-range ABA, should display lower interlayer resistance locally than fast-ramp products that remain more turbostratic, while fast to 900 °C yields AB-biased but still defect-rich states. This picture is consistent with device data on rGO films: multilayer stacked low-temperature-reduced GO used as electrodes in polymer memory devices reaches sheet resistances of about 160–500 Ω/sq and a conductivity of ≈26 S/cm once a continuous, partially ordered graphitic network is established, whereas poorly reduced GO remains several orders of magnitude more resistive [37,38] Recent multiscale studies on multilayer rGO networks further show a crossover from variable-range hopping to more metallic transport as graphitic order and effective interlayer overlap increase upon optimized reduction, in line with the trends implied by our process-structure map [8].

Because GO is non-universal, a process-structure map is therefore more predictive than final-temperature recipes: choosing ramp rate and dwell steers rGO between AB-enriched small-domain states and AB plus short-range ABA at 240 °C, and it also enables deliberately trapping amorphous-like states by minimizing dwell and quenching through the disordered window.

The emergence at 240 °C of AB pairing with short-range ABA provides a structurally grounded rationale for employing thermally reduced GO in electronic and sensing functions that benefit from moderate baseline conductivity and defect-assisted sensitivity. This microstructure enhances interlayer pathways relative to fully turbostratic rGO, yet it preserves a density of sites and microstrain that enable large signal modulations. Nevertheless, the short coherence length and persistent disorder argue against its use in high-mobility graphene electronics without additional chemical or thermal healing. Thus, 240 °C reduction is justified for sensing-oriented and low-thermal-budget electronics [39], whereas performance-driven graphene devices will require further ordering beyond the short-range ABA observed here.

The complementary AFM/KPFM measurements (Fig. S13 and Table S1) show that the nanosheet morphology (thickness and roughness) remains essentially unchanged between ordered rGO and the amorphous-turbostratic counterpart, indicating that the strong modifications observed by XRD are not associated with macroscopic deformation or flake collapse. However, KPFM reveals a ≈70 mV shift in surface potential for the amorphous sample, consistent with a higher density of electrically active defects. These findings support the picture of a structurally distinct graphenic network produced by fast ramps, in which local disorder persists even after high-temperature processing.

These results also suggest a practical route to deliberately stabilize amorphous graphenic states by kinetic trapping: use fast ramps, minimal dwell, and quench, verifying in situ the temporary collapse of the (100) intensity and suppressing subsequent recovery. This path-dependent control is a top-down complement to bottom-up amorphous 2D-carbon syntheses and can be tuned for applications that benefit from high defect density and surface reactivity, whereas slower protocols recover AB with short-range ABA when crystallinity is desired.

### 4. Conclusions

This work establishes a process-structure map for GO thermal reduction that highlights the primacy of kinetics over final temperature. Continuous fast ramps drive powders through a transient amorphous-like window (≈140–190 °C), during which in-plane order nearly vanishes before partially recovering under isothermal holds. Below about 240 °C, slow ramps allow AB-paired bilayers with short-range ABA to emerge, whereas a fast excursion to 900 °C leaves a turbostratidominant matrix; during the dwell the ordered fraction grows only modestly, with AB exceeding ABA, and Bernal coherence remains short. Across all protocols, the (100) reflection is shifted to higher q$_{‖}$, evidencing a persistent in-plane contraction consistent with defect-
induced strain. Film measurements corroborate this contraction while showing that long rests suppress the amorphous signature, underlining the kinetic nature of amorphization. Within the Basic Structural Components framework, the AB-pair state emerges as a genuine structural basin of reduced GO. These findings have practical consequences. Interlayer coupling in rGO stacks follows the realized registry, so AB with short-range ABA at moderate temperature should lower local interlayer resistance relative to fully turbostratic states while preserving defect-assisted pathways useful for sensing, filtration and electrochemistry. This structural differentiation is consistent with charge-transport models for rGO networks, in which the effective localization length and the sheet-to-sheet conduction path are governed by the overlap and continuity of sp² domains rather than by the nominal layer number [10]. Conversely, minimizing dwell and quenching through the disordered window provides a top-down route to stabilize amorphous-like two-dimensional carbons with potential as ultrathin dielectrics or highly reactive membranes.

Complementary Raman and AFM/KPFM measurements support this structural picture. Raman spectra of samples subjected to fast ramps display broadened D/G bands and higher A<sub>D</sub>/A<sub>G</sub> ratios, consistent with the enhanced disorder inferred from the in-situ collapse of the (100) reflection. AFM shows that flake morphology remains comparable across thermal histories, whereas KPFM reveals a more negative surface potential (≈70 mV) for the amorphous-like counterpart, indicating a higher density of electrically active defects. These multimodal observations corroborate that fast thermal pathways yield graphitic networks that remain structurally and electronically distinct from the AB/ABA-enriched states accessed under slow ramps.

Next steps should be explicitly process-oriented. To trap amorphous-like states, adopt fast ramps (β > 8 °C/min), insert only brief stabilization rests, avoid isothermal holds, and quench; verify in situ the temporary collapse of the (100) and confirm ex situ that recovery is suppressed. Pulsed or Joule heating can compress the thermal budget further and should be benchmarked against continuous ramps. Atmosphere and thickness are likely levers: inert or vacuum environments and thin films will favor kinetic trapping, whereas reducing gases may promote repair and should be used when the goal is to extend ABA coherence at low temperature with slow ramps (≤0.5 °C/min) and dwell in the 200–240 °C range. By explicitly connecting kinetics, structure, and transport, this study lays the groundwork for reproducible GO processing and for the rational design of rGO states ranging from amorphous-like films to AB/ABA-enriched stacks, thereby bridging fundamental diffraction fingerprints to device-relevant performance.

### CRediT authorship contribution statement

**Nicolò Galvani:** Writing – review & editing, Visualization, Software, Methodology, Formal analysis, Data curation. **Jasper R. Plaisier:** Writing – review & editing, Resources, Methodology, Investigation. **Cosimo Anichini:** Methodology, Investigation. **Alicia Moya:** Investigation, Formal analysis, Data curation. **Paolo Samori:** Writing – review & editing, Supervision, Resources, Funding acquisition. **Andrea Liscio:** Writing – review & editing, Visualization, Supervision, Formal analysis. **Fabiola Liscio:** Writing – original draft, Visualization, Supervision, Resources, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

### Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Fabiola Liscio reports financial support was provided by European Commission. Fabiola Liscio reports financial support was provided by Ministry of University and Research (MUR). Paolo Samori reports financial support was provided by European Commission. Andrea Liscio reports financial support was provided by European Commission. Alicia

Moya reports financial support was provided by European Research Council. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

The authors acknowledge financial support from the European Commission through the Graphene Flagship Core 3 project (Grant Agreement No. 881603). P.S. acknowledges financial support from the European Commission through the HORIZON-CL4-2023-DIGITAL-EMERGING-01-Cnect project “2D-PRINTABLE” (Grant Agreement No. 101135196), the Agence Nationale de la Recherche via the Interdisciplinary Thematic Institute SysChem through IdEx Unistra (ANR-10-IDEX-0002) within the Investissement d'Avenir program, the Foundation Jean-Marie Lehn, and the Institut Universitaire de France (IUF). A.L. acknowledges support by Project ECS 0000024 Rome Technopole, NRP Mission 4 Component 2 Investment 1.5, Funded by the European Union – NextGenerationEU and the Italian Ministry for Research (MUR) through CNR – Short Term Mobility program. F.L. acknowledges support from iENTRANCE@ENL (Infrastructure for Energy TRAnsit iond Circular Economy @ EuroNanoLab; code IR0000027; CUP B33C22000710006). The Raman instrument, at ISTerre MicroAnalytical Plateforme (IMAP) in University Grenoble Alpes, was funded by the grants from: the European Research Council (ERC) under the European Union's Horizon H2020 research and innovation program (Synergy Grant MEET, grant agreement no.856555); Auvergne-Rhône-Alpes region (2020 AURA P3 - CPER 2015/2020) and CNRS-INSU.

### Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.carbon.2026.121247.

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