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# Charge transfer during sodium-ion intercalation in graphite-like anodes as determined by Raman spectroscopy

Pascal Puech, Damien Tristant, Shaorui Chen, Shae Wetzel, Yuxin Xiang, Tianzhao Hu, Lili Zhang, Marc Monthioux, Feng Li

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Pascal Puech, Damien Tristant, Shaorui Chen, Shae Wetzel, Yuxin Xiang, et al., Charge transfer during sodium-ion intercalation in graphite-like anodes as determined by Raman spectroscopy. Carbon Trends, 2025, 20, pp.100547. 10.1016/j.cartre.2025.100547. hal-05250928

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Submitted on 11 Sep 2025

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# Charge transfer during sodium-ion intercalation in graphite-like anodes as determined by Raman spectroscopy

Pascal Puech<sup>a,*</sup> <sup>●</sup>, Damien Tristant<sup>b</sup>, Shaorui Chen<sup>c</sup>, Shae Wetzel<sup>b</sup> <sup>●</sup>, Yuxin Xiang<sup>c</sup>, Tianzhao Hu<sup>c</sup>, Lili Zhang<sup>c</sup> <sup>●</sup>, Marc Monthoux<sup>a</sup> <sup>●</sup>, Feng Li<sup>c,d</sup> <sup>●</sup>

## ARTICLE INFO

Keywords:

Sodium

Batteries

Intercalation

Raman

Electron-phonon coupling

## ABSTRACT

Sodium intercalation in graphite is known to be unstable, posing a challenge for energy storage applications based on this cation. This study combines Raman spectroscopy with first-principles calculations, including electron-phonon coupling, to investigate charge transfer mechanisms and stability in Na-intercalated graphite. Contrary to theoretical predictions on a pure Na graphite intercalated compound, Raman data show no evidence of so-called mechanical coupling between Na⁺ ions and graphene layers. As we have selected a partially graphitized carbon with an intense 2D band for the anode, analyzing the Raman shifts of both the G and 2D bands is possible and allows us to discriminate between doping and lattice expansion treated as strain effects. The observed shifts are fully explained by a simple charge-transfer mechanism to each graphene layer. At stage one intercalation, a charge transfer value of -0.17±0.02 |e| per carbon atom is determined. These findings highlight the ability of Raman spectroscopy to quantify charge transfer and differentiate intercalation behaviors between the various alkali metals.

## 1. Introduction

The growing need for energy storage is a major area of research around the world. Sodium (Na) could be a cheap alternative to lithium (Li), the primary alkali metal currently used as the intercalate in graphite intercalated compounds (GIC). The natural abundance ranking of Na is 6, to be compared to 33 for Li, justifying the large and current interest in Na-based batteries [1]. From an electrochemical point of view, the cell performance is governed by the characteristics of the materials making the cathode and the anode on the one hand, and of the electrolyte which should match with the electrochemical windows on the other hand, and all should be adapted in function of the cation. The research on Na-ion batteries is active in both academic institutions and industry [2]. The intercalation chemistry of Na and Li are supposed to be similar, allowing to use of carbon compounds in both cases and to compare them, however with a notorious exception: Na intercalation into graphite is unstable [3], in the sense that intercalation energy is less favorable than in the case of Li or K, making intercalation very difficult and the intercalation rate lower. The cationic radii of Li⁺, Na⁺, and K⁺

are 0.74, 1.02, and 1.33 Å, respectively. As sodium presents higher solubility and hydrophobicity, adapting the electrolyte is required. All the modifications regarding the electrodes and the electrolyte carried out for Na-ion batteries have a valuable advantage, which is to make them useable at low temperatures, which is a highly desirable property in high-latitude countries [4]. For Li, a graphite anode (large crystallite size and ABAetc. stacking) presents a good specific capacity of around 370 mAh·hg⁻¹ [5], while for Na, "hard carbon" (even powderized) presents promising results, presumably due to the suitable surface chemistry and pore size distribution [6]. For Na⁺ intercalation, small domain sizes combined with the presence of pores lead to high specific capacities, in the range of 250–550 mAh·hg⁻¹ [7], which is much higher than with genuine graphite, unless it is optimized by using nanosized flakes or functionalization, thereby allowing to reach ~100 mAh·g⁻¹ [8] and 250 mAh·g⁻¹ [9], respectively. Such a statement, which is specific to Na⁺ with respect to Li⁺ and K⁺, is not fully understood yet. Therefore, it is worth studying further the intercalation of Na⁺ in graphitized carbon materials. The improvement of batteries using Na, both in terms of specific capacity and the reduction of losses during charge-discharge

<footnote><sup>a</sup> CEMES, UPR-8011 CNRS, Université de Toulouse, 29 rue Jeanne Marvig, 31055 Toulouse Cedex 4, France</footnote>

<footnote><sup>b</sup> Department of Physical Science, School of Science, Technology, Engineering, and Mathematics, Northwestern State University, Natchitoches, LA 71497, USA</footnote>

<footnote><sup>c</sup> Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang 110016, China</footnote>

<footnote><sup>d</sup> School of Materials Science and Engineering, University of Science and Technology of China, Shenyang 110016, China</footnote>

<footnote>* Corresponding author.
E-mail address: pascal.puech@cemes.fr (P. Puech).</footnote>
cycles, is thus a very active area of research. In this context, research including *in operando* observation is of great importance to understand in detail the mechanisms involved. The techniques used to monitor *in operando* the intercalation in carbon (or other anode materials such as silicon) are generally X-ray diffraction, transmission electron microscopy (TEM), nuclear magnetic resonance spectroscopy (NMR), and, to a lesser extent, Raman spectrometry [10–12]. The evolution of temperature during *in operando* measurements with electron microscopy allows for analyzing the coexistence of multiple intercalation stages in the carbon anode in greater detail. The color change is also a convenient indicator to monitor the degree of intercalation [13].

Raman spectrometry is a powerful, non-invasive optical method, but it is limited by the weak intensity of the signals. In the case of graphite, it is possible to obtain enough Raman signal to carry out precise analyses, although the related spectral decomposition is complex [14]. One reason is that the Raman signal is dependent on the experimental conditions. For example, for lithium intercalation in graphite, the G-band is sharp at high excitation laser power, while a Fano shape - which reveals a coupling with an electronic continuum (typical of GIC), and is as more visible as the linewidth of the coupled mode is larger - is observed at low laser power [15]. Even within a cell, both behaviors (i.e., G band exhibiting a narrow peak [16] or with a Fano shape [17,18]) have been reported for the graphite anode. Likewise in the case of K graphite intercalation compounds (K-GIC), for stage 1, the linewidth of the G band remains narrow and an upshift is reported during *in operando* observation of the graphite anode [19], or presents a Fano shape at low power excitation [20]. For Na intercalation, only dominant Lorentzian shapes for the G and 2D bands are reported [21,22]. On the other hand, for K-GIC obtained after exposure to K vapor, always a clear Fano shape is reported [23]. Plotting the Raman shifts of the G-band *versus* intercalation stages is used to follow the trends, but for high stages, the Raman shift is rarely decomposed into the shift due to lattice dilatation (equivalent to strain) and that due to doping [24]. When the electronic charge of the materials is changed, the optical phonon signatures, i.e., the shape and position of the G band, are modified, making it possible to extract electronic information. For the Fano shape associated with the G-band, changing the excitation wavelength makes it possible to determine the position of the Fermi level [23], and to deduce from it the partial charge associated with each carbon atom.

First-principles calculations have investigated the stability of the Na-GIC [25]. With the development of studies on graphene, the role of electron-phonon coupling in the G band characteristics has been taken into account and accurately analyzed [26,27]. Then, GICs were studied, in which a "mechanical coupling" with the intercalant (calculated considering adiabatic/harmonic approach) leads to a wavenumber downshift while an electron-phonon coupling (considering a nonadiabatic approach) leads to a wavenumber upshift, both relating well with the Raman spectral features [28]. Unfortunately, no similar study involving $Na^+$ as the intercalant was considered in the literature. For pristine graphene, i.e. graphene deposited on a substrate, and then combined with a dopant, the detailed understanding and tracking of the 2D band position, combined with the G band position, allowed the mechanical strain effect and the doping effect to be separated [29] through the use of the so-called Lee plot [30]. For intercalated graphene layers (as in graphite), due to the complexity of the coupling between the intercalant and the graphene layers, the analysis is usually limited to associating the Raman spectra with the electrical potential of the cell, and plotting the latter *versus* the wavenumber position [21].

In order to conduct a Raman analysis of Na-GIC, we selected a carbon material exhibiting an intense 2D band with a Lorenzian shape, allowing an easy determination of its shift with respect to its pristine position, which can be combined with the study of the G band (shape and position). Thanks to the use of these two indicators, it is possible to deduce in return two parameters, strain and doping. This material corresponds to a partially-graphitized coke with an annealing temperature of 2100 °C, exhibiting a rather large average in-plane crystallite size $L_a$ of 25 nm

[17]. This material was selected because it corresponds to a change in the behavior of the specific capacity and lithiation-delithiation behavior with the annealing temperature in the case of Li intercalation [17]. First-principles calculations with adiabatic and non-adiabatic phonon calculations were carried out to compare and tentatively correlate with the spectral observations. Such a study is likely to help figure out why the intercalation of $Na^+$ does not occur well in graphite whereas it does with either $K^+$ or $Li^+$, contributing to acquiring the knowledge needed to optimize the intercalation of $Na^+$ in graphenic materials.

## 2. Methods

### 2.1. *Carbon material selected for the anode*

A coke carbonized at 2100 °C was selected among a well-studied series of coal-tar-pitch-based graphitizable cokes carbonized from 1000 to 2650 °C [31,32]. With such a precursor and treatment, the resulting material is partially-graphitized, which is different from the so-called "hard carbons" mostly used for the anodes of Na-ion batteries. Such a partially-graphitized carbon material is not genuine graphite but is close to it, as seen from its large crystallite in-plane dimensions $L_a$ (~25 nm), XRD features, and good Li-intercalation ability, as investigated in our previous work [17]. It was preferred to genuine graphite because of its Raman signature. Indeed, the prevalence of AB pairs in this material induces that, for the laser excitation energy used in the current study, it provides Raman spectra showing a sharper and more intense 2D band (along with a narrow and intense G band) among the whole series, including more graphitized materials and graphite. This 2D band is composed of a single contribution (see SI, Figure S1). Therefore, this 2100 °C-coke represents the best compromise among graphenic materials exhibiting a one-component 2D band and those exhibiting an intense 2D band, which are both features facilitating the interpretations compared to materials exhibiting weak or broad bands composed of several contributions. This 2100 °C-coke was also preferred to the coke partially graphitized at 2000 °C - despite the latter also exhibiting an intense and narrow 2D band (Figure S1) - because, when intercalated with $Li^+$, the 2100 °C-coke corresponded to an inflection point where the trend of the specific capacity with respect to the carbonization temperature of the cokes starts to increase [14].

### 2.2. *Anode preparation*

The anode was prepared by mixing 80 wt % of the powderized coke, 10 wt % of acetylene black (Super-P) as a conductive agent, and 10 wt % of polytetrafluoroethylene (PTFE) as a binder, all dispersed in ethanol. The paste was shaped by passing between two closely spaced rollers, forming a uniform thin film. The film was dried at 80 °C for 12 h to remove solvent. It is then cut into 10 mm diameter disks and pressed onto stainless steel mesh to create the anodes. The mass loading of the anode was approximately 3.0–4.0 mg cm⁻².

### 2.3. *Electrochemical cell*

The device used for the test is a customized cell with a quartz window, and its internal structure is similar to that of a coin-type cell. A sodium foil with a diameter of 10 mm was employed as the counter/reference electrode, glass fiber paper (Whatman) was used as the separator, and 1 mol L⁻¹ of sodium trifluoromethanesulfonate (NaOTf) dissolved in diethylene glycol dimethyl ether was used as the electrolyte. The cells were assembled in an argon-filled glove box (H₂O < 0.01 ppm, O₂ < 0.01 ppm). The anode was placed under the quartz window for optical observation and tested on an electrochemical workstation (BioLogic VSP-300). A current density of 100 mA g⁻¹ was used for the cycle.
## 2.4. Raman spectroscopy

A Witec Raman spectrometer, ALPHA300R, with an excitation wavelength of 532 nm and a low laser power of 0.5 mW was used. A long working-distance objective × 50 was selected to collect the signal. Accumulation time of 200 s was chosen to achieve a reasonable signal-to-noise ratio. The optical images were captured with automatic white balance correction. The in-situ Raman spectrometry was carried out after the initial discharge and charge process. It is reminded that the penetration depth $d_p$ of the excitation laser is low, in the range of $d_p = 1/(2a) = 15$ nm where the absorption coefficient in graphite is $a(532 \text{ nm}) = 3.3 \times 10^7 \text{ m}^{-1}$ [33]. Therefore, with respect to the overall anode thickness, the Raman signal comes from the anode surface. Reported Raman spectra in figures are normalized on the G band height.

## 2.5. Computational details

The structural, vibrational, and electronic properties of the bulk partially-graphitized coke of the anode (taking into account the presence and proportions of AB-pair stacking sequences, graphitic AB*A*tc sequences, and residual turbostratic stacking sequences [17]), and of the same after Na-intercalation at stage 1 (NaC<sub>6</sub>) were obtained using the Quantum Espresso [34,35], a density functional theory (DFT) code. Ultrasoft pseudopotentials (USPP) [36] for C (2s, 2p) and Na (2s, 2p, 3s) were used. Converged total energy and forces were obtained with a plane-wave basis energy cut-off of 120 Ry and a Gaussian smearing of

0.005 Ry. All atoms and cells were relaxed using a force cut-off of 10<sup>-6</sup> Ry/bohr. Each self-consistent field calculation was performed until the total energy change between two consecutive iterations fell below 10<sup>-9</sup> Ry. The k-point sampling was based on a Γ-centered grid for all calculations with a (12 × 12 × 8) grid. Charge transfer per atom was conducted with a Bader charge analysis [37–39]. Both harmonic phonon and anharmonic electron-phonon coupling calculations were carried out through Quantum Espresso packages [34,35] and electron-phonon Wannier code [40]. From Table S1, the exchange-correlation functional including van der Waals interactions (vdW-optB88 [41]) accurately reproduces the lattice constants of the crystallites with AB*A*etc-stacked graphene layers, with relative errors of –0.2 % and 0.3 % along the *a* and *c* lattice parameters, respectively. Consequently, the vdW-optB88 scheme was retained for all subsequent calculations.

# 3. Experimental results

## 3.1. Intercalation and deintercalation

In Fig. 1, the Raman spectra obtained at low laser power are reported during both the intercalation and the deintercalation process. After deintercalation, in Fig. 1b, three visible features show up in the Raman spectra in addition to those expected for the G and 2D bands: (i) the D band becomes more intense and sharper (ii) a new band occurs at 1500–1550 cm<sup>-1</sup>; (iii) the downshift of the G band allows a faint D' band to be revealed, as a right-shoulder located at 1625 cm<sup>-1</sup>. The changes

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** In-situ Raman spectra during (a) intercalation and (c) deintercalation with a current density of 100 mA g<sup>-1</sup>. The typical deintercalated spectrum is reported in (b). The potential (*V* versus Na/Na<sup>+</sup>) is indicated on the right sides. The potential *V* versus Na/Na<sup>+</sup> as a function of the specific capacity during the experiment is reported in (d). The cell was pre-cycled twice before the first measurements. The red curves are the fit. The spectrum for the pristine 2100 °C-coke material is provided in **Figure S1**.</figcaption></figure>
affecting the D band is not surprising as local distortions can lead to the activation of the D band [42] even without structural defects. The new band located at 1500–1550 cm⁻¹ is not present at 1.565 V, and increases along with the D and 2D bands, meaning that this band is also activated by the double resonance effect (labelled D.R. for Double Resonance). Between the G and the 2D band are also visible some features also linked to double resonance. The specific phonons associated to D.R. are not known yet but some of them are possible (around the M point in the Brillouin zone for 1500 cm⁻¹ and as a combination of acoustic and out-of-plane modes around 2200 cm⁻¹). Finally, the occurrence of the D' band allows calculating the $I_D/I_{D'}$ ratio, which is close to 3, corresponding to the value associated to boundaries (crystallite limits) in graphene [43]. In the following, we focus only of the two bands G and 2D During the intercalation of Na, the G band typically upshifts from

1580 to 1606 cm⁻¹ while the 2D band downshifts from 2700 cm⁻¹ to 2620 cm⁻¹ and then vanishes. The clear co-existence of two 2D bands from 1 to 0.7 V reveals that some heterogeneity is present during intercalation, and some heterogeneity is present for a potential between 1 and 0.7 V, explaining the clear existence of two 2D bands. Therefore, the kinetics of intercalation are not the same for all carbon crystallites. As the 2 bands are clearly separated, we can attribute them to the coexistence of two stages, already observed by several techniques [8]. The wavenumber values for both G and 2D bands obtained through fitting are reported in Fig. 2. During deintercalation up to the reappearance of the 2D band, in the low-wavenumber range below the G band, the excess signal can be described by some Fano shape with a small negative coupling factor (see SI, Figure S4). The process of deintercalation shows less heterogeneity regarding the 2D bands, as only

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Raman shift for G (a) and 2D band (b) deduced from fitting the spectra reported in Fig. 1. In (b), the red and blue circles on the one hand and the magenta and light-blue diamonds on the other hand, correspond to the position of two sub-bands which sometimes happen to compose the 2D band.</figcaption></figure>
for a potential of 1.345 V, two 2D bands are necessary to describe the spectra. At each measurement, a photograph was taken (see SI, Figure S3).

In Fig. 2 the Raman shifts for the 2D, and G bands are reported. The D band, due to the presence of defects, is not affected in the same way as the 2D band, since the shift from the pristine position is not a simple factor of 2 (see SI, Figure S5). For fitting the Raman curve, two sub-bands were sometimes clearly needed or even observed for the 2D band, consistently with the heterogeneity observed, specifically well-marked during the intercalation (Fig. 1a).

## 3.2. First-principles calculation

Two compounds can be considered at stage 1: $NaC_8$ and $NaC_6$. Previous reports [3,41] indicate that both compounds are unstable from a DFT perspective, with only a minor difference in their formation enthalpies. Wang et al. [44] report positive formation enthalpies of +20.8 and +19.9 kJ.mol⁻¹ for $NaC_6$ and $NaC_8$, respectively. A similar small difference is also reported by Moriwake et al. [3]. Fig. 3 shows the atomistic model considered for $NaC_6$ in our calculations, with the Na atom positioned in three different sites: "Top", "Bridge", and "Hollow". Calculations involving both compounds are provided in the SI. For $NaC_6$ in the classical hollow position, we find a similar formation enthalpy of +15.3 kJ.mol⁻¹ (+0.158 eV) [3,44]. Upon testing both systems, we observe that $NaC_6$, with Na in the hollow position, does not exhibit any negative frequencies. This allows for more confident calculations of non-adiabatic effects in this case. Therefore, $NaC_6$ was selected for further analysis, as the results would be comparable to $NaC_8$.

The phonon observed at the Γ point is the Raman active mode. A shift of the G band is expected in $NaC_6$ in comparison to the band position in pristine graphite. In the latter case, the absence of negative wavenumbers (as shown in Fig. 4a) confirms the vibrational stability of the material. It is the same for the $NaC_6$ with the Hollow configuration (Fig. 4b), which is the most stable (see Table S2). The other configurations (Top, Bridge) were also considered and are reported in the SI. They generate negative wavenumbers (Figures S6 and S7), as previously reported for several intercalated compounds (e.g., $CaC_6$ [45]), which explain specific properties.

In the adiabatic approach, the electron redistribution in a metal (as doped graphene is) during atomic motion is not considered. In the non-adiabatic approach, this electronic cloud redistribution is considered and costs some energy, leading to an upshift of the phonon wavenumber. In the latter approach, the electron-phonon coupling downshifts the vibrational mode equivalent to $E_{2g}$ for $NaC_6$ (mode #19, see all vibrational modes in Tables S3 and S4) by typically 198 cm⁻¹ for the most stable position (Hollow, Table 1). This value is consistent with that reported in the literature [26].

<figure><img src="image_6.png" /><figcaption>Fig. 3. The various configurations of $Na^+$ (yellow atoms) when intercalated between two graphene layers in AA stacking (for simplicity and because it is the case in the last stage one of GIC), as used in the computational study: (H) "Hollow" site, where $Na^+$ is positioned above the center of a hexagonal ring; (T) "Top" site, where $Na^+$ is located directly above a carbon atom; and (B) "Bridge" site, where $Na^+$ is located between two adjacent carbon atoms.</figcaption></figure>

## 4. Discussion

The shape of the G band (see Fig. 5.a) for the fully intercalated coke anode does not exhibit a Fano shape with a small coupling factor $q$ (strongly asymmetric shape, see SI Figure S4), and its spectral position, between 1580 and 1610 cm⁻¹, is not compatible with the mechanical mode of $NaC_6$ (strong downshift) coupled with the electron (upshift but not enough to overtake the previous downshift), whatever is the position of $Na^+$ (see Table 1). In DFT calculations, we have considered all the situations to figure out if a mispositioning of the $Na^+$ (with respect to the most stable configuration, i.e., Hollow) atom can play a role during intercalation. Even if the wavenumbers are different from one $Na^+$ position to another, in all cases, we expect a strong downshift of the G band of the Na-intercalated coke corresponding to the mechanical coupling of graphene with the $Na^+$ ions taking into account the non-adiabatic effects (Table 1). However, this is not what is observed experimentally, as the G band position remains above 1580 cm⁻¹, whatever the intercalation rate (Fig. 2a). This point is important, as it means that the electrolyte plays a crucial role by intercalating as well, thereby allowing it to keep interacting with the $Na^+$ inside the host carbon, consistently with the co-intercalation situation reported in the literature from X-ray technique [10]. Consequently, the Raman response of the carbon host is affected by charge transfer effects in a way we will discuss. Besides, a broad band is visible ranging from 2000 to 2500 cm⁻¹, and the intensity increases as the intercalation increases (Fig. 1a). Previously, with the same carbon material as the anode but with $Li^+$ intercalation, we have observed the same spectral signature, tentatively attributed to the electrolyte [17]. However, the electrolyte is different here, therefore the origin of this band can be also a signature of overtones of the $sp^2C$ honeycomb lattice [46] activated by intercalation. The G band is always observable and remains narrow, while the 2D band is visible for potential higher than around ~ 0.7 V. In the following, we analyze it in association with the 2D band. The disappearance of the 2D band is due to a loss of the double resonance process. In the latter process, both a photo-excited electron and a hole are backscattered each by a phonon, going both from the Dirac cone around K to the Dirac cone around K' and finally recombining vertically in the Brillouin zone to emit a photon. If the Dirac cone is modified, or if, due to charging, the probability of creating a photoexcited electron is reduced, the 2D band disappears. As the shape of the G band remains similar at various potentials, and as a charge of -0.15|e| expected at stage 1 corresponds to a Fermi level shift in the range of half the laser energy [26], a small variation of the doping can induce a disappearance of the 2D band without any fundamental structural change. Another possibility is carbon surface corrugation due to overdensation beyond the 0.7 V threshold [10]. At high potential, the Raman shift can be analyzed. For large potential, an analysis of the Raman shift can be easily done. As we have selected a graphenic carbon with an observable 2D band with a Lorenzian shape, it is possible to analyze the origin of the shifts of both bands at the same time. These shifts are due to two effects, strain and doping, which can be discriminated [30]. In the following, we assume that the law remains valid for large n-doping, which is a reasonable hypothesis (the linearity is obtained for 2D Raman shifts as large as 50 cm⁻¹) even if the relationship between the doping and the frequency shift of G and 2D may be slightly imprecise. Theoretically, there is no reason to use different values between n- and p-doping for $\Delta\omega_{doping-G}$. The coefficients in the next laws from the publication by Lee et al. [30] seem to be well adapted to our case. When considered as free parameters, there is no significant improvement in the agreement. It is important to note that, in Lee et al. work [30], in the case of doping, the graphene layer was deposited on a substrate and connected to an electrode, which means that the reported value is:

$$ \Delta\omega_{doping} = \left(\frac{\partial\omega}{\partial q}\right)_{\text{strain}}, $$

This is a partial derivative with respect to the charge, $q$, while all the
<figure><img src="image_7.png" /><figcaption>Fig. 4. Phonon dispersion (THz) of (a) graphite, and (b) NaC₆ in the "Hollow" configuration, showing only harmonic wavenumbers within the Brillouin zone.</figcaption></figure>

<table><caption>**Table 1**
E₂g vibrational mode for graphite, or its equivalent for NaC₆ with 3 different positions of the Na atom. The difference in wavenumber for graphite is due to the selected functional. All modes are given in the SI, tables S3, S4, S7 and S9.</caption><thead><tr><th>Raman active vibrational modes</th><th>ω<sub>G</sub> adiabatic (cm<sup>-1</sup>)</th><th>ω<sub>G</sub> non-adiabatic (cm<sup>-1</sup>)</th></tr></thead><tbody><tr><td>Graphite (E<sub>2g</sub> - mode #10)</td><td>1509.7</td><td>1516.0</td></tr><tr><td>Top (mode #19)</td><td>1256.0</td><td>1358.0</td></tr><tr><td>Hollow (mode #19)</td><td>1141.0</td><td>1338.9</td></tr><tr><td>Bridge (mode #19)</td><td>1255.6</td><td>1400.7</td></tr></tbody></table>

other parameters are fixed, which means that the effects of lattice contraction or dilatation reported in the calculation [26] are not taken into account.

$$ \Delta\omega_G = \Delta\omega_{\text{biaxial strain-G}} + \Delta\omega_{\text{doping-G}} $$

$$ \begin{aligned} \Delta\omega_{2D} &= \Delta\omega_{\text{biaxial strain-2D}} + \Delta\omega_{\text{doping-2D}} \\ &= 2.2 \times \Delta\omega_{\text{biaxial strain-G}} + 0.7 \times \Delta\omega_{\text{doping-G}} \end{aligned} $$

From the work by Lazzeri and Mauri [23], we have

$$ \Delta\omega_{\text{biaxial strain-G}} = 350 f_C \text{ and } \Delta\omega_{\text{doping-G}} = 216 \sqrt{|f_C|}, $$

Where $f_C$ is the charge per carbon atom in the unit cell, as successfully used previously in the case of nanotubes [47]. Of course, the accuracy of these equations is questionable as they have not been validated for strong n-type doping. Moreover, for a very small value of $|f_C|$ corresponding to $|\Delta\omega_G| < 2 \text{ cm}^{-1}$ at room temperature, an additional term is required [26] which is not necessary here. Nevertheless, as we shall see, each equation, for strain and doping respectively, allows determining a value for $f_C$, which should theoretically be the same. Fig. 5a and c. From the 2D band position, the blue-line spectrum shown in Fig. 5a corresponds to an intercalation at stage 1, according to [21].

Fig. 6 reports the values of $f_C$ determined separately from $\Delta\omega_{\text{biaxial strain-G}}$ and $\Delta\omega_{\text{doping-G}}$ considering the deintercalation part (as there is no splitting of the G and 2D bands). It is remarkable that the ultimate value found for $f_C$, around $-0.17 \pm 0.02 |e^-|$, is close to $-0.15 |e^-|$, which corresponds to stage 1 of Na intercalation. Indeed, in the case of NaC₆, the theoretical charge transfer per Na atom to the graphene network is $-0.9 |e^-|$, corresponding to $-0.15 |e^-|$ par carbon atom (see

Table S6). This means that the Na intercalation in the carbon anode was optimum, at least regarding the anode surface (as the penetration of the excitation laser is low, see Section 2.4), and confirms that there is no difference in the intercalation ability between our 2100 °C-coke and genuine graphite.

The mechanical coupling between Na and the graphene layers is not effective. The shift of the G and 2D bands can be fully explained by considering only the charges taken by the graphene layers. Our approach is valid for stage 1 and stage 2 as the layers experience the same charge in both cases. For higher stages, graphene layers are not all surrounded by the same environment, which means that discriminating between strain and doping cannot be done as simply as for NaC₆.

When the 2D band disappears, the position of the G band remains the same. From Fig. 5b, we see that the position of the G band is relatively constant for a large range of negative $f_C$ values, meaning that small variations of $f_C$ are not observable. As the specific capacity continues to increase anyway (see Figure S2), it is clear that Na insertion continues.

In the case of graphite exposed to Na vapor, we found only one report [22] in which the related Raman spectrum is composed of the G band of graphite with a shoulder corresponding to a narrow peak located at 1608 cm⁻¹. This demonstrates that the presence of an electrolyte is not required to observe such spectral features (we assume that, in this case, the Na⁺ ions start to interact with the graphite, but not to form a full GIC crystal). Interestingly, there is a slight lack of intensity around 1250 cm⁻¹, which corresponds to a Fano shape typically observed for GICs. After scanning and fitting these data (see SI Figure S9), we have obtained for the Fano shape associated to this lack of intensity a coupling factor of $q = -0.15$, a linewidth of $\Gamma = 45 \text{ cm}^{-1}$, and a wavenumber of $\omega = 1245 \text{ cm}^{-1}$. This feature can be associated with Na inserted between graphene layers (the most stable position for Na in graphite is the Hollow position. The value obtained is in the middle of the adiabatic and non-adiabatic wavenumber of the coupled mode. Anyway, the Raman spectrum of the full intercalation(= stage-1) of Na⁺ from a vapor phase has never been reported. To have easier intercalation of Na⁺, two strategies are possible: expanding the intergraphene distance in the host-graphite [48] or using a co-intercalant [21], i.e., the electrolyte in our case. From their X-ray data, the inter-graphene distance for LiC₆ and KC₈ is 0.370 nm and 0.535 nm, respectively [49]. As the ionic radius increases from 0.074 nm for Li⁺ to 0.102 nm for Na⁺ and 0.133 nm for K⁺, our theoretical value for the inter-graphene distance in NaC₆ of 0.457 nm is consistent with what is expected. If the Na⁺ ions are located in a Hollow position, mechanical coupling should be present and should lead to a downshift, as partly visible in Akuzawa et al.'s work [22]. To confirm the absence of fully-intercalated NaC₆ without co-intercalant, we explore whether
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** (a) Comparison, during deintercalation, of Raman spectra of the coke material at stage 1 (blue line, corresponding to the 1.115 V spectrum in Fig. 1a), and then after full deintercalation leading to recovering the pristine state (2.4 V, grey line). (b) General shift with respect to the pristine spectral position for the G band, due to some charge per carbon atom ($f_C$) in the case of freestanding monolayer graphene calculated with the equations reported in the text. (c) same as (b), for the 2D band. In both (b) and (c), the red dashed-dotted lines show the contribution of strain (linear with $f_C$), and the green dashed-dotted corresponds to the contribution of doping (the one always positive). The values marked by colored solid disks in (b) and (c) correspond to stage 1 in (a).</figcaption></figure>

weak bonding could exist and also be at the origin of the lack of mechanical coupling. We did this by calculating the energy change of $Na^+$ when moving from the hollow to the top positions (See SI, Figure S10), The energy variation has a quadratic dependence close to the hollow and top positions. There is no double potential nor unusual behavior (the

case of $LiC_6$ is added to Figure S10 for comparison). Finally, in the 400–450cm⁻¹ range (our calculation and [50,51]), there is no lorentzian Cz mode (See Figure S11). Therefore, based on these findings, we attribute the lack of mechanical coupling to the random distribution of $Na^+$ ions in the network due to co-intercalation, which is common in the
<figure><img src="image_9.png" /><figcaption>Fig. 6. Charge transfer $f_c$ par carbon atom in elementary unit versus the potential during the deintercalation process.</figcaption></figure>

case of our electrolyte (NaOTf dissolved in diethylene glycol dimethyl ether) [52,53]. As reminded in Section 2.4, Raman spectroscopy gives information from the carbon material surface. On the other hand, information dominated by the bulk of the carbon anode can be obtained from the position of the $d_{002}$ peak in X-ray diffraction patterns. Using XRD, Kim et al. [10] have reported an additional sodiation stage to stage 1 through a spacing between graphene layers of >1 nm when intercalated at a potential ranging from 0.7 to 0 V in the case of an electrolyte composed of 1 M $NaPF_6$ in diethylene glycol dimethyl ether. As the formation energy of the Na-intercalated compound is positive (unstable, considering solid Na as reference energy), co-intercalation is the only possible explanation, as reported in the literature [10,52,53], but is a consequence of the particular behavior of $Na^+$ with graphene. Therefore, the choice of the right co-intercalant (the electrolyte) is another parameter to tentatively improve the specific capacity of Na/graphite-based batteries [54,55].

## 5. Conclusion

Raman spectroscopy is a versatile, non-contact technique for analyzing the stability of Na-intercalated compounds. During intercalation and deintercalation in a graphenic material close to graphite, it is possible to observe both the G and 2D Raman bands until the potential remains higher than ~ 0.7 V. These two bands are characteristic of graphene and the G band shape is not deformed by coupling with the electronic continuum, i.e., it does not present a Fano shape, meaning

that the mechanical coupling between the graphene layer and the intercalated $Na^+$ is not observed. This lack of coupling is due to the location of $Na^+$ which does not form a network in Hollow position and to the positive formation energy of the related graphite intercalated compound. The presence of co-intercalant is presently the only possible explanation. As both the G and 2D band shifts can be measured thanks to the features of the material specifically selected for this purpose, it is possible to separate the strain (lattice expansion) and the doping effects at a constant lattice. Both values are fully explained by the charge transfer alone, which can be decomposed into an upshift (electron-phonon coupling) and a downshift (lattice expansion), somewhat compensating for each other. When the intercalation potential ranges between 0 and 0.5 V, the 2D band disappears, corresponding to the loss of the usual double resonance process predicted by the Raman theory, while the G band remains at the same spectral position. *In operando* Raman spectroscopy is a reliable tool for quantifying charge transfer during the intercalation of graphitic carbon even in the case of the Raman shifts of G and 2D bands which are made complex due to antagonist contributions.

## CRediT authorship contribution statement

**Pascal Puech:** Writing – review & editing, Writing – original draft, Methodology, Investigation, Funding acquisition, Conceptualization.
**Damien Tristant:** Writing – original draft, Methodology, Formal analysis.
**Shaorui Chen:** Writing – original draft, Validation, Methodology,
Investigation, Formal analysis, Data curation. **Shae Wetzel:** Writing – original draft, Methodology, Formal analysis. **Yuxin Xiang:** Methodology, Investigation. **Tianzhao Hu:** Writing – original draft, Methodology, Investigation. **Lili Zhang:** Methodology, Conceptualization. **Marc Monthoux:** Writing – review & editing, Writing – original draft. **Feng Li:** Writing – original draft, Methodology, Conceptualization.

## Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Pascal Puech reports financial support was provided by Programme des Investissements d'Avenir NanoX ANR-17-EURE-0009. Damien Tristant reports financial support was provided by Louisiana Optical Network Infrastructure (LONI). 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.

## Acknowledgements

P.P. was supported by a mobility scholarship from the grant NanoX n°ANR-17-EURE-0009 in the framework of the “Programme des Investissements d'Avenir”. Computational resources were provided by the Louisiana Optical Network Infrastructure (LONI).

## Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.cartre.2025.100547.

## Data availability

Data will be made available on request.

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