Sodium-Intercalated Graphite

• Sodium-intercalated graphite is a family of graphite intercalation compounds where sodium occupies galleries between graphene layers, forming high-stage metastable and pressure-stabilized phases.
• Pressure and cointercalation strategies enable diverse Na–C stoichiometries, which modify charge transfer and can induce superconductivity with critical temperatures exceeding 20 K.
• Sodium acts as a transient intercalant and catalytic intermediate, lowering activation barriers for subsequent metal insertions in battery and superconducting material applications.

Sodium-intercalated graphite comprises graphite intercalation compounds (GICs) in which Na occupies galleries between graphene layers, together with ternary cointercalation phases in which Na enters graphite alongside molecular guests. In current research, the term spans metastable high-stage NaC$_x$ phases formed chemically at room temperature, pressure-stabilized stage-1 and stage-2 Na-C compounds, and solvated or molecularly cointercalated phases relevant to Na-ion electrochemistry (Iyo et al., 2023, Mishra et al., 2024). Pristine graphite at its equilibrium spacing remains thermodynamically incompatible with dense Na intercalation, so sodium-intercalated graphite is not a single ambient-pressure analogue of LiC$_6$, but a structurally conditional family whose accessibility depends on staging, interlayer spacing, chemical potential, and pressure (Liu et al., 2016, Radchenko et al., 13 Dec 2025).

1. Structural chemistry and phase space

The simplest chemically observed Na-GIC in bulk graphite is a high-stage NaC$_x$ phase centered on NaC$_{64}$. In room-temperature as-mixed Na/C or Ca/Na/C mixtures, X-ray diffraction identifies a broad NaC$_x$ peak at $2\theta \approx 25.5^\circ$ with $d \approx 3.49~\text{\AA}$, consistent with NaC$_{64}$ and non-uniform staging centered around stage 8; related lanthanide work describes the intermediate more generally as stage 6–8 Na-GIC with $x$ of 48–64 (Iyo et al., 2023, Iyo et al., 2024). In the Na-catalyzed synthesis literature, this phase is deliberately denoted NaC$_x$ because the high-stage peaks lie close together and the observed reflections are broadened, implying multistage mixtures rather than a single perfectly ordered stoichiometry (Iyo et al., 2023).

Pressure opens a much broader Na-C phase space. Evolutionary searches and convex-hull analyses have proposed NaC$_6$0, NaC$_6$1, and NaC$_6$2 as low-pressure stable or near-stable Na-GICs, with NaC$_6$3 in $_6$4 emerging as a particularly important phase (Hao et al., 2023). A more focused pressure-composition survey later identified additional viable stoichiometries, notably Na$_6$5C$_6$6, NaC$_6$7, NaC$_6$8, and NaC$_6$9, and distinguished stage-1 compounds such as NaC$_x$0, NaC$_x$1, and Na$_x$2C$_x$3 from stage-2 compounds such as NaC$_x$4, NaC$_x$5, and NaC$_x$6 (Mishra et al., 2024). Experimentally, compressed sodium-intercalated graphite near $_x$7–$_x$8 GPa is dominated by an orthorhombic stage-2 phase of approximate stoichiometry NaC$_x$9 with space group $_{64}$0, together with a minor monoclinic stage-2 NaC$_{64}$1 phase in $_{64}$2 (Huang et al., 27 Sep 2025).

Stage index remains the central structural descriptor. In the classical GIC notation, stage $_{64}$3 means one intercalant layer every $_{64}$4 graphene layers. For stage-$_{64}$5 compounds, the repeat distance along the stacking direction satisfies

$_{64}$6

where $_{64}$7 is the graphite-plane spacing across an intercalant gallery and $_{64}$8 is the spacing of host graphite (Iyo et al., 2023, Huang et al., 27 Sep 2025). In the chemically accessible high-stage NaC$_{64}$9 regime, Na primarily perturbs the $_x$0-axis; one NaC$_x$1 pellet analysis assigned $_x$2, essentially identical to host graphite, and $_x$3 for an inferred stage-8 NaC$_x$4 model (Iyo et al., 2023).

2. Thermodynamic constraints and the Na anomaly

A persistent result across first-principles studies is that Na is an anomalously weak binder in graphite. For MC$_x$5 and MC$_x$6 compounds, the formation energy is positive for NaC$_x$7 and NaC$_x$8, but negative for Li, K, Rb, and Cs analogues, explaining why graphite has high capacity for Li yet very low Na capacity under standard electrochemical conditions (Liu et al., 2016). The origin is not a simple steric penalty: in the decomposition

$_x$9

the decohesion term $2\theta \approx 25.5^\circ$0 and strain term $2\theta \approx 25.5^\circ$1 do not peak at Na, whereas the weak Na-substrate binding term $2\theta \approx 25.5^\circ$2 does (Liu et al., 2016).

Expanded graphite changes that conclusion quantitatively. Cluster-expansion and DFT calculations over controlled interlayer spacings show that no Na-C compounds are stable on the convex hull at equilibrium spacing for either AA or AB stacking, but Na intercalation becomes thermodynamically possible in large concentrations above $2\theta \approx 25.5^\circ$3 even without a change in interlayer spacing (Radchenko et al., 13 Dec 2025). AA-stacked domains consistently offer stronger ion bonding and higher voltages than AB-stacked domains for both Li and Na; at $2\theta \approx 25.5^\circ$4, AA-expanded graphite supports stable NaC$2\theta \approx 25.5^\circ$5, NaC$2\theta \approx 25.5^\circ$6, NaC$2\theta \approx 25.5^\circ$7, and NaC$2\theta \approx 25.5^\circ$8, with a maximum Na capacity of $2\theta \approx 25.5^\circ$9 (Radchenko et al., 13 Dec 2025). This places sodium-intercalated graphite on a structural threshold: pristine AB graphite excludes dense Na insertion, whereas expanded or AA-like graphitic domains can stabilize it.

The experimentally observed high-stage NaC$d \approx 3.49~\text{\AA}$0 phases are therefore best regarded as metastable but kinetically accessible. In room-temperature Na-catalyzed CaC$d \approx 3.49~\text{\AA}$1 synthesis, NaC$d \approx 3.49~\text{\AA}$2 forms spontaneously on mixing Na and graphite, persists long enough to be measured by XRD at $d \approx 3.49~\text{\AA}$3 h, and is later consumed as CaC$d \approx 3.49~\text{\AA}$4 grows (Iyo et al., 17 Jun 2026). In Na-catalyzed CaC$d \approx 3.49~\text{\AA}$5 synthesis at $d \approx 3.49~\text{\AA}$6C, the NaC$d \approx 3.49~\text{\AA}$7 peak does not appear until the nominal Na:C ratio reaches about $d \approx 3.49~\text{\AA}$8, even though NaC$d \approx 3.49~\text{\AA}$9 stoichiometrically requires only about $_{64}$0, which the authors interpret as evidence that substantial excess Na occupies non-interlayer sites, plausibly graphite edges or defects, before a detectable Na-GIC nucleates (Iyo et al., 2023). Taken together, these results indicate that the statement “Na does not intercalate into graphite” is accurate for pristine graphite under standard equilibrium conditions, but incomplete for chemically driven, expanded, or pressure-stabilized regimes.

3. Sodium as transient intercalant and catalytic intermediate

A major development in the field is the recognition that Na can function not only as an intercalant, but as a catalytic intermediate that activates graphite for other metals. In the broadest demonstration of this effect, LiC$_{64}$1 ($_{64}$2), KC$_{64}$3, KC$_{64}$4 ($_{64}$5), and NaC$_{64}$6 were synthesized simply by mixing alkali metals and graphite powder with Na at room temperature, while AEC$_{64}$7 ($_{64}$8) formed after heating Na-added reagents at $_{64}$9C only for a few hours (Iyo et al., 2023). In this framework NaC$x$0 is the reaction intermediate: Na first intercalates into graphite, forming a high-stage Na-GIC that lowers the activation energy for subsequent intercalation by Li, K, or alkaline-earth metals (Iyo et al., 2023).

The room-temperature Ca/Na/C system provides the clearest kinetic evidence. Pellets prepared from Ca, Na, and graphite at a molar ratio Ca:C:Na $x$1 show NaC$x$2, unreacted Ca, and unreacted Na after short storage; with increasing storage time, CaC$x$3 peaks intensify while NaC$x$4 and Ca peaks diminish, and no CaC$x$5 is detected in the Na-free control even after $x$6 h (Iyo et al., 17 Jun 2026). Both the field-cooled diamagnetic signal at $x$7 K and the strongest CaC$x$8 XRD intensity scale linearly with $x$9,

$_x$0

indicating diffusion-controlled growth of CaC$_x$1 through Na-opened galleries (Iyo et al., 17 Jun 2026).

The same mechanistic picture extends to lanthanides. In Na-assisted synthesis of SmC$_x$2, EuC$_x$3, and YbC$_x$4, the as-mixed samples contain NaC$_x$5 plus unreacted lanthanide, and heating converts NaC$_x$6 into LnC$_x$7; for YbC$_x$8, a high-intensity diffraction peak appears after only $_x$9 h at $_6$00C, accompanied by a significant decrease in NaC$_6$01 and Yb peaks (Iyo et al., 2024). After the two-step Na reduction process, the final pellet composition reaches $_6$02, showing that Na is largely displaced and removed even though it is indispensable during formation (Iyo et al., 2024).

This catalytic role is specific rather than generic among alkali metals. K does not replicate the effect: K forms its own stable K-GICs, but does not catalyze Li- or AE-GIC formation under the tested conditions (Iyo et al., 2023). A plausible implication is that Na’s value derives from a particular combination of rapid room-temperature entry into graphite, metastability of the resulting NaC$_6$03, and low-barrier exchange with more stable intercalants.

4. Charge transfer, electronic structure, and superconductivity

Charge transfer from Na to graphitic $_6$04 states is a recurring theme across sodium-intercalated graphite. In ternary Na(diglyme)-graphite, both the diglyme molecules and Na donate electrons to the graphene layer, producing ionic bonding between graphene and the moiety of the diglyme molecule (Yu et al., 2017). In Na-alkylamine stage-I compounds $_6$05, charge-density differences and atomic populations likewise show electron donation from Na and electron gain on the graphene layer, with the total density of states remaining metallic at the Fermi level (Ri et al., 2015). In the quasi-two-dimensional limit of epitaxial graphene on SiC, Na intercalates at room temperature and strongly electron-dopes graphene: DFT places the Dirac point at $_6$06 eV for SiC/B/Na/G and $_6$07 eV for SiC/Na/G, while SiC/Na/G/G exhibits a $_6$08 eV bandgap and reduced doping, demonstrating that the interfacial location of Na strongly controls the electronic response (Sandin et al., 2011).

Superconductivity emerges when this charge transfer is combined with suitable Na-derived or interlayer electronic states and the right phonon spectrum. Ab initio structure prediction identified $_6$09 NaC$_6$10 as a strong candidate: at $_6$11 GPa it has $_6$12, $_6$13, and a predicted $_6$14 for $_6$15, with about $_6$16 of $_6$17 arising from low-frequency Na-C coupled modes and the states at $_6$18 dominated by C $_6$19 orbitals (Hao et al., 2023). A later stability-superconductivity map refined this picture, finding that NaC$_6$20 and Na$_6$21C$_6$22 are the most promising superconductors among viable Na-GICs under $_6$23–$_6$24 GPa, with anisotropic Migdal-Eliashberg calculations pushing NaC$_6$25 to $_6$26 K at $_6$27 GPa and revealing a well-defined two-gap structure (Mishra et al., 2024).

Experiment has now established bulk-like superconductivity in compressed sodium-intercalated graphite. Slightly over-stoichiometric stage-2 Na$_6$28C$_6$29 in $_6$30 reaches $_6$31 K at $_6$32 GPa, with clear zero resistance, $_6$33 T, and $_6$34 nm (Huang et al., 27 Sep 2025). Hall measurements give electron concentrations of $_6$35 at the optimum pressure, and the superconductivity is attributed primarily to interactions between out-of-plane carbon electrons and low-frequency Na/C vibrations (Huang et al., 27 Sep 2025). In the same system, stoichiometric NaC$_6$36 has only $_6$37 and a negligible calculated $_6$38, whereas electron doping of about $_6$39 e/atom increases $_6$40 to $_6$41, showing that slight Na over-stoichiometry is electronically decisive (Huang et al., 27 Sep 2025).

5. Cointercalation, solvation, and electrochemical regimes

Electrochemical sodium-intercalated graphite is often realized not as a binary Na-C phase, but as a cointercalated complex. In Na-diglyme graphite, stage-I ternary compounds $_6$42 are stable in first-principles calculations; the Na(digl)$_6$43C$_6$44 compound has the negatively lowest intercalation energy at $_6$45, the solvated Na(digl)$_6$46 ion diffuses fast in the interlayer space, and the electronic conductance is enhanced compared to graphite (Yu et al., 2017). In the closely related alkylamine family, stage-I $_6$47 compounds are predicted by PBEsol to have negative formation energies, strong interlayer binding, and a Na migration barrier of $_6$48 eV for Na-nC$_6$49-GIC, with the general stability trend Li $_6$50 Na $_6$51 K (Ri et al., 2015).

Strong solvation can also stabilize Na inside graphite while weakening direct Na-graphite interaction. In metadynamics for NaTFSI$_6$52 between graphite layers separated by $_6$53, the lowest free-energy minima correspond to Na solvated by 3 or 4 DMSO molecules; the free-energy difference between the dominant 3-DMSO and 4-DMSO states is $_6$54 eV, and the simulations explicitly report weak interactions of sodium with graphite sheets (Kachmar et al., 2018). This implies a cointercalation regime in which Na is stabilized primarily as a solvated complex rather than as a dense binary Na-GIC, a picture consistent with the low capacity of pristine graphite for Na and the importance of electrolyte chemistry.

Expanded graphitic carbons bridge the gap between these binary and solvated limits. When interlayer spacing is treated as an explicit design variable, Na intercalation becomes thermodynamically possible above $_6$55, and AA-stacked expanded graphite supports stable NaC$_6$56 at $_6$57 with a maximum Na capacity of $_6$58 (Radchenko et al., 13 Dec 2025). This provides a structural rationale for why hard carbon and expanded graphite can host Na even though conventional AB graphite cannot. A plausible implication is that sodium-intercalated graphite in practical Na-ion systems is better described as a continuum spanning high-stage metastable NaC$_6$59, expanded-domain NaC$_6$60, and fully ternary cointercalation compounds.

6. Applications, misconceptions, and unresolved problems

The practical interest in sodium-intercalated graphite extends well beyond Na-ion storage. Na-catalyzed formation of CaC$_6$61 at room temperature was explicitly proposed as relevant to electrode materials in Ca-ion batteries (Iyo et al., 17 Jun 2026). Rapid Na-assisted synthesis of CaC$_6$62 was presented as a route toward practical GIC materials for battery electrodes and superconducting wires, with residual Na reduced to a Na:Ca ratio of approximately $_6$63 after post-processing (Iyo et al., 2023). The same catalytic framework has already been extended to SmC$_6$64, EuC$_6$65, and YbC$_6$66, with the stated goal of rapid mass production of lanthanide GICs for superconducting and rechargeable battery materials (Iyo et al., 2024).

A common misconception is that Na is simply excluded from graphitic hosts. The evidence is more specific. Pristine graphite is thermodynamically incompatible with dense Na intercalation at equilibrium spacing (Liu et al., 2016, Radchenko et al., 13 Dec 2025); nonetheless, Na can form high-stage NaC$_6$67 chemically at room temperature (Iyo et al., 2023, Iyo et al., 17 Jun 2026), can stabilize dense Na-C phases under moderate pressure (Hao et al., 2023, Huang et al., 27 Sep 2025), and can enter graphite electrochemically when the galleries are expanded or when solvent or molecular cointercalants restructure the host (Yu et al., 2017, Kachmar et al., 2018). The real controversy therefore concerns conditions of stability rather than the bare possibility of Na entry.

Several mechanistic questions remain open. In the NaC$_6$68 $_6$69 CaC$_6$70 pathway, the exact by-products of the reaction $_6$71 are not resolved (Iyo et al., 17 Jun 2026). The detailed atomistic exchange mechanism by which Na is replaced by Ca or lanthanides is explicitly identified as a future theoretical and experimental problem (Iyo et al., 2023, Iyo et al., 2024). For high-pressure Na-GICs, the relative stability of proposed phases depends sensitively on the density-functional treatment and on whether graphite or diamond is used as the carbon reference, and some phases may stabilize only through vibrational entropy or cold compression from graphite (Mishra et al., 2024). Finally, the possibility that high-pressure Na-GIC superconductors could be quenched to ambient pressure remains suggestive rather than established (Hao et al., 2023).

Sodium-intercalated graphite is therefore best viewed as a controlled departure from the equilibrium chemistry of pristine graphite. In one limit it is a high-stage, metastable, weakly ordered NaC$_6$72 phase; in another it is an expanded or solvated electrochemical host; in a third it becomes a pressure-stabilized superconductor with $_6$73 above $_6$74 K. The unifying feature across these regimes is that Na substantially alters the interlayer electronic and structural landscape of graphite, but only when staging, interlayer spacing, or auxiliary chemical species push the system out of the conditions under which the Na anomaly dominates.