The distinction requires combining electrochemical kinetics with direct structural evidence. In hard-carbon anodes, sodium adsorption is typically associated with the higher-voltage sloping region, where Na⁺ binds to defects, edges, or accessible surfaces and exhibits relatively faster apparent diffusion. Interlayer intercalation is associated with the low-voltage plateau, where sodium enters carbon galleries, producing slower kinetics and measurable expansion of the interlayer spacing.
A voltage plateau alone does not prove intercalation. The strongest assignment combines the plateau or slope in the electrochemical profile with GITT/differential-capacity analysis and structural measurements—especially tracking the hard-carbon (002) reflection during sodiation.
What the Electrochemical Profile Reveals
Sloping voltage region: adsorption-dominated storage
The region above approximately 0.1 V vs. Na/Na⁺ is generally attributed mainly to Na⁺ adsorption at defects, edges, and disordered or graphitic nanodomain surfaces.
This process usually produces a broad slope rather than a sharp, flat plateau because the adsorption sites have a distribution of binding energies.
At still higher potentials, particularly above approximately 1.0 V, heteroatom-containing defects may contribute strongly through specific sodium binding. This should be distinguished from ordinary surface or edge adsorption in the lower-voltage portion of the slope.
Low-voltage plateau: interlayer or pore-filling processes
The region below approximately 0.1 V vs. Na/Na⁺ is commonly associated with sodium insertion into the denser carbon structure. In a structural model involving interlayer intercalation, Na⁺ enters the galleries between partially ordered carbon layers.
However, a low-voltage plateau is not uniquely diagnostic of interlayer intercalation. Hard carbon can also store sodium through nanovoid or pore filling, which may generate a similar plateau without requiring extensive gallery expansion.
Differential capacity as a supporting test
The dQ/dV profile helps separate broad adsorption features from sharper low-voltage storage features.
A broad feature distributed across the sloping region is consistent with a range of adsorption environments. A concentrated low-voltage feature indicates a more specific storage process, but its interpretation still requires structural verification because both interlayer insertion and pore filling can contribute.
How GITT Distinguishes the Kinetics
Higher apparent diffusivity supports adsorption
GITT-derived sodium diffusivity is typically higher in the sloping region than in the low-voltage plateau region.
Surface and defect adsorption can occur without requiring Na⁺ to penetrate between closely spaced carbon layers. The shorter transport path and lower structural constraint produce comparatively lower kinetic resistance.
Lower apparent diffusivity supports interlayer insertion
During the plateau, the apparent sodium diffusivity commonly decreases.
If Na⁺ is entering carbon interlayers, it encounters restricted galleries and electrostatic repulsion from sodium already stored nearby. These effects increase the kinetic resistance relative to surface or defect adsorption.
Diffusivity is evidence, not proof
GITT measures an apparent chemical diffusivity that depends on several factors, including particle geometry, state of charge, phase changes, and electrode polarization.
Therefore, a lower plateau diffusivity supports a more constrained storage mechanism, but it cannot independently prove interlayer intercalation. Structural measurements are needed to distinguish gallery insertion from pore filling.
What XRD Reveals Directly
The (002) peak is the key structural marker
Hard carbon contains partially ordered carbon layers whose average interlayer spacing is reflected by the (002) X-ray diffraction peak.
According to Bragg’s law, expansion of the interlayer spacing causes the (002) reflection to shift toward a lower diffraction angle.
Peak movement supports interlayer intercalation
If the (002) peak shifts measurably to lower angle during the low-voltage plateau and returns or partially returns during desodiation, the result is direct evidence that sodium storage is accompanied by interlayer expansion.
This is the strongest structural signature distinguishing gallery intercalation from adsorption on external or defect surfaces.
Lack of expansion favors adsorption or pore filling
If substantial sodium storage occurs without a corresponding shift or expansion of the (002) reflection, the result favors mechanisms that do not significantly separate the carbon layers.
These mechanisms include surface or defect adsorption and nanovoid pore filling, although the sensitivity and interpretation of XRD must be considered carefully.
The Most Reliable Evidence Combination
Adsorption assignment
A storage contribution is most credibly assigned to adsorption when it shows:
- A sloping voltage profile, generally above approximately 0.1 V vs. Na/Na⁺.
- Relatively higher apparent Na⁺ diffusivity in GITT.
- Broad or distributed dQ/dV features.
- No substantial, reversible expansion of the carbon-layer spacing in XRD.
Interlayer-intercalation assignment
A storage contribution is most credibly assigned to interlayer intercalation when it shows:
- A low-voltage plateau, generally below approximately 0.1 V vs. Na/Na⁺.
- Lower apparent diffusivity or greater kinetic resistance in GITT.
- A concentrated low-voltage feature in dQ/dV.
- A measurable shift of the (002) XRD peak toward lower angle, indicating increased interlayer spacing.
Why multimodal testing matters
No single measurement is decisive across all hard carbons.
Voltage identifies electrochemical regimes, GITT identifies kinetic changes, and XRD identifies lattice or gallery expansion. Their agreement provides a much stronger mechanistic assignment than any one measurement alone.
Distinguishing Intercalation from Nanovoid Pore Filling
The shared electrochemical signature
Both interlayer intercalation and nanovoid filling can occur near the low-voltage plateau.
Both may also exhibit reduced apparent diffusivity because sodium transport and local rearrangement become more constrained at high states of charge.
The structural difference
Interlayer intercalation should produce a measurable change in the average carbon-layer spacing, reflected by movement of the (002) peak.
Nanovoid filling can store sodium in internal cavities without producing the same systematic interlayer expansion. Thus, a plateau without clear (002) expansion should not automatically be labeled intercalation.
The role of TEM and complementary analysis
In-situ or ex-situ TEM can complement XRD by examining changes in local carbon-layer arrangement and nanovoid structure.
XRD provides an average structural response, whereas TEM can reveal local heterogeneity. Using both is particularly valuable because hard carbon is structurally disordered and may contain adsorption sites, galleries, and nanovoids simultaneously.
Understanding the Trade-offs
Voltage regions are not chemically pure
The boundaries near 1.0 V and 0.1 V are useful working assignments, not universal mechanistic cutoffs.
Different hard-carbon precursors, heat treatments, defect concentrations, pore structures, and electrode conditions can shift the voltage distribution and cause mechanisms to overlap.
Peak shifts can be subtle
Hard carbon has broad and disordered diffraction features. A small or broadened (002) shift may be difficult to quantify and may represent an average response rather than uniform expansion throughout every carbon domain.
GITT can be distorted by polarization
During intermittent-current measurements, inadequate relaxation, side reactions, electrode resistance, or phase transitions can distort the calculated diffusivity.
GITT trends should therefore be compared under consistent experimental conditions rather than interpreted from one isolated diffusivity value.
Ex-situ measurements can miss transient states
Removing and preparing electrodes may alter the sodium distribution or relax the structure.
When possible, in-situ or operando XRD provides stronger evidence because it tracks the structural response under electrochemical control, although careful cell design and calibration remain essential.
Making the Right Choice for Your Goal
Use a combined electrochemical–structural workflow rather than assigning mechanisms from voltage alone.
- If your primary focus is identifying surface or defect adsorption: Look for sloping-region capacity, relatively high GITT-derived diffusivity, broad dQ/dV response, and little or no (002) interlayer expansion.
- If your primary focus is proving interlayer intercalation: Correlate the low-voltage plateau and reduced apparent diffusivity with a reversible shift of the (002) XRD peak toward lower angle.
- If your primary focus is separating intercalation from pore filling: Use in-situ or ex-situ XRD together with TEM, because both mechanisms can produce low-voltage plateau capacity but only interlayer insertion should systematically expand the carbon galleries.
- If your primary focus is obtaining defensible mechanistic conclusions: Test multiple states of charge with GITT, dQ/dV, and structural characterization in the same cell system and under matched cycling conditions.
The most defensible conclusion comes from matching each electrochemical feature to its kinetic and structural signature, rather than treating the voltage profile as mechanism-specific by itself.
Summary Table:
| Feature | Adsorption | Interlayer Intercalation |
|---|---|---|
| Voltage region | Sloping above ~0.1 V vs Na/Na+ | Plateau below ~0.1 V |
| GITT apparent diffusivity | Higher | Lower |
| dQ/dV profile | Broad features | Sharp feature at low voltage |
| XRD (002) peak | Minimal shift | Shift to lower angle (expansion) |
| Mechanism | Surface/defect binding | Gallery insertion |
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