Revealing the interfacial kinetic mechanisms in high-entropy doped Na$_3$V$_2$(PO$_4$)$_3$ through electrochemical investigation and distribution of relaxation times

We designed a high-entropy doped NASICON cathode, Na$3$V${1.9}$(CrMoAlZrNi)$_{0.1}$(PO$_4$)$_3$ and investigate its electrochemical performance for sodium-ion batteries (SIBs) to understand the diffusion mechanism including distribution of relaxation times analysis of interfacial kinetics. This trace doping induces high-entropy mixing at the vanadium site, tuning the lattice and enhancing specific capacity, activating V$^{4+}$/V$^{5+}$ redox couple 3.95V. Interestingly, it delivers a reversible capacity of 119mAhg$^{-1}$ at 0.1C, and demonstrate excellent stability of 68% after 1000 cycles at 10C. The calculated diffusion coefficient values are found within the range of (10^{-11})–(10^{-13}\mathrm{cm^2,s^{-1}}). The systematic investigation of temperature and voltage-dependent impedance data using the distribution of relaxation times provides deeper insights into the underlying charge-transfer and transport processes. The full cells with hard carbon delivers 326Whkg$^{-1}$ (with respect to cathode mass) at $\approx$3.2V and retained $\sim$79% capacity after 100 cycles at 2C. Our study opens new avenues for developing high-entropy doped cathodes for enhanced structural stability, extended redox activity, and optimized electrochemical kinetics for practical implementation of SIBs.

💡 Research Summary

In this work, the authors introduce a high‑entropy (HE) doped NASICON cathode, Na₃V₁.₉(CrMoAlZrNi)₀.₁(PO₄)₃ (denoted NVP‑HE), and comprehensively investigate its structural, electrochemical, and interfacial kinetic properties for sodium‑ion batteries (SIBs). The material is synthesized via a sol‑gel route followed by a two‑step calcination (350 °C/4 h and 800 °C/8 h) under Ar/5 % H₂, with 5 wt % carbon nanotubes (CNTs) added to improve electronic conductivity. A reference Na₃V₂(PO₄)₃ (NVP) is prepared under identical conditions for comparison.

Structural Characterization
X‑ray diffraction with Rietveld refinement confirms that NVP‑HE retains the rhombohedral R‑3c NASICON framework (a = b = 8.7369 Å, c = 21.8378 Å). The (012) reflection shifts to lower 2θ by ~0.18°, indicating a modest lattice expansion caused by the trace HE dopants. Bond‑valence site energy (BVSE) calculations reveal three‑dimensional Na⁺ migration pathways with an activation barrier of 0.465 eV, slightly lower than the 0.483 eV for pristine NVP, suggesting widened diffusion channels. Raman spectroscopy shows characteristic PO₄³⁻ modes and carbon‑related D₁, D₂, and G bands; the I_D₁/I_G ratio of 0.88 points to a moderate degree of disorder in the carbon coating. High‑resolution TEM images display a uniform ~7 nm carbon layer and embedded CNTs, while selected‑area electron diffraction confirms the crystallinity of the NASICON phase. Elemental mapping (EDS) and ICP‑MS verify homogeneous distribution of Cr, Mo, Al, Zr, and Ni at the intended 0.02 mol % each. XPS analysis detects V⁴⁺/V⁵⁺ coexistence, Mo⁶⁺/Mo⁴⁺, Cr³⁺/Cr²⁺, and the expected oxidation states of the other dopants, confirming successful incorporation without secondary phases.

Electrochemical Performance
In CR2032 half‑cells (Na metal counter/reference, 1 M NaPF₆ in PC + 2 wt % FEC), NVP‑HE delivers an initial discharge capacity of 119 mAh g⁻¹ at 0.1 C (2.0–4.3 V). Two voltage plateaus are observed at ~3.4 V (V³⁺/V⁴⁺) and ~3.95 V (V⁴⁺/V⁵⁺), the latter being activated by the high‑entropy dopants. Rate capability is impressive: capacities of 119, 106, 92, 78, and 55 mAh g⁻¹ are retained from 0.1 C to 5 C, with a voltage hysteresis of only ~0.05 V, indicating low polarization. Long‑term cycling shows 93 % capacity retention after 100 cycles at 2 C and 68 % after 1000 cycles at 10 C (56 mAh g⁻¹). Galvanostatic intermittent titration technique (GITT) yields Na⁺ diffusion coefficients ranging from 10⁻¹¹ to 10⁻¹³ cm² s⁻¹ throughout the charge/discharge window, comparable to or slightly better than undoped NVP.

Interfacial Kinetics via DR‑T
Electrochemical impedance spectroscopy (EIS) is performed from 0.01 Hz to 100 kHz with a 10 mV AC perturbation at open‑circuit potential. Kramers‑Kronig consistency is verified (residuals < 1 %). The distribution of relaxation times (DR‑T) is extracted using Tikhonov regularization (λ = 0.0001) and a radial basis function (FWHM = 0.5). The DR‑T spectra display distinct peaks: a high‑frequency peak (~10⁻³ s) attributed to charge‑transfer resistance (R_ct) at the electrode/electrolyte interface, and a low‑frequency peak (~10⁻¹ s) corresponding to Warburg‑type diffusion of Na⁺ within the bulk. Temperature‑dependent DR‑T shows exponential reduction of R_ct with increasing temperature, confirming thermally activated charge transfer, while the diffusion peak shifts modestly, reflecting the modest temperature dependence of Na⁺ mobility. Voltage‑dependent DR‑T reveals that during the V⁴⁺/V⁵⁺ plateau the charge‑transfer resistance is slightly higher, consistent with the higher redox potential, yet still remains below 30 Ω cm², underscoring the beneficial effect of the HE dopants and carbon network.

Full‑Cell Demonstration
A full cell is assembled using hard carbon (HC) as the anode (≈9 µm particles) and NVP‑HE as the cathode, with a mass ratio optimized for a balanced capacity. The cell delivers an initial discharge capacity of 106 mAh g⁻¹ (based on cathode mass) at an average voltage of 3.2 V, corresponding to an energy density of 326 Wh kg⁻¹ (cathode‑based). At 2 C, the full cell retains ~79 % of its capacity after 100 cycles, with minimal voltage decay, demonstrating that the high‑entropy cathode can sustain practical power demands while maintaining high energy.

Mechanistic Insights and Significance
The trace high‑entropy dopants (Cr, Mo, Al, Zr, Ni) increase configurational entropy, suppress phase separation, and act as “structural pillars” that stabilize the NASICON lattice during deep sodiation/desodiation. The slight V–O bond elongation widens the Na⁺ bottleneck, while the shortened P–O bonds reinforce the PO₄ framework, together lowering the migration barrier. The carbon coating and CNT network provide a percolating electronic pathway, reducing charge‑transfer resistance as quantified by DR‑T. Importantly, the DR‑T analysis separates interfacial charge transfer from bulk diffusion on distinct time scales, offering a powerful diagnostic tool for future cathode engineering.

Conclusions
The study demonstrates that high‑entropy trace doping of NASICON Na₃V₂(PO₄)₃ simultaneously enhances structural robustness, activates the high‑potential V⁴⁺/V⁵⁺ redox couple, and improves Na⁺ transport kinetics. The combination of conventional electrochemical techniques with distribution of relaxation times analysis yields a comprehensive picture of interfacial processes, guiding rational design of next‑generation SIB cathodes. The reported energy density (326 Wh kg⁻¹) and long‑term cycling stability position NVP‑HE as a promising candidate for practical sodium‑ion battery applications.