Fundamental investigations on the sodium-ion transport properties of mixed polyanion solid-state battery electrolytes

Abstract

Lithium and sodium (Na) mixed polyanion solid electrolytes for all-solid-state batteries display some of the highest ionic conductivities reported to date. However, the effect of polyanion mixing on the ion-transport properties is still not fully understood. Here, we focus on Na_1+xZr₂Si_xP_3-xO₁₂ (0 ≤ x ≤ 3) NASICON electrolyte to elucidate the role of polyanion mixing on the Na-ion transport properties. Although NASICON is a widely investigated system, transport properties derived from experiments or theory vary by orders of magnitude. We use more than 2000 distinct ab initio-based kinetic Monte Carlo simulations to map the compositional space of NASICON over various time ranges, spatial resolutions and temperatures. Via electrochemical impedance spectroscopy measurements on samples with different sodium content, we find that the highest ionic conductivity (i.e., about 0.165 S cm^-1 at 473 K) is experimentally achieved in Na_3.4Zr₂Si_2.4P_0.6O₁₂, in line with simulations (i.e., about 0.170 S cm^-1 at 473 K). The theoretical studies indicate that doped NASICON compounds (especially those with a silicon content x ≥ 2.4) can improve the Na-ion mobility compared to undoped NASICON compositions.

Fig. 1. Characteristics of sodium-ion transport in NASICON.

Structural models of Na_1+xZr₂Si_xP_3−xO₁₂ (a–d) and Na-ion migration barriers (e). In (a–d), the Na(1) sites are indicated by silver spheres, the Na(2) by orange spheres, the (Si/P)O₄ groups by red tetrahedra, Si/P atoms by red spheres, and ZrO₆ units by blue octahedra. b and c depict the local environment of Na(1), with each Na(1) surrounded by six neighboring Na(2) atoms (orange spheres) and six Si/P (red spheres) atoms. For simplicity, O and Zr atoms are not shown in (b–d). Each silver hexagonal prism in (b) or (c) represents the first coordination shell of a Na(1) site. Panel (d) is the migration unit used to study Na-ion migration in NASICON, and Na must hop across several different migration units to ensure Na diffusion. Red triangles in (d) indicate the bottlenecks caused by Si/PO₄ tetrahedra (oxygen atoms are not shown). (e) shows the averaged kinetically resolved activation (KRA) barriers for Na(2)⟷Na(1) hops, with varying Na(2) site occupation and Si/P content per migration unit. The barriers were extracted from a local cluster expansion model, which was fitted to the calculated nudged elastic band (NEB) barriers (Supplementary Table 1). The diagonal line in (e) shows locally charge neutral Si/P configurations. The computed NEB barriers used to generate the heatmap in (e) are available in Supplementary Fig. 1, Supplementary Fig. 2, and Supplementary Fig. 3.

Fig. 2. Computed Na-ion transport properties of Na_1+xZr₂Si_xP_3−xO₁₂ bulk based on kinetic Monte Carlo simulations.

Calculated Na⁺ diffusivity (a), conductivity (b), Haven’s ratio (c) and averaged correlation factor (d) of Na_1+xZr₂Si_xP_3−xO₁₂ at several temperatures: 373 (dark blue circles), 473 (orange squares) and 573 (red triangles) K, respectively. In panel (b), the computed ionic conductivities are compared with the experimental values of this work (Supplementary Fig. 6) at selected temperatures. Experimental values in (b) from this work are depicted with light blue (373 K), yellow (473 K), and red (573 K) crosses belonging to the same Na_1+xZr₂Si_xP_3−xO₁₂ compositions but of pellets with different compacities (>70 and >90%, see legend). An exhaustive comparison with our and previous experimental values of ionic conductivities is shown in Supplementary Fig. 6. The gray band in panel (b) shows the interval of confidence of our predictions at 573 K, which is lower in magnitude than the variance of Na-ion conductivities observed experimentally (Supplementary Fig. 6).

Fig. 3. Sodium site occupancies as a function of Na content.

Panel (a) shows the average Na site occupancy at the Na(1) site (blue circles) and the Na(2) site (blue triangles) from the kMC simulations at 443 K; they are compared with previous Grand Canonical Monte Carlo simulations (red circles and triangles) at the same temperature, and existing experimental data (in orange circle and triangles). Dashed lines are used as guide for the eye. Panel b shows $\mathrm{N}\left(\mathrm{N}{\mathrm{a}}^{\mathrm{+}}\right)\times \mathrm{N}\left(\mathrm{Vacancy}\right)$ (solid blue curve, per f.u.) at 443 K from kMC simulations. The contributions to $\mathrm{N}\left(\mathrm{N}{\mathrm{a}}^{\mathrm{+}}\right)\times \mathrm{N}\left(\mathrm{Vacancy}\right)$ from individual sodium sites, Na(1) and Na(2) are shown as blue dashed lines. In panel (b), the shaded regions mark areas where Na-ion conductivity is highly (red) or slightly (blue) impacted by the charge carrier concentration.

Fig. 4. Powder X-ray diffraction results for selected NASICON compounds at 298 K and their ionic conductivities measured using pellets.

In panel a, powder X-Ray diffraction patterns (dark blue, orange, and red circles) and Rietveld refinements (solid lines in cyan, dark brown and dark red) for Na_1+xZr₂Si_xP_3−xO₁₂ (x = 1.5, 2.0, and 2.4) are shown. b Arrhenius plots from electrochemical impedance measurements of three samples (x = 1.5 in dark blue, x = 2.0 in orange, x = 2.4 in red). Complex impedance plots (i.e., Nyquist plots) are shown in Supplementary Fig. 10, while Supplementary Fig. 11 shows the total, grain boundary, and bulk conductivities of the NASICON samples.

Fig. 5. Sodium hopping frequencies in NASICON materials.

Heatmap representation of the frequency (in Hz) of Na-ion migration from selected kMC simulation supercells (8×8×8 of the primitive cell, including 1024 migration units) at Na contents of x = 0.3, 2.4 and 2.97. The temperature in all panels is 573 K. Each colored hexagonal prism represents a migration unit, as exemplified in Fig. 1d. The hopping frequency of each migration unit is taken by averaging the probability of the six possible migrations of Na⁺ between the central Na(1) site and the six Na(2) sites in each unit. The top and bottom panels show views along the c-axis from above and below the supercells.