Na⁺/vacancy disordering promises high-rate Na-ion batteries

We demonstrate that Na⁺/vacancy disordering of P2-type layered cathodes ensures both fast Na mobility and a low Na diffusion barrier.

Abstract

As one of the most fascinating cathode candidates for Na-ion batteries (NIBs), P2-type Na layered oxides usually exhibit various single-phase domains accompanied by different Na⁺/vacancy-ordered superstructures, depending on the Na concentration when explored in a limited electrochemical window. Therefore, their Na⁺ kinetics and cycling stability at high rates are subjected to these superstructures, incurring obvious voltage plateaus in the electrochemical profiles and insufficient battery performance as cathode materials for NIBs. We show that this problem can be effectively diminished by reasonable structure modulation to construct a completely disordered arrangement of Na-vacancy within Na layers. The combined analysis of scanning transmission electron microscopy, ex situ x-ray absorption spectroscopy, and operando x-ray diffraction experiments, coupled with density functional theory calculations, reveals that Na⁺/vacancy disordering between the transition metal oxide slabs ensures both fast Na mobility (10⁻¹⁰ to 10⁻⁹ cm² s⁻¹) and a low Na diffusion barrier (170 meV) in P2-type compounds. As a consequence, the designed P2-Na_2/3Ni_1/3Mn_1/3Ti_1/3O₂ displays extra-long cycle life (83.9% capacity retention after 500 cycles at 1 C) and unprecedented rate capability (77.5% of the initial capacity at a high rate of 20 C). These findings open up a new route to precisely design high-rate cathode materials for rechargeable NIBs.

INTRODUCTION

Na-ion batteries (NIBs) are enjoying renewed interest as a viable alternative to Li-ion batteries especially for future large-scale energy storage in light of the low cost, nontoxicity, and large abundance of Na resources (1–3). Among the cathode candidates, Na_xTMO₂ layered oxides (where TM refers to transition metal) have attracted intensive attention due to their high capacities and feasible synthesis (4, 5). Depending on the atomic environment of Na (prismatic or octahedral) and stacking sequence of O layers (ABBA or ABCABC), they can be commonly categorized into P2 and O3 phases (6). In contrast with O3 counterparts, P2-type layered frameworks own better structure stability during the sodium extraction process owing to direct Na-ion diffusion and more open prismatic paths within TMO₂ slabs. However, they usually undergo undesired P2-O2 phase transition in high-voltage regions, which leads to large volume change and rapid capacity decay (7, 8). Recently, this problem has been significantly mitigated by doping inactive metal (Li, Mg, Cu, or Zn) in the TM layers, with the aim of eliminating phase transformations during cycling and extending the solid-solution zone over a wider Na intercalation range, although at the expense of some capacity (9–13). Apart from the issue of phase transition, there are three kinds of ordering in P2-type oxides containing more than one TM species: Na⁺/vacancy ordering in the Na layer, charge ordering, and TM1/TM2 cationic ordering on the TM lattice (14–16). It is well acknowledged that Na⁺/vacancy ordering, which is closely related to the Na⁺ ion mobility in the interlayer, occurs frequently when the Fermi levels (ca. redox potentials) between the TM1 and TM2 species are similar (17–21). In this manner, most P2-type oxides differ from one another in commensurable or incommensurable Na⁺/vacancy-ordered superstructures between the TMO₂ slabs within single-phase domains upon Na⁺ extraction/insertion (22, 23). Because the presence of ordered intermediate phases caused by Na ordering rearrangement in these compounds affects both voltage plateaus in electrochemical curves and Na diffusion path, understanding intercalation ordering is indispensable for tailoring the material to achievable electrochemical applications.

In this context, our interest focused on the electrochemical (de)intercalation of sodium in P2-Na_2/3Ni_1/3Mn_2/3O₂ (NaNM), which has a relatively high operating voltage based on Ni²⁺/³⁺/⁴⁺ redox reactions and a highly symmetric crystal structure free from the Jahn-Teller active center (24). This material exhibits a complete reversibility and single-phase region between the Na_2/3Ni_1/3Mn_2/3O₂ and Na_1/3Ni_1/3Mn_2/3O₂ compositions within a lower voltage than 4.2 V (25). There are two obvious voltage plateaus at 3.3 and 3.7 V, which might imply the rearrangement of different Na⁺/vacancy ordering across the Na extraction/insertion range, thus making it possible to embark on the effects of TM mixing on the Na ordering mechanism using it as a model system. Considering the same valence, smaller ionic radii ratio, and substantial difference in the Fermi level between Ti⁴⁺ (60.5 pm) and Mn⁴⁺ (53 pm), substituting a number of Mn⁴⁺ with Ti⁴⁺ in TMO₂ slabs might be effective for suppressing cationic ordering, charge ordering within TMO₂ slabs, and Na-vacancy ordering in Na layers.

Hence, Ti-free P2-NaNM and Ni/Mn/Ti-mixed P2-Na_2/3Ni_1/3Mn_1/3Ti_1/3O₂ (NaNMT) compounds were synthesized to present a comprehensive study on the influence of Na⁺/vacancy ordering on their electrochemical properties, structural evolution, and Na⁺ kinetics toward Na (de)intercalation. The substitution of Ti for Mn in the P2-NaNM crystal framework enlarges the distance of Na layers with the contraction of the TMO₆ octahedron; thus, electron delocalization is limited, and charge coupled to Na⁺/vacancy ordering is thoroughly broken. Consequently, the two voltage plateaus in the charge/discharge profiles of P2-NaNM are fully eliminated without affecting the capacity, manifesting characteristic sloping curves for complete solid-solution reaction. The Na-vacancy–disordered P2-NaNMT material exhibits a specific capacity of 88 mA·hour g⁻¹ with a high average voltage of ca. 3.5 V versus Na⁺/Na, excellent cycle performance (ca. 83.9% capacity retention at 1 C after 500 cycles), a very small decrease in the volume (0.64%), and outstanding rate capability (ca. 87.9 and 77.5% capacity retention at high rates of 10 and 20 C, respectively). Via Na⁺ kinetics analysis using an electrochemical characterization technique [galvanostatic intermittent titration technique (GITT)], the nature of rate performance, together with the use of density functional theory (DFT) calculations, both experimental and theoretical information are provided to reveal the relationship between Na-vacancy ordering/disordering mechanisms and Na diffusion properties. These results indicate that Na⁺/vacancy disordering increases the degree of freedom of Na⁺ upon cycling, thus ensuring fast Na-ion mobility (average, 10⁻¹⁰ cm² s⁻¹) and a low diffusion barrier (170 meV) in the interlayer, which successfully establish the linkage between Na-vacancy disordering and high-rate cathode materials for NIBs.

RESULTS

Crystal structures of P2-NaNM and P2-NaNMT

The P2-NaNM and P2-NaNMT compounds were synthesized by a simple solid-state reaction. Figure 1 (A and B) shows x-ray diffraction (XRD) patterns and Rietveld refinement of P2-NaNM and P2-NaNMT samples, and all the diffraction lines can be indexed to a hexagonal symmetry with a space group of P6₃/mmc. Two superstructure peaks at ~27.2° and ~28.3° are clearly observed (fig. S1), which originate from the in-plane Na-vacancy ordering in P2-NaNM (26) and cannot be resolved using the classical refinement model. These superstructure peaks vanished in this region for P2-NaNMT, suggesting successful suppression of Na⁺/vacancy ordering by Ni/Mn/Ti mixing. The superstructure manifests a thermodynamic reversible characteristic (27), which could be eliminated by thermal treatment and then recovered after cooling to room temperature (fig. S2). According to the refined crystallographic data listed in tables S1 and S2, the Ni, Mn, and Ti ions occupy the octahedral 2a Wyckoff sites, indicating a uniform incorporation of Ti⁴⁺ into the TM oxide layer. Note that less Na ions occupy the Na_f sites, and more Na ions occupy the Na_e sites in P2-NaNMT, implying the modification of the Na_f/Na_e site energies. Comparing the lattice parameters and structural information of P2-NaNMT [a = b = 2.9253(7) Å, c = 11.133(2) Å] with that of P2-NaNM [a = b = 2.8859(1) Å, c = 11.146(5) Å], Ti substitution leads to the contraction of TMO₂ layers and expansion of Na layer spacing associated with the increase in interaction between TM and O and reduction of the binding energy between Na and O (table S3). Thus, electronic delocalization, charge ordering, and Na⁺/vacancy ordering are effectively refrained because of the substantial difference in the Fermi level between Ti⁴⁺ and Mn⁴⁺. As plotted in Fig. 1C, the crystal structures of typical P2-NaNMT are composed of alternate TMO₂ (TM = Ni, Mn, and Ti) layers and Na layers with ABBA oxygen stacking patterns. Na ions occupy two kinds of trigonal prismatic sites, either sharing edges with the six TMO₆ octahedrons (Na_e, 2d Wyckoff sites) or sharing two faces with the lower and upper TMO₆ octahedrons (Na_f, 2b Wyckoff sites).

Fig. 1. Structure of P2-NaNM and P2-NaNMT materials.

(A and B) XRD and Rietveld plots of (A) P2-NaNM and (B) P2-NaNMT samples. a.u., arbitrary units. (C) P2-type crystal structure viewed along the a axis (left) and c axis (right). (D and E) (D) ABF and (E) HAADF-STEM image of P2-NaNMT at the [010] zone axis. (F and G) (F) ABF and (G) HAADF-STEM image of P2-NaNMT at the [001] zone axis. (H) Transmission electron microscopy (TEM) image and EDS maps of P2-NaNMT samples.

Detailed atomic-scale structural information on P2-NaNMT compounds was confirmed by aberration-corrected scanning transmission electron microscopy (STEM) with annular bright-field (ABF) and high-angle annular dark-field (HAADF) techniques. The positions of the TM (Ni, Mn, and Ti) columns are revealed by the dark-dot contrast in the ABF-STEM images and bright-dot contrast in the HAADF-STEM images. The faint dark-dot contrast with the interlayer positions in the ABF-STEM images corresponds to the light element Na and O columns in the layered structure (28, 29). The ABF-STEM observations of octahedral TMO₂ at the [010] zone axis are highly consistent with the P2 atomic model, as inserted in Fig. 1D for convenient visualization. The Na atoms are clamped by layered TMO₂, the O columns follow a distinct ABBA-stacking mode, and every two layers of TMO₂ display a mirroring symmetry. The distance of the adjacent layer d_c in HAADF-STEM images (Fig. 1E) is measured to be ca. 0.56 nm, which is consistent with the interslab distance by refined crystallographic data. The ABF-STEM images (Fig. 1F) at the [001] zone axis demonstrate the arrangement of the TM atoms with a hexagonal symmetry. In addition, the distance of the adjacent TM atoms in corresponding HAADF-STEM images is ca. 0.29 nm (Fig. 1G), which matches well with the value of cell parameter a. The particle size of the samples is about 1 to 5 μm with plate-like morphology (fig. S3). The width of 2.09 Å between neighboring lattice fringes revealed by high-resolution transmission electron microscopy (HRTEM) image corresponds to the (103) planes of P2-NaNMT sample (fig. S4). Energy-dispersive spectroscopy (EDS) mapping, as shown in Fig. 1H, demonstrates uniform Na, Ni, Mn, Ti, and O element distribution in the P2-NaNMT particle.

Electrochemical performance

The electrochemical properties of P2-NaNM and P2-NaNMT were examined in a Na half-cell between 2.5 and 4.15 V at the current density of 0.1 C (1 C = 173 mA g⁻¹). As shown in Fig. 2 (A and B), the galvanostatic charge/discharge profiles of P2-NaNM obviously involve two voltage plateaus at 3.3 and 3.7 V, respectively, suggesting different Na-vacancy ordering arrangements between neighboring TMO₂ slabs. In contrast, the typical charge/discharge curves of P2-NaNMT become completely sloping lines, and two voltage plateaus totally disappeared without affecting the capacity, which results from a solid-solution reaction without a Na⁺/vacancy-ordered superstructure, as discussed later. Disordered P2-NaNMT displays a reversible capacity of 88 mA·hour g⁻¹ with a high average voltage of 3.5 V, smooth charge/discharge profiles, and little polarization (Fig. 2B). There is no obvious capacity decay and voltage drop over extended cycles (Fig. 2C), showing its great potential for future practical application. P2-NaNMT shows the same cycling performance as P2-NaNM (94.6% versus 95.2%) at a low rate of 0.1 C after 100 cycles (fig. S5). However, as compared in the rate performance with a loading mass of 3 to 4 mg cm⁻² in Fig. 2D, the P2-NaNMT electrode can still deliver ca. 87.9 and 77.5% of its initial capacity even cycled at 10 and 20 C, respectively, whereas the P2-NaNM electrode is approaching 0 mA·hour g⁻¹. It can be seen that Na-vacancy disordering favors charge/discharge capability at high current density. Therefore, when cycled at a high rate of 1 C, the P2-NaNMT cathode demonstrates remarkable improvement in its cycle stability, as shown in Fig. 2E, delivering an outstanding capacity retention of 83.9% even after 500 cycles with a high Coulombic efficiency of >99% due to the slight side reactions occurring between electrode materials and electrolyte during cycling. By comparison, the P2-NaNM electrode exhibits very fast capacity decay from 80 mA·hour g⁻¹ in the first cycle to 3.5 mA·hour g⁻¹ after 500 cycles, corresponding to only 4.4% capacity retention. In addition, the morphology of the P2-NaNMT cathode is well maintained, whereas P2-NaNM shows pulverization after long cycling (fig. S6). Moreover, the P2-NaNMT cathode also exhibits obvious improvement in its cycling performance in a wider potential range of 2.5 to 4.3 V due to the suppressed P2-O2 phase transition at high voltage regions, delivering a capacity retention of 83.4% at 0.1 C after 100 cycles (figs. S7 and S8). In total, Ti incorporation into P2-NaNM could suppress Na⁺/vacancy ordering, smooth the charge/discharge curves, and extend solid-solution zone over a wider compositional range, so faster ionic transport between the interlayers is achieved under Na⁺ (de)intercalation, resulting in better battery performance at high rates.

Fig. 2. Electrochemical performance of P2-NaNM and P2-NaNMT compounds in Na cells.

(A and B) Typical charge/discharge profiles of (A) P2-NaNM and (B) P2-NaNMT between 2.5 and 4.15 V at a rate of 0.1 C. (C) Charge/discharge profiles of P2-NaNMT during the 2nd, 5th, 10th, 20th, 50th, and 100th cycles at 0.1 C, demonstrating no obvious decay in the voltage and capacity. (D) Rate performance comparison of P2-NaNM and P2-NaNMT samples at different rates. (E) Capacity retention with Coulombic efficiency of P2-NaNM and P2-NaNMT over 500 cycles cycled at 1 C.

Charge compensation mechanism

The cyclic voltammograms (CVs) in Na half-cells were tested at a scan rate of 0.1 mV s⁻¹, as shown in fig. S9. Consistent with the voltage plateaus in charge/discharge curves, the P2-NaNM electrode shows two pairs of reversible redox peaks located at 3.39/3.23 and 3.72/3.52 V, respectively, which arise from multiple Na-vacancy ordering in sodium layers. In marked contrast to the P2-NaNM electrode, the observed CV behavior for P2-NaNMT electrode resembles that of capacitors with only one large and broad oxidation/reduction peak, further demonstrating that the Na⁺/vacancy ordering is successfully prevented in the Na intercalation process after Ni/Mn/Ti mixing into the crystal lattice. Ex situ x-ray absorption spectroscopy (XAS) (Fig. 3), combined with x-ray photoelectron spectroscopy (XPS) (fig. S10), was performed to elucidate the charge compensation mechanism of Na_1−xNMT upon Na⁺ extraction/insertion. As displayed in the x-ray absorption near-edge structure (XANES) spectra at Ni and Mn K-edges, the Ni K-edge absorption spectrum (Fig. 3A) shows apparent shifts toward the higher-energy region (~2 eV), demonstrating the oxidation of Ni²⁺ to Ni³⁺ as charge increases from 2.5 to 4.15 V (30, 31). In contrast, the Mn K-edges (Fig. 3B) show no apparent changes, indicating that the tetravalent manganese ions are electrochemically inactive. So, it indicates that the Ni²⁺/Ni³⁺ redox couple is responsible for the charge compensation mechanism (1 e⁻ transfer) within the explored 2.5 to 4.15 V voltage window, which is highly consistent with CV results. The interatomic distance information of Na_1−xNMT was also revealed by extended x-ray absorption fine structure (EXAFS) spectra at the Ni and Mn K-edges (Fig. 3, C and D). In the first TM-O coordination shell of Na_1−xNMT, lowered Fourier transform magnitude and shortened interatomic distance are observed at the Ni K-edge, whereas the Mn K-edge shows almost no change upon Na removal from the crystal lattice. In this region, the electrochemically active nickel ions compensate for the charge balance, and the manganese ions always maintain the +4 state (32), which are consistent with the ex situ XANES results. In the second TM-TM coordination shells, both Ni and Mn K-edges confirm a similar shift of the decreased in-plane interatomic distances after electrochemical oxidation, which is in good agreement with the change of a_hex lattice parameters upon Na ion extraction by in situ XRD observation in the latter parts.

Fig. 3. Charge compensation mechanism of P2-Na_2/3−xNMT upon Na⁺ extraction/insertion.

(A and B) Ex situ XANES spectra at the (A) Ni K-edge and (B) Mn K-edge of Na_2/3−xNMT electrodes collected at different charge/discharge states. (C and D) Corresponding ex situ EXAFS spectra at the (C) Ni K-edge and (D) Mn K-edge of Na_2/3−xNMT electrodes collected at different charge/discharge states. FT, Fourier transform.

Structural evolution and reaction mechanism

To understand the structural evolution during the charge/discharge process, in situ XRD experiments were carried out, as shown in Fig. 4. As Na⁺ is being extracted, the (002) and (004) peaks of P2-NaNM consecutively shift to a lower angle, whereas (100), (102), and (103) diffraction lines shift toward a higher angle (Fig. 4A). It indicates that the c axis is expanding, and the ab plane is contracting because of increased electrostatic repulsion between adjacent oxygen layers and smaller ionic radius, respectively, by Ni²⁺→Ni³⁺ (33). Noticing that no additional diffraction lines beyond the P2 structure are detected, the shape of the (004) peak becomes an asymmetry with a broad feature, which could be attributed to the rearrangement of different in-plane Na orderings (34). These observations suggest that the Na extraction in P2-NaNM is actually a quasi-solid–solution reaction, which matches well with the voltage plateaus in charge/discharge curves. Similar structure evolution was observed for P2-NaNMT except that the (004) peaks only show peak position shift without any shape change (Fig. 4B), indicating an absolute solid-solution behavior consistent with the sloping electrochemical curves. Moreover, these peak shifts are highly reversible after sodium is inserted back to the crystal lattice. The detailed change of the lattice parameter during the charge/discharge process is shown in fig. S11. In contrast with P2-NaNM, the lattice parameters (a and c), especially unit cell volume of P2-NaNMT, all change linearly with the slope of the charge/discharge curves, demonstrating sustainable structure evolution and complete single-phase reaction upon Na⁺ extraction and insertion. Furthermore, the unit cell volume change of P2-NaNMT before and after Na extraction is merely −0.64%, which is close to zero-strain characteristics and responsible for the excellent cycling stability cycled at 1 C over 500 cycles. Not only could a half substation of Ti for Mn in P2-NaNM eliminate in-plane orderings within sodium layers but it also could suppress the frequent P2-O2 phase transition at 4.2 V by preventing the TMO₂ slabs from gliding to form the O2 phase, as illustrated in fig. S12. It is evidenced that the O2 characteristic (002′) and (112′) peaks that are located at about 21° and 70° (24), respectively, disappeared in P2-Na_1−xNMT electrodes even charged to 4.3 V (fig. S13), resulting in an improved cycling performance in a wider potential range of 2.5 to 4.3 V.

Fig. 4. Crystal structural evolution under electrochemical Na⁺ (de)intercalation.

(A and B) In situ XRD patterns collected during the first charge/discharge of the (A) Na/Na_2/3−xNM and (B) Na/Na_2/3−xNMT cells under a current rate of 0.1 C between 2.5 and 4.15 V.

Combining in situ XRD results and electrochemical curves, there are two major intermediate phases in P2-Na_δNM at 3.5 and 4.0 V, which corresponds to the Na concentration of ¹/₂ and ¹/₃ with different in-plane ordering, respectively. Figure 5 (A and B) illustrates the two-dimensional (2D) in-plane Na ordering patterns with respect to the typical charge/discharge curves of P2-Na_δNM, which consist of Na_f connecting in a very intriguing pattern (25, 35–37). In “large zigzag” (LZZ) pattern for δ = ²/₃, Na_f sites form a zigzag pattern with distance 2|a_hex| between the nearest Na_f sites. When the concentration is reduced to ¹/₂, the ordering is converted from LZZ to rows in which Na orders alternate in one row of Na_f and two rows of Na_e in the plane. At δ = ¹/₃, either Na_f or Na_e arranges in rows within a single layer. It can be concluded that two voltage plateaus located at 3.3 and 3.7 V in P2-Na_δNM arise from the in-plane ordering rearrangement of LZZ-row-row (38, 39). As discussed above, there are two types of Na sites that are Na_f and Na_e in the P2 structure. The calculated total DFT energies (Fig. 5C) demonstrate that Ni/Mn/Ti mixing effectively decreases the site energy difference between Na_e and Na_f, thus suppressing the Na-vacancy ordering, which could refrain the formation of strongly ordered intermediate phases, and promote complete solid-solution behavior over a wider range of Na content. So, the Na⁺/vacancy ordering-disordering transition phenomenon in this system mainly originates from the different Na_e-Na_f site energy after Ti substitution into the lattice.

Fig. 5. 2D Na⁺/vacancy ordering-disordering transition mechanism.

(A) Typical charge/discharge profiles of P2-NaNM. The two voltage plateaus indicates the rearrangement of Na⁺/vacancy ordering. (B) In-plane Na⁺/vacancy orderings of Na_δNi_1/3Mn_2/3O₂ in the triangular lattice at δ = ²/₃, δ = ¹/₂, and δ = ¹/₃, respectively (empty red circles, Na⁺ on Na_e sites; solid blue circles, Na⁺ on Na_f sites; thick green lines, unit cell). (C) Calculated energy difference between the Na_e and Na_f site for P2-NaNM (purple background) and P2-NaNMT (blue background).

Na⁺ kinetics study

Owing to different Na-vacancy in-plane orderings at different Na contents in P2-NaNM, it can be assumed that such a fast self-arrangement upon charge/discharge might sacrifice Na-ion mobility. To verify this hypothesis, the apparent diffusion coefficients of Na⁺ of the two compounds were investigated by GITT (40, 41). The equilibrium voltage of P2-NaNMT shows a continuous change, confirming the single-phase reaction process during Na⁺ (de)intercalation between 2.5 and 4.15 V (fig. S14). Figure S15 compares the calculated Na diffusion coefficient (D_Na⁺) in P2-NaNM and P2-NaNMT samples based on the GITT curves. The Na-ion mobility in P2-NaNMT is increased by two orders of magnitude with diffusion coefficients ranging from 10⁻¹⁰ to 10⁻⁹ cm² s⁻¹, whereas P2-NaNM showed diffusion coefficients of 10⁻¹² to 10⁻¹¹ cm² s⁻¹ in the Na range of ²/₃ ≤ δ ≤ ¹/₃. Moreover, no jumps in the Na diffusion coefficient values are observed for P2-NaNMT, which could be attributed to Na-vacancy disordering in the compound and consistent with the sloping characteristic of the electrochemical curves. Noticeably, this fast diffusivity of Na ions in P2-NaNMT could accelerate its self-discharge as compared in fig. S16, which needs to be further mitigated. A lower charge transfer resistance (R_ct) at the electrode/electrolyte interface and faster Na⁺ diffusion associated with Warburg impedance (Z_w) are obtained for P2-NaNMT using an electrochemical impedance spectroscopy (EIS) technique (fig. S17), which provides another side evidence that Na disordering facilitates electronic and Na⁺ migration (42, 43).

Given that Na⁺ in P2-type layered structure occupies open trigonal prisms thus providing wide ionic transport channels, the presence of Na⁺/vacancy disordering will decrease the activation energy barrier for Na⁺ hops between adjacent prismatic sites and consequently enhance Na⁺ diffusion. First-principles molecular dynamics (FPMD) calculations were performed at temperatures ranging from 500 to 900 K to obtain Na⁺ ion transport property in this disordered P2-NaNMT. From the mean square displacements (MSDs) of Na⁺ for P2-Na_0.58NMT observed for all temperatures (fig. S18), the Na⁺ diffusion gets easier as the temperature increases. It is clearly seen that the Na⁺ migrates through 2D passages characterized by interconnected diffusion paths (Fig. 6A), which favors the fast ion mobility and excellent kinetic property. The corresponding top view of trajectories in single sodium layer suggests the pathways along ideal Na_f-Na_e-Na_f sites. The slope of MSD time curves is fitted to obtain the diffusion coefficient (D). According to the slope of Arrhenius plot in Fig. 6B, the calculated diffusion energy barrier (E_a) is a very low barrier of 0.17 eV, which is in good agreement with the GITT results. A summary of the diffusion coefficients and activation energies of the most common Na-based layered oxides studied in the literatures is compared in table S4. It is highlighted that both Na diffusion coefficients and computed activation energy of the P2-NaNMT correspond to the top level among TM layered oxides (44–52). In short, we may surmise that Ti substitution in P2-NaNM has two effects: (i) the suppression of Na-vacancy ordering, resulting in a wider range of complete solid-solution behavior, and (ii) the reduction of site energy difference between Na_e and Na_f and hence diffusion properties.

Fig. 6. Na⁺ kinetics of P2-NaNMT obtained by FPMD simulations.

(A) Trajectories of Na⁺ in P2-Na_0.57NMT simulated at a temperature of 800 K. The top view of each Na⁺ layer is given in the right panel. (B) Arrhenius plot of Na⁺ diffusion coefficients.

DISCUSSION

In summary, we have successfully constructed a fully disordered P2-NaNMT material on Na lattices over the studied range of Na concentrations (δ = ²/₃ to ¹/₃). Partial Ti substitution for Mn with compatible ionic radii and very different Fermi levels in P2-NaNM effectively refrains electron delocalization, hence charge ordering and Na⁺/vacancy ordering. As a result, a high Na⁺ mobility and low activation energy barriers are achieved in the Na interlayer, leading to smooth electrochemistry without any voltage plateau, outstanding cycling stability (83.9% capacity retention after 500 cycles at 1 C), and excellent rate capability (77.5% capacity retention at 20 C) in NIBs. Therefore, reasonable ionic substitution by inactive dopants, such as Li⁺, Ti⁴⁺, Mg²⁺, and Zn²⁺, with no d electrons, might be a sensible strategy to modulate the composition of the metal lattice so as to avoid the Na-vacancy ordering for optimal Na diffusion. Our study offers new insights into the rational design of high-rate layered cathode materials and also pushes the practical application of NIBs as a decisive step forward.

MATERIALS AND METHODS

Synthesis

The P2-NaNM and P2-NaNMT samples were synthesized by a solid-state reaction method from stoichiometric mixtures of Na₂CO₃ (99.5%; 5 mole percent access; Alfa Aesar), NiO (99%; Alfa Aesar), Mn₂O₃ (98%; Alfa Aesar), and TiO₂ (anatase, 99.6%; Alfa Aesar). The mixtures were ground and pressed into pellets under 20 MPa, and then the pellets were calcined at 950°C in air for 15 hours, cooled to room temperature, and stored in an argon-filled glove box until use.

Characterizations

X-ray powder diffraction was done in a Bruker D8 Advance diffractometer with Cu Kα radiation (λ = 1.5418 Å). A General Structure Analysis System program was used to perform Rietveld refinement. For the in situ XRD experiment, a specially designed Swagelok cell was equipped with an aluminum window for x-ray penetration. The morphology and microstructure were characterized by scanning electron microscopy (SEM; JEOL JSM-6701F). The HRTEM image and EDS maps were examined by TEM (JEM 2100F). ABF and HAADF imaging were executed using a JEOL ARM200F (JEOL) STEM operated at 200 kV with a cold field-emission gun and double hexapole Cs correctors (CEOS GmbH). XPS measurements were carried out with a ESCALAB 250Xi spectrometer (Thermo Fisher Scientific) using an Al Kα achromatic x-ray source. XAS measurements were done at beamline BL14W1 of the Shanghai Synchrotron Radiation Facility (SSRF), China, operating with a Si(111) double-crystal monochromator.

Electrochemistry

The working electrode was prepared by mixing 75% active material, 15% Super P carbon, and 10% polyvinylidene difluoride (Sigma-Aldrich) binder onto aluminum foil, followed by drying at 80°C in vacuum overnight. The loading mass of active material was 3 to 4 mg cm⁻². The electrolyte was 1 M NaPF₆ in ethylene carbonate and diethyl carbonate (1:1 in volume; 5% fluoroethylene carbonate). Sodium foil and porous glass fiber (GF/D) were used as the counter electrode and separator, respectively. Coin cells (CR2032) were assembled in an argon-filled glove box (H₂O and O₂ < 0.1 parts per million). An Arbin battery test system was used to perform discharge and charge measurements over a voltage range of 2.5 to 4.15 V and 2.5 to 4.3 V at a rate of 0.1 C at 25°C. CV measurements were performed on an Autolab PG302N electrochemical workstation at a scan rate of 0.1 mV s⁻¹. For the GITT tests, the batteries were charged at a current of 17 mA g ⁻¹ for 30 min, followed by open-circuit relaxation for 10 hours.

$$\mathit{D}=\frac{4}{\mathrm{\pi }}{\left(\frac{\mathit{i}{\mathit{V}}_{\mathrm{m}}}{{\mathit{z}}_{\mathit{A}}\mathit{F}\mathit{S}}\right)}^2{\left(\frac{\mathrm{d}\mathit{E}/\mathrm{d}\mathrm{\delta }}{\mathrm{d}\mathit{E}/\mathrm{d}\sqrt{\mathit{t}}}\right)}^2$$

where i is the pulse current (A), V_m is the molar volume (cm³ mol⁻¹), z_A is the charge number (1 for Na/Na⁺), F is the Faraday’s constant (C mol⁻¹; 96485 C mol⁻¹), S is the surface area of electrode (cm²), dE/dδ is the change of voltage with respect to composition during current pulse, and dE/dt^1/2 is the change of voltage with respect to the square root of time during the period in between current pulse.

For the self-discharge tests, the batteries were charged to 4.15 V at 0.1 C, followed by open-circuit relaxation at 45°C for 24 hours, and then the open-circuit voltage (OCV) was recorded at room temperature every 15 min.

DFT calculations

To calculate the energy difference between the Na_e and Na_f sites, the 3a × 3b × 1c supercell with one Na ion was constructed to avoid the Coulombic repulsion between different Na ions. The difference of site energy is given by the following equation

$$\mathrm{\Delta }\mathit{E}=\mathit{E}({\text{Na}}_{\mathrm{e}})-\mathit{E}({\text{Na}}_{\mathrm{f}})$$

where E(Na_e) and E(Na_f) are the total DFT energies of bulk models with one ion occupying Na_e and Na_f site, respectively.

To simulate the Na ion transport properties in P2-Na_0.58NMT, the DFT calculations were performed within the 3a × 3b × 1c supercell as implemented in Viena ab initio simulation package. The projector augmented-wave method and generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof parameterization were used. GGA + U was applied in this work, in which the applied effective U value given to Ni ions was 6.1 eV, to Mn was 4.0 eV, and to Ti was 2.3 eV. For ensuring the configuration, an energy cutoff of 520 eV and a k-mesh of 0.03 Å⁻¹ were used. The force convergence criterion for the relaxation was 0.01 eV Å⁻¹. For the FPMD calculations of each temperature, a time step of 1 fs was used to simulate a total time of 10 ps by a Nose-Hoover thermostat. An energy cutoff of 450 eV was used with a k-point sampling at the Γ point. The ionic diffusion behavior can be calculated by a time-dependent MSD

$$\text{MSD}(\mathit{t})=\langle {|{\mathit{r}}_{\mathit{i}}(\mathit{t})-{\mathit{r}}_{\mathit{i}}(0)|}^2\rangle$$

in which r_i(t) is the site of the i-th Na⁺ at the time t. According to the Einstein equation, the diffusion coefficient D is given by the slope of MSD

$$\mathit{D}=\frac{1}{6}\underset{\mathit{t}\to \infty }{\text{lim}}\frac{\mathit{d}}{\mathit{d}\mathit{t}}\langle {\mathit{r}}^2(\mathit{t})\rangle$$

Thus, the activation energy barrier is correlated with the diffusion coefficients at various temperatures based on Arrhenius equation.

SUPPLEMENTARY MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/3/eaar6018/DC1

fig. S1. Powder XRD patterns of as-synthesized P2-NaNM and P2-NaNMT samples.

fig. S2. In situ XRD patterns of P2-NaNM and P2-NaNMT powders at different temperatures.

fig. S3. SEM images of P2-NaNM and P2-NaNMT sample.

fig. S4. TEM and HRTEM images of P2-NaNMT sample.

fig. S5. Cycling performance comparison of P2-NaNM and P2-NaNMT electrodes at 0.1 C in the voltage range of 2.5 to 4.15 V during 100 cycles.

fig. S6. SEM images of P2-NaNM and P2-NaNMT electrodes after long cycles.

fig. S7. Charge/discharge profiles of P2-NaNM and P2-NaNMT electrodes between 2.5 and 4.3 V.

fig. S8. Cycling performance comparison of P2-NaNM and P2-NaNMT electrodes at 0.1 C in the voltage range of 2.5 to 4.3 V during 100 cycles.

fig. S9. CVs of P2-NaNM and P2-NaNMT electrodes.

fig. S10. XPS spectra of P2-NaNM and P2-NaNMT powders.

fig. S11. Variation of lattice constants and unit cell volume during cycling.

fig. S12. Schematic illustration for P2-O2 phase transition.

fig. S13. In situ XRD patterns of P2-NaNM and P2-NaNMT electrodes between 2.5 and 4.3 V.

fig. S14. GITT curves and the quasi-equilibrium potential as a function of the stoichiometry.

fig. S15. Calculated Na chemical diffusion coefficients from GITT.

fig. S16. OCV decay of P2-NaNM and P2-NaNMT electrodes.

fig. S17. Nyquist plots of EIS and the fit for P2-NaNM and P2-NaNMT electrodes.

fig. S18. MSD curves for each kind of ions in P2-Na_0.58NMT.

table S1. Crystallographic parameters of P2-NaNM refined by the Rietveld method.

table S2. Crystallographic parameters of P2-NaNMT refined by the Rietveld method.

table S3. Atomic distances, slab thickness, and d-spacing of the Na layer and interslab distance for as-prepared materials.

table S4. Summary of Na⁺ diffusion coefficients and activation energies in layered oxides.