The discovery of intercalation chemistry in layered transition-metal oxides AMO2 (A=Li, Na and M=transition metal)1,2 in the early 1980s has led to the commercialization of lithium-ion batteries3. Tremendous effort has since been devoted to understanding how alkali-metal ions reversibly (de)intercalate in AMO2 because this is essential to exploit their large theoretical capacities (~275 mAh g−1 for LiCoO2 and ~235 mAh g−1 for NaCoO2, respectively). It is now well understood that, at the early stage of A+ deintercalation, AxMO2 (0.4 < x < 1.0) exhibit an increase of their interlayer distance because the depletion of screening A+ layers enhances the effective Coulombic repulsion between oxide ions of adjacent MO2 layers4,5,6,7,8. At the late stage of A+ deintercalation (0.0 < x < 0.4), high-valent M increases the covalency of MO bonds, and thus decreases the negative charge on oxide ions. In this situation, OO van der Waals attraction forces are not sufficient to maintain the layered structure, and the large volume variations induced at the end of charge often initiate crack formation and delamination/exfoliation8,9,10. Furthermore, the lack of alkali ions in the interlayer space leads to structural degradation with migration of transition-metal ions to neighboring tetrahedral sites11,12,13. This established knowledge on the intercalation chemistry of AxMO2 explains the practical limit of their reversible capacity (approximately for 0.4 < x < 1.0, i.e., 170 mAh g−1 for A = Li and 140 mAh g−1 for A = Na). Therefore, the control of the competing Coulombic and van der Waals forces in layered transition-metal oxides is of great importance to achieve a large reversible capacity.

Layered A-excess transition-metal oxides (A1+yM1−yO2 or A1[AyM1−y]O2) are recent major targets to increase the cathode capacity by virtue of additional oxygen-redox reactions. Li2MnO3-LiMO2 solid solutions have been reported to deliver large capacities over 200 mAh g−114,15,16, and have more recently been followed by Li2MO3 (M = Ru17, Ir18, RuSn17, and RuMn19) and Na2MO3 (M = Ru20,21, RuSn21, and Ir22), all delivering large capacities exceeding that of solely M redox. Although the changes in the electronic state during the additional oxygen-redox reactions have been intensively investigated, less attention has been paid to the essential interaction dominating the phase transformation during the charge/discharge processes, presumably because most oxygen-redox electrodes exhibit severe structural degradation (i.e., oxygen-gas evolution, cation migration) at the initial charge16,17,23,24. However, the extra A+ are expected to play a crucial role in the structural transformation during the charge/discharge processes. For example, the depletion of screening A+ layers upon charging can be compensated by the A+ supplied  from the [AyM1−y]O2 layers18,20,22. Moreover, A+ (or vacancy after deintercalation) in the [AyM1−y]O2 layers is expected to modulate the balance of competing Coulombic/van der Waals forces, and hence largely influence the intercalation chemistry.

We have recently studied the structure and electrochemistry of O3-Na2RuO3 (or Na[Na1/3Ru2/3]O2), where [Na1/3Ru2/3]O2 layers have a honeycomb-type ordered arrangement of Na and Ru20,25. According to the classification of layered oxides, O3 denotes a structure where Na+ ions occupy octahedral interlayer sites and the stacking of oxide ions is ABCABC (Supplementary Fig. 1)26. Importantly, in contrast to most oxygen-redox electrodes, O3-Na2RuO3 exhibits highly reversible (de)sodiation without structural degradation but rather exhibits progressive structural ordering upon charging, which provides an opportunity for not only detailed structural investigation as a model system but also for essential strategies toward much larger reversible capacity.

In this work, synchrotron X-ray diffraction coupled with planar-defect refinement analyses are applied to honeycomb ordered NaxRuO3 phases (x = 2, 1, and 1/2), revealing a self-repairing phenomenon of stacking faults upon charging, which significantly stabilizes the reversible large capacity operation. Driving force of the 3D self-ordering is strong long-range cooperative Coulombic interactions between MO3 slabs intermediated by ordered vacancies.


Stacking faults in Na2RuO3

O3-Na2RuO3 was synthesized by decomposing Na2RuO4 at 850 °C for 12 h under Ar atmosphere20,25. Figure 1a shows the experimental and calculated synchrotron XRD patterns of O3-Na2RuO3, in which the most of intense diffraction peaks can be fitted by the usual rhombohedral lattice of O3-AMO2 layered oxides20. However, the main difficulty hindering an accurate pattern fit lies in the broad nature of some diffraction peaks and diffuse scatterings, which are highlighted by the dashed rectangle in Fig. 1a. Such broadening is typically observed for A2MO3 with honeycomb ordered [A1/3M2/3]O2 layers, and arises from stacking disorder. These stacking faults can be described by an occasional shift of the [A1/3M2/3]O2 layers perpendicularly to the stacking direction. In fact, in layered materials, the crystal grows perpendicularly to the layer plane. When a nucleation starts in a wrong position, a stacking fault appears while the oxygen packing remains ideal. As a result, the honeycomb ordering of the [A1/3M2/3]O2 layers is maintained but the honeycomb stacking deviates from the ideal sequence (Fig. 1b), which causes the peculiar asymmetric peak broadening (Warren fall) observed in Fig. 1a as well as the diffuse streaks on the selected area electron diffraction (SAED) pattern along the [100]−<110>C2/m direction (Fig. 1c).

Fig. 1
figure 1

Stacking faults in Na2RuO3. a Observed and calculated (FAULTS refinement) synchrotron XRD patterns of O3-Na2RuO3 (pristine state). Observed data, the calculated pattern, and the difference between observed and calculated data are shown as plus sign (red), solid line (black) and continuous line (blue), respectively. The positions of Bragg reflections are indicated by vertical tick marks (green). The first diffraction peak has been excluded from the refinement due to important asymmetry that FAULTS does not take into account. The insert is a zoom of the initial superstructure peaks (Warren fall). b Representation of the stacking faults in O3-Na2RuO3, using the FAULTS unit cell described in the text. c, d Experimental and simulated SAED pattern along the [100] (= <[110]C2/m>) direction, respectively

To refine the powder diffraction data for the structure containing stacking faults, a FAULTS analysis, which allows the incorporation of the occurrence probabilities of possible stackings, was conducted27. As shown in Fig. 1a (Supplementary Tables 1 and 2), the FAULTS analysis provides a satisfactory description of the superstructure peaks and indicates the occurrence of ~40% stacking faults between the [Na1/3Ru2/3]O2 layers in pristine O3-Na2RuO3. This result is further supported by the FAULTS-simulated SAED pattern that well reproduces the diffuse streaks observed in the experimental SAED pattern (Fig. 1d).

After evaluation of the stacking faults in pristine O3-Na2RuO3, we studied the structural evolution of NaxRuO3 during the first charge and discharge using in situ XRD. Figure 2 shows that the phase transformation of NaxRuO3 involves three main phases: O3-NaxRuO3, O1-Na1RuO3, and O1′-Na1/2RuO3. (De)sodiation at 2.7 V vs. Na/Na+ (1.0<x<2.0) mainly proceeds through a two-phase process between O3-NaxRuO3 and O1-Na1RuO3. As reported previously, O1-Na1RuO3 has an ilmenite-type structure (ABAB oxide-ions stacking and Na+ ions in interlayer octahedral sites) where the honeycomb ordered [Ru2/31/3]O2 and [Na2/31/3]O2 layers (□: Na+ vacancy) stack alternatively (Supplementary Fig. 2)20. At the second charging plateau, a new phase (O1′-Na1/2RuO3) with a shorter interlayer distance (4.91 Å vs. 5.21 Å for O1-Na1RuO3) appears at the expense of the O1 phase. Its structure was determined from the synchrotron XRD pattern of an electrochemically deintercalated sample, whose Rietveld refinement is presented in Supplementary Fig. 3 and Supplementary Table 3. The diffraction peaks are successfully indexed in a hexagonal lattice with P\(\bar{3}\)1 m symmetry with a = 5.1876(9) Å and c = 4.906(1) Å. As the oxide-ion stacking sequence is ABAB and Na+ occupies an octahedral site, we will refer to this phase as O1′-Na1/2RuO3, where the alternate stacking of the honeycomb ordered [Ru2/31/3]O2 and [Na1/32/3]O2 layers is maintained. Then, the difference between the O1 and O1′ structures lies in the Na content and on the respective stacking of the [Ru2/31/3]O2 layers, which are shifted from one another in O1-Na1RuO3 while directly stacked in O1′-Na1/2RuO3 (Supplementary Figs. 2 and 3). It is noteworthy that the superstructure peaks highlighted by the arrows in Fig. 3a exhibit remarkable sharpening upon charging. This suggests that stacking faults tend to disappear, assisted by the adjustable layer gliding involved in the O3→O1′ transition. The FAULTS refinements (Fig. 3c, d and Supplementary Tables 46) indicate that the occurrence probability of stacking faults indeed decreases from 40% in O3-Na2RuO3 to 10% (O1-Na1RuO3) and then to 2% (O1′-Na1/2RuO3) (Fig. 3b). Therefore, Na+ deintercalation (charging) from Na2RuO3 involves a self-reorganization process that significantly diminishes the initial amount of stacking faults. Importantly, the stacking faults are reformed after discharging, making this ordering/faulting process reversible, even after several cycles (Supplementary Figs. 4 and 5).

Fig. 2
figure 2

Structural evolution upon charging/discharging Na2RuO3. a XRD patterns recorded in situ during the first cycle of Na2RuO3 with the corresponding cycling curve. The dashed area corresponds to a potentiostatic break whose aim was to ensure the equilibrium state at 4.0 V before discharging the cell. b Phase diagram as determined from the in situ experiment as a function of the sodium content

Fig. 3
figure 3

Progressive stacking-fault-depression (self-ordering) upon charging Na2RuO3. a Synchrotron XRD patterns of O3-Na2RuO3, O1-Na1RuO3 and O1′-Na1/2RuO3. Arrows indicate the most intense superstructure peaks. b Evolution of the ordered stacking (absence of stacking faults) as a function of the Na content. The error bars are smaller than the mark size. c, d Observed and calculated (FAULTS refinement) synchrotron XRD patterns of O1-Na1RuO3 and O1′-Na1/2RuO3, respectively. Red crosses: experimental, black line: calculated, blue line: difference plot and green bars: Bragg positions in the R\(\bar{3}\):h and P\(\bar{3}\)1m space groups for O1-Na1RuO3 and O1′-Na1/2RuO3, respectively. The dashed rectangles indicate the most intense superstructure peaks

Self-ordering of stacking faults upon charging Na2RuO3

Based on the complete knowledge of the structural evolution from O3-Na2RuO3 to O1-Na1RuO3, and then to O1′-Na1/2RuO3, let us now consider the Coulombic origin of the consolidation on the phase transformation with the effect of gliding vectors t of the [Ru2/3Na1/3]O2 (or [Ru2/31/3]O2) layers (Fig. 4a–c). Note that the vectors are given in the pseudo-hexagonal cell (O3-Na2RuO3) or in the hexagonal cells (O1-Na1RuO3 and O1′-Na1/2RuO3; Supplementary Table 7). In O3-Na2RuO3 (Fig. 4a), the NaO6 octahedron in Na layers shares edges with two NaO6 and four RuO6 octahedra in the adjacent [Ru2/3Na1/3]O2 layers (Fig. 4d). As the stacking faults only impact the stacking of the [Ru2/3Na1/3]O2 layers, the Na+ ions in the Na layer have the same local environment (Fig. 4e) and it can be considered that a different stacking is equally probable in O3-Na2RuO3. However, in O1-Na1RuO3 consisting of honeycomb ordered [Ru2/31/3]O2 and [Na2/31/3]O2 layers with the ABAB oxygen packing (Fig. 4b), all the octahedral positions in the slab share faces with the octahedral positions of the interslab space (Supplementary Fig. 6). As a result, the gliding vectors t that shift each layer of O3-Na2RuO3 to the ones of O1-Na1RuO3 are ideally adjusted to set each NaO6 octahedron in the [Na2/31/3] layers to share faces with a □O6 octahedron and a RuO6 octahedron in the adjacent [Ru2/31/3]O2 layers (Fig. 4f and Supplementary Fig. 7). The stronger attraction of the oxygen atoms surrounding a vacancy on the Na+ ion (later referred to as Na+−□ Coulombic attraction for simplicity) and the Na+−Ru5+ Coulombic repulsion cooperatively displace the Na+ ion toward □20. When assuming the hypothetical stacking faults (Fig. 4g, h), one of two NaO6 octahedra is trapped between two RuO6 octahedra, where strong Ru5+−Na+−Ru5+ Coulombic repulsions make the faulted structural option unfavorable. Consequently, during the O3 to O1 transformation, slab gliding tends to occur in a way which minimizes the Coulombic energy and as a consequence removes the stacking faults, as described in Fig. 4 and Supplementary Fig. 7. Owing to the three-directional gliding possibilities, most of the stacking faults disappear during the transformation. However, the NaO6 octahedron can occasionally be stabilized by the local □−Na+−□ Coulombic attraction (Fig. 4h), and some stacking faults may remain in O1-Na1RuO3.

Fig. 4
figure 4

Coulombic forces and resultant stacking–fault–depression (self-ordering) in Na2−xRuO3. Structural representation and projected stacking sequences of the Ru atoms of a O3-Na2RuO3, b O1-Na1RuO3 and c O1′-Na1/2RuO3. The monoclinic cell of O3-Na2RuO3 has been converted to a pseudo-hexagonal supercell (black lines) for comparison. The transition vectors in the hexagonal supercell from one [Ru2/3Na1/3]O2 or [Ru2/31/3O2] layer to another are indicated with respect to the pseudo-hexagonal or hexagonal cells. Note that the transition vectors assigned to faulted layers are a few examples out of many possibilities listed in Supplementary Figs. 5 and 6. dj Comparison of the Na environments in ideal and faulted stacking highlighted with dashed circles in the structures shown in ac

On the other hand, in O1′-Na1/2RuO3 (Fig. 4c and Supplementary Fig. 3b), which consists of honeycomb ordered alternating [Ru2/31/3]O2 and [Na1/32/3] layers, the NaO6 octahedron shares faces with two □O6 octahedra in the adjacent [Ru2/31/3]O2 layers (Fig. 4c, i). Again with hypothetical stacking faults resulting from t different from the ideal ones shown in Supplementary Fig. 8, the NaO6 octahedron in the [Na1/32/3] layer shares faces with □O6 and RuO6 octahedra, and the local Na+-Ru5+ Coulombic repulsion prohibits the formation of the faulted structure (Fig. 4j). Therefore, the amount of the stacking faults in NaxRuO3 (1/2 ≤ x 2) continuously diminishes as desodiation proceeds, because the ordered stacking sequences become electrostatically more favorable. As discussed above, no peculiar local environment is stabilized in O3-Na2RuO3, which allows for stacking faults reformation upon sodiation (Supplementary Figs. 4 and 5).


The aforementioned importance of the attractive A+−□ and repulsive A+−M5+ Coulombic interactions can lead to more general discussions on the phase stability of A2MO3 and AMO2 upon charging. Figure 5a shows the experimental evolution of the interlayer distance upon charging various NaxMO2 (M = 3d)8,28 and Na2MO3 (M = 4d, 5d)22 compounds as a function of the sodium content. Figure 5b shows the similar plots for the lithium analogs, LiMO2 and Li2MO34,6,7,17,18. It is noteworthy that all AMO2 (A = Li, Na and M = 3d) and all A2MO3 (A = Li, Na and M = 4d, 5d) respectively follow the same tendencies.

Fig. 5
figure 5

Overviewing dominant forces for phase transformation during A+ de-intercalation from AMO2 and A2MO3. Comparison of the general trends in interlayer distance evolution between a NaxMO2 (M = Cr28 and Fe2/3Mn1/38) and Na2MO3 (M = Ru (this study) and Ir22) and b LixMO2 (M = Co4, Ni6 and Ni1/3Mn1/3Co1/37) and LixMO3 (M = Ru17 and Ir18)

As mentioned in the introduction, the phase transformation of AxMO2 is dominated by the competing O−O Coulombic repulsion (0.4 < x < 1.0) and van der Waals attraction (0 < x < 0.4) between adjacent MO2 layers4,5,6,7,8, which initiates the increase of the interlayer distance (0.4 < x < 1.0) followed by its abrupt decrease upon deeper charging (0 < x < 0.4). Structural evolution in the “Coulombic domain” with large A+ content (0.4 < x < 1.0) are highly reversible and is the basis of commercial positive electrode materials such as LiCoO2 and Li[Ni1-y-zMnyCoz]O2, while the “van der Waals domain” with smaller A+ content (0 < x < 0.4) marks the limit of reversibility of many practical layered oxides as a result of cation migration, spinel transformation, crack formation, and delamination/exfoliation8,9,10,11,12,13.

On the contrary, the highly ordered nature of the [Ru2/31/3]O2 layers of AxMO3 (M = Ru or Ir) triggers a progressive gain in A+−□ Coulombic energy upon A+ extraction as the remaining A+ ions cooperatively act as robust pillars between adjacent [Ru2/31/3]O2 layers to prevent structural collapse. The slight decrease of the interlayer distance is driven by Coulombic A+−□ attractive forces which are strong enough to induce the slab glidings, O3 → O1 → O1′, forming a more-ordered structure upon charging. It is this situation that realizes reversible charge–discharge reactions in ordered A2MO3 over a wide compositional domain of the guest ion A+.

In summary, we identified a spontaneous reorganization of the stacking faults in NaxRuO3, a model material to understand oxygen-redox reactions in layered oxides for large-capacity battery electrodes. In particular, the progressive ordering upon charging process is a general phenomenon to A2MO3 (A = Li, Na and M = 4d, 5d) materials and is induced by the cooperative effect of maximizing the A+−□ Coulombic attraction and minimizing the A+−M5+ Coulombic repulsion, which significantly enlarges the reversible operation range of layered oxides. Complementarily to our previous work, in addition to generate redox-active “orphaned” nonbonding oxygen 2p orbitals to “activate” additional oxygen-redox reactions, honeycomb ordering of M and □ contribute to “stabilizing” reversible phase transformation. In this regard, the importance of the overall material design that includes ordered vacancies with its neutral charge to attract alkali cations was highlighted. By establishing proper ways to control the stacking faults29,30,31 or vacancies32, the concept of progressive ordering upon charging may be extended to stabilize other related compounds33.


Synthesis of Na2RuO3

Na2RuO3 was prepared according to the literature25. First, Na2RuO4 is prepared by mixing stoichiometric amounts of Na2O2 (Sigma-Aldrich) and RuO2 (Kanto chemicals). Pellets are then made and introduced in a tubular furnace to be annealed at 650 °C for 12 h under O2 atmosphere. After the synthesis, Na2RuO4 is grinded and shaped into pellets again to be thermally decomposed into Na2RuO3 at 850 °C for 12 h under Ar atmosphere. After cooling down to room temperature, the sample is introduced in an Ar filled glovebox.


The synchrotron XRD patterns were recorded at Aichi Synchrotron Radiation Center (Aichi-SR, O3-Na2RuO3), and Photon Factory at High Energy Accelerator Research organization (KEK-PF, BL-8B) or SPring-8 (O1-Na1RuO3 and O1′-Na1/2RuO3, beamline 02B2). All samples were protected from air exposure during the measurement. Rietveld refinement was performed using Jana200634. Analyses of the stacking faults in the materials were carried out using the FAULTS software27. The crystal structures were drawn using VESTA35. Selected Area Electron Diffraction (SAED) patterns were recorded using an electron microscope (HF-3000S; Hitachi Ltd. and Titan Cubed; FEI Co.) operated at 300 kV. The camera length for SAED was calibrated with a Si crystal.


Electrochemical measurements were carried out in Na2RuO3/electrolyte/Na half-cells assembled in CR2032 type coin cells. The electrolyte was 1 mol/L NaPF6 in EC:DEC (1:1) purchased from Chameleon Reagent. Positive electrodes were prepared by coating a slurry made of active material (80 wt%) mixed with acetylene black (10 wt%) and polyvinylidene (10 wt%) in NMP onto Al foil. Sixteen-mm-diameter electrodes were cut after drying for one night under vacuum at 120 °C. The positive and negative electrodes were separated by a layer of Whatman glass fiber separator soaked with electrolyte. The galvanostatic curve was recorded and controlled using a TOSCAT-3100 battery tester. The charge/discharge rate was C/10 which corresponds to the (de)intercalation of 1 Na+ per NaxRuO3 in 10 hours. The O1-Na1RuO3 and O1′-Na1/2RuO3 samples were prepared by cycling sintered pellets (diameter 10 mm, weight ≈10–15 mg) of O3-Na2RuO3 at C/50 (one Na+ exchanged in 50 h) until a given voltage (3.07 V and 4.0 V vs. Na/Na+ for O1-Na1RuO3 and O1′-Na1/2RuO3, respectively). The recovered materials were then washed 3 to 5 times with dimethyl carbonate in the glovebox before sending to the synchrotron facility.

In situ X-ray diffraction. In situ XRD was carried out in operando using an in situ cell purchased from Bruker on a Bruker-AXS D8 ADVANCE (Co Kα radiation) in 0.02o steps over the 2θ range of 17–25o at a C/10 rate. The cell configuration is similar to the one described above except for the positive electrode that consisted in a mixture of Na2RuO3 (85 wt%), acetylene black (10 wt%), and polytetrafluoroethylene (5 wt%). Two layers of glass fiber separators were used to prevent dendrite formation.