(b) Intensity (A.U.) (d) st discharge th discharge th discharge

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1 (a) E (V vs. Na/Na + ) (c) E (V vs. Na/Na + ) th 40 th 30 th 20 th 10 th 5 th 2 nd 1 st D-Na 2 RuO 3 O-Na 2 RuO 3 Capacity (mah g -1 ) 1 st charge 5 th charge 10 th charge Capacity (mah g -1 ) E (V vs. Na/Na + ) (b) Intensity (A.U.) (d) 003 After 1 cycle After 2 cycles After 5 cycles After 10 cycles st discharge 5 th discharge 10 th discharge 2θ (degree, Cu Kα 1,2 ) Capacity (mah g -1 ) D-Na 2 RuO 3 O-Na 2 RuO 3 Supplementary Figure 1. (a) Evolution of the charge/discharge profiles of O-Na2RuO3 after the 1st, 2nd, 5th, 10th, 20th, 30th, 40th and 50th cycles. (b) XRD patterns of the electrodes at V vs. Na + /Na after the 1st, 2nd, 5th and 10th cycles. With repeating the cycle, the diffraction peaks become broad, suggesting slight decrease of the crystallinity. However, the arrowheads highlight that the superstructure peaks corresponding to the honeycomb lattice are still observed even after 10 cycles. (c) Comparison of the 1st, 5th, and 10th charge curves of D-Na2RuO3 and O-Na2RuO3. (d) Comparison of the 1st, 5th, and 10th discharge curves of D-Na2RuO3 and O-Na2RuO3. The charge curve shows a voltage plateau around 3.6 V in every cycle. 1

2 003 O3 006 O3 101 O3 102 O3 104 O3 105 O3 003 P3 006 P3 101 P3 102 P3 104 P3 105 P3 E (V vs. Na/Na + ) Intensity (A.U.) a) x 1.8 x x θ ( ) Cu Kα 1,2 b) x in D-Na x RuO 3 Supplementary Figure 2. (a) Ex situ XRD patterns of D-NaxRuO3 electrodes at x = 1.8, and 1.2 upon charge. The hkl indices of the O3 (blue) and P3 (green) phases are given. (b) Charge-discharge curves of D-NaxRuO3. Arrows correspond to the Na contents given above. 2

3 Supplementary Figure 3. Observed and calculated (Rietveld method) synchrotron X-ray diffraction patterns for disordered Na1RuO3. Red crosses: experimental, black line: calculated, blue line: difference and green bars: Bragg positions. The inset shows the resulting P3 structure. 3

4 a) b) E (V vs. Na/Na + ) g f e d c b a charge discharge Z Y O3 O1 X O3 O1 Z Y g 2θ ( ) Co Kα f 1,2 e charge d c b a h i discharge j k l x in O-Na x RuO 3 h i j k l Supplementary Figure 4. (a) Selected in situ X-ray diffraction patterns recorded during the first cycle of a battery assembled with O-Na2RuO3 as positive electrode material. (b) The charge-discharge curve of O-Na2RuO3. The a-l labels as well as the blue and red arrows correspond to the different states of (dis)charge for the recorded diffraction patterns. While showing the overall structural reversibility, unidentified X phase is observed at the plateau around 2.7 V during the charge, which is similar to the ex situ XRD experiment. However, during the discharge, the X phase is not observed. Presumably, the X phase is formed kinetically as a metastable state during the charge. 4

5 Intensity (A.U.) Na 0.60 RuO Na 0.70 RuO Na 1.02 RuO 3 Na 1.27 RuO Na 1.42 RuO 3 Na 6 RuO x in Na x RuO 3 X O1 Na 1.71 RuO 3 Na 1.85 RuO O3 Na 2 RuO θ ( ) Cu Kα 1, E (V vs. Na/Na + ) Supplementary Figure 5. Selected ex situ X-ray diffraction patterns recorded at different states of charge of O-NaxRuO3. The symbols indicate the position of the superstructure peaks associated to (blue) Na2RuO3, (purple) X-NaxRuO3 and (orange) Na1RuO3. The three phases (O3, X, and O1) are clearly observed from x = 1.71 to The vertical dashed line indicate the peak from the XRD sample holder. 5

6 Supplementary Figure 6. Ex situ Ru L3-edge X-ray absorption spectra during charge-discharge for ordered NaxRuO3. The (i)-(v) labels correspond to the state of (dis)charge highlighted on the galvanostatic curves. 6

7 Supplementary Figure 7. Ex situ Oxygen K-edge X-ray absorption spectra during charge-discharge for ordered NaxRuO3. The (i)-(vii) labels correspond to the state of (dis)charge highlighted on the galvanostatic curves. 7

8 velocity (mm s -1 ) Supplementary Figure Ru Mössbauer spectrum of O-Na0.62RuO3 recorded at 4.2 K. Black dots: experimental, black line: fit with a doublet (δ = +0.21(6) mm s -1, ΔEQ = 0.60(5) mm s -1, and Γ = 0.60(3) mm s -1 ). Vertical error bars represent 1σ s. d. of counting statistics. 8

9 Relative capacity (%) Li 2-x RuO Li 2-x Ru 0.75 Sn 0.25 O Li 2-x Ru 0.60 Mn 0.40 O Li 2-x IrO Li 2-x MnO Li 1.2-x Mn 0.54 Ni 0.13 Co 0.13 O O-Na 2-x RuO 3 190: first charge capacity (mah g -1 ) : irreversible capacity (first cycle) : reversible capacity (first cycle) Supplementary Figure 9. Relative irreversible capacity of O-Na2RuO3 vs. that of various Li excess materials. Corresponding references can be found in the main text. 9

10 a) Disordered Na2RuO3 Space group: R _ 3m:h, a = 969(3) Å, c = (2) Å Fractional coordinates Atom Site x y z Occupancy g B (Ų) Na(1) 3a Ru 3a (4) Na(2) 3b 0 0 1/ (2) O 6c (1) (2) Rwp = 8.50 %; RB = 4.23 %; Berar s factor = 2.7. b) Ordered Na2RuO3 Space group: R _ 3m:h, a = (5) Å, c = (4) Å Fractional coordinates Atom Site x y z Occupancy g B (Ų) Na(1) 3a Ru 3a (7) Na(2) 3b 0 0 1/ (3) O 6c (1) (4) Rwp = %; RB = 7.18 %; Berar s factor = (with excluded superstructure peaks). Rwp = %; RB = 7.08 % (without excluded superstructure peaks). Supplementary Table 1. Structural parameters and reliability factors calculated from the synchrotron X-ray diffraction patterns for (a) disordered and (b) ordered Na2RuO3. The relatively high values of B for Na and O are explained by the weak stacking faults, which slightly distorts the local structure. 10

11 a) Disordered Na1RuO3 (Na0.708(12)RuO3) Space group: R _ 3m:h, a = 2.927(2) Å, c = (12) Å Fractional coordinates Atom Site x y z Occupancy g B (Ų) Na 6c (6) 0.237(4) Na(2) 3a Ru 3a /3 1.73(5) O 6c 1/3 2/ (3) 1 2(14) Rwp = 5.41 %; Rp = 3.92% ; GoF = 2.93 ; RB = 1.28 % b) Ordered Na1RuO3 Space group: R _ 3:h, a = (1) Å, c = (6) Å Fractional coordinates Atom Site x y z Occupancy g B (Ų) Na 6c (3) 1 0(1) Ru 6c (8) 0.87(2) 0.5 Ru 3a (2) 0.5 O 18f (8) (9) (1) Rwp = 9.47%; Rp = 6.97% ; GoF = 4 ; RB = 4 % Supplementary Table 2. Structural parameters and reliability factors calculated from the synchrotron X-ray diffraction patterns for (a) disordered and (b) ordered Na1RuO3. The relatively high values of B for Na and O are explained by the weak stacking faults, which slightly distorts the local structure. 11

12 O-O in RuO 6 Ru-O Ru-Ru Na-O Na-Na Na-Ru Na-Vacancy 3 80(4) Å (4) Å (4) Å 3 80(6) Å (4) Å 3 43(3) Å 3 320(1) Å (5) Å (5) Å (2) Å 91(1) Å 2.207(5) Å Supplementary Table 3. Interatomic distances in O-Na1RuO3. 12