Supplementary Information. Department of Chemistry, Brookhaven National Laboratory, Upton, NY 11973, USA

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1 Supplementary Information Removal of interstitial H 2 O in hexacyanometallates for a superior cathode of a sodium-ion battery Jie Song 1, Long Wang 2, Yuhao Lu 2, Jue Liu 3, Bingkun Guo 1, Penghao Xiao 4, Jong-Jan Lee 2, Xiao-Qing Yang 5, Graeme Henkelman 4 and John B. Goodenough 1* 1 Materials Science and Engineering Program and Texas Materials Institute, The University of Texas at Austin, Austin, TX 78712, USA 2 Sharp Laboratories of America, Camas, WA 98607, USA 3 Department of Chemistry, State University of New York at Stony Brook, Stony Brook, NY 11794, USA 4 Department of Chemistry and the Institute for Computational and Engineering Sciences, The University of Texas at Austin, Austin, TX 78712, USA 5 Department of Chemistry, Brookhaven National Laboratory, Upton, NY 11973, USA These authors contributed equally. *Corresponding author. jgoodenough@mail.utexas.edu Solving and refining the structure of R-Na 2-δ MnHCF and M-Na 2-δ MnHCF Synchrotron XRD data of the R-Na 2-δ MnHCF sample was first indexed by using the R3 space group. Then Le Bail fittings of both TOF neutron diffraction data and XRD data were carried out in Jana 2006 software 1 by utilizing the indexed unit cell. For the refinement of TOF neutrondiffraction data, a split Pseudo-Voigt function was further convoluted with a back-to-back TOF function to model diffraction peaks. For fitting of synchrotron XRD data, a Pseudo-Voigt S1

2 function that included both size and strain contribution was used to model the diffraction peaks. After the refinement converged, the obtained hkl file was used to solve the initial structure by utilizing the charge flipping algorithm 2-3. Since Mn, Fe, and Na have much stronger X-ray scattering power than that of C or N, only heavy atom (Fe, Mn and Na) positions were clearly identified by using charge flipping of XRD data, and it is impossible to distinguish the Fe site from the Mn site since they have quite similar scattering factors. However, neutrons are quite sensitive to N or Fe and Mn has a negative scattering length, so by using neutron diffraction data, Mn, Fe and N positions were successfully identified. After the positions of the Na, Mn, Fe and N atoms were obtained, a further Rietveld refinement of the synchrotron XRD data was carried out in Jana ; a difference Fourier map was calculated to identify the possible C positions. Finally, the structure model including Na, Mn, Fe, C and N atoms was Rietveld refined by using Topas software (version 4.2): atomic positions, sodium site occupancy and isotropic atomic displacement factors were simultaneously refined until the refinement converged. To double check the validation of the structure model, the obtained structure was used as the initial model for further Rietveld refinement of TOF neutron diffraction data 4. It turns out this model can fit neutron-diffraction data quite well except for slightly different atomic displacement factors. The SXRD pattern of the M-Na 2-δ MnHCF sample was first indexed in the P2 1 /n space group. It is impossible to find the accurate hydrogen position based on powder diffraction data, but the oxygen position can be identified by using a difference Fourier map. S2

3 a b Figure S1.(a) Typical SEM image of Na 2-δ MnHCF samples showing non-cubic shape with a particle size of nm. (b) Photo of air-dried Na 2-δ MnHFC (1) and vacuum-dried Na 2- δmnhfc (2). S3

4 a b Figure S2. (a) XRD pattern (λcu) and (b) TOF neutron-diffraction pattern of R-Na 2-δ MnHCF. Without any exposure to moisture, XRD pattern shows a single phase of R-Na 2-δ MnHFC. S4

5 Table S1: (a) Atomic coordinates for M-Na 2-δ MnHCF (SXRD: R exp =1.48%; R p = 3.92% ; R wp =5.22%; χ 2 = 3.52). S.G. P2 1 /n a= (11) Å b= (12) Å c = (11) Å Atom Wyck. x/a y/b z/c occ B iso (Å 2 ) Mn 2a (5) Fe 2d (5) N1 4e (57) (64) (58) (10) N2 4e (36) (13) (72) (10) N3 4e (64) (55) (47) (10) C1 4e (87) (48) (73) (10) C2 4e (41) (16) (83) (10) C3 4e (87) (59) (50) (10) O 4e (54) (54) (57) (10) Na 4e (48) (41) (60) 0.84(3) 4 (b) Atomic coordinates for R-Na 2-δ MnHCF (SXRD: R exp =0.77%; R p = 2.60% ; R wp =3.48%; χ 2 = 4.50). S.G. R-3 a= (35) Å c= (11) Å Atom Wyck. x/a y/b z/c occ B iso (Å 2 ) Fe 3a (8) Mn 3b 1/3 2/3 1/ (11) Na 6c (14) (10) N 18f (11) (63) (18) (17) C 18f (12) (71) (22) (18) (c) Atomic coordinates for R-Na 2-δ MnHCF (PND: R exp = 2.27%; R p = 2.47% ; R wp = 1.83%; χ 2 =1.24) S.G. R-3 a = (16) Å c = (54) Å Atom Wyck. x/a y/b z/c occ B iso (Å 2 ) Fe 3a (15) Mn 3b 1/3 2/3 1/ (32) Na 6c (18) 0.90(7) 1.21(14) N 18f (88) (67) (33) (15) C 18f (71) (79) (31) (15) S5

6 Figure S3. Volume change at the initial charge of M-Na 2-δ MnHCF and R-Na 2-δ MnHCF. The monoclinic and rhombohedral unit cells are related to the classic Prussian blue translation. The unit cell dimensions of M-MnHCF are approximately a 1, a 2 / 2, a 3 / 2, β 90, while the rhombohedral unit cell has the approximate lattice parameters a 1 / 2, a 2 / 2, a 3 / 3. The volume (calculated as a 1 a 2 a 3 ) of corresponding orthorhombic unit cell is and Å 3 for M-MnHCF and R-MnHCF, respectively. S6

7 Figures S4. XRD patterns of (a) monoclinic Na 2-δ MnHCF and (b) rhombohedral Na 2-δ MnHCF after exposure to air for 20 h. a b Figure S5. (a) Charge and discharge curves of M-Na 2-δ MnHCF on the 1 st, 2 nd, 5 th and 10 th cycle. (b) The derivative curves (dq/dv) vs. voltage of the 1 st, 2 nd, 5 th and 10 th cycle. S7

8 Figure S6. XRD pattern of the M-Na 2-δ MnHCF electrode after 20 cycles. Figure S7. Rate performance of a hard carbon/r- Na 2-δ MnHCF full cell. The cell was charged at 10 ma g -1 and discharged at different currents. The specific capacity was calculated by the mass of R-Na 2-δ MnHCF. The capacity ratio of anode/cathode is 1.05/1. S8

9 Table S2. Comparison of reported cathode materials for sodium-ion batteries. Composition Reversible Average Rate Cycle life capacity in working performance Na cells voltage ( mah g -1 ) * (V vs.na + /Na) Na 0.44 MnO (50) % at 5 C 94%@20 th cycle Na 0.85 Li 0.17 Ni 0.21 Mn 0.64 O % at 25C 98%@ 50 th 7 O3-NaNi 0.5 Mn 0.5 O 2 8 NaNi 1/3 Mn 1/3 Co 1/3 O 2 9 P2-Na 2/3 Fe 1/2 Mn 1/2 O 2 10 FePO 4 11 Na 3 V 2 (PO 4 ) % at 1C 50 th % at 1C ~100%@50 th 190(140) % at 1C th 120(0) % at 0.5C 50 th % at 1C 50 th Na 3 V 2 O 2 (PO 4 ) 2 F % at 5C 91%@200 th Na 2 FeP 2 O Na 2 MnP 2 O 7 15 Na 2 NiFe(CN) % at 5C ~100%@80 th NA 15 th % at 8C ~100%@180 th FeFe(CN) 6 4H 2 O (0) % at 20 C 500 th Na 0.61 FeFe(CN) 6 18 Na 1.89 Mn[Fe(CN) 6 ] 0.97 in 170(54) % at 3.5C ~100%@150 th % at 20 C th this work S9

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