Supplementary Information
Yttrium-Sodium Halides as Promising Solid-State Electrolytes with High Ionic Conductivity and Stability for Na Ion Battery
Yu Qie,a Shuo Wang,a Sijie Fu,a Huanhuan Xie,a Qiang Sun,a,b,* and Puru Jenac a Department of Materials Science and Engineering, Peking University, Beijing 100871, China b Center for Applied Physics and Technology, Peking University, Beijing 100871, China c Department of Physics, Virginia Commonwealth University, Richmond, VA 23284, USA
1. Site ordering of the NYB and NYC
Na3YCl6 and Na3YBr6 have the same symmetry with Li3ErCl6 (ICSD No. 50151, space group P3_m1) and Li3ErBr6 (ICSD No. 50182, space group C2/m), respectively, where Na atoms partially occupy 6h sites in NYC and 4h sites in NYB. To determine the preferred Na configurations, we first use the pymatgen package 1 to generate all symmetrically distinctive structures for optimization using DFT. As shown in Figure S1, the structure with the lowest energy is identified as the ground state structure.
Figure S1. Ordering of Na ions (a) NYC and (b) NYB. The final structures with lowest energy (left) and the structures next in energy. The relative energies are marked below each structure diagram.
2. Phase stability
To check the phase stability of NYC and NYB, we first construct the phase diagram by using the data from the MP database 2-3 and our results on NYC/NYB, as shown in
Figure S2 and Table S1, S2. Next, the energy above hull Eabove hull_ is determined by comparing the energy of all relevant phases in the compositional space (Na-Y-Cl/Br). At 0 K, Eabove hull_ is the negative value of the reaction energy for NYC/NYB to decompose into the predicted equilibrium phases. WhenEabove hull_ is positive, the system is thermodynamically unstable. Besides, the Eabove hull_ value can be used to estimate the feasibility that the predicted materials can be synthesized experimentally. The analysis is carried out using pymatgen python framework 1, 4.
Figure S2. Phase diagram of (a) Na-Y-Cl and (b) Na-Y-Br ternary system.
Table S1 and Table S2 are the materials in and the corresponding formation energies used in phase calculations for Na-Y-Cl and Na-Y-Br ternary systems.
Table S1. The energy-above-hull (Ehull) of all phases for Na-Y-Cl ternary system.
NYC in this work Na3YCl6 0.00863 1.00 Na3 Y1 Cl6 mp-675104 Na3YCl6 0.00000 1.00 Na3 Y1 Cl6 mp-31362 Na3YCl6 0.00283 1.00 Na3 Y1 Cl6 mp-1111487 Na3YCl6 0.13857 1.00 Na3 Y1 Cl6 mp-999501 Na 0.15431 1.00 Na20 mp-974920 Na 0.02841 1.00 Na20 mp-567772 Na 0.03657 1.00 Na20 mp-982370 Na 0.02883 1.00 Na20 mp-10172 Na 0.02581 1.00 Na20 mp-973198 Na 0.02604 1.00 Na20 mp-1186040 Na 0.05990 1.00 Na20 mp-1186055 Na 0.00000 1.00 Na20 mp-1079952 Na 0.09486 1.00 Na20 mp-127 Na 0.02715 1.00 Na20 mp-974558 Na 0.02850 1.00 Na20 mp-1093989 Na 1.09789 1.00 Na20 mp-1186081 Na 0.06327 1.00 Na20 mp-112 Y 0.00000 1.00 Y2 mp-9 Y 0.02754 1.00 Y2 mp-1187717 Y 0.00594 1.00 Y2 mp-1187739 Y 0.00464 1.00 Y2 mp-22848 Cl2 0.00000 1.00 Cl4 mp-570778 Cl2 0.00000 1.00 Cl4 mp-1008394 Cl2 0.00000 1.00 Cl4 mp-1186191 NaY3 0.31504 0.75 Y2 + 0.25 Na20 mp-1186202 NaY3 0.30372 0.75 Y2 + 0.25 Na20 mp-1080771 NaCl7 0.00000 1.00 Na1 Cl7
mp-990084 Na2Cl 0.11094 0.67 Na1 Cl1 + 0.33 Na20 mp-1095060 Na3Cl2 0.22543 0.80 Na1 Cl1 + 0.20 Na20 mp-1018810 Na2Cl 0.15507 0.67 Na1 Cl1 + 0.33 Na20
mp-22862 NaCl 0.00000 1.00 Na1 Cl1
mp-22851 NaCl 0.15360 1.00 Na1 Cl1
mp-1064484 Na3Cl 0.14430 0.50 Na1 Cl1 + 0.50 Na20
mp-1189265 NaCl3 0.00000 1.00 Na4 Cl12
mp-1077015 Na2Cl 0.23710 0.67 Na1 Cl1 + 0.33 Na20 mp-1077288 Na2Cl 0.23230 0.67 Na1 Cl1 + 0.33 Na20
mp-1078558 NaCl3 0.23933 1.00 Na4 Cl12
mp-1069676 Na3Cl2 0.17254 0.80 Na1 Cl1 + 0.20 Na20
mp-27678 Y2Cl3 0.00000 1.00 Y4 Cl6
mp-540884 YCl 0.05199 0.83 Y4 Cl6 + 0.17 Y2
mp-1209960 NaYCl4 0.01262 0.56 Na3 Y1 Cl6 + 0.44 Y2 Cl6
Table S2. The energy-above-hull (Ehull) of all phases for Na-Y-Br ternary system.
Materials ID Composition Ehull (eV/atom) Decomposition
NYB in this work Na3YBr6 0.00000 1.00 Na6 Y2 Br12
mp-999501 Na 0.15431 1.00 Na20 mp-974920 Na 0.02841 1.00 Na20 mp-567772 Na 0.03657 1.00 Na20 mp-982370 Na 0.02883 1.00 Na20 mp-1186055 Na 0.00000 1.00 Na20 mp-1186040 Na 0.05990 1.00 Na20 mp-973198 Na 0.02604 1.00 Na20 mp-10172 Na 0.02581 1.00 Na20 mp-1079952 Na 0.09486 1.00 Na20 mp-127 Na 0.02715 1.00 Na20 mp-974558 Na 0.02850 1.00 Na20 mp-1093989 Na 1.09789 1.00 Na20 mp-1186081 Na 0.06327 1.00 Na20 mp-112 Y 0.00000 1.00 Y2 mp-9 Y 0.02754 1.00 Y2 mp-1187717 Y 0.00594 1.00 Y2 mp-1187739 Y 0.00464 1.00 Y2 mp-673171 Br 0.61596 1.00 Br4 mp-23154 Br 0.00000 1.00 Br4 mp-998864 Br 0.12829 1.00 Br4 mp-1010048 Br 0.16761 1.00 Br4 mp-1062055 Br 0.59214 1.00 Br4 mp-998861 Br 0.65627 1.00 Br4 mp-1120813 Br 0.11566 1.00 Br4 mp-1186191 NaY3 0.31504 0.75 Y2 + 0.25 Na20 mp-1186202 NaY3 0.30372 0.75 Y2 + 0.25 Na20 mp-22916 NaBr 0.00000 1.00 Na1 Br1 mp-865605 YBr3 0.06121 1.00 Y2 Br6 mp-754815 YBr3 0.00000 1.00 Y2 Br6 mp-865534 YBr2 0.15897 0.56 Y4 Br6 + 0.44 Y2 Br6 mp-1205567 Y2Br3 0.00000 1.00 Y4 Br6
mp-29080 Na3YBr6 0.01879 1.00 Na6 Y2 Br12
mp-1111697 Na3YBr6 0.15862 1.00 Na6 Y2 Br12
3. Thermal and dynamical stability
To check the thermal and dynamical stability, we carried out AIMD simulation at 1000 K and calculated the phonon spectra of NYC and NYB. The results are given in Figure S3.
Figure S3. Total energy fluctuation during the AIMD simulation at 300 K of (a) NYC and (b) NYB. Phonon band structures and the corresponding frequency density of states of (c) NYC and (d) NYB.
4. Na ion migration and conductivity
Ab initio molecular dynamics (AIMD) simulations are performed with supercells to calculate the diffusivity and conductivity. Only gamma k-point is used. The optimized ground state geometries are used as the initial structures with an initial temperature of 100 K, and then the systems are heated to 1000 K by velocity scaling over a time period of 2 ps. Then the NVT ensemble using a Nosé–Hoover thermostat 5 is used with a time step of
2 fs. For NYC, a 1x1x2 supercell (60 atoms) is used and the AIMD simulation time ranges from 80 to 250 ps at different temperatures (600, 700, 800, 900, 1000 K), corresponding a mean-squared displacement (MSD) of 80~180 Å2. For NYB, a 2x1x2 supercell (80 atoms) is used and the AIMD simulations run for 80 to 160 ps at different temperatures (600, 700, 800, 900, 1000 K) with MSD of 30~200 Å2. All the AIMD calculations (except for the slow ionic diffusion in NYB at 600K) correspond to 150-300 effective ion jumps with a relative standard deviation (RSD) of diffusivity in the range of 25~40% as reported in previous work 6.
The mean square displacement (MSD) of each individual Na ion is calculated as follows: 2 2 0 0 1 1 t N i t+t i t i r r r N （ ）
（ ）- （ ）where ri( t ) is the displacement of the ith ion at time t, and N is the total number of ions in the system. The MSD value is an effective indicator of ionic mobility from the statistical scale, which can be further applied to calculate the diffusion coefficient D. According to the Einstein equation:
2 1 t 2 （ ） D r d t
where d is the dimension of the diffusion. The ionic conductivity is calculated according σ to Nernst-Einstein relationship: 2 B nq D k T
where n is the mobile ions’ volume density and q is the ionic charge.Based on Arrhenius equation7, the activation energies (E
a) can be determined from plots of the diffusivity over temperature.
exp(
a)
BE
D A
k T
where kB, T and A are the Boltzmann's constant, the environmental temperature, and the
pre-exponential factor, respectively. The data analysis is carried out with the aimd code developed under pymatgen python framework 1, 6, 8-9.
Figure S4. The MSD of Na, Y and Cl/Br in (a) NYC and (b) NYB versus time during the AIMD simulation at 1000 K, respectively.
To get a better understanding of the Na ions’ diffusion in NYC and NYB, the MSD method is used with elevated temperatures for accelerating the migration process. We check the structures after AIMD simulation for 45~85 ps at 1000 K, as shown in the Figure S4, which indicates the prominent migration of Na ions while Y and Cl/Br ions only vibrate in the lattice.
Figure S5. MSD of Na ions in (a) NYC and (b) NYB along different directions as a function of time at 600 K.
Figure S6. MSD of Na ions in NYC along different directions as a function of time at different temperatures (600, 700, 800, 900, 1000 K).
Figure S7. MSD of Na ions in NYB along different directions as a function of time at different temperatures (600, 700, 800, 900, 1000 K).
Table S3. Na ion diffusion coefficient D (10-9 cm2/s) and activation energy E
a (eV) along
a, b and c directions in NYC and NYB at room temperature (300 K).
NYC NYB Da 7.050 6.150 Db 5.110 5.650 Dc 53.80 6.790 Ea 0.331 0.315 Eb 0.326 0.322 Ec 0.239 0.317
We have calculated the diffusion energy barriers for Na ions using the climbing-image nudged elastic band (CI-NEB) 10-11 and compared the results with values obtained from
a) Path1: Na cations migrate along the c direction by directly hoping from one octahedral (Oct) site to the adjacent Oct sites (Oct-Oct).
b) Path2: Na cations migrate in ab plane via tetrahedral (Tet) sites when hopping from one Oct site to the other Oct site (Oct-Tet-Oct).
As shown in Figure S8, the diffusion barriers are 0.30 and 0.43 eV for path1 and path2, respectively, which are comparable to the values from MSD (see Figures 2&3), confirming the fast 1D diffusion channel in NYC. The NEB values have the similar trend with the MSD results, showing faster 1D diffusion channel along c direction in NYC
For NYB, a 2x1x2 supercell is used and two paths have been considered:
a) Path1: Na cations migrate along the c direction by hoping from one octahedral (Oct) site to the adjacent Oct sites via a tetrahedral (Tet) site (Oct-Tet-Oct).
b) Path2: Na cations migrate in ab plane via a Tet site when hopping from one Oct site to the other Oct site (Oct-Tet-Oct).
As shown in Figure S9, the diffusion barriers of the two paths in NYB are 0.37 and 0.29 eV, respectively, which are comparable to the value of 0.33 eV from MSD.
Figure S8. The considered Na-ion migration (a) path1 and (b) path2 in NYC. The corresponding diffusion energy barrier profiles for (c) path1 and (d) path2. The Na ions in the migration path are denoted by blue spheres.
Figure S9. The considered Na-ion migration (a) path1 and (b) path2 in NYB. The corresponding diffusion energy barrier profiles for (c) path1 and (d) path2. The Na ions in the migration path are denoted by blue spheres.
5. Electrochemical stability
Figure S10. Electrochemical stability of NYC/NYB and some of the most well-known SSEs 12-13 for Na all-solid-state-sodium-ion batteries.
6. Chemical interface stability with cathode materials
Figure S12. Calculated mutual reaction energy
E
D min mutual, , of SE-cathode interface for (a) NYC, (b) NYB, (c) cubic-Na3PS4 (NPS) and (d) Na10GeP2S12 (NGPS). The different cathode materials are featured in solid lines with different colors.Table S4. Phase equilibria and minimum decomposition energies ED min mutual, , of the interfaces between cubic-Na3PS4 (NPS) and Na10GeP2S12 (NGPS) cathode materials. (CSSE and Celectrode are the compositions of SSE and electrode materials, xm is the molar fraction
of the SSE at the minimum reaction energy)
SSE
C Celectrode xm Phase equilibria at xm
, , D min mutual E (meV/a tom) , , D min total E (meV/at om) NaCoO2 0.41 Na2S, Na2SO4, Na3PO4, Co9S8 -385 -388 NaCrO2 0.5 NaCrS2, Na3PO4 -172 -175
Na2FePO4F 0.28 NaF,FeS2,FePS,Na4P2O7 -41 -43
Na3V2(PO4)3 0.23 NaPO3,Na5P3O10,V3S4,VS2 -51 -52
NPS
Na3V2(PO4)2F3 0.16 NaF, Na5P3O10,V4OF12,V3S4,Na2PS3 -41 -42
NaCoO2 0.44 Na2GeO3, Na2S, Co9S8, Na3PO4, Na2SO4 -323 -345 NaCrO2 0.61 Na3PO4, NaCrS2, Na2S, Na6Ge2S7 -135 -164 Na2FePO4F 0.34 FeP, NaF, Na4P2O7, Na6Ge2S7, FeS2, Na2GeS3 -42 -58 Na3V2(PO4)3 0.27 VS2, Na5P3O10, Na4P2O7, V3S4, V4GeS8 -58 -71 NGPS Na3V2(PO4)2F3 0.43 GeS2, Na5P3O10, VS2, V4GeS8, Na2PS3, NaF -48 -69 Reference
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