PS 4. Cl 2. Superionic Conductors Predicted from Silver. Thiophosphates using Efficiently Tiered Ab Initio. Molecular Dynamics Simulations

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1 Li 3 Y(PS 4 ) 2 and Li 5 PS 4 Cl 2 : New Lithium Superionic Conductors Predicted from Silver Thiophosphates using Efficiently Tiered Ab Initio Molecular Dynamics Simulations Supporting Information Zhuoying Zhu, Iek-Heng Chu, and Shyue Ping Ong Department of NanoEngineering, University of California, San Diego, 9500 Gilman Drive, Mail Code 0448, La Jolla, CA 92093, USA ongsp@eng.ucsd.edu Methods details Structure relaxation and phase stability All structures were fully relaxed using parameters similar to those used in the Materials Project (MP), 1 which has been extensively tested over a broad range of chemistries and materials. All calculations were spin-polarized and performed using the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA) 2 functional. A k-point density of at least 1000/(number of atoms in the unit cell) and an energy cutoff of 520 ev was used. Where available, pre-relaxed structures were first obtained from the MP using the Materials Application Programming Interface (API) 3 to reduce computational cost. 1

2 The phase stability of all compounds of interest were estimated by constructing the relevant Li-P-S and Li-M-P-S phase diagrams using the convex hull construction. 4 The energy above hull E hull is then used as an estimate of thermodynamic stability. Stable compounds have an E hull of 0, and the higher the value, the more unstable the compound is at 0 K. To account for overbinding of sulfur in PBE, an energy correction for sulfides, as reported in a recent work 5 by the authors, was applied. Li + conductivity Non-spin-polarized ab initio molecular dynamics (AIMD) simulations were performed in an NV T ensemble at elevated temperatures with a Nose-Hoover thermostat. 6,7 A smaller plane-wave energy cutoff of 280 ev, a minimal Γ-centered k-point mesh, and a time step of 2 fs were adopted. The volume (V ) was fixed at the relaxed 0 K volume for AIMD simulations at elevated temperatures, in line with the usual approximations used in previous works. The simulation supercell sizes were at least 9 Å along each lattice direction. All calculations were automated by an in-house automated AIMD workflow. 5,8,9 From the AIMD simulations, the Li + self-diffusivity can be obtained via the following expression: D = [ r(t)] 2 2dt = MSD 2dt, (1) where d is the dimensionality factor that equals 3 for 3D crystal structure, and [ r(t)] 2 is the average Li + mean square displacement (MSD) over a time duration t. The self-diffusivity was obtained via a linear fit of the MSD vs 2dt. The Arrhenius plot was constructed from diffusivities at multiple temperatures to obtain the activation energy (E a ) and the extrapolated room-temperature self-diffusivity (D 300K ). The room-temperature Li + conductivity was then estimated via Nernst-Einstein relation: σ 300K = (ρz 2 F 2 /RT ) D 300K, (2) 2

3 where ρ, R and F are the molar density of Li + in the unit cell, gas constant and Faraday s constant, respectively, and T = 300 K and z = +1 were used in the expression. Electrochemical Stability To estimate the electrochemical stability of solid electrolytes against electrodes, we applied the grand potential approach to predict the phase equilibria at the solid electrolyte/electrode interfaces, as were detailed in our recent work. 10,11 The grand potential approximation assumes Li as the main mobile species, and the solid electrolyte/electrode interfaces can be modeled as an open system respect to Li ions. Under that condition, the relevant thermodynamic potential is then approximated as the grand potential φ = E µ Li N Li in which E, N Li and µ Li are DFT total energy, number of lithium atoms in the open system, and lithium chemical potential, respectively. The solid electrolyte at the metallic Li anode (charged cathode) is modeled as the solid electrolyte at high µ Li = µ Li (low µ Li = µ Li 5 ev), and the corresponding grand potential phase diagram can be constructed and analyzed. Electronic Structure Given the well-known band gap issues by semi-local functionals, the Heyd-Scuseria- Ernzerhof (HSE) hybrid functional was adopted for electronic structure calculations of the promising solid electrolytes for the electronic band gap as well as the density of states (DOS). On account of the relatively high computational cost of HSE compared to PBE, non-spinpolarized calculations with a k-point density of 500/(number of atoms in the unit cell) were utilized. Vacancy Migration Barriers Climbing image nudged elastic band (CI-NEB) calculations were carried out to determine the Li + vacancy diffusion barriers for the most promising lithium superionic conductors identified. A negatively charged Li + vacancy was introduced and overall charge neutrality 3

4 was achieved via adding a positive background charge. The supercell size of for Li 3 Y(PS 4 ) 2 and for Li 5 PS 4 Cl 2 were chosen which consist of 112 atoms and 96 atoms respectively. All the calculated NEB paths comprise five intermediate images and are < 5 Å between the end points. All the ionic forces were converged to within 0.05 ev/å and Monkhorst-Pack k-meshes of and were used for Li 3 Y(PS 4 ) 2 and for Li 5 PS 4 Cl 2, respectively. Modeling the Li 9.54 Si 1.74 P 1.44 S 11.7 Cl 0.3 superionic conductor The Li 9.54 Si 1.74 P 1.44 S 11.7 Cl 0.3 superionic conductor reported recently by Kato et al. 15 has an extraordinarily high ionic conductivity of 25 ms/cm, and has the same framework as the Li 10 GeP 2 S 12 (LGPS) earlier reported by Kamaya et al. 16 To estimate its diffusion characteristics for comparison with our proposed candidates, we first constructed a model based on an approximate composition of Li 10 Si 1.5 P 1.5 S 11.5 Cl 0.5. Starting from the conventional cell of LGPS with formula Li 20 Ge 2 P 4 S 24, all Ge were replaced with Si, one P atom was replaced with Si, and one S atom was replaced with Cl, yielding a cell formula of Li 20 Si 3 P 3 S 23 Cl, which reduces to Li 10 Si 1.5 P 1.5 S 11.5 Cl 0.5. An enumeration was performed using the algorithm of Hart et al. 17 was performed to yield all symmetrically distinct orderings of Si/P and S/Cl, and all structures were fully relaxed using DFT calculations employing the same parameters as outlined in the Methods section. The ordering with the lowest energy structure was then used for subsequent investigations, e.g., AIMD, stability analyses, etc. It should be noted that the experimental structure is a disordered one, but we do not expect the diffusion characteristics to be significantly affected by the choice of the starting structure. 4

5 Derivation of mean square displacement criteria based for short AIMD screening Short AIMD simulations of 60 ps were performed for the quick screening step. The first 10 ps ( 5,000 time steps) was used for heating up as well as for equilibration, and the trajectories from 10 ps to 60 ps were used to estimate the MSD. Based on our previous AIMD calculations, the diffusivities for most known superionic conductors at 800 K are at least 10 6 cm 2 /s. By combining Eqn. (1) and benchmarking results shown in Figure 2, we have set set MSD 800K > 5 Å 2 as the baseline diffusivity criterion. Assuming that the diffusivity follows an Arrhenius relationship, we can also write the diffusivity as: D = D 0 e Ea kt, (3) where E a is the activation barrier and k is Boltzmann s constant. Combining equations (1) and (3), we can write: MSD = 2D 0 dte Ea kt (4) Let us consider the ratio of MSD at 1200 K and 800 K for the same simulation time period t. MSD 1200K MSD 800K = e Ea 1200k + Ea E a = 2400 k ln 800k, (5) ( ) MSD1200K. (6) MSD 800K For MSD 1200K MSD 800K < 7, E a < 402 mev. 5

6 Other NEB vacancy migration barriers in Li 3 Y(PS 4 ) 2 and Li 5 PS 4 Cl 2 Energy (mev) mev Reaction coordinate Figure S1: Calculated CI-NEB migration barriers for Li1-Li2 (C E: 4.79 Å) hop in Li 3 Y(PS 4 ) 2 structure. 6

7 Energy (mev) Energy (mev) Energy (mev) mev Reaction coordinate mev (a) J I (3.43 Å) Reaction coordinate (b) G I (4.07 Å) 396 mev Reaction coordinate 1.0 (c) K I (3.99 Å) Figure S2: Calculated CI-NEB migration barriers for Li1-Li2 hops in Li 5 PS 4 Cl 2 structure. 7

8 Distinct part of van Hove correlation function for Li3Y(PS4)2 and Li5PS4Cl2 Time (ps) 4 3 Gd (t,r) r ( Å) (a) Li3 Y(PS4 )2 Time (ps) 4 3 Gd (t,r) r ( Å) (b) Li5 PS4 Cl2 Figure S3: Plots of distinct-part of the van Hove correlation function (Gd ) for (a) Li3 Y(PS4 )2 and (b) Li5 PS4 Cl2 at 800 K. The emergence of the pronounced peak near r=0 within 10 ps provides an estimate of the time scale at which a diffusing atom is replaced by another. 8

9 Li grand potential analysis of Li 3 Y(PS 4 ) 2 and Li 5 PS 4 Cl 2 Li uptake per atom 1.5 Li 3 P, YP, Li 2 S Li 3 P, LiCl, Li 2 S LiCl, Li 15 P 4 S 16 Cl 3 Li 3 Y(PS 4 ) 2 Li 5 PS 4 Cl 2 YPS 4, Li 3 PS 4 YPS 4, S, P 2 S 5 P 2 S 5, S 2 Cl 2, PCl Voltage vs Li/Li + (V) Figure S4: Li grand potential phase stability plots for Li 3 Y(PS 4 ) 2 and Li 5 PS 4 Cl 2 solid electrolytes. At low voltage, Li 3 Y(PS 4 ) 2 and Li 5 PS 4 Cl 2 undergo reduction process and uptake Li whereas at high voltage, they are oxidized and lose Li. Text in the plot indicates predicted phase equilibria at corresponding regions. 9

10 Elastic properties of Li 3 Y(PS 4 ) 2 and Li 5 PS 4 Cl 2 Table 1: Elastic constants for Li 3 Y(PS 4 ) 2 and Li 5 PS 4 Cl 2 using PBE functional. Formula Bulk modulus Shear modulus Young s modulus Poisson s ratio (GPa) (GPa) (GPa) Li 3 Y(PS 4 ) Li 5 PS 4 Cl

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