Modeling Crystalline Electrolytes: Li 7 P 3 S 11 and Analogous Phosphates

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1 Modeling Crystalline Electrolytes: Li 7 P S and Analogous Phosphates Wake Forest University February 27, 22

2 Why Study Thiophosphate Solid Electrolytes Many solid electrolytes have safety advantages over traditional organic liquid electrolytes Electrochemical stability window for solids allows new battery chemistries Lithium thiophosphates have high conductivities relative to LiPON and many other solid electrolyte materials Conductivity increase associated with crystallization

3 Li 7 P S 2c 4b a 42 atoms (2 formula units)/unit cell Triclinic (P symmetry) Mixture of PS 4 tetrahedra and P 2 S 7 dimers No fractional occupancy

4 Summary of Experimental Findings Synthesis Heated glass precursor Water quenched melt Metastable with respect to Li 4 P 2 S 6 and Li PS 4 Conductivity of x S/cm Activation energy of.2 ev per formula unit Described as superionic conductor

5 Goals for this theoretical study Understanding Structures and Stability Calculate heats of formation Exploring Detailed Mechanisms for Conductivity Evaluate vacancy and interstitial defect migration mechanisms Energy cost for migration (E m ) Energy cost for defect pair formation (E f ) Conductivity relations σ(t ) = ( C T )e E A/k B T 2 E A = E f/2 + E m

6 Methods Calculational Methods Density functional theory LDA approximation USPP Quantum Espresso(PWscf) Exploring Detailed Mechanisms for Conductivity Defect calculations were carried out in 84 atom supercell Add/remove ion and compensate with a uniform charge of the opposite sign Nudged Elastic Band(NEB) method used to estimate migration barriers

7 Structures and Stability Li 7 P S Metastable Li 7 P S Li PS 4 + Li 4 P 2 S 6 + S.78 ev Corresponds to exothermic decomposition seen in experiment Crystal is stable at room temperature Li 7 P O Metastable Li 7 P O Li PO 4 + Li 4 P 2 O 7.5 ev Structure has not been experimentally realized Li 8 P O N Metastable Li 8 P O N Li PO 4 + Li 5 P 2 O 6 N.6 ev Structure has not been experimentally realized

8 Understanding Conductivity: Li 7 P S Interstitial Sites β γ α ε δ ζ Found via grid search 6 inequivalent interstitial positions 7 perfect crystal Li positions Table: Li 7 P S interstitial energies relative to α Label E i (ev) α. β.7 γ. δ. ɛ.8 ζ.9

9 Understanding Conductivity: Li 7 P S Interstitial Migration β γ ε ζ δ α Not evenly distributed Pure interstitial E m =.49 ev E path (ev) Along c-axis α ε β β ε α E m

10 Understanding Conductivity: Li 7 P S Vacancy Migration 2c 4b a Energy range of vacancies is 8 ev Large number of possibilities Pairwise steps Shortest path problem with E m as weight

11 Understanding Conductivity: Li 7 P S Vacancy Migration 2c b 2a Energy barriers (E m ) c.42 ev a 9 ev b.5 ev Calculated value agrees with experiment:.5ev.2ev E path (ev) E path (ev) Lowest energy complete path along a,b,c Paths contain significant structure Along c axis Along a axis E m E path (ev).4.. Along b axis E m E m 4 4

12 Understanding Conductivity: Li7 P S Vacancy Migration Structure in paths can be related to locations of interstitial sites Em Delta..4 Epath (ev) Vacancy only mechanism involves interstitial locations Along c axis Along a axis. Em Gamma 2 Many interstitial locations near lowest energy vacancy path Beta Delta Epath (ev) Epath (ev).4 Along b axis. Em Beta. 4 4 Purple γ Blue δ Green β β γ ε δ ζ α Modelling Li7 P S and related materials

13 Understanding Conductivity: Li 7 P S Defect Pair Formation Table: Li 7 P S interstitial energies Label E f (ev) E fm (ev) 5ɛ -.. 4γ.2.8 β.5.9 7ɛ.7. β γ ε α δ ζ Several E f values near zero E fm is the barrier height for pair formation Negative value is within error due to limited supercell Low energy interstitials are similar to fractional occupancy

14 Li 7 P O and Li 8 P O N 2c Neither structure has been synthesized Insight into possible local structures in LiPON 4b 2a

15 Li 7 P O Conductivity The activation energy for Li 7 P O was found in the same manner as its thiophosphate analogue. E path (ev).6.4 Along c axis E path (ev).6.4 Along a axis 7 7 Along b axis E path (ev) E m E m E m =.52 ev No structure corresponding to low energy metastable sites Typical E f.8 Close to experimental values for similar materials v v 2 v

16 Li 8 P O N Conductivity 2c 4b 2a Conductivity in Li 8 P O N was evaluated in a similar way. E m =.6 ev E f.2 Close to experimental values for similar materials E path (ev) E m

17 Conclusions Stabilized crystal structure approximately corresponds to experiment Calculated metastability agrees with experiment Calculated E A (.6 ev) agrees well with experiment (.2eV) Vacancy mechanism dominant Low energy interstitial sites appear to play an important role in conductivity Nitrogen addition increased stability, not conductivity

18 Acknowledgements Supported by NSF grant DMR-7529 Computer Modeling of Crystalline Electrolytes Lithium Thiophosphates and Phosphates N. D. Lepley and N. A. W. Holzwarth, J. Electrochem. Soc. 59, A58-A547 (22)