Ab initio Li-S battery calculations

Lin-Wang Wang

Guoping Gao, Swastika Banerjee

Materials Sciences Division

Lawrence Berkeley National Laboratory, Berkeley, CA

BMR theory deep dive, Sept.25-26.

The projects

Li-S battery cathode design

• “2D framework C2N as a potential cathode for lihitum-Sulfur batteries: an ab initio density functional study”, J. Wu, L.W. Wang, J. Mat. Chem. A, 2018, 6, 2984.

• “Phosphorene oxides as a promising cathode material for sealed non-aqueous Li-oxygen batteries”, Y. Li, F. Ma, L.W. Wang, J. Mat. Chem. A, 2018, 6, 7815.

• “Theoretical investigation of 2D conductive microporous coordination polymersas Li-S battery cathode with ultrahigh energy density”, G. Gao, F. Zheng, F. Pan, L.W. Wang, Advanced Energy Mat. https://doi.org/10.1002/aenm.201801823

Li Solid electrolyte design and mechanistic studies

• “Design principles for oxysufilde class of Lithium superionic conductors”, S. Banerjee, X. Zhang, L.W. Wang, Environ. Energy Science (in review)

• “Cooperative transport enabling fast Li-ion diffusion in thio-LISICON Li10SiP2S12 solid electrolyte”, B. Zhang, L. Yang, L.W. Wang, F. Pang (submitted)

• “Finding Li ion diffusion pathway in typical solid state electrolytes and electrode materials by BV-Ewald method”

D. Chen, M. Weng, J. Jie, S. Li, D. Chen, F. Pan, L.W. Wang (submitted)

Li/S cathode electrode design principles

Prevent Li2Sn dissolution Electric conductive Mechanical and redox stable Proper binding energy (high capacity) Light weight Dense in volume

Use upper-right corner elements Using 2D materials Curve up the 2D into amorphous

structures

The first system, C2N as cathode

2Li 3Li 4Li 5Li

6Li 7Li 8Li

Using genetic algorithm to search the structure (fix thesubstrate).

J. Wu, L.W. Wang, J. Mater. Chem. A, 2018, 6, 2984

Oxidized black phosphorene can be used as a Li battery electrode

Energy density and voltage for phosphorene oxides as Li-cathodes

Y. Li, F. Ma, L.W. Wang, J. Mat. Chem. A2018, 6, 7815

(a) Li1P4O1; (b) Li2P4O2; (c) Li3P4O3; (d) Li4P4O4

The conductivities of the electrodes

Structural stability of the system: N_Li must be < N_O

Experimental realized, and electronic properties is tuneable

through transition metal. (J. Am. Chem. Soc. 2017, 139, 19)

2D Coordination Polymers

Conductive

Transition metal: Adsorption sites for terminated S.

Nitrogen: Adsorption sites for terminated Li.

Porous:

Charge polarized solvent model for Li2Sn in electrolyte

ref our result

S8→Li2S8 2.39 2.39

Li2S8-Li2S6 2.37 1.92

Li2S6-Li2S4 2.24 1.36

Li2S4-Li2S2 2.20 2.18

Li2S2-Li2S 2.15 2.33

S8+Li-Li2S 2.20 2.21

Table 1 Experiment voltage vs calculatedvoltage (eV)

The experimental Formation energy of bulk Li2S is obtained by the α-octasulfur,

and Li crystal structures

Li2S2 should be crystal or larger cluster

Li2S4, Li2S6, Li2S8 with solvent effect fit very well with experimental value

Combine experiment and theory, better reliability

The adsorption energy of isolated S8, and Li2Sy molecule on Mn-HAB-CP in the vacuum (bars without pattern) and solvent (bars with net pattern).

The absorption (anchoring) of Li2Sn on Mn-HAB-CP

Optimized Stable Structures

7

isolated

linear

meshed

The genetic algorithm to search the LinSm structure on a substrate

Energy Density

8

The lithiation formation energy is almost a straight line of the number of Li atoms,

indicating a constant voltage of about 1.74 V for the whole charge/discharge

process

The final energy density for the Mn-HAB-CP-Li20S8-Li16S8 final product is 1395

Wh/Kg

Stablitity

Li10S8 Li9S4+1/2Li2S8 Li9S5+1/2Li2S6 Li9S6+1/2Li2S4 Whether dissolved

0 0.59 -0.23 -0.49 Partially

Li20S8 Li19S4+1/2Li2S8 Li19S5+1/2Li2S6 Li19S6+1/2Li2S4 Whether dissolved

0 13.86 10.31 6.24 No

Table 2 The separation energies of Mn-HAB-CP-LixSy into dissolved Li2Sy and the remaining Mn-HAB-CP bounded cluster.

9

Conductivity

10

Volumetric Expansion

10

only 2.7% lattice constant increases in the z-direction, and is similar to that of the

LIB battery.

Optimized Stable Structures

7

No significant volume expansion (lattice constant increases in the z-direction)

during the charge process.

Challenges For Diffusion Rate

12

Nudged elastic band to calculate barrier Only when pathway is simply and well defined system

MetadynamicsNeeds a well defined reaction coordinate

Higher temperatureThe sulfur will be melt !

How about the diffusion in the complex materials, especially in liquid or with liquid involved?

Assumption

13

Our way: Forces are applied to targeted atom (Li atoms) in Molecular Dynamics to drive the diffusion. Then the minimum external force and the diffusion velocity are chosen as new parameters of diffusion ability.

Fexternal

Our method vs NEB

15

The barrier obtained from the

potential in our method is consistent

with the barrier obtained by NEB

calculation. Therefore, our method

is robust.

Time (fs)

Time (fs)

Applied on Li-S battery

15

F = 0.55 eV/Å in X direction

Cut off

15

If di < r, Pot =σ𝑝𝑜𝑡𝑖, if di ≥ r, Pot =σ𝑝𝑜𝑡𝑖 × 𝑒(𝑑−𝑟)2/2.5

F = 0.55 eV/Å in X direction

Applied on Li-S battery

15

F =

0.5

0 e

V/Å

in Z

dir

ecti

on

The diffusion is much easier in the Z direction than that in the X direction

Improve the moisture stability of LiGePS solid electrolyte

M- S + H2O Decomposed product + H2S

Li10GeP2S12 has a high Li-ion conductivity (~ 20 mS cm-1)

But it is moisture unstable:

The problem is at the PS4 motif

Can we selectively replace PS4 to PO4 ?

Change Li10GeP2S12 to Li10GeP2S4O8

Solid electrolyte

From Li10GeP2S12 to Li10GeP2S4O8

PS4 + 4H2O PO4 + 4H2S

Moisture instability happens at PS4 tetrahedron

The stability of the quinary compound decomposition to quaternary compounds

Stability against all the other decompositions

Use a linear program to test all other possible decomposition (~100 possible compounds) Like LiGePO, it is unstable against decompose into ternary compounds (but can have

kinetic barrier) Stable against decomposition into any binary (gas) compounds It is moisture stable

The Li-ion conductivity

The path has changed, instead of a 1D path, it is more a 3D path

The mobility is even higher than pure LiGePS !

More distorted system More possible path (3D instead of 1D) Li goes through LiSxO4-x tetrahedrons, the transition point has lower barrier

Redox stability window

Future plans and challenges (from a methodology point of view)

Large scale linear scaling calculations for solid-liquid, SEI, or solid electrolyte/Li-metal interface, or grain boundary?

Direct ab initio liquid electrolyte chemical free energy calculations?

Machine learning force field?

Linear scaling 3 dimensional fragment (LS3DF)

LS3DF DFT calculations for >10,000 atom systems

It works for metal !

A bi-canonical AIMD for thermal dynamic integration

It is very important to calculate the free energy of Li2Sn in different electrolytes, and to study their configurations (dissociated, or cluster)?

But there is a lack of classical potential to describe the interaction accurately, and it is difficult to calculate them using ab initio method

A recent bi-canonical AIMD method (Frenzel eta, JCTC, 13, 3455, 2017)might make it possible

We will like to implement this method in our code.

It allows thermal dynamic integration (to calculate the free energy) using ab initio method

The bi-canonical AIMD calculation

At least it works for simple ion and water

Does it work for more complicated solvate and solvent ?

Our new algorithm

Old method(the Ei for each atom is not known, only the total energy is known).

New method(Ei is calculated directly from DFT, significantly simplify the training, increase the dataset).

The NNFF accuracy compared to DFT

Acknowledgment

Thanks Tien for the funding !

Thanks the BMR program !