van der waals dft study of the energetics of alkali metal

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Trondheim, Nov. 29, 2013

Van der Waals DFT Study of the Energetics of

Alkali Metal Intercalation in Graphite

Zhaohui Wang, Sverre M. Selbacħ and Tor Grande

Department of Material Science and Engineering

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Background• Graphite and its alkali metal

intercalation compounds are important in many fields

– Graphite anode in Li (Na?) ion battery

– Graphite cathode in primary aluminium reduction cell

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8Na NaL c

Ha D

d=

Cathode heaving

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Outline

• VASP with van der Waals Functionals• Energetics of the first stage alkali-metal graphite intercalation

compounds (AM-GICs)• Energetics of higher stage AM-GICs (n = 2 to 5)• Charge transfer in AM-GICs• Abnormal behavior of Na-GICs and Li-, K-GICs• Diffusion

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AM-GICs - basics

• Graphite and its intercalation compounds– Weak inter-planer force – van der Waals force– Easily to be intercalated by both electron donor (Li, K, Na?) and acceptor

(AlCl3, SbF5 ..)

+3.42Å 4.53Å

AB stacking AA stackingNa bulk

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VASP with van der Waals functionals

• Vienna Ab initio Simulation Package– Periodical boundary condition

• Test of new developed vdW functionals– Binding energy of graphite

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Outline



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AM-GICs and their polytypes

• In plane super cell and polytypes –Stage I

– MC6: α, β,γ(LiC6: 100- 220 K)– MC6: α, β(EuC6)– MC8: α, β,γ, δ (KC8, RbC8)– MC8: α, β,γ (CsC8)

P6/mmm C/2m P63/mmc Fddd

MC6 MC8

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Energetics – first stage Li –GICs

Exp: Libulk + 6C in graphite LiC6 -/Aα

Unit: kJ/mol (meV/f.u.)

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Energetics – first stage K –GICsUnit: kJ/mol (meV/f.u.)

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Energetics – first stage Na –GICs

All first stage Na-GICs are not stable!

Unit: kJ/mol (meV/f.u.)

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Outline



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Higher Stage AM-GICs• Stage III (/αABA/…)

-- odd stages

• Stage II (/αABβBA/…) -- even stages

Graphene layers withAAstacking or ABstacking

Literature: Stage II and above has AB stacking …?

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Higher Stage AM-GICs

• Formation energy of stoichiometric AM-GICs. Composition given as mole fraction of alkali metal xm.

• Stage II: empty graphite layer has AA stacking, from stage III keep AB stacking

Na-GICs are not stable in all stages (n=2 to 5)!

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Outline



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Density of state – Charge transfer

• Higher electrical conductivity– Shift in fermi energy

• Chemical bond– Characterized by complete charge transfer of AM to carbon

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Objective



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Abnormal behavior of Na-GICs

ΔE1 ΔE2 ΔE3 Sum/ΔHf

LiC6 0.101 0.657 -0.928 -0.170

NaC6 0.236 0.278 -0.298 0.216

KC6 0.326 0.143 -0.673 -0.204

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Outline

• Why density functional theory (DFT)?• VASP with van der Waals Functionals• Energetics of the first stage alkali-metal graphite intercalation


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Defect Diffusion

• Point defects in alkali metal layer

– Interstitial– Vacancy– Frenkel defect

(1) (2)

(1)

(2)

Self-interstitial

VacancyFrenkel defect

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Defect Diffusion

• Energetics of point defects in

– LiC6, NaC6, NaC8, KC8

ΔH (eV/f.u.) Interstitial 1 Interstitial 2 Vacancy Frenkel 1 Frenkel 2

LiC6 0.460 0.460 0.166 0.397 0.651

NaC6 0.946 x -0.068 1.273 (Static) 1.210

NaC8 0.882 0.882 -0.057 0.332 0.857

KC8 0.561 x 0.523 2.698 (Static) 1.381 (Static)

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Defect Diffusion• Transition state theory

– Minimum energy path and saddle point for well defined initial and final state

– Diffusion barrier – Nudged Elastic Band (NEB)

A

B

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Defect Diffusion• Transition state theory

– Minimum energy path and diffusion barrier by Nudged Elastic Band (NEB)

– Vacancy diffusion (LiC6)

Meta stableSaddle pointInitial FinalSaddle point

Meta stable

Saddle point

Initial Final

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Defect Diffusion

• LiC6

– Vacancy diffusion (preliminary)

ω=kT/h exp [-(ΔEmig+ ΔFvib)/kT]

ω=ν0 exp (-ΔEmig/kT)

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Defect DiffusionLiC6 NaC6

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Summary

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Thank you for your attention!

van der waals dft study of the energetics of alkali metal

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