Stochastic Phase Transformation in LiFePO4 Porous Electrodes

Peng Bai,1,3 Martin Bazant1,2 and Guangyu Tian3

1Chemical Engineering and 2Mathematics, MIT, USA3Automotive Engineering, Tsinghua University, P. R. China

Outline

• Background • Phase Transformation Dynamics

– Single Particles– Porous Electrodes– Statistical model– KJMA theory

• Discussion• Conclusion

2

Background

• LiFePO4 batteries– Wide voltage plateau– Binary phase-separating (PS) system– Properties are well explored– Implications for other PS materials

• Phase transformation dynamics– Single particle scale

• Slow two-phase mechanism• Ultrafast discharge• Suppression of phase separation

– Porous electrode scale

Padhi et. al., J. ECS 1997

Bai, et al. Nano Letters (2011)

3

Lithium Intercalation in Single Particle

4

Suppression of Phase Separation

Bai, et al. Nano Letters (2011)

0 0

R Rc

t e e

5

Oyama et al, JPCC (2012)

Validation by Voltage-Step Experiments

Kolmogorov-Johnson-Mehl-Avrami (KJMA) Theory

Kolmogorov-Johnson-Mehl-Avrami (KJMA) Theory

1 exp nf kt

1 expn nI Ct kt KJMA

Mechanism

Monotonic homogeneousNon-monotonic two-phase Bai and Tian, Electrochimica Acta (2013)

Porous Electrode = Single Particle ?6

Porous Electrode: A Many-Particle System

Bai and Tian, Electrochimica Acta (2013)

Chueh et al., Nano Lett. (2013)

Brunetti et al., Chem. Mater.

(2011)

Delmas et al., Nat. Mater. (2008)

• State of charge = number fraction• Fraction of half-filled particles < 2%

1

rN t

a k tk

r t

dN t n dt dN t

nN t dt dN t

1

aN t

t k ak

dN t m dt mN t dt

KJMA Mechanism

7

Population Dynamics of Active Particles

1

rN t

a k t r tk

dN t n dt dN t nN t dt dN t

1

aN t

t k ak

dN t m dt mN t dt

Population DynamicsHomogenizationPhase-separating Materials

1 2exp expaN C mt C nt

1 21 exp expt

mN C mt C nt

n

0 1 1 01 2

1 1,

N m N n N N nC C

m n m n

Bai and Tian, Electrochimica Acta (2013) 8

Transient Currents

1 1

a aN N

k k k a ak k

I m Q i iN mQN

Oyama et al, JPCC (2012)

1 expn nI Ct kt

Bai and Tian, Electrochimica Acta (2013) 9

Another ExampleSato et al. ECS Meeting Abstract (2012) LiNi0.5Mn1.5O4

NrNaNt

10

Nucleation Rates and Reaction Rates

Bai and Tian, Electrochimica Acta (2013) 11

Transient currents of a monolayer

Chidsey, Science (1991) 12

Transient Currents of Porous Electrodes

0 1000 2000 3000

10-2

10-1

Time / sI

/

mA

0 1000 2000 30000

0.1

0.2

0.3

0.4

0.5

0.6

Time / s

I /

m

A

~200mVKJMA fails

Not homogeneousn is finite

Generalized activation rate: n =kA Apparent reaction rate: m =k Bai and Bazant, under review 13

Validation of the Population Dynamics

Levi et al. J. Phys. Chem. C (2013) 14

Conclusion• Non-monotonic transient currents do not necessary indicate

the nucleation-and-growth mechasnim; it could simply be a result of population dynamics

• Statistical effects (population dynamics) must be considered in interpreting experimental results of porous electrodes.

• Generalized activation rate captures the random activation process, and is a indicator for whether the reaction is homogenous

• Reaction rate must be decoupled from the activation rate, which is not possible for the KJMA equation

• This simple model could be improved with transport effects and particle size distributions

15

Acknowledgements• Collaborators

– Prof. Chunsheng Wang, University of Maryland– Prof. Xiangming He, Tsinghua University– Prof. Jianbo Zhang, Tsinghua University

• Funding Sources– Tsinghua University – State Key Lab of Automotive Safety and Energy– MIT Lincoln Lab (Postdoc)

16

Thank You!

Peng BaiPostdoctoral Associate

Department of Chemical EngineeringMIT

pengbai@mit.edu

Fitting Examples

18Bai and Bazant, under review

Charge/Discharge Asymmetry

19

Qualitative Explanations

20