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
Fitting Examples
18Bai and Bazant, under review
Charge/Discharge Asymmetry
19
Qualitative Explanations
20
