Stochastic Phase Transformation in LiFePO 4 Porous Electrodes Peng Bai , 1,3 Martin Bazant 1,2 and Guangyu Tian 3 1 Chemical Engineering and 2 Mathematics, MIT, USA 3 Automotive Engineering, Tsinghua University, P. R. China
Jan 15, 2016
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