Yue Qi

Chemical Sciences and Materials Systems Lab

General Motors R&D Center

yue.qi@gm.com

Integrating material properties and 

Microstructures into Li-ion battery 

failure modeling

Example: Graphite Anode Deformation during Lithiation

In collaborations with:

S. Harris, I. Dutta, A. Timmons, L. Hector, YT Cheng
V

PF6

-

Charge mechanism (reverse of discharge)

PF6

-

PF6

-

PF6

-

Li+

Li+

Li Li+ +

Cathode is full of lithium when 

manufactured and at the end of 

discharge Li+

e

-

Li+

e

-

Li+

e

-

Li+

e

-

Li+

e

-

PF6

- Li+

PF6

- Li+

PF6

- Li+

PF6

- Li+

PF6

- Li+

Metal oxide Electrolyte Carbon

By putting energy into the cell, lithium is forced 

out of the metal oxide (positive) and into the 

carbon (negative).

Li+

e

-
General Needs for Li-ion Batteries

• Simultaneously address these critical challenges

– Performance 

• low-temperature operation

• energy (capacity X voltage)

• power

– Cost

• Cell (material + manufacture) + other components in the pack

– Life

• Calendar life

• Cycle life

– Abuse tolerance

These problems are inter-connected, for example: life & 

cost
Choice of application decides 

the critical problems to be solved

•EV: Need double the energy density of presently available Li batteries

•Plug-in hybrid: life and cost 

•HEV: low-T operation, cost, and abuse tolerance
Mechanical Degradation of Graphite Negative 

Electrode

• During cycling, graphite particles can crack into smaller pieces. The free 

surface is then covered by SEI, which consumes Li, thus leads to capacity 

fading. 

• The swelling and shrinking of graphite particles can also lead to 

decohesion of the electrode from the current collector, to failure of the 

binder, and to movement of conductive carbon, all of which reduce 

connectivity 

 loss of active materials and loss of capacity

• Packing of graphite particles with different geometries will influence 

whether or not porosity is significantly affected by the swelling and 

shrinking of graphite particles. 

Li0

Li

~10 mm
Cracking of Graphite Negative Electrode
Analyses comprehending both electrochemistry 

and solid mechanics

• R. A. Huggins and W. D. Nix, Ionics 6, 57 (2000)

• R. E. García, Y-M. Chiang, W. C. Carter, P. Limthongkul, and C. M. Bishop, J. 

Electrochem. Soc. 152, A255 (2005).

• J. Christensen and J. Newman, J. Electrochem. Soc. 153, A1019 (2006).

• J. Christensen and J. Newman, J. Solid State Electrochem. 10, 293 (2006).

• X. Zhang, W. Shyy, and A. M. Sastry, J. Electrochem. Soc. 154, A910 (2007).

• X. Zhang, A. M. Sastry, and W. Shyy, J. Electrochem. Soc. 155, A542 (2008).

• YT. Cheng and MW Verbrugge, J. Appl. Phys., 104, 083521 (2008)

• M. W. Verbrugge, Y-T. Cheng, The Electrochemical Society Transactions 16 (2008) 

127. 

• ..... 

How materials change? Microstructure? Validation? 

electrochemistry  Li concentration gradient 

 volume change  solid mechanics
Atomic Charges in Li-GIC Structures

3a

3a

a

b

g

Side 

view

9.6%

-0.6%

-0.6%

A

a

A

B

A

a

A

10.4%

-3.7%

A

a

A

A

A

A

a

7.4%

A

a

A

A

A

A

a

a

a

3a

3a

Side 

view

9.9%

0.2%

A

a

A

A

A

a

A

LiC18 LiC12 LiC6

dilute stage-2 LiC18

stage-3 LiC18

Li, with +0.8e

C, with -0.14e

C, with -0.06~-0.07e

C, with 0~-0.01e

[ ]

 -  -

Li  e  S  Li - S

Li insertion reaction in graphite (S is 

the site for Li+) 
Atomic Bonding in Li-GIC

LiC18 LiC12 LiC6 C C

C C C

C C

C C

Li Li

C C

C C

C C

Li Li

C C

C C

Li Li

C

( r )

Inter-layer bonding: The ionized Li and the C-ring above and below it form a strong 

cation-p interaction  Stronger

Intra-layer bonding: Excess electrons fill the anti-p bonding orbitals in graphite, and 

in-plane s-bonds loss electrons  Weaker 
0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.2 0.4 0.6 0.8 1

Cij (Li) / Cij

0

x in LixC6

C11 C66

C33 C44

Elastic Properties Changes for Single Crystals 

Inter-layer bonding: stronger

Intra-layer bonding: weaker

C11 C12 C13 C33 C44 C66

Graphite 1104.8 203.9 -2.5 30.9 5.6 450.45

stage-3 LiC18 1058.1 194.8 -2.5 43.4 8.4 431.65

LiC12 1047.7 191.9 -5.9 68.3 9.7 427.9

LiC6 988.6 170.6 2.1 78.0 21.9 409

[ Y. Qi, H. Guo, L. Hector, A. Timmons, J. Electrochemical Society, 157 (5) A558 (2010) ]

DFT 

predicted
Averaged Elastic Properties for Polycrystals

Young’s Modulus increases with

Li concentration / SOC

Reuss average ER Reuss average m

Graphite 32.47 0.31522

stage-3 LiC18 28.57 0.39

LiC12 58.06 0.34

LiC6 108.67 0.24

R Li Li E (x ) 19.2582.23x

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.2 0.4 0.6 0.8 1

Cij (Li) / Cij

0

x in LixC6

ERER ER (xLi)

FIB Sideview TEM
Lithiation induced hardening and softening

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.2 0.4 0.6 0.8 1

Cij (Li) / Cij

0

x in LixC6

ERER ER (xLi)

Li-Graphite Li-Si (crystal and amorphous) 

[ Y. Qi, H. Guo, L. G. Hector and A. Timmons, Journal of The Electrochemical Society , 157, A558-A566 (2010). ]

[ V. B. Shenoy, P. Johari, Y. Qi, J. Power Sources, 195, 6825 (2010) ]

E=E0+k*c
• Young’s Modulus of 

electrode material as a 

linear function of Li 

concentration

E= E0 +k*C 

(K= -90 Gpa, -40Gpa, 0Gpa , 

90Gpa, 200 Gpa)

Concentration profiles are 

symmetric during insertion 

and de-insertion

Resolve the DIS for a solid particle with 

E(SOC)
Softening electrode is less likely to crack in 

the center during Li insertion

[R.D. Deshpande, Y. Qi, Y.T. Cheng, J. Electrochemical Society, 157, A967 (2010) ]
Hardening electrode is less likely to crack at 

the surface during Li removal
Influence from micro-structures

Shrinking Core Model: Li transport within particles is macro-homogeneous. 

Can solid spheres or fibers represent real electrodes? 

Inside of an electrode particles. 

graphite particle
Diffusion in a cylindrical particle (1 mm) 

with a small pore (10 nm)

• Diffusion of Li+

• Under a potentiostatic charging-discharging condition or constant 

concentration of Li ions surrounds the electrode particle. 

• Compare Three Cases: 

– Solid electrode, no pore

– Filled mesopore: 

Pre-existing coaxial pore

of radius a, filled with electrolyte

– Empty mesopore: Pre-existing 

coaxial pore of radius a, empty 

(not accessible to the electrolyte)

Li

;

;

.

;

;

. 

;

.

a=1% R
Filled Mesopores Enhance Diffusion 

Solid electrode Filled mesopore Empty mesopore

Time
Radial Stress During Lithiation 

Solid electrode Filled mesopore

Empty mesopore

Solid electrode particle fails at the center. Presence of the pore 

prevents failure at the center and reduces failure inside the particle.

[S. J. Harris, R.D. Deshpande, Y. Qi, I. Dutta, Y.T. Cheng, J. Mat. Res., 25, 1433 (2010) ]
Visualization of Diffusion Induced Deformation

Lishen laptop 18650

Carbon electrode

Step 1: Optical Half-Cell to visualize Li diffusion

P. Maire, A. Evans, H.Kaiser, W. Scheifele, and P.Novák, J. Electrochem. Soc. , 155 , 862 (2008)

LiC6

LiC12

1 cm

Teflon separator

Li metal Electrode

Graphite Electrode

Electrolyte

Steel support

Steel support

Steel support

color maps (Li concentration)
Li diffusion

Color maps Li concentrations and diffusion 

T12
DIC Strain Map along major Diffusion Direction

Li main diffusion direction

Strain

along this 

direction 

From T1 to T2

[ Y. Qi and S.J. Harris, J. Electrochemical Society, 157, A741-A747, (2010) ]
Yue Qi, Stephen J. Harris

Expansion Zones

T1 T2
Compression Zones

Li stiffening is responsible for the 

compression during Lithiation

Li main diffusion direction, strain direction

T1 T2
Conclusions and future work

• Li stiffens graphite during intercalation (proved by DIC)

• Li softens Si during lithiation 

• The fracture energy of Li-graphite decreases with voltage 

• Most material properties are functions of SOC

• Internal defects can change diffusion and diffusion induced stress

• Future Work: To connect material chemistry and structure 

with degradation mechanisms 

• Chemistry, Surface treatment, Particle structure, Defects

• Microstructure (packing, porosity ... )

• Goal: To model failure modes and predict batteries life