By directly solving the prescribed differential equations, an analytical method based on the cohesive model has been developed to investigate the interfacial debonding process induced by lithiation in an axisymmetric thin film electrode where an elastic active layer is bonded on a rigid substrate. The assumption of rigid substrate has been proved acceptable for high-modulus substrates such as copper and aluminum which are common materials for current collectors in lithium-ion batteries. For the case where the weak interface is assumed and the radial concentration gradient is neglected, an extremely simplified solution has been obtained. The simplified solution which has acceptable accuracy provides a good guidance for understanding and predicting the interfacial debonding.

References

1.
Green
,
M.
,
Fielder
,
E.
,
Scrosati
,
B.
,
Wachtler
,
M.
, and
Moreno
,
J. S.
,
2003
, “
Structured Silicon Anodes for Lithium Battery Applications
,”
Electrochem. Solid-State Lett.
,
6
(
5
), pp.
A75
A79
.
2.
Kasavajjula
,
U.
,
Wang
,
C.
, and
Appleby
,
A. J.
,
2007
, “
Nano- and Bulk-Silicon-Based Insertion Anodes for Lithium-Ion Secondary Cells
,”
J. Power Sources
,
163
(
2
), pp.
1003
1039
.
3.
Boukamp
,
B. A.
,
Lesh
,
G. C.
, and
Huggins
,
R. A.
,
1981
, “
All Solid Lithium Electrodes With Mixed Conductor Matrix
,”
J. Electrochem. Soc.
,
128
(
4
), pp.
725
729
.
4.
Winter
,
M.
, and
Besenhard
,
J. O.
,
1999
, “
Electrochemical Lithiation of Tin and Tin-Based Intermetallics and Composites
,”
Electrochim. Acta
,
45
(
1–2
), pp.
31
50
.
5.
Lee
,
S.-J.
,
Lee
,
J.-K.
,
Chung
,
S.-H.
,
Lee
,
H.-Y.
,
Lee
,
S.-M.
, and
Baik
,
H.-K.
,
2001
, “
Stress Effect on Cycle Properties of the Silicon Thin-Film Anode
,”
J. Power Sources
,
97–98
, pp.
191
193
.
6.
Beaulieu
,
L.
,
Hatchard
,
T.
,
Bonakdarpour
,
A.
,
Fleischauer
,
M.
, and
Dahn
,
J.
,
2003
, “
Reaction of Li With Alloy Thin Films Studied by In Situ AFM
,”
J. Electrochem. Soc.
,
150
(
11
), pp.
A1457
A1464
.
7.
Ryu
,
J. H.
,
Kim
,
J. W.
,
Sung
,
Y.-E.
, and
Oh
,
S. M.
,
2004
, “
Failure Modes of Silicon Powder Negative Electrode in Lithium Secondary Batteries
,”
Electrochem. Solid-State Lett.
,
7
(
10
), pp.
A306
A309
.
8.
Chan
,
C. K.
,
Peng
,
H.
,
Liu
,
G.
,
McIlwrath
,
K.
,
Zhang
,
X. F.
,
Huggins
,
R. A.
, and
Cui
,
Y.
,
2008
, “
High-Performance Lithium Battery Anodes Using Silicon Nanowires
,”
Nat. Nanotechnol.
,
3
(
1
), pp.
31
35
.
9.
Li
,
J.
,
Dozier
,
A. K.
,
Li
,
Y.
,
Yang
,
F.
, and
Cheng
,
Y.-T.
,
2011
, “
Crack Pattern Formation in Thin Film Lithium-Ion Battery Electrodes
,”
J. Electrochem. Soc.
,
158
(
6
), pp.
A689
A694
.
10.
Xiao
,
X.
,
Liu
,
P.
,
Verbrugge
,
M. W.
,
Haftbaradaran
,
H.
, and
Gao
,
H.
,
2011
, “
Improved Cycling Stability of Silicon Thin Film Electrodes Through Patterning for High Energy Density Lithium Batteries
,”
J. Power Sources
,
196
(
3
), pp.
1409
1416
.
11.
He
,
Y.
,
Wang
,
Y.
,
Yu
,
X.
,
Li
,
H.
, and
Huang
,
X.
,
2012
, “
Si-Cu Thin Film Electrode With Kirkendall Voids Structure for Lithium-Ion Batteries
,”
J. Electrochem. Soc.
,
159
(
12
), pp.
A2076
A2081
.
12.
He
,
Y.
,
Yu
,
X.
,
Li
,
G.
,
Wang
,
R.
,
Li
,
H.
,
Wang
,
Y.
,
Gao
,
H.
, and
Huang
,
X.
,
2012
, “
Shape Evolution of Patterned Amorphous and Polycrystalline Silicon Microarray Thin Film Electrodes Caused by Lithium Insertion and Extraction
,”
J. Power Sources
,
216
, pp.
131
138
.
13.
Wang
,
Y. H.
,
He
,
Y.
,
Xiao
,
R. J.
,
Li
,
H.
,
Aifantis
,
K. E.
, and
Huang
,
X. J.
,
2012
, “
Investigation of Crack Patterns and Cyclic Performance of Ti–Si Nanocomposite Thin Film Anodes for Lithium Ion Batteries
,”
J. Power Sources
,
202
, pp.
236
245
.
14.
Taheri
,
P.
,
Hsieh
,
S.
, and
Bahrami
,
M.
,
2011
, “
Investigating Electrical Contact Resistance Losses in Lithium-Ion Battery Assemblies for Hybrid and Electric Vehicles
,”
J. Power Sources
,
196
(
15
), pp.
6525
6533
.
15.
Yang
,
F.
,
2011
, “
Criterion for Insertion-Induced Microcracking and Debonding of Thin Films
,”
J. Power Sources
,
196
(
1
), pp.
465
469
.
16.
Haftbaradaran
,
H.
,
Xiao
,
X.
,
Verbrugge
,
M. W.
, and
Gao
,
H.
,
2012
, “
Method to Deduce the Critical Size for Interfacial Delamination of Patterned Electrode Structures and Application to Lithiation of Thin-Film Silicon Islands
,”
J. Power Sources
,
206
, pp.
357
366
.
17.
Pal
,
S.
,
Damle
,
S. S.
,
Patel
,
S. H.
,
Datta
,
M. K.
,
Kumta
,
P. N.
, and
Maiti
,
S.
,
2014
, “
Modeling the Delamination of Amorphous-Silicon Thin Film Anode for Lithium-Ion Battery
,”
J. Power Sources
,
246
, pp.
149
159
.
18.
Liu
,
M.
,
2015
, “
Finite Element Analysis of Lithiation-Induced Decohesion of A Silicon Thin Film Adhesively Bonded to A Rigid Substrate Under Potentiostatic Operation
,”
Int. J. Solids Struct.
,
67–68
, pp. 263–271.
19.
Lu
,
B.
,
Song
,
Y.
,
Guo
,
Z.
, and
Zhang
,
J.
,
2013
, “
Modeling of Progressive Delamination in A Thin Film Driven by Diffusion-Induced Stresses
,”
Int. J. Solids Struct.
,
50
(14–15), pp.
2495
2507
.
20.
Lu
,
B.
,
Song
,
Y.-C.
,
Guo
,
Z.-S.
, and
Zhang
,
J.-Q.
,
2013
, “
Analysis of Delamination in Thin Film Electrodes Under Galvanostatic and Potentiostatic Operations With Li-Ion Diffusion From Edge
,”
Acta Mech. Sin.
,
29
(
3
), pp.
348
356
.
21.
Lu
,
B.
,
Song
,
Y.
, and
Zhang
,
J.
,
2015
, “
Time to Delamination Onset and Critical Size of Patterned Thin Film Electrodes of Lithium Ion Batteries
,”
J. Power Sources
,
289
, pp.
168
183
.
22.
Shenoy
,
V. B.
,
Johari
,
P.
, and
Qi
,
Y.
,
2010
, “
Elastic Softening of Amorphous and Crystalline Li–Si Phases With Increasing Li Concentration: A First-Principles Study
,”
J. Power Sources
,
195
(
19
), pp.
6825
6830
.
23.
Qi
,
Y.
,
Hector
,
L. G.
, Jr.
,
James
,
C.
, and
Kim
,
K. J.
,
2014
, “
Lithium Concentration Dependent Elastic Properties of Battery Electrode Materials From First Principles Calculations
,”
J. Electrochem. Soc.
,
161
(
11
), pp.
F3010
F3018
.
24.
Baggetto
,
L.
,
Niessen
,
R. A. H.
,
Roozeboom
,
F.
, and
Notten
,
P. H. L.
,
2008
, “
High Energy Density All-Solid-State Batteries: A Challenging Concept Towards 3D Integration
,”
Adv. Funct. Mater.
,
18
(
7
), pp.
1057
1066
.
25.
Liu
,
X. H.
,
Wang
,
J. W.
,
Huang
,
S.
,
Fan
,
F.
,
Huang
,
X.
,
Liu
,
Y.
,
Krylyuk
,
S.
,
Yoo
,
J.
,
Dayeh
,
S. A.
,
Davydov
,
A. V.
,
Mao
,
S. X.
,
Picraux
,
S. T.
,
Zhang
,
S.
,
Li
,
J.
,
Zhu
,
T.
, and
Huang
,
J. Y.
,
2012
, “
In Situ Atomic-Scale Imaging of Electrochemical Lithiation in Silicon
,”
Nat. Nanotechnol.
,
7
(
11
), pp.
749
756
.
26.
Wang
,
J. W.
,
He
,
Y.
,
Fan
,
F.
,
Liu
,
X. H.
,
Xia
,
S.
,
Liu
,
Y.
,
Harris
,
C. T.
,
Li
,
H.
,
Huang
,
J. Y.
,
Mao
,
S. X.
, and
Zhu
,
T.
,
2013
, “
Two-Phase Electrochemical Lithiation in Amorphous Silicon
,”
Nano Lett.
,
13
(
2
), pp.
709
715
.
27.
Obrovac
,
M. N.
, and
Christensen
,
L.
,
2004
, “
Structural Changes in Silicon Anodes During Lithium Insertion/Extraction
,”
Electrochem. Solid-State Lett.
,
7
(
5
), pp.
A93
A96
.
28.
McDowell
,
M. T.
,
Lee
,
S. W.
,
Harris
,
J. T.
,
Korgel
,
B. A.
,
Wang
,
C.
,
Nix
,
W. D.
, and
Cui
,
Y.
,
2013
, “
In Situ TEM of Two-Phase Lithiation of Amorphous Silicon Nanospheres
,”
Nano Lett.
,
13
(
2
), pp.
758
764
.
29.
Camacho
,
G. T.
, and
Ortiz
,
M.
,
1996
, “
Computational Modelling of Impact Damage in Brittle Materials
,”
Int. J. Solids Struct.
,
33
(
20–22
), pp.
2899
2938
.
30.
Cheng
,
Y.-T.
, and
Verbrugge
,
M. W.
,
2009
, “
Evolution of Stress Within A Spherical Insertion Electrode Particle Under Potentiostatic and Galvanostatic Operation
,”
J. Power Sources
,
190
(
2
), pp.
453
460
.
31.
Zhang
,
J.
,
Lu
,
B.
,
Song
,
Y.
, and
Ji
,
X.
,
2012
, “
Diffusion Induced Stress in Layered Li-Ion Battery Electrode Plates
,”
J. Power Sources
,
209
, pp.
220
227
.
32.
Lu
,
B.
,
Song
,
Y.
, and
Zhang
,
J.
,
2016
, “
Selection of Charge Methods for Lithium Ion Batteries by Considering Diffusion Induced Stress and Charge Time
,”
J. Power Sources
,
320
, pp.
104
110
.
33.
Bhandakkar
,
T. K.
, and
Gao
,
H.
,
2010
, “
Cohesive Modeling of Crack Nucleation Under Diffusion Induced Stresses in a Thin Strip: Implications on The Critical Size for Flaw Tolerant Battery Electrodes
,”
Int. J. Solids Struct.
,
47
(
10
), pp.
1424
1434
.
34.
Yan
,
Y.
,
Sumigawa
,
T.
,
Shang
,
F.
, and
Kitamura
,
T.
,
2011
, “
Cohesive Zone Criterion for Cracking along the Cu/Si Interface in Nanoscale Components
,”
Eng. Fract. Mech.
,
78
(
17
), pp.
2935
2946
.
35.
Soni
,
S. K.
,
Sheldon
,
B. W.
,
Xiao
,
X.
,
Verbrugge
,
M. W.
,
Ahn
,
D.
,
Haftbaradaran
,
H.
, and
Gao
,
H.
,
2012
, “
Stress Mitigation During the Lithiation of Patterned Amorphous Si Islands
,”
J. Electrochem. Soc.
,
159
(
1
), pp.
A38
A43
.
36.
Song
,
Y.
,
Shao
,
X.
,
Guo
,
Z.
, and
Zhang
,
J.
,
2013
, “
Role of Material Properties and Mechanical Constraint on Stress-Assisted Diffusion in Plate Electrodes of Lithium Ion Batteries
,”
J. Phys. D
,
46
(
10
), p.
105307
.
37.
Yang
,
X.-G.
,
Bauer
,
C.
, and
Wang
,
C.-Y.
,
2016
, “
Sinusoidal Current and Stress Evolutions in Lithium-Ion Batteries
,”
J. Power Sources
,
327
, pp.
414
422
.
You do not currently have access to this content.