A Computational Model of the Mechanical Behavior Within Reconstructed LixCoO2 Li-ion Battery Cathode Particles

7/24/2019 A Computational Model of the Mechanical Behavior Within Reconstructed LixCoO2 Li-ion Battery Cathode Particles

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Electrochimica Acta 130 (2014) 707717

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Electrochimica Acta

journal homepage: www.elsevier .com/ locate /e lectacta

A Computational Model ofthe Mechanical Behavior withinReconstructed LixCoO2Li-ion Battery Cathode Particles

Veruska Malav,J.R. Berger, Huayang Zhu, RobertJ. Kee

Department of Mechanical Engineering, Colorado School ofMines, Golden, CO 80401, USA

a r t i c l e i n f o

Article history:

Received 31 December 2013

Received in revised form 18 March 2014Accepted 24 March 2014

Available online 1 April 2014

Keywords:

Lithium ion battery

Diffusion induced stress

Intercalation process

Phase transformations

Anisotropic stress-strain

Discharge rate

Particle morphology

a b s t r a c t

A coupled electrochemical-mechanical model is developed and applied to predict transient three-

dimensional stress fields within reconstructed Lix

CoO2

cathode particles from commercial Li-ion

batteries. The reconstructed particle geometries are derived from focused-ion-beamscanning-electron-

microscopy (FIB-SEM) experiments. The study uses three individual particles, representing typical sizes

and shapes. The mechanical model incorporates measured anisotropic strain within the LixCoO2 lattice

and includes strains due to phase transformations. The stresses are generally found to be compressive in

the particle interiors and tensile near the surfaces. Small-scale surface morphology, high Li concentration

gradients, and phase transformations are found to have a major influence on the stresses, with partic-

ularly high tensile stresses near small protuberances and concave notch-like features on the electrode

surfaces. The study considers 1C and 5C discharge rates. The qualitative behaviors are similar at different

discharge rates, but the stress magnitudes are higher at higher discharge rates.

2014 Elsevier Ltd. All rights reserved.

1. Introduction

This paper reports the development of a micro-scale three-

dimensional (3D) finite element (FE) linear elastic approach to

predict the mechanical behavior within reconstructed LixCoO2Li-ion battery (LIB) cathode particles during discharge. The

mechanical model, which is coupled directly to an electrochem-

istry model, includes the effects of crystal anisotropy and phase

transformations. The study is particularly concerned with predict-

ing the influence of particle size and surface morphology, as well

as discharge rates. Results show that tensile stresses, especially on

the particle surfaces, can be sufficiently high as to suggest particle

fracture.

Representative cathode particles are reconstructed from a

commercial battery using focused-ion-beamscanning-electron-

microscopy (FIB-SEM) [1]. The FIB-SEM experiments typicallyproduce reconstructions for an assembly of particles within a 3D

rectangular domain measuring a few tens of microns on a side [2].

Individual particles can be extractedfrom the assembly of particles,

and the present study uses three individual reconstructed particles

with different sizes and shapes.

The particle mechanical behavior is closely coupled with

the transient Li-concentration field within the cathode particles.

Corresponding author. Tel.: 1 303 273 3682; fax:+1 303 2733602.

Thus, the approach depends upon coupling an electrochemical

simulation with the mechanical simulation. The electrochemical

simulation is accomplished in a finite-volume (FV) setting using

extensions of the ANSYS Fluent software [2]. The mechanical sim-

ulation is accomplished in an FE setting using extensions of the

ANSYS Mechanical software.1 At each time step during a transient

discharge simulation, the Li-concentration field within the parti-

cles must be communicated from the electrochemical simulation

to the mechanical simulation.

The mechanical simulations depend upon constitutive relation-

ships between the stress and strain tensors. The present study

uses data published by Reimers, et al. [3], considering the effects

of both isotropic and anisotropic stress-strain relationships. The

LixCoO2 lattice experiences significant volume changes and phase

transformations during the lithiation (discharge) process [3]. The

diffusion-induced stresses (DIS) can be very high, potentiallyexceeding the material strength and leading to electrode degra-

dation and particle fracture. The present results show that stresses

can be particularly high in the vicinity of notch-like features on

the particle surfaces. Results also show that high discharge rates

and phase transformation occurringduring the Li intercalation also

contribute to high stresses.

1 ANSYS, Inc., Canonsburg, PA 15317; www.ansys.com

http://dx.doi.org/10.1016/j.electacta.2014.03.113

0013-4686/ 2014 Elsevier Ltd. All rightsreserved.
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708 V. Malav et al./ Electrochimica Acta 130 (2014) 707717

The study focuses on isolated particles that are not constrained

by neighboring particles (i.e., under free-expansion conditions).

The present study also considers isothermal behavior. Thus the

results reveal behaviors that are solely attributed to internal

diffusion-induced stresses.

The electrode particles from actual batteries can vary signif-

icantly and randomly in size, shape, and surface morphology.

The physical connections between particles within the electrode

assembly and the electrical contacts vary randomly within the

porous electrodeassembly.Moreover, the crystallographicorienta-

tions within particles are random. Thus, although the simulations

presented here are quantitative using actual reconstructed parti-

cles, the results must be understood in a qualitative context. The

broad objective is to glean observations and trends that are gener-

ally applicable.

2. Prior literature

There is significant foregoing research concerning the mechani-

cal behavior of Li-ion battery cathodes.ReconstructedLIB electrode

particles have been extracted from electrodes using a variety of

microscopic techniques [46,2,7]. Lim et al. [5] developed com-

putational simulations to show that lithiation-induced stressesdepend on geometric characteristics, with the stresses being much

higher in reconstructed LiyC6 and LixCoO2 particles than in ideal-

ized, spherical particles. Likewise, Seo et al. [4] and Chung et al. [6]

used reconstructed particles of LiMn2O4compounds in an FE solid

mechanics simulation. Chung et al. [6] reported that the DIS are

much greater in actual particles that in spherical particles. These

investigations [46] were based on elastic, isotropic, single-phase

individual particles and made use of the thermal analogy to com-

pute diffusion strains [8,9]. The present investigation develops an

analogous approach, but additionally considers phase transforma-

tion and crystal anisotropy as well as particle surface morphology.

Although a few recent studies have considered anisotropic Li

diffusion in polycrystalline LixCoO2particles [1012], the effects of

anisotropy on the stress response in geometrically complex elec-trode particles has not been reported. Additionally, most analytical

and numerical investigations of DIS in LIBs have not incorporated

the effects of volumetric and/or lattice strains that result from

phase transformations. However, Park et al. [13] have incorporated

phase-transformation-induced stresses in a 3D numerical model

of spherical LiMn2O4 particles. Their results showed that stresses

associated with phase transformations were greater than those

developed when considering the intercalation process alone. Ana-

lytical methods, such as moving boundary and porous electrode

theory, have been developed to investigate the effects of phase

transition and/or phase coexistence during Li intercalation [1417].

Theseapproaches,however, werelimited by the followingassump-

tions: a) isotropic elastic behavior in smooth, idealistic particles, b)

two phases concentrically coexisting, c) Li transport is decoupledfrom intercalation-induced stress phenomena, and d) phase coex-

istence modeled as Li-poor or Li-rich phases. Regarding the latter,

no published literature suggests that either of the two hexagonal

phases in the phase coexistenceregion of LixCoO2 is richerin Lithan

the other. In addition, smooth and spherical particles are unable

to capture stress concentrations that can develop in local concave

regions of actual cathode particles. Understanding and predicting

the mechanical behavior of electrodes is practically important. For

example, capacity fade can be associated with diffusion-induced

stress [4]. Even under normal operating conditions, particles can

fracture and thus degrade battery performance. Particle fracture

can originate from locally high stresses leading to the formation

and growth of microcracks [18]. Such processes are known to be

intensified at highdischarge rates [19]. If a fractured particle looses

electrical contact with neighboring particles or current collection

foils, it can no longer participate electrochemically and the bat-

tery resistance increases and capacity fades [13,20]. Additionally,

fragmentation exposes fresh electrode surfaces to the electrolyte

solvent, thus promoting the growth of new surface solidelectrolyte

interface (SEI) films [20,4].

Hydrostatic stress gradients are known to influence Li diffu-

sion with electrode particles [21]. Thus, in addition to mechanical

degradation associated with diffusion-induced stress, the stress

state couples back into the electrochemistry problem. This effect

is neglected in the present study, but is the subject of active model

development.

3. Particle reconstruction andcomputational discretization

Fig. 1 illustrates the process used to define the single parti-

cles used in the present study. A commercial cell (here, Lishen2

LR18650AH) is disassembled and a small portion of a cathode is

prepared for FIB-SEM imaging [1]. The raw data from the FIB-SEM

consists of approximately 200 two-dimensional SEM slices, with

each slice being separated by approximately 60 nm. In Fig. 1 the

white areas in the FIB-SEM slices represent the cathode particles

and the black space represents the pore space that would be filled

by electrolyte solvent. As discussedby Wiedemann et al. [2], the3D

cube is reconstructedusing theMimics software.3 The 3D geometry

is represented in STL (STereoLithography) format, which is a com-

putational definition of the particlesurfaces.For the purposes of the

present study, individual particles are extracted from the rectan-

gular assembly of many particles. The individual particle geometry

is also represented in STL format, which is used as the basis for

computational discretization.

Fig. 2 illustrates the three reconstructed cathode particles used

in the present study. The particles, labeled P1, P2, and P3, are ren-

dered at the same scale to show the relative particle sizes. In

addition to the reconstructed particles, a perfectly smooth spheri-

cal particle (labeled Ps) is also modeled. Cathode particles may be

polycrystalline with a few grains or be composed of a single grain

[22]. The present model assumes that each particle is composed ofa single crystal for the anisotropic studies.

To be electrochemically active, the particles must be connected

to other particles and ultimately to current-collection foils in the

battery. The yellow patches on particles (Fig. 2) indicate the sur-

face positions through which electrical current enters the particle

during discharge. Lithium enters the particles via charge-transfer

reactions on the surfaces that are in contact with the electrolyte

solution. The anisotropic LixCoO2crystal grain orientation is illus-

tratedby thexyzaxes whichcorrespond to the abccrystallographic

axes. In the present study, the electrical contact areas (yellow

patches) and crystal orientation are assigned somewhat arbitrarily.

However, in all cases the electrical contacts are essentially aligned

with the c-axis of the LixCoO2lattice.

The electrochemical model, which has been described pre-viously [2], uses an FV mesh that is generated using the

TGRID algorithm. The structural model uses the five degree-of-

freedom (DOF) element SOLID 227 that is implemented in ANSYS

Mechanical v14.5. This element consists of a 3D 10-node tetra-

hedron. The tetrahedral elements were selected for a variety of

reasons. First, coupled-field elements are required in order to cou-

ple the mechanical response to the chemical diffusions. These

particular elements in ANSYS Mechanical are tetrahedral or hex-

ahedral elements. However, the tetrahedral elements provide a

lower error when numerical solutions are compared to analytic

2 Tianjin LishenBattery Co., Ltd., Tianjin, China, http://en.lishen.com.cn3

Materialize, NV; Leuven, Belgium; http://www.materialise.com
http://en.lishen.com.cn/http://www.materialise.com/http://www.materialise.com/http://en.lishen.com.cn/


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V. Malav et al./ Electrochimica Acta 130 (2014) 707717 709

Fig. 1. Individual particles are extracted from FIB-SEM cathode reconstructions.

Fig. 2. Three reconstructed cathode particles and a 2.7-m spherical particle. The

electrical contact areas are shown as yellow patches. As indicated by the Cartesian

axis, thezaxis of the LixCoC2 is essentially normal to theelectrical contact area.

solutions, and provide a good representation of the DIS state for

the reconstructed surfaces based on the original STL image format.

Because twodifferentdiscretizationsare used,the Li-concentration

field from the FV simulation of the electrochemistry must be inter-

polated onto the FE mesh at each time step during the simulation.

Table 1 provides some summary information about each of the

particles.

4. Phase transformation and strain

Fig. 3a illustrates a pseudo phase diagram, which shows the

possibility of three phase transformations as a function of Li inter-

calation [3,18,2326]. Fig. 3b shows that the lattice can experience

Table 1

Particle geometric and mesh characteristics and current densitiesat 1C

Particle Volume Surface Area Size FE Nodes i at1C

(m3) (m2) (m) (A m2 )

P1 4 .10 15.0 2.6 86,015 7.56

P2 16.50 37.1 3.6 106,506 7.92

P3 82.34 116.7 10.2 316,624 7.58

Ps 82.34 91.6 2.7 65,637 9.14

asmuch as a 2.6% contraction upon full lithiation. There is also sig-

nificant discontinuity between the lattice volumes associated with

the two hexagonal phases. Figs. 3c-d show significant anisotropy

between thea and clattice parameters. Thea and b lattice parame-

ters are equal in the hexagonal phases. However, in the monoclinic

Fig. 3. Li/LixCoO2 pseudo phase diagram (adapted from Reimers, et al. [3]). The

monoclinic phase is labeled as M1. Two hexagonal phases are labeled as H1 and

H2.


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phase, where b /= a, the average lattice parameter is expressed as[3]

aM1=1

3aM1 + bM1

Note that there is a very small increase in thea lattice parameter

as the Li fraction increases. However, there is a much more signif-

icant contraction in the caxis as Li fraction increases (i.e., during

battery discharge).

The coincidence of two hexagonal phases (Fig. 3, 0.75


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Table 2

Li/LixCoO2 cathode model parameters used in theFE structural analysis

Name Symbol Value Reference

Density 2328.5kg m3 [2]Youngs modulus E 370.0 GPa Current study

Elastic stiffness C11 596.0GPa [10], [30]

C12 200.0GPa

C13 133.0GPa

C33 375.0GPa

C44 124.0GPaPoissons ratio 0.20 Current study

Li saturation concentration C94%Li

22.37kmolm3 [2]Initial Li concentration C50%

Li 11.95kmolm3 Current study

Li diffusivity DLi 5.3871015 m2 s1 [2]

expressed assumingmechanical equilibrium in the absence of body

forces as

ijxj

= 0, (8)

where xj are spatial coordinates. The total elastic strain tensor, Tij

,

can be decomposed into the mechanical mij

and chemical diffusion

dij

contributions [19],

Tij= mij + dij. (9)

The present model neglects external loads (i.e., the surface of

the electrode particle is traction free). Thus, the cathode particle is

considered to be in a free-expansion, quasi-static, state wherein

equilibrium (Eq. 8) is satisfied everywhere within the particle.

However, the spatially non-uniform Li concentration field creates

non-uniform elastic strain andstress fields within the particle(irre-

spective of external constraints).

As a basis for comparison, the material properties within cath-

ode particles are first assumed to be isotropic. Then, in subsequent

simulations, the LixCoO2 lattice is assumed to be anisotropic. A

thermal analogy is used to compute the strains resulting from Li

diffusion [8,9]. A single stress-strain relationship is used to rep-

resent the strains that are induced by Li intercalation as well as

phase transformations. This approach is facilitated by defining a

concentration-dependent chemical expansion tensor, ij. This ten-sor specifies the changes of the crystal volume in the isotropic

case (Fig. 3b), and the changes in the lattice parameters for the

anisotropic case (Fig. 3c-d). Thus, the diffusion-induced strain is

both structure and composition sensitive.

6.1. Isotropic strains

The elastic strains in the isotropic case, where ij =ij, are

expressed as

Tij=

1

E

[(1

+)ij

kkij]

+ijC, (10)

where E is the Young modulus, is the Poisson ratio, ij is theKronecker delta, ij is the stress tensor, and C is the concentra-tion difference between the current and initial Li composition (i.e.,

C=CC0). In the isotropic case, it is assumed that the particlecontains a sufficientnumberof grains to use effectiveisotropic elas-

tic parameters. Reuss averages are used, with an effective Youngs

modulusEandaneffective Poissonratioevaluatedfrom thehexag-onal elastic-constant data reported by Hart and Bates [30]. To the

authors best knowledge, no data have been reported regarding

the LixCoO2 monoclinic-phase material properties. Therefore, the

anisotropic models use the hexagonal elastic constants. Previous

studies have used a wide range of values for the Youngs modulus

of LixCoO2 [16,5,31,30]. The value used here, E=370 GPa(Table 2),

lies within previously reported ranges.

The value of for the isotropic case can be extracted

from the lattice-volume data shown in Fig. 3b. For a given

volumetric strain (represented in Cartesian coordinates), the vol-

ume at a given intercalation fraction x may be evaluated as

V(x) =( da+da)(db+db)(dc+ dc). Expanding this relationship,

and neglecting higher-order contributions, the normal strain due

to both intercalation and phase-transformation can be represented

as

ij= 13V(x) V0

V0

ij, (11)

daa= dbb= dcc=

1

3

jV0

C= jC, (12)

where

j=1

3

jV0

. (13)

In these expressions jis the slope of the linear function corre-sponding to the specific Li intercalation fraction andV0is the initial

crystal volume (evaluated atx0.5).

6.2. Anisotropic strains

Most previous studies of mechanical response in LIB cathodeshave used isotropic elastic properties, even for LixCoO2. How-

ever, among the commonly used cathode materials, anisotropic

lattice strains are especially significant for LixCoO2 [32]. The

anisotropy is particularly important because individual particles

can be monocrystalline or polycrystalline with only a few grains

[22].

Anisotropic stress analysis is based upon directional lattice

strains instead of overall volumetric strains. The diffusion strain is

determined fromthe anisotropic crystal lattice behavior(Fig. 3c-d).

The anisotropic elastic stress-strain relationships may be repre-

sented as

Tij= Sijkk + ijC, (14)

where ij is the anisotropic expansion coefficient and Sijk is theelastic-compliance tensor. The components ofSijk can be deter-

mined from the elastic stiffness values provided in Table 2. The

concentration-dependent ij is evaluated from the linear fits tothe lattice expansion data (Fig. 3c-d). The present model incorpo-

rates the anisotropic ijtensor into the normal strain relationship.These anisotropic relationships capture the combined effect of

the lattice-contraction and phase-transformation strains that are

induced during battery discharge. The anisotropic strains may be

written as

daa= dbb=a

a0, dcc=

c

c0, (15)

where a0and c0are the correspondinga and clattice-constant val-

ues atx

0.5 (i.e., beginning of the discharge process).The resulting

anisotropic stress-strain relationship is then decomposed as

Tij= Sijkk + dij, (16)

where dij

is the strain tensor expressed in Eq. 15.

6.3. Effect of Li intercalation

Fig. 5 plots the approximate isotropic and anisotropic strain

functions that are derived from the Reimers et al. [3] data and

used in themodel. Fig.5a shows slightly swelling anisotropic strain

in the a and b lattice directions as the Li fraction increases. Con-

versely, Fig. 5b shows significanty stronger anisotropic contraction

in the clattice direction as Li fraction increases. By definition, the

isotropic strain must be the same in all directions. Figs. 5a-b show


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xin LixCoO2

-8000

-6000

-4000

-2000

0

2000

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9

b) caxis

0

ChemicalSt

rain(strains)

a) aand baxes

-2500

-2000

-1500

-1000

-500

500

1000

Isotropic model

Isotropic model

Isotropic model

Anisotropic model

Anisotropic model

Anisotropic model

Fig. 5. Approximate linear strains as functionsof Li intercalation, a) alignedwith a

and b lattice directions, daaand dbb

and b) aligned with clattice direction, dcc. The

isotropic strains are the same in both panels, but plotted using different scales for

the ordinates.

the same isotropic strains, but plotted on different ordinate scales.

The discontinuities atx0.75 is the result of phase transformationbetween the H1 and H2 hexagonal phases.

Fig. 5 shows isotropic and anisotropic strain functions to be

significantly different. Thus, it should be anticipated stress fields

predicted by isotropic models will be quite different from those

that assume the more-realistic anisotropic behavior.

7. Results and discussion

Table 2 lists physical parameters that are used in the present

study. Other parameters and implementation details for the

electrochemical model can be found elsewhere [2]. Theresults pre-

sented here express the DIS as maximum principal stresses, whichare especially significant for predicting the failure of ceramic, non-

ductile, materials.

7.1. Isotropic andanisotropic comparison

Fig. 6 shows stress fields in particle P2 at t= 1 820 s during a

1C discharge, using the isotropic and anisotropic models. In both

cases the stresses are compressive in the particle interior, but ten-

sile in the outer regions near the particle surfaces. The anisotropic

Fig. 6. Diffusion-induced stress fields in particle P2 using a) the isotropic model

and b) the anisotropic model. In both cases the battery is discharging at 1C and the

stress fields are shown at t=1820 s, which is approximately midway through the

discharge. The arrow points to a notched region on the surface with high tensile

stress.

Fig. 7. Diffusion-induced stress fields in fully lithiated particles Ps and P3 at th e

end of a 1C discharge(i.e., t= 3600 s).Both simulations arebasedon theanisotropic

model. These two particleshave comparable volumes (Table 1).

model predicts significantly higher tensile stresses. As indicated by

the arrow in Fig. 6b, concave or notched features on the particle

surface show particularly high tensile stresses. Such high tensile

stresses are likely to cause crack initiation and fracture. Although

different particles with different crystallographic orientations and

different electrical contacts will lead to different stress fields, this

result suggests strongly that using an isotropic model may signifi-

cantly under-predict deleterious tensile stresses.

7.2. Surface morphology

Fig.7 compares predictedstressfields in the ideal spherical par-

ticle Ps with the reconstructed particle P3 that has a comparable

volume (Table 1). Both cases use the anisotropic model, but the

spherical particle has a smooth convex surface compared to the

relative rough features of the reconstructed particle. At the end

of a 1C discharge, the maximum predicted tensile stress in Ps is

approximately 53.8 MPa. By comparison, the maximum predicted

tensilestressinP3 is approximately79.9 MPa.In bothcases,stresses

in the core of the particles are compressive, with tensile stresses

in the outer regions. The non-smooth surface morphology of the

actual particle leads to much higher local stress variations than arepredicted in the smooth-surface spherical particle.

The stress field withinthe sphericalparticle tends to be concen-

tric, which is the result of an essentially concentric Li concentration

field. However, because the electrical contact occupies a portion

of the particle surface, the fields are not exactly concentric. In

any case, the shapes of actual particles are usually very different

fromspheres. Consequently,although thepredicted fields maylook

qualitatively concentric (i.e., more compressive toward the inte-

rior), the actual fieldscan bequitedifferent from those ina spherical

particle.

These results demonstrate that surface features dominate the

mechanical response of the cathode particle. Local small-scale pro-

trusions in thesurface topology createlocal areas that lithiate more

quickly than the surrounding areas. Consequently, these locationsundergo phase transformations more rapidly than the surrounding

material, leading to high, localized, stresses. Such behavior is not

captured by simulations using smooth spherical particles.

7.3. Particle shape and size

Figs. 810 show predicted maximum-principal-stress fields in

the three reconstructedparticles at t= 1650s intoa 1Cdischarge. In

all cases, the stress patterns are qualitatively similar. That is, com-

pressive in the interior and tensile near the outside edges. Concave

features on the surfaces tend to be regions of relatively high ten-

sile stress. Particles P1 and P2, which are comparable in particle

size, show comparable stress distributions. Particle P3 is larger and

shows a wider range of DIS. However, as discussed subsequently,


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Fig. 8. Maximum principal stress field in P1 at t=1650 s under a 1C discharge. a)

stresscontours on thesurface and b) stress contours on a cross-section cut.



the particle size itself may not be the dominant factor in governing

the maximum stress.Although not shown in Figs. 810, the model reveal that the

magnitude of the principal stresses depend upon the magnitude of

theLi-concentration gradients. In P3 themaximumLi concentration

gradients are on the order of 108 kmol m4, while inP1and P2themaximum Li concentrationgradients wereon the orderof 106 kmol

m4.Althoughthe predictedresults are basedupon quantitative sim-

ulations, they should be understood in terms of qualitative trends.

Individual particle shapes and sizesare random within the full elec-

trode. The electrical contacts and crystallographic orientations are

also random. Thus,any particularsimulation cannot produce a fully

general result.



x

Discharge time (s)

100 600 1100 1600 2100 2600 3100 3600

Max.

Prin.

Stress(MPa)

0

100

200

300

400

500

600

700

a) Variation in Li

b) Maximum DIS

1C discharge

P3

P2P1

P3

P2

P1

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Fig. 11. a) Variationof intercalatedLi fraction withinthe three reconstructed cath-

ode particles during 1C discharge. b) Maximum principal tensile stress within the

reconstructed particles throughout a 1C discharge.

7.4. Maximum principal stress

Fig. 11a shows the maximum variation in Li fraction x withinthe three reconstructed particles. The relatively small particles (P1and P2) show relatively small variations that are essentially con-

stant atx0.02. The variations in thelarger particle(P3)aremuchgreater, reaching a peak at x0.14 about midway through thedischarge. Fig. 11b shows the transient maximum principal tensile

stresses during a 1C discharge. The maximum-stress profiles are

qualitatively similar for all the particles, but the magnitudes are

greater for P3. The stress peaks at approximately midway through

the discharge are caused by the phase transformations between the

two hexagonal phases (H1 to H1+H2) that occur atx0.75 (Figs. 3and 5). These sharp increasesin tensile stress, whichtendto be con-

centrated around features such as small protuberances or notches

on the particles surfaces,can serve to damage, crack, or fracturethe

cathode particles.

Fig. 12, which shows contours of maximum principal stress,

strain, and Li concentration on the surface of P3at t= 1820 s during

a 1C discharge, helps to explain the profiles shown in Fig. 11. The

dominantbehaviors arelocalized around a small protruding surface

feature that is also shown at an expanded scale. The peak compres-

sive and tensile stresses are highly localized around this surface

feature (Fig. 12a). The strain is relatively small on the tip of the

feature, but increases greatly near the base of the feature where it

joins the bulk of the particle (Fig. 12b). Because thefeature is small,

the Li intercalation fraction is highest near the tip of the feature(Fig. 12c). Because the small feature lithiates so rapidly relative

to its nearby surroundings, a highly localized phase transforma-

tion (H1 to H1+H2) contributes to locally high stresses. The local

phase transformation results in a relaxation of the local diffusion

strains.

7.5. Discharge rate

Increasing the discharge rate increase the stresses, but the

general behaviors remain qualitatively similar. The present study

compares mechanical behaviors at 1C and 5C. At the higher dis-

charge rate, the resulting Li concentration field is found to be more

non-uniformly distributed spatially. As a consequence, there is an

increase in the concentration gradients of at least one order of


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Fig. 12. Localized fields within P3 at t= 1820 s during a 1C discharge. a) Maximum principal stress; b) equivalent diffusion strain; c) local Li fractionx.

magnitude. The increases in maximum stresses are approximately

proportional to the increases in Li concentration gradients. In large

measure, the stresses increase at higher discharge ratesbecausethe

Li-concentration variations within the particle are greater at high

rates.

Figs. 13, 14, and 15 show maximum principal stress maps forforP1, P2, and P3, respectively. As is the case at lower discharge rates,

stresses are generallycompressive in the particle interiors andten-

sile near the surfaces. Also, locally high stresses are evident around

small protuberances and concave features on the surfaces. These

observations are consistent with the previously reported results

[19,5].

Fig. 16a shows that after an initial transient, the maximum vari-

ations in intercalated Li are approximately steady at x0.07

Fig.13. DIS fieldin P1at t= 335s duringa 5C dischargecondition.a) Particlesurface

and b) Particle cross section.

Fig.14. DIS fieldin P2at t= 335s duringa 5C dischargecondition.a) Particle surface


Fig.15. DIS fieldin P3at t= 335s duringa 5C dischargecondition.a) Particle surface



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x

0.05

0.10

0.15

0.20

0.25

Max.

Prin.

Stress(M

Pa)

20 120

220

320

420

520

620

720

Discharge time (s)

0

200

400

600

800

0

a) Normalized Li

b) Maximum DIS

P1

P2

P3

P3

P2

P1

5C discharge

Fig.16. a) Maximum difference in intercalation fractionxwithin particles during

a 5C discharge. b) Maximum principalstress historiesfor threeparticles duringa 5C

discharge.

for P1 and x

0.10 P2. The Li variation is greater for P3, with

larger variations during the course of the lithiation. The peakvariation x0.23 occurs during the H2-to-(H2+H1) phase tran-sition (t= 413 s) and gradually declines for the remainder of the

lithiation process. As was the case in the 1C discharge, the small

feature illustrated in Fig. 12 plays a significant role.

Fig. 16b shows the history of the DIS for the particles during a

5C discharge. Comparison with Fig. 11 shows that maximum prin-

cipal stresses in the M1 and H1 phases are generally greater than

they are during a 1C discharge. The H2-to-(H2+H1) phase transi-

tion occurs at t400 s, leading to the highest stresses. Becausethe intercalation-induced strains decline in the later stages of

the discharge where the H1 and H2 phases coexist, the stress

levels decrease. The stress state depends upon the Li intercala-

tion fraction, x, its variation, x, and the concentration gradient

throughout the particle. This agrees withthe observations reportedin [33]. Both of these factors are highly dependent on the dis-

charge rate as well as particle size and morphology. The stresses

are generally higher at higher discharge rates because x is

greater.

Fig. 17 illustrates maximum tensile stress histories at four

selected points on the surface of P3with discharge rates of 1C and

5C. The particular locations are chosen near topological features

that would tend to create high local stresses. To assist compari-

son between 1C and 5C the abscissa is a normalized time, t = t/tD,where tD is the time required for full discharge (e.g., tD =3600

s at 1C). At most points the stress histories are similar but the

magnitudes are greater at high C rates. The most striking behav-

ior occurs at t0.5, where the H2-to-(H2+H1) phase transitiontakes place at pronounced concave and convex locations. Thesesites are accommodating regions under stress peaks and decays.

Enteringthe coexistence region, a comparable stressevolution pat-

tern occurs at all sites evaluated in the particle throughout the

remainder of the lithiation.

Fig.18 illustratesamatrixofcross-sectionalimagesforP 3,show-

ing principal stresses, strain, and lithium intercalation fractions at

three times during a 5C discharge. The row at t= 85 s corresponds

to the M1-to-H2 phase transition. The row at t= 413 s corresponds

to the H2-to-(H2+H1) phase transition. The row at t= 7 20 s cor-

responds to the end of the 5C discharge. Fig. 18a shows surface

tensile stresses around 550MPa. Fig. 18d shows that during the H2-

to-(H2+H1) phase transition the surface tensile stresses are even

higher, in the range of 670 MPa. Even within the particle interior,

tensile stresses can exceed 300 MPa. At t= 4 13 s, Fig. 18d show

Fig. 17. Maximum principal stress histories at selected sites on the surface of P3when discharged at 1C and5C. Thetime is normalized between 0 t 1 toaccom-modate thedifferent C rates (t= 1 corresponds to full discharge).

a nominally concentric ring of stresses that are relatively more

compressive than the surrounding regions outside the ring. The

ring corresponds to a chemical strain misfit at x0.75 as the Liintercalation proceeds inward (Fig. 18e). Fig. 18g shows that at

the end of the lithiation process (t= 720 s) the stress magnitude

decreases, which is caused by the increasingly uniform Li interca-

lation. Although the stress magnitudes decrease near the end of

discharge, the general pattern of being tensile near the surface and

compressive in the interior is preserved.


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Fig. 18. Mechanical and chemical response of particle P3 at three instants in time during a 5C discharge.

8. Summary and conclusions

The present study is based upon the computational simula-

tion of reconstructed LixCoO2 cathode particles during discharge.

Threeindividual particles were selected fromFIB-SEM reconstruct-

ions of a commercial battery, with the particles being selected to

represent a range of sizes and shapes. The approach couples three-

dimensional finite-volume simulations of the electrochemistry and

Li transport with three-dimensional finite-element simulations of

the mechanical response. The mechanical models compare both

isotropic and anisotropic behavior, considering phase transitions

(monoclinic and two hexagonal phases) associated with the extent

of lithiation in the LixCoO2lattice.

A number of general observations can be drawn from the study.

During discharge, the stresses are generallycompressive in the par-

ticle interiors and tensile near the particles surfaces. By comparingthe behavior of a smooth spherical particle with the reconstructed

particles, it is evident that the surface morphology plays a strong

role on the maximum tensile stresses. Especially high stresses are

found near concave, notch-like, features on the surfaces. Surface

features such as small protuberances that lithiate rapidly relative

to the surrounding surface also promote high stresses.

The anisotropic strain characteristics of the LixCoO2 lattice

are important. Comparison with equivalent isotropic stress-strain

models show that that stresses are significantly higher when

the anisotropic models are used. Thus, predictions based on

isotropic assumptions are likely to under-estimate the propensity

for electrode degradation, crack formation, and particle fracture.

Additionally, a major factor contributing to the stress state in

the individual Lix

CoO2

particles was the phase transformation the

crystal structure undergoes after half lithiation. This phase trans-

formation, combined with large concentration gradients, allowdramatic changes in the stress that evolve in the particle.

The mechanical behavior depends significantly upon discharge

rate. The present study compared 1C and 5C discharges. Although

the qualitative behaviors are similar at differentdischarge rates, the

stresses are significantly higher at higher discharge rates. Larger

Li-concentration gradients at high discharge rates contributes to

the higher stresses. Spatially varying lithiation rates, especially

near small-scale surface features, also contributes to high stresses.

Assuming that one is concerned with mechanical damage and par-

ticle fracture, the study suggest some considerations for electrode

design and operation. As much as practical, nominal spherical par-

ticles with smooth surface morphologies are desirable. Because

crystal anisotropy is important, it may be desirable to fabricate

polycrystalline particles with numerous randomly oriented grains,leading to overall more isotropic behavior. Limiting high discharge

rates is also desirable from the perspective of limiting mechanical

degradation.

Acknowledgements

We are grateful to Prof. Scott Barnett (Northwestern Univer-

sity), who provided datafrom FIB-SEM experiments and to Andreas

Wiedemann who assisted with the generation of the model geom-

etry. The authors also gratefully acknowledge the assistance of Drs.

Graham Goldin and Bill Bulat (ANSYS, Inc.) in the development of

the computational models. This effort was supported by the Office

of Naval Research via Grant N00014-08-1-0539.


11/11


References

[1] J.R. Wilson, J.S. Cronin, S.A. Barnett, S.J. Harris, Measurement of three-dimensional microstructure in a LiCoO2 positive electrode, J. Power Sources196 (2011) 4433447.

[2] A.H. Wiedemann, G.M. Goldin, S.A. Barnett, H. Zhu, R.J. Kee, Effects of three-dimensional cathodemicrostructureon theperformanceof lithium-ionbatterycathodes, Electrochim. Acta 88 (2013) 580588.

[3] J.N. Reimers, N. Jan, J.R. Dahn, Electrochemical and in situ x-ray diffractionstudies of lithium intercalation in LixCoO2, J . Electrochem. Soc. 139 (1992)20912097.

[4] J.H. Seo, M. Chung, J.M. Park, S.W. Han, X. Zhang, A.M. Sastry, Generation ofrealisticparticle structuresand simulations of internal stress:A numerical/afmstudy of LiMn2 O4particles, J. Electrochem.Soc. 158 (2011) A434A442.

[5] C. Lim, B. Yan, L. Yin, L. Zhu, Simulation of diffusion-induced stress usingreconstructedelectrodesparticlestructures generatedby micro/nano-CT,Elec-trochim. Acta 75 (2012) 279287.

[6] M.D. Chung, J.H. Seo, X.C. Zhang, A.M. Sastry, Implementing realistic geome-try and measured diffusion coefficients into single particle electrodemodelingbasedon experiments withsingle LiMn2O4spinel particles,J. Electrochem. Soc.158 (2011) A371A378.

[7] T. Hutzenlaub, S. Thiele, R. Zengerle, C. Ziegler, Three-dimensional reconstruc-tion ofa LiCoO2Li-ionbatterycathode,Electrochem.Solid-State Lett.15 (2011)A33A36.

[8] X. Zhang, W. Shyy, A.M. Sastry, Numerical simulation of intercalation-inducedstress in Li-ion battery electrode particles, J. Electrochem. Soc. 154 (2007)A910A916.

[9] X.Zhang,A.M. Sastry,W. Shyy,Intercalation-induced stressand heat generationwithin single lithium-ion battery cathode particles, J. Electrochem. Soc. 155

(2008) A542A552.[10] D. Chung, N. Balke, S.V. Kalinin, R.E. Garcia, Virtual electrochemical strainmicroscopy of polycrystalline LiCoO2 films, J. Electrochem. Soc. 158 (2011)A1083A1089.

[11] N. Balke, E.A. Eliseev, S. Jesse, S. Kalnaus, C. Daniel, N.J. Dudney, A.N.Morozovska, S.V. Kalinin, Three-dimensional vector electrochemical strainmicroscopy, J. Appl. Phys. 112 (2012) 052020.

[12] S. Yamakawa,H. Yamasaki,T. Koyama, R. Asahi,Numerical study of Li diffusionin polycrystalline LiCoO2, J. Power Sources 223 (2013) 199205.

[13] J. Park, W. Lu, A.M. Sastry, Numerical simulation of stressevolution in lithiummanganesedioxideparticlesdue to coupled phasetransition andintercalation,

J. Electrochem.Soc. 158 (2011) A201A206.[14] R.T. Purkayastha, R.M. McMeeking, An integrated 2-D model of a lithium ion

battery: The effect of material parameters and morphologyon storage particlestress, Comput. Mechanics 50 (2012) 209227.

[15] Q. Zhang, R. White, Moving boundary model for the discharge of a LiCoO2electrode, J. Electrochem. Soc. 154 (2007) A587A596.

[16] S. Renganathan, G. Sikha, S. Santhanagopalan, R.E. White, Theoretical analysisofstresses in a lithium ion cell, J. Electrochem. Soc. 157 (2010) A155A163.

[17] S. Golmon, K. Maute, M.L. Dunn, Numerical modeling of electrochemicalmechanicalinteractions inlithiumpolymerbatteries,Comput.Struct.87 (2009)15671579.

[18] J. Park, S. Kalnaus, S. Han, Y.K. Lee, G.B. Less, N.J. Dudney, C. Daniel, A.M. Sastry,In situ atomic force microscopy studies on lithium (de)intercalation-inducedmorphology changes inLixCoO2micro-machined thin film electrodes, J. PowerSources 222 (2013) 417425.

[19] R.E.Garcia, Y. Chiang, W.C.Carter, P. Limthongkul, C.M.Bishop,Microstructuralmodeling and design of rechargeable lithium-ion batteries,J. Electrochem. Soc.

152 (2005) A255A263.[20] M. Zhu, J. Park, A.M. Sastry, Fracture analysis of thecathode in Li-ionbatteries:

A simulation study, J. Electrochem.Soc. 159 (2012) A492A498.[21] Y.M. Choi,S.I. Pyun, Effects of intercalation-inducedstress on lithium transport

through porous LiCoO2electrodes, Solid State Ionics 99 (1997) 173184.[22] K. Zhao, M. Pharr, J.J. Vlassak, Z. Suo, Fracture of electrodes in lithium-ion bat-

teries causedby fast charging, J. Appl. Phys. 108 (2010) 073517.[23] H. Wang, Y.I. Jang, B. Huang, D.R. Sadoway, Y.M. Chiang, Batteries and energy

conversion - TEM studyof electrochemical cycling-induced damageand disor-der in LiCoO2 cathodes for rechargeable lithium batteries, J. Electrochem. Soc.146 (1999) 473.

[24] T. Bak, J.Nowotny,M. Rekas, C.C.Sorrell,S. Sugihara,Properties of theelectrodematerial LiCoO2 , Ionics 6 (2000) 92106.

[25] G.A.Nazri, G. Pistoia,Lithium Batteries:Scienceand Technology, Springer,NewYork, 2009.

[26] S.H. Choi, J. Kim, Y.S. Yoon, A TEM study of cycled nano-crystalline HT-LiCoO2cathodes for rechargeable lithium batteries, J . Power Sources 135 (2004)286290.

[27] M. Park, M.X. Zhang, M. Chung, G.B. Less, A.M. Sastry, A review of conduction

phenomenain Li-ion batteries, J. Power Sources 195 (2010) 79047929.[28] M. Guo, R.E. White, Thermal model for lithium ion battery pack with mixed

parallel andseriesconfiguration,J. Electrochem. Soc.158 (2011) A1166A1176.[29] F. Yang, Interaction between diffusionand chemical stresses, Mater.Sci. Eng. A

409 (2005) 153159.[30] F.X. Hart, J.B. Bates, Lattice model calculation of the strain energy density and

other properties of crystalline LiCoO2, J. Appl. Phys. 83 (1998) 75607566.[31] M. Qu, W.H. Woodford, J.M. Maloney, W. Carter, Y.M. Chiang, K.J. van Vliet,

Nanomechanical quantification of elastic, plastic, and fracture properties ofLiCoO2, Adv. Energy Mater. 2 (2012) 940944.

[32] W .H. W oo dfo rd, W .C. Car ter , Y.M. Chiang, Design criter ia f or electr o-chemical shock resistant battery electrodes, Energy Environ.l Sci. 5 (2012)80148024.

[33] Y. Song, X. Shao, Z. Guo, J. Zhang, Role of material properties and mechan-ical constraint on stress-assisted diffusion in plate electrodes of lithium ionbatteries, J. Phys. D: Appl. Phys. 46 (2013) 105307.
http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0005http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0005http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0005http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0005http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0005http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0005http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0010http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0010http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0010http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0010http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0015http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0015http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0015http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0015http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0015http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0015http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0015http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0015http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0020http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0020http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0020http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0020http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0020http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0020http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0020http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0020http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0020http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0025http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0025http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0025http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0025http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0030http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0030http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0030http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0030http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0030http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0030http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0030http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0030http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0030http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0035http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0035http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0035http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0035http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0035http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0035http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0040http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0040http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0040http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0040http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0040http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0045http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0045http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0045http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0045http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0045http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0050http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0050http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0050http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0050http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0050http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0050http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0055http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0055http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0055http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0060http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0060http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0060http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0060http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0060http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0060http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0065http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0065http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0065http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0065http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0065http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0065http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0070http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0070http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0070http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0070http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0075http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0075http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0075http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0075http://refhub.elsevier.com/S0013-4686(14)00626-4/sbref0080http://refhu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