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`To cite this article: Pankaj Arora et al 1999 J. Electrochem. Soc. 146 3543
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`1
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`

`Journal of The Electrochemical Society, 146 (10) 3543-3553 (1999)
`S0013-4651(99)01-088-5 CCC: $7.00 © The Electrochemical Society, Inc.
`
`3543
`
`Mathematical Modeling of the Lithium Deposition Overcharge Reaction
`in Lithium-Ion Batteries Using Carbon-Based Negative Electrodes
`
`Pankaj Arora,a,* Marc Doyle,b,** and Ralph E. Whitea,**
`
`aCenter for Electrochemical Engineering, Department of Chemical Engineering, University of South Carolina, Columbia, South
`Carolina 29208, USA
`bDuPont Central Research and Development, Experimental Station, Wilmington, Delaware 19880-0262, USA
`
`The processes that lead to capacity fading affect severely the cycle life and rate behavior of lithium-ion cells. One such process is
`the overcharge of the negative electrode causing lithium deposition, which can lead to capacity losses including a loss of active
`lithium and electrolyte and represents a potential safety hazard. A mathematical model is presented to predict lithium deposition
`on the negative electrode under a variety of operating conditions. The LixC6|1 M LiPF6, 2:1 ethylene carbonate/dimethyl carbon-
`ate, poly(vinylidene fluoride-hexalfuoropropylene)| LiMn2O4 cell is simulated to investigate the influence of lithium deposition on
`the charging behavior of intercalation electrodes. The model is used to study the effect of key design parameters (particle size, elec-
`trode thickness, and mass ratio) on the lithium deposition overcharge reaction. The model predictions are compared for coke and
`graphite-based negative electrodes. The cycling behavior of these cells is simulated before and after overcharge to understand the
`effect of overcharge on extended cycling. These results can be used to establish operational and design limits within which safety
`hazards and capacity fade problems, inherent in these cells, can be minimized.
`© 1999 The Electrochemical Society. S0013-4651(99)01-088-5. All rights reserved.
`
`Manuscript submitted January 25, 1999; revised manuscript received May 10, 1999.
`
`The goal of this work is to predict the conditions for the lithium
`deposition overcharge reaction on the negative electrode (graphite
`and coke) and to investigate the effect of various operating condi-
`tions, cell designs and charging protocols on the lithium deposition
`side reaction.
`
`Model Development
`Lithium deposition is expected to occur in lithium-ion cells due
`to either a higher than desired initial mass ratio, lower than expect-
`ed lithium losses during the formation period, adverse charging con-
`ditions, or accidental overcharging (malfunctioning charger, mal-
`functioning safety circuit, or electrical misuse/abuse of the battery
`pack). The freshly deposited lithium covers the active surface area of
`the negative electrode leading to a loss of cyclable lithium and con-
`sumption of electrolyte because of the highly reactive nature of
`metallic lithium. This may occur at high charge rates even for cells
`with a conservative mass ratio because of the polarization at the neg-
`ative electrode under charging conditions.4
`However, a common circumstance leading to lithium deposition
`may be poorly balanced cells having too much positive electrode
`mass initially. Note that there is no industry standard for electrode
`mass ratio or anode excess for lithium-ion cells. The mass ratio (␥)
`of a lithium-ion cell is defined as
`
`[1]
`
`⫺ ⫹
`C C
`x y
`⌬ ⌬
`
`␥
`
`theoretical
`
`⫽
`
`⫽
`
`␦ ⑀ ␳
`⫹ ⫹ ⫹
`␦ ⑀ ␳
`⫺ ⫺ ⫺
`
`⫹ ⫺
`m m
`
`␥
`
`actual
`
`⫽
`
`where ␥actual is the actual mass ratio and ␥theoretical is the theoretical
`mass ratio. The intercalation-deintercalation reaction on the negative
`electrode (graphite or coke) may be written as
`
`charge
`C6 ⫹ xLi⫹ ⫹ xe⫺o LixC6
`discharge
`
`[2]
`
`and the primary side reaction involved in the overcharge process is
`
`Li⫹ ⫹ e⫺ r Li(s)
`
`[3]
`
`The lithium metal is expected to form first near the electrode-sep-
`arator boundary where the surface overpotential is greatest. Lithium
`metal deposited on the negative electrode reacts quickly with solvent
`or salt molecules in the vicinity giving Li2CO3, LiF, or other insolu-
`ble products as shown in Fig. 1.7,8 A thin film of products (formed
`above) protects the solid lithium from reacting with the electrolyte.
`This lithium, if in electronic contact with the negative electrode, can
`
`Two major issues facing lithium-ion battery technology are safe-
`ty and capacity fade during cycling. A significant amount of work
`has been done to improve the cycle life and to reduce the safety
`problems associated with these cells. This includes newer and better
`electrode materials, lower-temperature shutdown separators, non-
`flammable or self-extinguishing electrolytes, and improved cell
`designs. The performance of these cells is based on the complex
`chemical and electrochemical reactions occurring during charge,
`discharge, and storage, many of which are irreversible and lead to
`changes in the performance of the cells during extended cycling. A
`detailed discussion of lithium-ion battery mathematical models and
`side reactions can be found elsewhere.1 These complex phenomena
`can be understood in a more detailed manner through mathematical
`modeling of the full-cell sandwich.
`Several mathematical models of lithium-ion cells have been pub-
`lished.2-6 None of these models has the capability to predict capacity
`fade observed in these cells. Doyle et al.4 modified their dual lithium-
`ion model to include film resistances on both electrodes and made
`direct comparisons with experimental cell data for the LixC6|LiPF6,
`ethylene carbonate/dimethyl carbonate (EC/DMC), poly(vinylidene
`fluoride-hexafluoropropylene)|LiyMn2O4 system. The discharge per-
`formance of the cells was described satisfactorily by including either
`a film resistance on the electrode particles or by contact resistances
`between the cell layers or current collector interfaces.4,5
`Recently Darling and Newman made the first attempt to model
`side reactions in lithium batteries by incorporating an electrolyte
`(1 M LiClO4 in PC) oxidation side reaction into a lithium-ion bat-
`tery model.6 Even though a simplified treatment of the oxidation
`reaction was used, these authors were able to make several interest-
`ing conclusions about self-discharge processes in these cells and
`their impact on positive electrode state-of-charge.
`Present battery models, except the one by Darling and Newman,
`consider the “ideal behavior” of the systems, neglecting the phenom-
`ena that led to losses in capacity during repeated charge-discharge
`cycles. Fundamental models of capacity fade phenomena are less
`common because their processes are not as well understood. Also,
`models of failure modes in batteries are not usually applicable to a
`wide range of systems. However, the importance of these phenome-
`na in the safe and efficient operation of high-energy lithium-ion bat-
`teries requires that they be incorporated into future battery models.
`
`** Electrochemical Society Student Member.
`** Electrochemical Society Active Member.
`
`2
`
`

`

`3544
`
`Journal of The Electrochemical Society, 146 (10) 3543-3553 (1999)
`S0013-4651(99)01-088-5 CCC: $7.00 © The Electrochemical Society, Inc.
`
`graphite-based negative electrodes are compared with coke-based
`negative electrodes.
`The main side reaction in the negative electrode during over-
`charge is given by Eq. 3, which can be written in general notation as9
`
`[4]
`
`→
`
`e⫺
`
`n
`
`i
`
`iz
`
`s M
`i
`
`∑
`
`i
`
`The rate of the lithium deposition reaction is charge-transfer-kinetic
`controlled and can be expressed by a Butler-Volmer expression as
`follows
`
`[5]
`
` 
`
`
`␩
`s,k
`
`␣
`
`F
`
`c,k
`RT
`
`⫺
`
`
`
`⫺
`
`exp
`
`
`
`␩
`s,k
`
`␣
`
`F
`
`a,k
`RT
`
`
`
`exp
`
` 
`
`i
`k
`
`⫽
`
`i
`o,k
`
`A number of different approximations can be made to simplify
`the computational process while including the lithium metal deposi-
`tion side reaction. Either a Tafel or linear approximation to the But-
`ler-Volmer rate expression can be used depending on the reaction
`conditions and simplifying assumptions. The cathodic Tafel expres-
`sion can be used to describe the rate expression if either the deposi-
`tion reaction is considered to be irreversible or if the amount of lithi-
`um deposited is very small and reacts quickly with the solvent. In
`that case, the rate expression will be
`
`[6]
`
`
`
`␩
`s,k
`
`␣
`
`F
`
`c,k
`RT
`
`⫺
`
`
`
`i
`k
`
`⫽ ⫺
`i
`o,k
`
`exp
`
`The lithium deposition reaction is a facile process under many con-
`ditions; the surface overpotentials may be sufficiently low that the
`reaction can be expressed adequately using the linear approximation
`
`i
`k
`
`⫽
`
`i
`o,k
`
`(
`
`␣ ⫹ ␣
`a,k
`
`c,k
`
`)
`
`F
`
`RT
`
`␩
`s,k
`
`[7]
`
`In this work, we have assumed that the lithium deposition reac-
`tion is semireversible, i.e., at least part of the deposited lithium can
`dissolve during discharge. Some amount of the lithium may react
`with the electrolyte to form insoluble products such as Li2CO3, etc.
`A cathodic Tafel rate expression is also incorporated in the model
`and model predictions will be compared for both cases (Butler-
`Volmer and Tafel rate expression). In the above expressions (Eq. 5,
`6, and 7), io,k is the exchange-current density and ␩s,k is the local
`value of surface overpotential defined by
`
`␩s,k ⫽ ␾1 ⫺ ␾2 ⫺ Uk ⫺ Fjn,kRfilm
`
`[8]
`
`where Uk is the open-circuit potential. The potential variables ␾1 and
`␾2 represent the potentials in the solid and solution phases, respec-
`tively, and io,k, ␣ak, and ␣ck are the kinetic parameters. Here
`
`␣s,k ⫹ ␣c,k ⫽ 1
`
`[9]
`
`Based on the above discussion and assumptions, application of
`Eq. 5 to reactions 2 and 3 results in the following kinetic expressions
`
`
`
`␣
`
`F
`
`⫺
`
`
`
`Figure 1. Reactions occurring on the negative electrode during charge and
`overcharge.
`
`still dissolve during discharge. The film formed over the solid lithi-
`um is a direct loss of both active lithium and electrolyte. The prod-
`ucts formed may block the pores, leading to a loss of rate capability
`as well as capacity losses. Formation of lithium metal is also a safe-
`ty hazard due to its extreme reactivity with liquid solvents.
`A schematic of a lithium-ion cell is shown in Fig. 2. It consists of
`a composite negative electrode (active material ⫹ filler ⫹ binder),
`separator and a composite positive electrode. The negative and pos-
`itive active materials simulated in this work are graphite (MCMB
`2528) and LiMn2O4, respectively. Other details and data for the
`LixC6|1 M LiPF6, EC/DMC, p(VdF-HFP)|LiyMn2O4 system are
`given elsewhere.4 Lithium metal deposition may be more of a con-
`cern with graphitic carbon electrodes than with coke electrodes due
`to the lower average open-circuit potential of the former. For this
`reason, mass ratios in cells using graphite are usually chosen to be
`much smaller than the optimum in order to provide a buffer against
`lithium deposition, with the consequence that the full 372 mAh/g
`capacity of the graphite is not utilized. The model predictions for
`
` 
`
`
`]
`
`␾ ⫺ ␾ ⫺
`1
`2
`
`
`U c(
`1
`s
`
`)
`
`Fj R
`n,1 film
`
`[
`
`a,1
`RT
`
`
`
`exp
`
` 
`
`[
`
`␾ ⫺ ␾ ⫺
`1
`2
`
`
`U c(
`1
`s
`
`)
`
`⫺
`
`Fj R
`n,1 film
`
`]
`
`␣
`
`F
`
`c,1
`RT
`
`⫺
`
`
`
`exp
`
`
`
`j
`n,1
`
`⫽
`
`i
`0,1
`F
`
` 
`
`⫺
`
`
`
` 
`
`
`
`[10]
`
`[11]
`
`
`
`
`
`and
`
`j
`n,2
`
`⫽
`
`i
`0,2
`F
`
`
`
`
`
`
` 
`
`
` 
`
`
`]
`
`␣
`
`F
`
`a,2
`RT
`
`[
`
`␾ ⫺ ␾ ⫺
`1
`2
`
`U
`2
`
`⫺
`
`Fj R
`n,2 film
`
`[
`
`␾ ⫺ ␾ ⫺
`1
`2
`
`U
`
`2
`
`⫺
`
`Fj R
`n,2 film
`
`]
`
`␣
`
`F
`
`c,2
`RT
`
`⫺
`
`
`
`exp
`
`
`
`exp
`
` 
`
` 
`
`⫺
`
`
`Figure 2. Schematic of lithium-ion cell during charge.
`
`where jn,1 and jn,2 correspond to the rates of the lithium intercalation
`and lithium deposition reactions. The normal component of the cur-
`
`3
`
`

`

`Journal of The Electrochemical Society, 146 (10) 3543-3553 (1999)
`S0013-4651(99)01-088-5 CCC: $7.00 © The Electrochemical Society, Inc.
`
`R
`i
`
`⫽ ⫺
`
`s a
`i,k
`n F
`k
`
`i
`n,k
`
`3545
`
`[18]
`
`rent density is related to the pore wall flux by in ⫽ Fjn. The open-cir-
`cuit potential U2 is equal to zero because we are measuring the
`potential with respect to a lithium metal reference electrode in solu-
`tion at the same local concentration. Rfilm (⍀ cm2) is a resistance
`caused by the film formed over the electrode surface. The resistance
`of the film is treated by modifying the Butler-Volmer kinetic expres-
`sion for the insertion reaction and the lithium deposition reaction as
`shown in Eq. 10 and 11. The exchange-current densities for the inser-
`tion reaction (i0,1) and lithium deposition reaction (i0,2) have the form
`
`For solids such as metallic lithium, the flux will be zero to a very
`good approximation. Thus the mass balance on the solid lithium
`reduces to
`
`⫽ ⫺
`a
`
`i
`n,2
`F
`
`[19]
`
`∂
`
`∂c
`
`Li
`t
`
`i0,1 ⫽ F(ka,1)␣c,1(kc,1)␣a,1(ct ⫺ cs)␣a,1(cs)␣c,1(c)␣a,1
`
`i0,2 ⫽ F(ka,2)␣c,2(kc,2)␣a,2(c)␣a,2
`
`[12]
`
`[13]
`
`where cLi is the moles of lithium metal per volume of electrode, and
`a is the surface area to volume ratio as defined below for spherical
`carbon particles
`
`a
`
`⫽
`
`3 1(
`
`⫺ ⑀ ⫺ ⑀ ⫺ ⑀
`l
`p
`
`f
`
`)
`
`R
`s
`
`[20]
`
`By assuming that the negative-electrode particles are spherical in
`nature, the rate of the side reaction can be related to the growth of a
`film on the surface of the electrode particles according to
`
`∂
`␦
`film
`∂
`t
`
`⫽ ⫺
`
`i M
`n,2
`␳
`F
`
`[21]
`
`where ␦film is the film thickness composed of solid lithium and other
`products and M and ␳ are the molecular weight and density of lithi-
`um and products. The resistance [Rproducts(t)] of the film formed by
`lithium and other products (Li2CO3 is used as an example here) is
`given by
`
`R
`products
`
`
`
`t( ) ⫽
`
`z
`
`i
`L
`
`␦
`
`⫹
`
`z
`
`␦
`
`film
`
`[22]
`
`The open-circuit potential U1 is a function of the amount of lithi-
`um inserted and can be described by Eq. 14 for mesocarbon
`(MCMB) 25284
`
`
`1 x
`
`
`U1 ⫽ 0.7222 ⫹ 0.13868x ⫹ 0.028952(x0.5) ⫺ 0.017189
`
`⫹ 0.28082 exp[15(0.06 ⫺ x)]
`
`
`
`1 1
`
`5x .
`
`
`
`⫹ 0.0019144
`
`⫺ 0.79844 exp[0.44649(x ⫺ 0.92)]
`
`[14]
`
` 
`
`␬
`
`i
`L CO
`2
`
`3
`
` 
`
`i
`L CO
`2
`
`3
`
` 
`
`film
`␬
`
`i
`L
`
` 
`
`where zLi and zLi2CO3 are the volume fractions of lithium and Li2CO3
`present in the film. The film resistance in Eq. 8 is given by
`
`Rfilm ⫽ RSEI ⫹ Rproducts(t)
`
`[23]
`
`for the negative electrode, where RSEI corresponds to the resistance
`offered by the solid electrolyte interface (SEI) layer formed on the
`negative electrode active material during the formation period.
`Recently Peled et al. proposed a complex two-layer multicompo-
`nent structure for the SEI layer formed on lithium and lithiated car-
`bon electrodes.13 According to these authors, the inner layer (closer
`to the negative electrode) is rich in Li2O and LiF and low in Li2CO3,
`whereas the outer layer consists of 13% Li2CO3 and other semicar-
`bonates, 10% LiF, and the remainder polyolefins. In order to simpli-
`fy the present mathematical model, the composition of the film
`formed during overcharge is assumed to consist of only Li and
`Li2CO3 in a single layer.
`The mathematical model requires a number of physical proper-
`ties. The design adjustable parameters and other parameters for the
`electrodes are given in Tables I, II, and III. The mathematical equa-
`tions describing the electrochemical reactions, mass transport, and
`other physical processes within the cell are discussed in detail in
`Ref. 2 and 3. This nonlinear system of six independent governing
`equations and six dependent variables (c, ␾2, cs, i2, jn, ␾1) is solved
`using Newman’s BAND subroutine.9
`
`Table II. Parameters for the electrodes.
`
`Parameter
`
`Ds (cm2/s)
`␴o (S/cm)
`io (mA/cm2)
`ct (mol/dm3)
`␳ (g/cm3)
`
`LixC6
`
`2.0 ⫻ 10⫺10
`11.01
`10.21
`30.54
`12.20
`
`LiyMn2O4
`
`1.0 ⫻ 10⫺9
`10.038
`10.131
`22.861
`14.141
`
`where x is cs/ct . The kinetic and thermodynamic parameters used to
`simulate the electrochemical reactions on the negative electrode are
`summarized in Table I. According to Jasinski et al.10 Li/Li⫹ has a
`high exchange current density in 1 M LiClO4-PC, at least on the
`order of 2 to 5 mA/cm2 for a smooth surface and a cathodic transfer
`coefficient ranging from 0.66 to 0.72. The exchange current density
`for lithium deposition as reported by Verbrugge is 31.6 mA/cm2 and
`the cathodic transfer coefficient is 0.67.11,12 In this work, the value
`of exchange current density is varied from 0.1 to 3 mA/cm2 to exam-
`ine its effect on overcharge.
`The pore-wall flux jn,k is defined as the reaction rate per unit vol-
`ume of the porous electrode and is equal to the divergence of the cur-
`rent density in solution
`
`1
`
`F
`
`i
`2
`
`ⵜ ⫽ ∑ n,k
`
`aj
`
`k
`
`[15]
`
`The pore-wall flux across the interface is related to the flux of lithi-
`um ions into the solid phase by the boundary condition
`
`[16]
`
`[17]
`
`at
`
`r
`
`⫽
`
`R
`s
`
`c r
`∂ ∂
`
`s
`
`j
`n,1
`
`⫽ ⫺
`D
`s
`
`A material balance on solid lithium can be expressed as
`
`⫽ ⫺ⵜ ⫹
`N
`i
`
`R
`i
`
`c t
`∂ ∂
`
`i
`
`where Ri is the production rate of species i per unit volume of the
`electrode due to the electrochemical reaction
`
`Table I. Kinetic and thermodynamic parameters.
`
`Parameters
`
`io (mA/cm2)
`␣a
`␣c
`n
`U (vs. Li/Li⫹)
`
`Intercalation reaction
`(Eq. 1) Value
`
`Deposition reaction
`(Eq. 2) Value
`
`0.21a
`0.5b1
`0.5b1
`11.1b
`See Eq. 145
`
`1.010,11
`0.310,11
`0.710,11
`11.10,11
`0.010,11
`
`a Calculated at initial conditions.
`b Assumed.
`
`4
`
`

`

`3546
`
`Journal of The Electrochemical Society, 146 (10) 3543-3553 (1999)
`S0013-4651(99)01-088-5 CCC: $7.00 © The Electrochemical Society, Inc.
`
`Table III. Design-adjustable parameters.
`
`Parameter
`
`␦ (␮m)
`
`Rs (␮m)
`o (mol/dm3)
`cs
`⑀l
`␦cc (␮m)
`T (⬚C)
`co (mol/dm3)
`␦s (␮m)
`⑀ls
`⑀ps
`⑀SiO2
`␳l (g/cm3)
`␳p (g/cm3)
`
`LixC6
`
`99 (19% ECEa)
`85 (5% ECEa)1
`80 (0% ECEa)1
`12.511
`21.511
`10.360
`13.611
`21.011
`11.001
`76.211
`0.593
`0.266
`0.141
`1.320
`1.750
`
`LiyMn2O4
`
`179.311
`
`118.511
`113.921
`110.416
`116.011
`
`a Excess carbon electrode.
`
`Results and Discussion
`Lithium deposition is observed on carbon-based negative elec-
`trodes when lithium-ion cells are overcharged. To minimize the lithi-
`um deposition reaction most lithium-ion cells are manufactured with
`excess negative electrode (excess capacity). That is, if a lithium-ion
`cell consists of a positive electrode and negative electrode of equal
`reversible cyclable capacity, then at the end of charge (or at the
`beginning of overcharge) most of the applied current would go to the
`lithium deposition side reaction on the negative electrode. However,
`if excess negative electrode is present, then at the end of charge the
`negative electrode will still be undergoing the normal charging
`process (lithium intercalation). The lithium lost during lithium depo-
`sition may lead to changes in the capacity balance (Eq. 1).
`For optimum performance, the ratio of the lithium-ion capacities
`of the two host materials should be balanced. The actual mass ratio
`calculated for the cell [mesocarbon microbead (MCMB) 2528/
`LiMn2O4] modeled in this study is 2.47. The theoretical mass ratio
`calculated on the basis of the theoretical capacity of the positive (148
`mAh/g) and negative electrodes (372 mAh/g) is 3.03 when using
`⌬x ⫽ 1.0 and ⌬y ⫽ 0.83. This leads to the conclusion that an excess
`of 18.6% capacity exists in the negative electrode. Considering also
`the irreversible capacity on the negative electrode (which can be 8-
`12% for MCMB type graphite), it is apparent that a wide safety mar-
`gin exists to prevent accidental lithium deposition on the graphite
`during charging. In commercial cells where other safety features
`would exist, cells might be designed differently to provide even high-
`er energy densities by using a larger mass ratio closer to the theoret-
`ical value. On changing the thickness of the negative electrode to 80
`and 85 ␮m, the excess capacity in the cell reduces to 0 and 5%,
`respectively. The excess capacity in this work is defined as
`
`Figure 3. Simulated reaction rates as a function of charge time for 19%
`excess negative electrode (graphite). The cell is charged at 2.9 mA/cm2 to
`4.45 V and the results are shown at the negative electrode/separator interface.
`
`The excess negative electrode active material used in commercial
`cells is often small to reduce the irreversible capacity loss to a min-
`imum during the formation period. This improves the performance,
`but compromises the safety of these cells. Figure 4 shows the lithi-
`um deposition reaction as a function of charge time when the excess
`negative electrode is reduced to 5%. As soon as the overpotential on
`the negative electrode reaches zero, the lithium deposition reaction
`becomes favorable. The rate of the lithium deposition reaction com-
`pared to that of lithium intercalation is very high at this location in
`the cell, and leads to a large amount of deposition within a short
`time. The cells with no excess negative electrode will be more prone
`to deposition compared to cells with excess negative electrode.
`Lithium deposition will also start earlier (53 min for 0% excess
`anode, 57 min for 5% excess anode) in the absence of any excess
`negative electrode. The excess negative electrode clearly has a major
`effect on reducing the lithium deposition overcharge reaction.
`Figure 5 shows the effect of charge cutoff voltage on the lithium
`deposition and intercalation rates. The cells were overcharged to three
`different cutoff voltages (4.25, 4.35, and 4.45 V) at 2.906 mA/cm2
`with 5% excess negative electrode. As expected, the lithium deposi-
`tion reaction rate is higher when the cells are charged to higher cutoff
`voltages. The lithium deposition reaction dominates as soon as it be-
`gins, leading to an increase in the deposition rate and decrease in the
`intercalation rate. This problem becomes worse as the charging rate is
`increased. The value of the exchange current density for the lithium
`deposition/dissolution reaction as reported in the literature varies by
`two orders of magnitude.10,11 The large variation in values reported in
`the literature is likely due to the surface condition of the lithium under
`study. Freshly deposited lithium will have a high exchange current
`density compared to lithium covered with more-developed surface
`
`100%
`
`[24]
`
` 
`
`⫺ ␥
`
`actual
`
`theoretical
`␥
`
`theoretical
`
`␥
`
` 
`
`Excess capacity (%)
`
`⫽
`
`Figure 3 shows the simulated reaction rates at the negative elec-
`trode/separator interface for the lithium intercalation and lithium
`deposition reactions as a function of charge time. The cell was
`charged galvanostatically at 2.906 mA/cm2 (ca. 1 C rate) to a cutoff
`voltage of 4.45 V. The overpotential on the negative electrode is also
`shown as a function of charge time. The dashed line at 0.0 V (vs.
`Li/Li⫹) shows the lithium deposition potential. It is clear from the
`figure that no lithium was deposited even when the cell was over-
`charged to 4.45 V because the cell had 19% excess negative elec-
`trode. The excess negative electrode makes the cell safer but com-
`promises the performance of the cell. It also leads to larger irre-
`versible capacity losses during the formation period.
`
`Figure 4. Simulated reaction rates as a function of charge time for 5% excess
`negative electrode (graphite). The cell is charged at 2.9 mA/cm2 to 4.45 V
`and the results are shown at the negative electrode/separator interface.
`
`5
`
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`

`Journal of The Electrochemical Society, 146 (10) 3543-3553 (1999)
`S0013-4651(99)01-088-5 CCC: $7.00 © The Electrochemical Society, Inc.
`
`3547
`
`Figure 5. Simulated reaction rates as a function of charge time for different
`cutoff voltages (4.25, 4.35, and 4.45 V). The cell with 5% excess negative
`electrode is charged at 2.9 mA/cm2 and the results are shown at the negative
`electrode (graphite)/separator interface.
`
`films. Figure 6 shows the effect of exchange current density on the
`lithium deposition reaction (0.1, 1.0, and 3.0 mA/cm2). At high
`exchange current densities, the rate of lithium deposition is very high
`and leads to a rapid depletion of lithium in the system.
`Figures 3-6 model the lithium deposition reaction rate using a
`Butler-Volmer rate expression. If we assume that the lithium deposi-
`tion reaction is irreversible and all the lithium deposited reacts with
`the electrolyte to form insoluble products, then a cathodic Tafel rate
`
`Figure 6. Simulated reaction rates as a function of charge time for different
`exchange current densities (0.1, 1.0, and 3.0 mA/cm2) for the lithium depo-
`sition reaction. The cells with 5% excess negative electrode are charged at
`2.9 mA/cm2 to 4.45 V and the results are shown at the negative electrode
`(graphite)/separator interface.
`
`Figure 8. The predicted thickness of the lithium deposit under different oper-
`ating conditions as a function of charge time. The cells with 5% excess neg-
`ative electrode are charged to 4.45 V and the results are shown at the nega-
`tive electrode (graphite)/separator interface.
`
`expression (Eq. 6) will suffice to describe the kinetics for the lithi-
`um deposition reaction. Figure 7 shows the lithium deposition reac-
`tion rate when a Tafel rate expression is used. In this case, the lithi-
`um deposition begins before the overpotential on the negative elec-
`trode reaches zero. The amount of lithium deposited in this case is
`larger compared to the Butler-Volmer rate expression under similar
`operating conditions.
`As discussed above, a film is formed over the particles in the neg-
`ative electrode during overcharge. This film consists of solid lithium
`and products formed by the reaction of lithium with electrolyte com-
`ponents. The thickness of this film under different operating condi-
`tions is shown in Fig. 8 assuming the film consists of solid metallic
`lithium only. As expected, a thicker film is formed when the cell is
`charged at higher rates. The film begins growing earlier when the
`excess capacity on the negative electrode is smaller.
`Figure 9 summarizes the effect of different charging rates, charge
`cutoff voltages, and mass ratios on the amount of lithium deposited.
`The comparisons are shown for three different mass ratios (0, 5, and
`19% excess negative electrode), two different cutoff voltages (4.25
`and 4.45 V) and several different charging rates (1.0-5.0 mA/cm2). In
`the case of cells with 19% excess negative electrode, lithium deposi-
`tion will only occur when the cells are charged at rates greater than
`3.9 (4.45 V) and 4.2 mA/cm2 (4.25 V) depending on the cutoff poten-
`tial. Similarly, in the case of 5% excess negative electrode, the lithi-
`um deposition will begin at 2.5 (4.45 V) and 2.9 mA/cm2 (4.25 V)
`
`Figure 7. Simulated reaction rates as a function of charge time using a Tafel
`rate expression for the lithium deposition overcharge reaction. The cell with
`5% excess negative electrode is charged at 2.9 mA/cm2 to 4.45 V and the
`results are shown at the negative electrode (graphite)/separator interface.
`
`Figure 9. Amount of lithium deposited at the negative electrode/separator
`interface as a function of charge rate, mass ratio, and charge cutoff voltages
`for graphite negative electrodes.
`
`6
`
`

`

`3548
`
`Journal of The Electrochemical Society, 146 (10) 3543-3553 (1999)
`S0013-4651(99)01-088-5 CCC: $7.00 © The Electrochemical Society, Inc.
`
`and in the case of 0% excess negative electrode, the lithium deposi-
`tion will begin at 1.8 (4.45 V) and 2.25 (4.25 V) mA/cm2. Thus in a
`cell with 5% excess negative electrode, lithium deposition will occur
`when it is charged to 4.25 V at the 1 C rate (2.906 mA/cm2).
`Active material particle size and negative electrode thickness
`play important roles in cell design. For these simulations, it is
`assumed that all of the particles are spherical and of equal size. Fig-
`ure 10 compares the lithium deposition onset potential and amount
`of lithium deposited for three different grades of MCMBs (628,
`1028, and 2528 with average particle sizes of 6, 10, and 25 ␮m,
`respectively). The cells with 5% excess anode were charged (and
`overcharged) at different rates (2-8 mA/cm2) and to two different
`cutoff voltages (4.25 and 4.45 V). It is clear from Fig. 10 that the
`cells with larger particles are more prone to lithium deposition com-
`pared to cells with smaller particles. This is because diffusion limi-
`tations lead to an increase in overpotential across the negative elec-
`trode in the cells with larger particles. Thus, for larger particles the
`overpotential on the negative electrode will reach zero earlier com-
`pared to smaller particles. However, smaller particles (larger surface
`area) lead to a larger irreversible capacity loss during the formation
`period. Thus optimization of particle size can be a subtle undertak-
`ing with several important considerations.
`Figure 11 compares the amount of lithium deposited at the nega-
`tive electrode/separator interface as a function of charge rate (C rate)
`for cells with different electrode thicknesses. The thicknesses of both
`electrodes were changed to keep the mass ratio constant (5% excess
`negative electrode). The thicker electrodes are more prone to lithium
`deposition compared to thinner electrodes. Just as with the solid-phase
`diffusion limitations discussed above, solution-phase diffusion limita-
`tions become more prominent for thicker electrodes leading to more
`rapid lithium deposition. As shown in Fig. 11, the lithium deposition
`begins at 0.57 C for thicker electrodes (negative: 150 ␮m and positive:
`316 ␮m), at 0.90 C for medium electrodes (negative: 85 ␮m and pos-
`itive: 179 ␮m), and at 0.96 C for thin electrodes (negative: 70 ␮m and
`positive: 148 ␮m), respectively when overcharged to 4.45 V.
`Low rates are typically used in constant-current charging so that
`lithium can intercalate uniformly throughout the electrode. The
`major disadvantages of constant-current charging are the longer time
`required and incomplete charging (nonuniform distribution of lithi-
`um). Constant-current charging followed by constant-voltage charg-
`ing (taper charge) is a typical method of charging lithium-ion
`rechargeable batteries. In this method, constant-current charging is
`performed until the battery voltage reaches a preset value. After this
`voltage is reached, charging is switched to constant-voltage charging
`at the preset value. By increasing the charging current during the
`constant-current charging, the time needed to achieve full charge can
`be reduced. However, even though the constant-current charging
`
`Figure 11. Amount of lithium deposited as a function of charge rate for dif-
`ferent electrode thicknesses. The cells have 5% excess negative electrode and
`the results are shown at the negative electrode/separator interface. Both pos-
`itive and negative electrode thicknesses were changed to maintain the mass
`ratio constant.
`
`time is reduced by increasing the current, it does not follow that the
`more the charging current is increased, the more the charging time
`will be reduced. Further, when the charging current is increased
`above a certain level, degradation in battery performance becomes
`an issue. In this work, the two charging protocols (constant current
`and taper charge) will be compared to study their effects on the lithi-
`um deposition overcharge reaction.
`During normal charging, all of the charge promotes lithium inter-
`calation and none leads to deposition. During overcharge, lithium
`deposition occurs and a portion of the charge is consumed by the
`
`Figure 10. Amount of lithium deposited as a function of charge rate for dif-
`ferent particle sizes (MCMB 628, 1028, and 2528) for graphite negative elec-
`trodes. The cells have 5% excess negative electrode and the results are shown
`at the negative electrode/separator interface.
`
`Figure 12. Charge efficiency at negative electrode (graphite)/separator inter-
`face as a function of charge time for (a) constant current and (b) taper charg-
`ing. The capacity of the cell during charge is also shown.
`
`7
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`

`Journal of The Electrochemical Society, 146 (10) 3543-3553 (1999)
`S0013-4651(99)01-088-5 CCC: $7.00 © The Electrochemical Society, Inc.
`
`3549
`
`graphs that the deposition begins first at the negative electrode/sep-
`arator interface and then moves into the negative electrode. Lithium
`deposition was observed only in roughly a third of the negative elec-
`trode. During taper charging (Fig. 12b) lithium continues to deposit
`for a short time after the charging shifts from constant current to
`constant potential. This leads to a slightly larger lithium deposit in
`the negative electrode during taper charging as shown in Fig. 13b.
`The maximum film thicknesses observed for constant-current charge
`and taper charge were 0.1920 and