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Lithium batteries--When mechanics meets chemistry

Zhigang Suo's picture

When I learned chemistry in college, the subject was presented to me with equations of chemical reactions.  It took me some time to realize a couple of simple points:  reactants need to meet to produce a product, and compounds take space.

The connection between chemistry and mechanics is made vivid to me in recent years in studying lithium batteries.  As an example, here is a recent paper when chemistry is linked with plasticity, mass transport, and fracture—essential ingredients of solid mechanics.

Kejie Zhao, Matt Pharr, Joost J. Vlassak and Zhigang Suo. Inelastic hosts as electrodes for high-capacity lithium-ion batteries. Journal of Applied Physics 109, 016110 (2011).

As you can see in the list of references, a large number of papers on the combination of electrochemistry and mechanics have appeared recently.  The subject, however, is at its infancy.

The theme of the July 2011 issue of the MRS Bulletin is Electromechanical Energy Storage.  The magazine reached my office on Friday, and I have quickly looked through the articles.  They are extremely well written, and well illustrated.  Here are a few points I marked in my copy:

  • A practical battery with energy > 500 Wh/kg is sufficient to deliver a 300 mile driving range.
  • Theoretical specific energy for a lithium-ion battery is 387 Wh/kg.
  • All existing commercial technologies are inadequate to power pure electric vehicles.
  • Theoretical specific energy for a lithium-air battery is 3505 Wh/kg.
  • The anode of lithium-air battery can be lithiated silicon.
  • Large strain is induced during lithiating silicon.
  • Nanostructured anodes do not fracture.
  • To enhance electromechanical stability, a particle of electrode material may be coated with another material.
  • The core-shell may fracture due to mismatch strain during lithation.

Many more really interesting connections between chemistry and mechanics.  Go take a look at this issue of MRS Bulletin

You may also wish to check out a recent book:  Bottled Lightning—Superbatteries, Electric Cars, and New Lithium Economy.


Kejie Zhao's picture

Thanks Zhigang for initiating this intriguing topic. Indeed, lithium-ion battery is an example system that couples chemistry and mechanics.  The mechanical and chemical stability have become the top criteria for the selection of a viable electrode of commercial batteries – that is, the chemistry of lithiation reaction gives rise to pronounced effects on the mechanical properties of the electrode materials, and the mechanical failure significantly limits the cyclic life of the battery. A little more detailed picture is following. Each electrode in a lithium-ion battery is a host of lithium. Lithium is shuttled between two electrodes during cycles. For instance, during discharge, lithium atoms are dissociated into lithium ions and electrons on the interface between the anode and electrolyte. Lithium ions pass through the electrolyte, electrons pass through the external wire. Upon reaching the cathode, lithium ions and electrons recombine to form neutral lithium atoms. Lithium atoms diffuse into the cathode, and react with the cathode. The diffusion and reaction cause mechanical deformation, and a field of stress in the electrodes. The stress induces plasticity, fracture and fatigue.  Fracture and fatigue are generally observed for almost all the commercial batteries, particularly challenging the stability of high energy density electrodes, such as silicon.

We have been studying the mechanical behaviors of silicon electrodes during lithiation reaction recently.

Kejie Zhao, Wei L. Wang, John Gregoire, Matt Pharr, Zhigang Suo, Joost J. Vlassak, and Efthimios Kaxiras. Lithium-assisted plastic deformation of silicon electrodes in lithium-ion batteries: a first-principles theoretical study. Nano Letters 11, 2962-2967 (2011)

In a system involving a variety of physical processes, such as thermal, structural and chemical ones, “chemistry always wins” (quoted from W. D. Nix and F. Spaepen). In lithium-ion batteries, however, it might be an exception – mechanics can be competitive to chemistry, stress can significantly influence the reaction, or even be large enough to shut down the chemical reaction.

Matt Pharr's picture

Chemical phenomena can influence the mechanics of the electrode system in various ways.  During discharge, the difference in chemical potential drives lithium to move from the cathode to the anode.  When lithium enters the anode, it tends to cause swelling of the electrode.  The amount of swelling depends primarily on the chemistry of the lithiated anode (where lithium atoms tend to sit in the electrode, how much attraction/repulsion they cause with neighboring host atoms, etc.).  As mentioned in this thread, this swelling and shrinking of the electrode can cause fracture (mechanical failure) of the electrode, causing the capacity of the battery to fade.

Another interesting interplay between mechanics and chemistry is outlined in the paper Kejie and linked above:  Lithium-assisted plastic deformation of silicon electrodes in lithium-ion batteries: a first-principles theoretical study .  Here, it was found that insertion of lithium can cause breaking and reforming of silicon bonds.  After only a small amount of lithium is inserted, this leads to yielding of the lithiated silicon electrode.  This has been observed experimentally in the silicon-lithium system, initial by: 

Vijay A. Sethuraman, Michael J. Chon, Maxwell Shimshak, Venkat Srinivasan, and Pradeep Guduru, In situ measurements of stress evolution in silicon thin films during electrochemical lithiation and delithiation, Journal of Power Sources 195, 5062-5066 (2010).

This chemical interplay causing yielding in the material has important consequences in terms of mechanics.  In particular, the energy release rate for a crack in a body takes the form G=Zhσ^2/E where Z is a dimensionless number of order unity, σ is a representative stress, h is the feature size of the electrode, and E is the modulus of the lithiated silicon.  If we did not know about yielding in silicon, we might take the stress to be the product of the modulus and the strain induced by lithiation (i.e. use Hooke's law to calculate the stress, σ=Eε).  However, this would predict a huge energy release rate.  Namely, using representative values of the fracture energy: Γ = 10 J/m^2, strain: ε = 100% linearly, and modulus: E = 80 GPa, we would predict the critical feature size (below which we will have no fracture) to be sub-atomic.  This is not agreeement with experimental observations that silicon electrodes with feature sizes around 100 nm do not fracture.  However, as suggested, the chemistry causing the material to yield has important consequences.  In the paper listed above by Sethuraman, the yield strength was found to be 1.75 GPa.  Taking the representative value of the stress to be on the order of the yield strength, the critical particle size instead is calculated to be 130 nm, which agrees with experiments quite well.  For a further discussion of this topic, please see:  

Kejie Zhao, Matt Pharr, Joost J. Vlassak and Zhigang Suo. Inelastic hosts as electrodes for high-capacity lithium-ion batteries. Journal of Applied Physics 109, 016110 (2011).


Ting Zhu's picture

The chemomechanics of batteries is an emerging field full of surprises, challenges and opportunities. Here are a few examples from our recent studies of nanowire/nanoparticle electrodes by coupling the chemomechanics modeling with in situ TEM imaging.

1. Unexpected surface cracking during lithium insertion

X.H. Liu et al., Anisotropic swelling and fracture of silicon nanowires during lithiation, Nano Letters, (2011)

X.H. Liu et al., Size dependent fracture of silicon nanoparticles during lithiation, submitted (to be posted)

A number of theoretical models of lithiation-induced stress predicted/implied fracture at the center of nanoparticles/wires, contradicting our in situ TEM observations of surface cracking. These models also predicted the compression in the surface layer, thus excluding the possibility of surface cracking. The new physics underlying our model is the unexpected lithiation mechanism by motion of an atomically sharp two-phase interface. This is entirely different from the commonly assumed lithiation mechanism by Li diffusion in a single-phase material.

2. Fracture in coatings

L.Q. Zhang et al., Controlling the lithiation induced strain and charging rate in nanowire electrodes by coating , ACS Nano, 5, 4800-4809 (2011)

It has been proposed that the coating could enable the simultaneous control of electrical and mechanical behaviors of nanowire/nanoparticle electrodes. We found that the large lithiation strain often causes the fracture of coatings.

3. Reversible nanoporosity formation

X.H. Liu et al., Reversible nanopore formation in Ge nanowires during lithiation-delithiation cycling, submitted (to be posted)

It has been predicted that delithiation-produced vacancies can quickly leave the nanowire/nanoparticle electrodes due to the short diffusion length to surface. We discovered the nanopore formation in Ge nanowires during the first cycle of delithiation, similar to the formation of porous metals in dealloying. A striking phenomenon seen in the TEM is the so-called "pore memory effect" during cycling. Reversible nanoporosity formation has important implications for retaining the cycling stability of microstructures in electrode materials.


Lithium is a rare metal and its widespread use in car batteries depends on its cost.  You can see the estimated reserves (from 2009) here .  The recoverable portion of a reserve is usually less than 50%.

-- Biswajit

Zhigang Suo's picture

Interesting issue.  I have not looked into it myself, but a casual reading of the book,  Bottled Lightning—Superbatteries, Electric Cars, and New Lithium Economy, leaves me an impression that the reserve of lithium is sufficent to power the "lithium economy".  I have returned the book to the library.  People having the book or any link to the original analysis can help us to learn more.

Kejie Zhao's picture

Ultimately lithium reserve might become a concern for the large scale electric vehicles industry. The book Bottled Lightning lists the latest survey of global lithium reserves and identified resources as of Jan.2011.  I copied it here.  Reserves are mineral sources that can today be economically and legally extracted; identified resources are known mineral deposits. The unit is thousand tons

Reserves                                      Identified resources

Chile    7500                                 Bolivia   9000

China   3500                                 Chile      7500

Argentina  850                               China      5400

Austrialia  580                                US         4000

Brazil   64                                      Argentina  2600

US       38                                      Brazil       1000

Zimbabwe  23                                 Congo      1000

Portugal     10                                 Serbia      1000

Total          12565                            Australia   630

                                                     Canada     360

                                                     Total         32490

Thanks for the information Kejie/Zhigang.

As a mining engineer, the feasibility of mineral extraction and processing has always been of interest to me.  Light metals are usually quite abundant in the earth's crust (e.g., Li, Na, K, etc.).  When I say "rare metal", I mean that even though the total quantity in the crust may be large, extraction is an energy hog because of low concentrations.

In the case of Li, the current reserve estimate is 50-150 million tons of Lithium carbonate (~10-30 million tons Li).  People often count unmineable resources into the reserve estimate.  For instance, if a coal reserve is given as y tons, the actual mineable reserve can be as low as 0.2y ton (U/G) and as high as 0.9y ton (O/C). 

In the case of Li extracted from brines, the energy cost of processing can be quite large (even though solar energy is used to evaporate the brine) and the environmental impact can be significant.  Does anyone know what percent of the lithium carbonate remains in the waste after processing?

A related paper is


-- Biswajit

Kejie Zhao's picture

Hi Biswajit,   you might want to take a look at Chapter 9 "the prospectors" of Bottled Lightning. It describes the historical debate of lithium reserve, which was ignited by Tahil and his paper "the trouble with lithium".  A few papers in this theme are following

"An abundance of Lithium":

"The trouble with lithium 2":

Also I read a paper this morning, which claims "the doubts about lithium abundance are groundless".


Thanks Zhigang for starting this very interesting topic. Li-ion battery system is a unique system where mechanics and chemistry interact in various domains. Capacity fading is a particular important issue for large format batteries. This process involves several mechanical and electrochemical actions, such as fracture of active electrode materials, formation of SEI layers, phase transition due to overlithiation, dissolution of electrodes, heat generation. Solving the problem requires coupled calculation of mechanical, chemical and thermal processes. It should be noted that mechanics plays various roles at different size scales from particle, cell to system level. Eventually, surrogate models need to be developed to bridge these physics-based complicated models to real-time control algorisms that can be used for optimized performance and prolonged battery life. We looked into some aspects of these problems.

J. Park, W. Lu, and A.M. Sastry, "Numerical Simulation of Stress Evolution in Lithium Manganese Dioxide Particles due to Coupled Phase Transition and Intercalation," Journal of the Electrochemical Society, 158, A201-A206, 2011.

J. Park, J.H. Seo, G.L. Plett, W. Lu and A.M. Sastry, "The Effect of the Dissolution of Lithium Manganese Oxide Particles on Li-ion Battery Performance," Electrochemical and Solid State Letters, 14, A14-A18, 2011.

Following previous posts on the significant role mechanics play
in Li-ion batteries, I think this is also facilitated by the fact that
1) Compared to other chemical reactions, the chemistry involved in Li intercalation into Li-ion electrodes is relatively weak. In fact, this is a main reason such reactions are highly reversible and Li-ion batteries can be easily recharged.

2) Many Li insertion electrodes undergo large volume change upon Li insertion/removal, from several percent (already very significant for inorganic materials) to several hundred percent, and they also tend to have large elastic moduli, which can push the strain energy to the 1eV level.
As Kejie commented earlier, chemical energy is usually the king among various energy forms when it comes to thermodynamics. But 1) and 2) make it possible for the mechanical energy to compete with the chemical energy in Li insertion electrodes. We recently studied the lithium intercalation process in an important cathode material called lithium iron phosphate (LiFePO4) through continuum modeling. One finding is that, depending on the relative magnitude of chemical driving force with respect to strain energy, very different lithium transport pathways and phase growth morphology may be produced under different charge/discharge conditions, which in turn dramatically impact electrode performance. Some of the results can be found in:
M.Tang, J. F. Belak, M. Dorr, J. Phys. Chem. C 115, 4922 (2011).a
Like Zhigang and others who have commented in this thread, I’m convinced understanding the interplay between mechanics and chemistry is of extreme importance to fully realize the potentials of lithium battery materials. On the other hand, lithium insertion electrodes seem to provide an excellent platform to probe the fundamental physics underlying stress-chemistry coupling.

Kejie Zhao's picture

Thanks Ming for the very nice summary.   1) reminds me that one difficulty in Li-air battery is the reversibility of redox reaction, the solid lithium preoxide is not easy to decompse into oxygen and lithium.  On the mechanical energy particularly in silicon, we also found that it can be high enough (1ev) to counteract the electrochemical driving forces for the reaction, even with the consideration of plastic flow and softening effect during lithiation. 

Hanqing Jiang's picture

Thanks Zhigang for posting this note. The coupling between
electrochemistry and mechanics is indeed fascinating. We noticed that the main
efforts in this area is to study how electrochemical reactions affect mechanics
and deformation, while the inverse route has been not explored that much. I
think part of the reason is that the energy for electrochemical reactions
(hundreds of kJ/mole) is much greater that typical elastic energy. However, for
electrodes in Lithium ion battery experiencing large volumetric change, these
two energies are comparable. We have unpublished experimental results showing
that the charge/discharge voltage and the lithium diffusivity into silicon
electrode depend on the stress level. There are some other indirect evidence
showing this effect, such as


Vijay A. Sethuramana, Michael J. Chonb, Maxwell Shimshakb,
Venkat Srinivasana and Pradeep R. Gudurub, In situ measurements of stress
evolution in silicon thin films during electrochemical lithiation and
delithiation, Journal of Power Sources, Volume 195, Issue 15, 1 August 2010,
Pages 5062-5066.


Thanks Zhigang for initiating the topic. My comments are the following.

The reaction paths of Li with electrodes are: intercalation, conversion, displacement, or alloying. High energy capacity anodes such as Si, Ge, Al usually alloys with Li to form LixMey, this alloying process always accompanies with large volume expansion, and in the reverse dealloying process there is large volume shrink. It is this repeated expansion/shrink that causes pulverization, and failure of the electrodes. This is certainly a very good mechanical problem for mechanicians to work with. Mechanician can help to understand what is the volume expansion/shrink mechanism, what are the mechanical properties of the LixMey alloys (supposedly very different from the Metal), and is there a way to mitigate the volume expansion? The answer to the latter question may be no, because the volume changes appear to be intrinsic to the alloying process, or in other words, if it holds that much Li, there is that volume expansion. If you avoid the volume expansion, then you are not going to hold that much Li. So one way to go around this problem maybe to find a flexible framework (architecture) to hold Si (nanoparticles) and let the framework to accommodate the large volume change: kind of a small host in a big host concept. Another way may be coating the electrode: our recent study in Al nanowires showing that the surface thin Al2O3 layer is always lithiated first to form a Li-Al-O glass with exceptional mechanical properties which survives almost 100% volume expansion (to be published). A theoretical explanation is needed for the remarkable mechanical properties of such thin coating layers.

For a review of the latest in-situ TEM studies on anode materials, see:

In-situ TEM electrochemistry of anode materials in lithium ion batteries, Energy Environ. Sci., 2011, DOI: 10.1039/C1EE01918J

In the cathode side, there are a lot of efforts going on in LiFePO4, the lithiation mechanism in this system appears to very unclear, see latest work by MIT:

Kinetics of non-equilibrium lithium incorporation in LiFePO4, Nature Materials 10, 587-590 (2011)

Kejie Zhao's picture

Thanks Jianyu for the comments.  I read a few recent papers on Al2O3 coating, which improves the cyclebility and rate capability of silicon anode. Al2O3 is an insulator, I was wondering if the electronic conduction would cause some problems on the reaction?

BTW thanks for sharing your very nice work on imechanica!


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