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Journal Club December 2010: Mechanics of Energy Storage

Hanqing Jiang's picture

   One of the greatest challenges facing the electric power industry worldwide is how to deliver the energy in a useable form as a higher-value product, especially in the area of renewable energy. By storing the power produced from immense renewable sources off-peak (e.g., daytime for solar energy) and releasing it during on-peak (e.g., nighttime) periods, energy storage can transform low-value, unscheduled power into schedulable, high-value “green” products.

Developing these resources will not only lessen environmental impacts, but also increase each country’s domestic energy security. Therefore, the development of high-energy and high-power storage devices has been one of the research areas of top-most importance in recent years. Among energy storage devices, full cells and/or rechargeable batteries are primary sources of power storage units for modern-day requirements. In this journal club, we will review the mechanics of energy storage, focusing on fuel cells and lithium ion batteries.

   1. Solid Oxide Fuel Cell
   Structure and material aspects: Solid oxide fuel cell (SOFC) is one of the alternative energy conversion technologies for its high conversion efficiency and pollution-free being. Its schematic structure and working process are shown in the figure. Nowadays, some doped rare earth metal oxides, such as gadolinium-doped ceria (GDC), and strontium-doped lanthanum oxides (LSCF), have been developed as a replacement of the conventional electrolyte material yttria-stabilized zirconia (YSZ) in SOFCs, due to their relatively high ionic conductivity at lower working temperatures. A large amount of extrinsic defects are introduced in the process of doping, such as oxygen vacancy. The efficiency of an electrolyte mainly depends on how fast the oxygen vacancies diffuse under the action of electrical and chemical driving forces. Therefore, mechanisms for charge transport and distribution have been studied in the solid state physics and material society [1-4].
   Mechanics problems: However, there exists a significant volume change in these material when their compositions deviate from the stoichiometric values [5,6], which could introduce significant mechanical stress if this volume change is inhomogeneous or some constrains are applied. This stress may in turn affect the electrochemical process and ionic transportation, as implied by some experiments [7,8]. In the preceding works, the coupling of the mechanical and electrochemical process has not been considered.
   Mechanics models: Jianmin Qu et al. [a] have developed a fully coupled field theory of defects in ionic solids, taking into account the concurrent processes of electrostatic equilibrium, mechanical equilibrium, defects transportation and chemical dynamics. In their theory, the coupling of the multiple fields is demonstrated by the construction of stress dependent electrochemical potential for defects diffusion and stress dependent rate constant for chemical reaction. Aiming at the analysis of the electrochemical performance, they studied the materials in different geometry [b,c], subjected to various working condition (applied voltage/partial oxygen pressure). The distribution of field variables, such as electrical current, defect concentration, and mechanical stress are discussed in detail.
   The dependence of chemical potential could be understood intuitively as following. For example, if the local stress state of a material point is compressive, it will cost extra energy to generate a defect associated with volume expansion. Considering its definition, chemical potential of such kind of defect under compression should be higher than that in the case of stress free. Thus the larger compressive stress leads to higher chemical potential. Consequently, the defects tend to diffuse away from the area with higher compressive stress to that with lower compressive stress.


   2. Lithium Ion Battery
   Structure and material aspects: Lithium (Li) ion batteries are an attractive choice for application such as portable electronic devices and satellites because of their high energy density, no memory effect, reasonable life cycle, and one of the best energy-to-weight ratios. In fact, advances in Li-ion batteries have the potential to usher in a wireless revolution, particularly the much desired use for powering electric vehicles using batteries. A typical Li-ion cell is illustrated in the following, which has three primary participants, namely, anode, cathode and electrolyte. Both anode and cathode are capable of reversible intercalation/insertion of Li-ions, and the electrolyte function is to transfer ions between electrodes. There is being great interest in developing next generation of lithium ion battery for higher energy capacity and longer life of cycling. To do that, people are looking for alternative materials for electrode and electrolyte. Now Si is one of the most promising candidates for the anode material, because it has the highest theoretical specific energy capacity [9].
   Mechanics problems: However, the biggest problem with this anode material is huge volume change during the process of insertion and extraction of lithium ions, which induces very high level of stress, leading to the mechanical failure of the anode material and the quick fading of electrical performance [10]. The extraordinarily high energy capacity of Si, however, has motivated researchers to explore new techniques that curb the limitation of Si as a practical anode material for Li-ion batteries. Exploration of Si nanostructures is one of the encouraging and priority research directions.
   Mechanics models: By making the size of the anode structure into nanoscale, the performance has been improved [11,12]. These experiments imply silicon anode has a critical size for flaw tolerance. In one of their papers [d], Huajian Gao et al. analyzed this phenomena from mechanical point of view, using a cohesive model of crack nucleation under diffusion induced stress in a thin strip. The one-way coupling of stress and diffusion was considered by treating the problem as a thermal stress problem. 
   Similar phenomena are observed in the one of the possible cathode materials [13,14]. Zhigang Suo et al [e] explained them by treating as a competition between surface energy of crack and the elastic energy due to the lattice mismatch at the phase boundary between two different phases. The critical size of cathode structure was determined through FEM simulation.
Later, Huajian Gao et al [f] developed a fully coupled model for highly nonlinear behavior associated with atomic-scale diffusion at high solute concentration and very large stresses. The following factors were considered, the dependence of chemical potential on stress, the dependence of stress on solvent concentration, and the dependence of diffusivity on stress. Explicit expressions were given directly and validated by molecular dynamics simulations. In addition, the maximum stoichiometric solvent concentration was recognized in this model.
Recently, Pradeep Guduru et al. conducted two experiments [g,h]. In the earlier one, by in situ measurements of the stress evolution in a silicon thin film anode during insertion and extraction of lithium, plastic flow of anode material was observed.  In the latter one, using the same method, the modulus was seen to decrease as the cycling of charging and discharging. These two papers show that during the electrochemical reactions, there exists significant irreversible deformation, which could not be addressed in the aforementioned mechanics models that based on elasticity.

 lithium ion battery


Key reference:
[a] N. Swaminathan, J. Qu, Y. Sun, Philos. Mag. 2007, 87,1705.
[b] N. Swaminathan, J. Qu, Y. Sun, Philos. Mag. 2007, 87,1723.
[c] N. Swaminathan, J. Qu, Fuel Cell 07, 2007, No. 6, 453.
[d] T.K. Bhandakkar, H. Gao, Int. J. Solids Struct. 47 (2010) 1424–1434.
[e] Y. H. Hu, X. H. Zhao, and Z. G. Suo, Journal of Materials Research 25 (6) 1007 (2010).
[f] Hamed Haftbaradaran, Jun Song, W.A. Curtin, Huajian Gao, Journal of Power Sources 196 (2011) 361–370.
[g] Vijay A. Sethuraman, et al, Journal of Power Sources 195 (2010) 5062–5066.
[h] V.A. Sethuraman, et al, Journal of The Electrochemical Society, 157 (11) A1253-A1261(2010).

Other reference:
[1] Y.W. Da, D.S. Park, J. Griffith, et al., Solid State Ionics 2 95 (1981).
[2] A. Atkinson, Solid State Ionics Diffus. React. 95 249 (1997).
[3] A. Atkinson and T.M.G.M. Ramos, Solid State Ionics Diffus. React. 129 259 (2000).
[4] Z. Chen, J. Electrochem. Soc. A 151 1576 (2004).
[5] S.B. Adler, J. Am. Ceram. Soc. 84 2117 (2001).
[6] S.R. Bishop, K. Duncan and E.D. Wachsman, Paper presented at 29th International Conference on Advanced Ceramics and Composites, ACerS, Cocoa Beach, FL, 23–28 January (2005).
[7] K.L. Duncan, Y. Wang, S.R. Bishop, et al., J. Am. Ceram. Soc. 89 3162 (2006).
[8] M. Greenberg, E. Wachtel, I. Lubomirsky, et al., Adv. Funct. Mater. 16 48 (2006).
[9] B. A. Boukamp, G. C. Lesh, and R. A. Huggins, 1981. J.  Electrochem. Soc. 128 (4), 725-729.
[10] Winter, M., Besenhard, J.O., Spahr, M.E., Novak, P., 1998. Advanced Materials 10, 725–763.
[11] Graetz, J., Ahn, C.C., Yazami, R., Fultz, B., 2003. Electrochemical and Solid-State Letters 6, A194–A197.
[12] Chan, C.K., Peng, H., Liu, G., McIlwrath, K., Zhang, X.F., Huggins, R.A., Cui, Y., 2008. Nature Nanotechnology 3, 31–35.
[13]. C. Delacourt, P. Poizot, S. Levasseur, and C. Masquelier. Electrochem. Solid-State Lett. 9, A352 (2006).
[14]. H. Gabrisch, J. Wilcox, and M.M. Doeff. Electrochem. Solid-State Lett. 11, A25 (2008).

Kejie Zhao's picture

Hi Hanqing, 

Thanks a lot for raising this thread. The mechanics aspect of energy storage mediums has intrigued so many research in recent years. In the case of fuel cell, are you aware of any mechanical failure in practice?



Hanqing Jiang's picture

Hi Kejie:


I am not quite familiar with the mechanical failure mode in fuel
cells. But one thing I know is that the failure is not caused by thermal mismatch
among the components but is driven by non-homogenous chemical potential. I
guess Dr. Wang may be able to address this question.

 Hanqing and Kejie,

 I am not familiar with PEM fuel cell. SOFCs typically work at 700~800oC and go through thermal cycles. It is common they fail due to thermal expansion coefficient mismatch between individual layers. SOFC anode is a metal-ceramic composite (Ni-YSZ, e.g.); fuel starvation at anode can cause metal to oxidize and the whole cell to crack. For certain cases such as when oxygen ions transporting from a good electronic conductor to a poor electronic conductor, oxygen gas pressure can build up to the extent to cause cell to fail.

I list a couple of references in case you are interested in more specifics

Anil Virkar et al., J. Am.Ceram. Soc. 73[11]3382 (1990)

Hyung-Tae Lim, Anil Virkar, J. Power Sources 185 (2008) 790

D. Sarantaridis et al., J.Power Sources 180 (2008)704

Kejie Zhao's picture

Dear Dr.Wang,

Thank you so much for the reply and valuable references. To summarize the origin of stresses as you mentioned,  1. thermal mismatch of individual layer of cathod anode and electrolyte,  2.oxidization of electrode 3. inhomogeneity of oxygen which causes differnet chemical potential at places. Is my understanding right? Does it also involve diffusion of species (H2 or O2)?

For cracking problem, does it often take place at interfaces of individual layers, or the electrode and electrolyte itself cracking limits the performance? Is there any technique to prevent mechanical failure in practice?  




Hope you had a fantastic holiday season.

Your understanding is quite on the point. SOFC cathodes are usually an oxide composite and fairly stable in air and over certain range of PO2. Inhomogeneity of oxygen (stoichiometry) in perovskite component does exist during operation due to electric polarization or oxygen concentration gradient in gas phase. The materials expand or contract with stoichiometry variation. Stress is expected to evolve accordingly, I am not aware of any literature evaluating this issue. 

Cracking can occur in any layer depending on specific circumstances. In practice we reject a cell when we see visible cracks as they would cause cell to fail sooner or later. Ideally we want electrolyte to be perfectly dense. When cracks are present, fuel will leak through. In addition to cracking, delamination is a typical defect.

SOFCs have experienced tremendous advances. Making defect free cells and even stacks is no longer a problem. One of the challenges is how to realize the reliability under practical conditions such as thermal cycles, vibrations, extreme weathers, etc.

Matt Pharr's picture

Hi Dr. Jiang,

Thanks so much for the article.  It is a very nice summary of some mechanical problems with these two technologies.  I'm also curious if you know of any other mechanical issues in energy storage.  For instance, are there some difficulties with hydrogen storage, etc.?




Hanqing Jiang's picture

Hi Matt:


Thanks for raising the hydrogen storage problem. In this
area, one of the key mechanics problems is the hydrogen embrittlement of
hydrogen fuel containers (usually metals), which susceptibly leads to cracking
because of the diffusion of hydrogen atoms into the metals. There exist many
different mechanisms that are trying to explain the hydrogen embrittlement. One
possible mechanism is the interaction between hydrogen and localized
plasticity. ABAQUS uses hydrogen embrittlement as their examples to conduct the
mass diffusion analysis.


Hi Dr. Jiang,

First I want to make a correction, SOFC works as an energy generator rather than storage device. It converts chemical energy to electricity and heat through electrochemical approach. It is easy to get confused with batteries which store energy.

Manufacture and operation of SOFC involve almost every aspects of mechanics. The problem gets highly complicated during operation. There are a number of publications out there, the subject is still not well understood. Lacking a reliable tool for guidance, we are dealing with our problem by try and error.

Hanqing Jiang's picture

Hi Dr. Wang:


Thanks for your note. We thought that it may be appropriate
(or convenient) to discuss both SOFC and batteries in a single Journal Club
thread because their similarity in terms of the coupling between diffusion,
electrochemical reactions, and mechanical stress, although SOFC is not energy
storage unit strictly speaking. Yes, I agree with you that we should
differentiate them more specifically. Thanks for pointing it out.

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