SCIENCE CHINA Technological Sciences, Volume 62 , Issue 8 : 1365-1374(2019) https://doi.org/10.1007/s11431-018-9499-x

A chemo-mechanical model for fully-coupled lithiation reaction and stress generation in viscoplastic lithiated silicon

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  • ReceivedNov 7, 2018
  • AcceptedMar 19, 2019
  • PublishedJul 11, 2019


Development of stresses in silicon (Si) anodes of lithium-ion batteries is strongly affected by its mechanical properties. Recent experiments reveal that the mechanical behavior of lithiated silicon is viscoplastic, thereby indicating that lithiation-induced mechanical stresses are dependent on the lithiation reaction rate. Experimental evidence also accumulates that the rate of lithiation reaction is conversely affected by the magnitude of mechanical stresses. These experimental observations demonstrate that lithiation reaction and stress generation in silicon anodes are fully coupled. In this work, we formulate a chemo-mechanical model considering the two-way coupling between lithiation reaction and viscoplastic deformation in silicon nanoparticle anodes. Based on the model, the position of the lithiation interface, the interface velocity, and the lithiation-induced stresses can be solved simultaneously via numerical methods. The predicted interface velocity is in line with experimental measurements reported in the literature. We demonstrate that the lithiation-induced stress field depends on the lithiation reaction through two parameters: the migration velocity and the position of the lithiation interface. We identify a stress-mitigation mechanism in viscoplastic silicon anodes: the stress-regulated lithiation reaction at the interface serves as a “brake” to reduce the interface velocity and mitigate the lithiation-induced stresses, protecting the Si nanoparticle anode from being subjected to excessive mechanical stresses.

Funded by

the National Natural Science Foundation of China(Grant,Nos.,11802269,11525210,&,11621062)


This work was supported by the National Natural Science Foundation of China (Grant Nos. 11802269, 11525210 & 11621062). The authors acknowledge the Fundamental Research Funds for the Central Universities. Zheng Jia also acknowledges the financial support from the One-Hundred Talents Program of Zhejiang University.


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  • Figure 1

    (Color online) (a) In the reference state, a silicon nanoparticle anode exhibits an initial radius of B (we only sketch the cross-section). A representative material element at a radius of R is labeled by the red dot; (b) once lithiated, at time t, the element is deformed and pushed out to a new position of radius r(t). The interface and the particle outer surface are identified by radii A(t) and b(t), respectively; (c) the interface (dark blue) exhibits a velocity |A˙(t)| and a thickness of w (~1 nm). Lithiation reaction Li++e+1xSi=1xLixSi takes place at the interface, causing the migration of the interface toward the particle center.

  • Figure 2

    (Color online) ΔGmech, the contribution of mechanical stresses to the driving force of the interfacial lithiation reaction (Li++e_+1xSi=1xLixSi), is sketched as a function of time. ΔGmech acts as the resistance to the reaction and asymptotically approaches the critical value eΦ–ΔGmech which stalls the lithiation at the interface as well as the interface migration.

  • Figure 3

    (Color online) The interface velocity |A˙| is plotted as a function of time. (a) For particle radius B=45 nm, |A˙| shows an initial velocity about 2.4 nm/s and a precipitous decrease due to the coupled viscoplasticity and interface migration. The drop of velocity in the first 40 s of lithiation is shown in the figure inset. Interface velocity at t=5 and 40 s are highlighted by green and red dashed lines to quantitatively demonstrate the rapid velocity drop; (b) effect of particle radius on the interface velocity.

  • Figure 4

    (Color online) The interface diameter of 2A(t) is sketched over time. The curve shows an initial rapid decrease in the silicon core diameter, followed by a slowing of the reaction interface. The prediction agrees well with experimentally measured data reported in ref. [12].

  • Figure 5

    (Color online) Lithiation-induced stress field is plotted in the reference state. At time t=10 s, the predicted radial stress σr and the hoop stress σθ are shown as the blue lines in (a) and (b), respectively. Results of two control studies are also included. Case No.1 (red line): when the lithiation reaction is assumed to be stress-insensitive, the interface velocity remains to be a constant, the resulting stresses are of larger amplitude. Case No.2 (black line): if the lithiated silicon is considered to be a rate-independent material, the stresses can be obtained by setting |A˙|=0 and they set the theoretical lower limit for the lithiation-induced stresses under viscoplastic deformation. Stresses at time t=300 s are sketched in (c) and (d). Interface position is highlighted by the purple dashed lines.

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