Self-Limiting Lithiation and Viscoplasticity of Electrode Nanoparticles in Li-Ion Batteries

A model is derived for the viscoplastic behavior of a host medium driven by stress-induced diffusion of guest atoms. The constitutive equations are applied to study development of stresses in a spherical electrode particle subjected to insertion of lithium. Numerical simulation demonstrates ability of the model to capture basic phenomena observed in anode nanoparticles under lithiation: formation of a sharp interphase between a Li-poor core and a Li-rich shell, slowing down of the interphase motion revealed as self-limiting lithiation, and growth of tensile hoop stresses at the outer surface of a particle leading to its fracture. Good agreement is demonstrated between observations on interphase propagation in silicon nanoparticles and predictions of the model.

Our approach is grounded on the following assumptions:

Electrochemical alloying of guest atoms with a host medium is treated as their (temporary or permanent) immobilization in an electrode particle.

Two types of guest atoms are distinguished: mobile and immobilized (trapped). Transport of mobile atoms is described by the diffusion equation with a reaction term (that accounts for their binding with host atoms) and diffusivity affected by concentration of immobilized atoms. The rate of immobilization is proportional to concentrations of mobile atoms and available traps.

A sharp boundary (interphase) between the domains rich and poor in guest atoms is formed when the rate of trapping exceeds the rate of diffusion.

To characterize development of stresses in a host medium, plastic flow is associated with evolution of its structure  (each elementary act of plastic deformation reflects rearrangement of the host matrix induced by alloying with a guest atom).

Within the regular solution model, free energy of a mobile atom is treated as the sum of two (entropic and enthalpic) components. Self-limiting lithiation of electrode particles is described by presuming the Flory-Huggins  parameter  to be affected by pressure.

To reduce the number of adjustable parameters in the governing equations, simplifying assumption are introduced: (i) changes in elastic moduli with concentration of guest atoms are disregarded, (ii) transport of guest atoms through a host medium is considered within the concept of small strains, (iii) anisotropic volume expansion of electrode particles is not taken into account.

Ability of the model to describe self-limiting lithiation of silicon nanoparticles is illustrated in Figure 1 where dimensionless thickness of a Li-rich outer shell h is plotted versus dimensionless time t(symbols:  experimental data (McDowell et al., 2012), filled circles: results of numerical simulation).

Acknowledgement: Financial support by the EU Commission through FP-7 Project Evolution-314744 is gratefully acknowledged.

References:

1. A.D. Drozdov, Int. J. Solids Struct. 2014 (in press).

2. A.D. Drozdov, P. Sommer-Larsen, J.deC. Christiansen, J. Appl. Phys. 2014 (in press).