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Abstract
Mechanical stresses which develops during lithiation of crystalline silicon particles in lithium silicon battery causes fracture and limits the life of silicon based lithium batteries. We formulated an elasto-plastic stress formulation for a two-phase silicon model and investigated the influence of different mechanical properties of lithiated silicon on the fracture of nanoparticles during first cycle charging. A chemo-mechanical model was developed to determine lithium distribution and associated stress states during first cycle lithiation. The concentration gradient of lithium and an elastic perfectly plastic material behavior for silicon were considered to evaluate stress distribution formulation and determine stress field in the particle. The stress profile was used to perform a crack growth analysis. The stress distribution formulation was validated by evaluating stress field for different elastic modulus value for lithiated silicon and comparing our inference against observations from prior experiments. The results showed lower modulus of lithiated silicon yielded results like experimental observations for nanoparticles. The size dependent fracture behavior was also observed in lower elastic modulus of lithiated silicon. We conclude that accurate mechanical characterization of lithiated silicon nanoparticle is necessary to model the failure of silicon particle and improving the mechanical properties may suppress crack growth in silicon nanoparticles during charging.
Highlights
Lithium ion Batteries (LIBs) are the leading source of energy storage in the electronic devices and electrical vehicles.[1]
Lithiation process causes the crystalline silicon nanoparticle to convert into amorphous lithiated silicon (Li15Si4)
Lithiation initiates with the formation of lithiated silicon amorphous shell on the crystalline silicon nanoparticle
Summary
Lithium transport in the silicon nanoparticle was modeled based on the following assumptions: 1) Steady state diffusion in amorphous shell, 2) Negligible diffusion in the crystalline core, 3) Sharp concentration change at the reaction front thickness, 4) Linear decay of surface lithium concentration as the reaction front penetrates the particle,14 5) Traction free particle expansion on the surface. To solve for steady state, the surface of silicon was initially considered to be at maximum concentration followed by a linear decay of the surface concentration as the lithium reaction front penetrated the crystalline silicon particle. Jb is the surface flux of lithium ion, y is the relative location of the reaction front with respect to the particle surface which changes from 0 to 1, R is the particle radius, r0 is the crystalline silicon radius and cmax is the maximum lithium concentration possible during lithiation of a silicon particle. We formulated a piecewise function for the concentration that was dependent on the location of the reaction front
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