Modeling large patterned deflection during lithiation of micro-structured silicon

Abstract

The application of silicon (Si) as potential anode material in Li-ion batteries provides a more than nine-fold increase in gravimetric storage capacity compared to conventional graphite anodes. However, full lithiation of Si induces the volume to increase by approximately 300%. Such enormous volume expansion causes large mechanical stress, resulting in non-elastic deformation and crack formation. This ultimately leads to anode failure and strong decrease in cycle life. This problem can be resolved by making use of structured anodes with small dimensions. Particularly honeycomb-shaped microstructures turned out to be beneficial in this respect. In the present paper, finite element modeling was applied to describe the experimentally observed mechanical deformation of honeycomb-structured Si anodes upon lithiation. A close agreement between simulated and experimentally observed shape changes is observed in all cases. The predictive ability of the model was further exploited by investigating alternative geometries, such as square-based microstructure. Strikingly, dimension and pattern optimization shows that the stress levels can be reduced even below the yield strength, while maintaining the footprint-area-specific storage capacity of the microstructures. The pure elastic deformation is highly beneficial for the fatigue resistance of optimized silicon structures. The obtained results are directly applicable for other (de)lithiating materials, such as mixed ionic-electronic conductors (MIEC) widely applied in Li-ion and future Na-ion batteries.

Topological optimization of patterned silicon anode by finite element analysis

“…However, the dependence of mechanical properties on lithium concentration was not considered in this work. Laptev et al included this dependence during FEM modeling by ANSYS [18]. The appearance of plastic deformation during lithiation and bending of self-constrained honeycomb walls was predicted.…”

“…1b). Further optimization of honeycomb geometry has shown that the plastic deformation can be decreased or even eliminated, but only at the expense of a drastic reduction in footprint-area-specific storage capacity [18]. Subsequent analysis of the square-patterned microstructure storing the same energy per unit footprint-area has shown a lower -but still high -bending stress.…”

“…Upon further analysis and discussion of this structure, Baggetto's basic honeycomb structure was taken as a reference [15]. In particular, a maximal lithiation of 80 % theoretical value was assumed, in accordance with the highest level achieved in experiments [15,18]. An initial wall thickness of t0 = 0.25 µm and an initial wall height of h0 = 1.1 µm were taken as in the basic honeycomb structure.…”

“…The fillet radius between the walls was taken as r0 = 0.1 µm. The footprint-area-specific storage capacity Sfa was normalized by a value of Sfabh = 88.65 µAh•cm -2 , which is the capacity of Baggetto's honeycomb [18]. The aim of our study was to develop an approach for finding out a combination of R0 and L0 resulting in pure elastic deformation after lithiation and providing a footprint-area-specific storage capacity no less than that of the basic honeycomb structure.…”

“…The chemical expansion coefficient was taken as β = 0.445 from our previous work [18]. Since our goal was to avoid plastic deformation, the perfectly elastic behavior of lithiated silicon was considered.…”