Molecular Dynamics Studies of Diffusion Dynamics during Lithiation of Si Electrode: Increasing Si Vacancies Can Improve the Lithiation Rate
Authors: Kim Kwang Jin , Qi Yue 
Published: February 2020

Introduction

Silicon, which exhibits the highest specific capacity upon alloying with lithium, is considered one of the most promising anode materials for next-generation lithium-ion batteries [1]. However, its application is limited due to 300% volume expansion and structural changes occurring during lithiation which results in mechanical fracture, capacity loss, and limited cycle life [2]. Since the stress generation and rate performance are significantly affected by the diffusion of active materials, it is necessary to study diffusion kinetics of both silicon and lithium during lithiation.

Theoretical approaches, including Density Functional Theory (DFT), have been applied to investigate diffusion dynamics during lithiation of silicon [3]. However, these studies provided limited understanding due to small system size and short simulation time. Recently, reactive force field (ReaxFF) has been developed for Li-Si system, enabling longer dynamics calculation for larger system size. Therefore, we present a molecular dynamics using ReaxFF to study diffusion kinetics of both lithium and silicon. Specifically, the role of silicon vacancies on lithiation kinetics was investigated.

Methods

Simulation cells with the same number of silicon and lithium atoms and a density identical to that of a-LiSi (1.91 g/cm3) were prepared. A silicon slab,  which was either a crystalline Si (c-Si) with surface orientation of (100), (110), and (111) or an amorphous Si (a-Si), was sandwiched by amorphous Li. NVT molecular dynamics  were performed at temperatures ranging from 900K~1500K to reduce the simulation time by accelerating the mixing process. Due to the periodic boundary condition in all three directions, two interfaces were included in each simulation cell and the lithiation direction is perpendicular to the silicon surface.  Fig 1. clearly shows that  lithium and silicon atoms were separated initially and the lithium diffused into the silicon during the MD simulations.

In order to investigate the characteristic diffusion pattern among different silicon surface orientations, the simulation cell length corresponding to lithiation direction was divided into bins with equal distance and the concentration at each bin was compared. Lithiation rate was analyzed by correlating the local mean-square-displacement (MSD) of lithium and silicon with the local concentration. Finally, to determine the rate-limiting factor or lithiation of silicon, 10% random vacancy in silicon and lithium was created separately and the movement of the reaction front and required time to fully mixed LiSi structure were studied.

Results

Correlation of local MSD with corresponding local concentration suggested that diffusion of lithium and silicon should be separated into two distinct stages; one before the system is fully mixed, the other after the system is fully mixed. Upon lithiation, diffusion of lithium and silicon are concentration dependent, which is followed by self-diffusion after the system is fully mixed. The time to reach a fully mixed amorphous LiSi is much faster in a-Si slab. Diffusion patterns among c-Si strongly depend on the location of the (111) planes since the dissociation of c-Si is caused by bond breakage between (111) planes, as  Li hops through the tetrahedral sites in c-Si. As a result, Li diffuses into c-Si with (100) and (110) surface orientation via a continuous fashion whereas a layer-by-layer cleavage represents the diffusion pattern along (111) surface orientation. The required time to reach uniform concentration indicated that lithium diffuses faster along <110> direction comparing the three crystal orientations.  For self-diffusion, the diffusion coefficient at room temperature for lithium and silicon is 1.97*10-9 cm2/s and 1.28*10-11 cm2/s, which indicated that lithium moves 100 times faster than silicon. Also, both lithium and silicon diffuses faster in a-Si than in c-Si. Determination of the control factor of the diffusion was performed by comparing the concentration profile of structures with 10% random lithium and silicon vacancies at 10ps. It was observed that silicon vacancy accelerated the movement of the reaction front and shortened the overall lithiation time (Fig. 1d), while lithium vacacny has negligible impact on lithiation time. This clearly demonstrated that the movement of the silicon plays the dominating role in the lithiation rate, or the time to be fully mixed. 

Conclusion

In conclusion, lithium diffusion patterns in silicon are affected by the location of (111) planes of c-Si. Diffusion is concentration dependent during mixing and becomes random after the system is fully mixed. Finally, the movement of the silicon plays a dominating role in Li-Si system. These findings provide great insight into understanding lithiation process and increasing the lithiation rate in silicon, which contribute to enhance the rate performance of lithium-silicon. 

References

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2. L.Y. Beaulieu, K.W. Eberman, R.L. Turner, L.J. Krause, and J.R. Dahn, Electrochem. Solid-State Lett., 4, A137-A140 (2001)

3. P. Johari, Y. Qi, and V.B. Shenoy, Nano Lett., 
131, 9239-9249 (2009)

Figure 1