Studies of Anomalous Diffusion in Composite Silicon Anodes

1.            Introduction

The diffusion coefficient is an important parameter of active materials for lithium ion batteries, particularly in higher rate applications like electric vehicles. It is useful to know the diffusion coefficient as a function of state of charge, and other parameters like temperature. Silicon has a very high lithiation capacity (3579 mA hr g^-1), but a correspondingly large expansion when fully lithiated (> 270 %). On the first charge, crystalline silicon is converted to amorphous Li_xSi, and then to crystalline Li₁₅Si₄ at full lithiation. The diffusion coefficient in a-Li_xSi will have an important influence on the movement of these two phase boundaries, which in turn will impact upon the performance and operating life of the electrode. The two main techniques used to measure diffusion coefficients are a. c. impedance, via the Warburg coefficient, and galvanostatic intermittent titration technique (GITT). This report describes the use of both of these methods on composite silicon anodes.

 2.            Results

Electrodes were prepared using 3 µm silicon powder, with partially neutralised poly acrylic acid as binder and conductive carbon. Following a slow formation cycle (C/20), impedance spectra were recorded in two electrode half cells, at different states of charge. Figure 1 shows typical results at lithiation capacities of 300, 600, 900 and 1200 mA hr g^-1. The data was fitted to equivalent circuits, with a series resistance, two resistor // CPE parallel combinations, and a low frequency constant phase element (CPE) tail. Apart from the fully delithiated anode, the tail was always at a much steeper angle than the standard Warburg value of 45^o (power term = 0.5). Figure 2 shows plots of the fitted power term {n in Z = (iw)^-n C^-1}, at three different states of charge, during cycling.

 3.            Discussion

One explanation for the steeper gradient is that the diffusion is anomalous or non-Fickian ^[1]. This can occur for charge carrier movement in amorphous solids, like Li_xSi. After each hop, the charge carrier can wait “for a period drawn from a broad power law distribution” ^[1], reducing the overall rate of diffusion. Interestingly, a recent theoretical study has calculated a wide range of activation energies for lithium hopping in amorphous silicon (0.1 to 2.4 eV ^[2]). The difference in the power term at 600 mA hr g^-1 during lithiation and delithiation implies a structural hysteresis, which may match the voltage hysteresis observed with silicon anodes.

 Further results, including GITT experimental data and analysis, will be presented at the conference.

 References

[1]          J. Electroanal. Chem. 499 (2001) p. 112          J. Bisquert & A. Compte

[2]          J. Phys. Chem. C 116 (2012) p. 22212              G. A. Tritsaris, K. Zhao, O. U. Okeke & E. Kaxiras