Volume Expansion and Phase Transformation in Single Lithium Insertion Silicon Electrode Particle

Introduction:

            Silicon is being considered for negative electrodes in lithium ion batteries because of their high specific energy, 4200 mAh/g[i]. Recent literatures[ii]^,[iii] suggest that alloying of lithium in silicon proceeds through an amorphous phase transition. Isotropic volume expansion is suggested to be associated with this amorphous phase transition[iv] . It should be noted that, however, even at room temperature, towards the end of lithiation, a-Li_xSi suddenly crystallizes to Li₁₅Si₄[ii]. Few literatures have suggested that amorphous silicon phase is only a metastable phase and arises due to selective equilibrium at room temperature[v] and that the order-disorder transition is reversible[vi].Moreover at high temperatures[vii], the lithiation proceeds through distinct crystalline phases. So, overall, it will be worthwhile to pursue a unique modeling approach for silicon electrodes among lithium insertion electrodes since both phase transformation[i] and associated huge volume expansion[iii] occur in silicon electrodes. If one wants to consider lithiation through distinct crystalline phases, the interface between the inner phase and the outer phase moves towards the center of the particle as lithiation occurs and simultaneously the overall radius of the particle increases. Thus we have two moving boundaries. Literature[viii] suggests that a shrinking core model to capture the interface motion is applicable only when there is a three-dimensional growth mechanism which need not be the case always. Moreover, it is also suggested[ix] that one needs to consider phase transformation kinetics along with solid state diffusion to study phase transformation electrodes.

            Current work will help in a better understanding of the solid phase transport for the case of increasing particle size in silicon electrodes during lithiation, which could then be used in cell sandwich model. Thus, this work attempts to develop a particle model to capture the growing particle size considering amorphous lithiation and associated solid state transport processes in silicon electrodes. In future, to model both volume expansion and phase transformation, one could adopt the framework provided by Harrison et al[x]  to model phase change in lithium ion batteries for an arbitrary number of phases using diffuse interface method considering phase transformation kinetics as done by Kasavajjula[ix], while considering growing particle size as suggested in this work for silicon electrodes. While doing so, it should be noted that diffusion co-efficient of silicon-lithium alloy is at least two orders of magnitude more than that of the silicon[xi]. Current work considers a particle size such that fracture does not occur[xii]. But for a complete picture, stress generation and fracture as done by Christensen and Newman can also be incorporated in future.

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