Silicon Anodes in Lithium-ion Batteries
By Ian Roper
Lithium-ion batteries (LIBs) are used in mobile phones, laptops and electronic vehicles and thus make up a large proportion of the energy storage industry. The performance of an LIB depends heavily on the materials used for the anode and the cathode. Graphite has been the industry’s most common anode material for a long time but the maximum theoretical capacity for LIBs with graphite anodes is believed to have been reached. Therefore, to produce LIBs with higher capacity, new anode materials are being investigated.
A very promising new anode material is silicon as it has the highest theoretical capacity – how much charge can be stored – of any material currently being developed. However, when a silicon anode is charged and lithium ions move into it, it expands to around three times its original size in order to accommodate the lithium. This can cause high stresses in the anode since non-uniform amounts of lithium within the anode cause different parts to expand by different amounts. Further, if the silicon is used with other materials, the interface between them can be under a lot of stress. These stresses can cause cracks within the anode, which in turn cause loss of connectivity, damaging the battery and worsening the performance. Our aim is to understand how the lithium causes the observed expansion and stresses, and how to mitigate them without sacrificing the high capacity that the silicon provides.
We focus on a design of anode in which microparticles consisting of a silicon core surrounded by a shell material (for example graphite) are agglomerated to form the whole anode, as in the image. We consider a single spherical microparticle and model the stresses and displacements upon charging using a model analogous to a thermal stress model. We use a quasi-static model for the distribution of lithium in the anode (assuming that diffusion is instant through the anode) and calculate the concentrations in each material assuming an equal chemical potential between them. Given a total amount of lithium ions, we calculate the concentration in the silicon, the concentration in the shell material, the displacements from the fully discharged state and the stresses. We then aim to use these results to find an optimal design of a core-shell microparticle in order to maintain high capacity while having low expansion and stresses.
One key feature of this model is stress-assisted diffusion. Compressive stresses on the materials increase the total potential of the silicon, allowing fewer lithium ions to be absorbed. Likewise, tensile stresses have the opposite effect. This causes a two-way coupling between the electrochemical model and the mechanical model, on which the results are highly sensitive.
So what are the findings? Unfortunately, when using graphite as the shell material, we find that the design that maximises the capacity per expanded volume is a solely silicon microparticle with no shell. This is likely due to the shell material being too weak to constrain the silicon expansion. The next steps are to expand the scope of the designs, using void spaces and different materials in the anode design. Eventually, we wish to utilise homogenisation techniques to calculate macroscale changes of the anode caused by changes to the microparticle.
Ian Roper is a DPhil student in Cohort two of the EPSRC InFoMM CDT at the Mathematical Institute, Oxford.
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