Our goal for this research is trying to model the voltage dip in the two phase reaction of lithium insertion to anode. This voltage dip occurs in the reconstitution phase, which two phases of the anode material exist, while one phase is turning to the other phase. For example, if we are doing lithium insertion on Aluminum. For example, as we are passing a constant current to insert lithium into aluminum, there would be a voltage dip in the beginning of the two phase reaction (marked with the purple arrow in the picture). In this two phase reaction, the alpha phase Aluminum(Al) is turning into beta phase Aluminum(AlLi). Since this process of turning one phase of the anode material to another phase of the anode material thus making the other phase of the anode material to be bigger is similar to the process of plating more lithium onto the preexisting nuclei and making the nuclei bigger, and the second I just described has the similar voltage dip as we observed in the two phase reaction, we decide to apply the pre-existing model, Barton-Bockris Model, which is used to model the overpotential during the plating process, to model the overpotential during the two phase reaction, the reconstitution process in lithium insertion. With this modeling, we are able to extract key parameters such as exchange current density, diffusivity, and interfacial energy, which are some constants that are hard to obtain in  classical lab result. Furthermore, with this modeling, we can have a better understanding of which parameters have really caused the overpotential, so that we can make some modification later on to increase the energy density of the battery.

2 Phase Reaction Modeling:

Future Step: I would like to continue to better the equation that model the overpotential during the plating process as well as for the two-phase reaction. As you can tell from both sodium plating modeling and Al-Li system modeling, even though the fit looks good on the graph, the parameters we extracted are pretty off from the accepted values from other literatures: the diffusivity and interfacial are too large to be accepted. There could be two explanations for this deviation, the first explanation would be that the two growth models on nuclei size are not ideal and the second explanation would be that the Barton-Bockris model has neglected something term critical. I could improve on the growth models by digging deeper into the specific time point throughout the nucleation and growth while reading more literature about it. I already have some considerations on how to improve the Barton-Bockris model. For example, it has neglected the ohmic resistance polarization. Further, for the interfacial overpotential term, I am still not convinced by the radius they used in the derivation, which they assume to vary from the beginning to the end, but based on the actual derivation it should just be the critical nuclei size and remains to be a constant. After I have improved on both of these models, I will try to fit them again and see whether we will obtain some reasonable values for diffusivity and interfacial energy .