With the increasing depletion of fossil energy and the environmental problems caused by the burning of fossil energy, it is urgent to develop new clean energy sources for the next generation. Although solar and wind energy are sought after due to their environmental friendliness, their intermittent nature also limits their application. On the other hand, rechargeable batteries or supercapacitors, due to their high energy density, portability, and relative safety, have gradually developed into the leading new energy source of the next generation. As a type of rechargeable battery, lithium-ion batteries have developed rapidly in recent decades and have been widely used in automobiles, cell phones, electronics, industry, and so on. In recent years, the main research direction of lithium-ion batteries is to develop high energy density, high voltage cathode materials, and lithium-sulfur (Li-S) or lithium-air (Li-O2) batteries with lithium metal cathodes [1].
The First-Principle method (FPM) is widely used as an ab initio algorithm for materials design, materials prediction, and interpretation of experiments. Starting from Schrödinger's equation, it has been developed by John Pope, Walter Kohn and others to DFT (Density Functional Theory), which can be programmed by computer. With only a few classical parameters, DFT can calculate most of the properties of a material. Further combined with the Born-Oppenheimer hypothesis, DFT can also be used to simulate molecular dynamics, i.e. Ab initio molecular dynamics (AIMD). DFT is widely used in lithium and other related fields. Due to its accuracy, it can effectively guide experiments and thus save costs.
In this paper, we discuss the application of DFT calculations in lithium-related fields, sort out a few common calculation methods for readers, and mention some calculation techniques. Since the author often uses VASP (Vienna Ab initio Simulation Package) for material-related calculations, the following discussion is based on this software, which can of course be extended to other commercial software or open source code.
Charge and discharge platform for material calculations
Lithium-ion batteries are also known as "rocking chair". This is because in a lithium-ion battery, lithium ions travel between the positive and negative electrodes through the electrolyte. When charging, lithium ions are removed from the cathode material (such as LiCoO2) lattice and embedded in the negative material (such as graphite), making the negative electrode rich in lithium and the positive electrode poor in lithium; when discharging, due to the higher chemical potential of lithium on the negative side, lithium ions are removed from the negative electrode and inserted into the cathode material lattice, thus completing a cycle. Where the electrolyte only acts as a conductor of lithium ions. A good electrolyte needs to have a high lithium ion conductivity, a low electron conductivity, and a wide electrochemical window to prevent redox reactions.
At equilibrium, the embedding voltage of a Li-ion battery is defined as the difference between the Li chemical potential at the positive and negative terminals, i.e.
where z is the transfer charge and F is the Faraday constant. Integrating the above equation gives
where is the total Gibbs free energy change of the embedded reaction process system. Without considering the temperature and volume change, it can be approximated as. The equilibrium voltage with lithium metal as the negative electrode and the cathode material as the transition metal oxide LiMO2 can then be calculated as
The chemical reaction formula during charging is
where χ1 > χ2 and relative to the cubic phase lithium metal.
Therefore, the charging working platform can be calculated by simply calculating the energy of the system before and after shedding the lithium ion. Of course, the above equation can also be used to calculate the voltage plateau of sodium ion batteries. For example, Ceder's group [2] has done calculations for NaxMnO2 and compared it with experimental data. It can be seen that the calculated results match well with the experimental discharge platform.
