Monte-Carlo Simulation Combined with Density Functional Theory to Investigate the Equilibrium Thermodynamics of Electrode Materials: Lithium Titanate As Model Compounds
Authors: Kiyobayashi Tetsu , Tada Kohei , Ozaki Hiroyuki 
Published: December 2020

Thermodynamics of the electrode materials is of interest in understanding their mechanism of electrochemical reactions, which should in turn contribute to designing and developing a new material for rechargeable batteries. While the recent development in the computational power has remarkably advanced the highly accurate electronic structure simulations, such as density functional theory (DFT), it is not always straightforward to extract from those theoretical studies certain insights that are “understood” or “interpreted” in simple terms. One also occasionally comes across the situation where the thermodynamics at the finite temperature T > 0 is beyond the general DFT considerations. Monte-Carlo simulation, on the other hand, tries to describe the physical process at the finite temperature in a simple (or an abstract) manner of which the meaning is clear to understand, although one has to worry if the simple model represents the reality.
Dealing with lithium titanate (LiTi2O4 and Li4/3Ti5/3O4, LTO) as a model electrode material, we propose a method to describe its equilibrium thermodynamics based on the Monte-Carlo simulation (MC), for which the energetic parameters are determined by the density functional theory (DFT). The electrochemical potential profile is simulated by a simple topological model which consists only of three parameters representing the Li site energies; namely, the binding energy of the 8a site (ε8a), the difference in the site energy between the 8a and 16c sites (∆ε) and the repulsion between two Li atoms situated at the adjacent 8a and 16c sites (J).
Parameter physics by the MC revealed that the term ∆ε plays a decisive role, with a collateral effect from J, for characterizing the thermodynamics of the material whereas the term ε8a determines the electrochemical potential at which the reaction takes place. For instance, if ∆ exceeds the thermal energy at the temperature under consideration, i.e., if ∆ε > 3kT, the first order phase transition takes place during which two phases coexist, resulting in a plateau region in the potential profile. On the other hand, if ∆ε < 3kT, the lithiation of LTO is viewed as a phenomenon above the critical point, above which the material is in a homogeneous uniphasic state.
A multiple regression analysis of a set of the total energy of LiTi2O4 calculated by DFT allows us to determine these energetic terms. The MC simulation with the determined parameters well reproduces the shape and position of the experimental potential profile of LTO. Since the determined value, ∆ε/eV ~ 0.4, far exceeds the thermal energy at ambient temperature, the potential plateau of LTO is explained by the first-order phase transition as long as the equilibrium state is concerned. Unlike for LiTi2O4, we were unsuccessful in determining the parameters for Li4/3Ti5/3O4, for which the reason we will briefly address on site.
In the paper, the outline of the methodology will be presented, of which the details are available in our recent publication.[1]

Reference

[1] H. Ozaki, K. Tada and T. Kiyobayashi, Phys. Chem. Chem. Phys., 21, 15551 (2019).

Figure Caption

Potential profile of LTO. Exp: Li4/3Ti5/3O4 experimentally determined by the galvanostatic intermittent titration test (GITT) during the Li extraction process at T/K = 303. Sim: Result of the grand canonical Monte-Carlo simulation at T/K = 300, for which the energetic parameters were determined by the DFT calculations based on LiTi2O4. The error bar placed in the middle of the potential plateau for the simulated result indicates twice the standard deviation (±2σ) estimated from the multiple regression analysis of the DFT total energy data set. The abscissa is scaled so as to fit the experimental data.

Figure 1