Computational Studies on O2-P2 Phase-Transition Dynamics in Layered-Oxide Sodium-Ion Cathode Materials

TL;DR

This work develops a Coulomb-Buckingham potential fitted to extensive DFT data via a genetic algorithm to study O2-P2 phase transitions in NaxCoO2, enabling μs-scale molecular dynamics under laboratory conditions. The authors demonstrate that desodiation lowers transition barriers and that dynamic relaxation further reduces barriers, with phase transitions proceeding gradually through OPn intergrowths. They show that the potential reproduces static barrier trends from DFT and, under dynamic conditions, yields lower activation energies and observable layer gliding, along with diffusion coefficients in the P-phase that agree with experimental measurements for single crystals. The methodology provides atomistic insights into phase-transition mechanisms and Na diffusion in layered oxide cathodes, offering a framework to explore other compositions and stacking variants for improved SIB performance.

Abstract

Sodium-ion batteries have gained much interest over the past years and especially layered oxides are highly considered as cathodes for the next generation of batteries. However, there are still significant challenges to overcome in these materials for practical applications mainly related to capacity degradation and voltage fading. A key influence factor for these challenges are phase transitions that occur by gliding of layers during operation of these materials. Until now there is limited atomistic-level understanding on such transitions as simulations of these processes are computationally demanding. In this work, we trained a classical pairwise Coulomb-Buckingham potential versus extensive \textit{ab initio} data using a genetic algorithm to study O2-P2 phase transitions in Na\textsubscript{\textit{x}}CoO\textsubscript{2}. Our density functional theory~(DFT) and classical potential calculations show that phase transition barriers decrease upon desodiation and are further lowered if dynamic conditions are considered through molecular dynamics simulations. Our developed classical potential is able to capture phase transitions and its related increase in the Na-ion diffusivity under standard lab conditions at the $\upmu$s timescale of molecular dynamics simulation. Furthermore, it is found that the phase transition occurs gradually \textit{via} various OP\textit{n} phases.

Figures (7)

• Figure 1: Schematic procedure of database creation, potential fitting, and application in molecular dynamics (MD) for the NaxCoO2 cathode material performed in this work. First, more than 40000 structures with finite displacements of lattice parameters and ion positions (indicated by arrows in the figure) were evaluated by density function theory (DFT) calculations. Second, a Coulomb-Buckingham potential was fitted to energy differences and forces of the reference database leveraging a Genetic Algorithm (GA). Finally, the obtained potential was applied in large-scale classical MD simulations in the $\upmu$s regime to study phase transitions.
• Figure 2: Fitting plots of the process of obtaining the potential parameters. a) Convergence plots of Genetic Algorithm for fitting different potential models with decreasing numbers of parameters. b) Dependence of $\rho$ in interactions with Co on sodium concentration as obtained from the potential model with 43 parameters. Crosses indicate the parameter value of the best fit, circles the mean value of the first 1000 best optimized parameter sets and error bars their standard deviation. Fitted functions that were considered in further potential models are shown by dashed lines. c) Dependence of $\epsilon$ on sodium-concentration as obtained from the potential model with 43 parameters. Symbols, error bars and lines correspond to same quantities as in plot b).
• Figure 3: Visualization of a reaction pathway and computational convergence considerations. a) Reaction path of the O2-P2 phase transition as obtained from DFT calculations of the perfect images (no relaxation of lattice parameters) normalized to the energy of O2 at a sodium concentration of 0.67. The O2 to P2 ($\Delta E_{\text{O2} \to \text{P2}}$) as well as the P2 to O2 ($\Delta E_{\text{O2} \to \text{P2}}$) phase-transition barriers can be obtained from the reaction path and are indicated by blue and red lines, respectively. b) Convergence of the applied DFT settings with respect to energy cut-off and k-point sampling. Energy differences to the plot in a) are shown. c) Convergence with respect to supercell size in c-direction by treating more O-layers beyond the transitioning layer explicitly. The transitioning layer is highlighted by a red box in the shown structure models.
• Figure 4: O2-P2 phase-transition barriers in NaxCoO2 as function of sodium concentration x. Non-relaxed and relaxed cells were considered and all transition barriers were obtained by DFT, the fitted Coulomb-Buckingham potential, and by employing just a Buckingham potential for the Na-O interactions along with full electrostatics. a)-c) O2 to P2 barriers ($\Delta E_{\text{O2} \to \text{P2}}$) and d)-f) P2 to O2 barriers ($\Delta E_{\text{P2} \to \text{O2}}$) for a perfect cell (a) and d)), for a cell with lattice parameters relaxed by DFT for each image (b) and e)), and for cells with lattice parameters optimized with the Coulomb-Buckingham potential fitted in this work (c and f).
• Figure 5: Sodium and cobalt coordination during a npT molecular dynamics simulation at 600 K and 1 bar with fitted Coulomb-Buckingham potential for Na0.67CoO2. a) Sodium coordination-angles per sodium layer over a runtime of 30 ps. The structure models indicate the sodium layers the bars in the plot correspond to while the sodium coordination is given as the angle $\theta$. As also sketched in the Figure, $\theta$ describes the rotation angle between the upper three (light-red) and lower three (dark-red) oxygen ions that coordinate a sodium ion (yellow). Thus, an angle of 60° corresponds to an octahedral coordination (O2 phase) and an angle of 0° to a prismatic coordination (P2 phase). b) Number of oxygen ions in a coordination sphere of 3 Å around cobalt ions over run time with the actual data in black and the running average over 1 ps in red.