Quantification of Rotational and Magnetic Disorder in Aprotic Sodium-Oxygen Batteries
Authors: Sapunkov Oleg B. , Viswanathan Venkatasubramanian 
Published: February 2020

Recent research in electrification of transportation, particularly road and air transportation, has led to increased interest in high-energy-density rechargeable batteries. In particular, the metal-air battery group is attractive, thanks to high theoretical energy density, both gravimetric and volumetric. At present, the Li-O2 battery, one of the most promising members of the class, exhibiting the highest energy density of any known battery chemistry, suffers from electrolyte and electrode instability, as well as limited rechargeability and discharge capacity.
Hartmann et al. have demonstrated a rechargeable Na-O2 battery, with the primary observed discharge product reported to be sodium superoxide (NaO2).[1] Their battery shows superior cycle life and Coulombic efficiency to state-of-the-art Li-O2 batteries. Rigorous description of the Na-O2 battery reaction mechanism requires detailed understanding of the electronic structure throughout the phase space of sodium oxides. The roles of nucleation, nanoscale stabilization, and surface energetics of various sodium-oxygen compounds have been examined through a combination of Density Functional Theory (DFT) calculations and electrochemical measurements.[2] This research has led to improved understanding of Na-O2 battery reactions, which, as proposed, constitute a combination of surface and solution mechanisms involving the NaO2 discharge product. As a group, alkali superoxides are known to be highly disordered materials, both in internal geometry and magnetic ordering.[3] Presently, there is limited understanding of geometric and magnetic disorder in bulk NaO2. It is crucial to map out disorder in room-temperature NaO2, considering its importance in determining electronic structure, surface energetics, and growth properties relevant to Na-O2 battery cycling.
In this work, we aim to fill gaps in the current understanding of the electronic structure of bulk NaO2. We perform a series of DFT calculations, incorporating the Hubbard U correction applied to oxygen, to describe geometric and magnetic disorder in bulk NaO2. DFT-calculated energies are used to construct an Ising Model of interactions between oxygen dimer units within the bulk NaO2. We find that both 2-body and 3-body nearest-neighbor interactions, which take into account both the geometric and magnetic disorder of the structure, are critical to accurately describe bulk NaO2. Further, we extend the study to examine the role of next-nearest-neighbor interactions within the bulk; although these interactions are lower in energy, they influence long-range ordering within the bulk material. The constructed Ising Model is used within the framework of a Metropolis Monte Carlo simulation to calculate bulk properties for supercells of increased dimension; these simulations demonstrate phase transitions within the bulk material, which are most clearly seen within the largest simulated supercells, as is demonstrated in the accompanying figure.[5] Further, we observe that the calculated bandgap of bulk NaO2 is strongly affected by the degree of internal disorder of the material.
References:
[1] Hartmann, Pascal, et al. "A comprehensive study on the cell chemistry of the sodium superoxide (NaO 2) battery." Physical Chemistry Chemical Physics 15.28 (2013): 11661-11672.
[2] Yang, Sheng, and Donald J. Siegel. "Intrinsic Conductivity in Sodium–Air Battery Discharge Phases: Sodium Superoxide vs Sodium Peroxide." Chemistry of Materials 27.11 (2015): 3852-3860.
[3] Ren, Xiaodi, and Yiying Wu. "A low-overpotential potassium–oxygen battery based on potassium superoxide." Journal of the American Chemical Society 135.8 (2013): 2923-2926.
[4] Kang, ShinYoung, et al. "Nanoscale stabilization of sodium oxides: implications for Na–O2 batteries." Nano letters 14.2 (2014): 1016-1020.
[5] Sapunkov, Oleg, et al. "The role of disorder in NaO2 and its implications for Na-O2 batteries." arXiv preprint arXiv:1702.05520 (2017).

Figure 1