First-Principles Study of the Thermodynamic Stability of Sodium Oxides As a Function of Temperature, Pressure and Particle Size; And Its Implications for Na−O₂ <sub/> Batteries

Recently, Na−O 2 batteries have shown their potential as a high energy density electrical storage. Unlike Li−O 2 batteries that have only one discharge product, Li 2 O 2 , the Na−O 2 battery system has three potential discharge products: Na 2 O, Na 2 O 2 and NaO 2 . Recent experiments observed either Na 2 O 2 or NaO 2 as a discharge product, and the performance of Na−O 2 batteries is undoubtedly influenced by which particular discharge product is formed.[1-4] We investigated the thermodynamic stability of each phase as a function of temperature, O 2 partial pressure, and particle size using first-principles calculations. Our results reveal that in bulk Na 2 O 2 is the stable phase at the standard state (300 K, 1 atm) in agreement with experiments. Bulk NaO 2 can only be formed at P O2 &gt; 8.5 atm and/or T &lt; 230 K (FIG. 1), both of which are unlikely to be accessed during the operation of typical Na−O 2 batteries. To understand the relative stability of these two competing compounds at the nanoscale, we calculated their surface energies and found that the lowest surface energies of Na 2 O 2 are in the range of 30−45 meV/Å 2 , while that of NaO 2 is only 12 meV/Å 2 , rendering the possibility of stabilization of NaO 2 over Na 2 O 2 at the nanoscale. To confirm this idea, we constructed the phase diagram of Na 2 O 2 and NaO 2 as a function of particle size in FIG. 2. Indeed, the low surface energies of NaO 2 stabilizes NaO 2 nanoparticles, for example, up to 3 nm at P O2 = 0.1 atm. Moreover, we found that the nucleation energy barrier for NaO 2 nanoparticles is much smaller than that of Na 2 O 2 , particularly when there is a small discharge overpotential and/or enough O 2 supply. We expect our findings to direct efforts towards understanding and controlling the formation of desired Na−O compounds in battery operation, and furthermore invigorate interest on the potential of Na−O 2 batteries.[5] References [1] P. Hartmann, C. L. Bender, M. Vracar, A. K. Durr, A. Garsuch, J. Janek, and P. Adelhelm, Nat Mater 12 , 228 (2013). [2] Q. Sun, Y. Yang, and Z.-W. Fu, Electrochemistry Communications 16 , 22 (2012). [3] S. K. Das, S. Xu, and L. A. Archer, Electrochemistry Communications 27 , 59 (2013). [4] J. Kim, H.-D. Lim, H. Gwon, and K. Kang, Physical Chemistry Chemical Physics 15 , 3623 (2013). [5] S. Kang, Y. Mo, S. P. Ong, and G. Ceder, Nano Letters 14 , 1016 (2014).