context: To investigate the electrochemical Na ion storage mechanism to predict the theoretical properties of Nax[Ni0.5Mn0.5]O2, we performed first-principles calculations based on the structural information verified through the Rietveld refinement analysis. At this stage, even though 0.01 mol of Ca2+ ions was incorporated into the bulk Na sites, Na0.98Ca0.01[Ni0.5Mn0.5]O2 showed a nearly identical crystal structure with Na[Ni0.5Mn0.5]O2; hence, we assumed that Na0.98Ca0.01[Ni0.5Mn0.5]O2 experienced the same O3–P3 phase transformation during the Na+ extraction/insertion process. Various Na/vacancy configurations on O3-Nax[Ni0.5Mn0.5]O2 compositions (0 ≤ x ≤ 1) were generated through the cluster assisted statistical mechanics (CASM) code and then, we predicted the theoretical formation energies of the O3-Nax[Ni0.5Mn0.5]O2 composition. Based on information of the formation energies, we calculated the redox potentials of O3-Nax[Ni0.5Mn0.5]O2 during Na+ extraction/insertion using the following equation where E(x) indicates the formation energy on the most stable Na/vacancy configuration of x species. By considering the typical O3–P3 phase transition in the O3-type layered oxide cathode in SIBs, we calculated the formation energies of P3-Nax[Ni0.5Mn0.5]O2 and then applied this information to compare the thermodynamic stability between O3- and P3-phases. As presented in Fig. 4a, we predicted that the O3–P3 phase transition occurred after extraction of 0.25 mol of Na ions from O3-Na1[Ni0.5Mn0.5]O2, and then, when the Na content in P3-Nax[Ni0.5Mn0.5]O2 was reduced to less than 0.25 mol, the O3–P3 phase transition re-occurred. Moreover, we verified that in the case of O3-/P3-Nax[Ni0.5Mn0.5]O2, the redox potentials required for Na+ extraction/insertion were less than ∼4.11 V (vs. Na+/Na) and more than ∼2.48 V, which indicates that 1 mol of Na ions can be reversibly extracted/inserted from/into the O3-Na1[Ni0.5Mn0.5]O2 structure despite the O3–P3 phase transition. Fig. 4b illustrates the predicted redox potential range of the O3/P3-Nax[Ni0.5Mn0.5]O2 cathode as a function of the Na content (0 ≤ x ≤ 1) with experimentally measured galvanostatic intermittent titration technique (GITT) profiles in the voltage range of 2.0–4.3 V. To confirm our hypothesis that the Ca-substituted cathode would undergo a similar O3–P3 phase transformation during the sodiation/de-sodiation process, we checked the GITT profiles of the Na0.98Ca0.01[Ni0.5Mn0.5]O2 cathode and overlaid the results with the predicted theoretical redox potential of the Nax[Ni0.5Mn0.5]O2 cathode. Interestingly, we confirmed that the slope of the charge/discharge curve of O3-Na0.98Ca0.01[Ni0.5Mn0.5]O2 matched the predicted redox potential of the Nax[Ni0.5Mn0.5]O2 cathode well within the wide voltage window of 2.0–4.3 V; this clearly verified our hypothesis and confirmed that ∼1.0 mol of Na+ ions could be extracted/inserted from/into Na0.98Ca0.01[Ni0.5Mn0.5]O2.
answer: O3/P3-Nax[Ni0.5Mn0.5]O2