An Ab Initio Study of Li/Ni-doped NaxMeO2 Cathode Material for Na-Ion Batteries

The current state-of-the-art quantum mechanics methodologies were applied to derive information on the bulk and surface properties of the P2-type layered oxide Na0.85Li0.17Ni0.21Mn0.64O2 (NLNMO), a cathode material. The special quasi-random structure (SQS) approach was employed to identify the arrangement of Li, Ni, and Mn ions in a supercell containing 115 atoms. Both the cell parameters and atomic positions were determined from DFT-PBE+U calculations to highlight specific distortions induced by the dopants (Ni and Li). The analysis of atomic partial charges and atomic magnetic moments revealed that Li has a purely structural role, while Ni and Mn actively participate in both redox processes and electronic conduction. Using a new surface slab model, the interaction between the layered Na0.85Li0.17Ni0.21Mn0.64O2 (001) surface and the Na ions was examined to identify the most favorable adsorption sites and the possible paths for the migration of the Na ions on the electrode surface.

sodium layered oxides [15][16][17][18][19], whereas only P2-O2/O3-P3 phase transitions have been reported in the case of NLNMO kind of materials [20]. Despite these structural issues, the P2-types have shown greater power performance than the O3-type analogues because of the wide diffusion paths for Na ions [20]. Previous studies have shown that the P2 structure persists until x decreases to ∼1/3 (corresponding to a charge voltage of ∼4.2V). At this point, O2-type stacking defects begin to appear, leading to the coexistence of both P2 and O2 phases when Na content is significantly reduced (for x < 1/3). The P2→O2 phase transformation upon Na extraction has been widely observed as the primary cause for severe material degradation and huge capacity loss. Several studies have indicated the possibility of such structural evolution in terms of formation energies [21]. Few studies have reported that phase transitions could be established through the formation of ordered superstructures involving the Na + /vacancy ratio, which could lower the Na + diffusion coefficient resulting in sluggish Na transport and poor electrochemical efficiency. Also, Na + /vacancy disordering ensures fast Na + mobility in P2-type compounds [22]. Decomposition of the oxidizable electrolyte is another problem related to high working voltage conditions since it decreases the Coulombic efficiency (CE). Upon discharge, the reduction of Mn 4+ can lead to the formation of Mn 3+ ions that are soluble in the electrolyte, with poor cyclic stability. Reduction of Mn 4+ contributes to the capacity exhibited by the material when the cell voltage is brought to 1.6 V vs. Na/Na + , while upon charging, only Ni 2+ is oxidized.

Figure 1
Schematic representation of layered transition metal oxides with general formula Na x MeO 2 . The arrows indicate phase transition processes induced by sodium extraction. Adapted from Ref. [14].
The above discussion clarifies that the electrochemical performance of Na 2/3 Ni 1/3 Mn 2/3 O 2 can be improved by (i) suppressing the structural transformation P2→O2; (ii) increasing the Na + /vacancy ratio; (iii) avoiding or reducing the participation of the redox pair Mn 4+ /Mn 3+ ions, and (iv) inhibiting the decomposition of the electrolytes. Numerous approaches have been suggested to improve the performance of P2-type sodium compounds. The replacement of sodium with other alkali metal ions (e.g., lithium) or alkaline-earth ions (e.g., magnesium) has been one of the most studied strategies. It is recognized that lithium ions used as dopants preferably occupy the TM layers since the large size of sites in the Na layers cannot allow the Li ions to remain stable. The typical plateau seen in the voltage profiles upon charge/discharge gradually disappears after the introduction of Li ions, suggesting that the reaction mechanism changes from a series of phase transition reactions to solid solution-like behavior. The presence of Li ions can prevent the phase transition with a stabilizing effect of the P2 structure over a wide range of Na ions concentrations (voltage range 2.0-4.4 V), with varying reticular parameters, thereby improving the overall performance [23][24][25]. The function of Li in stabilizing the structure may be closely related to the migration of Li ions from the TM layer to the Na layer that occurs only at high voltage. The higher electropositive Li ions that migrate to the Na layers can hold the adjacent TM layers together, thereby inhibiting both the flow of the oxygen layer and the phase transformation [26].
The charge/discharge dynamics, the specific role of each constituent element in the material, the electrical conduction properties, and the surface chemistry of these electrodes present several fundamental questions, despite numerous studies carried out so far. Density functional theory (DFT) calculations have proven to be a useful technique for evaluating the thermodynamic, structural, and kinetic properties of manganese oxide (MnO 2 ) with monoclinic [27] and spinel structure [28] for their use as cathode materials for NIBs. Therefore, we applied an advanced quantum mechanics (QM) method based on DFT [29,30] and combined with a statistical approach to evaluate the Na 0.85 Li 0.17 Ni 0.21 Mn 0.64 O 2 (NLNMO) material as P2-type layered oxide with the promising application as a cathode electrode in NIBs [31]. The choice of NLNMO material was driven by the increasing interest in Li-doped NaMeO 2 materials, owing to the enhanced capacity in a wide voltage range ensured with Me = Ni, Mn (160 mAh g -1 within 2.0-4.5 V range) [20,24] and the excellent rate capabilities enabled by Li substitution (single smooth voltage profile) [31]. Despite these encouraging improvements, an in-depth analysis of Na ions intercalation and diffusion mechanisms in such innovative materials is still lacking. Possibly, the current study will set the direction for future works to develop and optimize high-energy cathode materials in effective NIB devices.

Materials and Methods
To build a realistic structural model for NLNMO bulk, we applied a statistical method that could simulate a disordered distribution of Mn/Ni/Li atoms within the Me-based layers of the material. The special quasi-random structure (SQS) method allows modeling of a random solid solution in a supercell of the desired size by building periodic structures whose properties simulate those of random material, i.e., at the limit of a perfectly random alloy (considering the two-and three-body correlation functions in a random alloy, through the interactions of each element grid with the nearest neighbor, and so on) [32,33]. The SQS model represents the best choice of a supercell with a random distribution of TM centers in the lattice obtained to maximize the configurational entropy within the limit of the given supercell. For sodium distribution over (e) (coordinated to the octahedron edge) and (f) (coordinated to the octahedron face) sites, we considered the occupancy ratio as previously reported in the literature and placed Na atoms accordingly [34,35]. We applied the solid-state physics code Vienna ab-initio simulation package (VASP) that performs firstprinciples quantum-mechanics calculations within DFT using the projector augmented wave (PAW) pseudopotentials and plane waves basis set with periodic boundary conditions. The spin-polarized DFT calculations were done using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional based on the generalized gradient approximation (GGA). The DFT functionals showed significant problems of self-interaction error (SIE) with localized electrons. Since we dealt with highly localized d electrons of Mn and Ni, the DFT+U scheme was employed. The DFT+U method is a more convenient method to rectify the SIE compared to theoretical approaches based on different hybrid functionals. The DFT+U method enabled us to gain useful theoretical insights into the electronic structures of complex materials and interfaces with good accuracy/computational cost ratio [36][37][38]. The basic idea was to analyze the strong Coulombic interaction of localized electrons with the Hubbard model, which is based on the U (Exchange) and J (Coulomb) parameters and can be derived either from ab initio calculations or bandgap values measured experimentally. Herein, we used U-J = 4 eV for d electrons of both Mn and Ni. Kinetic energy cut-off of 750 eV and a 2 × 3 × 4 -centered k-points grid to converge the plane-wave basis set.

Results and Discussion
We first developed the structural model of NLNMO through the SQS approach, starting with a 5 × 3 × 1 supercell of 115 atoms. The geometry optimization of both cell parameters and atomic positions was done to obtain the minimum-energy structure at the PBE+U level of theory. Figure 2 shows the corresponding energy structure with a volume of 82.5 Å 3 /fu that is in good agreement with the experimental value of ∼80.4 Å 3 obtained with X-ray diffraction (XRD) (See Table 1 for structural details) [31]. Figure 2 also shows the electronic properties of the bulk of the material. The nature of the electronic states close to Fermi Energy allows the identification of the responsible or involved species in the electronic conduction. It can be concluded that both valence and conduction bands are dominated by Ni (black) and Mn (purple) d states that are strongly hybridized with O p states (red), while Na and Li s states (yellow and green, respectively) are rather absent in the energy range around E F . This showed that only Ni, Mn, and O atoms play the electrochemically active role in NLNMO cathode material. The analysis of the atomic partial charges and magnetic moments validated the qualitative results obtained by pDOS. Li showed zero magnetic moment, while Ni and Mn had an average magnetic moment of 1.14 µB and 3.21 µB, respectively. These results corresponded to the X-ray absorption near edge structure (XANES) analysis of the material, which indicated the presence of Ni (II) and high spin Mn (III) [31]. In order to obtain structural information, we analyzed the distances between the cations and the oxide anion. Figure 3 shows the distribution of these distances in the form of a pair distribution function (PDF). The distribution of the distances between the cation and the oxide in the TM layer of Li, Ni, and Mn showed a similar pattern, indicating that the same octahedral coordination is shown by all the cations with oxygen. Li exhibited a slightly longer distance than Ni and Mn. Mn showed a partial elongation of some bonds, according to the Jahn-Teller distortion that is typical for Mn (III) with a high-spin d 4 configuration. Overall, the PDFs confirmed the perfect miscibility of the three cations in the oxide layer and the choice of the SQS approach to building a realistic and robust model. In the case of sodium-oxide distances (Figure 3, right panel), the corresponding PDF showed greater variability, with distances ranging from ∼2.2 to ∼2.9 Å. By decoupling the two components from the total Na-O PDF, the distribution of distances for the sodium ions lying in (e) and (f) positions were obtained. The intensities of these two PDFs reflected the sodium occupancy in the structural model, with Na (e)-O distances being more dominant than Na (f)-O ones. The greater variability of the distances was due to the sodium cations in (f) position, while the Na (e) PDF was more compact, demonstrating a higher structuring for these Na sites.
Out of this bulk structure, we cleaved the lattice along the (001) direction to obtain a surface model. An appropriate understanding of the interaction of the Na ion with the NLNMO surface is vital to study the complete characterization of the Na-ion intercalation reaction and the detailed mechanism of Na-ion diffusion occurring at the cathode surface. Our structural model for (001) NLNMO surface had a 5L-slab with a symmetric pattern (two oxide-based terminations) to avoid a strong electrostatic dipole and a 12Å-vacuum layer to avoid fictitious interactions resulting from the periodic boundary conditions (Figure 4). Though applied to study different materials, the surface slab approach has not been applied to this kind of electrode. We addressed the Na-(001) NLNMO interaction to the adsorption of one Na ion on two possible sites: Na (e) and Na(f), as depicted in Figure 4. The total sodium concentration was lower than that in the bulk state. Comparison of Na (e)-and Na (f)-adsorbed systems allowed to identify which site is favored and which site may represent a metastable state along the migration coordinate in the direction parallel to the electrode surface. We observed that after optimizing the Na-adsorbed states, the sodium ions located in position (f) site became slightly more stable compared to the one in position (e). However, the energy difference between these two minima was only 0.15 eV in favor of the (f) site. This was as per the expectations because in the (f) site the positive Na + interacts directly with three oxide anions, thereby maximizing the Coulomb interaction between ions with opposite charge, while in the position (e) there were only two neighboring oxide anions. The slightly higher stability of Na(f) sites might also be associated with the larger structural flexibility of these configurations compared to Na (e) ones evident from the wider peaks in the PDF illustrated in Figure 3. Our findings suggested that the sodiation process would commence with Na-adsorption on face sites, and then the complete sodiation will be achieved through the edge ones. Future works should address the Na-Na interaction to unveil the surface activity upon subsequent Na + intercalation (i.e., discharging process of NLNMO cathode material till full sodiation is achieved) and also explore Na-NLNMO interaction on different crystal facets. In this way, the sodium transport process at the electrode surface will be chased with detailed pathways and energetics.

Conclusions
This study highlighted the theoretical characterization of the physico-chemical properties of NLNMO as a possible high-energy cathode material for sodium-ion batteries. The material possesses a layered structure where TM oxide layers alternate with Na cations. In the TM oxide layer, both Li and Ni occupy the positions of Mn as substitutional defects. We first defined the methodology to build a realistic structural model of the material. To represent the disordered distribution of Li, Ni, and Mn, the SQS approach was adopted. Through this method, a supercell of the material could be considered where the arrangement of Li, Ni, and Mn is constructed to maximize the configurational entropy of the total system. The sodium cation, in turn, can assume two possible lattice positions differing for the coordination to the oxide anions (on the edge of the octahedron or in the center of the octahedron face). The results showed that the sodium cations in position (f) were slightly less ordered than that in position (e). This structural variability can result in a flat potential energy surface at position (f) and, therefore, a more favorable condition to diffuse. The analysis of the electronic structure showed the mixed nature of the valence and conduction bands that included Mn d states, Ni d states, and O p states, thereby excluding the non-participating Na and Li cations in the electronic conductivity.
In summary, our findings confirmed that lithium has a purely structural role, while nickel and manganese actively participate in both redox processes and electronic conduction. Therefore, the optimum ratio between these elements is crucial to obtain a material with good mechanical stability and enhanced electrical conduction. The optimization of the atomic positions for the surface of the material showed the absence of significant surface reconstruction, thereby demonstrating the stability of the oxide layer. The adsorption of a sodium atom at sites (e) and (f) on top of the (001) surface showed that the face coordination is slightly favored for about 150 meV. This suggested that the sodiation process begins with adsorption on (f) sites, and then the complete sodiation is achieved through the more abundant (e) sites.