On the origin of phase transition suppression of P2–Na_0.67MnO₂ by substitution of Mn with Li

Abstract

Mn-based layered oxides are promising cathode materials for Na-ion batteries, but their low cyclability due to phase transition during charge/discharge remains a challenge. P2–Na_0.67MnO₂ compound undergoes a severe phase transition of P2 → O2 during charging. It has been proposed that this behavior results from the desodiation-induced change in the Jahn–Teller (J–T) activity of Mn after its oxidation from 3+ to 4+. In this work, we show that the driving force of the phase transition is indeed the oxidation of Mn³⁺ to Mn⁴⁺ but not the suppression of J–T activity with desodiation. Combining density functional theory calculations and electrostatic analyses indicates that the main factor stabilizing the P2 phase is the Na–Mn interaction, which strongly favors this phase over the O2 phase. Desodiation induced-weakening of this interaction leads to the formation of O2–Na_0.11MnO₂, which is driven by O–O interaction. Substituting Mn with Li stabilizes P2–Na_xLi_0.22Mn_0.78O₂ even at low Na content (x = 0.11). This is because the Na–Mn interaction is more favorable for the P2 phase, and this energy preference remains almost unchanged after desodiation. The absorption energy of Na at Na sites close to Li_TM is much stronger than at sites near Mn_Mn, and favors P2 phase. As the overall Na absorption energy (dictated by Na–Mn repulsion) is mainly determined by the nearest Na–Mn neighbor interaction, which does not change much with desodiation, no phase transition to O2 occurs for Na_xLi_0.22Mn_0.78O₂ at x = 0.11. Overall, the phase stability of Na-based layered oxide materials is driven by electrostatic forces, which can be tuned by substitution of Mn by a metal ion of appropriate charge and concentration.

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Introduction

After the successful application of Li-ion batteries (LIBs) in portable electronic devices and electric vehicles, significant attention has been directed to sodium-ion batteries (SIBs) because of the low cost and natural abundance of sodium (Na) resources.^1,2 Mn-based layered oxides, Na_x[M_1−yMn_y]O₂ (M: metals), are perhaps among the most promising cathode materials because of their low toxicity and high energy density.^3,4 The basic compound Na_xMnO₂ can be classified into P- and O-type depending on the site occupation preference for Na⁺, prismatic or octahedral coordination, respectively.⁵ The most common layered oxide types are P2 and O3, where the numbers represent the number of distinguishable oxygen layers stacking arrangements per unit cell. Compounds with O3 phases often undergo multiple phase transitions, such as O3–P3–O3′–O1 during charging with a gradual capacity loss during cycling.⁶ The P2-type materials generally show a better rate performance and higher initial capacity than O3-type.^7–10 Delmas et al.⁵ introduced, to our knowledge, the first work on the structural properties of P2–Na_0.7MnO₂. They found that there is a P2 → O2 phase transition during charging. This behavior decreases the capacity of this compound with cycling and was assigned to the co-operative Jahn–Teller distortion of Mn³⁺. To solve this issue, Dahn et al.¹¹ substituted Mn with Ni and reported P2–Na_0.67Ni_0.33Mn_0.67O₂ with a capacity of 173 mAh g⁻¹. However, the drastic volume change of ∼23% after desodiation, originating from the P2 → O2 phase transition, still decreases the capacity retention of this material. Additionally, Konarov et al.¹² reported a reduction in the volume change (∼13%) in P2–Na_0.67Ni_xMn_1−xO₂ by varying the Ni-content from x = 0.0 to 0.2. They found that the P2–Na_0.67Ni_0.2Mn_0.8O₂ material shows the best electrochemical performance compared to other Ni contents. The small volume changes in P2–Na_0.67Ni_0.2Mn_0.8O₂ was possible because of Ni²⁺ → Mn³⁺ substitution, which can suppress Jahn–Teller distortions. However, suppression of P2 → O2 phase transition during charging is still challenging. In order to enhance the electrochemical properties of P2-type materials, Yabuuchi et al.¹³ reported that the P2 → O2 phase transition in P2-type Na_0.67Mn_0.5Fe_0.5O₂, which showed a reversible capacity of 190 mAh g⁻¹ with electrochemically active Mn³⁺/Mn⁴⁺ and Fe³⁺/Fe⁴⁺ redox processes, is suppressed. However, they found that a reversible P2 → OP4 phase transition occurs at x = 0.13 during charging. Bruce et al.¹⁴ applied Ni besides Fe to partially substitute Mn, and found that their synthesized cathode material, P2–Na_0.67Ni_0.17Fe_0.33Mn_0.50O₂, also shows the P2 → OP4 phase transition during charging and less volume change, as compared to the typical P2 → O2 phase transition, which enhances the capacity retention. These previous studies show the importance of doping/substitution to stabilize the P2–Na_xMnO₂ structure by minimizing/reducing the effect of Jahn–Teller distortion in Mn³⁺ and by suppressing the volume change during charging. An improved cycling stability and better capacity retention can be achieved not only by redox-active transition metal substituents such as Ni and Fe but also by electro-inactive elements such as Li and Mg in P2–Na_xMnO₂ structure. Yabuuchi et al.¹⁵ reported that the Li-substitution at Mn-sites can suppress the P2 → O2 phase transition in P2–Na_0.75Li_0.25Mn_0.75O₂. Density functional theory (DFT) has also been applied to gain further insight into this mechanism. For example, Yang et al.¹⁶ studied P2–Na_0.67Li_0.2Ni_0.2Mn_0.6O₂ using experimental measurements and DFT calculations. They were able to suppress the P2 → O2 phase transition in Na_0.67Li_0.2Ni_0.2Mn_0.6O₂ upon charging and showed a reversible capacity of 110 mAh g⁻¹ over 100 cycles. Their DFT analysis found that the capacity originated from both cationic and anionic redox processes. Further computational studies show that the extraction of sodium ions increases the oxidation state of manganese during charging. This results in a higher concentration of Mn³⁺, which is prone to Jahn–Teller (J–T) distortions. It has been proposed that these J–T distortions alter the MnO₆ octahedra by changing bond lengths and angles, ultimately destabilizing the P2-structure leading to structural phase transitions.^17,18 Experimental studies have also proposed that the J–T distortion is a driving force of structural instability and phase transition during charging.¹⁹ However, the fundamental mechanism behind the P2 → O2 phase transition in P2–Na_xMnO₂ and the role of low valent substitution (Li⁺, Ni²⁺, and Fe²⁺) to stabilize the P2 structure during charging/discharging is, however, to our knowledge still unclear and a more detailed understanding is required. In this work, we study the origin of the P2 → O2 phase transition as well as the impact of Li → Mn substitution on the phase stability and transition in P2–Na_xMnO₂. Our DFT-PBE calculation reproduces J–T distortions for Na_0.67MnO₂ (as also reported earlier by Delmas,⁵ Langella et al.¹⁷ and Jung et al.¹⁸) and no J–T distortions for Na_0.67Li_0.22Mn_0.78O₂, and confirms phase transition in the former and its suppression in the latter case. Our simple electrostatic model without considering J–T distortions also predicts the same trend as DFT which shows the key role of electrostatic interaction rather than J–T distortion on the phase stability. Moreover, for the first time, we also provided a simple quantitative explanation for the phase stabilization (as-synthesized material) and transition (during operation) of P2–Na_0.67MnO₂ materials with and without Li → Mn substitution, which is an important phenomenon in Na-ion batteries.

Results and discussion

The most favorable atomistic structure for each compound and Na concentration, as well as their corresponding relative electrostatic energies are presented in Fig. 1. We studied the influence of desodiation on the phase stability of Na_xLi_yMn_1−yO₂ materials, by computing the energy difference of P2, O2, and O3 phases as a function of Na (x = 1.00, 0.67, and 0.11) and Li (y = 0, 0.06, 0.22) concentrations using DFT-PBE (Fig. S1). For the fully sodiated case of Na_1.00MnO₂, the O3 phase is more favorable than the P2 and O2 phases which agrees with the previous experimental study by Xiaohua et al.²⁰ With a x = 1.0 → 0.67 decrease in Na concentration, the P2 phase becomes more stable than O3 and O2 phases for Na_xMnO₂ by 13 meV and 23 meV (per formula unit) respectively. Stabilization of the P2 phase has also been reported by experimental measurements from Delmas et al.⁵ For the desodiation structures, we focused on P2 and O2 phases. After desodiation from x = 0.67 → 0.50, the P2 phase remains more stable by 15 meV than the O2 phase.

Fig. 1 (top) Computed electrostatic energy difference between the P2 and O2 phase ΔE (eV) = E^P2_tot − E^O2_totversus Na-concentration using the Ewald summation (with point charges). (bottom) Side views of atomistic structures.

However, after further desodiation the Na_xMnO₂ system undergoes a P2 → O2 phase transition at x = 0.17, as the O2 phase is 2 meV more stable than the P2 phase. With a further decrease in Na-concentration (x = 0.11), the O2 phase remains more stable than the P2 phase (by 4 meV per formula unit). Our results indicating the P2 → O2 phase transition during charging is consistent with experimental results by Delmas et al.⁵ and Dahn et al.¹¹ DFT calculations show the following phase transitions to occur for x = 1.00 → 0.67 → 0.50 → 0.17 → 0.11: O3 → P2 → P2 → O2 → O2.

The DFT calculations indicate that in the case of Na_1.00Li_0.06Mn_0.94O₂ (Fig. S1), in which 6% of Mn is substituted with Li, the P2 phase is more favorable than the O2 and O3 phases. For the Na concentration of x = 0.67, the P2 phase remains more favorable for Li concentrations of y = 0.06 (Na_0.67Li_yMn_1−yO₂) showing similar behavior to the case of y = 0.0. Furthermore, for Na_xLi_0.06Mn_0.94O₂ (x = 0.67), our DFT-PBE calculation shows that the P2 phase is more stable than the O2 phase by 30 meV (per formula unit) and after desodiation from x = 0.67 to 0.11, a P2 → O2 phase transition occurs and the O2 phase becomes more stable than the P2 phase by 20 meV per formula unit. This means that with 6% Li at Mn sites there is only one phase transition occurring: P2 → P2 → O2 for desodiation of x = 1.00 → 0.67 → 0.11.

After increasing the substitution of Mn by Li to 22% the P2 phase remains the most favorable in Na_1.00Li_0.22Mn_0.78O₂ (Fig. S1). For the Na concentration of x = 0.67, the P2 phase forms for Li concentrations of y = 0.22 (Na_0.67Li_yMn_1−yO₂) similar to the cases of y = 0.0 and y = 0.06, which agrees well with experimental measurements by Myung et al.²¹ However, with such large amount of Li on the Mn sites (Na_xLi_0.22Mn_0.78O₂) there is no phase transition occurring, and the P2 phase is always more stable than the O2 phase by 11 meV and 4 meV (per formula unit) for high (x = 0.67) and low (x = 0.11) Na-concentrations respectively. Experimental studies by Myung et al.²¹ also show that 22% of Li-doping in Na_xMnO₂ (x = 0.67, 0.11) can suppress the phase transition during charging. The absence of a desodiation-induced phase transition has also been reported by Tarascon et al. for Na_xLi_yMn_1−yO₂ with larger values of y = 0.33.²² These results indicate a strong influence of Li on the phase stability of Na_xLi_yMn_1−yO₂.

Our DFT calculations show that the lattice parameter a decreases with a reduction of the Na-concentration from 0.67 to 0.11 for all studied systems (see Table S1 in SI) due to the oxidation of Mn and O, which will be discussed later. The lattice parameter c contracts strongly after desodiation from 0.67 to 0.11 for the cases in which either no Li or a small amount of Li exist at the TM sites (Na_xLi_yMn_1−yO₂, y ≤ 0.06), which is because of the phase transition as well as migration of half of the Li cations from TM to Na sites after desodiation. However, the decrease in c parameter in the compound with a high amount of Li at TM sites, namely Na_xLi_0.22Mn_0.78O₂, in which no P2 → O2 phase transition occurs, is very small. The small decrease in c parameter is most likely due to the Li-migration from TM to Na-sites during charging. An experimental study by Tarascon et al.²² on O3–NaLi_0.33Mn_0.67O₂ also indicates Li migration from TM to Na-site during charging and the presence of Li in the Na-layer leads to a decrease in the c parameter with respect to a discharged system which is consistent with our findings. In the discharged state of Li-doped compounds, Li ions occupy TM sites, but upon charging they migrate from TM to Na sites (see Fig. S2 in SI). To determine whether the migrated Li ions from TM to Na sites stay at the Na sites or move to the surface of the cathode during charging, we removed the Li-ions from Na-site in Na_0.11Li_0.06Mn_0.94O₂ and Na_0.11Li_0.22Mn_0.78O₂ and optimized both structures and lattice parameters. An expansion in the c-value was found for this model, which agrees with the o-XRD measurement by Myung et al.²¹ This result indicates a spontaneous migration of fractional Li ions from TM to Na sites and subsequent segregation to the surface of Na_0.11Li_0.22Mn_0.78O₂. Therefore, we conclude that most of the migrated Li-ions from TM to Na sites do not stay in those Na sites, but segregate to the surface of the cathode consistent with previous study.²¹ Therefore, we used Na_0.11Li_0.03Mn_0.94O₂ and Na_0.11Li_0.11Mn_0.78O₂ to calculate the electronic structure. However, it is important to mention that we calculated electrostatic calculations for both models instead of Na_0.11Li_0.06Mn_0.94O₂ and Na_0.11Li_0.22Mn_0.78O₂.

Furthermore, the redox mechanism of Na_xLi_yMn_1−yO₂ were investigated to determine change states of elements for further electrostatic analysis on phase transition, which will be discussed later. To achieve this aim, magnetic moments (represented as number of unpaired electrons (N_unp)) on elements as well as spin density difference (SDD) plots (Fig. 2 and 3) were computed using DFT-HSE06. The calculated average value of unpaired electrons on Mn in Na_0.67MnO₂ (Fig. 2) indicates that 36.11% of Mn exhibit a charge state of ∼3.8+ (t³_2ge⁰_g, ), and the rest have a charge state of 3.0+–3.3+, from which 44.44% are in the low spin (t⁴_2ge⁰_g, ), and 19.44% in high spin (t³_2ge¹_g, ). The formation of Mn³⁺ in the high spin state leads to the Jahn–Teller (JT) distortion as the average axial Mn–O bond lengths (đ^Mn_axial = 2.27 Å) are longer than average equatorial Mn–O bond lengths (đ^Mn_equatorial = 1.96 Å). A similar Jahn–Teller effect for Mn³⁺ has been reported earlier by Delmas et al.⁵ With the desodiation of x = 0.67 to 0.11, Mn cations that had charge states between 3.0+ and 3.3+ are oxidized and the average charge state of Mn cations becomes ∼3.8+ .

Fig. 2 Calculated number of unpaired electrons N_unp on Mn in P2–Na_xMnO₂ (Na_xMO), P2–Na_xLi_0.06Mn_0.94O₂ (Na_xL_0.06MO), and P2–Na_xLi_0.22Mn_0.78O₂ (Na_xL_0.22MO) using DFT-HSE06. Inset represents visualization of oxidation state of Mn. Yellow and blue colors represent the up- and down-spin electrons respectively and red arrow represents from discharged to charged state.

Fig. 3 Calculated number of unpaired electrons N_unp of O ions (left figure) and spin density difference (SDD) plots (with an isosurface of 0.006 eV Å⁻³) of chosen O–TM–O layers of (a) P2–Na_xMnO₂ (Na_xMO), (b) P2–Na_xLi_0.06Mn_0.94O₂ (Na_xL_0.06MO), and (c) P2–Na_xLi_0.22Mn_0.78O₂ (Na_xL_0.22MO) with x = 0.67 (middle figure) and x = 0.11 (right figure) using DFT-HSE06. Yellow and blue colors represent the up- and down-spin electrons respectively. The red arrow represents from discharged to charged state.

For Na_0.67Li_0.06Mn_0.94O₂, the computed for 53% of Mn (t⁴_2ge⁰_g, , low spin) and 47% of Mn (t³_2ge⁰_g, ) indicates that Mn cations have an oxidation state of ∼3+ and ∼4+, respectively. After desodiation of x = 0.67 to 0.11, 53% of Mn cations that had an initial charge state of ∼3+ experiences oxidation and exhibits a charge state of ∼4+ , which can be clearly seen in the SDD plots (Fig. 3) where the Mn features shrink after desodiation. It is noteworthy that, in comparison to the Na_0.67MnO₂ compound, the Na_0.67Li_0.06Mn_0.94O₂ system shows no cooperative Jahn–Teller distortion in the discharged state but shows phase transition from P2 → O2 during charging of x = 0.67 → 0.11. The computed of all Mn cations is 3.05 for Na_0.67Li_0.22Mn_0.78O₂ indicating the oxidation state of Mn cations to be 4+ (t³_2ge⁰_g, ). This can also be seen in the SDD plot (Fig. 3) where small features exist on Mn. Upon desodiation from x = 0.67 → 0.11, the calculated for Mn remains almost the same, indicating an oxidation state of ∼4+.

Compared to Na_0.67MnO₂, there is no cooperative JT-effect and no phase transition from P2 → O2 for the Na_xLi_0.22Mn_0.78O₂ (for x = 0.67 → 0.11) system as all of Mn shows an oxidation state of 4+ before and after desodiation. Therefore, it seems that this amount of Li acts as a structure stabilizer for Na_0.67Li_0.22Mn_0.78O₂ as well as Na_0.11Li_0.11Mn_0.78O₂.

The calculated values of on O for Na_xMnO₂, Na_xLi_0.06Mn_0.94O₂, and Na_xLi_0.22Mn_0.78O₂ in the discharge state (x = 0.67) are equal to or smaller than −0.05 indicating that the average charge state on O is between 2− and 1.95− (Fig. 3). The small features on O anions in the SDD plot confirm that the charge state of O is close to 2− in the discharge state. Computed of O in Na_xMnO₂ for x = 0.11 shows only a small charging-induced oxidation of oxygen. Similarly, the O anions in Na_0.11Li_0.03Mn_0.94O₂ do not experience much oxidation as the calculated value of is −0.12. The oxidation of O in this composition is, however, slightly higher than Na_0.11MnO₂, which is because of Li for Mn substitution. In particular, some of O anions (e.g. O3, O5, and O40) close to the vacant site, which are created after Li migration, undergo the highest oxidations . The larger blue feature on O3, O5, and O40 in the SDD plot of Na_0.11Li_0.03Mn_0.94O₂ compared to all O anions in Na_0.11MnO₂ (Fig. 3) visualize this result. As we discussed earlier, Mn is inactive for Na_0.11Li_0.11Mn_0.78O₂, and, therefore, the ion that contributes to the redox mechanism is oxygen. This result is in agreement with previous DFT studies by De la Llave et al.²³ and Kim et al.²⁴ who studied P2–Na_0.6Li_0.2Mn_0.8O₂ and P2–Na_0.67Li_0.33Mn_0.67O₂, respectively, and found extra oxygen states appearing near the Fermi level (in the computed projected density of states) indicating an oxygen anion redox to compensate the charge imbalance. After desodiation of x = 0.67 → 0.11, higher N_unp and larger SDD (more blue features) of O anions close to the vacant site (e.g. O6, O7, O10, O11) show that they experience strong oxidation. Higher oxygen redox activity in Na_0.11Li_0.11Mn_0.78O₂, as compared to Na_0.11MnO₂ and Na_0.11Li_0.03Mn_0.94O₂, is most likely due to the formation of more 8% TM vacancies in the crystal structure. This triggers oxygen redox reaction as the oxygen anions that have lost their binding to removed Li ions undergo significant oxidation . The sequence of oxygen redox activity in our studied systems from lower to higher is as follows: Na_0.11MnO₂ → Na_0.11Li_0.03Mn_0.94O₂ → Na_0.11Li_0.11Mn_0.78O₂. The electrostatic interaction between different cations as well as between them and the oxygen anions might explain the phase stability/transition.

To study this, the differences in total electrostatic energies were calculated using Coulomb energy analysis by using elementary charge states, which balance the system, as well as by applying computed charge states from Fig. 2 and 3 between the P2 and O2 phases (ΔE (eV) = E^P2_tot − E^O2_tot) for Na_xLi_yMn_1−yO₂ with different Na (x = 0.67, 0.11) and Li (y = 0, 0.22) concentrations (Fig. 4). The P2 phase is found to be electrostatically more stable than the O2 counterpart for x = 0.67 in all compositions, namely Na_0.67MnO₂ and Na_0.67Li_0.22Mn_0.78O₂. This finding is in line with both our DFT results (Fig. S1) as well as experimental studies on Na_0.67MnO₂ and Na_0.67Li_0.22Mn_0.78O₂ by Delmas et al.⁵ and Myung et al.²¹ respectively. Our electrostatic calculation (Fig. 4) for low Na concentrations (charged state) shows that the O2 phase becomes more favorable in the case of Li free, namely Na_0.11MnO₂ and consistent with DFT calculations and with experimental studies by Delmas et al.⁵ and Dahn et al.¹¹ However, for the case of high concentrations of Li, namely Na_0.11Li_0.22Mn_0.78O₂, the P2 phase remains stable after desodiation, in agreement with DFT and experimental study by Myung et al.²¹

Fig. 4 Computed ΔE is in eV which is the electrostatic energy difference for (a) Na_1−xMnO₂ (b) Na_1−xLi_0.22Mn_0.78O₂ between the P2 and O2 phase versus Na-concentration represented in yellow color. Aqua and magenta color represents the discharged and charged state respectively that shows an individual contribution of each element in total electrostatic energy.

Furthermore, we analyzed the pairwise ion–ion interaction by computing their corresponding electrostatic energy differences between P2 and O2 phases for two compounds with the largest difference in Li and Na concentrations, namely Na_0.67MnO₂, Na_0.11MnO₂, Na_0.67Li_0.22Mn_0.78O₂, and Na_0.11Li_0.22Mn_0.78O₂ (Fig. 4). Moreover, we analyzed pair distribution function (pdf) of ions to determine the underlying mechanism for the phase stability and transition in these materials (Fig. 5 and Fig. S3).

Fig. 5 Calculated pair distribution function which is the difference of O–P (G_O(r) − G_P(r)) corresponding to atomic pairs of Na–Mn, inset shows top view of the layer and bond length in angstrom (Å) of (a) Na_0.67MnO₂, (b) Na_0.11MnO₂, (c) Na_0.67Li_0.22Mn_0.78O₂ and (d) Na_0.11Li_0.22Mn_0.78O₂ and shaded area represent the nearest neighbors.

In all cases, the O–O interaction favors the O2 phase, i.e. E_O–O is lower for the O2 phase. This is most likely due to the shorter distances (r_O–O) of nearest neighbors in P2: e.g. r_peak(P2) = 3.40 Å < r_peak(O2) = 3.80 Å and r_peak(P2) = 4.40 Å < r_peak(O2) = 4.84 Å (Fig. S3). With desodiation, the values of ΔE_O–O remain unchanged for Na_0.11MnO₂ (Fig. 4) because of the same oxidation state of O before and after desodiation. However, the O–O interaction changes slightly for Na_xLi_0.22Mn_0.78O₂ (x = 0.11) after desodiation because of a very small oxidation of O (1.95− → 1.92−). The cation–O interactions (cation: Mn, Na, and Li) do not stabilize significantly any of the P2 or O2 phases in both studied systems (ΔE_cat–O < 0.18 eV from Fig. 4). Although the Mn–Mn interaction does not stabilize any of these phases for Na_xMnO₂ as ΔE_Mn–Mn = 0.02 eV, it does prefer O2 phase over P2 phase (ΔE_Mn–Mn = 2.62 eV) for Na_xLi_0.22Mn_0.78O₂, which is probably due to the stronger interlayer Mn–Mn repulsion (as all of Mn become 4+) in the P2 phase after replacing partial Mn by Li cations.

Fig. 4 indicates that the Na–Mn interaction is the determining factor controlling the phase stability of the studied materials. This can be due to the high charge of the Mn cations (from 3.34+ to 4+ depending on the Li and Na concentrations) as well as the distinct phase-dependent Na–Mn separations as discussed later. Since the other pairwise interactions do not change much with desodiation, we will focus on Na–Mn pairs.

The Na–Mn interaction favors the P2 phase in all cases due to the shorter Na–Mn distances for the O2 phase. This can be clearly observed from the pdf plots in Fig. 5. The decrease in the phase stability of the P2 phase over the O2 phase after desodiation in the case of Na_xMnO₂ is probably because of oxidation of Mn from 3.34+ to 4+ (Fig. 2) as well as a decrease in the number of nearest neighbors Na–Mn pairs (r_peak(O2) = 2.73 Å and r_peak(O2) = 3.20 Å). However, in the case of Na_xLi_0.22Mn_0.78O₂, the charge states of Mn cations do not change much. Moreover, the intensities of nearest neighbor Na–Mn pairs do not decrease significantly in contrast to the case for Na_xMnO₂. This is because Na ions prefer occupying the Na sites that are closest to the Li ions to reduce the Na⁺–Mn⁴⁺ repulsion. Our DFT calculation shows that these Na sites (shown by Na^LMMM_Na and Na^LMMLMM_Na for the O2 and P2 phases, respectively, in Fig. 5) are much more favorable (by 2.82 eV) for Na occupation than the other Na sites that are next to Mn⁴⁺ (shown by Na^MMMM_Na and Na^MMMMMM_Na for the O2 and P2 phases, respectively, in Fig. 5). Therefore, they are the determining sites for the electrostatic energy difference between the P2 and O2 phases. For the aforementioned reasons, the phase stability of the P2 phase over the O2 phase does not change much after desodiation. The similar energy difference between P2 and O2 phases for high and low Na concentrations of the Li-doped case (in spite of their different PDF intensities of next nearest neighbors) confirm our assumption that the interactions between the first nearest Na–Mn neighbors determine the phase stabilities.

We additionally calculated all pairwise interactions for y(Li) = 0.06, 0.11, 0.33, and 0.4 and found that Na–Mn interaction still favors the P2 phase for y(Li) = 0.06, 0.11, and 0.22. With higher Li concentrations of 0.33 and 0.40, the O–O interaction becomes dominant and favors the O2 phase.

As mentioned earlier, there is a Li migration from TM- to Na-sites for Na_0.11Li_0.06Mn_0.94O₂ and Na_0.11Li_0.22Mn_0.78O₂ structures. We found that for example in Na_0.11Li_0.22Mn_0.78O₂, Li at the transition metal (TM) site is 7.96 eV less favorable than that in the Na site. Consequently, after the geometry optimization, Li migrates from the TM site to the Na site. Probably, Li is not even stable in the octahedral Na sites due to its small size (compared to Na). Our previous theoretical/experimental study has shown that partially migrated Li to TM sites migrate further to the surface of electrode forming a CEI layer.²¹ Therefore, we removed the Li-ions from the Na-sites and studied the phase transition. However, a similar result to the case without Li migration was found: the O2 phase is more favorable than the P2 phase in Na_0.11Li_0.03Mn_0.94O₂, while the P2 phase is more favorable than the O2 phase in Na_0.11Li_0.11Mn_0.78O₂. Moreover, in these models containing TM vacancies (due to Li migration), Na ions prefer to occupy Na sites next to a TM vacancy to lower the electrostatic energy. A mechanism, similar to Na_0.11Li_0.22Mn_0.78O₂ containing Li ions at TM sites, is expected for Na_0.11Li_0.11Mn_0.78O₂ containing TM vacancies (created by Li migration) to explain why the P2 → O2 phase transition is prevented.

Method

To obtain the most favorable structures of P2–Na_xMnO₂, P2–Na_xLi_0.06Mn_0.94O₂ and P2–Na_xLi_0.22Mn_0.78O₂, with different x values, we modeled and calculated the total Coulomb energy (E_C) of a large number of likely structures. Total Coulomb energy (E_C) calculations on possible combinations were carried out using the so-called supercell code.²⁵ We computed electrostatic energies (E_C) for specific elements using the Pymatgen code.²⁶ By performing DFT-PBE calculation on the electrostatically most favorable configuration, we determined the lowest total energy structure for each Na concentration and used the optimized geometries for further DFT-PBE-D3 and -HSE06 calculations. The total number of considered configurations for E_C calculation and the charge states of ions are discussed in detail in SI. Spin-polarized DFT calculations were performed using the projector augmented wave (PAW) potential method²⁷ implemented in the Vienna ab initio Simulation Package (VASP) code.²⁸ The Perdew–Burke–Ernzerhof (PBE)²⁹ form of generalized gradient approximation (GGA) was used for the exchange and correlation potential. The dispersion D3 correction by Grimme³⁰ was applied to calculate atomistic structures. We have not applied the PBE+U³¹ functional for geometry optimization as it is known from previous theoretical works that it does not provide a better description for lattice parameters compared to PBE.^32,33 Performing geometry optimizations with Heyd–Scuseria–Ernzerhof (HSE06)³⁴ functional is not a common approach to compute the atomistic structure either, because HSE06 is often used for calculating electronic properties such as band gaps and magnetic moments. Moreover, it's computationally expensive and usually doesn’t change the structure much compared to PBE.³⁵ Therefore, it is a more common approach to optimize the geometry with PBE first, then use this optimized geometry and perform single-point calculations with HSE06 functional.^36–38 Therefore, we used HSE06 functional to compute the electronic structure (i.e. number of unpaired electrons (N_unp) on elements and spin density difference (SDD) plots). Na_xMnO₂, Na_xLi_0.06Mn_0.94O₂, and Na_xLi_0.22Mn_0.78O₂ were modeled by 3 × 6 × 1 supercells with the following number of atoms per supercell: P2–Na_0.67MnO₂ (Na₂₄Mn₃₆O₇₂), P2–Na_0.11MnO₂ (Na₄Mn₃₆O₇₂), P2–Na_0.67Li_0.06Mn_0.94O₂ (Na₂₄Li₂Mn₃₄O₇₂), P2–Na_0.11Li_0.06Mn_0.94O₂ (Na₄Li₂Mn₃₄O₇₂) and P2–Na_0.67Li_0.22Mn_0.78O₂ (Na₂₄Li₈Mn₂₈O₇₂), P2–Na_0.11Li_0.22Mn_0.78O₂ (Na₄Li₈Mn₂₈O₇₂). Afterwards, we also studied the influence of desodiation on the phase stability of Na_xLi_yMn_1−yO₂ materials by using a large supercell (3 × 6 × 3) to decrease the uncertainty in the energy differences (Fig. SI). A Gamma-centered k-points mesh of 2 × 1 × 2 and an energy cut off of 500 eV were applied. We performed convergence tests for the energy cut off and k-points sampling (see SI). An electronic and a force convergence criterion of 10⁻⁴ eV and 2 × 10⁻² eV Å⁻¹, respectively, were used for DFT calculations. Atomistic structures and SDD plots were visualized with the VESTA program.³⁹

Conclusions

We investigated the origin behind the phase transition in the P2–Na_0.67MnO₂ cathode by performing DFT calculations and electrostatic energy analyses. We also simulated the effect of substitution of Mn by Li on the stability of P2–Na_0.67MnO₂. It is found that the Na–Mn interaction is the most determining factor controlling the phase stability of Na_0.67MnO₂, which is strongly Na concentration (x) dependent. This pairwise interaction prefers the P2 phase over the O2 phase independent of x value, but this preference weakens with decreasing x. The O–O interaction, which is the second most important parameter determining the phase stability, favours the O2 phase with a very weak Na concentration dependency. For the aforementioned reasons, the preference of the P2 phase due to the Na–Mn interaction becomes weaker than that of the O2 phase due to the O–O interaction leading to the P2 → O2 phase transition in Na_xMnO₂ at low x values (e.g. x = 0.11). Decrease in the number of nearest neighbor Na–Mn pairs and the oxidation of Mn^3.34+ to Mn⁴⁺ after charging are probably responsible for the phase transition. We also explained the reason behind the suppression of the phase transition through the substitution of Mn by low-charge state elements such as Li. It was found that the 22% doping with Li retains the P2 phase during charging. The higher stability of the P2 phase as compared to O2–Na_xLi_0.22Mn_0.78O₂ even after desodiation (x = 0.67 → 0.11) is dictated by Na–Mn interaction, which is much weaker (more favorable) for Na absorption close to Li at TM sites for the P2 phase. This preference is determined mainly by nearest Na–Mn neighbours which does not change with Na concentration. This work not only quantitatively proves the phase preference in the as-synthesized and desodiated P2–Na_xMnO₂ and P2–Na_xLi_0.22Mn_0.78O₂ but also the corresponding driving force behind the phase stabilities.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d5cp02620b.

Acknowledgements

Computation time granted through JARA HPC on the supercomputer JURECA at Forschungszentrum Jülich under Grant No. jiek12 is gratefully acknowledged by the authors. P. K. thanks for the financial support from the “Deutsche Forschungsgemeinschaft” (DFG, German Research Foundation) under project No. 501562980.

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