Rahul
Kumar
and
Abhijit
Chatterjee
*
Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai, 400076 India. E-mail: abhijit@che.iitb.ac.in
First published on 5th June 2025
The poor stability of transition metal (TM) layered oxide cathode materials upon exposure to moisture poses a significant challenge, hindering their widespread practical use in sodium-ion batteries. To facilitate the selection of suitable dopants for enhancing air stability, we propose energy-based descriptors to assess material stability and water–material interactions. These descriptors are assessed through density functional theory (DFT) calculations, focusing on the onset of water insertion in NaTmxNi1−xO2 (Tm = Ti, Mn) cathode materials. The importance of energy-based descriptors is highlighted by examples discussed where, despite having large sodium layer disruption and expansion of the surface layers due to water insertion, the formation of hydrogen bonds and charge transfer between water and the oxide layers greatly stabilize the NaTmxNi1−xO2 structure, thus promoting water insertion. The energy descriptors are used in a materials screening protocol to predict the water stability trends in sodium-ion battery materials and to understand the effect of dopants in mitigating the air stability issue.
Several past studies have investigated the role of moisture.4,17 Ambient H2O present at >0.01 ppm level can cause material degradation,16,18,19 which can ultimately lower the battery capacity.20,21 During charging, Na vacancies are created, which enable intercalation of water. The presence of Na vacancy defects assists the overall process.13 Although moisture attacks certain surface sites more readily,16 the structural damage continues, and it becomes apparent only at the end of life. To mitigate the degradation problem, doping or elemental substitution in Tm-layers is commonly explored.22,23 Given the vast compositional space, first-principles calculations can help in the efficient selection of appropriate dopants. It is believed that dopant cations that cause contraction of the Na-layer spacing via expansion of the Tm layer result in more stable materials. This is because water insertion in the Na layer becomes less likely for geometric reasons.17 Such structural parameters can be augmented with additional attributes, such as charge and size of transition metals (see the review article15 and the references therein) – all quantities being determined from first-principles calculations. A surprising aspect of these calculations is that they essentially involve water-free systems, i.e., one arrives at a conclusion regarding the material stability even without considering the nature of the water–material interactions. We address this gap by studying the energetic aspects of water insertion. Moreover, we introduce energy-based descriptors that are used to determine the optimal dopant composition.
From an experimentalist's viewpoint, material stability relates to the duration before visible signs of material degradation appear. At the end of life, the material structure comprises a significant amount of water. Computationally assessing the full kinetics of material degradation is a complex task. Even a rigorous first-principles thermodynamic treatment of the complete degradation process is computationally expensive,18,24–26 as free energy calculations typically require water to be inserted in multiple configurations to calculate an ensemble-averaged quantity,26–29 like 〈exp(−βΔE)〉, where ΔE denotes the associated energy change. To simplify the problem, we focus on the early stages of water insertion. The analysis involves the insertion of one water molecule into the material structure. The associated ΔE, sampled over multiple water and cation configurations, is shown to be a better descriptor for understanding material stability than the aforementioned structure-based ones. Although one water molecule alone cannot destabilize the structure, the proposed energy descriptor allows us to investigate the water–material interactions and the material's tendency to absorb water. As demonstrated later, our approach provides a more thorough evaluation than geometry-based assessments when screening for air-stable sodium-ion battery cathode materials.
With this simplification, we answer the key question: whether elemental substitution in the Tm layers promotes/inhibits the early stages of water insertion. Selected Mn–Ni, Ti–Ni, and Cu-doped transition metal-based layered oxides are probed. New insights into the structural changes and water–material interactions and coupling effects governing water insertion are reported. Comparisons with experimentally-observed trends are made. Our automated framework enables the identification of the optimal dopant composition, which is not possible with structure-based descriptors.
A slab for Na(Tm1Tm2)1O2 with symmetrical surfaces (along the z-axis) is generated (Fig. 1c and d). It contains a sufficient number of layers (11 layers with an approximate size of 12.5 Å). LDIPOL is set to true for the corrections of potential and forces which is necessary during slab calculations. The surface is selected along the z-axis (001) plane, keeping in mind that the oxide layer is followed by the Tm-layer and then by the Na-layer and is symmetrical from the top and bottom. It is found the 10 Å vacuum above and below the slab is sufficient along with 5 × 5 × 1 gamma-centered k-points. Spin polarization is included in all calculations. The effective charge on an atom is determined as the Bader charge via integration of the electron density.36
Bulk systems for O3-Na12Mn6Ni6O24 (O3-NMNO) and O3-Na12Ti6Ni6O24 (O3-NTNO) in the hexagonal Rm space group are shown in Fig. 1a and b, respectively. The choice of configurations for DFT calculations is complicated by the fact that there can be many possible arrangements of Mn/Ti and Ni ions in the Tm layer. For bulk NaMn0.5Ni0.5O2, we consider twelve distinct configurations. Detailed descriptions of these configurations are provided in the ESI (ESI Fig. S1† panels a-l). This is an improvement over the typically reported configurations for bulk NaMn0.5Ni0.5O2 materials where each layer is either pure Mn or pure Ni. Our findings indicate that mixed Mn–Ni layers can be more stable. Based on the comparison of formation energies, we identify the most stable configuration, which serves as the foundation for creating slab models in subsequent surface calculations. In particular, we discuss results for the configurations where each layer is composed of two Mn ions and two Ni ions. Similar considerations have been made for NaTi0.5Ni0.5O2 structures. The lowest energy configurations for the bulk systems of O3-Na12Mn6Ni6O24 (O3-NMNO) and O3-Na12Ti6Ni6O24 (O3-NTNO) in the hexagonal R
m space group are shown in Fig. 1a and b, respectively.
Lattice parameters for both systems (as listed in Table S1†) are in good agreement with experimentally reported values. Thus, the U parameters for Mn4+ ions and Ni2+ ions used for PBE + U + D3 calculations are found to be reasonable.7 Our DFT calculations predict the contraction of the Na layer spacing upon Ti substitution of Mn (from bulk O3-NMNO to O3-NTNO) consistent with the previous experimental/DFT results.17
Water insertion at a vacant Na-site in O3-NMNO and O3-NTNO is accompanied by an increase in Na-layer spacing (Fig. S2a–S2d†). ΔE values for water insertion (ΔE (eV) = Eslab(Na-vacancy)+water − Eslab(Na-vacancy) − Ewater) in such a case are +0.75 and +0.78 eV for Na vacancy based O3-NMNO and O3-NTNO, respectively. Here, Ewater is the energy of a single water molecule in a vacuum. The positive ΔE shows that water insertion is unfavorable in both bulk O3-NMNO and O3-NTNO. Furthermore, the values of ΔE are quite similar for the two materials. However, it is well known that compared to O3-type NaNi0.5Ti0.5O2, O3-type NaNi0.5Mn0.5O2 is more prone to degradation via water insertion. Thus, we conclude that bulk systems, although used extensively in the literature for stability assessment, are not reliable models for understanding water insertion.
It should be noted that the single Na vacancy-containing configurations chosen for our study serve as a useful starting point for assessing the water–material interactions. Multiple vacancies create many possible Na arrangements, and one again needs to determine the energetically favored configurations, which complicates the study.
To accommodate the water molecule, the Na layer opens up in structures 1–3. The layer spacing increases by 0.40–0.65 Å with respect to the Na vacancy based O3-NMNO system. In addition, the sodium ions in a layer are found to undergo a significant amount of displacement from their original positions in the water-free Na vacancy containing structure. The average displacement for the Na ions in relaxed structures 1, 2 and 3 (with respect to the positions of sodium when the water molecule was absent) is 2.43, 0.54 and 1.12 Å, respectively. Such a large disruption of the sodium ion layer is bound to be associated with an energetic penalty and does not appear to be consistent with the negative ΔE (−1.1 eV). For situations where water insertion is favorable, NMNO is slightly less ionic than the water-free Na vacancy containing structure shown in Fig. 2a. In general, for the systems studied in this work, the effective charge is found to change slightly after water insertion. Nonetheless, charge transfer can be expected to contribute to water stabilization.
Next, we investigate the role of the final water molecule orientation at the Na site. The hydrogen bond between the H atom of the water molecule and the O atom in the oxide layer depends on the H–O distance – this can change depending on the water orientation, as well as parameters like partial charges and orbital overlap.40 In the relaxed structure 1 (see Fig. S3a of the ESI† for the initial configuration), the water molecule becomes oriented at an angle of 36.72° to the direction normal to the Na layer. The H–O distance (H from water and O from both upper/lower oxide layer) is 1.55 Å. For structure 2 (see Fig. S3b of the ESI† for the initial configuration), the water molecule is oriented at an angle of 22.32°. The corresponding H–O distance is 1.67 Å and 1.58 Å. On the other hand, the water molecule (with an angle of 90.56°) is unable to reorient itself in structure 3 (see Fig. S3c of the ESI† for the initial configuration), and it lies parallel to the Na layer. The reasonable H–O distances in structures 1 and 2 allow for hydrogen bond formation, which is not possible in structure 3. We conclude that there can be multiple stable water molecule orientations, but the ones that allow for proper hydrogen bond formation are energetically favored.
Competing effects arise: for instance, the hydrogen bond strength depends on the charge on the oxide layer (greater negative charge on the oxide layer is better); however, the increase in the Na layer spacing, required for accommodating the water molecule, is possible when there is less negative charge on the oxide layer. Next, we determine whether similar observations are made for NTNO.
Once again, we discuss, in particular, three stable water orientations. The relaxed structures of 1–3 are shown in Fig. 2f–h. Each structure contains one water molecule at a vacant Na site in the O3-NTNO slab. The ΔE values associated with water insertion are 0.90, 0.72 and 0.15 eV for relaxed structures 1–3 (with respect to the Na vacancy containing NTNO in Fig. 2e), respectively. Thus, the early stage of water insertion is energetically unfavorable in all three cases.
Interestingly, the structural changes in NTNO and NMNO are qualitatively similar, e.g., when we compare panels b vs. f, panels c vs. g, and d vs. h in Fig. 2. It is surprising that the values of ΔE are so different (−1.10 vs. 0.9 eV for structure 1), which again highlights that ΔE is a more appropriate parameter for assessing material stability. In fact, structure 3 (water parallel to the Na layer) is the lowest energy water configuration in O3-NTNO, unlike structure 1 where water prefers to be nearly perpendicular to the Na layer.
In the O3-NTNO structure 1, the water molecule becomes oriented at an angle of 37.8° to the direction normal to the Na layer and is accompanied by large Na displacement within the layer. The average displacement for the Na-ions is 2.50 Å. The H–O distances (H from water and O from the upper/lower oxide layer) are 1.59 Å and 1.61 Å, respectively. For structure 2, the water molecule is oriented at an angle of 20.3° and there is a smaller Na-layer displacement (average displacement is 0.54 Å). The corresponding H–O distances are 1.68 Å and 1.50 Å. In structure 3, again the water molecule is unable to reorient itself due to the initial in-plane arrangement of the H atoms. The average displacement for the Na layer is found to be 0.97 Å. The average charge on the oxygen layer in structures 1–3 is −4.16, −4.12 and −4.12e, respectively (see Table S3†), i.e., water insertion makes the NTNO system even more ionic. Upon inserting water, the increase in the Na layer spacing lies between 0.35 and 0.67 Å as witnessed in structures 1–3.
(1) Penalty arising from the significant Na ion displacement.
(2) Penalty arising from the increase in the Na-layer spacing.
(3) Proper orientation of water molecules to assist hydrogen bond formation.
(4) Charge on the Na, oxide and Tm layer.
The above factors can compete and are coupled. As mentioned earlier, to properly orient the water molecule, the Na ions have to be displaced, which incurs an energy penalty. In a situation where the ionic charge is large, the hydrogen bonding becomes strong, but opening up of the Na layer becomes challenging. Given the strong coupling, it is possible to guess the stability only using an energy-based analysis with and without water.
It should be noted that in a practical battery electrode, as a water molecule moves through the lattice, the structural relaxation will happen locally, i.e., local Na rearrangement, and local Na-layer expansion will simultaneously occur. The exact nature of the changes is sensitive to the local ion arrangement. However, a first-order broad assessment of the water–material interactions can be gained by constructing suitable thermodynamic paths.
To understand the magnitude of the energy penalties involved in an approximate sense, we consider a thermodynamic path involving the step-by-step incorporation of the above factors into Na vacancy containing NMNO (Fig. 2a) and NTNO (Fig. 2e) and calculate the respective ΔE along the path shown in Scheme 1. The steps followed are: Na-displacement → expansion of Na-layer → water insertion. Here the starting state in Scheme 1 corresponds to NMNO and a water molecule in a vacuum (the NMNO and the water molecule do not interact). Since local Na rearrangement is integral to accommodating the water molecule, it is reasonable to ask whether the rearrangement is feasible in the absence of the water molecule under constant volume conditions. The state labelled as Na-rearrange NMNO in Scheme 1 involves NMNO with the displaced Na-layer, keeping the volume unchanged from the starting state, and a water molecule in a vacuum. This is followed by a volume change to match the one of structure 1, which causes the Na-layer to expand (labelled as expanded NMNO), which allows us to probe whether Na-layer rearrangement has become more likely with the expanded volume, in the absence of water. Finally, the water molecule is inserted under constant volume conditions.
![]() | ||
Scheme 1 Flow chart to understand the energy penalty terms. E1 is the energy change from the relaxed Na vacancy based O3-NMNO and NTNO slab systems to the one with a rearranged Na layer (without expansion of the Na layer). E2 is the energy required to go from the rearranged Na-layer structure to the one additionally having an expanded Na-layer, such that the Na-layer spacing is identical to the relaxed water-containing structure 1. See Fig. 2 to understand structure 1. |
The energy change associated with Na rearrangement in the NMNO slab system is +0.5 eV (denoted as E1). The additional energy change for expanding the Na layer in O3-NMNO is E2 (−0.4 eV). E1 + E2 is small but positive (0.1 eV). Thus, the expansion of the Na layer makes the Na-layer rearrangement more feasible. Simultaneous Na-layer rearrangement and expansion is likely with a 2% relative probability at room temperature, in the absence of a water molecule. Finally, the insertion of water dramatically lowers the system energy. This indicates that Na-layer rearrangement is favored when the water molecule is present. The small values of E1 and E2 terms for the O3-NMNO term in the first place allow for the H-bond formation and charge transfer to compensate for the energy penalties associated with the Na-layer rearrangement. This suggests that the quantity E1 + E2 should be investigated for other systems.
Suppose the path were to involve Na-layer expansion as the first step, followed by Na-layer rearrangement, the respective energy changes for each step are 0.3 eV and −0.2 eV. The numbers have changed since this path entails a different set of constraints. However, E1 + E2 remains unchanged. We shall follow the sequence of steps mentioned in Scheme 1.
For the NTNO system, the corresponding E1 and E2 terms are +1.68 and +0.63 eV. Thus, a large energy penalty is involved for Na-layer rearrangement and expansion of the Na layer. Hydrogen bond formation cannot compensate for the energy penalty E1 + E2.
S. no. | Systems | E 1 (eV) | E 2 (eV) | E 1 + E2 (eV) | ΔE (eV) | Average displacement (Å) | |
---|---|---|---|---|---|---|---|
1 | O3-Na7Mn6Ni6O24 | 0.50 | −0.40 | 0.1 | −1.1 | Structure 1–3 | 2.43, 0.54, 1.12 |
2 | O3-Na7Mn5TiNi6O24 | 0.56 | 0.23 | 0.79 | −0.99 | Structure 1–3 | 1.98, 0.34, 1.04 |
3 | O3-Na7Mn4Ti2Ni6O24 | 0.63 | 0.41 | 1.04 | −0.48 | Structure 1–3 | 2.02, 0.29, 1.13 |
4 | O3-Na7Mn3Ti3Ni6O24 | 1.13 | 0.56 | 1.69 | 0.15 | Structure 1–3 | 2.04, 0.45, 1.16 |
5 | O3-Na7Ti6Ni6O24 | 1.68 | 0.63 | 2.31 | 0.9 | Structure 1–3 | 2.50, 0.53, 0.97 |
In bulk Na vacancy based O3-NMNO/NTNO materials, no Na rearrangement was observed upon water insertion. Significant disruption is possible only at/near the surface. Therefore, we speculate that as more water is inserted, the surface Na layers increasingly become more disrupted before water insertion proceeds into the interior of the material. This follows the experimental results for O3-NaNi0.5Mn0.5O2 in which water insertion leads to the destruction of the structure via extraction of Na+-ions and insertion of H2O molecules.17 NTNO is stable because the onset of water incorporation is relatively more difficult than NMNO.
To demonstrate the effect of Cu-doping, slab systems with chemical formulae Na7Mn5Ti1Ni5CuO24, Na7Mn4Ti2Ni5CuO24 and Na7Mn3Ti3Ni5CuO24 are considered. Table 2 shows the E1 and E2 values. In these systems, only one Ni ion is replaced by Cu, while Mn ions are sequentially replaced with Ti. Ease of water insertion now follows the trend O3-Na7Mn5Ti1Ni5CuO24 (ΔE = −1.08 eV for structure 1) > O3-Na7Mn4Ti2Ni5CuO24 (−1.05 eV) > O3-Na7Mn3Ti3Ni5CuO24 (0.79 eV).
S. no. | Systems | E 1 (eV) | E 2 (eV) | E 1 + E2 (eV) | ΔE (eV) | Average displacement (Å) | |
---|---|---|---|---|---|---|---|
1 | O3-Na7Mn5Ti1Ni5CuO24 | 0.58 | −0.36 | 0.22 | −1.08 | Structure 1–3 | 2.01, 0.48, 1.26 |
2 | O3-Na7Mn4Ti2Ni5CuO24 | 0.89 | 0.28 | 1.17 | −1.05 | Structure 1–3 | 1.98, 0.34, 1.13 |
3 | O3-Na7Mn3Ti3Ni5CuO24 | 1.10 | 0.53 | 1.63 | 0.79 | Structure 1–3 | 2.08, 0.45, 1.16 |
The addition of Cu can sometimes make water insertion more unfavorable, but not always (see purple arrows in Fig. 3, which show the effect of Cu doping). For instance, water insertion in Na7Mn4Ti2Ni5CuO24 and Na7Mn5Ti1Ni5CuO24 is in fact more favorable to the Na7Mn4Ti2Ni6O24 and Na7Mn5Ti1Ni6O24 structures. Using the computed ΔE, we predict that the ratio Mn:
Ti = 5
:
1 and 2
:
1 provides 2 and 7 times more air stability compared to NMNO at 300 K, whereas Mn
:
Ti = 1
:
1 will be ∼1031 times more stable. Experimentally, a Mn
:
Ti ratio of 4
:
1 has been found to be 20 times more stable compared to NMNO.16
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Fig. 3 Trends for ΔE vs. Na-layer spacing. Water insertion is energetically favored when ΔE is negative, i.e., in the blue-shaded region. |
To highlight that the correlation between the Na layer spacing and ΔE is weak, we compare the ΔE vs. Na layer spacing curves for Cu-free and Cu-containing systems in Fig. 3. The two curves do not overlap. This implies that for a given value of ΔE, e.g., ΔE = 0 there can be one Na layer spacing for the Cu-free system and a different one for the Cu-containing system. Moreover, the effect of replacing one Ni ion with a Cu ion sometimes causes the spacing to increase (from Na7Mn5Ti1Ni6O24 to Na7Mn5Ti1Ni5Cu1O24) and at other times the spacing to decrease (e.g., Na7Mn4Ti2Ni6O24 to Na7Mn4Ti2Ni5Cu1O24). The purple arrows/rounded rectangles in Fig. 3 show the direction of the change. Here, the Mn:
Ti ratio is kept fixed. Thus, Na layer spacing is not an appropriate descriptor for the water–material interactions.
Results for structures in Table 2 are provided in Fig. S8–S10 of the ESI.† Quantities like the Na-layer spacing are found to depend on the water orientation. In particular, we ask the question why Cu-doping in O3-Na7Mn3Ti3Ni6O24 (to yield O3-Na7Mn3Ti3Ni5Cu1O24) results in substantially higher ΔE values (from 0.15 eV without Cu to 0.79 eV with Cu present). Tables 1 and 2 show the E1 and E2. Upon doping, E1 decreases marginally from 1.13 to 1.1 eV, and E2 decreases from 0.56 to 0.53 eV. Thus, the E1 + E2 values are nearly the same with and without Cu doping. Fig. S7 and S10† show the corresponding water-inserted relaxed structures, which reveal that the charge on atoms remains nearly identical with and without Cu doping. This leaves the water–material interaction, which we conclude is weaker once Cu is introduced into Na7Mn3Ti3Ni6O24 making water insertion less favorable. We predict that trends for hydrogen bond formation are Mn > Mn,Ti > Mn,Ti,Cu > Ti.
These observations underscore the point made earlier in the introduction that directly probing the water–material interactions provides a more complete picture than the water-free material structure. Thus, our DFT-based strategy can be used for predicting the air/water stability of Na-based layered transition metal oxides and to screen dopant species for the sodium-ion battery cathode materials. The ideas presented here can be of broader interest. Overall, this approach can be used to explore other sodium-ion battery cathode materials as well, such as polyanionic compounds, Prussian blue compounds, and P2-type metal oxides.
Finally, if the goal is to simulate the complete water attack on a promising cathode material, the energetics (and the kinetics) of adsorption, Na extraction, water hopping events, etc., will have to be considered. However, performing such calculations for a range of materials is going to be significantly resource intensive.
Footnote |
† Electronic supplementary information (ESI) available: Figures and tables providing additional details on the NaTmxNi1−-xO2 configurations studied with density functional theory. See DOI: https://doi.org/10.1039/d5qi00892a |
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