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High-Throughput Evaluation of Discharge Profiles of Nickel Substitution in LiNiO2 by Ab Initio Calculations

Cite this: J. Phys. Chem. C 2021, 125, 27, 14517–14524
Publication Date (Web):July 2, 2021
https://doi.org/10.1021/acs.jpcc.0c11589

Copyright © 2021 The Authors. Published by American Chemical Society. This publication is licensed under

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Abstract

Substitution of a Ni cation in a LiNiO2 cathode is a common strategy for improving the lifetime and thermal stability of lithium-ion batteries. However, this strategy does not improve the discharging capacity more than that of pristine LiNiO2. We investigated whether the capacity of a cation-substituted battery can be improved by an exhaustive search based on ab initio calculations. To ensure a feasible search at a practical computational cost, many data points obtained by expensive ab initio calculations were bridged by interpolation using the cluster expansion method. Then, the candidates screened by the search were analyzed by more reliable calculations based on density functional theory with the strongly constrained and appropriately normed (SCAN) exchange–correlation functional, which determines the discharging voltage profiles. The screening predicted that partial substitution of Ni with Pt and Pd can improve the discharging capacity of a lithium-ion battery.

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1.. Introduction

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As the shift from gasoline to electric vehicles continues, the demand for lithium-ion batteries (LIBs) for electric and hybrid vehicles also increases. A battery consists of a cathode, an anode, an electrolyte, and a separator. A proper cathode material is essential for ensuring battery performance. The current circulating cathode materials LiNiO2, LiCoO2, and ternary LiNi1/3Mn1/3Co1/3O2 have their merits and demerits. For example, LiNiO2 achieves a large discharge capacity at a lower cost than LiCoO2; however, it has low chemical stability. (1−7)
Capacity improvement has largely motivated the recent development of cathode materials with higher Ni content. The research focus has now shifted to enhancing the thermal stability and lifetime of LiNiO2. Industrially, these improvements have been achieved using surface coating techniques and fine-tuning of the composition ratio with atomic substitutions. Atomic substitution has been a promising strategy for improving the battery properties. An example is an industrial product, lithium nickel cobalt aluminum oxides (NCA), where the lifetime is extended by partial substitution of Ni with Co and Al. (8−13) Partial Ni substitution with Co reportedly suppresses the undesirable structural transition in LiNiO2, whereas partial substitutions with Mg and Al reportedly extend the lifetime and improve the thermal stability of LiNiO2. (14,15) These tunings lower the battery capacity from that of pristine LiNiO2, indicating a tradeoff between battery capacity and other desirable properties. Because battery materials are used in automobiles, computers, smartphones, etc., the required properties vary depending on the application; however, the most important characteristics are considered to be discharge capacity, cycle characteristics, and thermal stability. From an industrial perspective, the cost and ease of production are added to these characteristics.
Efforts to search for substitution elements have been made for a long time, and in addition to Co and Al substitution, examples of Ni substitution with Ga, (16) Ti, and Mg (17) and Fe substitution (18,19) have been reported. Recently, a study on the substitution of Ni with Cu has been reported. (20) However, these are the results of individual synthesis and evaluation by different research groups. Therefore, they have not been systematically evaluated. Systematically evaluating the effects of each substituent experimentally is difficult, and we are forced to rely on computational science at present.
Exhaustive searching for preferred substitution is a problem that led to the use of computer simulation, as one of the representative forms of Materials Informatics (MI). (21−25) Several research groups have used MI to investigate the LIB performances. (26−30)
As an example of an exhaustive calculation, Ceder et al. comprehensively evaluated the voltage and stability of various cathode materials using first-principles calculations. (26) As an example of the search for substitutional elements, Nishijima et al. used first-principles calculations to comprehensively and systematically evaluate the volume change of LiFePO4 during charging and discharging and proposed substitutional elements that improve the cycle characteristics. (27) In addition, Ullah et al. have reviewed research on cathode materials using first-principles calculations. (31) Recently, there have been reports of more efficient searches using information science, such as the search for ionic conductors for all-solid-state batteries using a combination of Bayesian optimization and first-principles calculations. (32)
In LiNiO2, which is the target of this study, Yoshida et al. also reported an improvement in the lifetime of LiNiO2 using ab initio-based MI approaches. (29,30)
The abovementioned tradeoff indicates that we should reserve taking such predictions since they may reduce the battery capacity. Even though discharge capacity and voltage are more fundamental requirements of battery materials compared to cycle characteristics and thermal stability, no MI analysis for the properties is available to the best of our knowledge. The reason might be a higher computational cost for estimating the discharge capacity as explained below.
The discharge capacity can be estimated from the discharge profile (voltage change during the charging/discharging process). For LIBs, the profile is the dependence of the discharge voltage on the amount of Li in the battery. Dompablo et al. presented the profile of pristine LiNiO2 but not those of partially substituted variants. (33)
With their computational conditions, the profile was underestimated by approximately 0.5 V compared to experimental values.
Dixit et al. presented the profiles of Al-substituted NCM-523 (LiNi0.5Co0.2Mn0.3O2) with different Al ratios (approximately 50% of the Ni concentration). (34)
The study was within the limited scope of Al substitution only, not for the wider search.
Chakraborty et al. evaluated the profile using the strongly constrained and appropriately normed (SCAN) exchange–correlation functional. (35,36) By applying density functional theory (DFT) to a couple of pristine materials with simple crystal structures, LiNiO2, LiCoO2, and LiMnO2, they showed that LiNiO2 produces a lower discharge voltage than LiCoO2. (37)
Although SCAN–DFT ensures a reliable voltage prediction, it has a high computational cost. Thus, it is inappropriate for naive exhaustive searching.
According to Yan et al., the capacity can be improved by the anionic substitution of O with S. (38) This possibility is interesting, but cationic substitutions are more feasible; thus, they are commonly investigated in industries.
This study performs an exhaustive search for the cation substitution that improves the discharging capacity, which, as mentioned above, has been underinvestigated. We partially substituted Ni of LiNiO2 with other cations and evaluated the discharging profiles of the resulting materials in ab initio DFT calculations. We combined the cluster expansion method and DFT calculations to ensure the feasibility of exhaustive screening. Over a selected range of concentrations, we obtained the data using relatively inexpensive DFT called generalized gradient approximation (GGA) to the exchange–correlation functional (GGA–DFT). As described below, we fitted the GGA–DFT energy data to the cluster expansion form, where their fitting parameters were determined using the LASSO regression. The expansion interpolates over the range of concentrations, facilitating the evaluation of the discharging profiles. Through this computationally inexpensive evaluation of the profiles, we screened a limited number of candidates for the desired properties. Then, the voltage profiles of the selected candidates evaluated by SCAN–DFT were compared with the actual voltage profiles.

2. Methods

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The substitution of Li12Ni11XO24 was performed in a 2 × 2 × 1 supercell of conventional cells (LiNiO2)3 (Figure 1) with a portion of the Ni sites replaced with 35 different cations X(Ni/X = 11:1): X = Al, Sc, Ti, V, Cr, Mn, Fe, Co, Cu, Zn, Ga, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, and Bi.

Figure 1

Figure 1. 2 × 2 × 1 supercell of pristine LiNiO2 with Rm space group symmetry.

Since all the Ni sites are spatially equivalent, we can select a Ni site to be replaced by X without losing the generality of the modeling. To make deficiencies of Li sites (to describe discharged states), each structure with deficiencies may exhibit inequivalent spatial symmetry. The possible spatial configurations of Li vacancies in the 2 × 2 × 1 supercell (Li12–nNi11XO24; n = 0,..., 12), corresponding to LixNi11/12X1/12O2 (x = 0.00, 0.08, 0.16,..., 1.00), were finally sorted into 536 inequivalent structures based on group theory.
Ohzuku et al. synthesized Al-substituted materials with about 25% Al. (9) Yoshida et al. performed ab initio screening of Nb-substituted materials with improved charge–discharge cycle performance. (29) For comparison with these cases, we conducted full GGA–DFT calculations of the 536 structures.
Each structure is relaxed by the structural optimization to obtain different spatial symmetries from the original Rm.
GGA–DFT calculations of the other 33 cations were performed only on 102 structures with structural optimizations at both limits of the Li concentration range (0 < x < 0.25 and 0.75 < x < 1). The results over the remaining range were interpolated by cluster expansion, as explained later.
The ab initio DFT calculations were conducted in VASP. (39−42) In all calculations, the energy cutoff for the plane-wave basis set expansion was selected as Ecut = 648 eV. Each atom was described in the projector augmented wave pseudopotential framework, Li(1s,2s), Ni(3d,4s), and O(2s,2p) (where the orbitals in parentheses were treated as valence electrons). For each X, we used the core/valence separations recommended in VASP.
Since the present system has localized spin polarizations, the choice of the exchange–correlation functionals XC should be carefully considered. For the final quantitative predictions, we used the SCAN functional (35,36) because of its improved capability of handling the localized states. SCAN has been used in several studies on LIBs. Thus, it is convenient for quantitative comparison to calibrate the reliability. As explained in the Section 1., we used faster GGA for the prescreening in the Perdew–Burke–Ernzerhof scheme. (43) For both SCAN and GGA, we conducted spin-polarized calculations by putting the initial guess for the spin magnitude by +μB, as naively expected for pristine LiNiO2.
Each of the substituent structures was relaxed by geometrical optimization until the forces at all atomic sites were less than 0.02 eV/Å. The optimization identifies the lowest possible ground-state energy at each concentration x of the substituent. From the concentration dependence of the lowest ground-state energy, we can evaluate the following quantity
(1)
where e is an elementary charge.
From this expression, we can approximate the discharging voltage as a discretized function of x (discharging profile). (44) In our 2 × 2 × 1 supercell model of Li12Ni11XO24, the increase Δx is 0.08.
The cluster expansion was interpolated using the ICET package. (45) In the expansion, (46,47) the occupations at site i are denoted by the following Ising variables: σiLi = +1 (Li), σiLi = −1 (Vac), σiNi = +1 (Ni), and σiNi = −1 (X). In terms of these variables, the energy is expressed as follows
(2)
The pair-wise summation for pair (i, j) is performed only within the range |ij| < Lc. The cutoff lengths Lc(2) and Lc(3) of the second- (two-body) and third-order (three-body) terms with respect to the Ising variable, respectively, are introduced as hyperparameters to the model. In a previous study of LiNiO2, (33) this method was conducted with a single Ising variable, σi(Li). This study extends this method to two components. The expansion parameters {V0, Viα, Vijα,β,...} were determined by the LASSO regression (48) of the training data obtained by GGA–DFT calculations. The regulation term was parametrized by λ, and the intensity of λ was determined using cross-validation.

3. Results and Discussion

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Figure 2 shows the ground-state energies of the substituents over the range of concentrations x (536 structures). The graph appears as a convex hull. Here, the energies were shifted by a chemical potential to produce zero at x= 0 and 1. At each concentration, different configurations of the substituting cations produced structures with different space groups.

Figure 2

Figure 2. Plot of geometrically optimized ground-state energies over the concentration range of substituents (total of 536 structures) evaluated by GGA–DFT. Energy values are given per unit cell of LixNi11/12Al1/12O2.

After geometrically optimizing each structure, we obtained the concentration dependence of the lowest possible energy (Figure 3) using eq 1.

Figure 3

Figure 3. Discharging profiles [GGA–DFT] of the pristine material (black) and substituents X = Al (red) and Nb (blue), evaluated using eq 1 with the corresponding unit conversion to V.

Unlike the profiles of pristine LiNiO2 and the X = Nb substituent, the profile of the X = Al substituent declined much more steeply from x = 0 to 0.5 than from x = 0.5 to 1. These trend differences can be attributed to different cationic values of the X = Al and Nb substituents. During the charging process x → 0 (elimination of Li), the valence of Ni changes as the system transforms from Li12Ni11XO24 (x = 1) → Li1Ni11XO24 (x = 0 + Δx) → Li0Ni11XO24 (x = 0). In X = Al (+3 valence), all Ni sites possessed a valence number of +4 at x = 0 + Δx (Li1Ni11XO24). In X = Nb (+5 valence) at x = 0 + Δx, two Ni sites were in the +3 valence state. During charging, (x = 0 + Δx) → (x = 0), the required valence change in X = Nb can be accommodated by the two valence 3 sites to some extent, but in X = Al, no such accommodation is possible and the valence changes require a higher energy input.
The discharge profile of X = Al at x > 0.2 (red line in Figure 3) was predicted to behave almost identically to that of the pristine material, which is consistent with experimental observations of LiNi0.75Al0.25O2. (9) Due to systematic underestimation by GGA–DFT, the predicted voltage in Figure 3 is lower than the observed value (4 V). This quantitative discrepancy can be eliminated by replacing the conventional GGA with the SCAN exchange–correlation functionals. (37) This refinement is performed after screening all combinations through cheaper GGA–DFT.
From the optimized structures obtained at each concentration (Figure 2), we can predict the sites where Li is most easily extracted by discharging. At x = 0.75 (Li9Ni12O24), one Li was extracted from each Li layer (see Figure 1). At x = 0.5 (Li6Ni12O24) and x = 0.25 (Li3Ni12O24), equal numbers of Li ions were extracted from each Li layer. The same trend was observed in the X = Al and Nb substituents. Besides, Li ions were more easily extracted from the most distant Li layer (relative to the substituted cation) than from closer layers. It means that the Li ions distant from a substituent contributed more to the charging/discharging process than those close to the substituents.
In the cluster expansion, (46,47) we fitted 102 structures at the charging side (0 < x < 0.25) and another 102 structures at the discharging side (0.75 < x < 1). The number of Li ions on the charging and discharging sides are 0–3, and 9–12, respectively, and the values of charging and discharging are simply calculated from the amount of Li. The 434 structures in the mid-range of x were then obtained by interpolation. The entire 536 GGA–DFT data sets for X = Al and Nb were divided into 102 and 434 for training and test data, respectively. The test data were reserved for validation. The expansion given by eq 2 includes the cutoff lengths as hyperparameters, which were determined from the X = Al and Nb data as follows. For different cutoff lengths, the interpolation performance was determined using the root-mean-square error (RMSE) of the test data. The results are shown in Tables 1 and 3. When the expansion was truncated to the second order (Table 1), the RMSE was ∼0.017 eV/unit cell at Lc(2) > 6 Å. With this range of Lc(2), third-order expansions were investigated for different choices of (Lc(2), Lc(3); see Tables 23). The RSME reached ∼0.017 eV/unit cell at (Lc(2), Lc(3)) = (6, 6) Å for both X = Al and Nb. After setting the cutoff lengths to these values, the expansion involved two one-body terms, 13 two-body terms (including three interacting terms between σLi and σNi), and 56 three-body terms (including 36 interacting terms between σLi and σNi).
Table 1. RMSEs of the Interpolation by the Second-Order-Truncated Cluster Expansion for Different Cutoff Lengths Lc(2)a
Lc(2)[Å]4681012
X = Al
train data (RMSE)0.0310.0160.0160.0160.015
test data (RMSE)0.0260.0200.0190.0190.019
X = Nb
train data (RMSE)0.0200.0110.0110.0110.011
test data (RMSE)0.0200.0160.0160.0150.016
a

Values are given in the unit of eV/unit cell.

Table 2. RMSE of the Interpolation by the Third-Order-Truncated Cluster Expansion for Different Cutoff Lengths Lc(2) and Lc(3)a
(Lc(2), Lc(3)) [Å](6,4)(6,6)(6,8)(8,4)(8,6)(8,8)
X = Al
train data (RMSE)0.0130.0060.0060.0130.0060.006
test data (RMSE)0.0190.0170.0170.0190.0170.017
X = Nb
train data (RMSE)0.0090.0060.0060.0090.0060.006
test data (RMSE)0.0160.0120.0120.0160.0130.012
a

Values are given in the unit of eV/unit cell.

Table 3. ΔG Evaluated by eq 3 to Measure the Stability of Li12Ni11/ 12X1/12O2a
XΔG (eV)
Ti0.71
Ta1.08
Tc0.55
V0.52
Nb0.92
Cr0.50
Hf0.99
Fe0.26
Pd–0.12
Pt–0.01
Al0.27
a

The value for Al (0.27 eV) can be the reference where the compound can actually be composed.

Under the above conditions, the data were interpolated in the intermediate range (0.25 < x < 0.75). The test data of X = Al and Nb were consistent with the full GGA–DFT results, as shown in Figure 4. For the other 35 cations X, the GGA–DFT evaluations were conducted at the edges only (i.e., at x > 0.25 and x < 0.75) to parametrize the cluster expansion. The parametrized energy data can be input to Monte Carlo simulations within a finite temperature range, which runs at a feasible computational cost. Here, the parametrized data were used to obtain zero-temperature discharging profiles and their dependence on the concentration of cation X.

Figure 4

Figure 4. Comparison between the GGA–DFT results (vertical) and the interpolated results by the cluster expansion (horizontal) assuming the ground-state energy of X = Al (the results for X = Nb are provided in the SI).

The formation energy of Li12Ni11XO24 with 35 substitution elements including Al and Nb is negative. To calculate the stability of the substituted structure more realistically, evaluating the solid solubility from the energy difference with LiNiO2 is necessary. We will show a simple evaluation result later. Figure 5 shows the discharging profiles of the selected cations evaluated by the cluster expansion based on GGA–DFT (the profiles of all cations are provided in the SI). From these profiles, we can identify the cation(s) X that achieve(s) the desired properties: (i) maximum voltage at the discharging limit (x ∼ 1) and (ii) minimum voltage at the charging limit (x → 0). Property (ii) is an important measure of the discharging capacity. Above some cutoff voltage VC = 4.3 V, the Li ions cannot contribute to the discharge process (physically, this restriction is imposed by electrolyte limitations). (49,50) Thus, lowering the voltage of property (ii) increases the number of Li ions participating in the discharge, enlarging the discharging capacity.

Figure 5

Figure 5. Discharging profiles of the selected cation substituents and pristine LixNiO2 (“ref”) evaluated by the cluster expansion based on GGA–DFT. The minimum voltage at the charging limit is determined at x = 0.15 (vertical black dashed line).

For a more quantitatively reliable comparison of the voltage with VC, GGA–DFT is not a proper choice since it gives the underestimation of the voltage. (33,44) SCAN–DFT is known to provide reliable estimations for this purpose; (35,36) however, it is computationally expensive. To avoid these problems, we implemented the following procedure: (a) applying the relatively inexpensive [(GGA–DFT) + (cluster expansion)] method and selecting suitable candidates for the preferred cation X (Figure 5); (b) selecting the energetically stable structures (three structures from the lowest one) at each concentration x; and (c) applying SCAN–DFT to the candidates with limited structures to obtain quantitatively reliable profiles.
One might worry that the accuracy of the prescreening using the cluster expansion might be too coarse to narrow down the possible structures. Figure 6 shows the histogram of the structures distributing over the energy range estimated by GGA (horizontal axis), at x = 0.5, where the number of spatially inequivalent structures attains a maximum. The vertical axis counts the number of structures appearing in the energy range (ΔE = 0.1 eV/unit cell). Within the accuracy range (0.017 eV/unit cell) from the lowest energy structure, we observed that only five structures are included, ensuring the accuracy being enough for the prescreening of structures.

Figure 6

Figure 6. Histogram of the structures distributing over the energy range estimated by GGA (horizontal axis), at x = 0.5 (Li0.5Ni11/12Al1/12O2), where the number of spatially inequivalent structures attains a maximum. It corresponds to the histogram of the point at x = 0.5 in Figure 2, and the reference energy is the same as in Figure 2. The vertical axis counts the number of structures appearing in each energy span (ΔE = 0.1 eV/unit cell). The three structures with the lowest energy predicted by the cluster expansion method are shown in red.

After screening for property (i) in Figure 5, the candidates were identified as X = Ti, Ta, Tc, V, Nb, Cr, Hf, and Fe. The profiles of these candidates were obtained using SCAN–DFT and are shown in Figure 7. The voltage of pristine LixNi12O24 was predicted to reach VC at x = 0.25. This result is consistent with the experimental results, which reported that approximately 75% of the Li contributed to the discharge in this material. (3,9) Therefore, the quantitative reliability of our prediction can be asserted with reasonable confidence. As clarified in Figure 7, all of the selected candidates yielded a higher voltage at the discharging edge (x → 1) than pristine LixNi12O24. The increase ranged from 0.1 to 0.2 V.

Figure 7

Figure 7. (a) Discharging profiles of the candidates screened for the maximum voltage at the discharging limit (x ∼ 1) evaluated by SCAN–DFT and that of pristine LixNiO2 (“ref”) for comparison. (b) Discharge voltages of x = 0, 0.25, 0.50, and 0.75 for each element extracted and arranged for better visibility.

When screening for property (ii), we considered the voltages of the candidates at x = 0.15. The results are shown in Figure 8. Candidates X = Pt and Pd achieved lower voltage (i.e., higher discharging capacity) than pristine LixNiO2 (black bar in the figure). Interestingly, the predicted capacity of X = Co (red bar in the figure) was lower (i.e., higher voltage) than Mn and other popular substituents. This result was unexpected because LiCoO2 is a popular choice for cathode materials. In particular, the reaction Co3+ → Co4+ in this species contributes to the charging capacity. The discharging profiles of the X = Pt and Pd candidates, estimated by SCAN–DFT, are shown in Figure 10. Revising the predicted voltage around x = 0.15, we find that the cation substitution suppressed the discharge voltage by approximately 0.1 V from that of pristine LixNiO2, implying an enhancement of the discharging capacity. From Figure 8, we find that Re, Os, and Au also improved the capacity (in that order), implying that 5d transition metals are the preferred candidates for high-capacity batteries. However, the 5d transition metals shown here are expensive, and putting them to practical use industrially would be difficult even if they contribute to higher capacity. Finding an alternative way to achieve the same effect with a smaller amount of substitution, substitution of multiple elements, and anion substitution is necessary.

Figure 8

Figure 8. Discharging voltages at x = 0.15 (charging edge) evaluated by [(GGA–DFT) + (cluster expansion)]. Black and red bars are the results of pristine LixNiO2 (“ref”) and the X = Co candidate, respectively. Blue bars are eye guides appearing at five-bar intervals. Left to right: Pt, Pd, ref, Re, Os, Au (blue), Fe, Mn, V, Tc, Bi (blue), Mo, Ir, Ti, W, Co (red), Nb, Cr, Rh, Pb, Sn (blue), Ag, Ta, Cu, Hf, Zr (blue), Al, Zn, Ga, Tl, In (blue), Sc, Ru, Yu, Hg, and Cd (blue).

The charging/discharging voltage scales with the difference between the Fermi energy and anode level; an anion substitution can shift up/down the Fermi level and then reduce/increase the voltage. For example, LiNi(O,S)2 has a energetically higher Fermi surface than the pristine LiNiO2 because the 3p level of S is higher than the 2p of O; the higher Fermi surface reduces the voltage.38 When substituting O in LiNiO2 by S, the voltage is reduced, which is explained by the 3p level of S being energetically higher than 2p of O, pushing up the Fermi surface. (38) The reason for Pt or Pd substitution to suppress the voltage at the charging edge (property (ii)) may be attributed to a similar mechanism: in the present system, the Ni d orbital is the main constituent of the Fermi level. Since Pt and Pd d orbitals have higher levels than that of Ni, the substitution leads to the pushing up of the Fermi level and causes the voltage to decrease. On the other hand, for the voltage at the discharging edge [property (i)], such a discussion does not work since the d levels of the candidate substituents, X = Ti, Ta, Tc, V, Nb, Cr, Hf, and Fe, are not so different from that of Ni. Rather than such an effect due to the electronic structure, other factors such as structural relaxation would be more relevant for the shift of the voltage as implied (Figure 9).

Figure 9

Figure 9. Discharging profiles of the candidates screened for preference (ii), estimated by SCAN–DFT. The result of pristine LixNiO2 (“ref”) is shown for comparison. The horizontal red dashed line shows the voltage VC above which the electrolyte begins to decompose. The minimum voltage at the charging limit is determined at x = 0.15 (vertical black dashed line).

To investigate the reason for the high discharge voltage of these elements for 0.75 < x < 1, the bond distances between Ni–O and X–O were investigated for the structure of x = 1. Since there are 11 atoms of Ni, the average distance to the nearest six-coordinated oxygen was calculated for all 11 atoms. The results are shown in Figure 10. The difference between the shortest and the longest average distances to the oxygen of the 11 Ni atoms (vertical axis of the figure) is large for these substitution elements, except for Fe. In other words, these substitutional elements can be understood to exert a small strain on the Ni atoms. It can be interpreted that when Li is extracted, the strain proceeds in the direction of relaxation, resulting in a larger energy gain and an increase in the voltage. In other words, the improvement of the discharge voltage for 0.75 < x < 1 by these substitution elements can be attributed to the energy gain due to structural relaxation.

Figure 10

Figure 10. Plot of the bond distances between Ni–O and X–O at x = 1 for 35 substitution elements. The horizontal axis is the average distance between substituent X and six-coordinated oxygen, and the vertical axis is the difference between the maximum and minimum distances calculated for 11 Ni atoms. The red color indicates “Ti”, “Ta”, “Tc”, “V”, “Nb”, “Cr”, “Hf”, and “Fe”, and the difference between the maximum and minimum values is large except for Fe.

As the final screening, we examine the solid solution stability of the candidates as proposed so far by evaluating
(3)
By taking XxOy as the compounds known as stable oxides such as TiO2, Ta2O3, TcO2, V2O3, Nb2O3, Cr2O3, HfO2, PtO2, and PdO, the quantity ΔG can measure how difficult it is to form the solid solution with X. The evaluated values are shown in Table 3. The value for Al (0.27 eV) can be the reference where the compound can relatively easily be composed. (9) Compared to the reference, we would exclude the candidates X = Ta, Nb, and Hf giving higher ΔG.

4.. Conclusions

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We performed an exhaustive screening of cation X that can partially replace Ni in the LiNiO2-based cathodes of lithium-ion batteries. The selected substituent should enhance the discharging properties (that is, improve the capacity and durability against the voltage drop at the discharging edge) of the cathode. The screening was realized by ab initio evaluations of the discharging profiles (dependence of discharge voltage on Li concentration). To save the computational cost, we reduced the number of data points obtained by GGA–DFT calculations using cluster expansion interpolation. The limited number of candidates obtained by screening were more comprehensively evaluated in full ab initio calculations using the SCAN–DFT method. The resulting profiles were quantitatively consistent with known experimental data. The screening predicted that (i) substituents X = Tc, V, Cr, and Fe suppressed the voltage drop at the discharging edge and (ii) X = Pt, Pd enhanced the discharging capacity.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcc.0c11589.

  • Energy and convex hull of X = Nb calculated by GGA–DFT (corresponding to X = Nb in Figure 2); comparison between cluster expansion method and GGA–DFT for X = Nb (corresponding to X = Nb in Figure 4); discharge profiles obtained by interpolation with the cluster expansion method for 35 substitution elements; energy values calculated by GGA–DFT for the structure in the 0 < x < 0.25, 0.75 < x < 1 region of LiNi11/12X1/12O2; coefficients of the cluster expansion for Li12Ni11AlO24 and Li12Ni11NbO24 (PDF)

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Author Information

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Acknowledgments

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The computations in this work were mainly performed using the facilities of the Research Center for Advanced Computing Infrastructure at the Japan Advanced Institute of Science and Technology (JAIST). S.Y. would like to thank T. Y. and Y. Y. for their fruitful discussions and technical support. K.H. is grateful for financial support from the HPCI System Research Project (Project ID: hp190169) and MEXT-KAKENHI (JP16H06439, JP17K17762, JP19K05029, and JP19H05169). R.M. is grateful for financial support from MEXT-KAKENHI (JP19H04692 and JP16KK0097), FLAGSHIP2020 (Project Nos. hp190169 and hp190167 at K-computer), the Air Force Office of Scientific Research (AFOSR-AOARD/FA2386-17-1-4049; FA2386-19-1-4015), and JSPS Bilateral Joint Projects (with India DST).

References

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  • Abstract

    Figure 1

    Figure 1. 2 × 2 × 1 supercell of pristine LiNiO2 with Rm space group symmetry.

    Figure 2

    Figure 2. Plot of geometrically optimized ground-state energies over the concentration range of substituents (total of 536 structures) evaluated by GGA–DFT. Energy values are given per unit cell of LixNi11/12Al1/12O2.

    Figure 3

    Figure 3. Discharging profiles [GGA–DFT] of the pristine material (black) and substituents X = Al (red) and Nb (blue), evaluated using eq 1 with the corresponding unit conversion to V.

    Figure 4

    Figure 4. Comparison between the GGA–DFT results (vertical) and the interpolated results by the cluster expansion (horizontal) assuming the ground-state energy of X = Al (the results for X = Nb are provided in the SI).

    Figure 5

    Figure 5. Discharging profiles of the selected cation substituents and pristine LixNiO2 (“ref”) evaluated by the cluster expansion based on GGA–DFT. The minimum voltage at the charging limit is determined at x = 0.15 (vertical black dashed line).

    Figure 6

    Figure 6. Histogram of the structures distributing over the energy range estimated by GGA (horizontal axis), at x = 0.5 (Li0.5Ni11/12Al1/12O2), where the number of spatially inequivalent structures attains a maximum. It corresponds to the histogram of the point at x = 0.5 in Figure 2, and the reference energy is the same as in Figure 2. The vertical axis counts the number of structures appearing in each energy span (ΔE = 0.1 eV/unit cell). The three structures with the lowest energy predicted by the cluster expansion method are shown in red.

    Figure 7

    Figure 7. (a) Discharging profiles of the candidates screened for the maximum voltage at the discharging limit (x ∼ 1) evaluated by SCAN–DFT and that of pristine LixNiO2 (“ref”) for comparison. (b) Discharge voltages of x = 0, 0.25, 0.50, and 0.75 for each element extracted and arranged for better visibility.

    Figure 8

    Figure 8. Discharging voltages at x = 0.15 (charging edge) evaluated by [(GGA–DFT) + (cluster expansion)]. Black and red bars are the results of pristine LixNiO2 (“ref”) and the X = Co candidate, respectively. Blue bars are eye guides appearing at five-bar intervals. Left to right: Pt, Pd, ref, Re, Os, Au (blue), Fe, Mn, V, Tc, Bi (blue), Mo, Ir, Ti, W, Co (red), Nb, Cr, Rh, Pb, Sn (blue), Ag, Ta, Cu, Hf, Zr (blue), Al, Zn, Ga, Tl, In (blue), Sc, Ru, Yu, Hg, and Cd (blue).

    Figure 9

    Figure 9. Discharging profiles of the candidates screened for preference (ii), estimated by SCAN–DFT. The result of pristine LixNiO2 (“ref”) is shown for comparison. The horizontal red dashed line shows the voltage VC above which the electrolyte begins to decompose. The minimum voltage at the charging limit is determined at x = 0.15 (vertical black dashed line).

    Figure 10

    Figure 10. Plot of the bond distances between Ni–O and X–O at x = 1 for 35 substitution elements. The horizontal axis is the average distance between substituent X and six-coordinated oxygen, and the vertical axis is the difference between the maximum and minimum distances calculated for 11 Ni atoms. The red color indicates “Ti”, “Ta”, “Tc”, “V”, “Nb”, “Cr”, “Hf”, and “Fe”, and the difference between the maximum and minimum values is large except for Fe.

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    • Energy and convex hull of X = Nb calculated by GGA–DFT (corresponding to X = Nb in Figure 2); comparison between cluster expansion method and GGA–DFT for X = Nb (corresponding to X = Nb in Figure 4); discharge profiles obtained by interpolation with the cluster expansion method for 35 substitution elements; energy values calculated by GGA–DFT for the structure in the 0 < x < 0.25, 0.75 < x < 1 region of LiNi11/12X1/12O2; coefficients of the cluster expansion for Li12Ni11AlO24 and Li12Ni11NbO24 (PDF)


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