First-principles investigation on the structural, electronic properties and diffusion barriers of Mg/Al doped NaCoO₂ as the cathode material of rechargeable sodium batteries

Abstract

Mg/Al doped NaCoO₂ layered transition-metal oxides as potential cathode materials for sodium ion batteries have been investigated by first-principle calculations. The effects of divalent Mg ion or trivalent Al ion doping on the crystal structure, electron transfer, the changes of valence, average intercalation voltage and diffusion barriers of NaCoO₂ are studied. The DFT calculations indicate NaCoO₂ with Mg or Al ions doping will lead to a higher average intercalation voltage, which is beneficial for obtaining high energy density. Charge disproportionation induced by divalent Mg ion doping results in the appearance of electronic holes in Na(Co_0.92Mg_0.08)O₂, which may enhance its conductivity significantly. The nudged elastic band calculation results indicate that trivalent Al ion doping has a slight effect on the diffusion barriers of NaCoO₂, but divalent Mg ion doping can significantly decrease the diffusion barriers and enhance the Na ion diffusion rate, which is beneficial to the improvement of the rate capability.

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1. Introduction

Sodium-ion batteries are the most attractive alternative to lithium-ion batteries for electric vehicle propulsion and renewable electric power storage due to their potential advantages of lower cost and abundance of sodium resources.^1–5 The broad application of sodium-ion batteries will bring about substantial relief and expansion of the existing energy storage market, which is now primarily based on lithium-ion technology. To realize sodium-ion technology, a critical issue is to find suitable host materials that can accommodate sufficient sodium ions for a reversible electrochemical insertion reaction. Similar to the lithium ion cathode materials, layered transition-metal oxides have drawn significant attention as cathode materials in sodium-ion batteries. Although the lithium and sodium ions belong to alkali ions, the chemistry of Na layered cathode materials is expected to be different from their Li analogue. At present, a variety of layered sodium transition-metal oxides Na_xMO₂ (M = Co, Ni, Mn, V, Fe, Cr, etc.) cathode materials have been reported.^6–10 Among them, Na_xCoO₂ was early examined as intercalation hosts of Na ions via chemical sodiation and desodiation¹¹ and it becomes a notable cathode material for sodium-ion batteries at present.^12–16 However, the relatively low average intercalation voltage and poor conductivity limit its wider application. Nevertheless, the heavier atomic mass (Li: 6.9 g mol⁻¹, Na: 23 g mol⁻¹) and larger ionic radius (Li⁺: 0.76 Å, Na⁺: 1.02 Å) of Na ion make it difficult to intercalate and extract from the layered NaCoO₂ crystal. Therefore, the current work is mainly focused on improving the intercalation voltage, electronic conductivity as well as ion mobility which influences the electrochemical performances of sodium ion batteries.

In recent years, metal doping in cathode materials have been reported as one of the most significant method to improve the electrochemical performances of layered transition metal cathode materials.^17–20 In this work, divalence Mg ion or trivalence Al ion doping to NaCoO₂ was simulated by first principles calculations to study the effect of doping ions on its electrochemical properties. The changes of crystal and electronic structure, electron transfer, diffusion barrier of Mg or Al ions doped NaCoO₂ are studied by the calculations of density of states and electron density differences. Furthermore, the detail structural characteristics, average intercalation voltage (AIV), electronic conductivity and ion mobility of Mg or Al ions doped NaCoO₂ were predicted.

2. Computational details

The calculations have been performed using the ab initio total energy and molecular-dynamics program VASP (Vienna ab initio-simulation program) developed at the institute für Materialphysik of the Universität Wien.^21,22 The interactions between valence electrons and ions are described with the projector augmented wave (PAW) pseudo-potentials.²² The Hubbard U parameter is generally used to ascertain the bandgap and band structure of transition metal compound. Besides, the benchmark calculations indicate that the GGA/PBE + U method with U = 4.91 eV for Co-3d electrons taken from the literature²³ results in high-spin magnetic solution to the NaCoO₂ compound, which is in contradictory to previous experimental measurements.²⁴ Though a linear response approach has been proposed to evaluate the effective parameters in the GGA/PBE + U method which could improve the agreement with experiment,^25,26 for simplicity, the present computational study does not include the Hubbard U parameter. The convergence tests of the total energy with respect to the k-points sampling and cut-off energy have been carefully examined, which ensure that the total energy is converged to 10⁻⁵ eV per formula unit. The Monkhorst-Pack²⁷ scheme with 5 × 5 × 2 k-points mesh is used for the integration in the irreducible Brillouin zone. All the calculations are performed in a 12 formula NaCoO₂ supercell. The structure of Mg or Al ions doped NaCoO₂ consists of NaCoO₂ superlattice with the center Co atom substituted by Mg or Al atom as shown in Fig. 1. The stoichiometry of this superlattice cell is Na(Co_0.92M_0.08)O₂(M = Mg, Al). Energy cut-off for the plane waves is 520 eV. Before the calculation of the electronic structure, both the lattice parameters and the ionic position are fully relaxed. The final forces on all relaxed atoms are less than 0.01 eV Å⁻¹. All calculations are performed in a ferromagnetic (FM) ordering since the FM arrangements give lower energies than antiferromagnetic (AFM) arrangement.

Fig. 1 Schematic illustration of the supercell Na(Co_0.92M_0.08)O₂(M = Al or Mg) from NaCoO₂ unit cell: (a) NaCoO₂ unit cell, (b) Na(Co_0.92M_0.08)O₂ supercell.

The nudged elastic band (NEB) method was employed to study the diffusion barriers of Na⁺ migration in Na(Co_0.92M_0.08)O₂(M = Mg, Al) and pristine NaCoO₂ for comparison. The NEB is an efficient method to search the minimum energy pathway and saddle points between the given initial and final positions. It was performed with linear interpolating 11 images between the initial and final configurations of the diffusion paths. The geometry and energy of the images were then relaxed until the largest norm of the force orthogonal to the path is less than 0.02 eV Å⁻¹. Each image searches for its potential lowest energy configuration along the reaction path while maintaining equal distance to nearby images. We investigated the diffusion barrier of Na⁺ migration in Na(Co_0.92M_0.08)O₂(M = Mg, Al) and pristine NaCoO₂ for a divacancy mechanism, as proposed previously by Van der Ven et al. for a dilute vacancy LiCoO₂ and NaCoO₂ supercell.²⁸

3. Results and discussion

3.1 Crystal structures and stability of Mg or Al doped NaCoO₂

The detail lattice parameters of full relaxed Na(Co_0.92Al_0.08)O₂, Na(Co_0.92Mg_0.08)O₂ and NaCoO₂ are shown in Table 1. It can be seen that the change in value of lattice parameter a of Mg or Al doped NaCoO₂ are 0.17% and −0.19%, respectively, which is caused by the ionic radius differences of Mg²⁺, Al³⁺ and Co³⁺(r_Mg²⁺ = 0.72 Å, r_Co³⁺ = 0.55 Å, r_Al³⁺ = 0.54 Å). However, the lattice parameters c of Mg and Al doped NaCoO₂ both increase about 0.43%. These should be related to the differences between the electronic structures of Co, Mg and Al. There exist empty Mg/Al p orbitals well above the filled oxygen p states with no d states as in Co atom, which will increase coulomb repulsion between the oxygen atoms and lead to the increase of c value.

Table 1 Lattice parameters and average intercalation voltages (AIV) of pure NaCoO₂ and Mg/Al doped NaCoO₂

Structure	a (Å)	c (Å)	c/a	AIV (V)
NaCoO2	2.9295	15.3862	2.63	3.866
Na(Co0.92Al0.08)O2	2.9239	15.4527	2.64	3.946
Na(Co0.92Mg0.08)O2	2.9344	15.4528	2.63	4.018

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To study the relative stability of Mg/Al doped NaCoO₂, we further calculate the cohesive energies (E_coh) of Mg/Al doped NaCo_0.92M_0.08O₂. It is well known that cohesive energy can be used as an important index to estimate the stability of materials, the cohesive energy can be calculated using the following equation:

where E_total is the energy of Mg/Al doped NaCo_0.92M_0.08O₂, E^Na_atom, E^Co_atom, E^M_atom and E^O_atom are the energy of Na, Co, Mg/Al and O atoms in freedom states, respectively. Integers a, b, c and d are number of atoms of Na, Co, Mg/Al and O atoms. Therefore, a more negative cohesive energy (E_coh) indicates a more stable doped system phase. The calculated cohesive energies of NaCo_0.92Mg_0.08O₂ and NaCo_0.92Al_0.08O₂ are −4.76 eV per atom and −4.84 eV per atom, respectively, which indicates that Mg/Al doped NaCoO₂ are all stable, the stability of Al doped NaCoO₂ is a little more than that of Mg doped.

3.2 Average intercalation voltage

The average intercalation voltage can be estimated through the calculations of Gibbs energy of system via the first-principles calculations.^29,30 The intercalation voltage V̄ is given by eqn (1):where ΔG is the Gibbs free energy change for the intercalation reaction, and F is the Faraday constant. Assuming the changes of volume and entropy associated with the intercalation are negligible, the ΔG can be approximated by the potential energy term ΔE,²⁶ where ΔE is given by the difference in the total energies between NaMO₂ and the sum of oxide MO₂ and metallic sodium, in which the lattice parameters and atomic coordinates are fully relaxed.

ΔE = E_total(NaMO₂) − E_total(MO₂) − E_total(Na) (2)

where E_total(Na) is the total energy of metallic sodium in a body-centered-cubic(bcc) phase. The calculated average intercalation potential for NaCo_0.92Mg_0.08O₂, NaCo_0.92Al_0.08O₂ and NaCoO₂ are given in Table 1. It can be seen from Table 1 that Mg or Al substitution in transition metal oxides will lead to higher Na intercalation voltage, which is desirable for obtaining high energy density.

3.3 Electronic structure

In order to investigate the relationship between electronic structure and properties of Mg/Al doped NaCoO₂ material, the total density of states (TDOS) of NaCoO₂, Na(Co_0.92Al_0.08)O₂ and Na(Co_0.92Mg_0.08)O₂ were calculated as shown in Fig. 2. It can be seen that the bandgap between the occupied valence bands and empty conduction bands of NaCoO₂ is 1.05 eV, which show a typical semiconductor character. This is in agreement with the experimental results.^14,24 In case of the Al-doped NaCoO₂, the TDOS is nearly the same to pure NaCoO₂, which indicates that Al doping affects slightly on the electronic structure of NaCoO₂. However, the electronic hole appears in the TDOS of Mg-doped NaCoO₂ and the Fermi level shifts to the valence band. Based on charge balance mechanism: 2Co³⁺ → Mg²⁺ + Co⁴⁺, the electronic holes in the cobalt t_2g band of Co⁴⁺ ions are caused by the divalence Mg doping. The appearance of Co⁴⁺ electronic hole will provide electron-acceptor energy level, which is benefit to electronic transition. Therefore, the electron conductivity of NaCoO₂ can be significantly enhanced through doping a small amount of divalent Mg ions.

Fig. 2 Total density of states of (a) NaCoO₂, (b) Na(Co_0.92Al_0.08)O₂, (c) Na(Co_0.92Mg_0.08)O₂. The vertical line at zero point indicates the Fermi energy.

Since the properties of transition metal oxide depend much on the hybridization state of Co-3d and O-2p, the partial density of state (PDOS) for Co-3d and O-2p are further calculated, as shown in Fig. 3. It can be seen that the PDOS bands of Co-3d in Fig. 3(a) can be assigned to three main parts: the occupied valence band between −7 to −1.5 eV is attributed to bonding e^b_g; the occupied band within −1.2 to 0 eV is assigned to nonbonding t_2g; and the band in range of 1.05 to 2.15 eV corresponds to the unoccupied antibonding e^*_g. It is known that in octahedral symmetry of transition-metal ion,²⁹ the d_z2 and d_x2−y2 atomic orbits lose electron and make σ overlap with the p_x, p_y and p_z orbits of oxygen along the octahedral directions which correspond to the e^b_g and e^*_g bands. While the unoccupied antibonding band e^*_g mainly consists of the metal d states, and the occupied bonding counterpart e^b_g mainly shows oxygen p character. The orientations of remaining d_xy, d_xz and d_yz orbital are away from the oxygen and hence have no σ overlap with oxygen p orbital. These orbital can form a set of nonbonding t_2g bands whose width is mainly determined by the Co–Co interaction. So the state distribution of Co-3d in occupied t_2g and e_g^b bands indicates the electron number participating in the 3d–2p bonding. Larger density of states of Co-e^b_g as well as lower density of states of Co-t_2g represents a higher Co valence state. As shown in Fig. 3(a), compared to PDOS of 3d states of Co atoms in pure NaCoO₂, the changes in PDOS of Al doped Na(Co_0.92Al_0.08)O₂ are very small. However, the increase in the density of states of e^b_g and the decease in the density of states of t_2g in Mg-doped Na(Co_0.92Mg_0.08)O₂ indicate that d electrons move from nonbonding bands to bonding bands, and more d electrons participate in the 3d–2p bonding, which corresponds to a higher Co valence state. It is consistent with the above analysis. Meanwhile, it can be seen from the PDOS that the bandgap between e^b_g and t_2g becomes small after Mg doping which implies that the Co-3d and O-2p have a stronger rehybridization and result in more stronger covalence of Co–O in Mg-doped NaCoO₂.

Fig. 3 Partial density of state for Co-3d(left) and O-2p(right): (a) NaCoO₂, (b) Na(Co_0.92Al_0.08)O₂, (c) Na(Co_0.92Mg_0.08)O₂. The vertical line at zero point indicates the Fermi energy.

To further understand the electronic structures of Mg/Al doped NaCoO₂, the electron density differences of Na(Co_0.92Al_0.08)O₂, Na(Co_0.92Mg_0.08)O₂ and NaCoO₂ in the section cut from octahedron [CoO₆] equatorial plane are illustrated in Fig. 4. In comparison to NaCoO₂, the electron density differences of Mg/Al doped NaCoO₂ have the following characteristics: firstly, the electron densities of all Co atoms have no significant differences in Al doped Na(Co_0.92Al_0.08)O₂, which indicates that the valence state of all the Co ions is the same. However, the electron densities of Co ion adjacent Mg ion in Na(Co_0.92Mg_0.08)O₂ are less than that far from Mg ions, which indicates that Co ion adjacent Mg ion lose more electron and have a higher valence state. Secondly, the electron densities of O ions adjacent Mg ion in Na(Co_0.92Mg_0.08)O₂ are more than that far from Mg ions, which indicates divalent Mg doping in Na(Co_0.92Mg_0.08)O₂ will lead to an increasing number of oxygen participation in electron exchange. So the oxygen ions become more closed-shell characteristic than in NaCoO₂. In other words, oxygen ions in Na(Co_0.92Mg_0.08)O₂ are closer to the −2 valence state,¹⁹ which will lead to a stronger Coulomb repulsion between the oxygen layers.

Fig. 4 The electron density differences of (a) NaCoO₂, (b) Na(Co_0.92Al_0.08)O₂, and (c) Na(Co_0.92Mg_0.08)O₂ in two sections cut from octahedron [CoO₆] equatorial plane.

Thus, it is found that the electronic structure vary small with 8% mole Al doping in NaCoO₂. However, the charge disproportionation induced by 8% mole divalent Mg doping in NaCoO₂ affects both Co and O simultaneously. The electronic holes and the communization of Co-3d and O-2p electrons caused by Mg doping make its better conductivity and stronger Coulomb repulsion between the oxygen layers.

3.4 Na ion diffusion behavior

Na diffusion behavior in the electrode materials is a key factor of the rate capability and energy efficiency of rechargeable Na batteries. So it is important to investigate the Na⁺ diffusion kinetics in the electrode materials. According to the transition state theory,³¹ the diffusion constant is mainly determined by the activation barrier, that is, lower activation barrier energy means faster diffusion rate. Calculations on minimum energy path of Na diffusion in Na(Co_0.92Mg_0.08)O₂, Na(Co_0.92Al_0.08)O₂ and NaCoO₂ are performed. The calculation results indicate that Na ion moves from one octahedral site to another by passing through an intermediate O₄ tetrahedral site as shown in Fig. 5(a), and the calculated diffusion barriers for Na(Co_0.92Mg_0.08)O₂, Na(Co_0.92Al_0.08)O₂ and NaCoO₂ are shown in Fig. 5(b). It can be seen that in pristine NaCoO₂ host, the calculated activation energy barrier for Na diffusion is 0.35 eV. For Al doped Na(Co_0.92Al_0.08)O₂ crystal, the activation barrier is 0.36 eV, which is slightly higher than in NaCoO₂ host. While in Mg doped Na(Co_0.92Mg_0.08)O₂ host lattice, the computed Na diffusion barriers falls to 0.30 eV. According to the Arrhenius equation, the diffusion constant (D) is proportional to exp(−E_barrier/k_BT), where E_barrier and k_B are the diffusion energy barrier and Boltzmann constant, respectively. Therefore, it can be concluded that at room temperature the Na⁺ diffusion rate in Mg doped Na(Co_0.92Mg_0.08)O₂ host lattice is about 7 times faster than that in pristine NaCoO₂, which indicate that Mg doping is beneficial to Na diffusion. This might be ascribed to the closed-shell oxygen ions structure in Mg doped Na(Co_0.92Mg_0.08)O₂, which will lead to a stronger Coulomb repulsion between the oxygen layers and thus facilitate Na diffusion.

Fig. 5 (a) Crystal structure schematic of sodium migration path; (b) calculated diffusion barriers for Na(Co_0.92Mg_0.08)O₂, Na(Co_0.92Al_0.08)O₂ and NaCoO₂.

4. Conclusion

First-principles computational methods have been used to study crystal structure, electron transfer, the change of valence, and average intercalation voltage as well as diffusion barriers for the divalent Mg and trivalent Al ions doped NaCoO₂. The calculated results indicate that Mg/Al doping will lead to a higher average intercalation voltage, which is beneficial to obtain high energy density. Investigations on electronic structures show that trivalent Al ions doping affect slightly on the electronic structure of NaCoO₂. However, divalent Mg ion doping in Na(Co_0.92Mg_0.08)O₂ will lead to charge disproportionation, which affect simultaneously the electronic structure of both Co and O. The electronic holes of Co⁴⁺ and closed-shell O²⁻ caused by Mg doping make its higher conductivity and faster Na diffusion rate. Therefore, compared to trivalent Al ion doping, a small amount of divalent Mg ion doping in NaCoO₂ will be much beneficial to improve the average intercalation potential as well as electronic conductivity and enhance Na diffusion rate which make Mg-doped NaCoO₂ more attractive for promising cathode materials.

Acknowledgements

This work is funded by the National Natural Science Foundation of China under project no. 51472211, Scientific and Technical Achievement Transformation Fund of Hunan Province under project no. 2012CK1006, Key Project of Strategic New Industry of Hunan Province under project no. 2013GK4018, and Science and Technology plan Foundation of Hunan Province under project no. 2013FJ4062. YP is supported by Natural Science Foundation of China (Grant no. 21103144) and Hunan Provincial Natural Science Foundation of China (12JJ7002, 12JJ1003).

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