MgVPO₄F as a one-dimensional Mg-ion conductor for Mg ion battery positive electrode: a first principles calculation

Abstract

MgVPO₄F is proposed as a cathode material for rechargeable Mg ion batteries for the first time. First principles calculations were performed to study the electrochemical properties of MgVPO₄F as a positive electrode material for rechargeable Mg ion batteries. Our theoretical study gives an expectation of good battery performance by MgVPO₄F.

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Introduction

Despite the successful application of Li ion batteries (LIBs) in portable electronics in the past decades, the high prices and low energy density of LIBs still limit their application in plug-in hybrid electric vehicles and electric vehicles.^1,2 To increase the energy density, new battery systems such as Li–S and Li–air batteries have been extensively studied. Mg ion batteries (MIBs)^3–7 are another candidate for their safety of handling, higher volumetric energy density, high negative reduction potential and low cost. However, only a few materials can be used for positive electrode of MIB, including Chevrel phase M_xMo₆T₈ (M = metal, T = S, Se),^8–11 TiS₂ nanotubes,¹² graphene-like MoS₂,¹³ Mg_xCo₃O₄,¹⁴ α-MnO₂ (ref. 15) and mesoporous Mg_1.03Mn_0.97SiO₄.¹⁶ The development of MIB is mainly limited by the low Mg ions mobility in positive electrode. It shows a high activation barrier for Mg ion diffusion in many bulk electrode materials, largely due to the divalent nature of Mg ions, which have strong interaction with anions and cations in positive electrode materials.^17,18

First principles calculations were used to design and develop new electrode materials for MIB. Ling et al.¹⁹ investigated the electrochemical properties of TMSiO₄ (TM = Fe, Mn, Co, Ni) as cathode for MIB, and the redox reaction mechanism in the magnesiation of TMSiO₄ were studied. According to the results from Yang et al.²⁰ the Mg²⁺ diffusion barrier on the zigzag MoS₂ nanoribbon was found to be 0.48 eV, which is much lower than that of bulk MoS₂ material. In particular, Ling et al.²¹ found that the diffusion activation energy of Mg²⁺ in CaFe₂O₄-type MgMn₂O₄ is 0.4 eV, which is comparable with that of Li⁺ in typical LIB cathode materials.

As Li₂VPO₄F (ref. 22) shows a capacity of 312 mA h g⁻¹ and the activation energy for Li diffusion in VPO₄F is only 0.33 eV.²³ Hence, we dare to propose MgVPO₄F as a new candidate positive electrode material for MIB. With the introduction of F anions, we expect a relative weak interaction between Mg ion and anions and better ionic conductivity. To the best of our knowledge, this is the first time MgVPO₄F has been proposed as a positive electrode material for MIB.

In this paper, based on first principles calculations, the crystal structures of Mg_xVPO₄F (x = 0, 0.5 and 1) were obtained, and the OCV of MgVPO₄F as a positive electrode for MIB were calculated. Then, the electronic structures and Bader charge for Mg_xVPO₄F (x = 0, 0.5 and 1) were studied to reveal the redox reaction mechanism as Mg intercalation into VPO₄F. Finally, the diffusion activation energy for Mg ions along [100], [010], [101] and [111] direction of Mg_1−xVPO₄F were calculated to study the Mg ion conductivity of MgVPO₄F.

Methodology

The present calculations were performed using the Vienna ab initio simulation package (VASP)²⁴ with projector augmented wave pseudo potentials^25,26 (PAW) approach. The exchange and correlation energy functional were treated by the Perdew–Burke–Ernzerhof variant of the generalized gradient approximation (GGA)²⁷ and GGA + U (ref. 28) extension to it, and a U_eff = 3.1 eV was adapted for V, similar value has been used for LiVPO₄F.²³ The energy cutoff for the plane wave basis set was set to be 500 eV, and the total energy was converged to 10⁻⁵ eV. A k-points sampling of 8 × 8 × 6 was used to ensure the energies were converged within 5 meV per formula unit. In addition, the single point energies were calculated with different magnetic alignments including FM (ferromagnetic) and AFM (antiferromagnetic). The climbing-image nudged elastic band (Cl-NEB)²⁹ method implemented in VASP was used to investigate the Mg ion diffusion property in Mg_1−xVPO₄F. A super cell containing 2 × 2 × 2 unit cells was used to ensure that no magnesium ion vacancy was within 8 Å from its periodic image. The volume was frozen and only the k-point at Γ (center of Brillouin zone) was used. Ions in the super cell were relaxed with Quick-Min (QM) method as implemented in the VASP Transition State Tools. The NEB calculations were deemed to be converged when the force on each image was less than 0.03 eV Å⁻¹.

Results and discussion

The structure of LiVPO₄F (ref. 22) was used as the template for MgVPO₄F, after fully relaxation, Mg atoms were removed to obtain the structures of Mg_0.5VPO₄F and VPO₄F. The calculations predict FM ground states for VPO₄F and Mg_0.5VPO₄F, and AFM ground states for MgVPO₄F. As shown in Fig. 1, MgVPO₄F is composed by corner-shared VO₄F₂ octahedral chains connected by PO₄ tetrahedrons, with Mg ions located in the framework. MgVPO₄F crystallize in the triclinic space group P1̄ with two vanadium atoms occupy at 1a (0, 0, 0) and 1b (0, 0, 1/2) site respectively, and with Mg, O, P and F atoms occupy at 2i sites. After remove half Mg atoms from MgVPO₄F, the structure of Mg_0.5VPO₄F crystallize in the triclinic space group P1̄, the decrease of structure symmetry is mainly caused by the strong distortion of VO₄F₂ octahedron. VPO₄F crystallize in the monoclinic space group C2/c, with V atoms occupy at 4b sites, and F and P atoms occupy at 4e sites, and O atoms occupy at 8f sites. The lattice parameters of Mg_xVPO₄F (x = 0, 0.5 and 1) are listed in Table 1. The parameters of primitive cell of VPO₄F were obtained based on the data in ref. 30, all the lattice parameters of VPO₄F are a little overestimated, which is a reasonable error for the use of GGA + U.^31,32 Up on half magnesiation, the volume of VPO₄F is predicted to increase by 8.0%. However, further magnesiation from Mg_0.5VPO₄F to MgVPO₄F also lead to a volume expansion about 8.2%, which is similar with the volume expansion from LiVPO₄F to Li₂VPO₄F.³⁰ This indicated that full magnesiation of VPO₄F might cause structure instability, which is harmful to its cycle performance. Hence, charge/discharge Mg_0.5VPO₄F with half Mg might be a reasonable option.

Fig. 1 Crystal structure of MgVPO₄F: the red octahedra represent VO₄F₂, light magenta tetrahedron represent PO₄, red spheres represent O, dark gray spheres represent F and orange spheres represent Mg.

Table 1 Structure parameters of Mg_xVPO₄F (x = 0, 0.5 and 1)

	a/Å	b/Å	c/Å	α/°	β/°	γ/°	V/Å^3
VPO4F	5.175	5.175	7.501	110.754	110.754	91.655	172.90
Exp.^30	5.041	5.041	7.116	109.523	109.523	89.567	159.50
Mg0.5VPO4F	5.289	5.405	7.487	108.911	107.866	97.139	186.688
MgVPO4F	5.310	5.687	7.557	108.411	106.940	96.315	201.920

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The average OCV was obtained by calculating the difference of chemical potential between positive electrode (VPO₄F) and negative electrode (Mg).¹⁹ MgVPO₄F shows two discharge plateaus at 2.6 V and 1.5 V corresponding to the redox couples of V⁴⁺/V³⁺ and V³⁺/V²⁺. Each electrochemical reaction shows a theoretical capacity about 156mA h g⁻¹. Hence, if fully discharged, VPO₄F might show a high theoretical specific capacity about 312 mA h g⁻¹.

In order to analyze the redox reaction mechanism as Mg intercalation into VPO₄F, the density of states for VPO₄F, Mg_0.5VPO₄F and MgVPO₄F were studied in detail. Fig. 2 shows the total density of states (TDOS) for Mg_xVPO₄F and partial density of states (PDOS) for V-3d, O-2p and F-2p orbital, and the Fermi level is set at zero energy. In all three compounds, the valance bands of V-3d between −8 eV and −1 eV are hybridized with O-2p and F-2p bands. The p–d hybridization of V–O and V–F at low energy range is going to make a contribution to the stability of crystal structure. In VPO₄F, the PDOS of V-3d for V₁ and V₂ are nearly the same, indicating they have the same electronic structure. When VPO₄F was magnesiated into Mg_0.5VPO₄F, the electrons provided by Mg are mainly localized at V-3d orbital at the top valence band, and both V⁴⁺ are reduced into V³⁺. While Mg_0.5VPO₄F was magnesiated into MgVPO₄F, the magnetic alignment changed from FM to AFM, and V³⁺ were reduced into V²⁺. The redox reaction mechanism is similar with the magnesiation of MnSiO₄.¹⁹

Fig. 2 The total density of states (TDOS) for Mg_xVPO₄F: (a) VPO₄F, (b) Mg_0.5VPO₄F and (c) MgVPO₄F, and the Partial density of states (PDOS) of V-3d, O-2p and F-2p for (d) VPO₄F, (e) Mg_0.5VPO₄F, (f) MgVPO₄F, and the Fermi level is set at zero energy.

To analyze the charge transfer between Mg and the positive electrode host quantitatively, the average Bader^33–35 charge around each nucleus were calculated. As shown in Table 2, the Bader charges on Mg in Mg_0.5VPO₄F and MgVPO₄F are +1.70e and +1.69e, indicating the ionization of Mg. For VPO₄F, Mg_0.5VPO₄F and MgVPO₄F, the charge of V are +2.30e, +2.03e and 1.58e, respectively, suggesting its strong covalent interactions with O and F atoms. The Bader charge of V₁ and V₂ in Mg_0.5VPO₄F and MgVPO₄F are the same (+2.03e and 1.58e), indicating that the insertion of one Mg reduced two VO₄F₂ units instead of reducing only one VO₄F₂ unit.

Table 2 Average Bader charge (e) of Mg, V, O, P and F for Mg_xVPO₄F

	Mg	F	O	P	V1	V2
VPO4F		−0.67	−1.33	+3.68	+2.30	+2.30
Mg0.5VPO4F	+1.70	−0.75	−1.45	+3.68	+2.03	+2.03
MgVPO4F	+1.69	−0.82	−1.52	+3.66	+1.57	+1.58

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In order to investigate Mg ion conductivity in Mg_1−xVPO₄F, the Cl-NEB method implemented in VASP was performed. Fig. 3 shows the diffusion paths for Mg diffusion along [100], [010], [101] and [111] directions. All the Mg ion migration paths are a combination of two diagonal jumps, and these diagonal jumps form continuous diffusion paths. Jumps involved in each diffusion direction and the calculated activation energies for the diffusion paths in Mg_1−xVPO₄F are listed in Table 3.

Fig. 3 The diffusion pathways for Mg diffusion along [100], [010], [101] and [111] directions. The red octahedra represent VO₄F₂, light magenta tetrahedron represent PO₄, red spheres represent O, dark gray spheres represent F and orange spheres represent Mg.

Table 3 Activation Energies for paths in Mg_1−xVPO₄F

Diffusion direction	Jumps involved	Activation energy (eV)
[100]	L1 + L2	1.597
[010]	L3 + L4	1.483
[101]	L2 + L3	1.483
[111]	L2 + L4	0.704

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The energy barrier for Mg ion diffusion along [111] direction is 0.704 eV, which is much lower than that of bulk V₂O₅ (ref. 36) (1.40 eV) and MoS₂ (ref. 20) (2.61 eV). The activation energy for hops in other direction are at least 700 meV higher than the activation energy along [111], making Mg_1−xVPO₄F a 1D diffuser for Mg ion battery. This appeared to be similar with the paths for lithium diffusion in VPO₄F.²³

A rough diffusion coefficient can be estimate as

D = a²νe^(−E_A/kT)

where a is the distant of a diffusion jump, ν is the attempt frequency and E_A is the activation energy, and kT is Boltzmann's constant times the temperature. In this calculation, a typical value of 10¹³ s⁻¹ was used for ν, and the temperature was assumed to be 300 K. An estimated diffusion coefficient using the lowest activation energy is in the order of 10⁻¹⁴ cm² s⁻¹. Therefore, we can expect better Mg ion conductivity for MgVPO₄F. Here, we stress that the estimated diffusion coefficient requires unblocked channel.

Conclusions

Based on First principles calculations, MgVPO₄F is proposed as a new candidate positive electrode material for MIB. Two intercalation plateaus at 2.6 and 1.5 V corresponding to the redox couples of V⁴⁺/V³⁺ and V³⁺/V²⁺ were predicted, and each electrochemical reaction shows a theoretical specific capacity about 156mA h g⁻¹. In addition, the redox reaction mechanism was revealed in the process of Mg intercalation into VPO₄F. V⁴⁺ was reduced into V³⁺ when Mg_0.5VPO₄F formed, and further reduction of V³⁺ into V²⁺ took place as MgVPO₄F formed. The Bader charge analysis indicating that the insertion of one Mg reduced two VO₄F₂ units instead of reducing only one VO₄F₂ unit. The lowest energy barrier for Mg-ion migrates in Mg_1−xVPO₄F is along [111], and the corresponding activation energy is in the order of 0.704 eV, which is much lower than that of bulk V₂O₅ and MoS₂. The present results give expectation of good battery performance by MgVPO₄F. We believe this work will facilitate the future research of MIB with high performance.

Acknowledgements

The authors gratefully acknowledge the financial support by National Natural Science Foundation of China (grant numbers 51272179, 51072137, 51102183), Doctor Subject Fund of Education Ministry of China (grant no. 20100072110054), Shanghai Committee of Science and Technology (11nm0501300, 13JC1408700), National high-tech R-D program of china (863 program) (grant no. 2013AA031801). Some computations were also made possible thanks to Shanghai Supercomputer Center.

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