Computational Investigation of Two-Dimensional Vanadium Boride Compounds for Na-Ion Batteries.

Sodium (Na)-ion batteries have received widespread attention due to their low cost and good safety. The possibility of two-dimensional vanadium boride (V2B2, MBene) as the anode material for Na-ion batteries is explored by first principles. It is found that V2B2 has good dynamic stability, thermodynamic stability, and conductivity. V2B2 has a good performance as anode material: it can adsorb nearly 3 layers of Na ions, and the maximum capacity reaches 814 mAhg-1. It is found that V2B2 has a very low Na ion diffusion barrier, about 0.011 eV, which represents the ultrahigh ion diffusion rate of Na ions on the surface of V2B2. The average open circuit voltage of V2B2 is 0.65 V, and good metallicity is maintained during the entire Na ion adsorption process. The results indicate that two-dimensional V2B2 has a low diffusion barrier, low open circuit voltage, and high theoretical capacity and is a potential anode material for Na-ion batteries.

Introduction

Rechargeable Li-ion batteries have been widely used in various fields because of their high energy efficiency and high cycle times. In addition to Li-ion batteries, Na-ion batteries have also received extensive attention. There is more Na on the earth than Li; in addition, it is easier to mine and safer to use than Li for batteries. Therefore, people find that Na-ion batteries have great research value and may become a supplement or substitute for Li-ion batteries.[1−6] Metal-ion batteries are highly dependent on the performance of their electrode materials. However, it has been found that the effect of Na ions on the application of commercial anode material graphite in Na-ion batteries is not obvious.[7−9] On the basis of this situation, there is an urgent need for new anode materials to further improve the performance of Li-ion batteries and Na-ion batteries.

Two-dimensional (2D) materials as anode materials for Li-ion batteries and Na-ion batteries have received extremely high attention in recent years because of their high surface area, very high electron mobility, and excellent mechanical properties.[10−18] In recent years, many two-dimensional materials have been studied as anode materials and have achieved great success. Graphene was the first example of a two-dimensional electrode material for Li-ion batteries.[19] Since then, two-dimensional materials that have been studied include polypyrrole-modified Li5Cr7Ti6O25,[20] silylene,[21−24] and phosphorene[25,26] as anode materials for Na-ion batteries or Li-ion batteries. In addition, the application of two-dimensional transition metal carbides or nitrides (MXenes)[27,28] in electrode materials has also attracted great attention. Although it has been theoretically confirmed that many two-dimensional materials can be used as potential electrode materials, it is still necessary and important to find better-performing Na-ion batteries and Li-ion batteries. Recently, Bo et al.[29] studied two-dimensional transition metal borides (MBene) such as Fe2B2 and Mo2B2 for Li-ion battery anode materials. This is the first application research of two-dimensional MBene for Li-ion battery anode materials. These MBene precursors contain a honeycomb-like boron atomic layer similar to graphene, which is similar to MXene’s MAX phase and can be converted into a two-dimensional “sandwich” structure.

In this work, through first-principles calculations, we carried out the exploration of V2B2 in energy storage by exploring its possibilities as an anode material for Na-ion batteries. First, the kinetic stability, thermodynamic stability, and electrical conductivity of V2B2 were studied. Second, the most stable Na ion adsorption sites were determined by combining adsorption energy and Bader charge, and the charge distribution of these adsorption conditions was visualized by differential charge density. Then, the diffusion path and diffusion barrier of Na ions were studied by the climbing-image nudged elastic band (CI-NEB) method. It was found that V2B2 has a very low diffusion barrier of Na ions (0.011 eV), which means that Na ions have a very high diffusion rate on the surface of V2B2. Finally, we explored the adsorption process of Na ions on the surface of V2B2. According to the adsorption energy of different concentrations of Na ions, the open-circuit voltage (OCV) as a function of Na ion concentration and the maximum theoretical capacity of Na ions were calculated.

Computational Details

The calculation results of this work are based on density functional theory (DFT) and implemented in VASP[30] using the projector enhanced wave (PAW) method to describe the interaction between nuclear electrons and valence electrons. Electronic exchange related functions are described by Perdue–Burke–Ernzerhof (PBE).[31] The interlayer spacing along the z-direction is maintained at 40 Å. The cutoff energy of 520 eV is used for the plane wave function of the electrons. The total energy convergence standard is 10–5 eV. In the structural optimization, all structures are fully relaxed with a threshold maximum force of 0.001 eV/Å. The primitive cell and 2 × 2 × 1 supercell use 30 × 30 × 1 and 10 × 10 × 1 K points, respectively. The phonon spectrum calculation used a 2 × 2 × 1 super cell with an energy threshold of 10–8 eV.[32] The ab initio molecular dynamics (AIMD) simulation is calculated on a 3 × 3 × 1 supercell, and the K point is 2 × 2 × 1. The AIMD simulation lasts for 5 ps in the particle–volume–temperature (NVT) ensemble with a time step of 2 fs, and the temperature is controlled by the Nosé–Hoover method.[33,34] The diffusion path and diffusion barrier of Na ions are determined by the CI-NEB. 10–5 eV is set for the convergence standard of the initial state and the final state energy, and the structure is fully relaxed until the atomic force is less than the 0.001 eV/Å threshold. The convergence accuracy of the interatomic interaction force for the search of the intermediate transition state structure is set to 0.02 eV/Å. We calculated the capacity[23] bywhere c, z, M (V2B2), and F are the number of Na’s on V2B2, the valence number of Na, the molar weight of V2B2, and the Faraday constant, respectively.

Results and Discussion

Structure and Stability of the V2B2 Monolayer

The investigated configuration of our 2D V2B2 is the P6/mmm phase by referring to previous studies.[29,34,35] Then, we studied the structural characteristics and stabilities. The sandwich-like structure of V2B2 has the lattice constants a = b = 2.959 Å, which is shown in Figure . The black lattice represents the primitive cell, and the red and green balls represent the V and B atoms, respectively. To verify the reliability of our configuration, its dynamic and thermal stabilities were studied. The phonon dispersions are shown in Figure a. We can see that there is no imaginary frequency, which indicates that this structure is dynamically stable. The highest frequency of 2D V2B2 reaches up to 28 THz (932 cm–1), which is higher than those of the Zr2B2 (765 cm–1) and MoS2 (473 cm–1)[36] monolayers. The high value of frequencies in the phonon dispersion also indicates the stability of this 2D material.

Figure 1

Top (a) and side (b) views of the 2 × 2 × 1 monolayer V2B2; the black lattice represents the primitive cell. The red and green balls represent the V and B atoms, respectively.

Figure 2

(a) Phonon dispersion curves of V2B2. (b) The free energy of the 3 × 3 × 1 monolayer V2B2 after AIMD simulations at 300, 500, and 1000 K over the time scale of 5 ps.

In practical applications, it is often considered whether the electrode material can work stably at different temperatures. Therefore, the stability of the structure at different temperatures was studied by AIMD as in the published literature.[37,38] As shown in Figure b, the ordinate values of this structure at 300, 500, and 1000 K have been oscillating around a numerical law. This shows that the structure has no irreversible changes at these temperatures and has good thermal stability.

Na Adsorption and Diffusion on V2B2

Whether the anode material can stably absorb metal ions is an important index to judge the performance of the anode material. The adsorption energy is a good indicator of whether metal ions can be stably adsorbed on the surface. We defined three adsorption sites on the surface of V2B2 to study the adsorption energy of Na ions, as shown in Figure . From the symmetry of V2B2, it can be seen that the positions of all V atoms are the same, and the positions of all B atoms are also the same. Therefore, we define site 1 (S1) as that located directly above the V atom and take the site directly above the B atom as site 2 (S2). The site directly above the middle of the two B atoms and also directly above the middle of the two V atoms is chosen as site 3 (S3). The adsorption energy was calculated by the formula:where EMBene, ENa, and ENa+MBene are the total energies of MBene surfaces, the Na atom in the bcc crystal, and the Na adsorbed on the MBene surfaces, respectively. n indicates the number of adsorbed Na, and the results are presented in Table . The adsorption energies of positions 1, 2, and 3 are 2.26, 2.37, and 2.35 eV, respectively. It can be seen from eq that the adsorption energy should be positive, and the greater the adsorption energy, the stronger is the adsorption. Therefore, site 2 is the most stable position for Na ion adsorption. To fully consider the rationality of the adsorption energy, we calculated the Bader charge, which can quantitatively calculate the charge transfer between two atoms. As shown in Table , the charge transfer numbers at sites 1, 2, and 3 are 0.6652, 0.6679, and 0.6657 |e|, respectively. This also shows that the adsorption is the most stable at site 2.

Table 1

Binding Energy (Eb, eV) and Charge Transfer of Na Ions at Sites 1, 2, and 3, Respectively

	site 1	site 2	site 3
Eb (eV)	2.26	2.37	2.35
Bader	0.6652	0.6679	0.6657

The charge density difference can clearly show the charge distribution around the atoms. The calculation formula is as follows:where ρMBene+Na, ρMBene, and ρNa are the charge densities of MBene with adsorbed Na, MBene, and Na, respectively. From the differential charge density of the three structures of V2B2, as shown in Figure , we found that the charge is mainly concentrated between the outermost surface atom and Na atom. Additionally, the electrons are transferred from Na to the respective V2B2 surface, thus resulting in chemical bonding (Na–V), which is beneficial to prevent Na clusters from forming.

Figure 3

Charge density difference of V2B2 with the Na-adsorbed at (a) site 1, (b) site 2, and (c) site 3. Note that the yellow and blue colors represent the accumulation and depletion of charge, and the isosurface level is 0.001 e/Bohr.[3]

The diffusion barrier, which determines the diffusion rates of the metal ions during charging and discharging, is one of the important properties of the electrode materials. The lower the diffusion barrier, the faster is the metal ion diffusion. Therefore, after determining the most stable adsorption site for the metal ions, we further studied the diffusion barrier from the most stable adsorption site to another. First, we determined the initial state and the final state and then calculated the diffusion path and the corresponding diffusion barrier by the CI-NEB method. According to the symmetry, one possible pathway consists of three consecutive segments of S1–S3–S1 (labeled in Figure a). First, the S2 site was occupied by Na ions. The adsorption energy of the Na ion on site S2 is quite similar to that of site S3. Thus, it is easy for the Na ions to diffuse along the S2–S3–S2 direction. As shown in Figure b, the diffusion barrier is approximately 0.011 eV. The extremely low diffusion barrier shows that V2B2 has great potential in the application of anode materials. This is lower than many two-dimensional materials like phosphoene (0.04 eV)[39,40] and graphene (0.13 eV)[41] and also has a greater advantage over the same type of materials such as Mo2B2.[29] We also calculated the diffusivity of the Na ion on V2B2 as a function of temperature bywhere l is the Na migration distance from equivalent Na adsorption sites on the 2D V2B2, kB is the Boltzmann constant, ΔEbarrier is the diffusion barrier, T is the absolute temperature, and v0 is the vibrational frequency. The vibrational frequency (v0) is decided by the phonon frequency.[42] The diffusivity of Na on V2B2 is 0.011 cm2/s at 300 K, which is quicker than that of Si3N,[42] Y2C(OH)2,[43] and graphene.[41] These results indicate that, the higher the diffusion rate of the Na ion on 2D V2B2, the higher is the charge–discharge rate.

Figure 4

(a) Top view of the Na diffusion path for V2B2 indicated by the black dotted arrows. (b) The corresponding diffusion barriers for Na (green solid line) on V2B2.

Na Storage Capacity of V2B2 Monolayer and Average Open-Circuit Voltage

In order to understand the process of adsorption of large amounts of Na ions on the surface, we tried to adsorb as many Na ions as possible on the surface and calculated adsorption energy ions as a function of the number of Na ions. As shown in Figure , 8 Na ions are adsorbed in the first layer, followed by 8 Na ions in the second layer, and 8 Na ions are finally placed in the third layer.

Figure 5

Top views and side views of (a) V2B2Na2, (b) V2B2Na4, and (c) V2B2Na6 with layers of Na ions adsorbed on the surface of the 2D V2B2 monolayer. The V, B, and Na atoms are denoted by red, green, and yellow, respectively.

The relationship between the average adsorption energy and absorbed Na concentration was explored by eq . As shown in Figure , the results show that, with the increase of Na ion concentration, the average energy values display a decreased tendency. The reasons for this phenomenon are 2-fold: first, the interaction between Na ions is elevated as more Na is adsorbed; second, the adsorption energy of the outer Na ions is too small, which affects the overall average adsorption energy. However, the average adsorption energy remains a fairly large value ranging from 1.55 to 2.39 eV for Na, which is larger than the cohesive energy of the bulk Na metal of 1.19 eV per atom.

Figure 6

Functional relationship between the binding energy of Na ions on V2B2 and Na ion concentration. Note that blue line indicates the average binding energies, and the dotted line is the value of Na ions in bulk Na.

The open circuit voltage (OCV) is a very important property of anode materials. Generally speaking, the lower OCV of the anode material, the better is the battery performance.[44] The OCV of anode materials at different concentrations was calculated by the formula:where ENa and ENa are total energies of NaV2B2 at x1 and x2 Na concentrations and ENa is the Na atom energy in the bcc crystal. The relationship of OCV and Na ion concentration is shown in Figure . When Na ions begin to intercalate, the OCV is 1.2 V. Then, the open circuit voltage decreases as the Na ion concentration increases and finally becomes a negative number when the Na ion concentration is 3.75. The average open circuit voltage during the whole process is about 0.65 V, and the maximum capacity is 814 mAhg–1. This value is better than many new, two-dimensional materials such as borophene (596 mAhg–1),[45] Mo2B2 (251 mAhg–1),[29] and Ti2B2 (342 mAhg–1).[35]

Figure 7

OCV as a function of Na concentration (x) adsorbed on V2B2, which is represented by the red step curve.

To further verify the rationality of the process and diffusion performance, we compared the density of states (DOSs) before charging and after fully charging. The results are shown in Figure . We found that there is a large peak near the Fermi energy level of both DOS curves before and after Na ion adsorption, which indicates V2B2 shows good metallicity in both cases of no adsorption of Na ions and full adsorption of Na ions. The contribution of Na ions near the Fermi energy level increases with the increase of Na ion concentration during the charging process, but the mainly orbital contribution around the Fermi energy level comes from 2D V2B2. Thus, the system keeps its metallic properties during charging and discharging. When one comprehensively considers several key factors for the commercial application of ion batteries, 2D V2B2 with a high theoretical capacity and fast charge and discharge performance emerges as an all-around candidate for Na-ion batteries (NIBs).

Figure 8

Density of state of V2B2 with no adsorbed or completely filled Na ions. The Fermi energy is at 0. The total density of state diagram of V2B2 is represented as a black solid line, and the partial density of states of V and B are represented as red and blue lines. The Fermi energy set to zero is indicated as the black dotted line.

Conclusions

In summary, we explored the structural properties, stability, and electronic properties of V2B2 using first principles. The results show that V2B2 has good dynamic stability, thermodynamic stability, and metal properties. Then, the various properties of V2B2 as anode material are studied. V2B2 has good Na ion adsorption characteristics and can adsorb nearly 3 layers of Na ions, and its maximum capacity reaches 814 mAhg–1. The diffusion barrier of a single Na ion is as low as 0.011 eV, which gives V2B2 the ability to rapidly diffuse Na ions. The average open circuit voltage is 0.65 V, and good metallicity is maintained during the entire Na ion adsorption process. These properties are better than the current commercial anode materials and better than some MBenes that have been studied. It can be seen from these results that V2B2 has a low diffusion barrier, low open circuit voltage, and high theoretical capacity, indicating its good potential as an anode material.