Roles of Oxygen Vacancies in NiMoO4: A First-Principles Study

Introduction

As a typical transition metal oxides semiconductor, NiMoO₄ has attracted attention for its wide applications in electrochemical energy storage and conversion, such as supercapacitor and electrocatalytic water splitting (Du et al., 2018; An et al., 2019). However, the poor conductivity and electrochemical activity of NiMoO₄ limited its electrochemical energy storage performance. Defects engineering is a common method to change the physical chemistry property of transition oxide materials. As a typical representative of defects, oxygen vacancies can effectively modulate their electronic properties, tune their bandgaps, and optimize their electrical conductivity (Zhang et al., 2020a). It has been proven experimentally that oxygen vacancies also can alter the interlayer spacing of metal oxide to promote faster charge storage kinetics (Kim et al., 2017; Qing et al., 2018). However, theoretical mechanism analysis of oxygen vacancies in NiMoO₄ on its capacitance performance is still scarce.

NiMoO₄ has a typical monoclinic crystal structure. Both the Ni and Mo atoms are in octahedral site, and the distance between Mo and O atom was 2.3–2.4 Å (Rodriguez et al., 1998; Rodriguez et al., 2000). When redox reaction occurs, the Ni²⁺ has oxidized to Ni³⁺; meanwhile, the MoO₄²⁻ framework remains stable. Due to the band gap of NiMoO₄ of 2.23 eV in natural temperature, the actual pseudo-capacitance performance of NiMoO₄ was unsatisfactory (Yang et al., 2016).

In order to understand the physical property of oxygen vacancies in NiMoO₄, we performed first-principles calculation on the electronic structure, total density of states (TDOS), and partial density of states (PDOS) of NiMoO_{4 − x} for the case of x = 0.0, 0.125, 0.250, and 0.375 (call NMO-0, NMO-1, NMO-2, NMO-3, respectively) by the Vienna Ab-Initio Simulation Package (VSAP) based on density functional theory (DFT). We have constructed a supercell of eight unit cells consisting of 48 atoms. Furthermore, in order to understand the relationship between vacancies structures and electrical properties in NiMoO₄, the formation energy of neutral oxygen vacancy in different chemical environments has been calculated.

Theoretical Model and Computational Method

Theoretical Model

The study of oxygen vacancies in NiMoO₄ has been investigated by constructing a perfect supercell approach. Based on the optimized construction of perfect NiMoO₄, the unit cell is built by 2 × 2 × 2 in the x, y, and z directions, and a supercell consisting of 48 atoms is used for vacancies calculation. To introduce oxygen vacancies, an interior atom is removed from the supercell. The theoretical model is shown in Figure 1.

FIGURE 1

FIGURE 1. The side view of configuration of NiMoO₄ with different oxygen vacancies. (A) Zero, (B) one, (C) two, and (D) three.

Computational Method

In order to understand the relationship between vacancies structures and electrical properties in NiMoO₄, the formation energy of neutral oxygen vacancy in different chemical environments was calculated. The corrected formation energy of an isolated neutral O vacancy in NiMoO₄ (∆E_Vo) is defined as:

${\text{E}}_{V_0}={\text{E}}_{defective}-E_{perfect}+\frac{1}{2}{E}_{O_2}$

where E_defective is the total energy of a structure with oxygen vacancies, E_perfect is the total energy of the structure without oxygen vacancy, and E_O2 is the elemental chemical potential of oxygen in the gas phase.

The DFT calculation was implemented in the Vienna Ab-Initio Simulation Package (Kresse and Joubert, 1999). For the exchange and correlation functionals, the Perdew–Burke–Ernzerhof (PBE) version of the generalized gradient approximation (GGA) exchange correlation was used (Blöchl, 1994; Perdew et al., 1996). In the DFT calculation, the NiMoO₄ bulks with different concentrations of oxygen vacancies were used to uncover the electronic properties. Vacuum layer thickness of 20 Å was applied to avoid virtual interaction and obtain more accurate results. The k-grid mesh value was 5 × 5 × 1. In addition, DFT + U method was also introduced to describe the electronic properties and vacancies states in NiMoO₄ bulks. The value of U given to Ni ions was 4 eV (Hinuma et al., 2007). The energy cutoff of 450 eV was used for the wave functions expansion. The energy and force converged to 1.0 × 10^–5 eV atom⁻¹ and 0.03 eV Å⁻¹ to achieve high accuracy.

Results and Discussion

The calculated formation energy for different amount of oxygen vacancies in NiMoO₄ for a 2 × 2 × 2 bulk cell (48 molecular units) is shown in Table 1. The formation energy for different number of oxygen vacancies in NiMoO₄ was 0.73, 1.95, and 3.56 eV, respectively. The formation energy of two and three oxygen vacancies in NiMoO₄ are 2.67 and 4.88 times than that of the one vacancy, respectively, which suggested that one vacancy is more easily formed in NiMoO₄ crystal. This result shows that it is hard to synthesize two and three oxygen vacancies into NiMoO₄ under normal experimental conditions.

TABLE 1

TABLE 1. The formation energy of different concentrations of oxygen vacancy Vo in perfect NiMoO₄.

In order to reveal the oxygen vacancy electron doping effect on the electronic structure of NiMoO₄, the band structure, TDOS, and PDOS, of stoichiometric NiMoO₄ in 2 × 2 × 2 supercell with different amount of oxygen vacancies were calculated. Figure 2 shows the band structure of NiMoO₄ with different numbers of oxygen vacancies from zero to three. The Fermi levels of NMO-0, NMO-1, NMO-2, and NMO-3 were 6.1014, 6.0258, 5.9609, and 5.8729 eV, respectively. All of the Fermi levels were located at zero in all the figures. The valence band maximum of NMO-0 is located at −0.079 eV, and the conduction band minimum is located at 0.056 eV. NMO-0 is a semiconductor with an indirect gap of 0.136 eV. Furthermore, NMO-1, NMO-2, and NMO-3 showed metallic electrical conductivity characteristics. With the introduction oxygen vacancies into NiMoO₄, the extra-nuclear electrons of Mo have been released, which leading to increasing number of carrier concentration. The results are consistent with the DFT calculation result of SF Matar’s work (Matar et al., 2010).

FIGURE 2

FIGURE 2. Band structure of NiMoO₄ with different amounts of oxygen vacancies. (A) NMO-0, (B) NMO- 1, (C) NMO-2, and (D) NMO-3.

It can be obtained that the valence band of NiMoO₄ can be divided into lower and upper valence bands. The lower band mainly consisted of the O 2d, Ni 3d, and Mo 3d, as shown in Figure 3. The upper valence band consisted of Ni 3d and Mo 3d. While oxygen vacancies were introduced into the NiMoO₄ crystal, the band gap of NiMoO₄ has narrowed. The introduction of oxygen vacancies in NiMoO₄ gives more distribution of state density nearby the Fermi energy level, which indicates that more metallic properties of NiMoO₄ (Zhang et al., 2020b).

FIGURE 3

FIGURE 3. TDOS of NiMoO₄ with different amounts of oxygen vacancies. (A) NMO-0, (B) NMO-1, (C) NMO-2, and (D) NMO-3.

The PDOS of O 2p, Ni 3d, and Mo 3d for NMO-0, NMO-1, NMO-2, and NMO-3 are displayed in Figure 4. Nearby the Fermi level, the electronic states of NiMoO₄ mainly consist of Ni 3d and Mo 3d. With the number of oxygen vacancies from zero to three, the half-peak width of Ni 3d and Mo 3d decreased and exhibited higher electron localization effect. This suggests that NiMoO₄ has transformed to metallic properties with oxygen vacancies created into the NiMoO₄ crystal, which is in accordance with the calculation consequence of band structure.

FIGURE 4

FIGURE 4. PDOS for NiMoO₄ with different numbers of oxygen vacancies. (A) NMO-0, (B) NMO-1, (C) NMO-2, and (D) NMO-3.

Conclusion

In summary, we analyzed the formation energy, band structure, DOS, and PDOS from zero to three oxygen vacancies in 2 × 2 × 2 NiMoO₄ supercell with density functional theory calculation. The result revealed that only one oxygen vacancy can easily form in NiMoO₄ crystal. The original NiMoO₄ shows direct band gap semiconductor characteristic. With the amount of oxygen vacancies increase from one to three, the band gap of NiMoO₄ become narrower and exhibit stronger metallic properties. The electron state nearby the Fermi level of NiMoO₄ are mainly determined by Ni 3d and Mo 3d. Oxygen vacancies into NiMoO₄ accelerate the electron localization effect of Ni 3d and Mo 3d around the Fermi level.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author Contributions

All authors listed have made a substantial, direct, and intellectual contribution to the work, and approved it for publication.

Funding

The authors acknowledge the financial support of the Young Science Foundation of Yunnan (Grant No. 2019FD113), National Natural Science Foundation of China (11764047) and Education Science Foundation of Yunnan (2020J0095).

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Acknowledgments

The authors thank the Yunnan Key Lab of Opto-Electronic Information Technology.

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