Superior ionic and electronic properties of ReN$_2$ monolayers as Na-ion battery electrodes

TL;DR

This study demonstrates that ReN$_2$ monolayers are highly stable, conductive, and capable of high capacity with low ion diffusion barriers, making them excellent candidates for high-performance sodium-ion batteries.

Contribution

We introduce ReN$_2$ monolayers as a novel, stable, and highly efficient electrode material for sodium-ion batteries with superior capacity and low diffusion barriers.

Findings

ReN$_2$ monolayer is mechanically and dynamically stable.

It exhibits high capacity of 751 mA h/g for Na-ion batteries.

It has an ultralow Na diffusion barrier of 0.027 eV.

Abstract

Excellent two-dimensional electrode materials can be used to design high-performance alkali-metal-ion batteries. Here, we propose ReN$_2$ monolayer as a superior two-dimensional material for sodium-ion batteries. Total-energy optimization results in a buckled tetragonal structure for ReN$_2$ monolayer, and our phonon spectrum and elastic moduli prove its dynamical and mechanical stability. Further investigation shows that it is metallic and still keep metallic feature after the adsorption of Na or K atoms, its lattice parameter changes by only 3.2\% or 3.8\% after absorption of Na or K atoms. Our study shows that its maximum capacity reaches 751 mA h/g for Na-ion batteries or 250 mA h/g for K-ion batteries, and its diffusion barrier is only 0.027 eV for Na atom or 0.127 eV for K atom. The small lattice change, high storage capacity, metallic feature, and extremely low ion diffusion barriers make the ReN$_2$ monolayer become superior electrode materials for Na-ion rechargeable batteries with ultrafast charging/discharging processes.

Tables

Table 1. Table 1: The site-dependent adsorption energies of Na atom ( E a ​ Na subscript 𝐸 𝑎 Na E_{a{\rm Na}} ) and K atom ( E a ​ K subscript 𝐸 𝑎 K E_{a{\rm K}} ), and the charge transferred by Na atom ( q Na subscript 𝑞 Na q_{\rm Na} ) and K atom ( q K subscript 𝑞 K q_{\rm K} ).

Sites	$E_{a\mathrm{Na}}$ (eV)	$q_{\mathrm{Na}}$ (e)	$E_{aK}$ (eV)	$q_K$ (e)
S1	-0.97	0.88	-1.46	0.88
S2	-1.80	0.87	-2.12	0.88
S3	-1.31	0.88	-1.70	0.88
S4	-1.78	0.84	-1.99	0.88

Table 2. Table 2: Comparison of maximum capacity C M subscript 𝐶 𝑀 C_{M} and diffusion barrier E d subscript 𝐸 𝑑 E_{d} of 12 two-dimensional electrode materials for Na-ion batteries.

	$C_M$ (mA h g-1)	$E_d$ (eV)	Ref.
${\beta }_{12}$ borophene	1984	0.33	Ref. 38
${\chi }_3$ borophene	1240	0.34	Ref. 38
Ca2N	1138	0.08	Ref. s14
Phosphorene	865	0.04	Ref. 37
MoN2	864	0.56	Ref. 18
GeS	512	0.09	Ref. 40
TiS2	339	0.22	Ref. 41
Sr2N	283	0.016	Ref. s14
NbS2	263	0.07	Ref. 41
BP	143	0.217	Ref. 39
Mo2C	132	0.019	Ref. s11
W2C	113	0.019	Ref. added
ReN2	751	0.027	This work

Full text

I Introduction

Recent years have witnessed a booming development in two-dimensional materials since the experimental discovery of graphene 1 ; 2 ; 3 ; 4 . The two-dimensional materials are promising for applications in many fields, such as field-effect transistors 5 ; 6 , phototransistors 7 ; 8 , p-n junctions 9 ; 10 , supercapacitors 11 ; 12 , and batteries 13 ; 14 . Besides graphene, two-dimensional materials such as phosphorene and transition-metal dichalcogenides (TMDC) exhibit many novel physical properties which do not exist in their bulk counterparts. Since the commercialization of the lithium-ion batteries in 1991, rechargeable lithium-ion batteries, with the reversible capacity and cycle life, have attracted huge interest l1 ; l2 ; l3 ; l4 ; l6 ; l7 ; l8 ; l9 . Nevertheless, the Li-ion batteries still need to be improved for better reversibility and ion diffusivity and smaller volume change  s1 ; s2 ; s3 . On the other hand, it is highly desirable to develop new anode materials for high-performance ion batteries. Because of the large natural abundance of Na (23000 ppm) and K (17000 ppm) in comparison to that of Li (20 ppm) in the earth’s crust s4 , Na-ion and K-ion batteries have attracted much attention. To date, a tremendous number of 2D materials, including graphene systems s6 ; s7 , transition-metal dichalcogenides s8 ; s9 ; s10 , transition-metal carbides s11 ; s12 ; s13 ; added , and metal nitrides s14 , have been studied because of their excellent electrochemical performance as battery anode materials. The storage capacity for most of the two-dimensional materials is between 200 and 600 mA h g*-1* and the ion diffusion barrier ranges from 0.1 to 0.6 eV. It is still necessary to seek new materials for ion batteries with high capacity and low ion diffusion barrier.

Here, through first-principles calculation we study ReN2 monolayers as two-dimensional structures and investigate their electronic and mechanical properties for superior anode materials of alkali-metal-ion batteries. We obtain the stable tetragonal structure of ReN2 monolayer in terms of our calculated phonon spectra and in-plane stiffness constants. According to elastic theory, the tetragonal ReN2 can be freestanding without the support of substrate. Our calculations with the PBE functional and HSE functional with/without the spin-orbit coupling show that the ReN2 monolayer is metallic. After the absorption of Na and K atoms, the system still keep the metallic feature which is advantageous for the applications in Na-ion and K-ion batteries. The storage capacity of the ReN2 monolayer is 751 mA h g*-1* or 250 mA h g*-1* if taken as Na-ion and K-ion anode materials, and the corresponding ion diffusion barrier, 0.027 eV for Na or 0.127 eV for K, is very small. The high capacity and the extremely low diffusion barrier for Na atom make the ReN2 monolayer a superior anode material. More detailed results will be presented in the following.

II Computational methods

The first-principles calculations are done with the projector-augmented wave (PAW) potential method 22 as implemented in the Vienna ab initio simulation package software (VASP) 23 . We take the generalized gradient approximation (GGA), accomplished by Perdew, Burke, and Ernzerhof (PBE) 24 , for the exchange-correlation functional. The kinetic energy cutoff of the plane waves is set to 600 eV. For both optimization and static calculation, the Brillouin zone integration is carried out with a 10$\times$10$\times$1 special $\Gamma$-centered k-point mesh following the convention of Monkhorst-Pack 25 . All atomic positions are fully optimized with the conjugate gradient optimization until all the Hellmann-Feynman forces on each atom are less than 0.01 eV/Å and the total energy difference between two successive steps is smaller than 10*-6* eV. Furthermore, phonon dispersion calculation in terms of the density functional perturbation theory, by using the PHONOPY program 29 , is performed to ensure the structural stability of the monolayers. We take the 4$\times$4$\times$1 supercell for calculating the phonon spectra of the 2D structures. In order to make further confirmation, band dispersion calculations with Heyd-Scuseria-Ernzerhof (HSE) hybrid functional 26 ; 27 ; 28 are carried out, with the mixing rate of the HF exchange potential being 0.25. The semi-empirical correction scheme of Grimme (DFT-D2) D2 is employed to evaluate the effect of van der Waals (vdW) interactions on Na/K ion adsorption. In the calculation of Na/K diffusion, we use nudged elastic band (NEB) method to get the ion diffusion barrier.

III Results and discussion

III.1 Structures and stability

The three-dimensional materials of rhenium dinitride ReN2 have been synthesized by metathesis reaction under high pressure 19 , and X-ray Diffraction(XRD) shows that the samples have the same structure as the three-dimensional MoS2-like hexagonal structure. A systematical first-principles investigation shows that the three-dimensional MoN2-like structure is dynamically stable for ReN2 and there is a three-dimensional tetragonal structure with lower total energy 20 ; 21 . In addition, experiment indicates that the three-dimensional ReN2 may be layered in terms of its compressibility 19 .

As for the two-dimensional structure of ReN2 monolayer, four possible configurations are considered: T-phase structure, T*′-phase structure, H-phase structure, and tetragonal structure. The T-phase structure, which has been found in other two-dimensional materials 30 , is proved to be unstable for ReN2 in terms of its phonon spectrum result. Distorted T′*-phase structure 31 ; 32 ; 33 ; 34 is also proved to be impossible because our phonon spectrum calculation show that there are very large negative phonon frequencies near the $\Gamma$ point. Both H-phase structure and tetragonal structure have the phonon spectra without imaginary phonon modes. The total energy of the tetragonal structure is lower than the hexagonal one by 0.33 eV per formula unit. Therefore, the two-dimensional tetragonal structure is stable. It (P$\bar{4}$m2) is made up with three atom planes as shown in FIG. 1. The comparative study of spin-polarized and spin-unpolarized calculations show that the tetragonal structure is non-magnetic. Its in-plane lattice parameters $a$ is 3.178 Å, and the vertical distance between the top and bottom nitrogen planes is 1.96 Å. The Re-N bond length $l_{\rm Re-N}$ is 1.87 Å. The cohesive energy per formula unit is defined as $E_{coh}=E_{\rm Re}+E_{\rm N_{2}}-E_{\rm ReN_{2}}$, where $E_{\rm Re}$ and $E_{\rm N_{2}}$ are the total energies of isolated Re atom and N2 molecule. The cohesive energies 6.44 eV is much larger than 1.87 eV for the case of MoN2 mon2ce , which reveals that the synthesis of the buckled ReN2 monolayer is accomplishable.

In order to analyze the dynamical stability of the 2D tetragonal structure, the phonon spectrum calculations are performed by using the PHONOPY program 29 , and the calculated results are presented in FIG. 1. It is clear that there are nine phonon branches including three acoustic branches and six optical phonon bands. Non-existence of negative phonon frequencies in FIG. 1 proves the dynamical stability of the 2D tetragonal structures. It can be seen in FIG. 1 that in the vicinity of the $\Gamma$ point, the acoustical branches show linear dispersion, and the out-of-plane acoustical branch appears to be softer than the other two due to the special mode in the two-dimensional materials 35 .

To inspect the mechanical stability, we calculate the elastic constants of the ReN2 monolayer: C11 = 107.4 N/m, C22 = 108.0 N/m, C12 = 74.3 N/m, and C66 = 218.8 N/m. The Young’s modulus $Y$ is equivalent to 56.3 N/m. For two-dimensional materials, only $C_{11}$, $C_{12}$, $C_{16}$, $C_{26}$, $C_{66}$ and $C_{22}$ are meaningful quantities, and the criteria of mechanical stability require that $C_{11}C_{22}>C_{12}C_{21}$ and $C_{66}>0$ prb are satisfied. Thus the tetragonal ReN2 monolayer has the mechanical stability. Assuming that we have the square flake with the edge length $l$, the ratio between the out-of plane deformation $h$ induced by its own gravity and the edge length $l$ is $h/l\approx(\rho gl/Y)^{1/3}$, where g being the gravitational acceleration and $\rho$ the density of the two-dimensional material. Here, the density of the ReN2 monolayer is $3.54\times 10^{-6}$ kg$\cdot$m*-2*, and then we can obtain $h/l\approx(0.62l\times 10^{-12})^{1/3}$ for the ReN2monolayer, where $l$ is in micrometer. Even for $10^{4}$ $\mu$m2 flakes, the ratio is only $3.96\times 10^{-4}$, which is smaller than the previous result of Ca2N freestanding monolayer, $6.31\times 10^{-4}$ 36 . Therefore, the 2D ReN2 monolayer can keep its stability without the support of a substrate.

III.2 Electronic structures

The 2D tetragonal structure obeys the $S_{4}$ symmetry group. For the electronic wave function of the d orbits, the parity of mirror inversion is even for $d_{z^{2}}$, $d_{xy}$, and $d_{x^{2}-y^{2}}$, and odd for $d_{xz}$ and $d_{yz}$. The band dispersions of the 2D materials without the spin-orbit coupling, with the weights of atomic orbitals indicated, are presented in FIG. 2. The size of symbol is proportional to the weight of the orbital. In the energy spectra, all the N p bands are filled, and the nearly empty bands come from Re d states. Near the $\Gamma$ point, the band near the Fermi level is mainly from Re d${}_{x^{2}-y^{2}}$, and near the X point, the band near the Fermi level consists mainly of Re d${}_{z^{2}}$ and d${}_{x^{2}-y^{2}}$.

The band structure shows that the two-dimensional ReN2 monolayer is metallic, but we need to confirm that the system keep metallic feature with HSE calculation or spin-orbit coupling (SOC), because PBE calculation always underestimates the semiconductor gaps and the spin-orbit coupling can open a gap in the transition-metal system. For this purpose, we calculate the energy spectra with HSE with SOC, and the calculated results are presented in FIG. 2. As FIG. 2 shows, the tetragonal ReN2 monolayer is still metallic. This is advantageous for its applications in Na-ion and K-ion battery technology.

III.3 Ion adsorption

A 2$\times$2 supercell of the ReN2 monolayer is used as the substrate for the adsorption of the Na atom and K atom. After adsorbing a metal atom, the chemical formula of the system can be written as ARe4N8, where A represents Na atom or K atom. The adsorption energy $E_{a}$ is defined by $E_{a}=E_{\rm ARe_{4}N_{8}}-E_{\rm A}-E_{\rm Re_{4}N_{8}}$ where $E_{\rm A}$ is the total energy of bulk A metal per atom, and $E_{\rm ARe_{4}N_{8}}$ and $E_{\rm Re_{4}N_{8}}$ are the total energy of the Re4N8 monolayer with and without A adsorption. According to the symmetry of the Re4N8 monolayer, eight possible sites are considered, as shown in FIG. 1(d). Four of the eight sites remain after our geometrical optimization, and their adsorption energies are summarized in TABLE. 1. We can see that the adsorption energies of all the four sites are negative, which means that Na/K atom prefers to be adsorbed on the host material instead of forming a cluster.

The unit cell of the ReN2 monolayer includes one Re atom, one high-position N atom, and one low-position N atom. According to the adsorption energy, Na/K atom prefers to stay at the position above the low-position N atom (S2 site), and the distance between Na atom and the nitrogen atom right below it is 3.49 Å (3.89 Å for K atom). The adsorption energy at the hollow site (S4) is slightly larger than the adsorption energy at the S2, and much smaller than the adsorption energies at the S1 and S3 sites. Because of the Coulomb repulsion between Na/K atom and Re atom, the absorbed Na/K atom will not stay at the S3 site. Nearest the S1 and S4 sites are the high-position N atoms, but nearest the S2 site are two Re atoms. Thus the absorption of Na/K atom at the S2 site is lowest among the four possible sites, which can explain the absorption behavior of Na/K atom.

To further understand the absorption of Na/K atom, we make the Bader charge analysis and the results are summarized in TABLE. 1. The existence of charge transference by Na/K atom reveals that the adsorption is chemical, which can be regarded as redox reaction during the battery operation. The calculated charge density difference is showed in FIG. 3, which is defined by $\Delta\rho=\rho(\rm ARe_{4}N_{8})-\rho(\rm A)-\rho(\rm Re_{4}N_{8})$. This confirms the existence of chemical adsorption. The larger atom (K atom) reduces the adsorption energy difference between different sites. We also calculate the density of states (DOS) of the Re4N8 after absorbing Na/K atom. The calculated results show that the system still keep metallic character, which is advantageous for making electrode materials from the ReN2 monolayer.

III.4 Key storage parameters

Open circuit voltage (OCV) and theoretical storage capacity are the important parameters to describe the performance of electrode materials. The charge/discharge process of ReN2 monolayer can be described by ReN2 + $x$A+ + $xe^{-}\leftrightarrow$ AxReN2. For this reaction, the average open circuit voltage can be defined by $V_{ave}=(E_{\rm ReN_{2}}+xE_{\rm A}-E_{{\rm A}_{x}{\rm ReN_{2}}})/xe$ when we ignore the volume and entropy effects during the alkali metal adsorption process. $E_{\rm ReN_{2}}$ and $E_{{\rm A}_{x}{\rm ReN_{2}}}$ are the total energies of the ReN2 monolayer before and after the adsorption of A (Na or K) atom. In order to calculate the storage capacity, we choose 35Å as the thickness of vacuum slab to avoid the interaction between neighboring layers. In the process of Na/K intercalation, we calculate the average adsorption energy layer by layer, which is defined by $E_{n}=(E_{{\rm A}_{8n}{\rm Re_{4}N_{8}}}-E_{{\rm A}_{8(n-1)}{\rm Re_{4}N_{8}}}-8E_{\rm A})/8$. Here A represents Na or K atom and $E_{{\rm A}_{8n}{\rm Re_{4}N_{8}}}$ is the total energy of ReN2 with the adsorption of $n$ A atom layers. Negative $E_{n}$ means the adsorption of $n$ layers is accessible and we can obtain the maximum storage capacity by $C_{M}=xF/M_{\rm ReN_{2}}$. Here, $F$ is Faraday constant with a value of 26.8 A h mol*-1*, $M_{\rm ReN_{2}}$ is the molar mass of ReN2 per formula unit, and $x$ means the number of A atoms absorbed on the ReN2 per formula unit.

As shown in FIG. 4, the ReN2 monolayer can adsorb three layers of Na atoms on each sides for Na-ion batteries, and the maximal storage capacity of the ReN2 monolayer can reach 751 mA h g*-1*. The ReN2 monolayer adsorb only one layer of K atom on each sides and thus its storage capacity is 250 mA h g*-1* for K-ion batteries. The first Na atom layer is located at the S2 site (above the low-position nitrogen atom), and the average adsorption energy is -1.02 eV, which becomes -0.83 eV for first K atom layer adsorption. Compared to the adsorption energy of one Na/K atom (-1.80/-2.12 eV), this fact shows that the adsorption energy of K atom increases faster than that of Na atom while the concentration of Na/K atoms is increasing. Then for the second layer, Na atoms prefer to stay at the S1 site and the average adsorption energy is -0.20 eV, while the positive average adsorption energy for K atom (0.40 eV) reveals that the second K atom layer fails to be absorbed on the ReN2 monolayer. As for the third layer, Na atoms prefer to be adsorbed at the S4 site and the average adsorption energy becomes -0.08 eV. Three Na atom layers on each sides, in spite of the large mass of the ReN2, make the ReN2 monolayer a high-capacity anode material. The average open-circuit voltage decreases from 1.0 to 0.4 V with the increase of the adsorbed Na concentration from 8 to 24 atoms on the 2$\times$2 supercell. The open circuit voltage for K-ion batteries is 0.83 V with 8 atoms on the 2$\times$2 supercell. In the process of intercalation of Na (K) atom, the change of lattice parameter is only 3.2% (3.8%), which is propitious to achieve the rechargeable batteries.

III.5 Ion diffusion

The fast charging and discharging processes need the fast ion diffusion. The ion diffusion depends on the temperature-dependent molecular transition rate $D$, which is proportional to exp($-E_{d}/k_{B}$T), where $E_{d}$, $k_{B}$, and T are the diffusion barrier, Boltzmann’s constant, and temperature, respectively. A low diffusion barrier means a fast charging/discharging process for ion batteries. Three possible diffusion paths are taken into consideration, and the calculated results are shown in FIG. 5. The diffusion barrier of the path 1 is 0.027 eV and 0.127 eV for Na-ion and K-ion batteries, respectively, which is the lowest of three possible circumstances. It can be explained by the existence of hollow space in the monolayer which reduces the influence of the energy variation at the different sites. The extremely low diffusion barrier of Na atom can bring to ultrafast charging/discharging cycles in the Na-ion batteries.

It is noted that Na/K diffusion on the ReN2 monolayer is quite anisotropic. Coming from the S1 site, Na atom will encounter the hollow space along path1 or relatively high-position Re atom along path 3. It brings to the great anisotropy between the diffusion barriers along the two orthogonal directions, and the ratio is $E_{d3}/E_{d1}\approx$ 18 for Na atom or $E_{d3}/E_{d1}\approx$ 3 for K atom. The anisotropy is greater than phosphorene (the ratio is 8) 37 and can achieve the unusual transports along the different directions in the these systems.

III.6 Comparison with others

It is interesting to compare the ReN2 with other two-dimensional materials for ion batteries. For Na-ion batteries, the data are summarized in TABLE. 2. It can be seen that the maximal storage capacity of the ReN2 monolayer is smaller than those of borophene 38 , Ca2N s14 , phosphorene 37 , and MoN2 monolayer 18 , but better than those most of transition-metal dichalcogenides, MXenes, and so on. Actually, the maximum capacity of the ReN2 monolayer is twice or five times that of Sr2N or Mo2C. For K-ion batteries, the maximum capacity of the ReN2 monolayer (250 mA h g*-1*) is comparable to those of GeS (256 mA h g*-1*) 40 , Mo2C (smaller than 263 mA h g*-1*) s11 , and Ti3C2 (191.8 mA h g*-1*) s12 , but smaller than those of MoN2 (432 mA h g*-1*) 18 and BP (570 mA h g*-1*) 39 . The ReN2 monolayer is better serving as Na-ion storage materials than as K-ion ones. Compared to other two-dimensional materials, the ReN2 have the extremely low Na ion diffusion barrier that is lower than those of other 2D materials except Sr2N monolayer s14 and Mo2C monolayer s11 . The K-ion diffusion barrier of the ReN2 monolayer (0.127 eV) is smaller than those of MoN2 (0.49 eV) 18 and BP (0.155 eV) 39 , and larger than those of Mo2C (0.015 eV) s11 , GeS (0.050 eV) 40 , and Ti3C2 (0.103 eV) s12 . Very importantly, the ReN2 monolayer have both very high storage capacity and extremely low ion diffusion barrier, which makes it promising electrode materials for Na-ion batteries.

IV Conclusion

In summary, we have proposed the ReN2 monolayer as new 2D materials and superior anode materials for Na-ion and K-ion batteries by first-principles investigation. Our calculated results show that the two-dimensional ReN2 monolayer is promising as electrode materials because (1) it keeps metallic feature before and after the adsorption of Na/K atom and thus has the good electric conductivity; (2) the small lattice changes during the intercalation reveals the good recyclability; (3) the maximum storage capacity of the ReN2 monolayer reaches to 751 mA h g*-1* for Na-ion batteries, which is quite high among two-dimensional electrode materials to date; (4) the low ion diffusion barriers (0.027 eV for Na and 0.127 eV for K) can make the charging/discharging cycles fast. Therefore, our first-principles investigation shows that the ReN2 monolayer is superior as two-dimensional electrode materials for Na/K-ion batteries.

Acknowledgements.

This work is supported by the Nature Science Foundation of China (Grant No. 11574366), by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No.XDB07000000), and by the Department of Science and Technology of China (Grant No. 2016YFA0300701). The calculations were performed in the Milky Way #2 supercomputer system at the National Supercomputer Center of Guangzhou, Guangzhou, China.