Investigations on Nb₂C monolayer as promising anode material for Li or non-Li ion batteries from first-principles calculations

Abstract

First-principles calculations are performed to study the electronic properties and metal ion storage capabilities of the two-dimensional (2D) Nb₂C monolayer and its corresponding fluoride and hydroxide materials. We show that the Nb₂C monolayer and the derived Nb₂CF₂ and Nb₂C(OH)₂ are all metallic in their most stable configurations. We systematically investigate the adsorption and surface diffusion of different metal atom species A = Li, Na, K, Be, Mg, Ca, Al. We find that the bare Nb₂C monolayer has excellent performance in the case of Li or Mg: the material remains metallic after adsorption; the ion diffusion is fast with extremely low diffusion barrier; the storage capacity is high (∼542 mA h g⁻¹ for Li and ∼1084 mA h g⁻¹ for Mg); and the average intercalation potential is relatively low. Particularly, the diffusion barrier heights for the elements Li, Na, K, Mg and Ca are all lower than 0.1 eV. In addition, the functional groups tend to strongly degrade the performance, which should be avoided in experiment as much as possible. Our results suggest that the Nb₂C monolayer is a promising anode material for Li- or non-Li-ion batteries.

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1 Introduction

From portable electronic devices to electric vehicles and to large-scale power grid systems, energy storage has become an essential technology for our daily life. Among all kinds of energy storage systems, secondary batteries have the important advantages of high efficiency and compactness.^1–3 As the most prominent example, Li-ion batteries (LIBs) have undergone rapid development since their first commercialization by Sony in 1991. Nevertheless, currently the development of LIBs has been hampered by cost and safety issues.⁴ With the increasing usage of LIBs, the lack of lithium sources also emerges as one major challenge. Therefore, non-Li-ion batteries, in which Li is substituted by other metal species, are being actively explored. Particularly, Na-ion batteries (NIBs) have received a lot of attention because Na is much more abundant and cheaper than lithium.^5,6 Beyond NIBs, batteries with other alkali (such as K)^7,8 or multivalent metal ions (Mg,^9,10 Ca,¹¹ and Al¹²) have also been investigated. For developing all these various secondary batteries, a critical problem is to search for suitable electrode materials to optimize the battery performance.

Since the discovery of graphene, the novel properties and wide applications of two-dimensional (2D) layered materials have attracted tremendous interest. 2D materials such as graphene, phosphorene and dichalcogenides (such as NbSe₂ and MoS₂)^13–15 have been investigated as electrode materials for LIBs,^16–22 and the MoS₂/graphene 2D composite has also been tested as anode materials for NIBs.²³ Recently, a new family of 2D materials, the early transition-metal carbides and carbonitrides (M_n+1X_n, n = 1, 2, 3; X = C or N), known as “MXenes”, have attracted more and more attention in research. MXenes are typically synthesized from the MAX precursors (A represents one of the A group elements such as Al), which include more than 60 phases. One of the MXenes, Ti₃C₂, was first synthesized by Naguib et al.^24–27 by selectively etching the Al layers from Ti₃AlC₂ with hydrofluoric acid (HF). To date, many other MXenes have also been successfully synthesized, such as Ti₃CN, Ti₂C, (V_0.5Cr_0.5)₃C₂, (Ti_0.5Nb_0.5)₂C, Nb₂C, V₂C and Ta₄C₃, etc.^25–29

With more MXenes being realized, their properties have been actively studied.^30–34 It has been shown that these materials could have great potential for energy storage applications. For instance, Zhou et al.³⁵ proposed that monolayer Ti₃C₂ and its derivatives are promising anode materials for LIBs using first-principles calculations. Naguib et al. theoretically predicted that Ti₂C, (Ti_0.5Nb_0.5)₂C, Ti₃(C_0.5N_0.5), Ti₃CN, TiNbC, Nb₂C and Ta₄C₃ are all suitable electrode materials for LIBs.^36,37 Gogotsi et al. demonstrated that 2D Ti₃C₂ MXene layers could be spontaneously intercalated by Na⁺, K⁺, NH₄⁺, Mg²⁺ and Al³⁺ ions.³⁸ They also performed calculations and showed that the MXene nanosheet could be utilized as anodes for non-Li-ion batteries.³⁹

In recent experiments, two new kinds of MXenes (V₂C, Nb₂C) have been successfully synthesized for the first time by treating their corresponding MAX phases (V₂AlC, Nb₂AlC) in aqueous HF.⁴⁰ Preliminary experimental studies demonstrated that for V₂C-based electrodes, reversible capacities of 260 mA h g⁻¹ at 1C and 125 mA h g⁻¹ at 10C could be achieved; while for Nb₂C-based electrodes, 170 mA h g⁻¹ at 1C and 110 mA h g⁻¹ at 10C were obtained. The measured Li specific capacities are not high enough as expected. For V₂C, later on, it was clarified that the high capacity of bare V₂C might be decreased largely by the functional groups which remain after synthesis.⁴¹ Whether a similar scenario also occurs in the case of Nb₂C is currently not fully understood. In addition, it is worth noting that from low to high charge–discharge rates the capacity of Nb₂C-based electrodes decreases much slower than the V₂C-based electrodes, implying a much faster ion diffusion for Nb₂C. Furthermore, since Nb belongs to the 4d transition metals, the electronic correlation effects could strongly affect the material's chemical and physical properties. All these interesting observations call for a detailed theoretical study to fully investigate the properties of Nb₂C-based 2D materials.

Motivated by the reasons stated above, in this paper, we systematically investigate the electronic and metal ion storage properties of the Nb₂C monolayer and its fluorinated and hydroxylated derivatives as anode materials based on first-principles calculations. We determine the structural and electronic properties of the materials before and after adsorption. The adsorption and diffusion of different metal species A (A = Li, Na, K, Be, Mg, Ca, Al) are studied. We find that the bare Nb₂C monolayer has very good performance as an anode material. Especially, its surface diffusion barrier heights for various ions are all below 0.1 eV which is among the lowest of all the existing 2D materials discovered to date, indicating a very fast ion diffusion. We also show that the bare Nb₂C monolayer is metallic before and after adsorption, with a very high specific Mg capacity (∼1084 mA h g⁻¹) as well as a high Li capacity (∼542 mA h g⁻¹). The functional groups greatly reduce the Li or non-Li storage capacities, which should be avoided in experiment as much as possible.

2 Computational details

Our calculations are based on density functional theory (DFT) using the plane-wave pseudopotentials⁴² with the Perdew–Burke–Ernzerhof (PBE)^43,44 form of exchange–correlation functionals as implemented in the Vienna Ab initio Simulation Package (VASP).⁴⁵ A cutoff energy of 600 eV is employed for the plane wave expansion. Considering the strong correlation effects in niobium element, electronic structure calculations and structural relaxations are performed by using a GGA plus Hubbard U (GGA+U)^46,47 method. The U value of the Nb atom is set to be 6.5 eV.⁴⁸ The Brillouin zone is sampled with 6 × 6 × 1 Monkhorst–Pack k-point mesh⁴⁹ for the structural optimization, and with 12 × 12 × 1 mesh for the electronic structure calculations. The convergence criteria for the total energy and ionic forces were set to be 10⁻⁴ eV and 0.001 eV Å⁻¹, respectively.

Possible spin polarization is carefully tested and no spin-polarization effect is observed in our calculation. In addition, concerning the spin–orbital coupling (SOC) effects, we have compared the electronic structures of Nb₂C monolayer with and without SOC in our calculations. Results show that the SOC effect has little effect on the band structure. Therefore, in the following calculations we do not include the SOC effect.

The atomic model of the free-standing Nb₂C sheet constructed based on the Nb₂AlC structure is used as the initial configuration for geometry optimization. Each bare Nb₂C monolayer consists of a triple-layer stacked in the sequence of Nb(1)–C–Nb(2), which can be viewed as two Nb-atomic layers being cleaved with one C-atomic layer, forming edge-shared Nb₂C octahedra [Fig. 1(a)]. For the study of metal ion adsorption and diffusion on Nb₂C and Nb₂CX₂ (X = F, OH) monolayers, a 4 × 4 supercell containing 32 Nb and 16 C atoms is employed in our calculations. A 2 × 2 supercell is utilized for the study of structural and electronic properties, average open circuit voltage, and storage capacity.

Fig. 1 Optimized lattice structure of bare Nb₂C monolayer and its fluorinated and hydroxylated derivatives. (a) Side view and (b) top view of the bare Nb₂C monolayer consisting of a triple atomic layer with Nb(1)–C–Nb(2) stacking sequence. (c–h) Side views of the lattice structures of (c) I-Nb₂CF₂, (d) II-Nb₂CF₂, (e) III-Nb₂CF₂, (f) I-Nb₂C(OH)₂, (g) II-Nb₂C(OH)₂ and (h) III-Nb₂C(OH)₂. (i and j) Top views of I-Nb₂CF₂ and II-Nb₂CF₂, in which the F groups are on top of the C atoms or above the hollow sites formed by three neighboring C atoms, respectively. III-Nb₂CF₂ is a combination of I-Nb₂CF₂ and II-Nb₂CF₂, in which the F groups are located above the C atoms on one side and at the hollow sites on the other side. The geometric configurations of OH groups for I-Nb₂C(OH)₂, II-Nb₂C(OH)₂ and III-Nb₂C(OH)₂ resemble those of the corresponding fluorides shown in the figure.

3 Results and discussion

3.1 Structural and electronic properties of Nb₂C and Nb₂CX₂ (X = F, OH) monolayers

We first address the optimized crystal structures and the electronic properties of monolayer Nb₂C as well as its fluorinated and hydroxylated derivatives [denoted as Nb₂CF₂ and Nb₂C(OH)₂, respectively]. For a 2 × 2 supercell of the bare Nb₂C monolayer, the optimized lattice parameters are listed in Table 1. The vertical distance between Nb(1)-layer and Nb(2)-layer, i.e., the thickness of the monolayer, is 2.468 Å. The Nb(1)–C bond length is 2.198 Å, the same as that of the Nb(2)–C bond.

Table 1 The optimized structural parameters for the bare Nb₂C monolayer and its fluorinated and hydroxylated derivatives. The lengths are in Å

	Parameter	Bond length		Thickness
	a, b	Nb(1)–C/Nb(2)–C	Nb(1)–F/O/Nb(2)–F/O	Monolayer
Nb2C	6.302	2.198/2.198		2.468
I-Nb2CF2	6.526	2.188/2.188	2.335/2.335	4.984
II-Nb2CF2	6.100	2.227/2.227	2.270/2.270	5.592
III-Nb2CF2	6.200	2.250/2.164	2.289/2.326	5.492
I-Nb2C(OH)2	6.500	2.197/2.197	2.231/2.231	6.979
II-Nb2C(OH)2	6.176	2.237/2.237	2.261/2.261	7.435
III-Nb2C(OH)2	6.280	2.255/2.174	2.275/2.322	7.326

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The Nb₂CF₂ and Nb₂C(OH)₂ sheets are constructed by saturating the surface under-coordinated Nb atoms with F and OH, respectively. Three possible configurations are considered: type I: the F or OH groups are above the vertical site of each C atom on both sides of the Nb₂C monolayer [see Fig. 1(c) and (f)]; type II: the F or OH groups are located above each hollow site formed by three neighboring C atoms on both sides of the Nb₂C monolayer [see Fig. 1(d) and (g)]; type III: a mixture of type I and II, in which the F or OH groups are located above the vertical sites of three C atoms on one side while above the hollow sites of C atoms on the other side, forming different layouts on the two sides of the Nb₂C monolayer [see Fig. 1(e) and (h)]. The optimized lattice parameters for each type of configuration are shown in Table 1.

The relative structural stability of the three types of configurations for Nb₂CF₂ and Nb₂C(OH)₂ can be determined by comparing their total energies. The results show that the type I configuration is energetically the most favorable for both Nb₂CF₂ and Nb₂C(OH)₂. Specifically, the total energy of I-Nb₂CF₂ (denoting the type I structure) is lower than that of II-Nb₂CF₂ and III-Nb₂CF₂ by about 0.17 and 0.55 eV per unit cell, respectively. Also, the energy of I-Nb₂C(OH)₂ is lower than that of II-Nb₂C(OH)₂ and III-Nb₂C(OH)₂ by about 0.24 and 0.51 eV per unit cell, respectively. This indicates that both F and OH groups prefer to stay at the top sites of C atoms, rather than staying at the hollow sites. It is also worth noting that for both derivatives, their type I structures have the largest lattice parameter and the thinnest layer thickness.

In order to be utilized as battery electrode materials, it is desirable for the material to be metallic. Fig. 2 shows the total density of states (DOS) of Nb₂C, Nb₂CF₂ and Nb₂C(OH)₂ monolayers. For bare Nb₂C, the resulting DOS in Fig. 2(a) indicates that it is metallic, which is in agreement with previous work.⁵⁰ We find that when Nb₂C is passivated by F or OH, the generated Nb₂CF₂ or Nb₂C(OH)₂ monolayers still maintain metallic properties regardless of the specific adsorption configurations [see Fig. 2(b)–(g)]. This hence indicates that the bare Nb₂C monolayer and its fluorinated and hydroxylated derivatives all satisfy the requirement of being metallic for electrode materials. Fig. 2(a) also shows that the C atoms have almost no contribution to states near the Fermi level, namely, the low-energy carriers are originated from Nb atoms. We note that neglecting the correlation effect on Nb atoms would lead to insulating phases for the two derivatives,⁴⁰ which indicates the importance of electronic correlation effects in the current system. Due to the above analysis, we will mainly focus on the most stable structures, i.e. the type I structures for the two derivatives Nb₂CF₂ and Nb₂C(OH)₂ in the following investigations.

Fig. 2 Total DOS of (a) Nb₂C, (b) I-Nb₂CF₂, (c) II-Nb₂CF₂, (d) III-Nb₂CF₂, (e) I-Nb₂C(OH)₂, (f) II-Nb₂C(OH)₂ and (g) III-Nb₂C(OH)₂. The Fermi levels are set to zero.

3.2 Metal atom adsorption on Nb₂C and on Nb₂CX₂ (X = F, OH) monolayers

Since the Nb₂C monolayer and its fluorinated or hydroxylated derivatives are all metallic, in the following, we explore the possibility of these materials to be utilized as electrode materials for Li- and non-Li-ion batteries by investigating their adsorption of the metal species A (A = Li, Na, K, Be, Mg, Ca, Al). To this end, the first step is to analyze the adsorption energy and to determine the most favorable adsorption site. Herein, a 4 × 4 supercell is used to study the adsorption of one A atom on the surface, corresponding to the chemical stoichiometries of Nb₃₂C₁₆A, Nb₃₂C₁₆F₃₂A and Nb₃₂C₁₆(OH)₃₂A, respectively, for the three materials. Three different adsorption sites with high symmetry are considered in our calculations: (i) top site of C atom (which is above the F atom for I-Nb₂CF₂, and above the OH group for I-Nb₂C(OH)₂); (ii) top site of Nb(1) atom; (iii) top site of Nb(2) atom.

Here, the adsorption energy (E_ad) of an A atom on the monolayer is defined as:

E_ad = E_{Nb32C16X32A(X=□,F,OH)} − E_{Nb32C16X32(X=□,F,OH)} − E_A, (1)

where E_A is the energy per atom in the bulk metal of A, E_{Nb32C16X32A(X=□,F,OH)} and E_{Nb32C16X32(X=□,F,OH)} are the total energies of the Nb₃₂C₁₆X₃₂ (X = □, F, OH) monolayer with and without A adsorption. The symbol “□” here means the bare monolayer without functional groups.

A negative value of E_ad indicates that the corresponding atom A prefers to adsorb on the monolayer, instead of forming a metal cluster. The adsorption energies calculated for different adsorption sites are plotted in Fig. 3. One observes that for I-Nb₂CF₂, only Na and K can adsorb on the monolayer (for Na, only the top site of Nb(2) works), while other adatoms tend to form metal clusters by themselves. For I-Nb₂C(OH)₂, all the adsorption energies are positive indicating that none of the atoms can get adsorbed. Therefore the presence of F/OH groups on the surface would significantly degrade the storage capacity of Nb₂C. This is similar to the cases of other MXene materials.^35,41

Fig. 3 Adsorption energies for atom species A (A = Li, Na, K, Be, Mg, Ca, Al) on (a) Nb₂C, (b) I-Nb₂CF₂ and (c) I-Nb₂C(OH)₂ at different adsorption sites.

Fortunately, for the bare Nb₂C monolayer, almost all the adatoms prefer to adsorb on its surface as indicated by the negative adsorption energy values in Fig. 3(a), except for Be and Al which have relatively small E_ad. The result indicates that the bare Nb₂C monolayer possesses the possibility to be utilized as an electrode material for the A′-ion batteries with (A′ = Li, Na, K, Mg, Ca). Further, by comparing the adsorption energies for different sites, one can determine the most favorable adsorption site for each element. Specifically, the most favorable adsorption sites for Li, Na, K, Mg and Ca are on top of C, Nb(2), Nb(2), C and C, respectively. In the following calculations, we will focus on the adsorption of Li, Na, K, Mg and Ca atoms onto the bare Nb₂C monolayer.

We next present the optimized structures for A′-adsorbed Nb₂C monolayers (A′ = Li, Na, K, Mg, Ca). As shown in Fig. 4, for the cases of Na- and K-adsorption, the distances along the c-axis between Nb(2) and Na/K (or between C and Na/K) are 5.209/5.620 Å (or 3.978/4.391 Å), respectively. The adsorption height of K is larger than that of Na. For Li-, Mg- and Ca-adsorbed configurations, the distances along the c-axis between C and Li/Mg/Ca are 3.677/3.678/3.981 Å, respectively. To further investigate the charge transfer during the adsorption process, we carry out the Bader charge analysis. The results are listed in Table 2. One can see that in general the adatoms lose electrons, which are mostly transferred to the C atoms in the layer. To be specific, the Li atom transfers about 0.84e to the bare Nb₂C monolayer, and the transferred charges for Na/K/Mg/Ca are about 0.68/0.68/0.69/0.94e, respectively. This indicates that the atoms are chemically adsorbed on Nb₂C and they form chemical compounds, corresponding to the redox reaction similar to other electrode materials.

Fig. 4 Side views of the optimized structures of Nb₂C monolayers after adsorption with (a) Li, (b) Na, (c) K, (d) Mg and (e) Ca.

Table 2 Bader charge analysis. The number of valence electrons taken into account in the calculation for Li, Na, K, Mg, Ca, Nb and C are 1, 1, 9, 2, 10, 13 and 4, respectively

	Average charge state
	Nb	C	A′
Nb2C	11.91	6.18
Nb2C + Li	12.02	6.18	0.16
Nb2C + Na	11.99	6.18	0.32
Nb2C + K	11.99	6.18	8.32
Nb2C + Mg	12.00	6.17	1.31
Nb2C + Ca	12.03	6.17	9.06

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After adsorption, whether the monolayer would maintain a metallic character or become an insulator is important for its electrode performance. To answer this question, we calculate the total DOS of the A′-adsorbed Nb₂C monolayer. The results are shown in Fig. 5. We can see that, as desired for a good electrode material, the system remains metallic after adsorption with any kind of the A′ atoms (A′ = Li, Na, K, Mg, Ca).

Fig. 5 Total DOS of the bare Nb₂C monolayer after (a) Li, (b) Na, (c) K, (d) Mg and (e) Ca adsorption. The dotted vertical lines denote the Fermi levels.

3.3 Ion diffusion on Nb₂C monolayer

Next, we turn to study the ion diffusion of A′ (A′ = Li, Na, K, Mg, Ca) on the surface of the Nb₂C monolayer. The climbing-image nudged elastic band (NEB) method⁵¹ is used to seek the saddle points and the minimum energy path and to determine the diffusion barrier height. The most stable adsorption configuration (which is determined for each atom species in the previous section) is taken as the initial state. The configurations with A′ adsorption at the nearest-neighboring most stable site is chosen to be the final state. Fig. 6 shows the calculated diffusion energy profiles and the corresponding migration pathways. Our results show that the diffusion barriers are 0.032 eV (for Li), 0.015 eV (for Na), 0.004 eV (for K), 0.096 eV (for Mg) and 0.039 eV (for Ca), respectively. These low energy barriers indicate fast ion diffusion. For Li, Mg and Ca [Fig. 6(a), (e) and (f)], the diffusion paths are almost the same, from the T₁ site to the neighboring T₁′ site passing through the T₂′ site [see Fig. 6(c)]. These paths clearly show two saddle points. For Na and K, their diffusion paths are from T₂ to T₂′. The path for Na has two saddle points and it passes through the T₃ site. Meanwhile, one observes that the path for K goes from T₂ to T₂′ almost directly with only one saddle point located, which might be due to its very small barrier height (0.004 eV). Overall, the diffusion barrier heights are very low, indicating that all the A′ atoms could have fast diffusion on the surface of the Nb₂C monolayer, which is advantageous for applications as electrode materials.

Fig. 6 The diffusion barrier profiles of (a) Li, (b) Na, (d) K, (e) Mg and (f) Ca on the Nb₂C monolayer. The migration paths for A′ diffusion are shown in the inset of each panel. (c) labelling of the high symmetry points appearing in the diffusion paths. T₁ and T₁′ represent the two sites on top of two neighboring C atoms. T₂ and T₂′ represent the two sites on top of two neighboring Nb(2) atoms. T₃ represents the site on top of the Nb(1) atom.

We stress that all these diffusion barrier heights are less than 0.1 eV, which are among the lowest of the available anode materials. For example, in terms of diffusion barrier heights, we have for Ti₃C₂ (0.068 eV for Li,^3,35 0.096 eV for Na, 0.103 eV for K and 0.118 eV for Ca³), silicene (0.28 eV for Li,⁵² 0.25 eV for Na,⁵³ 0.11 eV for K⁵⁴), graphene^55,56 (>0.3 eV for Li, ∼0.10 eV for Na, K, Mg, Ca, Al^57,58), phosphorene (0.13–0.76 eV for Li,^59,60 0.04 eV for Na,⁶¹ 0.30 eV for Mg and 0.69 eV for Al⁶²), Mo₂S (0.21 eV for Li,²¹ 0.28 eV for Na,⁶³ 0.48 eV for Mg⁶⁴), TiO₂-based polymorphs (0.3–0.65 eV for Li,^65,66 0.4 eV for Na⁶⁷), and the commercialized graphite (0.2–0.4 eV for Li⁶⁸). All these are larger than the corresponding values of Nb₂C.

Experimentally it has been found that the reversible capacities of the Nb₂C-based electrode are 170 and 110 mA h g⁻¹ obtained at 1C and 10C respectively, while for V₂C-based electrode, the two values are 260 and 125 mA h g⁻¹ respectively.⁴⁰ The reversible capacity of Nb₂C-based electrodes is 65% of that of V₂C-based electrode at 1C, and this percentage is increased to 88% at 10C. According to our results above, the experimental observation might be attributed to the faster Li diffusion on Nb₂C surface than on V₂C surface (barrier height ∼ 0.045 eV for V₂C⁴¹).

3.4 Average open circuit voltage and storage capacity of Nb₂C monolayer

The average open circuit voltage and the storage capacity are important characteristics for battery electrode materials. To estimate the maximum possible capacity for A′ atom adsorption, we still employ the 2 × 2 supercell and increase concentration of A′ atoms adsorbed on both sides of the host Nb₂C monolayer. Here we assume the following half-cell reaction vs. A′/A′⁺:^69,70

Nb₂C + xA′^y+ + xye⁻ ↔ Nb₂CA′_x. (2)

The difference in total energies before and after A′ intercalation is used to determine the average open circuit voltage. The volume and entropy effects are usually negligible during the reaction. The average open circuit voltage can be approximately computed from the energy difference:

V_ave = (E_Nb2C + xE_A′ − E_Nb2CA′x)/xye (3)

where E_Nb2C and E_Nb2CA′x are the total energies of Nb₂C without and with A′ intercalation, and E_A′ is the energy per atom in the bulk metal A′.

We first take the Li case as an example to demonstrate the calculation of the average open circuit voltage and the storage capacity. In this case, the adsorption sites of the first Li layer are at the top sites of C atoms, because they correspond to the most stable sites for Li adsorption onto the bare Nb₂C monolayer. From symmetry, the Li layer could form on both sides of the Nb₂C monolayer. After the first-layer adsorption, the second layer Li atoms are adsorbed on the top sites of Nb(2) atoms (also on both sides). To evaluate the interaction between the host material and the Li layers, we calculate the layer-resolved average adsorption energy (Eⁿ_ave) of Li atoms in the n-th layer, which is defined as

Eⁿ_ave = (E_Nb8C4Lin×8 − E_{Nb8C4Li(n−1)×8} − 8E_Li)/8, (4)

where E_Li is the energy per atom in the bulk metal Li, E_Nb8C4Lin×8 and E_{Nb8C4Li(n−1)×8} are the total energies of the monolayer with n and (n − 1) Li layers, respectively. The number ‘8’ here corresponds to the totally eight adsorbed Li atoms in each Li layer (for one supercell on both sides). The calculated average adsorption energies for the first and the second layer are −0.50 and −0.02 eV, respectively. When still more Li layers are adsorbed, the layer-resolved adsorption energy will turn to be positive. It implies that then the Li metal cluster will begin to form, which prevents the further adsorption of the third Li layer. Hence the adsorption of Li atoms reach saturation after the formation of the second layer. Therefore, the 2 × 2 supercell could accommodate up to 16 Li atoms, and the corresponding chemical stoichiometry is Nb₂CLi₄. The evaluated average open circuit voltage decreases from 0.65 to 0.25 V with the increase of the adsorbed Li atoms. Compared with that of Ti₃C₂Li₂ (0.62 V³⁵), the average open circuit voltage values of Nb₂CLi₄ are much lower. The corresponding theoretical specific capacity of Nb₂C as electrodes for LIBs is 542 mA h g⁻¹, which is much larger than that of graphite (372 mA h g⁻¹ for LiC₆). We note that although the Li storage capacity of Nb₂C is lower than that of V₂C,⁴¹ they in fact both accommodate 16 Li atoms in one 2 × 2 supercell. The difference is due to the fact that the element Nb is heavier than V. This is in agreement with the corresponding experimental findings.⁴⁰ We also mention that the experimentally measured charge/discharge curves correspond to a dynamical process hence cannot be accurately determined by the equilibrium DFT approach employed here. Nevertheless, the obtained average open circuit voltages (corresponding to the endpoints of that curve) do provide a good estimate for the different materials.

For the rest of A′ atoms, namely Na, K, Mg and Ca atoms, we perform the calculations following the procedures described above. For Na and K, their chemical valences are both +1. We find that one supercell could accommodate up to 8 Na atoms and 4 K atoms, respectively. The corresponding chemical stoichiometries are Nb₂CNa₂ and Nb₂CK₁. The calculated average open circuit voltages and their corresponding theoretical specific capacities are 0.27 V and 271 mA h g⁻¹ for Nb₂CNa₂, and 0.29 V and 136 mA h g⁻¹ for Nb₂CK₁. As for Mg and Ca, their chemical valences are both +2. We find the bare Nb₂C supercell could accommodate up to 16 (two layers) Mg atoms but only 4 Ca atoms, respectively, with corresponding chemical stoichiometries Nb₂CMg₄ and Nb₂CCa₁. The calculated average open circuit voltages and their corresponding theoretical specific capacities are 0.18 V and 1084 mA h g⁻¹ for Nb₂CMg₄, and 0.06 V and 271 mA h g⁻¹ for Nb₂CCa₁. We note that although Nb₂C shows a fairly good capacity for Ca, when further considering the solid electrolyte interface (SEI) formation, due to the very low average open circuit voltage (0.06 V) for Nb₂CCa₁, the bare Nb₂C might not be a suitable anode material for Ca-ion batteries.

Typically the experimental samples would be a mixture of monolayer, few-layer, and even bulk materials. From experiment, it is observed that the interlayer distance is around 4 Å, which limits the amount of ions intercalated between the layers (and also decreases the diffusion efficiency). Therefore, to enhance the performance, appropriate methods need to be developed to decrease the thickness and to expose more surface area of the material.

From the above discussion, concerning the average open circuit voltage and the specific capacity, the bare Nb₂C monolayer is most suitable for anode materials of Li-ion and Mg-ion batteries.

4 Conclusions

In summary, we have studied the electronic properties and Li or non-Li storage capabilities of monolayer Nb₂C and its fluoride and hydroxide materials. We find that the Nb₂C monolayer and its derived Nb₂CF₂ and Nb₂C(OH)₂ in their the most stable configurations are all metallic before and after metal atom adsorption, which is the desired property of battery electrode materials. Among all the searched secondary batteries, the bare Nb₂C monolayer is most suitable as anode materials for Li-ion and Mg-ion batteries. It shows fast ion diffusion with very low diffusion barrier heights (<0.1 eV) and high storage capacities (with theoretical value 542 mA h g⁻¹ for Li and 1084 mA h g⁻¹ for Mg). In addition, we find that the functional groups tend to reduce the Li or non-Li capacity almost completely, which needs be avoided in experiment as much as possible. Moreover, the average intercalation potentials for Nb₂C-based materials are also found to be relatively low. Our results suggest that 2D Nb₂C is a promising anode material for Li- and non-Li-ion batteries.

Acknowledgements

This work was supported by SUTD-SRG-EPD2013062, the NSFC (Grant No. 11135001 and 11264014). The computations were performed on Texas Advanced Computing Center (TACC) of the University of Texas at Austin.

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