Metallic VS2 Monolayer Polytypes as Potential Sodium-Ion Battery

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Metallic VS monolayer polytypes as potential Sodium ion battery anode via ab-initio random structure searching Darwin Barayang Putungan, Shi-Hsin Lin, and Jer-Lai Kuo ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b03499 • Publication Date (Web): 04 Jul 2016 Downloaded from http://pubs.acs.org on July 4, 2016

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ACS Applied Materials & Interfaces

Metallic VS2 monolayer polytypes as potential Sodium ion battery anode via ab-initio random structure searching Darwin Barayang Putungan,∗,†,‡,¶ Shi-Hsin Lin,§,¶ and Jer-Lai Kuo∗,¶ Physics Division, Institute of Mathematical Sciences and Physics, University of the Philippines Los Ba˜ nos, College, Los Ba˜ nos, Laguna, Philippines, Department of Physics, National Taiwan University, Taipei, Taiwan, Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan, and Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung, Taiwan E-mail: [email protected]; [email protected]

Abstract We systematically investigated the potential of single-layer VS2 polytypes as Nabattery anode materials via density functional theory calculations. We found that sodiation tends to inhibit the 1H to 1T structural phase transition, in contrast to lithiation-induced transition on monolayer MoS2 . Thus, VS2 can have better structural stability in the cycles of charging and discharging. Diffussion of Na atom was found to be very fast on both polytypes, with very small diffusion barriers of 0.085 eV (1H) ∗

To whom correspondence should be addressed Physics Division, Institute of Mathematical Sciences and Physics, University of the Philippines Los Ba˜ nos, College, Los Ba˜ nos, Laguna, Philippines ‡ Department of Physics, National Taiwan University, Taipei, Taiwan ¶ Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan § Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung, Taiwan †

1 ACS Paragon Plus Environment


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and 0.088 eV (1T). Ab-initio random structure searching was performed in order to explore stable configurations of Na on VS2 . Our search found that both the V top and hexagonal center sites are preferred adsorption sites for Na, with the 1H phase showing a relatively stronger binding. Notably, our random structures search revealed that Na clusters can form as a stacked second layer at full Na concentration, which is not reported in earlier works wherein uniform, single layer Na adsorption phases were assumed. With reasonably high specific energy capacity (232.91 mAh/g and 116.45 mAh/g for 1H and 1T phase respectively) and open circuit voltage (1.30 V and 1.42 V for 1H and 1T phase respectively), VS2 is a promising alternative material for Na-ion battery anode with great structural sturdiness. Finally, we have shown the capability of the ab-initio random structure searching in the assessment of potential materials for energy storage applications.

Keywords Na-Ion Battery, Transition Metal Dichalcogenide, polytypes, DFT, Ab-initio random structure searching, cNEB

1

Introduction

Storing energy is one critical necessity for a sustainable and efficient utilization of energy resources. One such mechanism is by storing electricity as chemical energy in batteries. Lithium-ion batteries (LIBs) are among the most advanced and matured battery technologies, 1–3 given its high energy density and relatively long life cycle. As such, LIBs are the most commonly used battery technology in portable devices, new generation automotives and small- to mid-scale industry equipment. 4,5 As much as LIBs are desired to be the driving force in energy storage applications, there are several challenges that need to be addressed in order for its continued use to be fruitful. For one, the relative abundance of lithium on


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earth’s crust is only about 20 ppm, 6 which makes production costs quite high. Electrolyte stability is also a concern especially for long-term applications. 7,8 One alternative that is being eyed to replace lithium is sodium, and sodium-ion batteries (NIBs) 9,10 are currently attracting attention. Being much more abundant compared to lithium, 6 production cost could significantly go down. The availability of more stable nonaqueous electrolytes 11,12 makes sodium-based batteries safer in prolonged use. One main drawback of using sodium is its larger ionic volume and weight compared to lithium, which could lower the battery’s gravimetric energy density and thus limiting its adoption in the mobile applications segment. On another note, high energy density considerations becomes less important in large-scale applications such as smart energy grids and heavy industries areas where NIBs are potentially useful and would be in demand. The issue of relatively low energy capacity of NIBs can be solved by finding battery electrode materials that can accommodate sodium in high capacity, and with reasonable binding stability. The desired material should possess reasonably high Na intake capacity and excellent Na ion diffusivity, as well as good structural stability. Notably, progress in finding the appropriate negative electrode materials (called an anode) has been tremendous, most notably in the utilization of two-dimensional (2D) materials. 13–19 The ballooning popularity of 2D materials is associated with unique properties nonexisting in their bulk counterparts such as large surface-to-volume ratio. 20,21 Recently, a conducting single layer transition metal dichalcogenide (TMD), VS2 , has been succesfully fabricated, 22,23 and subsequent studies showed its capability as supercapacitor, 22 2D magnetic material with tunable ferromagnetism 23,24 and high-capacity anode material for LIBs. 13 Interestingly, single layer VS2 is known to be stable in both the 1H and 1T polytypes, with the 1H phase a few meV more stable than 1T in terms of cohesive energy. 25 On the other hand, it was shown that for bulk case, the 1T is the more stable phase relative to 1H. 26 In terms of electronic structure, both monolayer structural phases possess metallic bandstructures, 25 and therefore appropriate as battery anode electrode.



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In the present work, we systematically studied the potential of single-layer VS2 monolayer polytypes as anode materials for NIBs. We first calculate the structural phase transition barrier between the 1H and 1T phases, and our results indicate that it is comparable to other monolayer TMDs such as MoS2 and WS2 . 27–29 However, upon Na adsorption, it is found that the energy barrier increases, a result opposite to that of Li-MoS2 system. 27,28 It is found that for single Na adsorption, both the V top site and hexagonal center site are stable adsorption sites with minimal energy difference. Our climbing image nudged elastic band (cNEB) calculations revealed that Na diffusion on both phases is much more favorable than other potential single-layer Na anode materials and is comparable to phosphorene. 15 In order to assess stable adsorption phases especially at high Na concentrations, ab-initio random structure searching (AIRSS) method 30 was implemented. Here, random initial adsorption configurations are constructed, thereby giving a wider coverage of the potential energy surface. Thus, the end result of structural optimization does not depend on a particular initial guess structure, and thus it is possible to obtain low-energy stable and metastable structures not accessible via usual optimization schemes. 31–33 It has been successfully implemented in finding hydrogen molecules’ lowest energy configurations on Li-decorated MoS2 for hydrogen storage applications. 34 Compared to other widely-used structural optimization algorithms, notably the genetic algorithm (GA), which uses concepts in biological evolution such as reproduction, mutation, cross-over and fitness selection in the calculations, 35–37 the AIRSS is a simple method that uses full quantum-mechanical relaxation of random sensible structures. Since random sensible structures are randomly distributed in the potential energy surface, AIRSS minimizes the occurrence of local minima trapping/locking. The large number of possible initial structures can be much reduced by taking cues on some initial knowledge of the system, such as symmetries, and those can be obtained via test calculations, from literature or through experimental results. Our search pointed out that the seemingly ordered adsorption structure at full metal atom concentration reported in most metal-ion adsorption on 2D materials 13–15 is not the lowest energy, preferable configuration.


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Our results show that layered adsorption phases occur for fully-sodiated VS2 that is indicative of clustering, and therefore the maximum Na content that the material could hold is lower than the expected full Na concentration. Our calculations predict a specific energy capacity of 232.91 mAh/g and 116.45 mAh/g (1H and 1T phase respectively), with an average open circuit voltage of 1.30 V and 1.42 V (for 1H and 1T phase respectively). These findings point to the considerable potential of VS2 monolayer as a candidate anode material for NIBs. Moreover, we have shown that a simple but elegant structure searching method such as AIRSS could provide significant insights in the characterization of candidate materials for energy storage applications.

2

Methodology

The calculations employed spin-polarized density functional theory (DFT) in the generalized gradient approximation (GGA) as implemented in the VASP code, 38,39 with projectoraugmented wave method under the Perdew-Burke-Ernzenhof (PBE) 40 exchange-correlation functional. To correct for instantaneous charge fluctuations that are usually neglected in conventional exchange-correlation functionals, semi-empirical dispersion corrections by means of DFT-D3 method as implemented by Grimme 41–43 is incorporated in the calculations. It has been shown in previous works focusing on LIBs 44–46 and NIBs 13–15 that dispersion corrections improve the accuracy of metal binding energies and diffusion barriers. We used a k-mesh of 5 × 5 × 1 for Brillioun zone sampling, together with kinetic energy cut-off of 550 eV. Electronic convergence is set to 10−6 eV, while atomic positions were optimized until the final forces are below 0.01 eV˚ A−1 . A large vacuum space of more than 20 ˚ A in the z-direction separates the periodic supercell in order to avoid artificial interactions. Sodium adsorption configurations are expressed in terms of Nax VS2 stoichiometry (or as Nax 1H-VS2 and Nax 1T-VS2 when referring specifically to 1H and 1T respectively), where x denote Na concentration per VS2 formula unit. To search for the most stable adsorption



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configurations of sodium atoms on VS2 polytypes, we employed AIRSS. Sodium atoms were randomly placed on VS2 1H and 1T phases, with perpendicular distance ranging from 2.0 to 4.0 ˚ A, while a minimum distance of 2.0 ˚ A between nearest-neighbor atoms was set in order to prevent overlaps. Thus, a much wider sampling of the potential adsorption sites and configurations were considered in this work. We generated a total of 420 random adsorption structures for all Na concentrations considered in the study for optimization, and Na adsorption phases with lowest energies are chosen in succeeding analyses. In analyzing structural phase transition and sodium diffusion on VS2 monolayer, the cNEB method was used, 47 utilizing eight images constructed via the linear interpolation method. In the usual nudge elastic band method, 48 initial and final reaction configurations are optimized, and a series of images will be interpolated linearly between the two as a guess of the minimum energy pathway (MEP), connected by a spring force. A saddle point corresponding to a transition state in the MEP gives the reaction barrier, which is obtained by optimizing the images until the perpendicular force with respect to the path is zero. In cNEB, the highest energy image does not feel any spring force and climbs up the potential energy surface to the saddle point, allowing the use of smaller number of images.

3

Results and Discussions

This section starts with the discussion of structural parameters, 1H to 1T phase transition, energetics and single Na adsorption on VS2 polytypes (the first subsection). The second subsection outlines different high Na concentration adsorption phases as searched by AIRSS. Finally, the calculated theoretical specific energy capacity and open circuit voltage for both VS2 polytypes is presented in the third subsection.


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3.1

Single Na adsorption and diffusion VS2 polytypes

As with other MX2 TMDs, VS2 exhibits the sandwiched S-V-S configuration, and forms two distinct polytype structures depending on the coordination of V with respect to S. Shown in Figure 1 are the 1H (V in trigonal coordination with S) and 1T (V in octahedral coordination with S) structures of monolayer VS2 (structures I and IX respectively). The 1H and 1T structural parameters for VS2 are listed in Table 1, and are consistent with previous reports. 22,26,49 Furthermore, our calculations showed that 1H is energetically more stable than 1T by 40 meV/VS2 , and both structural phases possess spin-polarized ground state (0.99 µB /VS2 for 1H and 0.43 µB /VS2 for 1T), in good agreement with literatures. 13,23,24,26 It is also consistent with the previous theoretical analysis based on the d-band filling for MX2 TMDs 50 that the trigonal-prismatic coordination phase (1H) is more stable than octahedral one (1T) for VS2 with d1 filling, and even more for MoS2 with d2 filling, but the opposite for MX2 with d3 filling. We analyzed the 1H to 1T structural phase transition of VS2 monolayer, with the MEP shown in Figure 1. Our calculations predict a transition barrier of 0.68 eV/VS2 , which is quite comparable to that of other TMDs such as MoS2 27,28 and WS2 29 TMDs. We then looked into the effect of Na adsorption on the transition energy barrier, and results show that it increases to 0.98 eV/VS2 (one Na per VS2 ) and 1.12 eV/VS2 (two Na per VS2 ), implying that Na adsorption makes structural phase change energetically less favorable. The transition state structures for all considered cases (structures IV, V and VI for pristine VS2 monolayer, one Na per VS2 formula unit and two Na per VS2 formula unit respectively in Figure 1) point to the sulfur plane gliding as the mechanism for 1H to 1T structural phase transition, consistent with the experimental finding for MoS2 . 51 Here, sulfur atoms move from its initial position in the 1H phase (in trigonal prismatic coordination with Mo atoms) to a distance √ equivalent to a/ 3 (a is VS2 lattice constant), occupying the hexagonal center site to form the 1T phase. In short, sodiation tends to increase the 1H to 1T structural phase transition energy barrier, and is dependent on Na concentration. 7 ACS Paragon Plus Environment


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This result is quite interesting, as it was earlier reported that metal adsorption tend to reduce transition barrier and energetically stabilize the 1T phase as compared to 1H, for instance, Li adsorption on MoS2 . 27,28 Therefore, VS2 has better structural stability in the cycles of charging and discharging than other TMDs, which is essential for ion battery applications. As can be deduced from the MEP of 1H to 1T phase transition for Na-VS2 system (Figure 1), the relative energy difference between the 1H and 1T polytypes becomes larger with Na adsorption, with 1H still the more energetically favorable phase. This implies that the 1T phase becomes energetically less stable with Na adsorption, a finding that is also in contrast with that of Li-MoS2 system. 27,28 It is again consistent with the previously mentioned d-band filling analysis. 50 Na adsorption infuses electrons into the VS2 layer. V(d1 ) is charged into V(d2 ), thus the trigonal-prismatic 1H phase should be even more stable than the octahedral 1T phase, as in the case of MoS2 (Mo d2 ). The other reconstructed octahedral phase, known as 1T0 , has lower energy than 1T for MoS2 , although still higher than 1H even for MoS2 . For VS2 however, upon relaxation, we found that 1T0 reverted back to the 1T phase. We also noted here that 1T0 is not generally stable for all 2D TMDs. In particular for monolayer VS2 , there were several studies indicating that 1H and 1T phases are the stable structures, even in terms of dynamical stability. 13,25,26,49 We move on to single Na adsorption on 4×4-supercell VS2 polytytpes, that is the low concentration Na0.0625 VS2 adsorption phase. The binding energy of Na, Eb , is calculated via Eb = EVS2 +Na − EVS2 − µNa

(1)

where EVS2 +Na is the energy of the Na-VS2 system, EVS2 is the energy of specific VS2 polytype and µNa is the chemical potential of Na atom. With regards to Na chemical potential reference, it has been pointed out in most literatures 15,45,46 that in battery electrode calculations, the metallic bulk phase is a more reliable reference state compared to the neutral atom in gas phase. Using the metallic bulk state as a reference chemical potential


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directly compares the resulting binding energy with the metal’s bulk cohesive energy and thus provides more physical insights such as the possibility of clustering. Moreover, it was pointed out in previous works 15,16 that using the isolated metal atom in gas phase as a reference chemical potential affects calculations results, such as in the case of Li/Na on graphene. Most calculations employing isolated metal in gas phase as reference state 52–54 predicted pristine graphene to be a suitable candidate as metal-ion battery electrode but subsequent works proved otherwise. 16,45 As such, we used Na metallic bulk as the reference state, µbulk Na , in the calculation of the binding energies (see Table 2). In our binding energy definition, negative binding energy values denote favorable adsorption. Using AIRSS strategy, we found two distinct adsorption sites on both 1H and 1T VS2 polytypes: V top site (Vtop site) and hexagonal-center site (Hcenter site), as depicted in Figure 2(a). The binding energies, distances and charge transfer (via Bader charge analysis) are compiled in Table 2. Both binding energies obtained using different Na reference chemical potential are negative, implying stable adsorption. In both polytypes, the Vtop site is the preferable binding site, although adsorption on Hcenter site is energetically very close. The calculated binding energy difference between the Vtop and Hcenter sites for both polytypes is roughly around 20 meV. This implies that both sites are likely to be relevant adsorption sites for Na at higher concentrations, and thus the preferable adsorption phases at higher concentration was searched thoroughly via AIRSS, as both sites would play a vital role. Moreover, Vtop site adsorption is more stable on the 1H phase (-2.17 eV) compared to the 1T phase (-1.86 eV) by 0.31 eV. It is noteworthy to mention that single Na adsorption on VS2 monolayer is more stable compared to that of other potential candidate 2D materials such boron-doped graphene (-0.79 eV), 16 single-layer MoS2 (-1.27 eV) 14 and phosphorene (-1.59 eV). 15 Hence the ions have less tendency to cluster, making VS2 a better electrode candidate (also with better structural stability as discussed previously). In assessing the nature of Na-VS2 binding, we refer to the charge difference isosurfaces defined as ∆ρ = ρVS2 +Na − ρVS2 − ρNa shown in Figure 2(b). Electron rich region (red) 9 ACS Paragon Plus Environment


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appears between Na and VS2 while electron deficient region (blue) can be noticed above Na, suggesting an ionic character of Na-VS2 binding. Moreover, it can be observed that the bonding of Na appears to be triply coordinated with respect to S atoms, both for Vtop and Hcenter sites. To substantiate on these, Bader charge analysis indicate a large charge transfer of around 0.86 e from Na to VS2 , for both 1H and 1T polytypes. The capability of a metal-ion battery electrode, such as charge/discharge rates, also depends on the ease of transporting metal ions, and thus we examined the diffusion pathway and diffusion energy barrier of Na on different VS2 polytypes. We analyzed the diffusion path between two neighboring, most preferable binding sites (Vtop ), for 1H and 1T phases. The calculated MEPs are shown in Figures 3(a) and (b). For both polytypes, the MEP is in such a way that Na passes through Hcenter site along the Vtop -Vtop migration pathway. The calculated effective diffusion barriers are significantly minute, only 85 meV and 88 meV for 1H and 1T phase respectively, implying very fast Na diffusion kinetics that would result to a very effective anode electrode for Na battery applications. These diffusion barriers are much smaller compared to other 2D materials such as graphene (0.10 eV), boron-doped graphene (maximum, 0.22 eV) and MoS2 (0.11 eV), and comparable to that of phosphorene (40 meV). 14–16

3.2

AIRSS for high Na concentration adsorption

In order to assess stable adsorption phases at high Na concentration, especially at full Na concentration, we utilized AIRSS. Here, we define a specific adsorption phase as Nax VS2 , where x is Na concentration per VS2 formula unit. We searched the lowest energy adsorption phase among a total of 300 randomly-generated Nax VS2 adsorption structures on both sides of 1H and 1T VS2 phases for x = 0.125, 0.25, 0.5, 1.0 and 2.0. The formation energy Eformation of Nax VS2 per N Na atoms is calculated via Eformation =

1 (E − EVS2 − N µNa ) N VS2 +Na 10

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(2)

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where EVS2 +Na and EVS2 are the total energies of Nax VS2 adsorption phase and VS2 monolayer respectively, and µNa is Na chemical potential set with respect to metallic bulk Na as the reference state. With this definition, the formation of an adsorption phase is favorable if it is less than zero, otherwise the phase is unfavorable. The optimized, lowest energy Nax VS2 adsorption phases are shown in Figure 4 (a)-(d), together with the corresponding formation energies. As expected, the resulting adsorption structures appear to be a mix of configurations wherein Na atoms are adsorbed on either Vtop or Hcenter . This makes sense, as Na binding energy difference between these two sites is relatively small and thus both are likely to be occupied at higher Na concentrations. In terms of Nax VS2 formation energy, the calculated Eformation for all x becomes less negative as x increases. This is attributed to the increased repulsion between charged Na ions that tends to destabilize the adsorption phase. Moreover, we have found that higher Na concentration tend to induce lattice distortions for the case of Nax 1T-VS2 structure. For instance, vanadiumvanadium distance can vary from 2.69 ˚ A to 3.65 ˚ A in Na2 1T-VS2 . It can be inferred that sodiation of the 1T phase appears to induce modest structural changes compared to 1H, and thus the 1H polytype could be a more robust structural phase for Na battery anode. The calculated formation energies for full concentration Na2 1H-VS2 and Na2 1T-VS2 are -0.85 eV and -0.74 eV respectively. Our AIRSS calculations revealed that for Na2 VS2 , sodium adsorption layers occurs on both 1H and 1T adsorption phases (Figure 5), with the second Na layer separated from the first by about 2.98 ˚ A on the average. Our results also show that the most stable two-layer Na adsorption phase is lower in energy compared to that of a uniform all-Vtop -adsorbed phase (by 1.34 eV and 0.66 eV for 1H and 1T phase respectively), also shown in Figure 5. This can be attributed to the inherent strong Na-Na repulsion among them as a result of Na crowding on the surface. Such adsorption layers have also been observed in a recent study on lithium and sodium adsorption on borocarbonitride monolayer. 55 Those Na’s of the second layer bind directly to other Na’s, forming Na clusters. Metal atoms clustering could be a precursor



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to metal plating in which atoms tend to form bulk-like structures to be deposited on the electrode’s surface. The electrode reaction could not occur while Na clusters are formed and cover the surface. Previous works 13–15 assumed that metal ions would be adsorbed on the most preferable adsorption site at maximum concentration, and thus the adsorption phase is uniform and does not form layers. Intuitively, adsorption phases could be more complex especially if the adsorption sites bind metal ions with almost the same affinity and thus both would play a role at higher metal concentration. Moreover, as these metal ions are charged, strong ion-ion repulsion could lead to layered adsorption as the basal plane becomes crowded with increasing metal ion concentration. Therefore, our AIRSS indicated that, at high Na concentration x ≈ 2.0, Na would form clusters that stack as the second layer, instead of the uniformly distributed single Na layer as demonstrated in previous works. To explore the most thermodynamically stable Na adsorption structure, and hence the maximal Na capacity, we have further calculated the formation energy for the Na intercalation with the composition x: x x EN a2 V S2 + (1 − ) EV S2 , − 2 2

∆E = EN ax V S2

(3)

where EN ax V S2 is the energy of Nax VS2 per formula, EN a2 V S2 is the energy of Na2 VS2 , and EV S2 is the energy of VS2 . The convex hull of the calculated ∆E versus x is shown in Figure 6. The minimum of the convex hull plot corresponds to the maximum capacity. As a result, the 1H phase can maximally uptake Na at x = 1.0, and the 1T at x = 0.5 (x ≈ 0.69 if using a quartic fit). We note that for the case of 1H-VS2 , the maximum uptake could be higher than x = 1.0, as it might be that the minimum value of the curve is in the range 1.0 < x < 2.0 (refer to Figure 6(a)). The corresponding specific capacities were discussed in the next subsection. We noted here that there are few works on 2D material-based ion batteries adopting the convex hull plot to extract the maximum capacity. Most works on 2D


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materials used only the adsorption energy as criteria, and usually overestimated the capacity. The convex hull plot adopted by this work offers a more natural and unambiguous approach. Meanwhile, as shown in the convex hull plot, the clustering, or the high-density adsorption (x = 2.0) state, has much higher formation energy and is therefore not thermodynamically favored even the adsorption energy is still negative.

3.3

Electrochemical properties

We further predict the theoretical specific capacity of VS2 monolayer in storing Na ions, including the average open circuit voltage, OCV, (V ) for sodiation of VS2 . The theoretical specific capacity C (mAh/g) can be calculated using 17

C=

1 (xmax vF · 103 ) M WVS2

(4)

Here, M WVS2 is the molecular weight of VS2 formula unit, xmax is the maximum Na concentration that can be stored in a VS2 formula unit, v is Na valence electron equal to 1, and F is Faraday’s constant (26.801 Ah/mol). From Section II, we have found that the maximum Na concentration that VS2 can achieve is x = 1.0 for 1H phase and x = 0.5 for 1T phase. Thus, we predict a theoretical specific capacity of 232.91 mAh/g for 1H phase, and 116.45 mAh/g for 1T phase. Although this is smaller than that of MoS2 (335 mAh/g), 14 VS2 can still be a better electrode material with a better structural stability than MoS2 since there is no structural phase transition upon charging/discharging cycles. With regards to V , following previous discussions on charge/discharge processes on potential battery electrodes, 13–19 sodiation and de-sodiation of VS2 follows the common half-cell reaction vs. Na/Na+ in such a way that:

VS2 + xNa+ + xe− ↔ Nax VS2


(5)


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As such, the proposed method of calculating V via DFT results is given by

V ≈ −[EN ax2 V S2 − EN ax1 V S2 − (x2 − x1 )µNa ]/(x2 − x1 )e

(6)

where EN ax2 V S2 and EN ax1 V S2 are the total energies of the final configuration Nax2 VS2 and initial configuration Nax1 VS2 configurations, µNa is the chemical potential of Na referenced from metallic bulk state and e is the valence charge of Na. We set the sodiation configurations to x2 = 1.0 and x1 = 0, corresponding to OCV when VS2 is sodiated from zero Na concentration to maximal Na concentration (refer to Figure 6). The predicted OCV values are 1.30 V and 1.42 V for 1H and 1T phase respectively. It is consistent with a recent work 56 for Na-VS2 (1H) reporting roughly 1.46 eV, and slightly greater than that of Li-VS2 system (at 0.93 V). 13 With regards to the relatively close OCV values between Li-VS2 and Na-VS2 systems, this is to be expected as Li and Na have relatively similar electronic structures, specifically in terms of the number of valence electrons. Thus, the applicability of VS2 monolayer polytypes as Na battery anode is of considerable interest and could be of great importance as an alternative energy storage material in line with other interesting 2D materials such as MoS2 , modified graphene and phosphorene.

4

Conclusions

To summarize, we have investigated the capability of monolayer VS2 polytypes as potential anode materials for NIBs via density functional theory coupled to ab-initio random structure searching. In terms of structural phase transition, it was shown that the 1H to 1T transition is comparable to other 2D TMDs. However, it is also revealed that 1H to 1T transition energy barrier becomes larger after sodiation, and that 1T phase tends to become energetically less stable upon sodiation. Hence VS2 has no structural phase transition in the cycles of charging and discharging, providing better structural stability than other TMDs. It was found that Vtop and Hcenter sites of VS2 polytypes are both favorable adsorption sites for Na, 14 ACS Paragon Plus Environment

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with modestly stronger binding on the 1H phase. With Na metallic bulk as the reference for Na chemical potential, our results demonstrate directly that Na-Na aggregation can be suppressed at low Na concentration. Using cNEB, Na diffusion was shown to be very fast on both poyltypes, with diffusion barrier significantly lower than most 2D materials and is comparable to that of phosphorene. By performing ab-initio random structure searching, we comprehensively searched and found lowest energy Nax VS2 adsorption phases. Our calculations showed that indeed both Vtop and Hcenter sites play roles in Na adsorption at high concentrations due to small difference in Na binding energy on these two sites. The 1H phase appears to be the more robust polytype of VS2 compared to 1T in terms of structural rigidity during sodiation. Furthermore, our AIRSS search revealed that Na clusters can form as a stacked second layer at full Na concentration due to inherently strong Na-Na ion repulsion, which is not reported in previous works wherein uniform, single layer Na adsorption phases were assumed. Finally, with reasonably high specific energy capacity (232.91 mAh/g and 116.45 mAh/g for 1H and 1T phase respectively), descent open circuit voltage (1.30 V and 1.42 V for 1H and 1T phase respectively). In conclusion, 1H-VS2 is a better candidate electrode than 1T, due to it’s structural sturdiness, higher specific capacity, and lower OCV. Combined with the availability of synthesized single layer VS2 , we are confident that these would encourage experimentalist to conduct further studies on this material and design appropriate NIB anode electrode utilizing VS2 monolayer.

Acknowledgement This work was financially supported by various grants from Academia Sinica and the Ministry of Science and Technology (MOST) of Taiwan under MOST101-2113-M-001-023-MY3. D. B. P. thanks Taiwan International Graduate Program for scholarship and National Center for Theoretical Sciences (South) Physics Division for travel support. Computational resources are supported in part by the National Center for High Performance Computing.



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VS2

a (˚ A) 3.17 3.17

dM −X 2.34 2.36

dX−X 2.97 3.45

θ 78.16 94.92

Table 2: Single Na atom adsorption on VS2 polytypes: binding energy (Eb ), charge transfer to VS2 (qtransfer ), average distance of Na from triply-coordinated S atoms (dNa-S )

Site Vtop Hcenter

1H 1T 1H 1T

Eb (eV) (referenced to µbulk Na ) -2.17 -1.86 -2.15 -1.84

qtransfer (e) 0.86 0.86 0.857 0.856


dNa-S (˚ A) 2.72 2.71 2.72 2.70

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Figure 1: 1H to 1T structural phase transition of VS2 monolayer, for pristine and sodiated cases. Also shown are the corresponding configurations of the initial structures (I, II and III for pristine VS2 , one Na per VS2 formula unit and two Na per VS2 formula unit respectively), transition state structures (IV, V and VI for pristine VS2 , one Na per VS2 formula unit and two Na per VS2 formula unit respectively) and final structures (VII, VIII and IX for two Na per VS2 formula unit, one Na per VS2 formula unit and pristine VS2 respectively).



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Figure 2: AIRSS lowest energy structure for single Na adsorption on (a) 1H-VS2 and 1TVS2 . (b) The charge difference isosurface defined as ∆ρNa-VS2 = ρtotal − ρVS2 − ρNa (ρtotal , ρVS2 , ρNa are charge densities of the Na-VS2 system, VS2 substrate and Na atom respectively; isosurface level is set to 0.002 e/˚ A3 )


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Figure 3: Calculated MEPs via cNEB method for the diffusion of Na on (a) 1H and (b) 1T VS2 monolayer. 25 ACS Paragon Plus Environment


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Figure 4: AIRSS lowest energy Na2 VS2 adsorption phases for different Na concentration x: (a) 0.125 (b) 0.25 (c) 0.5 (d) 1, together with the corresponding formation energy for each adsorption phase, for both 1H and 1T polytypes.


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Figure 5: Lowest energy adsorption phases for Na2 VS2 . Shown in (a) are the most stable adsorption phases for both 1H and 1T polytypes as determined via AIRSS, while (b) are the adsorption structures wherein Na atoms are placed on Vtop sites.



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Figure 6: The convex hull of the calculated formation energy ∆E versus Na concentration x for both 1H (a) and 1T (b) VS2 polytypes.


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Metallic VS2 Monolayer Polytypes as Potential Sodium-Ion Battery

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