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Borophane as a Bench-mate of Graphene: A Potential 2D Material for Anode of Li and Na-ion Batteries Naresh K Jena, Rafael B. Araujo, Vivekanand Shukla, and Rajeev Ahuja ACS Appl. Mater. Interfaces, Just Accepted Manuscript • Publication Date (Web): 26 Apr 2017 Downloaded from http://pubs.acs.org on April 27, 2017

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ACS Applied Materials & Interfaces

Borophane as a Bench-mate of Graphene: A Potential 2D Material for Anode of Li and Na-ion Batteries Naresh K. Jena, a,* Rafael B. Araujo,a Vivekanand Shukla,a Rajeev Ahuja a,b,*

a

Condensed Matter Theory, Materials Theory Division, Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20, Uppsala, Sweden b Applied Materials Physics, Department of Materials and Engineering, Royal Institute of Technology (KTH), SE-100 44, Stockholm, Sweden *Corresponding author email: NKJ([email protected]; [email protected]) ; RA ([email protected])

Abstract Borophene, single atomic-layer sheet of boron (Science, 2015, 350, 1513), is a rather new entrant into the burgeoning class of 2D materials. Borophene exhibits anisotropic metallic properties whereas its hydrogenated counterpart borophane is reported to be a gapless Dirac material lying on the same bench with the celebrated graphene. Interestingly, this transition of borophane also rendered stability to it considering the fact that borophene was synthesized under ultra-high vacuum conditions on a metallic (Ag) substrate. Based on first principles density functional theory computations, we have investigated the possibilities of borophane as a potential Li/Na-ion battery anode material. We obtained a binding energy of -2.58 (-1.08 eV) eV for Li (Na)-adatom on borophane and Bader charge analysis revealed that Li(Na) atom exists in Li+(Na+) state. Further, on binding with Li/Na, borophane exhibited metallic properties as evidenced by the electronic band structure. We found that diffusion pathways for Li/Na on the borophane surface are anisotropic with x direction being the favorable one with a barrier of 0.27 eV and 0.09 eV, respectively. While assessing the Li-ion anode performance, we estimated that the maximum Li content is Li0.445B2H2, which gives rises to a material with a maximum theoretical specific capacity of 504 mAh/g together with an average voltage of 0.43 V vs. Li/Li+. Likewise, for Na-ion the maximum theoretical capacity and average voltage were estimated to be 504 mAh/g and 0.03 V vs. Na/Na+, respectively. These findings unambiguously suggest that borophane can be a potential addition to the map of Li and Na-ion anode materials and can rival some of the recently reported 2D materials including graphene.

Keywords: borophene, borophane, Dirac Material, Li-ion battery, Na-ion battery, Li/Nadiffusion

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1. Introduction Puny and trivial as it might sound that graphene is another allotrope of carbon, its implications to the realm of 2D materials is rather paradigmatic. Of special mention are the exotic electronic, mechanical and transport properties of graphene.1-3 The astounding ramifications that this wonder material has caused in terms of furthering science is truly reflected in the plethora of theoretical and experimental articles published on this subject matter. As a recognition of the far-reaching impact of graphene, Geim and Novoselov have been awarded with Nobel prize in physics within few years of its discovery. Moving a step further, the success of graphene has also paved the way for the realization of several other pertinent members of this family (2D materials) such as transition metal dichalcogenides (TMDCs), 4-6 hBN, 7-8 silicene, 9-10 stanene, 11 germanene 12 and phosphorene 13. Strong dimensionality effects in these materials which are in stark contrast to their bulk counterparts, coupled with their stability in one/few atomic layers make these materials suitable for many potential applications. 14 For elemental Boron, short covalent radius similar to that of carbon and its flexibility in terms of adopting sp2 hybridization facilitating the formation of several low-dimensional structures has always attracted intense curiosity. In fact, polymorphism in 2D boron has been the subject of several thought provoking computational studies. 15-16 Advancing along this curiosity driven research frontier, a very recent report demonstrates successful synthesis of 2D Boron sheet or borophene. 17 However, a key issue with borophene was its stability and it could only be grown on a metallic (Ag) substrate under ultra-high vacuum conditions. 17 Furthermore, scanning tunneling microscopy measurements revealed that borophene exhibits anisotropic metallic properties. Inspired by the above experimental realization of borophene, Peng et al. have probed its electronic and optical properties with first principles density functional theory (DFT) method and reaffirmed the anisotropic metallic nature. 18 Progressing a step further, an intuitive first principles study by Xu et al. predicted that borophene can be stabilized by complete surface hydrogenation and the resulting material known as “borophane” exhibits directional dependent Dirac cone and linear dispersion relation which are reminiscent of graphene. 19 Furthermore, the Dirac fermions are shown to possess Fermi velocity four fold higher than that of graphene and Young’s modulus comparable to steel. 19 This piece of fascinating study has widened new vistas for possible applications of borophane. Inching a step further, Kou et al. have uncovered the auxetic and ferroelastic properties of this novel 2D material (borophane) and have asserted its possible applications in nanoelectronic and microelectromechanical devices. 20 Following the same line of inspiration, a very recent study by Padilha et al. dealt with the directional electronic transport of 2D borophene and borophane employing ab initio calculations. 21 All these important articles underline the growing importance of first principles computations in predicting new materials and making realistic predictions of their properties. Our ever expanding energy requirements has put the onus on the design of materials with high-capacity rechargeable energy storage. 22-23 In mobile device applications and electrical vehicles, Lithium ion batteries (LIBs) have emerged as a crucial candidate because of their superior energy efficiency and portability when compared with other energy storage devices. 23-24 Similarly, research pertaining to post LIBs has also gathered significant pace in wake of increasingly high cost of Li and its limited accessibility. In this context, Sodium ion batteries (NIBs) have evolved as a potentially promising alternative to LIBs. 25-26 As new innovations pertaining to LIBs/NIBs are routinely happening with an aim to achieve simultaneously enhanced energy and power densities along with faster charging and discharging rate, several challenges still remain on frontiers like finding materials with high


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surface area, better electron transport properties and lower barriers for Li and Na diffusions. 26-27 In this context, tunable properties of 2D materials together with the ease of fabrication of heterostructures and their better integration widens their prospects as high-capacity battery material. 14 Additionally, high surface area, remarkably high electron mobility and superior mechanical properties of graphene and other related 2D materials have invigorated researchers to explore their potentials for rechargeable energy storage. 14 The importance of 2D materials for battery applications can be understood by taking the example of bulk silicon, which although exhibits high specific capacity as an anode material (4200 mA h/g), is unsuitable for realistic battery application owing to the degradation by significant volume change. 28-29 To circumvent such problems, there has been propositions that mixing oxygen with silicon (silicon-suboxides) can be suitable for the anode of LIBs. 30 On the contrary, 2D counterpart of silicon, silicene exhibits better stability during lithiation process yielding high capacity. 31 Graphene has been demonstrated successfully to work as both cathode and anode material. 32-34 From the TMDCs family of 2D materials, MoS2 and VS2 have been explored as an alternative anode materials for Li-ion battery. 35-36 Li et al. have made a DFT investigation of phosphorene as an anode material and they have concluded that Li diffusion is highly anisotropic along zig-zag and armchair directions. 37Likewise, for borophene, within a year of its report 17, several computational studies have estimated the potential of this new 2D material for battery applications. 38-41 In an independent and parallel experimental breakthrough, two different polymorphs of 2D boron (planar β12 and χ3 sheet) has also been reported to be grown epitaxially on Ag(111) surface. 42 The above mentioned polymorphs are planar in contrast to the buckled borophene we have introduced so far. These two planar 2D sheets of boron (β12 and χ3) have also been computationally estimated to be high capacity electrode materials for LIBs and NIBs. 40 A recent computational study envisages the possibilities of transition from buckled borophene to a planar structure due to oxidation. 43 All these studies, apart from underpinning the fundamental importance of 2D materials, also brings to fore the variegated nature of polymorphism in boron. Motivated by all these developments, in this current study, we have investigated the potential role of borophane as a Li/Na ion battery anode material from first principles density functional theory (DFT) calculations. The binding of Li/Na atom at different sites on borophane have been investigated and barrier for Li/Na diffusion have been computed. The anisotropic nature of this material yields different barriers along x and y directions. We have assessed the stability of this material from phonon dispersion calculations and ab initio molecular dynamics (AIMD) simulations. While detailing out the electronic structure of this material on Li/Na adsorption, we have computed the average potential and theoretical capacity of this material which offers great promises as a probable Li/Na-ion battery material. Considering the stability of borophane as a free standing monolayer as compared to borophene which requires substrate, we believe that our work will stimulate subsequent interest among the researcher community.

2. Computational Methods All the computational calculations have been performed within the framework of DFT44 with Vienna ab initio simulation package (VASP) 45-46. The projector-augmented-wave (PAW) 47-48 as implemented in VASP has been used and the Perdew-Burke-Ernzerhof49-50 (PBE) generalized gradient approximation (GGA) has been chosen for the exchange correlation functional. A plane-wave cutoff of 500 eV has been used for the kinetic energy. A Monkhorst-Pack51 k-mesh of (18x12x1) was used for the Brillouin zone integrations. We



have also considered Grimme’s semi-empirical corrections for the van-der Waals interactions52. The unit-cell of borophane consists of a B2H2 unit and for initial structural relaxation a stiff energy convergence criterion of 10-7 eV has been chosen. Subsequent structural relaxation with a single Li/Na-adatom was performed with an energy convergence criterion of 10-4 eV and in a 3x3x1 supercell. From this calculation, the favorable binding site of Li/Na-atom on top of borophane was found out and in subsequent calculations, this binding pattern was chosen. To estimate the charge transfer between the substrate and Li/Na-adatom, Bader53 charge analysis has been performed. To emerge with a deep understanding of the delivered potential with Li/Na insertion on the borophane structure, different Li/Na concentrations were explored by considering LixB2H2 with x amounting to 0.223, 0.445, 0.667 and 0.889. In this case, a larger supercell of 6x3x1 of borophane was considered. Then, all compounds were subjected to a global minimization procedure with a Monte Carlo based swapping basin hopping algorithm. 54 For each Li/Na content, hundreds of Li/Na arrangements were sampled with a lower accuracy. Subsequently, the ground state structure was obtained by a stiffer energy minimization criterion as mentioned above. A supercell of size 6x4x1 has been used to estimate the barrier for Li/Na diffusion within the framework of Climbing-image nudged elastic band (cNEB) 55. AIMD simulations56 has been performed to check the stability of borophane with a time step of 0.5 fs and total simulation time of 1.5 ps at 300K. The phonon dispersion relations have been computed with phonopy code57 where we input force constants computed through VASP using density functional perturbation theory (DFPT).

3. Results and Discussion 3.1 Structural and Electronic Properties To begin with our discussion, we will first focus on the structure of borophane. In this connection, it is also relevant to discuss the structure pristine borophene. Borophene has an orthogonal crystal group with Pmmn symmetry and it is reported to possess a buckled structure with corrugations that are anisotropic (uncorrugated along x and corrugated along y) in nature. 17 In our calculations, for borophene, we have obtained relaxed lattice constants a and b to be 1.62 Å and 2.92 Å, respectively, which are in close agreement with previously reported values of a=1.667 Å and b=2.89 Å. 17 On hydrogenation, a increases to 1.91 Å whereas b (2.91 Å) remains almost unchanged. This observation closely matches with the report of Xu et al. 19 For borophane, we get a buckling height of 0.84 Å and B-H bond distance of 1.18 Å. The optimized structure of borophane is presented in Fig. 1 where panels (a), (b) and (c) illustrate the view along z, y and x directions respectively. The structure of pristine borophene resembles with borophane imagining no hydrogens (represented as yellow balls in Fig. 1). The electronic band structures of borophene and borophane are presented in Fig 2. From Fig. 2 (a), we can clearly see that borophene shows metallic properties with bands crossing Fermi energy between Γ to X and S to Y. 18 This observation is also indicative of the anisotropic metallic nature of borophene along the un-corrugated x-direction which predominantly contributes to the electrical conductivity of this material. 18 Turning our focus to the hydrogenated counterpart borophane, we observe the characteristic Dirac cone (highlighted in Fig. 2(b)) between Γ to X. This observation is reminiscent of the well celebrated material graphene. There are, however, few differences with graphene such as the


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Dirac cone is asymmetric and distorted in case of borophane. 19 Xu et al. have estimated the Fermi velocity associated with the Dirac fermions in borophane to be one order of magnitude higher than that of graphene. 19 This observation was attributed to the unique bonding features in borophane involving in plane B px and py orbitals in contrast to pz like bonding states in graphene. Furthermore, the observation of ultra-high Fermi velocity can lead to extremely high carrier mobility and can surpass its rival material graphene, thus opening new possibilities for this unique material. Before exploring the potentials of borophane as Li/Na battery anode, we also wanted to check its dynamical stability from phonon dispersion calculations. We have presented our phonon dispersion plot along the high symmetric k-vectors in Fig. 3. This figure reveals that there is no imaginary frequency and suggests that the structure is dynamically stable. Furthermore, we have also performed AIMD simulations for 1.5 ps and found that the structure is quite intact and energy is well converged (Fig. S1 in Supporting Information(SI)). In addition to judge the stability of pristine borophane, we have also considered the effect of fractional hydrogen coverages (25%, 50%, and 75% H-coverages has been considered) and tested their dynamical stability by computing respective phonon dispersion band structures. Several possible structures for a given hydrogen coverage and their resulting phonon band structures are presented in figure S5 in the SI. From this figure, it is clearly evident that all these fractional hydrogen coverages lead to dynamically unstable structures. These results justify our selection of pristine borophane (100% H-coverage) as a robust 2D substrate for further investigation. 3.2 Binding of Li/Na and Insertion Potential Typically, a material’s suitability as an anode for a specific ion storage can be judged from the favorable binding of the ion with the surface. To investigate the binding of a single Li/Na-adatom on the surface of borophane, we considered three possible binding positions viz. H-top, B-top and H-H bridge. The relaxed structures of Li/Na-borophane at H-top, B-top and H-H bridge configurations are presented in panel (a), (b) and (c) of Figure 4. We have calculated the binding energy of Li/Na at these positions by subtracting the energy of individual Li/Na atom and bare borophane form the energy of ion(Li/Na)-borophane system. Accordingly, for Li-ion we get binding energies of -1.33 eV, -2.58 eV and -1.58 eV respectively for the above three binding sites. Similarly, for the case of Na-ion the results are -0.52 eV, -1.08 eV, and -0.64 eV, respectively, at H-top, B-top and H-H bridge positions. These results convey that the B-top position (on the furrow) is the most preferred mode of binding. We note that for pristine borophene, the B-top position is also the most stable binding mode and Zhang et al. have reported the binding energy for Li-ion to be -2.77 eV which is very close to our results. 38 For a better illustration of the binding process, we have made an attempt to present the charge density difference plots for the above three binding positions (Fig 4 (d)-(f) for Li and (g)-(i) for Na corresponding to H-top, B-top and H-H bridge positions respectively). Examining these plots, we clearly infer the stronger binding in B-top case where Li/Na-atom is making favorable bonding interactions with four H atoms. We, further, performed a Bader charge analysis for the three binding positions to get deeper information about the charge transfer process. Here, the net charge is computed as the charge calculated from the Bader analysis minus the total charge of the atomic nuclei. The net charge on Li atoms at three binding positions (H-top, B-top, H-H bridge) are +0.517, +0.865, +0.787 respectively. Likewise, the net charge on Na atom at these positions are +0.548, +0.765, +0.592 respectively. From this analysis, we conclude that, at the B-top position, the Li atom with a net charge of +0.865 behaves like a Li+ ion with transference of almost 1 electron to the



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borophane sheet. An analogous result is also obtained for Na case with a net charge of +0.765. This observation of charge transfer is consistent with the binding energy trends where the B –top position gives rise to the highest binding energy. It is worthy to note that that high electronic conductivity of the anode material favorably affects the performance of the battery. The internal electronic resistance of the battery is also dependent on the electronic conductivity. Furthermore, during the operation of the battery the ohmic heat generated is proportional to the electronic conductivity of the electrode materials. Hence, metallic property for the anode material is desirable for optimal battery performance. In this context, we have previously discussed that borophene exhibited metallic behavior and borophane showed semi-metallic nature (like graphene). Furthermore, it is intriguing to examine the band structure of borophane on Li/Na adsorption. Looking at the electronic band structure of Li adsorbed on the borophane (Fig. 5(a)), we interestingly find that the material becomes metallic with bands crossing at the Fermi-level. A similar observation is also obtained for Na-borophane case (Fig. 5(b)). This observation is encouraging from the point of view of the battery performance. Furthermore, we have also checked the electronic band structure of borophane with higher Li/Na atoms concentration. As a representative case, the band structure of borophane with 8 Li, forming Li0.445B2H2, is displayed in Figure S2 (a) of the Supporting Information. This result reveals, that even with higher ion concentration, borophane retains the metallic nature similar to the case of 1 Li adsorption. We got consistent results for the case of Na0.445B2H2 (Figure S2 (b) in the Supporting Information) indicating metallic behavior.

During the operation of the rechargeable battery, the Li/Na ions concentration vary with the current direction. To model this effect, we have systematically varied the Li/Na atom content on the borophane. For this subsequent Li/Na-insertion, on both sides of borophane sheet, only the global minimum structure obtained from the swapping basin hopping algorithm has been considered. The relaxed structures corresponding to insertion of 4, 8, 12 and 16 Li/Na atoms (x=0.223, 0.445, 0.667 and 0.889 with x in Li/NaxB2H2) are presented in Figure S3 and Figure S4 (in the Supporting Information). Then, to investigate the stability of the related intermediated phases, the formation energy of these compounds were computed by employing the following equation with respect to the two end structures, i.e., B2H2 and Li/Na0.889B2H2: E = E/ − [

/. . ! ] .

(1)

where Ef denotes the formation energy and E is the computed total energy of each subscribed compound. The inset graphs in Figure 6 represent the Ef for the Li and Na cases. Here, it is interesting to emphasize that two different features are captured when considering the Li and Na cases. The Li insertion winds up with all intermediate compounds laying on the tie line of the convex hull. Therefore, the computation of the Li insertion potential profile must contain all considered Li contents, x=0.223, 0.445, 0.667 and 0.889 (all stable phases in this system). On the other hand, the plotted convex hull for the Na counterpart presents only one stable intermediate phase, Na0.44B2H2. Therefore, the Na intercalation potential has to be computed by considering only the two end points and the phase laying in the hull, Na0.44B2H2. Figure 6 represents the delivered voltage upon Li/Na insertion computed using the following equation:


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# = −$

/ % % !&'(/)* / % %

+

(2)

where (x-x0) represents the number of Li/Na atom participating in the reaction per formula unit. For example, in the reaction Li/Na.001 B0 H0 −→ Li/Na.667 B0 H0 , x assumes the value 0.445 while x0 goes to 0.223. The energies of the metallic Li/Na (ELi/Na) were computed considering bcc unit cells. Following eq. 2, we infer that the Li/Na insertion on the borophane sheet can favourably occur until the voltage is a positive value. Figure 6(a) depicts the voltage profile for the Li insertion in B2H2. The lithiation process manifests with two main plateaus. The initial plateau shows a voltage of 0.61 V vs. Li/Li+ corresponding to the lithium concentration varying from x=0 to x=0.223. The second plateau goes to 0.23 V vs. Li/Li+ and it corresponds to the x values varying from 0.223 to 0.445. The next transformation, Li0.445B2H2 Li0.6667B2H2, displays a negative value of the voltage suggesting that the maximum Li concentration in this system is for x =0.445, corresponding to the compound Li0.445B2H2. The plotted voltage profile for the Na insertion is showed in Figure 6 (b). It reveals only one plateau at 0.03 V vs. Na/Na+. Similar to the Li case, the maximum predicted concentration of Na atoms goes to x=0.445 forming Na0.44B2H2. Any further attempt to insert more sodium atoms in the borophane layer may result in negative voltage. Hence, the sodiation reaction is no longer likely to occur and it would lead to formation of dendrites hindering the performance of the device. We have also estimated the volume change associated corresponding to this maximum Li/Na content. In general, a minimal volume change of the material is advantageous for battery performance as drastic changes in the volume leads to the collapse of the material and is detrimental. We have found out that, the volume change amounts to only ~2.5%, in both cases, which is a favourable indication of the robustness of this material. The maximum Li/Na content obtained, Li/Na0.445B2H2, gives rises to an electrode with maximum theoretical specific capacity of the order of 504 mA h/g for both ions (Li and Na), together with an average voltage of 0.43 V vs. Li/Li+ for the lithium insertion and 0.03 V vs. Na/Na+ for the Na intercalation. In comparison to other materials reported as the anode for Li rechargeable battery, borophane offers a greater capacity than the well-established graphite (372 mA h g−1) 23, Ti3C2 (320 mA h g−1) 58, TiO2 polymorphs (200 mA h g−1) 59 or phosphorene (432.79 mA h g−1) 60. In case of Na, the computed theoretical capacity of borophane (504 mAh/g) is greater than that of reported for MoS261 with a theoretical capacity of 146 mAh/g or the case of Ti3C258 with a capacity of 351.8 mAh/g. Considering these results, we assert that borophane can be a suitable addition into the map of possible anode material for Li and Na-ion batteries.

3.3 Barriers for Li/Na Diffusion In connection with the rechargeable battery performance, another factor that is of significance is the diffusion rate of ions. For better performance, faster diffusion of ions is highly desirable. To model this, we have employed the cNEB method to compute the activation barriers for the ionic diffusion. Considering the symmetry of borophane structure, two possible diffusion directions can be thought of; along X and Y directions. Within the framework of cNEB, we have considered migration of Li/Na-atom between two equivalent positions along X and Y directions (Fig. 7). The corresponding minimum energy path is presented in Fig. 8. Herein, the reaction coordinate is the distance between the Li/Na atom



position at a given point along the migration path with respect to its initial position. From our calculations, we have estimated the barrier for Li diffusion along X and Y directions as 0.21 eV and 0.68 eV, respectively. On the other hand, the barrier for Na is substantially lower than the computed values for Li and these are estimated to be 0.09 eV and 0.37 eV along X and Y directions, respectively. These results convey that the preferable Li/Na diffusion path is along X direction. Our results are in good agreement with the favored Li/Na diffusion path in bare borophene previously reported. 38-39, 41 It is however noted that the Li-ion barrier reported for pristine borophene is much lesser. For instance, Mortazavi et al. have predicted a Libarrier of 0.025 eV along the longitudinal direction (X) for bare borophene. 41 The same group have calculated the barrier for Na-atom to be 0.003 eV and 0.223 eV along X and Y directions. 41 Similarly, Zhang et al. have estimated this barrier (for Li) to be 0.007 eV for pristine borophene and when they consider borophene on top of Ag substrate, the barrier changes to 0.033 eV. 38 Viewing these results from the perspective of stability, we note that as pristine borophene is reported to be grown only on a metallic substrate under severe conditions (ultra-high vacuum), although it is shown to exhibit very low barriers for Li diffusion, it might not be very useful from practical application point of view. On the other hand, the hydrogenated counterpart of borophene (borophane), can withstand the rigors of practical applications considering the relatively low barrier and enhanced stability. In this context it is worthy to note the Li-barriers reported for other relevant 2D materials such as MoS2 (0.25 eV), 36 VS2 (0.22) 35 and graphene (0.32 eV) 62. Scrutinizing these values and keeping in mind the closely matching barrier for borophane (0.21 eV), the later also looks promising as Li-ion anode material. Additionally, our estimation of lower barriers for Na-ion also sounds promising.

4. Conclusions In contemporary time, the search for new 2D materials has received rapt attention of the researchers and has gained significant momentum following the success story of graphene. Recent developments in the field of Li and Na-ion batteries have brought to fore the growing importance of 2D materials as potential anode candidates. In this regard, borophene, a newly reported atomic layer sheet of boron becomes highly contextual. This material has been synthesized on top of Ag(111) substrate and shown to possess anisotropic metallic properties. On hydrogenation, borophene undergoes a transition from metallic to a semimetal (Dirac material similar to the graphene) and the resulting material is known as borophane. Here in, with DFT based first principle studies we have made a thorough assessment of this unique material borophane for Li and Na-ion battery anode. We have reaffirmed the stability of this material from AIMD simulations and phonon dispersion relations. Interestingly, we discovered that borophane structure is only dynamically stable when it is fully (100%) hydrogenated whereas fractional H-coverages leads to dynamically unstable structures. We further computed the binding of Li/Na atom at several possible sites of borophane and it was concluded that B-top position (on the furrow) is the most favorable binding site with a binding energy of -2.58 eV and -1.08 eV respectively. Bader charge analysis demonstrated that Li/Na atom exists in Li+/Na+ state. Interestingly, on binding with Li/Na atom, borophane becomes metallic which we have concluded from our band structure calculations. As we investigated the Li/Na-insertion process into this substrate, we found out the maximum Li-content as Li0.445 per formula unit of B2H2, which gives rises to a maximum theoretical specific capacity of 504 mA h/g and an average voltage of 0.43 V vs. Li/Li+. Similarly, the predicted theoretical capacity for the Na-ion case also amounts to 504 mAh/g but with an average de-intercalation voltage of 0.03 V vs. Na/Na+. The diffusion pathways of Li/Na have been probed with cNEB method which suggest anisotropic diffusion paths along x and y directions with Li-barrier heights of 0.21 eV and 0.68 eV, respectively. Significantly


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lesser barrier heights are obtained for Na (0.09 eV and 0.37 eV along x and y directions respectively). Hence, the preferred pathway for Li/Na diffusion is concluded to be along x direction. This estimation of barrier heights of borophane closely resembles to some other reported 2D materials like graphene, MoS2 or VS2. Moreover, borophane also manifest superior theoretical specific capacity in comparison to several pertinent benchmates from the family of 2D materials. Contingent on all these revelations, we reason that borophane can be a potentially useful anode material both for LIBs and NIBs. Nevertheless, the emergence of borophane as a new Dirac material and its novel electronic properties have fundamental ramifications and is likely to stimulate further curiosity among the community.

Acknowledgements The authors gratefully acknowledge computational resources from the Swedish National Infrastructure for Computing (SNIC2016-10-50, SNIC2016-1-243). VS acknowledges the European Erasmus fellowship program for funding. RA acknowledge support from the Swedish Research Council. Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: It contains further details pertaining to the stability of pristine borophane as well as borophane with different fractional hydrogen coverages, minimum energy structures with multiple Li/Na intercalation and additional band structures with 8 Li and Na ions.

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(a)

(b)

c

a

b

(c)

b

c

c

a

a

b

Figure 1: Structure of borophane as viewed from (a) XY plane, (b) XZ plane and (c) YZ plane. The unit cell is marked with lines in (a). (Atom color: B(purple); H(yellow))

Bandstructure Borophene Borophene

(a)

Bandstructure

(b)

12

12

8

8

Borophane Borophane-2x1

4 Energy (eV)

4 Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

-4

0

-4 -8

-8

-12

Γ

X

S

Y

Γ

-12

Γ

X

S

Y

Figure 2: Band structures of (a) borophane and (b) borophane. Bands crossing Fermi energy reveals the metallic nature for borophane and for borophane the characteristics Dirac cone(highlighted circle) can be seen between G to X.


Γ


80

60

Frequency

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

40

20

0 Y

Γ

S

Wave vector

X

Γ

Figure 3: Phonon dispersion plot for borophane along high-symmetric wave vectors. Absence of any negative frequency indicates dynamic stability of the structure.


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a

c

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a) H-top

(b) B-top

(c) H-H bridge

a

c

c

a

b

b

(d)

(e)

(f)

c

b

a

c

a b

(g)

(h)

(i)

c

b

a

Figure 4: Possible binding sites viz. (a) H-top, (b) B-top and (c) H-H bridge; of Li/Na atoms on borophane surface. The corresponding charge density difference figures for Li is presented in part (d)-(f) and for Na in part (g)-(i) respectively. Blue color indicates charge sufficient and red as charge deficient regions (isosurface value is 0.002 e/ Å3)



Bandstructure Borophane-1Li 8

Energy (eV)

4

0

-4

-8

Γ

X

Bandstructure S

Y

Γ

Γ

X

S

Y

Γ

-12

Borophane-1Na

8

4

Energy (eV)

1 2 3 (a) 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 (b) 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0

-4

-8

-12

Figure 5: Band structure for (a) Li and (b) Na adsorbed borophane (B-top positions). Bands crossing at the Fermi energy indicates metallic nature.


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Formation Energy (eV)

(a)

Insertion Potential (V)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.6

0.4

Li in LixB2H2

0.2

0

0

0.1

0.2

0.3

0.4

0.5

Li in LixB2H2 (b)

0.1

0

0

0.1

0.2

0.3

0.4

0.5

Figure 6: (a) Li intercalation potential profile for LixB2H2 layer. The inset graph represents the formation energy of LixB2H2 per formula unit where x assumes values of x=0.223, 0.455, 0.667, 0.889; (b) Na intercalation potential profile for NaxB2H2 layer. The inset graph represents the formation energy of NaxB2H2 per formula unit where x assumes values of x=0.223, 0.455, 0.667, 0.889. In both cases only the formation energy of the lowest energy configuration of each ionic content is shown for clarity.



Diffusion along X direction

z

y

x

y

x

z

Diffusion along Y direction

z

x

z

x

y

y

Figure 7: An illustration showing the possible pathways of Li/Na diffusion along X and Y directions


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MEP- along X

MEP- along Y

(a) Li

(b) Li

0.25

0.7

0.6 0.2

0.5 0.15

Energy [eV]

Energy [eV]

0.4

0.1

0.3

0.2

0.05

0.1 0

0 -0.05 0

0.5

1

1.5 Reaction Coordinate [A]

2

2.5

-0.1

3

(c) Na

0

0.5

1

1.5 2 2.5 Reaction Coordinate [A]

3

3.5

4

3

3.5

(d) Na

0.1

0.4

0.09

0.35

0.08

0.3

0.07

0.25 0.06

Energy [eV]

Energy [eV]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.05 0.04

0.2

0.15

0.03

0.1

0.02

0.05

0.01

0

0 0

0.5

1 1.5 Reaction Coordinate [A]

2

2.5

-0.05 0

0.5

1

1.5 2 Reaction Coordinate [A]

2.5

Figure 8: Minimum energy path (MEP) demonstrating the barriers for Li diffusion along (a) X, and (b) Y directions. Similarly, the barrier for Na diffusion along X and Y directions are presented in sections (c) and (d) respectively.



TOC/ Graphical Abstract


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Borophane as a Benchmate of Graphene - ACS Publications

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