Tetragonal and trigonal Mo2B2 monolayers: two new low … · 2020. 12. 31. · Tetragonal and trigonal Mo 2B 2 monolayers: two new low-dimensional materials for Li-ion and Na-ion

5178 | Phys. Chem. Chem. Phys., 2019, 21, 5178--5188 This journal is© the Owner Societies 2019

Cite this:Phys.Chem.Chem.Phys.,2019, 21, 5178

Tetragonal and trigonal Mo2B2 monolayers:two new low-dimensional materials forLi-ion and Na-ion batteries†

Tao Bo,ab Peng-Fei Liu, ab Junrong Zhang,ab Fangwei Wangabc andBao-Tian Wang *abd

In this study, we report two new Mo2B2 monolayers and investigate their stabilities, electronic structures,

lattice dynamics, and properties as anode materials for energy storage by using the crystal structure

prediction technique and first-principles method. The calculated phonon spectra and electrical structures

indicate that our predicted tetragonal and trigonal Mo2B2 (tetr- and tri-Mo2B2) monolayers possess excellent

electronic conductivity and great stability. The adsorption energies of Li/Na on them are negative enough to

ensure stability and safety under operating conditions. Besides, tetr-Mo2B2 possesses a theoretical specific

capacity of B251 mA h g�1 for both Li- and Na-ion batteries (LIBs and NIBs), while tri-Mo2B2 possesses

B251 and B188 mA h g�1 for LIBs and NIBs, respectively. The diffusion energy barriers of Li/Na over

tetr- (0.029/0.010 eV) and tri- (0.023/0.013 eV) Mo2B2 are very small, indicating their excellent charge/

discharge capability. In addition, the low electrode potential of Li/Na-intercalated tetr- and tri-Mo2B2 is

beneficial to their performance as anode materials. This work is of great importance for widening the

families of both anode materials for LIBs/NIBs and two-dimensional transition metal borides.

1. Introduction

Rechargeable LIBs, one of the most successful clean andefficient energy storage technologies, have been widely usedin portable electronic devices and electric vehicles.1–3 LIBs havemany advantages such as high power density, superior energyefficiency, long cycle life, and portability.4,5 However, the storageof lithium sources on Earth is rather limited,6 and the amount ofLi in the earth’s crust is only 20 mg kg�1.7 With the reduction oflithium resources, next-generation storage technology will relyon other metal-ion battery devices that are composed of earth-abundant materials. A potential candidate to replace LIBs is therechargeable NIBs, which have attracted increasing attention

because of the abundance of Na on Earth (28 400 mg kg�1)7 andtheir low cost. The challenge associated with applying LIBs andNIBs is obtaining a large storage capacity and high charging/discharging rates,8 which is highly dependent on the perfor-mance of their electrode materials.9,10 The widely usedcommercial anode material for LIBs, graphite, possesses severaladvantages such as high coulombic efficiency, relatively goodcycling stability, and low cost.11,12 However, its performance islimited due to poor rate capability arising from the low diffusivityof Li atoms within it.3 Moreover, graphite cannot function well inNIBs, primarily due to the weak Na–C interaction.13 Therefore,the search for a high-performance anode material is urgentlyneeded for the development of both LIBs and NIBs.

In recent years, owing to their superior mechanical properties,high surface area, and high electron mobility, two-dimensional(2D) materials including pristine/defected/doped graphene,14,15

phosphorene,16,17 borophene,18 silicene,19 MXenes,20 and transi-tion metal dichalcogenides21,22 (TMDs) have attracted wide atten-tion as promising choices as anode materials for LIBs and NIBs.23

It is generally known that MXenes24 are attracting increasinginterest due to their excellent properties for various applications.So far, many MXenes including Ti2C, Ti3C2, Nb2C, V2C, Ti4C3,Ti3CN, and Mo2C have been synthesized

25 and most of them havebeen explored as anode materials.20,26,27 Besides, 2D TMDs, suchas VS2 and MoS2, have also attracted wide attention and have beenapplied to a broad range of applications in catalysis, hydrogen

a Institute of High Energy Physics, Chinese Academy of Science (CAS),

Beijing 100049, China. E-mail: [email protected] Dongguan Neutron Science Center, Dongguan 523803, Chinac Beijing National Laboratory for Condensed Matter Physics, Institute of Physics,

Chinese Academy of Sciences, Beijing 100080, Chinad Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan,

Shanxi 030006, China

† Electronic supplementary information (ESI) available: (I) Metastable isomers of2D Mo2B2, (II) snapshots and variation of the free energy and RDFs for the tetr-and tri-Mo2B2 in the AIMD simulations from 300 to 2100 K, (III) adsorptionstructures of Li/Na with various concentrations on tetr- and tri-Mo2B2, and (IV)the detailed reasons why structures located on the hull are thermodynamicallystable relative to dissociation into other configurations. See DOI: 10.1039/c9cp00012g

Received 2nd January 2019,Accepted 7th February 2019

DOI: 10.1039/c9cp00012g

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storage, and electrode materials.21,22,28 Recently, the successfulsynthesis of borophene has aroused the research enthusiasm ofboron-related 2D materials.29 Scientists began to think aboutwhether transition metals and boron can form novel 2D materialssimilar to MXenes.30,31 For example, Guo et al.30 investigated thepossibility of exfoliating a family of layered orthorhombic transi-tion metal borides into 2D materials including Mo2B2, Cr2B2,Fe2B2, and W2B2 and studied the properties of Mo2B2 and Fe2B2 asanode materials for LIBs. Jiang et al.31 reported an orthorhombic2D MnB material by using ab initio high-throughput calculations.In our recent work, we reported a family of hexagonal 2Dtransition metal borides including Ti2B2, Mo2B2 and so on andexplored Ti2B2 as an anode material for LIBs and NIBs.

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As mentioned above, two kinds of structures were reportedfor 2D Mo2B2: orthorhombic and hexagonal phases. Owing tothe diversity of three-dimensional structures of molybdenumborides,33,34 a question arises naturally: Are there any otherstructures more stable than the reported ones? Through struc-tural prediction by using the CALYPSO code,35 in this work, weobtain two new 2D structures of tetragonal and trigonal Mo2B2(tetr- and tri-Mo2B2) with lower energies than the orthorhombicand hexagonal ones. Then, we use the first-principles methodto investigate the stabilities, electronic structures, lattice dynamics,and the properties of our obtained tetr- and tri-Mo2B2 monolayersas anode materials for LIBs and NIBs. The targeted researchinterests include: (1) geometrical structures, electrical structuresand phonon spectra of tetr- and tri-Mo2B2, (2) the adsorption sitesand energies of Li/Na on tetr- and tri-Mo2B2, (3) the theoreticalspecific capacities and voltage profiles of tetr- and tri-Mo2B2 forLIBs and NIBs, and (4) the diffusion barriers of Li/Na on tetr- andtri-Mo2B2 monolayers.

2. Computational method

The particle-swarm optimization (PSO) scheme, as implementedin the CALYPSO code,35–37 is employed to search for the lowest-energy structures of 2D Mo2B2. In our PSO calculations, bothplanar and buckled structures including one, two, and threelayers are all considered. The population size and the number ofgenerations are set to be 30. Simulating cells containing 1, 2, and4 formula units are considered for 2D Mo2B2. After all thestructure search calculations are completed, thousands of newstructures of 2D Mo2B2 are generated. The CALYPSO code canrank these new structures in order of enthalpy from low to high.Then we select more than ten different structures with the lowestenergies for more accurate optimization and phonon spectrumcalculation. After optimization, the accurate total energies ofthese structures are obtained and the structure with the lowesttotal energy is the global minimum structure.

The energy calculations and structure optimizations arecarried out by using the density functional theory (DFT) method,within the Perdew–Burke–Ernzerhof form of the generalized gra-dient approximation (PBE-GGA)38 as implemented in the ViennaAb initio Simulation Package (VASP).39 The projector augmentedwave (PAW) method40 is used to treat the electron–ion interaction.

Spin-polarization is included in all the studied systems. The cutoffenergy is set as 600 eV and the atomic positions are fully relaxeduntil the maximum force on each atom is less than 0.005 eV Å�1.The optB86b-vdW exchange functional41 is used for the van derWaals (vdW) correction since it can properly treat the long-rangedispersive interactions. A 2 � 2 supercell of Mo2B2 monolayers isemployed to model the adsorption and diffusion of Li and Na, andthe Brillouin zone (BZ) integration is performed using a 5 � 5 � 1k-point grid. A vacuum separation is set to more than 20 Å toprevent any interaction between two neighboring monolayers.

Phonon dispersion calculations are based on density-functionalperturbation theory (DFPT)42 as done in the Phonopy code.43 TheBorn–Oppenheimer ab initio molecular dynamics (AIMD) simula-tions in the NVT ensemble are employed at different temperaturesup to 2400 K to investigate the thermal stability of the Mo2B2monolayers. The AIMD simulations are performed using a 3 � 3supercell and last for 10 ps with time steps of 1.0 fs. The climbingimage nudged elastic band (CI-NEB) method44 is employed toinvestigate the diffusion pathway and energy barriers for transportof Li and Na over the Mo2B2 monolayers. Eight images includ-ing the initial and the final positions are used for the CI-NEBcalculations.

The cohesive energy is defined as:

Ecoh = (2EMo + 2EB � EMo2B2)/4 (1)

where EMo, EB, and EMo2B2 are the total energy of a Mo atom,a B atom and a unit cell of the Mo2B2 monolayer, respectively.The adsorption energy of Li/Na on the monolayer is defined as:

Ead = (EMMo2B2 � EMo2B2 � nEM)/n(M = Li, Na) (2)

where EMMo2B2 and EMo2B2 are the total energies of Mo2B2 withand without Li/Na adatoms, respectively, EM represents thetotal energy per atom for the bulk Li/Na metal, and n denotesthe number of adsorbed Li/Na atoms. The average adsorptionenergy of Li/Na on the second layer is defined as:

Eave = (EMmMo2B2 � EM(m�1)Mo2B2 � nEM)/n(M = Li, Na) (3)

where EMmMo2B2 and EM(m�1)Mo2B2 are the total energies of 2DMo2B2 with m and (m � 1) adsorbed Li/Na layers, n denotes thenumber of adsorbed Li/Na atoms in each layer, EM stands forthe total energy per atom for the bulk Li/Na. The theoreticalcapacity can be obtained from:

CA = czF/MMo2B2 (4)

where c is the number of adsorbed Li/Na atoms, z is the valencenumber of Li/Na, F is the Faraday constant (26 801 mA h mol�1),and MMo2B2 is the molar weight of Mo2B2. The enthalpies offormation for all MxMo2B2 (M = Li, Na) compounds with respectto Mo2B2 and Li/Na metal as the reference states are calculatedusing the following equation:

DHf = (EMxMo2B2 � EMo2B2 � xEM)/(x + 1)(M = Li, Na) (5)

where EMxMo2B2 is the energy of the MxMo2B2 compound perMo2B2 formula unit, EMo2B2 is the energy of Mo2B2 per Mo2B2formula unit, and EM is the energy per atom for the Li/Nabulk metal. For every concentration x of the MxMo2B2

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compound, the electrode potential V with respect to M/M+ iscalculated as:45

V ¼ �Eðx2Þ � Eðx1Þ � ðx2 � x1ÞEðMÞeðx2 � x1Þ

ðM ¼ Li;NaÞ (6)

where E(x2) and E(x1) are the total energies of MxMo2B2 at twoadjacent concentrations x2 and x1, and E(M) is the total energyper atom for the bulk Li/Na.

3. Results and discussion3.1 Geometrical structures of tetr- and tri-Mo2B2

We successfully obtained several low-energy 2D Mo2B2 structuresthrough a thorough structural search by using the CALYPSO code.The obtained tetragonal Mo2B2 monolayer (see Fig. 1a) is theglobal minimum structure, which is energetically (by 0.093 eV peratom) more stable than the obtained trigonal Mo2B2 monolayer(see Fig. 1b) which possesses the second lowest energy. The othermetastable structures are shown in Fig. S1 in the ESI.† We findthat the structure of the tetr-Mo2B2 monolayer (see Fig. 1a) issimilar to that of 2D TiC reported by Fan et al.,46 which issubjected to the tetragonal P4/nmm space group. The optimizedlattice parameters are a = b = 3.07 Å, which are close to those ofTiC (2.99 Å).46 In this tetr-Mo2B2 monolayer, each Mo (B) atom issurrounded by the nearest four B (Mo) atoms in the xy plane andthe nearest one B (Mo) atom in the z direction to form a tetragonallattice. The calculated bond length of Mo–B in tetr-Mo2B2 is 2.19 Åin the xy plane and 2.25 Å in the z direction. The minimum value ofline charge density along Mo–B bonds is about 0.07–0.08 e per a.u.3,which is prominently higher than that of the Na–Cl bond in thetypical ionic crystal NaCl (0.007 e per a.u.3)47 but is smaller than thatof the Si covalent bond (0.104 e per a.u.3).47 This indicates that Moand B atoms are bonded with covalent and ionic mixed features.The obtained tri-Mo2B2 (see Fig. 1b) is subjected to the trigonalP%3m1 space group, which consists of a distorted boron honeycombsheet sandwiched between two hexagonal planes of Mo atoms withthe calculated lattice parameters of a = b = 2.85 Å. The minimumvalue of line charge density for B–B bonds (0.116 e per a.u.3) is

higher than that of the Si covalent bond (0.104 e per a.u.3),47

indicating that the B layers are strongly bonded by B–B bonds.Besides, the minimum value for Mo–B bonds is about 0.08 e pera.u.3, which is similar to that for Mo–B bonds in tetr-Mo2B2,indicating covalent and ionic mixed features in the Mo–Bbonds. The optimized bond lengths of B–B and B–Mo are1.76 and 2.27 Å, respectively. We also obtain an orthorhombic2D Mo2B2 monolayer (see Fig. S1b, ESI†), which has beenreported by Guo et al.30 The energy of this orthorhombic 2DMo2B2 is higher by 0.205 (0.113) eV per atom than that of ourobtained tetr-Mo2B2 (tri-Mo2B2), indicating that our obtainedtetr- and tri-Mo2B2 monolayers are more stable in energy.

3.2 Electrical structures and phonon spectra of tetr-Mo2B2and tri-Mo2B2

The electronic properties of anode materials have an importantinfluence on the cycle characteristics of LIBs.48,49 Therefore,we calculated the electronic band structures and PDOS of thetetr- (see Fig. 2a) and tri-Mo2B2 (see Fig. 2c) monolayers.The nonzero DOS at the Fermi energy indicates that tetr- andtri-Mo2B2 possess metallic properties. The metallicity of tetr-Mo2B2 mainly originates from Mo 4p orbital contribution,while the metallicity of tri-Mo2B2 mainly originates from Mo4p and 4d orbital contribution. The contribution of B-2p isnegligible. The outstanding electronic conductivity indicatesthat these Mo2B2 monolayers have potential application prospectsfor LIBs and NIBs.

The stability of anode materials is very important due tohundreds of charge–discharge cycles in practical applications.Cohesive energy is a well-accepted parameter that can be usedto evaluate whether a predicted 2D material is easy to synthesizeexperimentally.6,50 According to eqn (1), the calculated cohesiveenergies of the tetr-and tri-Mo2B2 monolayers are 6.49 and6.40 eV per atom, respectively, which are higher than those ofCu2Si (3.46 eV per atom),

51 Al2C (4.58 eV per atom),52 Be2C

(4.86 eV per atom),53 and h-BeN2 (4.98 eV per atom)54 mono-

layers. The relatively large cohesive energies suggest that thesetwo Mo2B2 monolayers are likely to be synthesized under certainexperimental conditions. To obtain the dynamic stability of thetetr- and tri-Mo2B2 monolayers, we calculate their phonon dis-persion curves. There are no imaginary frequencies within theentire BZ, indicating that both tetr- (see Fig. 2b) and tri-Mo2B2(see Fig. 2d) monolayers are dynamically stable. Furthermore,the highest frequencies of the tetr- and tri-Mo2B2 monolayers are22 THz (733 cm�1) and 25 THz (833 cm�1), respectively, whichare higher than those of tetragonal TiN (668 cm�1),46 silicene(580 cm�1),55 Cu2Si (420 cm

�1),51 arsenene (225 cm�1),56 anti-monene (325 cm�1),56 and MoS2 (473 cm

�1),57 indicating strongabilities of these two 2D Mo2B2 structures. For both tetr- andtri-Mo2B2 monolayers, the main contribution to the phononmodes at high-frequency is entirely from the B atoms while atlow-frequency the contribution is entirely from Mo atoms. Inorder to understand the thermal stability, AIMD simulationswere carried out for these Mo2B2 monolayers at temperatures of300, 900, 1500, and 2100 K, respectively. Fig. S2 and S3 (ESI†)show the variation of total energy with time for the tetr- and

Fig. 1 Top and side views of the (a) tetr-Mo2B2 monolayer and (b) tri-Mo2B2monolayer. The Mo and B atoms are marked in violet and green, respectively.

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tri-Mo2B2 monolayers at different temperatures, respectively.The average value of the total energy of the tetr- and tri-Mo2B2monolayers remains almost constant during the whole simula-tion at 300, 900, and 1500 K. After simulating for 10 ps at1500 K, the original geometries of the tetr- and tri-Mo2B2monolayers remain intact with only slight in-plane and out-of-plane deformations (see Fig. S4 and S5, ESI†). These resultsconfirm that the tetr- and tri-Mo2B2 monolayers are thermallystable even at a high temperature of 1500 K. The radialdistribution function (RDF) of the tetr- (see Fig. S6, ESI†) andtri-Mo2B2 (see Fig. S7, ESI†) monolayers is also calculatedat 300, 900, 1500, and 2100 K, respectively. At 300, 900, and1500 K, for both tetr- and tri-Mo2B2 monolayers, the RDF hasmany peaks between 1 and 8 Å, indicating that these twomaterials are in long range order. The above results indicatethat the geometric configurations of these Mo2B2 monolayersare expected to be highly stable.

3.3 Adsorption sites of Li and Na on tetr- and tri-Mo2B2

If a material is to be used as an anode in LIBs/NIBs, it musthave a strong ability to adsorb the Li/Na adatoms. In order toobtain stable adsorption structures of Li/Na on the surfaces ofthe tetr- and tri-Mo2B2 monolayers, we carried out a lot ofsimulations starting with different initial states (as shown inFig. S8 and S9, ESI†). It can be seen that for different initialstates, the Li ions will eventually be optimized on the highsymmetry adsorption sites. According to the above results andthe symmetry of the structures, three and four high symmetryadsorption sites will be discussed for the tetr- (see Fig. 3a) and

tri-Mo2B2 (see Fig. 3b) monolayers, respectively. For tetr-Mo2B2,sites S1 and S3 are on top of Mo and B atoms, respectively,while site S2 is above the center of two B atoms. According toeqn (2), the adsorption energies of Li/Na (see Fig. 3c) are�0.450/�0.704, �0.777/�0.837, and �0.748/�0.826 eV on theS1, S2, and S3 sites, respectively. The calculated results showthat the most stable adsorption site for Li/Na is above thecenter of two B atoms (S2 site). The adsorption energy of Li onS2 (�0.777 eV) is comparable to that on the orthorhombic 2DMo2B2 monolayer (�0.81 eV) reported by Guo et al.30 Obviously,this adsorption energy (�0.777 eV) is much lower than that ontetr-TiC (�0.16 eV) and tetr-TiN (+0.31 eV),46 indicating morestable adsorption of Li on tetr-Mo2B2 than on tetr-TiC or tetr-TiNwhich has a uniform structure. For tri-Mo2B2, sites S1 and S4 areon top of B and Mo atoms, respectively, while sites S2 and S3 areabove the center of three Mo atoms and two Mo atoms, respec-tively. The adsorption energies of Li/Na (see Fig. 3d) are �0.540/�0.671, �0.542/�0.677, �0.519/�0.664, and �0.316/�0.537 eVon S1, S2, S3, and S4 sites, respectively. We find that theadsorption of Li/Na on S2 is the most stable, and the adsorptionenergies are comparable to those on the well-known Mo2C

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(�0.58/�0.77 eV for Li/Na) which is made up of two sheets of Moatoms and an intermediate sheet of C atoms. Besides, theadsorption energies on S4 are the largest, which are larger by0.127–0.226 eV than those on S1, S2, and S3. This indicates thatit is not possible for Li/Na to appear on top of Mo atoms. Thesimilarity of the adsorption energies on S1, S2, and S3 suggeststhat the Li/Na atoms easily transfer along the S1–S3–S2 direction.For both tetr- and tri-Mo2B2, the adsorption of Na is more stable

Fig. 2 Band structures and total and partial density of states (TDOS and PDOS) of (a) tetr-Mo2B2 and (c) tri-Mo2B2. The red, orange, and blue lines standfor the Mo-4p, Mo-4d, and B-2p PDOS, respectively, while the black line represents the TDOS. The phonon dispersions and projected phonon density ofstates (PhDOS) of (b) tetr-Mo2B2 and (d) tri-Mo2B2. The phonon dispersions are weighted by the motion modes of B and Mo atoms. The green, violet, red,and blue circles in (b) and (d) indicate B horizontal, B vertical, Mo horizontal, and Mo vertical modes, respectively. The blue and red lines in the rightcolumn of (b) and (d) represent B and Mo, respectively.

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than that of Li for all the adsorption sites. In general, negativeadsorption energies for all the adsorption sites mentioned aboveindicate that Li and Na atoms prefer adsorption over tetr- andtri-Mo2B2 rather than cluster formation, which is important forthe safe operation of LIBs and NIBs.

3.4 Theoretical specific capacity

As we know, the storage capacity is a key factor in evaluating theperformance of an electrode material, and promising electrodematerials require large storage capacity. In order to obtain thestorage capacities of tetr- and tri-Mo2B2, we calculate the Li/Naadsorption at higher concentrations on the surfaces of tetr- andtri-Mo2B2. We present in Fig. 4 the most stable adsorptionstructures and the corresponding adsorption energies for Liadsorption on the surface of tetr-Mo2B2. As discussed above,the S2 site is the most stable adsorption site for the adsorptionof a single Li atom which corresponds to Li0.25Mo2B2 andpossesses an energy of �0.777 eV. For the adsorption of twoLi atoms, corresponding to Li0.5Mo2B2, Li atoms adsorbed onthe S2 sites of both sides are the most stable. The averageadsorption energy is �0.772 eV, which is almost the same asthat of Li0.25Mo2B2. For the adsorption of three Li atoms,corresponding to Li0.75Mo2B2, two Li atoms adsorbed on theS3 sites of one side and the third Li atom adsorbed on the S2site of the other side are the most stable. We find that when two

Li atoms adsorb on one side of tetr-Mo2B2, they prefer to adsorbon S3 sites rather than on S2 sites, which is different from theadsorption of one Li atom. The average adsorption energy(�0.716 eV) is about 0.06 eV higher than those of Li0.25Mo2B2and Li0.5Mo2B2, which results from the repulsion between Liatoms. For the adsorption of four Li atoms, corresponding toLi1.0Mo2B2, unlike the above three configurations, the moststable adsorption structure is that in which all Li atoms adsorbon S3 sites at the same side. The average adsorption energy is�0.785 eV, which is lower than those of the above threeconfigurations. The same phenomenon occurred in tetr-TiN.46

In that work, the authors found that compared with theadsorption of a single Li atom, more electrons are transferredfrom the adsorbed Li to the substrate for the adsorption of fourLi atoms, resulting in the decrease in average adsorption energyof Li. For the adsorption of five, six, and seven Li atoms,corresponding to Li1.25Mo2B2, Li1.5Mo2B2, and Li1.75Mo2B2,respectively, the average adsorption energies are �0.799,�0.784, and �0.785 eV, respectively, which are comparable tothat of Li1.0Mo2B2. However, the average adsorption energy forthe adsorption of eight Li atoms is �0.835 eV, which is the lowestamong all the configurations mentioned above. The averageadsorption energy gradually decreases as the Li concentrationincreases from Li0.25Mo2B2, via Li1.0Mo2B2, to Li2.0Mo2B2. Thistrend is also seen in the orthorhombic 2D Mo2B2 monolayer.

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Fig. 3 High symmetry adsorption sites for Li/Na on the surface of (a) tetr-Mo2B2 and (b) tri-Mo2B2. Adsorption energies for Li/Na on the surface of (c)tetr-Mo2B2 and (d) tri-Mo2B2. The Mo and B atoms are displayed in violet and green, respectively.

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The adsorption energies of Li on the orthorhombic 2D Mo2B2monolayer are �0.81, �0.98, and �1.01 eV for Li0.25Mo2B2,Li1.0Mo2B2, and Li2.0Mo2B2, respectively.

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For Na adsorption on tetr-Mo2B2, we calculate the adsorp-tion of one to eight Na atoms and present in Fig. S10 (ESI†)the most stable adsorption structures and the correspondingadsorption energies. For the adsorption of one, two, and threeNa atoms, corresponding to Na0.25Mo2B2, Na0.5Mo2B2, andNa0.75Mo2B2, respectively, the most stable structures are thesame as those for Li adsorption. However, for the adsorption offour Na atoms (Na1.0Mo2B2), the most stable adsorption struc-ture is that in which two Na atoms adsorb on the S3 sites of oneside and the other two Na atoms adsorb on the S3 sites of theother side, which is different from the adsorption structure offour Li atoms. The average adsorption energies are �0.837,�0.822, �0.733, and �0.702 eV for Na0.25Mo2B2, Na0.5Mo2B2,Na0.75Mo2B2, and Na1.0Mo2B2, respectively. It can be seen thatthe average adsorption energy increases with the increase ofNa concentration, which is because of the large exchangeinteraction between the Na atoms. With the increase of Na

concentration, the adsorption energy continues to increase.Though the adsorption energy for Na2.0Mo2B2 (�0.515 eV) isabout 0.3 eV higher than that of Na0.25Mo2B2, the large negativevalue is enough to stabilize the adsorption of eight Na atoms.Thus, the first layer can accommodate at most eight Li/Naatoms on both sides of the tetr-Mo2B2 surface.

The most stable adsorption structures for Li and Na adsorp-tion on the tri-Mo2B2 surface are presented in Fig. S11 and S12(ESI†), respectively. For Li adsorption, the average adsorptionenergy remains almost unchanged as the Li concentrationincreases from Li0.25Mo2B2 to Li0.75Mo2B2 but keeps increasingas the Li concentration increases from Li0.75Mo2B2 to Li2.0Mo2B2.For Na adsorption, the average adsorption energy increasesrapidly from Na0.5Mo2B2 to Na1.5Mo2B2. The smaller latticeconstant of tri-Mo2B2 (2.85 Å) than that of tetr-Mo2B2 (3.07 Å)enables a larger exchange interaction between the adatoms. Wefind that the first layer can accommodate at most eight Li atoms(see Fig. S11, ESI†) or six Na atoms (see Fig. S12, ESI†) on bothsides of the tri-Mo2B2 surface.

It is well known that temperature rise can influence thesimulations. In order to evaluate the thermal stability for Li/Naadsorption on the tetr- and tri-Mo2B2 surfaces, we carry outAIMD simulations at a temperature of 300 K for the tetr- andtri-Mo2B2 monolayers adsorbed with one layer of Li/Na. Thevariation of total energies with time is presented in Fig. S13(ESI†), while the final structures after 3 ps simulations arepresented in Fig. S14 (ESI†). We find that the total energiesremain almost constant during the whole simulation. Besides,the final structures after 3 ps simulations remain intact andLi/Na ions are still adsorbed on the tetr- and tri-Mo2B2 mono-layers. These results confirm that Li/Na can adsorb on thetetr- and tri-Mo2B2 monolayers stably at an ambient tempera-ture of 300 K.

The adsorption of two layers of Li/Na on tetr- and tri-Mo2B2is also investigated. According to eqn (3) that has been appliedto many materials,26,58,59 the adsorption energies of Li/Na inthe second layer are close to zero or a very small positive value,which indicates that the adsorption of two layers of Li/Na is notstable on tetr- and tri-Mo2B2 monolayers. Furthermore, inpractical applications, a much larger spacing is needed betweenthe Mo2B2 monolayers to accommodate multilayer adsorption.Thus, the maximum capability of Li storage is Li2.0Mo2B2 for bothtetr- and tri-Mo2B2 monolayers, while the maximum capability ofNa storage is Na2.0Mo2B2 and Na1.5Mo2B2 for tetr- and tri-Mo2B2monolayers, respectively. The capability of Na storage for ourtetr- and tri-Mo2B2 is much larger than that of the well-knownhexagonal Mo2C monolayer (NaMo2C).

26 According to theseresults and eqn (4), the theoretical specific capacities of tetr-Mo2B2 as an electrode are B251 mA h g

�1 for LIBs and NIBs,while the theoretical specific capacities of tri-Mo2B2 are B251and B188 mA h g�1 for LIBs and NIBs, respectively.

3.5 Voltage profile

During the operation of the LIBs and NIBs, the Li/Na ionconcentration and the corresponding electrode potential varywith the current direction.60 The voltage profiles are of great

Fig. 4 Top and side views of the structures of (a) Li0.25Mo2B2, (b) Li0.50Mo2B2,(c) Li0.75Mo2B2, (d) Li1.0Mo2B2, (e) Li1.25Mo2B2, (f) Li1.50Mo2B2, (g) Li1.75Mo2B2,and (h) Li2.0Mo2B2 with Li ions adsorbed on the surface of the tetr-Mo2B2monolayer. The Mo, B, and Li atoms are displayed in violet, green, and blue,respectively.

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significance for deep understanding of the performance of anelectrode material. Thus, according to eqn (5), we calculate theenthalpies of formation for Li/NaxMo2B2 at each Li/Na concen-tration to investigate the stability of all the intermediatephases. Then, according to the stable intermediate phasesand eqn (6), we investigate the concentration-dependent profileof the electrode potential for Li/Na-intercalated tetr- and tri-Mo2B2. We present in Fig. 5a and b the enthalpies of formationfor LixMo2B2 and NaxMo2B2 with respect to tetr-Mo2B2 andLi/Na bulk metal and the convex hull for the enthalpies offormation. Structures located on the hull are thermodynami-cally stable relative to dissociation into other configurations.The detailed reasons are given in Section S4 of the ESI.† Asshown in Fig. 5a, the calculated convex hull of LixMo2B2displays only one stable intermediate phase, Li2.0Mo2B2. Thus,the calculation of the electrode potential vs. Li/Li+ only needs toconsider one phase located on the hull. We present in Fig. 5cthe voltage profile for Li insertion. It presents only one plateauat 0.835 V vs. Li/Li+. On the other hand, Na insertion winds upwith the NaxMo2B2 (x = 0.25, 0.5, 1.0, and 2.0) compounds lyingon the convex hull (see Fig. 5b). Therefore, the calculation ofthe electrode potential vs. Na/Na+ should contain stable Nacontents, NaxMo2B2 (x = 0.25, 0.5, 1.0, 2.0). As shown in Fig. 5d,the electrode potential for Na insertion varies in the range of0.328–0.837 V with a decreasing trend with increasing capacity.Four main plateaus exist in the whole process of Na insertion.The initial plateau displays a voltage of 0.837 V vs. Na/Na+

corresponding to Mo2B2 - Na0.25Mo2B2. The second and thirdplateaus show voltages of 0.807 V (Na0.25Mo2B2 - Na0.5Mo2B2)and 0.582 V (Na0.5Mo2B2 - Na1.0Mo2B2), respectively. Thefourth plateau goes to 0.328 V vs. Na/Na+ which correspondsto Na1.0Mo2B2 - Na2.0Mo2B2. The average electrode potential

of Na-intercalated tetr-Mo2B2 is 0.515 V, which is smaller thanthat of MoS2 (0.75 V).

21

For tri-Mo2B2, we present in Fig. 6a and b the enthalpies offormation for LixMo2B2 and NaxMo2B2 as well as the convexhull and in Fig. 6c and d the voltage profiles for Li and Nainsertion. As shown in Fig. 6a, the LixMo2B2 (x = 0.5, 0.75, 1.0,1.5, 2.0) compounds lie on the convex hull for Li insertion.Thus, there are five main plateaus in the Li insertion processfrom Mo2B2 to Li2.0Mo2B2 (see Fig. 6c), which correspond toMo2B2 - Li0.5Mo2B2, Li0.5Mo2B2 - Li0.75Mo2B2, Li0.75Mo2B2 -Li1.0Mo2B2, Li1.0Mo2B2 - Li1.5Mo2B2, and Li1.5Mo2B2 -Li2.0Mo2B2, respectively. The voltages of these five plateausare 0.562, 0.513, 0.464, 0.317, and 0.259 V vs. Li/Li+, respec-tively, and the average value is 0.407 V. For Na insertion, asshown in Fig. 6b, the NaxMo2B2 (x = 0.5, 0.75, 1.0, 1.5)compounds lie on the convex hull, which indicates that thereare four plateaus in the voltage profile. As shown in Fig. 6d,these four plateaus have voltages of 0.697, 0.379, 0.228, and0.149 V vs. Na/Na+, respectively, and the average value is0.383 V. The average potential of Na-intercalated tri-Mo2B2(0.383 V) is similar to that of Li-intercalated tri-Mo2B2 (0.407 V).Interestingly, they are both smaller than that of MoS2 (0.75 V vs.Na/Na+).21 Since ideally a good anode material should have alow electrode potential,21 our calculated plateaus for tetr- andtri-Mo2B2 suggest that these two Mo2B2 monolayers show goodperformance as anode materials for LIBs and NIBs.

3.6 Diffusion barriers of Li/Na on tetr- and tri-Mo2B2monolayers

The fast charge/discharge capability is a key factor in evaluatingthe performance of an electrode material. Because the rate capabilityof LIBs and NIBs is closely linked with Li/Na diffusion properties,

Fig. 5 Enthalpies of formation for (a) LinMo2B2 and (b) NanMo2B2 systems with respect to 2D tetr-Mo2B2 and Li/Na bulk metal. Data points located on theconvex hull (solid squares) represent stable adsorption against any type of decomposition. The metastable phases are indicated by open squares. Theabscissa represents the percentage of Li/Na in Li/Nan(Mo2B2). Electrode potential of (c) Li-intercalated tetr-Mo2B2 against Li/Li

+ and (d) Na-intercalatedtetr-Mo2B2 against Na/Na

+.

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we need to investigate the diffusion paths and the correspondingenergy barriers for Li/Na on tetr- and tri-Mo2B2. Fig. 7 illustratesthree possible pathways (A–B, A–C, and A–D) between the neighbor-ing lowest-energy adsorption sites (S2 sites) and the correspondingdiffusion energy barriers for Li/Na diffusion on tetr-Mo2B2. The A–B(see Fig. 7a) and A–C (see Fig. 7b) pathways are both from one S2 siteto another S2 site by passing over a boron atom on the surface.The energy barriers for Li diffusion along A–B and A–C pathways are0.031 and 0.029 eV, respectively, while those for Na diffusion are

0.013 and 0.010 eV, respectively. We find that the energy barriers forLi/Na diffusion along the A–C pathway are a little smaller than thosealong the A–B pathway. However, the A–D pathway (see Fig. 7c)starting from one S2 site to another S2 site by passing over onesurface Mo atom possesses very high energy barrier for Li/Nadiffusion. The values are 0.350 and 0.159 eV for Li and Na diffusion,respectively, which are about ten times larger than those for A–B andA–C pathways. In general, the A–C pathway is the most suitable pathfor Li/Na diffusion on tetr-Mo2B2 owing to the lowest energy barriers

Fig. 6 Enthalpies of formation for (a) LinMo2B2 and (b) NanMo2B2 systems with respect to 2D tri-Mo2B2 and Li/Na bulk metal. Data points located onthe convex hull (solid squares) represent stable adsorption against any type of decomposition. The metastable phases are indicated by open squares.The abscissa represents the percentage of Li/Na in Li/Nan(Mo2B2). Electrode potential of (c) Li-intercalated tri-Mo2B2 against Li/Li

+ and (d) Na-intercalatedtri-Mo2B2 against Na/Na

+.

Fig. 7 (a–c) Top views of three pathways for Li/Na diffusion on the tetr-Mo2B2 monolayer. The Mo, B, and Li/Na atoms are denoted in violet, green, andblue, respectively. (d) Diffusion energy barriers of Li and Na on tetr-Mo2B2.

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for Li/Na. Thus, according to the characteristics of the A–Cpathway, the Li/Na atom can diffuse along a straight line inthe B–B direction.

We present in Fig. 8 the most favorable pathway andcorresponding energy barriers for Li/Na diffusion on thesurface of tri-Mo2B2. Since the most stable adsorption site forLi/Na is the S2 site, we consider one possible pathway startingfrom one S2 site to another S2 site. As shown in Fig. 8a,the optimized pathway is from A to B and can be viewed asS2–S3–S1–S3–S2. The energy barriers for Li and Na diffusion are0.023 and 0.013 eV, respectively. We find that the diffusionenergy barrier for Li on tri-Mo2B2 (0.023 eV) is smaller than thaton tetr-Mo2B2 (0.029 eV), while that for Na on tri-Mo2B2 (0.013 eV)is a litter larger than that on tetr-Mo2B2 (0.010 eV). In any case, theenergy barriers for Li/Na diffusion on tetr- and tri-Mo2B2 are allvery low, which would be beneficial to increase the charge/discharge rate of LIBs and NIBs.

3.7 Comparison with other anode materials

To have a more comprehensive view of the properties oftetr- and tri-Mo2B2 as electrode materials, we compare theirtheoretical specific capacities and diffusion barriers with thoseof other previously reported 2D anode materials.19–22,26,30,60–64

For Li storage, as shown in Table 1, the theoretical specificcapacities of tetr- and tri-Mo2B2 are both 251 mA h g

�1, whichare smaller than those of graphite,65–67 orth-Mo2B2,

30 silicene,19

1T-Ti3C2,62 Mo2C,

26 and VS2,22 but are larger than that of

Li4Ti5O12.68,69 Here, the reason for the small theoretical specific

capacities of tetr- and tri-Mo2B2 is that we do not consider theadsorption of the second layer of Li. The diffusion energybarriers of tetr- and tri-Mo2B2 are 0.029 and 0.023 eV,

respectively, which are much lower than those of most materialsin Table 1. This indicates that tetr- and tri-Mo2B2 monolayerspossess very high rate capability for Li diffusion.

For Na storage, as shown in Table 2, the theoretical specificcapacities of tetr- and tri-Mo2B2 are 251 and 188 mA h g

�1,respectively, which are larger than those of 1T-MoS2

21 andMo2C.

26 This indicates that 2D molybdenum borides havehigher Na storage capacity than 2D molybdenum sulphidesand molybdenum carbides. Although the theoretical specificcapacities of tetr- and tri-Mo2B2 are lower than those of 1T-Ti3C2,

20

B2H2,60 and Ca2N,

64 their Na conductivities are much faster thanthose of 1T-Ti3C2,

20 B2H2,60 and Ca2N.

64 It is noteworthy that thediffusion energy barriers of Na on tetr- (0.010 eV) and tri-Mo2B2(0.013 eV) are much lower than those on any other materials inTable 2, indicating a very high rate capability. The above evidencedemonstrates that both tetr- and tri-Mo2B2 are promising candi-dates for anode materials in LIBs and NIBs.

4. Conclusions

The search for high-performance anode materials is urgentlyneeded for the development of both LIBs and NIBs. In thisstudy, we firstly reported two new 2D Mo2B2 structures withlower energies than that of previously reported ori-Mo2B2 byusing crystal structure prediction techniques. Then, the geo-metric structures, phonon spectra, dynamical properties, andelectrical properties of our obtained tetr- and tri-Mo2B2 mono-layers have been studied. The results confirm that both tetr- and

Fig. 8 (a) Top views of three pathways for Li/Na diffusion on the tri-Mo2B2 monolayer. The Mo, B, and Li/Na atoms are denoted in violet,green, and blue, respectively. (b) Diffusion energy barriers of Li and Na ontri-Mo2B2.

Table 1 Summary of theoretical specific capacities (mA h g�1) anddiffusion barriers (meV) of some previously reported promising anodematerials for LIBs

Species Theoretical specific capacity Diffusion barrier Ref.

Tetr-Mo2B2 251 29 This workTri-Mo2B2 251 23 This workGraphite 372 450–1200 65–67Orth-Mo2B2 444 270 301T-Ti2C 34 61Silicene 954 230 191T-Ti3C2 320 70 62Mo2C 526 35 26VS2 466 220 22Li4Ti5O12 175 300 68 and 69

Table 2 Summary of theoretical specific capacities (mA h g�1) anddiffusion barriers (meV) of some previously reported promising anodematerials for NIBs

Species Theoretical specific capacity Diffusion barrier Ref.

Tetr-Mo2B2 251 10 This workTri-Mo2B2 188 13 This workGraphene 130 631T-MoS2 146 280 211T-Ti3C2 352 96 20Mo2C 132 15 26B2H2 504 90 60Ca2N 1138 80 64Sr2N 283 16 64

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tri-Mo2B2 possess excellent electronic conductivity and greatstability. Then, we investigated the adsorption and diffusion ofLi and Na over tetr- and tri-Mo2B2 and evaluated their suitabilityas anode materials for LIBs and NIBs. The adsorption energiesof Li/Na on tetr- and tri-Mo2B2 are �0.777/�0.837 and �0.542/�0.677 eV, respectively, which are negative enough to ensurestability and safety under operating conditions. Besides, thecalculated theoretical specific capacities of tetr-Mo2B2 as anelectrode are B251 mA h g�1 for LIBs and NIBs, while thetheoretical specific capacities of tri-Mo2B2 are B251 andB188 mA h g�1 for LIBs and NIBs, respectively. The capabilityof Na storage for our tetr- and tri-Mo2B2 is much larger thanthose of the well-known Mo2C (B132 mA h g

�1) and MoS2(B146 mA h g�1). The calculated low electrode potential oftetr- and tri-Mo2B2 suggests that these two monolayers showgood performance as anode materials for LIBs and NIBs. Inaddition, it is interesting that both tetr- and tri-Mo2B2 showvery high Li/Na diffusion rates. The diffusion energy barriers ofLi/Na over tetr- (0.029/0.010 eV) and tri-Mo2B2 (0.023/0.013 eV)are very small, which indicates that these two monolayerspossess excellent charge/discharge capability for Li/Na. Overall,both tetr- and tri-Mo2B2 monolayers are excellent candidatesas anode materials for LIBs and NIBs. Our work also opens upan avenue to explore new 2D transition metal borides withexcellent properties.

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

F. W. W. and J. R. Z. acknowledge financial support from theNational Natural Science Foundation of China under Grant No.11675255, No. 11634008, and No. 11675195. J. R. Z. acknowledgesfinancial support from The National Key Basic Research Programunder Grant No. 2017YFA0403700. T. B. acknowledges the ChinaPostdoctoral Science Foundation (Grant No. 2018M641477). P. F. L.acknowledges the Guangdong Provincial Department of Scienceand Technology, China (No. 2018A0303100013).

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2019

5:4

2:03

AM



Documents

Tetragonal and trigonal Mo2B2 monolayers: two new low … · 2020. 12. 31. · Tetragonal and trigonal Mo 2B 2 monolayers: two new low-dimensional materials for Li-ion and Na-ion