Open Access Article

This Open Access Article is licensed under a Creative Commons Attribution-Non Commercial 3.0 Unported Licence

DOI: 10.1039/C9NA00610A
(Paper)
Nanoscale Adv., 2020, Advance Article

Xian-Hu Zha*^{a},
Pengxiang Xu^{a},
Qing Huang^{b},
Shiyu Du*^{b} and
Rui-Qin Zhang^{c}
^{a}Center for Quantum Computing, Peng Cheng Laboratory, Shenzhen, 518055, China. E-mail: zhaxh@pcl.ac.cn
^{b}Engineering Laboratory of Advanced Energy Materials, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo, Zhejiang 315201, China. E-mail: dushiyu@nimte.ac.cn
^{c}Department of Physics, City University of Hong Kong, Hong Kong SAR, China

Received
29th September 2019
, Accepted 12th November 2019

First published on 12th November 2019

Owing to their high specific area, good flexibility and many other unique properties, two-dimensional (2D) materials have attracted extensive attention in the recent two decades. As an analogy to the well-studied MXenes, MBenes also emerged. In this work, Mo_{2}B, an MBene member, is predicted both in H- and T-type configurations from first-principles calculations. Structural, mechanical, electronic, and thermal properties, and performances in lithium ion batteries (LIBs) for both configurations are investigated. The H-type Mo_{2}B is found to be the stable structure, which can be transformed into the T-type by applying strains. The elastic constants c_{11} in the H- and T-type Mo_{2}B are respectively calculated to be 187.5 and 157.6 N m^{−1}, which are higher than that in the previously reported Mo_{2}C. The electronic thermal conductivity and electrical conductivity are investigated based on the semiclassical Boltzmann transport theory. The electrical conductivities for both structures are of the order of 10^{6} Ω^{−1} m^{−1}. Because of the large phonon contributions, the thermal conductivities in the H- and T-type Mo_{2}B are much higher than that of the synthesized Mo_{2}C. Based on a 5 μm flake length, the phonon thermal conductivities at room temperature are calculated to be 146 and 141 W m^{−1} K^{−1} respectively for the H- and T-type configurations. The T-type Mo_{2}B shows promising performances in LIBs. The theoretical volumetric capacity is as high as 2424 mA h cm^{−3}, and the migration energy barrier is as low as 0.0372 eV. These data imply that Mo_{2}B has widespread applications, such as in conductive films and anode materials.

MBene, by replacing the X element of MXene with the neighboring B, naturally aroused increasing attention in the recent three years.^{29–33} Moreover, most boron-containing compounds are high-temperature refractory materials.^{34,35} With respect to the formula M_{n+1}X_{n}T_{x} for MXenes, MBenes have more adjustable space. For instance, M_{2}B_{2}T_{x} with two boron atomic layers intercalated in the transition metals are reported based on existing bulk precursors MAB, such as MoAlB.^{32} Theoretically, Guo et al. found that Mo_{2}B_{2} and Fe_{2}B_{2} show good electrical conductivities, small migration energy barriers, and high storage capacities for lithium ion batteries (LIBs). Moreover, Fe_{2}B_{2} was determined to be a potential catalyst for hydrogen evolution.^{31} Furthermore, Bo et al. reported a new type of M_{2}B_{2} MBenes with two boron atoms forming a planar honeycomb sandwiched by two M atomic planes. Six M_{2}B_{2} (M = Sc, Ti, V, Cr, Y, Zr, Mo) members were determined to be the global minimum structures. Ti_{2}B_{2} was determined to be a candidate anode material for LIBs and SIBs.^{29} Using a high-throughput structural search, Jiang et al. determined twelve metastable MBenes, MnB, HfB, ZrB, Au_{2}B, Mo_{2}B, Nb_{5}B_{2}, Nb_{3}B_{4}, Ta_{3}B_{4}, V_{3}B_{4}, OsB_{2}, FeB_{2}, and RuB_{2}, and they found that bare or functionalized MnB compounds are ferromagnets with high Curie temperatures.^{30} Although H-type Mo_{2}B has been predicted,^{30} this structure was not discussed in detail. In their experiment, Alameda et al. used MoAlB as the precursor to synthesize MBene, but they obtained MoAlB slabs of nanoscale thickness in their first attempt.^{32} Furthermore, they performed etching of MoAlB in two steps, and they identified isolated MoB layers inside the etched cavities.^{33} Based on the discussions above, MBenes have potential applications, which have been shown to be feasible in experiments. Thus, an in-depth investigation on MBene is justified.

Previously, Xu et al. synthesized the bare Mo_{2}C configuration by chemical vapor deposition (CVD), which was proven to show superconductivity^{36} and oscillatory magnetoresistance.^{37} Theoretically, the synthesized Mo_{2}C was also found to show high storage capacities and low migration energy barriers for Li, Na and K ions. Specifically, the storage capacity was determined to be 263 mA h g^{−1}, and the migration barrier is calculated to be as low as 0.043 eV for Li ion.^{38} In addition, Mo_{2}C is determined to be robust under varying temperatures and strains since it possesses relatively low thermal expansion coefficient and high mechanical strength.^{39} In analogy to Mo_{2}C, Mo_{2}B, both in the H- and T-type configurations, is predicted in this work. The structural, mechanical and thermal properties, and the performances in LIBs are studied. Compared with Mo_{2}C, both the H- and T-type Mo_{2}B are found to show comparable electrical conductivities, and much higher thermal conductivities. In addition to a relatively low migration energy barrier and a high storage capacity, the T-type Mo_{2}B is a potential candidate anode material for LIBs.

Regarding the thermal properties, the specific heat, thermal expansion coefficient, and phonon thermal conductivity are calculated. The phonon dispersions are calculated based on density functional perturbation theory (DFPT),^{47} which is implemented by a combination of the VASP and Phonopy^{48} softwares. For calculating the dynamical matrix, a 4 × 4 × 1 supercell with a 6 × 6 × 1 Γ-centered k-point mesh is employed. The phonon dispersions are plotted using a 120 k-point grid for various directions and the entire BZ. The specific heat and thermal expansion coefficient are calculated based on the Grüneisen approximation.^{39,49–51} The phonon thermal conductivity is calculated according to the Klemens theory.^{39,52–55} The details are presented in eqn (S1)–(S3) in the ESI.†

Regarding the Mo_{2}B performance in LIBs, 4 × 4 × 1 supercells for both H- and T-type Mo_{2}B are optimized. Diffusion energy barriers for Li atom on the supercells are calculated according to the climbing-image nudge elastic-band (CI-NEB) method.^{56} The binding energies of Li atoms on the 4 × 4 × 1 supercells are calculated according to the following equation:

E_{binding} = (E_{Mo2B} + xE_{Li} − E_{Mo2BLix})/x
| (1) |

(2) |

Mo_{2}B |
a | h | d | Mo–B | Mo–Mo | c_{11} |
c_{12} |
Y_{2D} |
---|---|---|---|---|---|---|---|---|

H-Type | 2.864 | 33.04 | 5.443 | 2.176 | 2.830 | 187.5 | 124.1 | 105.4 |

T-Type | 3.102 | 28.16 | 4.713 | 2.115 | 2.876 | 157.6 | 28.95 | 152.3 |

Regarding the transport properties of the H- and T-type Mo_{2}B, the electrical conductivities and the electronic thermal conductivities are further investigated based on constant relaxation time approximation. It is found that these transport coefficients are isotropic in the basal plane regardless of temperatures and chemical potentials. Therefore, σ_{xx}/τ and κ_{xx}/τ for both configurations are adopted to present the transport properties, as provided in Fig. 2. Here σ_{xx} and κ_{xx} respectively denote the electrical conductivity and electronic thermal conductivity along the x-axis direction, τ represents the electron relaxation time. According to this figure, temperature has a relatively weak influence on the electrical conductivity. In contrast, the electronic thermal conductivity is proportional to the increasing temperatures, and the shape of the relationship between the values of the electrical conductivity and electronic thermal conductivity meets the Wiedemann–Franz law.^{60} For the H-type Mo_{2}B, σ_{xx}/τ is determined to be 12.78 × 10^{20} Ω^{−1} m^{−1} s^{−1} at room temperature at μ = 0.0 eV, where the transport coefficient slightly decreases with increasing chemical potential. This behavior could be explained by the similar trend of PDOS with increasing energy presented in Fig. 1(h), since the electrical conductivity is approximately proportional to the PDOS. In the chemical potential range presented, the largest σ_{xx}/τ at room temperature is calculated to be 14.30 × 10^{20} Ω^{−1} m^{−1} s^{−1} at μ = −0.473 eV. From Fig. 2(b), κ_{xx}/τ of zero chemical potential is calculated to be 93.35 × 10^{14} W^{−1} m^{−1} K^{−1} s^{−1} at room temperature, which is increased to 155.7 × 10^{14} W^{−1} m^{−1} K^{−1} s^{−1} at 500 K. For the T-type configuration, σ_{xx}/τ and κ_{xx}/τ generally show minimum values at the zero chemical potential, which imply that one can enhance these transport coefficients by employing both n- and p-doping. At room temperature, σ_{xx}/τ and κ_{xx}/τ are respectively determined to be 4.121 × 10^{20} Ω^{−1} m^{−1} s^{−1} and 30.87 × 10^{14} W^{−1} m^{−1} K^{−1} s^{−1} when μ = 0.0 eV. To be more intuitive, the electrical conductivity and electronic thermal conductivity calculated are compared with those of Mo_{2}C, based on the same electron relaxation time (τ = 5.52 × 10^{−15}s) determined in experiments for Mo_{2}C.^{36} At zero chemical potential and at room temperature, the electrical conductivity and electronic thermal conductivity of Mo_{2}C have been previously calculated to be 3.590 × 10^{6} Ω^{−1} m^{−1} and 26.4 W^{−1} m^{−1} K^{−1} s^{−1}.^{39} Under the same conditions, the electrical conductivity and electronic thermal conductivity of the H-type Mo_{2}B are determined to be 7.546 × 10^{6} Ω^{−1} m^{−1} and 51.53 W^{−1} m^{−1} K^{−1}, respectively. Regarding the T-type Mo_{2}B, the corresponding values are determined to be 2.275 × 10^{6} Ω^{−1} m^{−1} and 17.07 W^{−1} m^{−1} K^{−1}. Moreover, the electron relaxation time ranging from 1.00 × 10^{−15} s to 1.00 × 10^{−14} s is also considered for Mo_{2}B. Based on τ = 1.00 × 10^{−15}s, σ_{xx} and κ_{xx} in the H-type Mo_{2}B at room temperature are calculated to be 1.278 × 10^{6} Ω^{−1} m^{−1} and 9.335 W^{−1} m^{−1} K^{−1} at zero chemical potential. With τ = 1.00 × 10^{−14}s, the corresponding σ_{xx} and κ_{xx} are an order of magnitude larger. Obviously, both H-type and T-type Mo_{2}B are promising electrical conductors.

Fig. 2 (a) and (b) Transport coefficients σ_{xx}/τ and κ_{xx}/τ, respectively, for the H-type Mo_{2}B. (c) and (d) Corresponding transport coefficients σ_{xx}/τ and κ_{xx}/τ for the T-type Mo_{2}B. |

Since the thermal conductivity comprises electron and phonon contributions, the phonon thermal conductivity is further investigated. The phonon dispersions for both the H- and T-type Mo_{2}B are provided in Fig. S1 in the ESI,† where ZA, TA and LA respectively denote the out-of-plane, transversal and longitudinal acoustic modes. The phonon dispersions are predicted without an imaginary frequency, which implies that both structures are dynamically stable. According to the method described in the Methods section,^{39,54,55} the phonon thermal conductivities along the ΓM and ΓK directions are calculated, where the high-symmetry directions ΓM and ΓK in BZs respectively correspond to the armchair and zigzag directions in the real spaces of both H- and T-type Mo_{2}B, as shown in Fig. S2 in the ESI.† The calculated values with increasing temperatures based on various flake lengths are provided in Fig. 3. Since the size of the synthesized Mo_{2}C is approximately 100 μm,^{36} the flake lengths of Mo_{2}B ranging from 1 to 100 μm are studied here. Apparently, the phonon thermal conductivity increases with a larger flake length when the flake length is smaller than 100 μm, and decreases with increasing temperature in the range from 100 to 500 K. Fig. 3(a) shows the phonon thermal conductivity along the armchair direction in the H-type Mo_{2}B. Based on the different flake lengths of 1, 2, 5, 50 and 100 μm, the phonon thermal conductivities are respectively determined to be 108.7, 125.0, 146.4, 200.2 and 216.4 W m^{−1} K^{−1} at room temperature. Regarding the increasing temperatures, the values based on the 5 μm flake length are calculated to be 362.1, 205.4, 146.4, 114.8 and 95.00 W m^{−1} K^{−1}, respectively at 100, 200, 300, 400 and 500 K. Fig. 3(b) shows the corresponding phonon thermal conductivity along the zigzag direction. Obviously, the phonon thermal conductivity is anisotropic, with much lower values in the zigzag direction. At room temperature, the phonon thermal conductivity with the flake length of 5 μm is determined to be 72.78 W m^{−1} K^{−1}. Fig. 3(c) and (d) respectively present the phonon thermal conductivities along the armchair and zigzag directions in the T-type configuration, whose values are generally similar to those in the H-type Mo_{2}B. Based on the 5 μm flake length, the phonon thermal conductivities along the armchair and zigzag directions at room temperature are 141.3 and 67.14 W m^{−1} K^{−1}. In a word, both the H- and T-type Mo_{2}B possess high phonon thermal conductivities, especially along their armchair direction. These calculated values are much higher than those of many well-known metals,^{61} and those in the reported Mo_{2}C.^{39}

In order to understand the high phonon thermal conductivities, each acoustic mode contribution is calculated and provided in Fig. S3 in the ESI.† According to this figure, each acoustic mode presents evident contribution to its phonon thermal conductivity in the H-type Mo_{2}B, although the ZA mode contribution is relatively smaller in the armchair direction. Regarding the T-type configuration, the phonon thermal conductivity is mainly dominated by the LA mode. The ZA mode presents little contribution in both directions. This behaviour could be explained from their phonon dispersions, where the frequency magnitude of the ZA mode is much smaller in the T-type configuration. Based on the low phonon frequency, the phonon velocity is smaller, which induces the small phonon thermal conductivity contribution. Compared with the reported Mo_{2}C, the larger phonon thermal conductivity of Mo_{2}B is mainly caused by its larger phonon group velocities and lower Grüneisen parameters(GPs). Since the T-type Mo_{2}B and Mo_{2}C possess the same space group, and their phonon thermal conductivities are both mainly dominated by the LA modes, the phonon thermal conductivities in the armchair directions of these two configurations are compared. In Mo_{2}B, the phonon group velocity and the square of the GP of the LA mode are respectively determined to be 2.967 × 10^{3} m s^{−1} and 1.454, while the corresponding values in Mo_{2}C are determined to be 2.167 × 10^{3} m s^{−1} and 53.88, respectively. According to eqn (S2) in the ESI,† the thermal conductivity of Mo_{2}B is naturally much higher than that in Mo_{2}C.

Combined with the electron and phonon contributions, both the H- and T-type Mo_{2}B could have outstanding thermal conductivities in a wide temperature range, since the electron part increases and the phonon part decreases with increasing temperature. Based on the 5 μm flake length and the constant electron relaxation time τ = 5.52 × 10^{−15} s, the thermal conductivities in the armchair direction in the H-type Mo_{2}B are determined to be 379.3, 239.8, 197.9, 183.5 and 180.9 W m^{−1} K^{−1}, respectively at 100, 200, 300, 400 and 500 K. Correspondingly, the values in the armchair direction of the T-type Mo_{2}B are 347.4, 208.0, 158.3, 134.6 and 122.3 W m^{−1} K^{−1}. These high thermal conductivities enable both the H- and T-type Mo_{2}B applications in thermal conductive materials. In addition, the specific heat and thermal expansion coefficients (TECs) of these two configurations are studied, and corresponding results are provided in Fig. 4. From Fig. 4(a), the specific heats of the H- and T-type Mo_{2}B are generally equivalent in the entire range of temperature investigated. The room temperature values are calculated to be 289.4 and 281.8 J kg^{−1} K^{−1}, respectively. Regarding the thermal expansion behaviors as shown in Fig. 4(b), the TEC of the H-type Mo_{2}B increases with increasing temperature. The value at room temperature is calculated to be 4.780 × 10^{−6} K^{−1}, which increases to 5.498 × 10^{−6} K^{−1} at 1000 K. For the T-type configuration, its TEC is much smaller than that in the H-type, and the corresponding value at room temperature is determined to be 2.148 × 10^{−6} K^{−1}. Interestingly, the TEC of the T-type configuration is negative under 50 K, and the negative TEC with the largest absolute value is determined to be −1.153 × 10^{−6} K^{−1} at 14 K. In order to understand the different thermal expansion behaviors between the H- and T-type Mo_{2}B, the GPs of the acoustic modes in the BZs of both configurations are calculated and provided in Fig. 4(c) and (d). From these figures, the GPs of the TA and LA are positive in the entire BZs for both H- and T-type configurations, which imply that both the TA and LA modes contribute to thermal expansion.^{50,51,62} The GP of the ZA mode in the H-type Mo_{2}B is generally positive, although it shows small negative values around the high symmetry K point. Consequently, the TEC of the H-type Mo_{2}B increases with increasing temperature. In the T-type configuration, the ZA mode shows large negative GPs, especially around its BZ center. The large negative value implies that the amplitude of ZA mode is significant, which contributes to the thermal contraction. As a result, this structure shows negative TEC in the low temperature range. For in-depth understanding, the different behaviors of the ZA modes in the H- and T-type Mo_{2}B are ascribed to the different layer thickness and mechanical strength of these two configurations.^{51} The configuration with a thinner layer thickness and weaker mechanical strength could be more flexible, and the amplitude of the ZA mode is more significant. In addition, the GP values in Fig. 4(c) and (d) could also explain the magnitude of the phonon thermal conductivity. For instance, the ZA mode in the T-type Mo_{2}B makes little contribution to its thermal conductivity, ascribed to the large absolute value of GP, since the phonon thermal conductivity is inversely proportional to the square of GPs.^{54,55,63} Based on the different thermal expansion behaviors of the H- and T-type Mo_{2}B, it is possible to obtain a zero TEC intuitively by combining these two phases, since two competitive phases can be obtained concurrently by applying strains or other techniques.^{64} This could be an interesting topic for future work.

Based on the high mechanical strength, promising electrical and thermal conductivities, and low TECs calculated above, both the H- and T-type Mo_{2}B could have widespread applications. In the following, the performances in LIBs of both configurations are further investigated. The key parameters, i.e., theoretical storage capacity and migration energy barrier are studied. Based on 4 × 4 supercells, the stable adsorption sites for the Li ion on both H- and T-type Mo_{2}B are investigated firstly. According to Fig. S4 and S5,† three possible locations for each configuration are considered, and corresponding relative total energies are provided in Table S2 in the ESI.† From the table, the Li atom is stabilized on the top-site of the hexagonal centre of the H-type Mo_{2}B, as shown in Fig. S4(c) and (f).† The distance between the Li atom and the MXene surface is calculated to be 2.416 Å. The corresponding total energy is 0.0263 eV lower than that of the structure with Li on the top-site of Mo atom. In the T-type Mo_{2}B, the Li atom is found to stabilize on the top-site of the bottom Mo atom, and its location is 2.311 Å higher than that of the MXene surface. The top- and side-views for the stable location are presented in Fig. S5(c) and (f),† respectively. The corresponding total energy is 0.0125 eV lower than that of the configuration with Li on the top-site of the middle B atom.

Since the migration energy barrier is a key parameter in determining the rates of charging and discharging, it is studied after the stable location of Li is determined. The migration barrier profiles for Li on the H- and T-type Mo_{2}B are respectively shown in Fig. 5(a) and (b), respectively. For each configuration, three possible migration pathways are studied. In the H-type Mo_{2}B, PATH I denotes the diffusion of the Li atom directly from the top-site of the hexagonal centre to the neighbouring top-site of the hexagonal centre. PATH II represents the diffusion of the Li atom from the top-site of the hexagonal centre to the top-site of neighbouring boron, and then moves to the neighbouring top-site of the neighbouring hexagonal centre. PATH III shows the diffusion path from the top-site of the hexagonal centre to the top-site of neighbouring molybdenum, and then moves to the top-site of the neighbouring hexagonal centre. The energy barriers for PATH I, PATH II and PATH III are determined to be 0.130, 0.050 and 0.188 eV, respectively. To give a clear view, only the two lower energy barriers are provided in Fig. 5(a). Based on the different stable locations for Li atom on the T-type configuration, PATH I shows the diffusion route directly from the top-site of the bottom Mo atom to the top-site of a neighbouring bottom Mo atom. PATH II shows that the Li diffuses from the top-site of the bottom Mo atom to the top-site of the middle boron atom, and then moves to the stable top-site of the neighbouring bottom Mo atom. PATH III is the route from the top-site of the bottom molybdenum to the neighbouring top-site of top molybdenum, and then diffuses to the top-site of bottom molybdenum. The corresponding energy barriers for PATH I, PATH II and PATH III are calculated to be 0.110, 0.037 and 0.152 eV, respectively. The energy barriers for PATH I and II are given in Fig. 5(b). Evidently, the diffusion energy barrier of PATH II is generally lower than those for PATH I and PATH III in both H- and T-type Mo_{2}B. The energy barriers of PATH II in both configurations are comparable to that in Mo_{2}C (0.043 eV).^{38} Moreover, these values are much smaller than that (0.35–0.65 eV) in the commercially used anode material TiO_{2}.^{65} Based on the relatively low diffusion energy barriers, both the H- and T-type Mo_{2}B could show rapid charge and discharge rate when applied as anode materials for LIBs.^{38}

Fig. 5 Diffusion barrier profiles for Li on (a) the H-type Mo_{2}B and (b) the T-type Mo_{2}B. The insets show the two migration pathways with low energy barriers on each configuration. |

After the diffusion energy barrier is calculated, the binding energy and open-circuit-voltage for LIBs are further studied. Based on the 4 × 4 × 1 supercells, increasing number of Li atoms from one to sixty-four are studied. From the previous discussion, the Li atom could prefer the top-site of the hexagonal centre in the H-type Mo_{2}B until its number reaches thirty-two, with both sides of Mo_{2}B adsorbing one atomic layer of Li atoms. If more Li atoms are adsorbed, an additional Li atomic layer will be formed based on the 4 × 4 × 1 supercells, and thus the stable location for the additional atomic layer must be investigated. As shown in Fig. S6,† three possible locations for the thirty-three Li atoms on the H-type Mo_{2}B are studied, and their relative total energies are provided in Table S3.† From the table, the second Li atomic layer is stabilized on the top-site of the Mo atomic layer. The top- and side-views for the stable location are provided in Fig. S6(a) and (d),† respectively. With a similar procedure, the second Li atomic layer is found to locate on the top-site of the neighbouring Mo atomic layer in the T-type Mo_{2}B, and the corresponding structures are provided in Fig. S7(a) and (d).† After all the structures with increasing Li atoms are optimized, the binding energies and open-circuit voltages for the adsorbed Li atoms are calculated according to eqn (1) and (2) in the Methods section. To facilitate elaboration, Mo_{2}BLi_{x} is adopted to denote the Li-adsorbed Mo_{2}B. Since sixty-four Li atoms are studied based on the 4 × 4 × 1 supercells, the x value ranges from zero to four. The corresponding binding energies and voltage profiles for Li atoms on both H- and T-type Mo_{2}B are provided in Fig. 6. From Fig. 6(a), the binding energies of Li on both H- and T-type Mo_{2}B are positive in the entire range of concentration x investigated, which imply that both configurations could adsorb at least four Li atomic layers on their surfaces. The binding energy for Li on the T-type Mo_{2}B is generally large than that on the H-type Mo_{2}B, which could be ascribed to the larger specific area of the T-type configuration. The three large binding energies around the Li concentration x = 2.0 on the H-type Mo_{2}B are due to structural distortion. It is noteworthy that, although the binding energies calculated are positive, it is better to estimate the theoretical storage capacity by inspecting the open voltage.^{38,66} Fig. 6(b) presents the corresponding voltage profiles. Obviously, the voltage varies significantly with the increasing concentration of Li atoms. Moreover, the first negative value appears at x = 0.625 (the number of Li atoms is 10) on the H-type Mo_{2}B, and x = 2.062 (the number of Li atoms is 33) on the T-type configuration. Based on the binding energies and open voltages calculated, the theoretical storage capacities for the H- and T-type Mo_{2}B are calculated to be 74.18 and 264.0 mA h g^{−1}, respectively (corresponding x values are 0.562 and 2.00, respectively). Based on the volumes of the bare H- and T-type Mo_{2}B, corresponding volumetric capacities are respectively calculated to be 647.8 and 2424 mA h cm^{−3}. Obviously, the volumetric capacity in the T-type configuration is much higher than those in commercial carbon-based electrodes.^{67} Therefore, Mo_{2}B could be a candidate anode material, especially for applications where size matters. Regarding the volume changes of the lithium adopted configurations, the volumes of the H-type Mo_{2}BLi_{0.562} and T-type Mo_{2}BLi_{2} are respectively 1.408 and 1.845 times of those for the bare H- and T-type Mo_{2}B. The averaged voltage in the range of 0 ≤ x ≤ 0.562 is calculated to be 0.386 V in the H-type Mo_{2}B. Similarly, in the T-type configuration, the averaged voltage averaged over 0 ≤ x ≤ 2.00 is calculated to be 0.628 V. As reported previously, the potential voltage range for an anode material is from 0.1 to 1.0 V.^{38} Both the average voltages for the H- and T-type Mo_{2}B fall in this potential range, which imply that both configurations are favourable anode materials.

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## Footnote |

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9na00610a |

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