The absorption energies characterize metal ions absorption strength. The negative values of absorption energies indicate the metal ions absorption behaviors are exothermic and spontaneous. The following equation has been used to calculate the adsorption energies Ead:
![](data:image/png;base64,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)
Where x is the ratio of the number of N atoms to the number C atoms,
and
represent the total energy of Mo2C1 − xNx with and without Mg absorption.
is the energy of the isolated Mg atom, which has been determined to be -86.461 eV. To investigate the absorption energies of Mg on N-doped Mo2C, four supercells of Mo2C1 − xNx (x = 0.0625, 0.125, 0.1875 and 0.25) have been constructed to accomplish different doping concentrations 6.67%, 14.29%, 23.08% and 33.33%, respectively. Hence, we consider one nitrogen atom, two nitrogen atoms, three nitrogen atoms and four nitrogen atoms to replace the carbon atoms in 4×4×1 supercell.
The four typical adsorption sites on pristine Mo2C have been considered: hollow (H), top (TC and TMo) and bridge (B) sites as shown in Fig. 1(a). Meanwhile, the adsorption energies of Mg adsorption on H1, H2, H3, H4, TC1, TC2, TMo1, TMo2 and B1 sites for four N-doped Mo2C structures have been calculated. The adsorption energies of Mg calculated on the same sites for N-doped Mo2C, the Mg adsorption on MoC0.875N0.125 represents the conformations of N-doped Mo2C as shown in Fig. 1(b), and the results are summarized in Table 1.
Table 1
Adsorption energies (eV) of Mg on N-doped Mo2C and Mo2C.
|
Mo2C0.9375N0.0625
|
Mo2C0.875N0.125
|
Mo2C0.8125N0.1875
|
Mo2C0.75N0.25
|
Mo2C
|
H1
|
-1.420
|
-1.567
|
-1.426
|
-1.437
|
-1.395
|
H2
|
-1.423
|
-1.625
|
-1.424
|
-1.546
|
H3
|
-1.438
|
-1.550
|
-1.422
|
-1.430
|
H4
|
-1.413
|
-1.567
|
-1.409
|
-1.436
|
TC1
|
-1.446
|
-1.580
|
-1.483
|
-1.514
|
-1.384
|
TC2
|
——
|
-1.639
|
-1.492
|
-1.505
|
TMo1
|
-1.431
|
-1.517
|
-1.374
|
-1.376
|
-1.363
|
TMo2
|
-1.437
|
-1.595
|
-1.459
|
-1.514
|
B1
|
-1.430
|
-1.552
|
-1.423
|
-1.427
|
-1.361
|
As shown in Table 1, the negative values of absorption energies indicate the Mg adsorption behaviors are spontaneous. The absorption energies of Mg on H, TC, TMo, B sites for pristine Mo2C are − 1.395 eV, -1.384 eV, -1.363 eV and − 1.361 eV, respectively. The absorption energies of Mg on the four considered N-doped Mo2C all have decreased, which suggest that N-doped Mo2C is benefit for Mg adsorption. Especially, the adsorption energies of Mg for Mo2C0.125N0.875 are about in the region between − 1.64 and − 1.55 eV, much lower than that of pristine Mo2C. For example, the adsorption energies of Mg on TC1 and H2 sites for Mo2C0.875N0.125 is -1.639 eV and − 1.625 eV, which has decreased by 16.49% and 18.43%. The adsorption energies of Mg for N-doped Mo2C show that the enhancement of Mg adsorption behaviors is attributed to nitrogen doping.
It is well-known that the diffusion barrier is an important feature to evaluate diffusion mobility of mental ions. In order to obtain the effect of nitrogen doping on Mg diffusion behaviors, the diffusion barriers of Mg on pristine Mo2C and Mo2C0.125N0.875 have been calculated. For pristine Mo2C, the energy barrier of Mg diffusion along H-B-H pathway is about 0.039 eV. For comparison, three diffusion pathways (H4-B-H3, H-B-H3, H-B-H) for Mo2C0.125N0.875 have been considered. The diffusion pathways are named path1, path2 and path3, respectively, with the corresponding diffusion energy barriers as shown in Fig. 2. It can be seen that the diffusion barriers are only 0.042 eV, 0.021 eV and 0.028 eV along three pathways, respectively, which indicate that the Mg diffusion behaviors can easily occur on Mo2C0.125N0.875. The diffusion barrier of Mg along path1 is slightly higher than that of pristine Mo2C, however, the diffusion barriers of Mg along the path2 and path3 is much lower than that on pristine Mo2C. The results show that nitrogen doping is a positive approach to decrease the diffusion barriers, which is beneficial to the diffusion of Mg on Mo2C0.125N0.875. The MoC0.875N0.125 shows lower adsorption energies and diffusion barriers of Mg, which indicate MoC0.875N0.125 is a potential anode material for MIBs.
To comprehensively understand the interaction between Mg and MoC0.875N0.125, the partial density of states (PDOS) has been calculated. The PDOS reveal the hybridization interaction of Mg and the neighboring C and Mo atoms. The present calculations indicate that the major electron contribution is mainly attributed to the s state of Mg, the p state of C and the d state of Mo, so, the PDOS of Mg-3s, C-2p and Mo-4d states are plotted in Fig. 3. As shown in Fig. 3, the Mg-3s(no), C-2p(no) and Mo-4d(no) states represent the PDOS for Mg adsorption on the pristine Mo2C. The Fermi level has been depicted by vertical dashed line in Fig. 3. Obviously, it can be seen that the Fermi level locates at the peak of Mg-3s orbits, which suggest that the Mg adsorption on pristine Mo2C and MoC0.875N0.125 is stable [37]. Additionally, the major electron contribution of Mo2C and MoC0.875N0.125 is Mo-4d orbits, which is similar to Li, Na and K adsorption on Mo2C [15, 17]. Furthermore, it is noticed that the C-2p, Mg-3s and Mo-4d states are across the Fermi level, which suggest that the metallic nature has been maintained for MoC0.875N0.125 [38, 39]. The metallicity of MoC0.875N0.125 indicate its good electronic conductivity, which is benefit for Mg diffusion [40]. Interestingly, it is found that nitrogen doping causes the peak of electron orbits transfer to lower energies. This indicate that the bonding between Mg and MoC0.875N0.125 is more stable [41]. It can be concluded that when pristine Mo2C is doped by nitrogen, the strong interaction between Mg and MoC0.875N0.125 is beneficial to the adsorption and diffusion of Mg.