P and Si functionalized MXenes for metal-ion battery applications

Li-ion batteries nowadays are widely used in portable electronic devices such as cell phones and laptops due to high energy densities, absence of memory effects, and long cycle lifes [1]. Na and K-ion batteries have been considered as promising alternatives in large scale applications such as power grids, since Na and K have similar properties to Li combined with the advantage of natural abundance [2, 3]. The Li, Na, and K capacities of graphite (commercial electrode material), however, are only 372 mAh g⁻¹ [1], 284 mAh g⁻¹ [4], and 273 mAh g⁻¹ [5], respectively. Bulk P and Si electrodes have theoretical Na and Li capacities of 2596 mAh g⁻¹ [6] and 4198 mAh g⁻¹ [7], respectively, due to the formation of Na₃P and Li₂₂Si₅. Regrettably, the huge volume changes of 420% and 491%, respectively, lead to rapid capacity loss and safety issues during charging and discharging. Dimension reduction from bulk to two or one-dimensional electrode materials has been able to partially overcome these issues, since the void space in the low-dimensional structures can accommodate strain and volume changes [8–10].

MXenes are two-dimensional early transition metal carbides, nitrides, and carbonitrides, such as Ti₂C, V₂C, Ti₃C₂, Ti₃CN, and Ta₄C₃ [11, 12]. They can be synthesized by selective etching of the A element from MAX phases (M: early transition metal, A: group 13–16 element, X: C and/or N) [13]. MXenes are considered to have great application potential in electronic devices [14, 15], catalysis [16], and energy storage [17]. Like other two-dimensional materials [18, 19], they also have been proposed for Li-ion batteries due to Li capacities comparable to commercial graphite electrodes and stable cycling performance [20]. Furthermore, the application in Na and K-ion batteries has been explored [21]. The Li capacity of MXenes currently is limited by 410 mAh g⁻¹ [20], which is much lower than that of P [6] and Si [7]. While the Li capacity of V₂C has been predicted to be 940 mAh g⁻¹ (based on a multilayer model) [22], the experimental value is only 260 mAh g⁻¹ [23]. The Na and K capacities are usually lower than the Li capacity due to larger ionic radii [24].

MXenes are usually functionalized by F and OH ligands as a consequence of the presence of HF and H₂O during the preparation [25]. These ligands come along with lower Li content in the products (LiF and LiOH) than P and Si (Li₃P and Li₂₂Si₅) and thus lead to lower Li capacities. Therefore, we investigate in the present work the feasibility of replacing the F and OH ligands with P and Si, using first-principles calculations. Aiming for metal-ion battery applications, it is promising to improve the capacities by this approach, since the crystal structure of MXenes can accommodate large volume changes. The Sc₂C, Ti₂C, and V₂C MXenes are selected due to their small atomic masses and the fact that they provide different numbers of valence electrons.

We perform adsorption calculations based on density functional theory and the projector augmented wave method, as implemented in the Vienna ab initio simulation package [26]. The generalized gradient approximation of Perdew, Burke and Ernzerhof is selected for the exchange-correlation potential together with the DFT-D3 approach [27] to take into account the long-range van der Waals interaction. A vacuum layer of 15 ${\mathring{\rm A}}$ thickness is added on top of $2\times 2$ in-plane supercells of the MXenes in order to avoid artificial interaction between periodic images. For the Brillouin zone integrations we use a $6\times 6\times 1$ k-mesh. The cutoff energy of the plane wave basis is set to 500 eV and the energy criterion of the iterative solution of the Kohn–Sham equations to 10⁻⁶ eV. All structures are relaxed until the residual forces on the atoms have declined to less than 0.01 eV ${{{\mathring{\rm A}}}^{-1}}$. We find spin degeneracy in each case. The diffusion paths and energy barriers are determined by the nudged elastic band method [28] with 9 images between the initial and final states.

The formation energies of the F and OH ligands, defined as (M  =  Sc, Ti, V and X  =  F, OH, P, Si)

$$\begin{eqnarray} &&\Delta H=E\left[{{\text{M}}_{2}}\text{C}{{\text{X}}_{2}}\right]-E\left[{{\text{M}}_{2}}\text{C}\right]-2E\left[\text{X}\right],\end{eqnarray} \tag{ 1 }$$

with E being the total energy, are calculated to be more negative than  −4 eV, see table 1, and therefore reflect chemical stability. E[X] is half of the total energy of F₂ for F, half of the sum of the total energies of O₂ and H₂ for OH, and the total energy per atom of the respective bulk compound for P and Si. The conversion reaction

$$\begin{eqnarray}&&{{\text{M}}_{2}}\text{C}{{\text{F}}_{2}}+2\text{Li}\to {{\text{M}}_{2}}\text{C}+2\text{LiF}\end{eqnarray} \tag{ 2 }$$

for F turns out to be neutral for Sc₂C and exothermic for Ti₂C and V₂C. It thus is feasible to remove the ligand from the MXenes. The conversion reaction

$$\begin{eqnarray}&&{{\text{M}}_{2}}\text{C}{{\left(\text{OH}\right)}_{2}}+2\text{Li}\to {{\text{M}}_{2}}\text{C}+2\text{LiOH}\end{eqnarray} \tag{ 3 }$$

for OH is endothermic and exothermic for Sc₂C and V₂C, respectively. The reaction enthalpy for Ti₂C turns out to be 0.128 eV, which is slightly endothermic but less than for Zr₂CO₂/Zr₂CS₂ interconversion (0.611 eV at 298 K) [29]. Although the reaction enthalpies are calculated at 0 K, these findings are qualitatively valid also at high temperature, because the entropy and temperature corrections are estimated to be only 0.026 eV at room temperature when gas phases are involved [25]. The low reaction enthalpy can be overcome by sonication, which is a standard method in the preparation of MXenes.

Turning to the feasibility of P and Si functionalization of Ti₂C and V₂C, we consider locations on top of the C atom and on top of the lower and upper Ti/V atoms. Figure 1 shows the lowest energy structures resulting from our relaxations. Negative formation energies, see table 1, reflect stability in each case. We find that P obtains more charge (calculated by the Bader approach) from the MXenes than Si due to its larger electronegativity, see table 2. In addition, V₂C transfers less charge to the ligands than Ti₂C, which agrees with a more covalent bonding character with shorter bond lengths. The functionalized MXenes are metallic, see the densities of states in figure 2, as required for battery applications. The Ti/V 3d states dominate around the Fermi level. In the case of Si functionalization there is also a significant amount of Si 3p states, much more than P 3p states in the case of P functionalization, reflecting reduced stability.

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Table 2. Structural parameters: M-X bond length (b, in ${\mathring{\rm A}}$), vertical distance between the M and X atoms (d, in ${\mathring{\rm A}}$), and charge transfer from X to M₂C ($\Delta q$, in electrons).

	Ti2CP2	V2CP2	Ti2CSi2	V2CSi2
b	2.62	2.46	2.74	2.67
d	1.97	1.81	2.15	2.12
$\Delta q$	−0.50	−0.38	−0.41	−0.27

Three locations are considered for Li/Na/K, namely on top of the M atom in the first layer (M₁), the C atom, and the M atom in the second layer (M₂). The M₁ site turns out to be energetically favorable and therefore is shown in figure 1. We obtain for Ti₂CP₂ and V₂CP₂ almost identical formation energies of  −1.0 eV, −0.7 eV, and  −0.6 eV for Li, Na, and K, respectively. On the other hand, the formation energies for V₂CSi₂ (−2.0 eV, −1.7 eV, and  −2.0 eV) and Ti₂CSi₂ (−1.5 eV, −1.3 eV, and  −1.5 eV) are not the same due to differences in the relaxation of the ligands. The vertical distance between the X and Li/Na/K atoms increases from Li to K, see table 3, because of the growing ionic radius. This effect lowers the charge transfer.

Table 3. Structural parameters: vertical distance between the X and Li/Na/K atoms ($\ell$, in ${\mathring{\rm A}}$) and charge transfer from Li/Na/K to M₂CX₂ ($\Delta m$, in electrons).

		Ti2CP2	V2CP2	Ti2CSi2	V2CSi2
Li	$\ell$	1.29	1.39	1.52	1.68
Li	$\Delta m$	0.86	0.84	0.84	0.84
Na	$\ell$	1.69	1.95	1.96	2.12
Na	$\Delta m$	0.79	0.77	0.76	0.75
K	$\ell$	2.18	2.41	2.40	2.53
K	$\Delta m$	0.76	0.71	0.75	0.73

The energy barriers for Li/Na/K diffusion on Ti₂CP₂, V₂CP₂, Ti₂CSi₂, and V₂CSi₂ are addressed in figure 3. The path connecting two M₁ sites through the C site provides lower energy barriers than that through the M₂ site as well as the direct connection. The diffusion barriers decrease from Li to K, since an adatom farther away from the ligand is less influenced by charge density fluctuations. The transition states are located near the middle between the M₁ and C sites, leaning towards the C site. The obtained Li diffusion barriers (0.32 eV, 0.26 eV, 0.29 eV, and 0.23 eV for Ti₂CP₂, V₂CP₂, Ti₂CSi₂, and V₂CSi₂, respectively) are comparable to those of F functionalized MXenes (Ti₃C₂F₂: 0.36 eV [30], Ti₂CF₂: 0.30 eV, V₂CF₂: 0.28 eV) and other two-dimensional materials (silicene: 0.23 eV [31], MoS₂: 0.21 eV [32]).

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Structures of Ti₂CP₂ decorated with different amounts of Li atoms are illustrated in figure 4. By reaction with three Li atoms, each P atom is converted in the lithiation process (forming Li₃P). Simultaneously, the created vacancy is filled by another Li atom, reflecting alternation of conversion and intercalation reactions. Results for the open circuit voltage

$$\begin{eqnarray}&&V=-\left(E\left({{x}_{2}}\right)-E\left({{x}_{1}}\right)\right)/\left({{x}_{2}}-{{x}_{1}}\right)-E\left[\text{Li}/\text{Na}/\text{K}\right],\end{eqnarray} \tag{ 4 }$$

where E(x) is the total energy of the full system with Li/Na/K coverage x [33], are shown in figure 5. The value decreases for Ti₂CP₂ (V₂CP₂) from 1.0 V to 0.2 V (0.1 V) when the Li coverage increases to 8 atoms per formula unit. Overall the lithiation process is similar for Ti₂CP₂ and V₂CP₂, whereas the open circuit voltage at high Li coverage is lower for V₂CP₂ (because the formation energy of P is more negative). We calculate the (specific) capacity as

$$\begin{eqnarray}&&C=x\centerdot F/M,\end{eqnarray} \tag{ 5 }$$

where F and M, respectively, are the Faraday constant and atomic mass of the material without adsorbed atoms [33]. Values of 1264 mAh g⁻¹ and 1220 mAh g⁻¹ (table 4) are found for Ti₂CP₂ and V₂CP₂, respectively, being much higher than corresponding values for F and OH functionalized MXenes (410 mAh g⁻¹) [20] as well as for graphite (372 mAh g⁻¹) [33]. The sodiation and potassiation processes of Ti₂CP₂ and V₂CP₂ turn out to be similar to the lithiation process but yield lower voltages due to weaker interaction between the ions and ligands. Low cohesive energies of the products lead to lower (and identical) Na and K capacities as compared to the Li capacity of both Ti₂CP₂ (711 mAh g⁻¹) and V₂CP₂ (610 mAh g⁻¹). Although P can be converted only partially in the sodiation and potassiation processes due to this reason, the values are still higher than reported for bare MXenes [24] and graphite [33].

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Si cannot be converted until Ti₂CSi₂ is fully intercalated by 2 Li atoms per formula unit, see figure 4. While the conversion process itself is similar to the case of Ti₂CP₂, the number of intercalated Li atoms varies. The maximal Li coverage turns out to be 10.8, exceeding that of Ti₂CSi₂ as the Li content is higher in Li₂₂Si₅ than Li₃P. Consequently, a higher Li capacity of 1767 mAh g⁻¹ is obtained. The corresponding Li capacity of V₂CSi₂ is only 1592 mAh g⁻¹ as the last Si atom shows higher stability and thus cannot be converted. Ti₂CSi₂ and V₂CSi₂ can only be intercalated by 1 Na or K atom per formula unit, so that the Na and K capacities are much lower.

Replacement of the standard F and OH ligands of MXenes with P and Si has been studied by first-principles calculations, aiming at improvement of the material properties for metal-ion battery applications. Removal of the F and OH ligands from Ti₂C and V₂C by reaction with Li is predicted to be feasible. In addition, both P and Si are found to be stable ligands on the two MXenes and to preserve metallicity. The diffusion barrier decreases from Li (0.32 eV) to Na (0.29 eV) and to K (0.19 eV), as in F functionalized MXenes. P and Si are fully converted during the lithiation process, delivering Li capacities (1264 mAh g⁻¹ and 1767 mAh g⁻¹,respectively) much higher than reported earlier for F and OH functionalized MXenes. Although the ligands can only be converted partially in the sodiation and potassiation processes, the corresponding capacities of 711 mAh g⁻¹ still clearly exceed those of bare MXenes and graphite. F and OH ligands can be removed from MXenes by sonication assisted reaction with Li, resulting in high chemical activity for P and Si functionalization. The enhancement of the Li/Na/K capacity by P and Si functionalization will significantly improve the performance of MXenes in metal-ion battery applications.

The research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST).