F IRST -P RINCIPLES I NVESTIGATION OF T I 2 CSO AND T I 2 CSS E J ANUS MX ENE S TRUCTURES FOR L I AND M G E LECTRODES

like investigated promising their excellent electronic conductivity and good mechanical and dynamical stability. Experimentally realized Janus MoSSe nanosheets provided promising results for battery electrodes. It is known that the surface terminations of MXenes highly affect on the electrochemical properties and the diffusion barriers of ions. Inspired by this, we studied Ti 2 CSO and Ti 2 CSSe Janus MXenes for Li and Mg electrodes. Our density functional theory-based, ﬁrst-principles calculations indicate that both monolayers are thermodynamically, mechanically, and dynamically stable. We calculated that the average voltages for Li and Mg adsorbed Ti 2 CST (T = O, Se) MXenes are approximately 0.95 and 0.2 V, respectively. The maximum voltage for Ti 2 CSTLi x is about 2 V, and that for Ti 2 CSTMg x is around 0.45 V. The Mg adsorbed Ti 2 CSO monolayer exhibits the highest gravimetric capacity (524.54 mAh/g) compared to that of other Janus MXenes considered in this paper. For Ti 2 CSSeLi x , we obtained a higher capacity (230.45 mAh/g) and a lower diffusion barrier (0.191 eV) than that of most of the Li adsorbed S-functionalized MXenes.


Introduction
Modern portable devices and electric vehicles are increasingly demanding high-performance, high-energy density storage materials with fast rechargeable capabilities. So far, lithium-ion batteries (LIBs) have been the fundamental energy source of those devices due to the high energy-density and power-density. However, the lack of Li sources, high production cost, and safety issues are significant drawbacks of LIBs. To address these issues, a vast amount of research has been carried out to find alternative energy carriers for rechargeable batteries [1,2,3,4,5]. Among various types of ions, Mg ions attracted enormous attention due to their bivalency which offers high energy-density. The cost of production of energy storage can also be reduced by utilizing Mg because of its high abundance [1,2].
The two-dimensional (2D) materials have become very popular as reliable electrode materials for energy storage. Their large specific surface areas offer a higher number of electrochemically active sites to store ions compared to that of bulk counterparts. This allows 2D electrodes to have enhanced capacities. Due to the reduced distance between those active sites in the nanosheets, fast charging and discharging rates can be achieved [6,7] while good power densities can be also be obtained. MXene is a large family of 2D materials with a general chemical formula of M n+1 X n T x where M is an early transition metal atom, X represents C or/and N atom, and T indicates the surface termination [8,9]. The most common surface terminations reported for MXenes are O, OH, F, and S. It is found that O and S terminated MXenes have better electrochemical properties for battery applications relative to the OH and F functionalized MXenes. The main advantage of M n+1 X n S x MXenes over M n+1 X n O x monolayers is that the former has lower diffusion barriers than the latter [10,11]. It is reported that Ti 2 CS 2 monolayers exhibit significantly higher gravimetric capacity for Mg compared to that of Ti 2 CO 2 nanosheets [3].

Computational Methods
The density functional theory (DFT) calculations were carried out based on the Vienna ab initio simulation package (VASP) [20,21,22,23]. The projected augmented wave (PAW) pseudopotentials with 500 eV plane-wave cutoff energy were considered for the electron-ion interactions [24,25]. The exchange-correlation functional was treated by using the generalized gradient approximation (GGA) using the Perdew-Burke-Ernzerhof (PBE) method [26,27]. The energy convergence criterion and the force convergence criteria were set as 10 −5 eV and 10 −2 eV/Å, respectively. The Γ-centered Monkhorst-Pack k-meshes were used for the Brillouin zone integration of the unit cells. We employed PHONOPY code [28] to assist our phonon dispersion calculations. We performed ab initio molecular dynamic (MD) simulations at 400 K temperature to see the stability of Ti 2 CSTA 2 (A = Li, Mg) MXenes. 4 × 4 × 1 supercell structures of Ti 2 CST monolayers were considered for both phonon and ab initio MD computations. The climbing image nudged elastic band (CI-NEB) method was used to calculate the diffusion barrier using VASP transition state tools [29,30].   Fig. 2. According to previous studies, Ti 2 CO 2 and Ti 2 CS 2 MXenes also have FCC as the minimum energy structure [31,32].
The lattice constant (a) of Ti 2 CSO MXene is 3.106 Å and that of Ti 2 CSSe MXene is 3.214 Å. The thickness (t) of the MXenes in out-of-plane direction were calculated as the distance between S and O/Se surfaces. The thicknesses of Ti 2 CSO and Ti 2 CSSe MXene are 5.000 and 5.684 Å, respectively. It is clear that Ti 2 CS 2 has a and t values which are almost equal to the respective values of Ti 2 CSSe MXene (see Table 2). As a consequence of having the shortest lattice constant and thickness, Ti 2 CO 2 has the lowest volume of the functionalized Ti 2 C materials in Table 2. This could be because of lower atomic radius of O relative to S and Se and higher attraction between Ti and O in Ti 2 CO 2 as proved by the short Ti-O bond lengths and high charge transfer of Ti and O.
Bader charge transfer analysis [33] was done for examining the charge transfer between atoms (see Table 2). C, S and O atoms of the MXenes gained electrons as indicated by the negative charge transfer. On the contrary, Ti lost  Table 1, E form values are negative for both materials indicating synthesizing these materials are highly possible. We also carried out spin polarized DFT calculations to investigate the magnetic nature of the structures. DFT provides zero magnetic moment for each atom of the unit cells implying that the nonmagnetic ground states are very stable.
The elastic constants were extracted from the DFPT calculations as shown in Table 2 Moreover, we calculated the Young's modulus (Y ) and Poisson's ratio (ν) based on Eq. 2 and 3 [34].
. This relationship indicates that the higher bond strength of T-O than that of Ti-S and Ti-Se, significantly affects the stiffness of the materials. Due to the smaller ν values of Ti 2 CO 2 , Ti 2 CS 2 , and Ti 2 CSO than that of Ti 2 CSSe, the resistance produced against strain by those three monolayers are higher than that from Ti 2 CSSe.
Top Bottom MXene   As can be seen in Fig.3 (c) and (d), the density of states (DOS) crosses the Fermi-level, which is marked by zero energy line. This confirms that both monolayers are metallic. In Ti 2 CSO DOS plot (see Fig.3 (c)), the Ti-d orbitals significantly dominate near the Fermi-level, while the p orbitals of the all the atoms contribute almost equally. However, the contribution from both Ti-d and C-p states are significant for the DOS of Ti 2 CSSe MXenes (see Fig.3 (d)). Since considerable amount of DOS of Ti-d orbitals present near the Fermi-level, we can expect a good metallic-character in both materials, which is important for an excellent electrode material. In order to study the effects on a single Li/Mg ion, we created 4 × 4 supercells of Ti 2 CST MXenes (Ti 2 CSTLi 0.0625 ). We found four different sites for introducing an ion to the systems. Those are labeled as S1, S2, S3, and S4, as shown in Fig.4. Here, the sites S1 and S2 exist on the O-layer or Se-layer, while S3 and S4 are placed on the S-layer. The Li-ions on S1 and S4 are aligned with a C atom, and S2 and S3 are right above or under a Ti atom.

Single Ion Adsorption
We calculated the binding energy of the Li atoms at each site based on Eq. 4. Here, E(M 2 CS 2 + nA) is the total energy of a Ti 2 CST MXene, which adsorbs n number of A=Li/Mg ions. E(M 2 CS 2 ) indicates the total energy of bare-MXene, and E(A) is the energy of a Li/Mg atom.
It is clear from Fig.5  We carried out charge transfer and bond length analysis to study the atomic properties' effects on the binding energy. We calculated the average charge transfer of the surface atoms (η), which form bonds with Li/Mg ions. For instance, η = O for S1 site of Ti 2 CSO MXene and η = S for S3 site of the same material. As can be seen in Fig 5, the magnitudes of Bader charge transfer (∆q η ) of those η atoms are maximum at the sites where binding energy of Li is minimum. The η−Li and η−Mg bond lengths are minimum at the sites which provide the lowest binding energies. Therefore, higher Coulomb interactions exist at the sites with low binding energies. The low binding energy of ions is preferable for electrodes since it prevents forming bulk Li and Mg compounds. Thus, this structure-binding energy relationship shows that ionic-interaction is one of the most important factors behind the stability of the Li/Mg ions adsorbed on the MXenes.

Multiple Ions Adsorption
Next, we considered the effects of multiple ions adsorption on Ti 2 CST MXene. The most challenging task of this step is that finding the ground state of electrodes with different Li/Mg ion concentrations. Most of the research on 2D material electrodes considered large supercells to find the energies of materials with multiple ions. But there is a where Vi is the positive voltages in Fig. 8 (b) and N is the number of positive voltage steps.
2. Vavg2 was calculated by using Eq.7, where x1 = 0 and x2 = xmax high possibility that one can select the wrong Li arrangement on the supercell as the minimum energy configuration. That can generate inaccurate voltage profiles and maximum capacities. Recently, alloy-theoretic automated toolkit (ATAT) [37] was used to search the minimum energy ion configurations of the electrodes [38,39,31]. ATAT code generates numerous structural candidates for a given composition by adopting an automatic cluster expansion method. Finally, the minimum energy candidates are found with the aid of VASP.
O/Se Ti C S Li/Mg S1 S2 S3 S4 Figure 6: The side views of the candidate structures for Ti 2 CSTA 2 (A=Li/Mg) MXenes ATAT recognizes low energy structures between two given compositions. In our work, we considered Ti 2 CST and Ti 2 CSTA 2 (A = Li/Mg) as the compositions with low-ion and high-ion concentrations. Our goal is to find Ti 2 CSTA 2−2α structures with different Li/Mg contents (α) to investigate the binding energies and open-circuit voltage as a function of ion content. We carried out the ground state search for different Li-contents until the cross-validation score becomes less than 0.02 eV. As a result of having two distinct surfaces on Ti 2 CST MXenes, we can identify four different candidate structures for Ti 2 CSTA 2 by placing the ions at different sites, as shown in Fig. 6. Those four configurations are labeled as S1, S2, S3, and S4. In the S1 structure, the ion on the O/Se surface is placed above the nearest Ti atom, and the ion on the S surface is located below the C atoms. Both ions are aligned with Ti (C) atoms for the S2 (S3) structures.
In the S4 configuration, the ion on the O/Se surface is located above C atoms, and the other ion is aligned with the nearest Ti atom. According to our calculations S4 is the preferred structure for Ti 2 CSOLi 2 , and that for Ti 2 CSOMg 2 and Ti 2 CSSeLi 2 is S3. S2 was found as the minimum configuration for Ti 2 CSSeMg 2 .
In ATAT, the formation energies (E form ) for the generated compositions are calculated based on Eq. 5. Here, E[Ti 2 CSTA 2−2α ], E[Ti 2 CST], and E[Ti 2 CSTA 2 ] are the total energy of Ti 2 CST with α content of A (Li/Mg) ions, the total energy of ion free Ti 2 CST, and the total energy of Ti 2 CSTA 2 , respectively. α = 0 of ATAT calculations indicates Ti 2 CSTA 2 composition, where 2 layers of Li/Mg ions are adsorbed. In Fig.7, the most stable compounds have the lowest formation energies. Both Ti 2 CSOLi 2−2α and Ti 2 CSOMg 2−2α MXenes have minimum formation energy at α = 0.5. The lowest energies for Ti 2 CSSeLi 2−2α and Ti 2 CSSeMg 2−2α MXenes are found at α = 0.64 and α = 0.67, respectively. The lower formation energies of Li adsorbed materials than that of Mg electrodes indicate that Ti 2 CSTLi 2−2α MXenes provide more stable phases compared to Ti 2 CSTMg 2−2α MXenes. Furthermore, we calculated the binding energy of Li/Mg ions as a function of ion content using Eq. 4 as shown in Fig. 8. It is clear that the binding energy rises when the ion content increases. This is mainly due to the enhanced repulsion between the ions when multiple ions are adsorbed on the monolayers. Both Li adsorbed Ti 2 CSO, and Ti 2 CSSe MXenes provide lower binding energies compared to that of Mg adsorbed counterparts. Those results agree with the formation energies calculated by cluster expansion, where the Li-based electrodes provided lower values compared to that from the Mg-based electrodes. Thus, we can expect the high stability of Li relative to Mg on those nanosheets.
To study the strain (∆a) induced by Li adsorption, we calculated ∆a based on the expression ∆a = (a−a0)×100

a0
. Here, a 0 is the lattice constant of the bare-MXene, and a is the lattice constant of Li/Mg adsorbed material. We calculated the strains of the single ion adsorbed monolayers (Ti 2 CSTA 0.0625 ) and the MXenes with double Li/Mg ion layers (Ti 2 CSTA 2 ). It is clear from Table 3 that ∆a is negligible for all the electrodes when a single ion is adsorbed. All the strains are less than 0.3 % for Ti 2 CSTA 0.0625 compounds. But, ∆a is considerable or negligible depending on the type of A and T atoms. Surprisingly, Ti 2 CSOLi 2 has no strain found. On the contrary, ∆a is around 1.2 % for Ti 2 CSOMg 2 . Ti 2 CSSeLi 2 exhibits the largest ∆a (4.1 %) in Table 3. Ti 2 CSSeMg 2 shows ∆a ≈ 2.3 %. Thus we can expect very low surface expansion in Ti 2 CSO MXenes compared to Ti 2 CSSe MXenes. We also computed the out-of-plane strain (∆t) by determining the thickness of the MXenes, as shown in Table 3. Even though the in-plane strain is very low in Ti 2 CSOA 2 monolayers, the out-of-plane strain is considerable. On the contrary, ∆t values of Ti 2 CSSeA 2 MXenes is more than three times lower than that of O-based counterparts. As will be explained later, Ti 2 CSOLi 2 , Ti 2 CSOMg 2 and Ti 2 CSSeLi 2 are thermodynamically stable. Therefore, we carried ab-initio MD simulations using VASP to investigate the stability of those materials at high temperatures. Our MD simulations were performed based on the isothermal-isobaric (NPT) ensemble at 400 K temperature, which is way higher than the room temperature. The MD simulations were carried out with 4 × 4 supercells for 5 ps. The total energy and the temperature variations in Fig. 9 suggest that those materials are stable at 400 K. This provides the evidence that Ti 2 CSOLi 2 , Ti 2 CSSeLi 2 and Ti 2 CSOLi 2 MXenes can exist at room temperature. We did not observe any bond breaking or formation of Li x S.

Electrochemical Properties
We investigated the voltage profiles of the Ti 2 CSTA x MXenes based on the following chemical reaction, where z is the valency. z = 1 and z = 2 for Li and Mg, respectively. The open-circuit voltage for the above reaction is the Gibbs free energy (G(x)) which is defined as G(x) = ∆E + P ∆V − T ∆S. Here, ∆E is the internal energy change (computing from the DFT simulations at T= 0K), P is the pressure, ∆V is the volume change, T indicates the temperature and ∆S represents the entropy change of the system. We can neglect P ∆V and T ∆S terms, since those quantities are approximately equal to 10 −5 eV and 25 meV, respectively [31]. As a result, voltage can be determined calculating G(x) using the total energy (E) of Ti 2 CSTA x1 , Ti 2 CSTA x2 , and A atoms, as shown in Eq.7.
We plotted the voltage profiles for Ti 2 CSTA x MXenes as a function of x as shown in Fig. 8. For the whole range of ion content (x = 0 -2), the Li electrodes has much higher voltages compared to their Mg counter parts. Table 3 provides the average (V avg ) and maximum (V max ) voltages of each electrode. V max of both Li electrodes are around 2 V and V avg values lie between 0.85-1.017 V. Li adsorbed Ti 2 CS 2 also provide about 2 V as V max and around 1 V as V avg [31]. V avg of Li adsorbed Ti 2 NS 2 is around 0.64 V, which is smaller than that of Ti 2 CS 2 and Ti 2 CST MXenes [5].  [3]. Thus, by functionalizing single or both sides of Ti 2 C MXenes with S, we can expect low voltages for Mg electrodes. Those Mg electrodes can be suitable as anodes to keep high voltage differences in batteries.
As illustrated by Fig.8 (b), full two layers of Li can be stored on both Janus MXenes, since the voltage is positive from 0 to 2 ion content. However, only Ti 2 CSO monolayer can adsorb two Mg layers. The maximum Mg ion content for Ti 2 CSSe was computed as 1.67. To further investigate the storage properties, we determined the gravimetric capacity based on the following equation, where M is the mass of Ti 2 CSTA x with maximum Li/Mg content (x = x max ) and F is the Faraday constant (26.81 Ah/mol). As illustrated by Table. 3, Ti 2 CSOMg x electrode shows the largest C g value, which is 524.54 mAh/g. This is mainly due to the bivalency of the Mg ion where it donates two electrons per ion. The double Mg layers adsorbed Ti 2 CO 2 electrodes exhibit a higher capacity (570 mAh/g) than that of Ti 2 CSO [4]. Ti 2 CSOLi x electrode provides a capacity around 315.94 mAh/g, which is greater than the capacity provided by Ti 2 CS 2 Li x (288.6 mAh/g). It should also report that Ti 2 CSOLi x , Ti 2 CSOMg x , and Ti 2 CSSeLi x electrodes have higher capacities than Ti 2 NS 2 Li x (308.28 mAh/g) and V 2 NS 2 Li x MXenes (299.52 mAh/g) [5]. All four electrodes reported in Table. 3 have capacities greater than that of M 2 CS 2 Li x MXenes, where M= Zr, Hf, V, Nb, Ta, Cr, Mo and W [31]. It has been reported that Ti 2 CS 2 has a significantly higher capacity for Mg-ions (1871.13 mAh/g) than that of Ti 2 CSO and Ti 2 CSSe electrodes. On the contrary, those three electrodes have approximately equal capacities for Li-ions [3].

Diffusion Barrier
Next, we calculated the diffusion barriers (E diff ) of Li/Mg adsorbed Ti 2 CSTA 0.0625 MXenes using the CI-NEB method as implemented in VASP. Since there are two different surfaces for each MXene, we calculated E diff of both surfaces, as shown in Fig.10. Here, red lines indicate the E diff of O/Se surfaces, while blue lines represent that of S-surfaces. As explained previously, Li/Mg ions prefer different locations on Ti 2 CST MXenes. Li ions' preferable site is right above a C atom for O-surfaces (i.e., S2), while it provides the minimum energy when Li ion is adsorbed right above a Ti atom (i.e, S3). Even though the minimum energy structures are S2 and S3 for Mg ions in Ti 2 CSO, those ions prefer S2 and S4 (S4 is a site right above a C atom on S-surface) sites in Ti 2 CSO (see Fig.11). Therefore, we used those minimum energy sites of each surface as the initial and final locations of the ions to calculate the energy barrier. On Ti 2 CSO monolayers, there are significant differences between E diff of O-surface and that of S-surface as illustrated by Fig.10. This can be possibly due to the considerable electronegativity difference between S and O. Li [3]. It is reported that a single Mg ion adsorbed 4 × 4 supercells of Ti 2 SO 2 , and Ti 3 CO 2 monolayers show E diff greater than 0.6 eV, which is higher than that of Ti 2 CSSeMg 0.0625 [4].
Ti 2 CSSeLi 0.0625 provides lower E diff than that of M 2 CS 2 Li 0.0625 MXenes, where M = Zr, Hf, V, Nb and Ta [31]. Due to the low E diff in Li adsorbed Ti 2 CST, we can expect higher charging and discharging rates.

Conclusion
We performed density functional theory based first-principles studies to examine the stability, electrochemical properties, and diffusion barriers of Ti 2 CSO and Ti 2 CSSe Janus MXenes for Li and Mg electrodes. We proved that both Janus structures are thermodynamically stable when Ti 2 C MXenes are functionalized with S and O/Se. The phonon calculations indicate that Ti 2 CST structures are dynamically stable at 0 K temperature. The elastic constants of both MXenes comply with the criteria for mechanical stability. The density of states plots of those Janus structures have metallic character while the region near the Fermi level is rich with Ti-d orbitals. This can offer good electronic conduction for the electrodes. The in-plain strain of the two Li/Mg layers adsorbed Ti 2 CSO MXenes is very small, while the out-of-plane strain is around 7 %. Ti 2 CSSe monolayers with two Li/Mg layers show strains between 2 % -4 %, whereas out-of-plane strain is less than 0.7 %. The ab initio MD calculations show that Ti 2 CSOLi 2 , Ti 2 CSOMg 2 and Ti 2 CSSeLi 2 structures are stable at 400 K temperature. The average voltage of Li adsorbed Janus MXenes are found as ≈ 0.95 V, and that of Mg adsorbed monolayers are ≈ 0.2 V. The theoretical capacities of the Janus MXenes are greater than 230 mAh/g, which is higher than the capacities of Li adsorbed M 2 CS 2 monolayers with M = Zr, Hf, V, Nb, Ta, Cr, Mo, and W. Ti 2 CSSe nanosheets show lower diffusion barrier compared to that of Ti 2 CSO MXenes. Ti 2 CSSeLi 0.0625 exhibits the lowest diffusion barrier (0.191 eV), which is lower than that of the 2D M 2 CS 2 electrodes, where M = Zr, Hf, V, Nb, Ta, Mo, and W.