Monolayer TiC—A high-performance Dirac anode with ultralow diffusion barriers and high energy densities for Li-ion and Na-ion batteries

Two-dimensional Dirac materials have stimulated substantial research interest as binder-free anodes in metal-ion batteries, owing to their ultrahigh electronic conductivity, large specific area, and higher energy density. Here, using first-principles density functional theory calculations, we have investigated the feasibility of monolayer TiC as a potential anode material for Li/Na-ion batteries. The results indicate that monolayer TiC exhibits excellent dynamical and thermal stability. The electronic structure of monolayer TiC shows semimetallic characteristics with a Dirac cone at the M high symmetry point and the formation of Ti or C vacancies transforms the Dirac cone into a nodal loop or a nodal surface, respectively. Thus, monolayer TiC possesses superior electrical conductivity, which can be further enhanced by the formation of Ti or C vacancies in the material. Furthermore, the calculated adsorption energy values of -0.85 and -0.46 eV for Li-ion and Na-ion, respectively, indicate that Li/Na atom adsorption over monolayer TiC is a favorable process. The density of states plots show that after the adsorption of a single Li/Na atom, monolayer TiC maintains its metallic state, which is advantageous for the diffusion of stored electrons. Most remarkably, monolayer TiC exhibits energy densities of 2684 and 2015 mWh/g for Li and Na, respectively, which are significantly higher than commercial graphite and most other 2D anode materials. The fully loaded TiC anode exhibits excellent cycle stability with volume expansions as low as 0.13 and 0.11%, for Li and Na, respectively. Furthermore, an ultrafast diffusivity with low energy barriers of 0.02 and 0.10 eV is found in monolayer TiC for Li-ion and Na-ion, respectively, which suggests that it has an excellent charge/discharge capability. These exceptional properties make monolayer TiC an excellent candidate as an anode material for Li-ion and Na-ion batteries. Finally, SiC(111) has been proposed as a candidate substrate for monolayer TiC due to its minimal lattice mismatch.


Introduction
Recent years have seen a rapid rise in the use of nonrenewable energy sources (such as fossil fuels) due to technological advances, resulting in severe environmental problems including global warming and greenhouse gas emissions.Therefore, the overall establishment of renewable energy sources will be crucial to help resolve the energy crises and maintaining sustainable global development.In this context, wind-driven generators, solar cells, and tides are extremely relevant; however, their intermittent nature hinders their global commercialization.Consequently, energy storage devices are essential for a more efficient utilization of renewable energies [1][2][3].Indeed, rechargeable batteries that can store renewable energy as electrochemical energy offers a green mechanism to power electronic devices.In this regard, lithium-ion batteries (LIBs) have gained tremendous interest as effective energy storage systems due to their intriguing properties, including high energy conversion efficiency, stable cyclability, lightweight, simple maintenance, and low toxicity [4].It is therefore, LIBs have been widely used in portable electronics, electric vehicles, and power grid systems.By far, graphite is the most common anode material for LIBs; however, its low capacity (372 mAh/g), electrical conductivity, and safety concerns limit its use in high-power applications [5][6][7].Thus, it is imperative to search for better electrode materials with improved capacity.Aside from LIBs, sodium-ion batteries (SIBs) have also recently gained a lot of interest as a potential alternative for energy storage because of their low costs and vast reserves, allowing them to be used in large-scale stationary energy storage systems [8][9][10].Furthermore, the energy storage mechanism in SIBs is similar to that of LIBs; therefore, the technologies developed for LIBs can be directly applied to SIBs [11].However, SIBs exhibit inferior electrochemical performance when compared with LIBs due to their larger ionic radius, higher standard https://doi.org/10.1016/j.apsusc.2023.158564Received 5 July 2023; Received in revised form 21 August 2023; Accepted 24 September 2023 potential, and heavier ionic weight, making them unsuitable for practical applications [12].It is therefore of great significance to develop high-energy electrodes for LIBs and NIBs to address these issues.
Two-dimensional (2D) materials have gained attention as potential candidates for next-generation anode materials due to their high surface area and electrochemical activity [10,11,[13][14][15][16][17][18][19][20][21][22][23][24][25].In this context, much of the research concerns graphene, whose Dirac cone is very efficient at carrying ballistic charges and contributes to a high carrier mobility, which improves battery conductivity.However, pristine graphene does not interact ideally with metal-ions.The electrochemical metal-ion storage of graphene can be improved by adding lattice defects or extra edges, but this causes a band gap opening and degradation of conductivity [26,27].In comparison, other 2D Dirac materials, such as silicene, germanene, and stanene, demonstrate a better affinity for metal-ions than graphene, but they have a higher deadweight [12].Meanwhile, other graphene-like 2-D materials, such as Ti [32], and Mg 2 C [33], have also been widely studied as anode materials for metal-ion batteries and demonstrated reasonably high theoretical capacities of 447.8, 400, 879, 670, 1785, 410, and 1770 mAhg−1, respectively.However, the presence of transition metals in these materials disrupts the distinctive Dirac structure of graphene, which adversely affects their electronic properties and is particularly detrimental to battery applications.Thus, the research for novel Dirac materials is still in progress to achieve a promising anode for Li-and Na-ion batteries.Furthermore, most previous theoretical works on 2D Dirac electrodes focused solely on their reversible capacities, while their energy density was completely ignored [34].The energy density is determined by its capacity times its working voltage, which is a more desirable parameter in industrial applications.Only anodes with high theoretical capacities and low average open circuit voltage (OCV) can attain high energy density, which is highly desirable for improving Li and Na-ion battery performance.
Recently, TiC has been acknowledged as a promising anode material for LIBs due to its low density (4.93 g/cm 3 ), high electrical conductivity (6.8 × 10 −5 Ω), superior structural stability, and mechanical properties [35,36].Furthermore, TiC demonstrates the highest chemical and electrochemical stability compared to other transition metal carbide thin films when used as supports for platinum group metals [37].Ren et al. [38] reported a nano-TiC anode for LIBs and demonstrated that it has potentially excellent lithium battery performance.Moreover, Xu et al. [39] reported nano-TiC (including 0D nanopowders, 1D nanorods, and 2D nanosheets) anodes for LIBs synthesized on the templates of acetylene black, multi-walled carbon nanotubes, and graphene nanosheets, respectively, and results showed that nano-TiC is promising as anode for LIBs.TiC-based composites have also been constructed by combining TiC with other materials, such as TiC@C-TiO 2 core-shell nanostructures [40], MoS 2 -TiC-C nanocomposites [41], and hierarchical m-TNO@TiC@NC composites [42], which demonstrated enhanced specific capacity with exemplary capacity retention.Other than that, the TiC with varying morphologies and structures, including TiC/C core/shell nanowire arrays [43], TiC/NiO core/shell nanoarchitecture [36], and nanostructured Si/TiC composites [44], all facilitate high overall capacity and excellent rate capability in Li/Naion batteries.In addition, the bilayer TiC is predicted to exhibit a high theoretical capacity of 895 mAh/g [45] and 460 mAh/g [46] for Li-and Na-ion batteries, respectively.Yang et al. [47] reported a high tendency for catalytic properties in monolayer (ML) TiC for electrochemical oxygen reduction reactions in Li-O 2 batteries.Thus, TiC or TiC-based nanostructured materials are obviously superior in the development of high-performance Li/Na-ion electrodes.Besides, ML TiC hollow spherical arrays with exceptional high-temperature supercapacitor performance were synthesized using an atomic layer deposition-assisted techniquezhong [48].Recently, Su et al. [49] have reported the successful synthesis of high-quality TiC ultrathin films with a thickness of 4 nm using chemical vapor deposition, demonstrating the significant potential of ML TiC fabrication.Furthermore, Polley et al. [50] reported a bottom-up strategy for synthesizing monolayers of non-layered materials.They fabricated ML SiC by preparing ultrathin films (t < 3 nm) of TaC, an isostructural and isovalent cousin of TiC, on SiC substrates, demonstrating that ML TiC can also be epitaxially grown using the same technique.Therefore, it is desirable to explore the dynamic and thermal stability and electrochemical performance of ML TiC in order to provide a fundamental understanding and reference for 2D TiC as a potential anode material for Li/Na-ion batteries.
Motivated by these previous reports, herein the possible suitability of ML TiC as anode material is thoroughly examined for Li and Na-ion batteries using density functional theory (DFT).The pristine ML TiC possesses a Dirac cone in its electronic band structure, which evolves into a nodal loop or surface nodal line by the formation of a Ti or C vacancy in TiC.This change in the electronic band structure promotes electronic conductivity, which helps to reduce non-active material in cell components.Furthermore, metal ion electrochemical reactions such as adsorption energy, OCV, theoretical capacity, ion migration, and energy density have been examined in order to establish ML TiC as a prominent anode material for use in Li/Na batteries.  molecular dynamics simulations were performed to evaluate the TiC anode stability during Li-ion and Na-ion intercalation.This study opens up a new avenue for exploring other transition metal carbide-based 2D Dirac materials as high-performance anodes for Li/Na-ion batteries.

Computational details
The first-principles calculations were performed within the framework of density functional theory (DFT) as employed in the Vienna   simulation package (VASP) [51,52].The exchange-correlation effects were treated by generalized gradient approximation (GGA) [53] in the Perdew-Burke-Ernzerhof (PBE) form.A kinetic energy cutoff of 500 eV was used for the plane-wave basis set, and the Brillouin zone was sampled by using a 15 × 15 × 1 and 6 × 6 × 1 Gamma-centered Monkhorst-Pack grid [54] for unit cell and a 3 × 3 × 1 supercell of ML TiC.The van der Waals interactions were corrected using Grimme's approach [55].Structural relaxation was taken into account until the Hellmann-Feynman forces on all atoms were less than 10 −3 eV/Å.To prevent artificial interactions caused by periodic boundary conditions, a 15 Å out-of-plane vacuum was added.The phonon dispersion calculations using the supercell approach were computed using the Phonopy code [56].To assess the thermal stability of pristine TiC and TiC loaded with Li and Na,   molecular dynamics (AIMD) simulations in canonical ensemble (NVT) were carried out using a Nose-Hoover thermostat [57] with a period of 5/6 ps at 300/350 K and a time step of 2 fs.To estimate the charge transfer between the substrate and Li/Naadatom, Bader charge analysis [58] has been performed.The climbing image-nudged elastic band (Cl-NEB) [59] approach was utilized to estimate the migration pathway and related diffusion barriers on ML TiC.Seven linearly interpolated images were used to construct the migration pathway between fully relaxed initial and final positions.The metal ion adsorption energies (  ) on the TiC anode were computed as follows.
where   + and   are the total energies of the metal-loaded TiC and the pristine TiC, respectively, and   is the chemical potential derived from the bulk metal atoms.
The theoretical capacity was calculated as follows: where   is the maximum number of metal-ions adsorbed on the TiC surface,  is the transferred charge (value of  is 1 for both Li and Na),  is the Faraday constant (26,801 mAh/g), and    is the molar weight of the ML TiC.
The volume variations were calculated using the following expression where   is the initial volume of ML TiC and   is the volume after the adsorption of metal-ions.The OCVs of metal-ions were determined by the following equation where  2 and  1 represent the two adjacent concentrations of adsorbed metal-ions on TiC,   2   and   1   are the total energies of ML TiC with  2 and  1 adsorbed metal-ions, and   represents the chemical potential per bulk metal atom.

Results and discussion
ML TiC belongs to the tetragonal crystal structure with space group P4/mmm (No. 123), as shown in Figs.1a and 1b.The primitive cell contains one Ti atom and one C atom, which occupy (0.5, 0.5, 0.5) and (0, 0, 0.5) atomic positions, respectively.The optimized lattice parameters of ML TiC are a = b = 3.06 Å.Moreover, each Ti atom is covalently bonded with four neighboring C atoms, with a Ti-C bond length of 2.17 Å and a C-Ti-C bond angle of 90 • .The computed phonon spectrum of ML TiC is shown in Fig. 1d, which exhibits no negative frequency, demonstrating the dynamical stability of the structure.The highest frequency of ML TiC is 19.77THz, which is comparable with those of the monolayers Ti 2 C (20.23 THz) and Ti 3 C 2 (21.28 THz) [60].Moreover, AIMD simulations are also performed to evaluate the thermal stability of ML TiC, and the results are presented in Figure S1(b).The small fluctuations in the total energy indicate good thermal stability of ML TiC.Notably, Zhang et al. [61] anticipated a buckled tetragonal structure for ML TiC; however, in our calculations, the planar structure is shown to be more stable since the buckled structure transforms to planar during relaxation.This could be explained by the fact that the van der Waals interactions are included in our calculations, which leads to more realistic results.Fig. 1c shows the band structure and the corresponding density of states of ML TiC calculated under the PBE level.It can be seen that valence and conduction bands cross each other at the M point and form a Dirac-type point near the Fermi level.The Dirac bands are mainly composed of Ti atom orbitals, with a minor contribution from the C atom.Furthermore, the conduction and valence bands appear to cross each other along the  − X line as well; however, there is a bandgap of 8.2 meV between the bands there.The band structure of ML TiC had also been calculated using the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional [62], and no significant change in the electronic band structure was found (see Figure S1(a)).Therefore, we will stick with the PBE results for the rest of this article.
There is always a chance of vacancy formation during electrode fabrication or with the lattice vibrations at elevated temperatures [11].Therefore, the effect of vacancy formations is examined on the electronic conductivity of ML TiC in Fig. 2. Two types of vacancies can be possible in ML TiC, i.e., Ti and C, which can be simulated by removing a single Ti or C atom from a 3 × 3 supercell of TiC.The appearance of vacancy results in an evident local atomic reconstruction in ML TiC.The atoms near the vacancy move away, causing the Ti-C bond length to increase along path I while decreasing along path II, as illustrated in Figs.2a and 2d.The formation energies for Ti and C vacancies are 7.17 eV and 2.21 eV, respectively.This shows that the formation of C vacancies is much easier than Ti vacancies in ML TiC.Moreover, the Ti vacancy has a nonmagnetic ground state, transforming the Dirac cone at M into a closed nodal loop as shown in Fig. 2c.In contrast, the C vacancy induces a magnetic moment of 1.22 μB in the ML TiC.Furthermore, in both spin-up and spin-down band structures, the conduction and valence bands degenerate and form almost flat nodal surfaces around M, as shown in 2f and 2g, respectively.The presence of flat nodal surfaces allowed several states to occupy nearly the same energy levels, which can be advantageous for achieving high intrinsic conductivity in ML TiC without the addition of an extra conductive additive and hence offers tremendous potential for use as binder-free anode material [11].However, defects in monolayers are exposed and can readily react with matter in its environment, like air molecules.
To assess the potential electrochemical performance of monolayer TiC, the adsorption energy of one Li/Na atom on a 3 × 3 × 1 supercell of monolayer TiC has been investigated.Three different sites, including A 1 , A 2 , and A 3 , were investigated to determine the most energetically favorable adsorption site, as shown in Figs.3a and 3b.The A 1 and A 3 sites are located above the Ti and C atoms, respectively, while the A 2 site is located over the center of the square.The most energetically favorable site for both Li and Na is A 3 , as shown in Figs.3c and  3d, respectively.The adsorption energies (  ) for Li and Na at the A 3 site are −0.85 and −0.46 eV, respectively, which are sufficient to avoid metallic dendrite formation and achieve the desired voltage.The amount of charge transfer between Li/Na and TiC interfaces was computed using the Bader charge analysis, and the values for maximum adsorption sites are given in Table 1.The charge is transferred from alkali metal ions to ML TiC, and the values are 0.83 e and 0.68 e for Na and Li, respectively, which is consistent with their   trend.Furthermore, the Na-ion distance (2.57Å) from the TiC surface is larger than the Li-ion (2.06 Å), due to the larger size of the Na-ion.
Next, the charge density difference of metal-ions adsorbed on the ML TiC is computed, as shown in Fig. 4. The red and green areas present electron accumulation and depletion, respectively.Clearly, the charge accumulates between the alkali metal atoms and the surface, and the charge depletion occurs around alkali metal atoms, which is completely consistent with the Bader charge analysis.Moreover, electrons transferred from the metal atoms to the TiC surface accumulate locally on the square patch around the adsorption site, causing an electrostatic repulsion between Ti-C that leads to a 0.01 Å increase in the Ti-C bond length in that region.The corresponding DOS of Li/Na adsorbed TiC structures were calculated and are shown in Figs.4e  and 4f, respectively.Clearly, the TiC electrode retains its metallic properties after the adsorption of metal-ions.Furthermore, the Fermi level is shifted upward because the electrons transferred from the metal atoms occupy the conduction band of TiC.This improves the electrical conductivity of TiC, which is beneficial for anode materials.
The rate performance of the battery is closely associated with the carrier mobility as well as the diffusivity of metal-ions on the electrode material.A promising anode material must be capable of effectively transporting metal-ions and electrons within it to facilitate redox reactions, and this requires a low diffusion barrier.Thus, the Li/Na-ion diffusion resistance on TiC is investigated by calculating their migration barrier.Two diffusion pathways (Path-I and Path-II) were considered for both Li and Na-ion migration, as illustrated in Fig. 5.The energy barrier curve for path-I is substantially lower than that for path II, showing that the Li/Na-ions prefer to diffuse through the C-C site rather than the C-Ti-C site.The calculated diffusion barrier for Li/Na is 0.022/0.10eV along Path-I.Here, it is worth noting that the diffusion barrier of TiC for Li is much smaller than most of the other reported 2D anodes, including h-BAs (0.522 eV) [24], MoS 2 (0.17 eV) [22], V 2 C (0.045 eV) [18], Nb 2 C (0.032 eV) [17], Ta 2 CS 2 (0.21 eV) [16], and Ti 3 C 2 (0.068 eV) [10], as shown in Table 1.With regard to the Na-ion, its diffusion barrier is smaller than CoB (0.32 eV) [63], black phosphorene (0.38 eV) [11], and h-BAs (0.248 eV) [24] and comparable to those for −Sb (0.1 eV) [25], and BC 3 (0.13 eV) [64].This demonstrates that ML TiC possesses high ionic conductivity, making it an excellent candidate to be used as an anode for Li-and Na-ion batteries.
Next, the OCV and theoretical capacity of the ML TiC are calculated, which are two other key factors to assess the performance of anode materials.To mimic the charging/discharging process, metal-ions were added in a step-wise manner on both sides of the TiC anode, from which the evolution of voltage and capacity with the concentration of Li/Na ions was derived.The metal-ions would be continuously adsorbed on the TiC anode until the slope of average formation energy (E  ) turns positive or convergent, where maximum storage capacity is reached.The E  is defined as   = (     −    −   )∕ ( +  ) , where      and    are the total energies of the TiC anode with  metalions and without metal-ions, respectively,   is the chemical potential of metal-ions in their bulk state, and  ( +  ) is the total number of atoms.Finally, the 3 × 3 × 1 TiC supercell can host up to 27 Li and 18 Na ions, which corresponds to the chemical stoichiometry of TiCLi 3 and TiCNa 2 , respectively, with formation energies of −0.33 and −0.25 eV.The further adsorption of Li/Na ions on the TiC surface drives the slope of the formation energy curves to become positive (see Figs. 6a and 6b).Moreover, the fully metalized phase meets the criteria established by Zhao et al. [65], i.e., negative formation energy for metal-ions, no metal ions escaping the anode, and no irreversible electrode deformation.Consequently, TiC anodes exhibit storage capacities of 1342 and 895 mAh/g for Li-and Na-ion batteries, respectively, which are much higher than that of bilayer TiC (895/460 mAh/g for Li/Na [45,46]).The relative formation energy (E  ) based on the two end structures corresponding to pure TiC and Li 3 TiC/Na 2 TiC is calculated to estimate the voltage evolution by Li/Na concentrations and to assess the intermediate phase stability.The E  is computed by means of the respective formula where E     corresponds to the total energy of TiC with  Li/Na ions and  is the maximum adsorption concentration of Li/Na atoms (p is 3 for Li and 2 for Na).Accordingly, the thermodynamically stable phases can be determined using the energy convex hull, as illustrated in the inset of Figs.6c and 6d.The intermediate stable phases with the lowest formation energies lie on the hull, while the unstable phases are above it.The OCV is computed using the two endpoints and the stable phases sitting on the hull.There are two primary voltage plateaus for Li/Na-ions adsorbed on the surface of TiC as shown in Figs.6c  and 6d.In the case of TiCLi 3 , the first voltage plateau at  = 0 to 2 exhibits a large value of ∼0.64 eV, which could be ascribed to the strong binding of Li with TiC.The second voltage plateau comes from  = 2 to 3, where a dramatic drop from 0.65 eV to 0.21 eV is observed due to the increasing repulsive interaction between Li ions.In comparison, TiCNa 2 exhibits lower potential values, ranging from 0.54 to 0.48 eV, as demonstrated in Fig. 6d.Furthermore, for both Li and Na, the voltage remains positive throughout the process, implying that the half-cell reactions can continue spontaneously to reach the final phases (TiCLi 3 /TiCNa 2 ).A decrease in voltage with increased metal-ion adsorption in the TiC anode is favorable since it increases the operational voltage of the battery when coupled with a cathode material.
AIMD simulations were performed to evaluate the thermal stability of ML TiC with the maximum capacity of Li-and Na-ion concentrations.Both systems (TiCLi 3 and TiCNa 2 ) were subjected to a 300 K temperature for up to 5 ps. Figure S2 illustrates the energy evolution for both systems during the AIMD simulation, where small fluctuations in the total energy indicate good stability for TiCLi 3 and TiCNa 2 .The final snapshots of the Li-and Na-saturated supercell models are also depicted in Figure S2, which show that the ML TiC structure remains stable with no major distortion while the adsorbed Li/Na atoms deviate slightly from their equilibrium positions.
In the last part, the possible synthesis route for the ML TiC anode is discussed.The rapid development of substrate-dependent epitaxy technology has made it much easier to synthesize two-dimensional materials.Recently, a bottom-up strategy has been proposed by Polley et al. [50] for synthesizing monolayers of non-layered materials.They fabricated ML SiC by preparing ultrathin films (t < 3 nm) of TaC on SiC substrates.Because TiC has the same configuration as TaC, we anticipate that ML TiC can also be epitaxially grown using the same approach.Furthermore, the optimized lattice constants of ML TiC (3.06 Å) and SiC (111) surface (3.07 Å) closely match (less than 1% lattice mismatch), indicating that SiC (111) is a good substrate for growing ML TiC.Fig. 7a depicts the lowest energy structure for the TiC/SiC(111) heterostructure, for which three lateral stackings were examined before arriving at this configuration (see Fig. S7).The binding energy is computed to determine the extent of binding between the constituent systems as   =  ( ∕) −  ( ) −  () , where  ( ∕) ,  ( ) , and  () are the total energies of the heterostructure, pristine TiC, and SiC, respectively.The obtained binding energy of −1.77 eV demonstrates strong binding between TiC and SiC (111), which provides further support to our proposal for epitaxial TiC growth on SiC (111).Fig. 7b depicts the DOS of TiC/SiC(111), demonstrating that ML TiC retains its metallicity upon an interface with SiC (111).It ensures that the TiC/SiC(111) heterostructure has high electrical conductivity, which is advantageous for anode materials.

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Fig. 1 .
Fig. 1.(a) Top and (b) side views of optimized ML TiC structure, (c) band structure and total and partial density of states, and (d) phonon band and density of states of ML TiC.

Fig. 2 .
Fig. 2. Relaxed configurations of the 3 × 3 TiC supercell with a (a) single Ti and (d) C vacancy.(b) The density of states and (c) electronic band structure with Ti vacancy.(e) The density of states and (f) spin-up and (g) spin-down electronic band structures with C vacancy.The green dotted circles represent the missing atom and the red arrows indicate the spin-up and down bands.

Fig. 3 .
Fig. 3. (a) Top and (b) side views of the three high-symmetry adsorption sites and (c) the adsorption energy of Li and (d) Na atoms on ML TiC.

Fig. 4 .
Fig. 4. (a-d) Top and side views of the charge density differences for Li and Na on ML TiC.The red and green areas refer to electron accumulation and depletion, respectively.(e-f) The total density of states of Li and Na adsorbed ML TiC, respectively.

Fig. 5 .
Fig. 5. Diffusion paths and energy barriers on the surface of the ML TiC; (a-b) Li diffusion paths and energy barriers and (c-d) Na diffusion paths and energy barriers on the surface of ML TiC.

Fig. 6 .
Fig. 6. (a-b) Formation energies with the increase of Li and Na concentrations and (c-d) the OCV for the interaction of Li and Na atoms on the surface of ML TiC.The inset figures give the corresponding relative formation energies.

Fig. 7 .
Fig. 7. (a) Side view of the relaxed configuration of ML TiC on SiC (111) substrate and (b) total and partial density of states of TiC/SiC(111) heterostructure.

Table 1
Adsorption energy (E  ), vertical height of metal-ions from the TiC surface, and total charge transfer (Q) from metal-ions to the TiC Surface.

Table 2
Comparison of the energy densities and diffusion barriers of various anode materials for Li-and Na-ion batteries determined from the literature.