Double transition metal-containing M2TiAlC2 o-MAX phases as Li-ion batteries anodes: a theoretical screening

Here, thermodynamic stability and lithium storage properties of double transition metal M2TiAlC2 o-MAX phases (M = Cr, V, Mo, Nb, Ta, Hf, Zr, Sc, Y, La) are theoretically investigated by density functional theory (DFT) calculation. M2TiAlC2 with a larger M atomic radius shows larger interlayer space that may benefit the Li-ion intercalation. A promising theoretical capacity of 276.87 mAh g-1 is predicted for Sc2TiAlC2. The low Li-ion diffusion barriers (0.57–0.64 eV) for M2TiAlC2 indicate the possibility to achieve fast Li-ion diffusion that is crucial for designing high-power batteries. This work provides opportunities to explore MAX phases as promising Li-ion storage materials. GRAPHICAL ABSTRACT IMPACT STATEMENT This work investigates the thermostability and lithium storage properties of double transition metal o-MAX phases by DFT calculation and provides a guideline for exploring MAX phases for lithium storage applications.


Introduction
MAX phases are hexagonal nanolaminated ternary metal/ceramics with the general formula M n+1 AX n , where M is the transition metal, A is the main III to V group elements, X is C or N and typically n = 1, 2, 3, 4, etc. [1,2]. There are currently more than 150 MAX phases known, including solid solutions [3,4]. Due to the alternative stacking between the A layer and ceramic layer, MAX phases possess high conductivity and structural stability that is being considered for electrical contacts, sensors, protective coating, microelectromechanical systems, and high-temperature structural applications [5][6][7][8]. In recent years, MAX phases are receiving increasing attention as precursor materials of two-dimensional MXenes that are extensively investigated as electrochemical energy storage materials [9][10][11][12][13]. Although much less attention has been paid to MAX phases as lithium storage materials, several studies confirmed the promising potential of using MAX phases as lithium storage CONTACT [17] reported V 2 SnC MAX phases could obtain high gravimetric capacity up to 490 mAh g −1 and proposed a lithium storage mechanism with V 2 C-Li and Sn-Li reactions.
To achieve high specific energy for Li-ion batteries, developing novel anode materials with a high specific capacity, low delithiation potential, high cycling stability, and reversibility are highly demanded [18][19][20]. MAX phases featured with layered structures and high electrical conductivities are believed to be promising lithium storage hosts. However, to the best of our knowledge, studies on MAX phases as an electrode for energy storage is scarce and the charge storage mechanism is not fully understood yet. Therefore, it is of great interest and significance to explore the lithium storage properties of MAX phases. DFT calculations are effective methods for theoretical investigation on materials' properties. Zhu et al. [21] predicted by DFT calculation that the stressenhanced V 2 SC MAX phases could achieve good lithium storage properties and soft interlayer in MAX phases provide the possibility for lithium storage. However, other researchers found the interlayer space of MAX phases is too narrow to incorporate lithium and the lithiation formation energy is positive [22,23]. Therefore, more studies focused on the exfoliation or interlayer expansion to enhance the chances of lithium interaction [24,25].
Elemental doping and substitution, in many cases, are effective routes to tune the electronic properties of MAX phases [26,27]. Therefore, we speculate that the ordered M 2 TiAlC 2 (M = Cr, V, Mo, Nb, Ta, Hf, Zr, Sc, Y, La) MAX phases with outer Ti atomic layers substitutional strategy may expand the interlayer space and achieve enhanced lithium storage properties. In the ceramic layer structure, the face-centered cubic (fcc) transition metal carbides are more stable. Thus, the Ti located inside of the ceramic layer can usually stabilize the structure [28]. Combining the M element substitution and the stability of Ti carbide layer, it can be expected that the M 2 TiAlC 2 may achieve high lithium storage properties and structural stability.
In this work, the structural stability and electronic properties of the M 2 TiAlC 2 MAX phases (M = Cr, V, Mo, Nb, Ta, Hf, Zr, Sc, Y, La) with or without lithium intercalation are investigated by DFT calculations. The phonon density of states is employed to predict the lithium storage capacity by checking the stabilities of M 2 TiAlC 2 containing the different numbers of Li-ions. The kinetic properties are evaluated for M 2 TiAlC 2 by analyzing the migration pathways of Li-ion.

Results and discussion
For selecting MAX phases as promising electrode materials, the thermodynamic stability, lithiation formation energy E Li , theoretical capacity, and Li-ion diffusion barrier are vital criteria and will be carefully screened step by step.

Stability of M 2 TiAlC 2
The calculated lattice constants and formation energies of M 2 TiAlC 2 are listed in Table 1, in which the values  Figure 1. Similar to Ti 3 AlC 2 , the DOS of M 2 TiAlC 2 has similar hybridization characteristics, including the covalent bonding of M and C and the metallic properties dominated by transition elements [30]. Since the insufficient number of valence electrons for filling the bonding states, the hybridization peaks of Sc 2 TiAlC 2 and Y 2 TiAlC 2 will shift toward a higher energy level. The DOS in higher energy levels tend to fill nonbonding/antibonding states, which reduces the stability of the structure. It is in good agreement with the calculated formation energies. Since Ti, Zr, and Hf have the same number of valence electrons, the bonding states of M 2 TiAlC 2 MAX phases are filled and their corresponding antibonding states remain unfilled, separating by a pseudogap in the Fermi level [31]. Thus, the substitution of Sc and Y would be less stable than Zr, and Hf substitution. Besides, the order of phase stability is Ti 3 AlC 2 > Zr 2 TiAlC 2 > Hf 2 TiAlC 2 , which conforms to the order of M atomic size (Hf > Zr > Ti), indicating the M atom size is opposite to thermodynamic stability.
As shown in Figure 2, the charge differences between Al and ceramic layers are calculated to obtain insight  into the structural changes. The degree of the charge transfer represents bonding strength. Compared with Ti 3 AlC 2 , the M 2 TiAlC 2 MAX phases show similar electronic distributions but less charge transfer, suggesting weaker M-Al bonding. The relatively weakening M-Al bonds represent the longer M-Al bonding length, further generating an expanding interlayer space [32]. Besides, the weaker bonding strength can also be explained by overlapped states shifting toward higher energy levels as shown in Figure 1. Combining the analysis of electronic structure and thermodynamics (formation energy), we reach the conclusion that the larger difference between the atomic sizes of M and Ti results in the larger interlayer space and the less structural stability, which agrees well with previous studies [31,33].    Table S1, which indicates H C is the most energetic favorable lithiation site.
To obtain insight into the lithiation process, the Bader charge and charge difference analyses are performed. In Table 2, the charge transfer of Li in M 2 TiAlC 2 is around −0.72 |e| that loses more electrons than in Ti 3 AlC 2 (−0.69 |e|), which indicates Li will be more ionic states in the large interlayer spaces. Meanwhile, Al gains more electrons that explain the increasing degree of Li-Al alloy reaction. The charge transfer of Ti remains almost unchanged, reflecting that lithiation has slight influences on the interior of the ceramic layer. Besides, charge differences show the interaction between Li and host material, as shown in Figure S1. The Coulomb force between Li and M elements is weaker with the interlayer space enlarging because the smaller positive electron cloud generates less repulsion. Specific capacity is a crucial parameter that determines the energy density of LIBs. To confirm the theoretical specific capacities of M 2 TiAlC 2 , the lithiation formation energy E Li for each continually inserting Li is calculated via Eq (S2) and presented in Figure  4(a). Obviously, Ti 3 AlC 2 shows the lowest E Li , indicating less thermodynamic stable for Li insertion. Once the value of E Li tends to be zero or positive, no more lithium can be inserted, which corresponds to the maximum saturation of Li storage. Base on the Eq (S3), the theoretical capacities of Ti 3 AlC 2 , Zr 2 TiAlC 2 , Hf 2 TiAlC 2 , Sc 2 TiAlC 2 , and Y 2 TiAlC 2 are calculated to be 243.54, 252.55, 105.03, 411.22, and 256.7 mAh g −1 , respectively. Furthermore, the dynamical stability of maximal Li insertions is investigated by performing lattice phonon calculations, as shown in Figure S2. Imaginary frequency demonstrates the structure is dynamically unstable and the partial phonon density of stats of ceramic layer and Al layer with Li-ions are calculated. Among all M 2 TiAlC 2 MAX phases, the ceramic layer is calculated without imaginary frequency, suggesting the dynamically stable and the optical and acoustical branches are well-separated, presenting a phonon dispersion characteristic of layered material [34]. Ti 3 AlC 2 phases can maintain only one Li atom per Al layer in a supercell with an imaginary frequency value of 100 THz, which indicates the theoretical capacity would be lower than ∼ 122.84 mAh g −1 calculated via Eq (S3). However, the Sc 2 TiAlC 2 could maintain two Li atoms per Al layer in a supercell without any imaginary frequency, and the theoretical capacity could be 276.87 mAh g −1 that is twice larger than Ti 3 AlC 2 . With the same Li storage number but different molar weights, the theoretical capacities of Zr 2 TiAlC 2 and Hf 2 TiAlC 2 are 169.39 and 105.03 mAh g −1 , respectively. After lithiation, as shown in Figure S3, the conductivities of M 2 TiAlC 2 have no significant change because the metallic property is contributed mainly by M elements' d orbital.
To clarify the effect of interlayer space on lithium storage, the M-Li, Al-Li, and Al-Al bonding lengths (representing different directions of interlayer space) are calculated, as shown in Figure 4(b-d). The sudden change of the Al-Li and Al-Al bonding lengths happens at the third Li insertion. On the one hand, the M-Li bonding length changes slightly, reflecting that lithiation hardly influences the ceramic layer. On the other hand, the Al-Li boding length increases, and Al-Al bonding length decreases as the inserted Li number increases, indicating the Al layer atoms will rearrange during lithiation/delithiation. Al can rearrange in M 2 TiAlC 2 easier because of the larger interlayer space that produces less Coulomb force and weaker M-Al bonding.
The charge/discharge rate capability of rechargeable LIBs is mainly determined by the ion diffusion kinetic. The intrinsic metallic behavior of M 2 TiAlC 2 has been demonstrated by DOS [35]. The NEB method is performed to estimate the Li diffusion. Three diffusion pathways along the high symmetry line between the two neighboring favorable sites (H C ) are designed to find the minimum energy barrier, as shown in Figure 5(a). However, the diffusion barrier of the HexM path is around 1.2 eV, which implicates M repulsive force hinders this diffusion path. Besides, the climbing path could not be realized because the ceramic layer's repulsive force is larger than the Al layer. The diffusion energy barriers of the HexC path are relatively low, as presented in Figure 5(b). The minimum energy barrier is 0.57 eV in Hf 2 TiAlC 2 . It is worth noting that along the HexC path, the diffusion trajectory of Li-ion passes through an Al position, resulting in the position derivation of the Al atom. Hence, if there is enough space for Al to move, the Li-ion would diffuse more easily. As demonstrated above, M substitution expands the interlayer space that facilitates the easy rearrangement of Al, thereby reducing the Li-ion diffusion barriers in M 2 TiAlC 2 .

Conclusions
We performed a computational investigation on the structural and lithium storage properties of M 2 TiAlC 2 MAX phases. DFT calculations demonstrate that M 2 TiAlC 2 MAX phases are thermally stable. M elements substituting expands the interlayer space expands and thus reduces lithiation formation energy, and the charge difference shows that the strong repulsion force decreases, suggesting the great potential for lithium storage. Next, the maximum theoretical capacities of the M 2 TiAlC 2 MAX phases are calculated. Zr 2 TiAlC 2 and Sc 2 TiAlC 2 are predicted with the maximum specific capacities of 169.39 and 276.87 mAh g −1 respectively. Finally, the different diffusion pathways were screened for investigating the diffusion barriers of Li-ion into M 2 TiAlC 2 MAX phases. The lowest diffusion energy barrier ( ∼ 0.57 eV) is obtained for Hf 2 TiAlC 2 .
In this work, the M elements substitution strategy was proposed for fine-tuning the interlayer space and electronic structure of MAX phases as promising lithium storage materials. The guideline to improve the lithium storage properties of MAX phases are summarized as following: (1) enlarge the interlayer space by larger radii elements substitution; (2) select proper A elements to make inserted Li in more ionic states.

Disclosure statement
No potential conflict of interest was reported by the author(s).