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First-Principles Calculations of TiN and TiNT (T = O, F, OH) Monolayers as Potential Anode Materials for Lithium-Ion Batteries and Beyond Dashuai Wang, Yu Gao, Yanhui Liu, Di Jin, Yury Gogotsi, Xing Meng, Fei Du, Gang Chen, and Yingjin Wei J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 05 Jun 2017 Downloaded from http://pubs.acs.org on June 5, 2017

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The Journal of Physical Chemistry

First-Principles Calculations of Ti2N and Ti2NT2 (T = O, F, OH) Monolayers as Potential Anode Materials for Lithium-ion Batteries and Beyond Dashuai Wanga, Yu Gaoa, Yanhui Liuc, Di Jina, Yury Gogotsia,b,*, Xing Menga,b, Fei Dua, Gang Chena,* , and Yingjin Weia,* a

Key Laboratory of Physics and Technology for Advanced Batteries (Ministry of Education),

College of Physics, Jilin University, Changchun 130012, China. b

Department of Materials Science & Engineering, and A.J. Drexel Nanotechnology Institute,

Drexel University, Philadelphia, Pennsylvania 19104, United States. c

Department of Physics, College of Science, Yanbian University, Yanji 133002, China.

KEYWORDS: MXene, Titanium nitride, Rechargeable batteries, First-principles calculations, Electrochemical performances

ACS Paragon Plus Environment

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ABSTRACT: The potential of a Ti2N monolayer and its Ti2NT2 derivatives (T = O, F, and OH) as anode materials for lithium-ion and beyond-lithium-ion batteries has been investigated by the first-principles calculations. The bare and terminated monolayers are metallic compounds with high electronic conductivity. The diffusion barriers on bare Ti2N monolayer are predicted to be 21.5 meV for Li+, 14.0 meV for Na+, 7.0 meV for K+, 75.9 meV for Mg2+, and 38.0 meV for Ca2+, which are the lowest values reported for state-of-the-art two-dimensional energy storage materials. The functional groups on Ti2NT2 increase the diffusion barriers by about one order of magnitude. The calculated capacities for the monovalent cations on Ti2N and Ti2NT2 are close to that of the conventional graphite anode in lithium-ion batteries. In comparison, the capacities for Mg2+ on Ti2N and Ti2NT2 are more than 2000 mAh g-1 due to the two-electron reaction and multilayer adsorption of Mg2+. Comparison of the electrochemical performances of Ti2N and Ti2C suggests that Ti2N is a more promising anode material than Ti2C due to its lower diffusion barriers for various cations.

1. Introduction Li-ion batteries have gained widespread interest in recent years due to the growing demand for portable electronics, electric vehicles, and grid-level energy storage. Nevertheless, their drawbacks, such as cost and safety issues, as well as highly localized natural resources of lithium justify exploration of alternatives to Li-ion batteries, in which Li is substituted by other metal species. This is an important area of research and development for the next-generation rechargeable batteries. Compared to the lithium element, sodium, potassium, magnesium, calcium, and aluminum are much more abundant in the earth's crust and easily available almost everywhere. Therefore, rechargeable batteries that include reversible storage/release of these


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metal ions have received much attention. A bottleneck for the development of these batteries is a limited choice of suitable cathode and anode materials that exhibit satisfactory battery performance. Two-dimensional (2D) materials including graphene1,2 and transition metal dichalcogenides3–6 have attracted much attention for use in electrochemical energy storage, especially in Li- and Naion batteries. Graphene is not an ideal Li+ or Na+ storage material because of its relatively low volumetric energy density and large initial irreversible capacity7. It is more frequently used as a conductive additive that can significantly improve the electronic conductivity of the electrode. Transition metal dichalcogenides such as MoS2 have a large theoretical capacity. However, the intrinsically low electronic conductivity of these semiconducting materials seriously limits their electrochemical performances3. 2D carbides and nitrides of transition metals with a general formula MnXn-1, where “M” represents an early transition metal and “X” represents C and/or N, 8–11

have metalling conductivity and are promising materials for electrochemical energy

storage12. Depending on the value of n, the M2X, M3X2, and M4X3 phases are usually referred to as the 21-, 32-, and 43-MXenes, respectively. As the synthesis of MXenes is usually performed in aqueous solutions containing fluoride ions, the transitional metal atoms on the surface of the monolayers are initially terminated with O, OH or F.10,13 Most MXenes are good electronic conductors making these materials very promising for electrochemical energy storage.14,15 Tang et al. predicted the Li+ ion storage in Ti3C2 and Ti3C2T2 (T = F, OH) by first-principles calculations. 16 The prediction was proved experimentally and Ti3C2Tx nanosheets could deliver a Li+ ion capacity up to 410 mAh g-1 with good rate capability10, and the values exceeding 700 mAh g-1 were reported from porous Ti3C2Tx after precycling17. Then, Lukatskaya et al. showed that Ti3C2Tx could accommodate a variety of cations including Li+, Na+, K+, NH4+, Mg2+ and


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Al3+, resulting in a large volumetric capacitance.18 Later, Xie et al. studied the energy storage of these mono- and multivalenet cations on bare and terminated MXene monolayers by firstprinciples calculations and revealed the cation storage mechanisms of MXenes on the atomic scale.19 About 20 MXenes have been prepared so far, including Ti3C2, Nb2C, Ti2C, V2C, Ta4C3, Nb4C3, (V0.5Cr0.5)3C2, Mo2C, (Ti0.5Nb0.5)2C, and Ti3CN 12,13,20–26. Compared with the carbide and carbonitride MXenes, there has been little progress in the preparation of nitride MXenes. To date, only Ti4N3 has been synthesized from Ti4AlN327, but alternative methods for synthesis of 2D nitrides are being developed28. The synthesis difficulty of nitride MXenes is likely due to the high formation energies of Mn+1Nn. This implies that the A atoms (Al and other) in Mn+1ANn MAX phase precursors are strongly bonded and thus high energy is required to break this bonding. Additionally, the low cohesive energy of Mn+1Nn indicates that the product after selective removal may be dissolved in presence of HF acid27. Because of the significant challenges of material preparation, there are few experimental studies of physical and electrochemical properties of 2D metal nitrides in general, but major efforts are underway. Recently, Pan has studied the electronic properties and Li storage properties of a series of nitride Mxene monolayers (Mi+1Ni, M = Ta, Ti, V, n = 1, 2). It shows that Li can be bonded to Ti2N monolayer with a moderate binding energy and a low diffusion barrier. The functionalized Ti2NT2 (T=O, F, OH) monolayers show inferior Li storage properties comparing to pure Ti2N 29. To obtain a detailed theoretical understanding of the basic properties and potential applications of nitride MXene in lithium-ion and beyond-lithium-ion batteries, we carried out a detailed computational study of the electrochemical properties of a Ti2N monolayer with a bare surface and terminated by O, F, and OH. The electrochemical performances of the materials including


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the electrode kinetic properties, maximum capacities, and open circuit potential were predicated by first-principles calculations for a variety of mono- and multivalent cations (Cat: Li+, Na+, K+, Mg2+, Ca2+ and Al3+). Finally, we compared the electrochemical properties of Ti2N with its carbide counterpart Ti2C. The results suggest that the nitride MXene Ti2N may be a more promising anode material for Li-ion and beyond-lithium-ion batteries. Particularly, when used in Mg-ion batteries, this material may provide a large theoretical capacity and high-rate capability. 2. Computational methods First-principles calculations were performed in the framework of density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP)30. The projector augmented wave (PAW)31 potential was used with a plane-wave cutoff energy of 600 eV which is enough for convergence of energy. The exchange correlation energy was described by the generalized gradient approximation (GGA) in the scheme proposed by Perdew-Burke-Ernzerhof (PBE)32. The pseudopotentials utilized the valence state 2s12p0 for Li, 3s13p0 for Na , 3s23p64s1 for K , 3s23p0 for Mg , 3p63d04s2for Ca, 3s23p1 for Al, 3d34s1 for Ti, 2s22p3 for N, 2s22p5 for F, 1s1 for H, and 2s22p4 for O. For geometry optimization, the Brillouin-zone integration was performed using a regular Γ centered 13 × 13 × 1 k-mesh and a denser 19 × 19 × 2 MP mesh for the density of states (DOS) calculations within the Monkhorst-Pack scheme33. Considering the strong correlation in titanium element, electronic structure calculations were performed by using a GGA plus Hubbard U (GGA+U) method34. Several U values, i.e. 2.535, 4.236,37, and 6 eV have been tested all of which result in consistent results. In this study, we used U = 4.2 whose efficacy has been proven in the Ti-based MXene Ti3C236. Moreover, pre-examination showed that spinorbital coupling (SOC) has slight influence on calculation results; therefore SOC was not used in our calculations because of its high computation cost. To avoid any interaction due to the use of


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periodic boundary conditions, a vacuum separation between two neighboring monolayers was set to more than 20 Å. The geometry optimizations were performed by using the conjugated gradient method, and the convergence threshold was set to be 1 × 10−5 eV/atom in energy and 0.01 eV/Å in force. Spin alignments were studied by spin-polarized calculations. To investigate the dynamical stability of the Ti2N monolayer, the phonon spectra were calculated using the PHONOPY package38. To simulate adsorption and diffusion of the metal cations (Li+, Na+, K+, Mg2+, Ca2+, and Al3+) on the Ti2N and Ti2NT2 (T = O, F, OH) monolayers, a 3 × 3 × 1 supercell containing one adsorbed cation was used. The PBE-D2 method39, which introduces empirical dispersion corrections implemented by Grimme, was incorporated in the calculations. Furthermore, in analyzing cation diffusion on the monolayers, the climbing-image nudged elastic band (CI-NEB) method was used40. For the diffusion of a single atom on a supercell, we used seven images including the initial and the final positions for CI-NEB calculations. For optimization, each image searched its lowest potential along the diffusion pathway, and the image with the highest energy was driven up to the saddle point. The energy difference between this image (saddle point) and the initial image was defined as the diffusion barrier. The force convergence criterion for the optimization was set as 0.01 eV/Å. 3 Results and discussion 3.1 Structure and electronic properties of the Ti2N and Ti2NT2 monolayers


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Figure 1. (a) Side and top views of the Ti2N monolayer. a, b, and c represent the possible adsorption sites for guest atoms. (b) Schematic illustration of different magnetic configurations for the Ti2N monolayer: FM, AFM1, AFM2, and AFM3. (c-e) Side views of the optimized lattice structures for Ti2NO2, Ti2NF2, and Ti2N(OH)2, respectively. Ti2N has a hexagonal structure in which the N atoms are located between the Ti(1)-Ti(2) bilayer forming an edge-shared Ti6N octahedral as shown in Figure 1a. Because of the lack of experimental lattice parameters, the atomic model of bulk Ti2N was constructed by extracting Al from Ti2AlC, then structural optimization of Ti2N was performed using the structure parameters of Ti2C41,42. In addition to the ferromagnetic (FM) configuration, we considered three collinear anti-ferromagnetic (AFM) configurations, AFM1, AFM2, and AMF3, as shown in Figure 1b. Using the energy of the non-magnetic (NM) configuration as a reference, the relative energies for the FM, AFM1, AFM2, and AFM3 configurations were determined to be -0.269, -0.370, 0.360 and -0.219 eV per formula unit, respectively. Therefore, the AFM1 is the ground state of the Ti2N monolayer. The corresponding equilibrium lattice constant is 2.983 Å, the thickness of the Ti2N triple layers is 2.286 Å with a Ti-N bond length of 2.067 Å. These values are in good


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agreement with the previously reported theoretical results of Ti2N (values within a reasonable difference of 0.5 % ) 29.

Figure 2. Calculated phonon dispersion along the high symmetrical directions of the Brillouin zone (left) and the phonon PDOS (right) for Ti2N (a), Ti2NO2 (b), Ti2NF2 (c) and Ti2N(OH)2 (d) monolayers. In order to investigate the thermodynamic stability of the Ti2N monolayer, we compared the formation energies of the bulk and monolayer Ti2N MXenes with the most thermodynamically stable phase of Ti2N (SG136-Ti2N)43,44. The energy difference between the bulk Ti2N MXene and the SG136-Ti2N is +0.24 eV/atom. This indicates that the bulk Ti2N MXene is an allowable metastable phase45. By comparison, the energy difference between the Ti2N monolayer and the SG136-Ti2N is +0.68 eV/atom. The large energy difference indicates that exfoliation of a Ti2N monolayer from bulk Ti2N MXene is difficult. Because of the significant challenges in material preparation, few experimental studies have been conducted on 2D nitride MXenes, but major efforts are underway. Considering the high formation energy and low cohesive energy of nitride MXenes, we propose employing a high annealing temperature and a moderate acidic etchant for


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the preparation of nitride MXenes. This approach has produced the first nitride MXene Ti4N3 by our partner group.27 Next, the dynamical stability of Ti2N monolayer was investigated by performing lattice phonon calculations as shown in Figure 2a. No imaginary frequency phonon was found at any wave vector, and the optical and acoustical branches were well-separated. Near the Γ point, the two in-plane acoustic phonons exhibited linear dispersion, and the out-plane acoustic branch displayed quadratic dispersion, presenting a phonon dispersion characteristic of 2D materials46,47. In this respect, the given structure of the Ti2N monolayer is dynamically stable. The chemical exfoliation of MXene from MAX usually leaves some O, F and OH on the surface, and these groups may have significant effects on the electrochemical properties of the material48. In order to determine the preferential site of the terminated groups, total energy calculations were performed for the T (T = O, F, or OH) saturated Ti2N monolayers, i.e. Ti2NT2. There are three possible positions for T, on top of the Ti(1) atom (site “a”), on top of the N atom (site “b”), or on top of the Ti(2) atom (site “c”), as shown in Figure 1a. We considered four possible configurations for these terminated groups. In Mode I, the T groups are at site “a” on both sides of the monolayer, in Mode II, at site “b” on both sides of the monolayer, in Mode III, at site “c” on both sides of the monolayer, or in Mode IV, a mixture of Mode II and Mode III, one T is located at site “b” on one side and the other T is at site “c” of the other side. Note that combinations of Mode I/II and Mode I/III were not considered since Mode I is definitely excluded due to its much large total energy as will be shown below. Unlike the AFM ground state of the bare Ti2N, calculations showed that all Ti2NT2 monolayers are stabilized in the NM ground state. For the three Ti2NT2 phases, the Mode III has the lowest total energy. The energy of Mode III for Ti2NO2 is lower than that of Modes I, II, and IV by about 5.635, 1.306, and 0.571 eV, respectively. Similarly, for Ti2NF2, the energy of Mode III for Ti2NO2 is lower by about


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2.077, 0.767, and 0.498 eV, respectively, and for Ti2N(OH)2 by about 2.501, 0.254, and 0.254 eV, respectively. These results clearly show that the terminating T groups prefer site “c”, as shown in Figure 1c-1e. The lowest energy of Mode III is likely due to the steric repulsion between the X groups and the nearby N atoms, as observed for Ti2C, Hf2C, V2C, Nb2C, Zr2N, and Cr2N.19,49 Therefore, only Mode III as the most stable configuration was considered in the following calculations. It is also worth noting that the Ti-N bond was elongated to a different extent for different X groups, 2.149, 2.069, and 2.082 Å for Ti2NO2, Ti2NF2, and Ti2N(OH)2, respectively. Of these, the largest elongation, ~ 4 %, was observed for Ti2NO2. Moreover, lattice phonon calculations confirm dynamical stability of the Ti2NT2 (T = O, F, or OH) monolayers as shown in Figure 2b-d. Next, the electronic structures of the unmodified Ti2N and terminated Ti2NT2 were calculated as shown in Figure 3. The band structure of Ti2N under the AFM ground state shows a metal property in which the majority-spin and the minority-spin overlap and both become metallic with sizable electron states crossing the Fermi level. The main partial density of states (PDOS) of Ti2N can be divided into three regions as shown in Figure 3a. Region 1 indicates p-d hybridization of the N 2p and Ti 3d orbits corresponding to the strong interaction of the Ti-N bond. Regions 2 and 3 are mainly composed of Ti 3d electrons with a small contribution from N 2p. The states near the Fermi level are almost occupied by the Ti 3d electrons, indicating that the low-energy carriers originated from Ti. After terminated by O, F, and OH, the generated Ti2NT2 monolayers still maintain metallic properties that are similar to the bare Ti2N monolayer (Figure 3b-d). Compared with semiconducting or insulating transitionmetal oxides, the metallic character of the Ti2N and Ti2NT2 monolayers offers an intrinsic advantage in electronic conductivity, which may confer promising electronic and electrochemical properties for multiple applications.


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Figure 3. Electronic structure and PDOS for Ti2N (a), Ti2NO2 (b), Ti2NF2 (c), Ti2N(OH)2 (d). The Fermi level is set to zero. 3.2 Cation adsorption on the Ti2N and Ti2NT2 monolayers

Figure 4. The adsorption energies for metal species Cat (Cat = Li, Na, K, Mg, Ca, Al) on Ti2N (a) Ti2NO2 (b), Ti2NF2 (c), and Ti2N(OH)2 (d) at adsorption sites a, b, and c. In order to evaluate the storage properties of mono- and multivalent cations (Cat: Li+, Na+, K+, Mg2+, Ca2+, and Al3+) on Ti2N and Ti2NT2 monolayers, it is important to know the preferred adsorption sites of these cations. Since cation insertion into the interstitial cube-center sites can lead to significant volume expansion accompanied by the breakage of the Ti-N bond50, we only considered cation adsorption on the surface of the monolayers. Hence, a 3 × 3 × 1 supercell containing one adsorbed cation was used which was sufficiently large to avoid interaction


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between cations. This corresponds to the chemical compositions of Ti2NCat1/9 and Ti2NT2Cat1/9. The adsorption energy of guest cations on the monolayer was defined as: = / − / − c ,

(1)

where is the adsorption energy, / and / are the total energies of the Ti2N or Ti2NT2 supercells with and without adsorbed cations, respectively, and

represents the energy per atom in metal. The calculations used the body-centered cubic Bravais lattice for Li, Na and K; the primitive hexagonal Bravais lattice for Mg, and the face-centered Bravais lattice for Ca and Al. Figure 4 shows the calculated E values of different cations for the different adsorption sites of the Ti2N and Ti2NT2 (T=O, F, OH) monolayers. Almost all the investigated cations can be effectively adsorbed on the bare Ti2N monolayer as indicated by the negative values. The slightly positive produced by Al3+ might suggest that only a small amount of Al3+ (< 1/9 per formula unit) can be chemically adsorbed on Ti2N. The values become more negative if terminated with O, indicating that the chemical bond between the adsorbed cations and Ti2NO2 increases in strength. The calculations showed that the cation storage ability of Ti2N was weakened when the monolayer was instead terminated by F or OH. Only the alkali cations Li+, Na+ and K+ can be adsorbed on Ti2NF2, but no cations can be adsorbed on Ti2N(OH)2, as observed for Nb2C(OH)251. For each cation specie, the “b” site always exhibits slightly smaller adsorption energy than the other sites. Overall, adsorption directly above the N atoms is more favorable than the other potential positions. This may be due to Columbic attraction between the N atoms and the adsorbed cations. To obtain greater insight into the adsorption process, we performed Bader charge analysis on the monolayers. Using Ti2NO2Cat1/9 as an example, we found that Li, Na, and K can transfer 0.887, 0.870, and 0.903 e/atom, respectively, to their surrounding atoms. This demonstrates that the adsorbed cations are


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chemically bonded with the monolayers. Compared with alkali cations, the multivalent ions can transfer more than one electrons, 1.637 (for Mg), 1.527 (for Ca), and 1.750 (for Al) e/atom. 3.3 Ion diffusion on the Ti2N and Ti2NT2 monolayers

Figure 5. Schematic representation of the considered migration pathways for metal atom diffusion on the Ti2N monolayer.

Figure 6. Diffusion barrier profiles of Li (a), Na (b), K (c), Mg (d) and Ca (e) on the Ti2N monolayer. The charge/discharge rate capability of rechargeable batteries is determined by the kinetics properties of the electrode for both electron transport and ion diffusion. The intrinsic metallic behavior of Ti2N and Ti2NT2 ensures high electronic conductivity of the electrodes. In this section, we studied the diffusion properties of the adsorbed cations on the surface of the Ti2N and Ti2NT2 monolayers. Based on the above analysis, only processes with negative adsorption


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energies ( ) were considered and the most favorable adsorption site was set as “b”. We predesigned three possible diffusion pathways between two neighboring adsorption sites, as shown in Figure 5. For Path 1, the cations migrate from one “b” site to the nearest “b’” site across a “c” site, i.e. b → c → b’. As for Ti2NT2, the nearest “c” site is occupied by T. In this case, the cations must cross the top T atoms. In Path 2, the cations move from one “b” site to the nearest “b’” site across an “a” site, i.e. b →a → b’. For Path 3, the cations are allowed to move directly to the nearest neighboring “b’” site, i.e. b → b’. The diffusion barrier profiles of the bare Ti2N monolayer for the three different pathways are displayed in Figure 6. For all cations, Path 2 showed the largest diffusion barrier with only one saddle point on top of Ti(1). This can be ascribed to the strong Columbic interaction between cations and Ti(1) due to the short Cat-Ti(1) distance. In comparison, the energy barrier along Path 1 is significantly smaller than that of Path 2. Except for K+ adsorption, a local energy minimum is observed at the intermediate site “a”, and two saddle points are observed in the middle of the b-a and the a-b’ bridges. The single saddle point obtained for K+ could be ascribed to the long vertical distance (3.092 Å) from K+ to the monolayer, resulting in only weak interaction between K+ and Ti2N. In comparison, the vertical distances between Ti2N and the other cations are much shorter, 2.31 Å for Li+, 2.62 Å for Na+, 2.27 Å for Mg2+, and 2.57 Å for Ca2+. The calculated diffusion barrier along Path 1 is 21.5 meV for Li+, 14.0 meV for Na+, 7.0 meV for K+, 75.9 meV for Mg2+, and 38.0 meV for Ca2+. The obtained diffusion barrier for Li+ is a little bit larger than that of 17 meV reported by Pan

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.

Therefore, the diffusion barrier in Ti2N monolayer follows the following sequence from lowest to highest: K+ < Na+ < Li+ < Ca2+ < Mg2+. Path 3 shows diffusion barrier profiles that are very similar to those of the Path 1. This indicates that the cations do not follow the predesigned linear


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b → b’ pathway, but instead behave similarly to those in the optimized Path 1, as demonstrated for Li+ adsorption on Ti3C216.

Figure 7. Diffusion barrier profiles for the three paths for Li (a), Na (b), K (c), Mg (d), Ca (e) and Al (f) on the Ti2NO2 monolayer.

Figure 8. Diffusion barrier profiles for the three paths for Li (a), Na (b) and K (c) on the Ti2NF2 monolayer. Figures 7 and 8 show the diffusion barrier profiles of different cations on the Ti2NO2 and Ti2NF2 monolayers, respectively. Unlike for the Ti2N monolayer, the diffusion along Path 1 is the most difficult for Ti2NO2 and Ti2NF2. In these terminated Ti2N monolayers, the “c” site is occupied by O or F, and in order to cross the terminating O or F atoms, the cations must overcome the strong Columbic interaction from O or F, which creates a significant diffusion barrier. In addition, the diffusion length is prolonged relative to that of bare Ti2N. For example, the total Li+ diffusion length in Ti2NO2 along Path 1 is 3.594 Å, but the corresponding diffusion


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length for bare Ti2N is 3.454 Å. Based on the calculations, the most favorable diffusion pathway for Ti2NO2 and Ti2NF2 is Path 2. Like for Ti2N, the cations do not migrate along the predesigned Path 3, but behave more similarly to the behavior of the optimized Path 2. The minimum diffusion barriers on the Ti2NO2 monolayer are 249.6 meV for Li+, 184.9 meV for Na+, 97.0 meV for K+, 722.4 meV for Mg2+, 526.8 meV for Ca2+, and 354.0 meV for Al2+. Again, K+ adsorption has the lowest diffusion barrier. For Ti2NF2, the minimum diffusion barriers are 278.8 meV for Li+, 186.7 meV for Na+, and 93.5 meV for K+, similar to those obtained for Ti2NO2. These diffusion barriers for Ti2NO2 and Ti2NF2 are at least ten times larger than those for the bare Ti2N. This indicates that the rate capability of bare Ti2N should be much better than the rate capabilities of the terminated Ti2NT2. The large cation diffusion barriers for Ti2NO2 and Ti2NF2 are likely ascribed to the steric hindrance induced by the surface F- and O- terminated groups16. 3.4 Storage capacities and open circuit voltage of the Ti2N and Ti2NT2 monolayers

Figure 9. The adsorption energies of different adsorption layers on Ti2N (a) and Ti2NO2 (b). The intrinsic metallic conductivity and low diffusion barrier of Ti2N and Ti2NT2 demonstrate the excellent MXene electrode kinetics. In rechargeable batteries, specific capacity and working voltage are two important parameters that determine the energy density of the batteries. The charge-discharge process of Ti2N and Ti2NT2 can be described as the following half-cell reaction vs. Cat/Catx+:


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Ti NTi NO , Ti NF + cCat + cx! " ↔ Ti NTi NO , Ti NF Cat $

(2)

The difference in total energies before and after cations adsorption was used to determine the average open circuit voltage (OCV) of the battery. Here, the Gibbs free energy was approximately simplified into the internal energy change, because P∆V is only on the order of 105

eV and the entropy term (T∆S) is around 25 meV at room temperature

52

. The average open

circuit voltage (OCV) is expressed by +,- = ( . , / + c − .,/ )/cx!,

(3)

where . , / ， .,/ , and are the total energies of Ti2N[Ti2NO2, Ti2NF2], Ti2N[Ti2NO2, Ti2NF2]Catc and bulk metal, respectively. x represents the valence state of fully ionized cations from electrolyte

53

. For example, x = 1 for Li+, x = 2 for

Mg2+. To determine the concentration (c) of adsorbed cations, we first calculated the maximum storage capacity of different cations on Ti2N, Ti2NO2, and Ti2NF2. Based on the results of the above section, we placed the first cation layer at the most stable adsorption site, “b”. For the second adsorption layer, three high symmetrical sites including “a”, “b” and “c”, were all examined. The corresponding average layer-by-layer adsorption energy ( 01-2 ) is given by 01-2 = ., / 3 − . , / (345) − 2 ,

(4)

where . , / 3 and ., / (345) are the total energies of Ti2N[Ti2NO2, Ti2NF2] with n and n-1 layers, respectively. represents the energy per atom in bulk metal, and “2” represents two absorbed cations for each monolayer. Figure 9 shows the calculated 01-2 values for different cations on the Ti2N and Ti2NO2 monolayers. Note that full layer adsorption on Ti2NF2 produced a positive 01-2 , indicating that the cations were unable to entirely cover the first layer. Hence the results for Ti2NF2 are not presented in this work. For the first adsorption layer on Ti2N, the calculated 01-2 is -1.345 eV for Li+, -0.882


17


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eV for Na+, and -1.298 eV for Mg+, ensuring stable adsorption of the first layer. By comparison, the positive 01-2 values for K+ (1.314 eV) and Ca2+ (0.704 eV) indicates that these cations only partially cover the first layer. For the second layer, only Mg2+ shows a negative 01-2 of 0.175 eV, and Li+ and Na+ calculations produce a positive 01-2 of 0.049 eV and 0.261 eV, respectively. Further calculations showed that a slightly negative 01-2 of -0.007 eV could be still obtained up to four adsorption layers, demonstrating the strong adsorption ability of Mg2+. For Ti2NO2, we found that all the Li+, Na+, K+, Mg2+, Ca2+, and Al3+ cations can entirely cover the first layer, but only Mg2+ can achieve multilayer adsorption. The 01-2 values of the second and third Mg2+ adsorption layers are -0.252 and -0.074 eV, respectively. Calculations of adsorption energies (Ead) showed that the second-layer Mg cations locate at site “c” and the third-layer Mg cations locate at site “a”. CI-NEB analysis showed that the c → a → c’ path is favor to the second layer with a diffusion barrier about 70 meV for both Ti2N and Ti2NO2 monolayers. In comparison, the a → b → a’ path is favor to the third layer. The corresponding diffusion barrier is decreased to 40 meV for Ti2N and 24 meV for Ti2NO2.

Figure 10. Electron localization functions of the (110) slice of Ti2N with a single adsorption layer, corresponding to the stoichiometry of Ti2NCat2 (Cat = Li, Na, K, Mg, Ca). To gain deeper insight into the diverse adsorption behaviors of different cations, we analyzed the charge distributions of Ti2N with one or two adsorption layers by electron localization


18

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functions (ELF). Figure 10 shows the ELF of the (110) slice of Ti2NCat2 (Cat = Li, Na, K, Mg, and Ca). The ELF refers to the jellium-like homogeneous electron gas and renormalizes the value to between 0.00 and 1.00. The values of 1.00 and 0.50 correspond to fully localized and fully delocalized electrons, respectively, while the value 0.00 refers to very low charge density.54,55 For Li, Na, and Mg, the electrons are spread out in the Cat layer forming a negative electron cloud (NEC). NEC can screen the repulsion between the positive metal ions (Cat-Cat and Cat-Ti), therefore acting to stabilize the adsorption layer

19

. In contrast, there are very few

NEC in the Ca layer of Ti2NCa2, and almost no NEC is found in the K layer of Ti2NK2. This causes strong repulsion between the K+ (or Ca2+) cations, resulting in a positive E 01-2 . To reduce the repulsive interaction, a long K-K (or Ca-Ca) distance is required. Thus requires that some adsorption sites remain unoccupied, resulting in partial coverage of the adsorption layer as in the Ti2NK1/9 composition discussed above. Figure 11 shows the ELF isosurface (0.5) of the (110) slice of Ti2NCat4 (Cat = Li, Na, and Mg). We can see that both the first and second Mg layers of Ti2NMg4 are surrounded by NEC, confirming that two layers of Mg2+ can be effectively adsorbed on the Ti2N monolayer. The second adsorption layer of Ti2NLi4 (or Ti2NNa4) is also surrounded by NEC. However, there is almost no NEC in the first adsorption layer. Thus, the Ti2NLi4 and Ti2NNa4 phases are unstable due to strong repulsive interactions in the first adsorption layer, which results in the positive 01-2 values of Ti2NLi4 (or Ti2NNa4).


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Figure 11. Electron localization function isosurface (0.5) of the (110) slice of Ti2N with two adsorption layers, corresponding to the stoichiometry of Ti2NCat4 (Cat = Li, Na, Mg). According to the above discussion, the adsorption capacities were estimated from 78 = cxF⁄9 . , / , (5) where c is the number of adsorbed cations, x represents the valence state of fully ionized cations from electrolyte

53

. F is the Faraday constant (26801 mAh/mol), and 9 ., / is the

molar weight of Ti2N and Ti2NT2. Table 1 shows the calculated storage capacities of different cations on Ti2N, Ti2NO2, Ti2NF2, and Ti2NOH2 monolayers. Note that for ions coverage below 1/16, the theoretical capacity was set as “--” because such a small capacity makes no sense for practical uses. For Ti2N, we considered one-layer adsorption (c = 2) for Li+ and Na+ and threelayer adsorption (c = 6) for Mg2+. Only partial-layer adsorption was allowed for K+ (c = 1), Ca2+ (c = 1), and Al3+ (c = 1/16). For Ti2NO2, we considered one-layer adsorption for Li+, Na+, K+, Ca2+, and Al3+, and three-layer adsorption for Mg2+. For Ti2NF2, partial-layer adsorption was allowed for all cations, that is, c = 1/2 for Li+, c = 1 for Na+ and K+, and c < 1/16 for Mg2+, Ca2+ and Al3+. For Ti2N(OH)2, only a small ions coverage ( c < 1/16) was allowed for all cations. The results show that only the Ti2N and Ti2NO2 monolayers are suitable for practical uses for ions adsorption. The theoretical capacities of multivalent cations are obviously larger than those of monovalent cations because they can carry more charges. The calculated capacities of monovalent cations are close to those of the conventional graphite anode used in Li-ion batteries. However, the capacities of multivalent cations stand out. For example, the calculated Mg2+ capacity for Ti2NO2 is very close to the theoretical capacity of metallic Mg (2205 mAh g-1). While, the bare Ti2N monolayer could accommodate an even larger Mg2+ capacity of 2930 mAh g-1. This is not surprising considering that theoretical capacity is inversely proportional to the


20

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formula weight of an active material. Up to 6 mol Mg2+ can be adsorbed on one mol of Ti2N (formula weight: ~ 110) under the multilayer adsorption mechanism. In comparison, only one mol Mg2+ could deposit on metallic Mg (formula weight: 24.3). Here, it is notable that the predicted capacities generally overestimate the experimentally determined capacities. For example, it has been reported that the theoretical Li+ capacity of Ti3C2 monolayer is 447.8 mAh g-1.56 But a smaller experimental capacity of ~ 410 mAh g-1 was obtained for the few-layered Ti3C2 nanosheets.10 These overestimated capacities could be attributed to multiple reasons, such as defects in the monolayer, stacking of the monolayers, side reactions between the electrode and the electrolyte, and these factors may not have been considered in DFT calculations. Table 1. Calculated storage capacities of different cations on Ti2N, Ti2NO2, Ti2NF2, and Ti2N(OH)2 monolayers (unit: mAh g-1). Metal ions Ti2N

Ti2NO2

Ti2NF2

Ti2N(OH)2

Li+

484

378

90

--

Na+

484

378

181

--

K+

242

378

181

--

Mg2+

2930

2269

--

--

Ca2+

488

756

--

--

Al3+

45

1134

--

--

Finally, we calculated the average OCVs of the fully covered monolayers based on Equation (2). The average OCVs of Ti2NLi2, Ti2NNa2, and Ti2NMg6 were 0.67, 0.44, and 0.13 V, respectively. In comparison, the average OCVs of Ti2NO2Li2, Ti2NO2Na2, Ti2NO2K2, Ti2NO2Mg6, Ti2NO2Ca2, and Ti2NO2Al2 were 1.00, 0.85, 2.39, 0.10, 0.14, and 0.09 V, respectively. Obviously, the O atoms slightly increased the OCV of the monolayer due to the


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increased adsorption energy. However, the calculated OCVs are rather low, suggesting that these Ti2N monolayers are suitable as an anode material for rechargeable batteries. The Ti2NO2K2 shows a much larger OCV. This exception may be attributed to a much stronger adsorption energy of K+ on the Ti2NO2 monolayers, as indicated in Figure 9. 3.5 Comparison between Ti2N and Ti2C

Figure 12. Electron localization function isosurface (0.5) of Ti2C and Ti2N monolayers. Rate capability is one of the most important performance factors for rechargeable batteries. The small theoretical diffusion barriers for various mono- and multivalent cations on bare Ti2N indicate that this nitride MXene is capable of excellent rate capability in lithium-ion and beyondlithium-ion batteries. For instance, the calculated Li+ diffusion barrier on Ti2N, 21.5 meV, is much smaller that those of other 2D energy storage materials, such as 250 meV for MoS257, 220 meV for VS257, 330 meV for graphene58, and 84 meV for black phosphor59. This suggests the Ti2N monolayer could be used as a high performance anode material for Li-ion batteries like carbide MXenes such as Sc2C, Ti2C, Nb2C, and V2C.60 Therefore, it is worthwhile to perform a comparison study on the kinetic properties of nitride MXene (Ti2N) and carbide MXene (Ti2C). Total energy calculations showed that the AFM1 configuration is also the ground state of Ti2C. Similarly, we calculated the diffusion barriers of different cations on a Ti2C monolayer along the b → c → b’ pathway, which are 36.1 meV for Li+, 23.1 meV for Na+, 5.8 meV for K+, 92.4 meV for Mg2+, and 49.0 meV for Ca2+. The diffusion barriers of all metal cations except K+ were larger than those of Ti2N by 9~17 meV. To better understand the improved diffusion kinetics of


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Ti2N, we compared the ELFs isosurface (0.5) of Ti2N and Ti2C monolayers as shown in Figure 12. Both Ti2N and Ti2C have nonbonding electrons above the Ti layer that form apparent NECs. These NECs do not entirely cover the Ti layer but distribute regularly in different ways. An inverted triangular pyramid-like NEC is located on the top of site “c” of the Ti2C monolayer, and the NEC forms a mesh structure on the Ti2N monolayer. As the N atom (2s22p3) possesses one more 2p electron compared to the C atom (2s22p2), the N atom requires less electrons from Ti to form an ionic bond. As a result, the Ti atom of Ti2N leaves more nonbonding electrons on the surface to form a larger NEC. The larger NEC could weaken the repulsion interaction between the adsorbed cations and the Ti atom, thus facilitating the diffusion of adsorbed cations. Thus, the low diffusion barrier of Ti2N can improve the kinetic properties of the nitride MXene, resulting in excellent rate capability for use as an anode material in rechargeable batteries. 4 Conclusions We performed a systematic computational investigation on the electrochemical performances of the 2D Ti2N monolayer and its terminated derivatives Ti2NT2 (T = O, F and OH) in rechargeable batteries. First-principles calculations demonstrated that the Ti2N monolayer is not only thermally and dynamically stable, but also exhibits exceptional metallic behavior. This ensures high structural stability and large electronic conductivity of the materials when they are used in rechargeable batteries. By calculation of the adsorption energy of different cations including Li+, Na+, K+, Mg2+, Ca2+, and Al3+, we confirmed that the storage capacity of Ti2N would be obviously reduced with presence of F or OH on its surface. Therefore, a post-annealing process on the exfoliated Ti2N should be used to eliminate these harmful groups. The most energetically favorable adsorption site for guest cations is predicted at the top of the N atoms. For bare Ti2N, the cations tend to migrate on the monolayer via the top of the Ti(2) atom, but for


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Ti2NT2, the cations prefer to migrate via the top of the Ti(1) atom. The diffusion barriers on bare Ti2N are very small, and possibly the lowest values of all state-of-the-art two-dimensional energy storage materials. The functional groups on Ti2NT2 increase the diffusion barriers by about an order of magnitude, but keep them in the same range or below graphene and TMDs. Due to the low open circuit voltage, Ti2N and Ti2NO2 could be used as an anode material for rechargeable batteries. The calculated low diffusion barriers and large capacities for the above mentioned mono- and multivalent cations imply that these monolayers can be used in different rechargeable batteries. Especially, the material exhibited a Mg2+ ion capacity of more than 2000 mAh g-1 due to the two-electron reaction and the unique multi-layer adsorption behavior. This suggests a possibility to replace the metallic Mg anode used in traditional Mg-ion batteries. Based on a comparison study, we demonstrated that Ti2N is better than Ti2C for energy storage uses due to the low diffusion barrier of Ti2N. This is encouraging for expanded application of nitride MXenes in lithium-ion and beyond-lithium-ion batteries. Considering the high formation energy and low cohesive energy of nitride MXenes, a high annealing temperature and a moderate acidic etchant are preferred for preparation of nitride MXenes. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]; [email protected]; [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. These authors contributed equally. ACKNOWLEDGMENT


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This work was supported by the Ministry of Science and Technology of China (No. 2015CB251103), the National Natural Science Foundation of China (No. 51472104, and 21473075), and the One Thousand Talents Recruitment Program of Foreign Experts. The calculations were carried out in Tianjin national supercomputer center. REFERENCES (1)

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First-Principles Calculations of Ti 2 N and Ti 2 NT 2 ... - ACS Publications

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