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Article

Atomic Vacancy Defect, Frenkel Defect and Transition Metals (Sc, V, Zr) Doping in Ti4N3 MXene Nanosheet: A First-Principles Investigation

by
Tingyan Zhou
1,2,
Wan Zhao
3,
Kun Yang
2,
Qian Yao
1,
Yangjun Li
2,
Bo Wu
2,4 and
Jun Liu
1,*
1
School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2
School of Physics and Electronic Science, Zunyi Normal University, Zunyi 563006, China
3
School of Physics, Beijing Institute of Technology, Beijing 100081, China
4
School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2020, 10(7), 2450; https://doi.org/10.3390/app10072450
Submission received: 8 March 2020 / Revised: 27 March 2020 / Accepted: 31 March 2020 / Published: 3 April 2020
Browse Figures
Versions Notes

Abstract

:
Using first-principles calculations based on the density functional theory, the effects of atomic vacancy defect, Frenkel-type defect and transition metal Z (Z = Sc, V and Zr) doping on magnetic and electric properties of the Ti4N3 MXene nanosheet were investigated comprehensively. The surface Ti and subsurface N atomic vacancies are both energetically stable based on the calculated binding energy and formation energy. In addition, the former appears easier than the latter. They can both enhance the magnetism of the Ti4N3 nanosheet. For atom-swapped disordering, the surface Ti-N swapped disordering is unstable, and then the Frenkel-type defect will happen. In the Frenkel-type defect system, the total magnetic moment decreases due to the enhancement of indirect magnetic exchange between surface Ti atoms bridged by the N atom. A relatively high spin polarizability of approximately 70% was detected. Furthermore, the doping effects of transition metal Z (Z = Sc, V and Zr) on Ti4N3 nanosheet are explored. All doped systems are structurally stable and have relatively large magnetism, which is mainly induced by the directed magnetic exchange between surface Z and Ti atoms. Especially in the doped Ti4N3-Sc system, the high spin polarizability is still reserved, suggesting that this doped system can be a potential candidate for application in spintronics.

1. Introduction

Graphene was discovered in 2004, breaking the classical theory that thermodynamic fluctuations do not happen in any two-dimensional (2D) crystal at a finite temperature [1,2]. Graphene had shown many excellent physical and chemical properties into wide material applications, such as big specific surface area is (2630 m2/g) [3], high electron mobility (1.5 × 105 cm2/v·s) [4], good thermal conductivity (5000 W/m·K) [5], high Young’s modulus (1.0 TPa) [6] and visible light transmittance (approximately 97.7%) [7]. However, the zero-band gap of graphene limits its application in the field of electronic devices, leading to a series of studies on graphene-like 2D materials [8], such as hexagonal boron nitride, transition metal sulfur compounds, transition metal oxides, black phosphorus and various MXenes. Many graphene-like materials making up for the inadequacy of graphene materials showed better physical and chemical properties, and then were applied in optoelectronics, spintronics, catalysis, biological and chemical sensors, lithium/sodium ion batteries, supercapacitors, fuel cells, polymer composite materials and other fields [9].
MXene is a new kind of graphene-like nanosheet, which is composed of transition metals and carbon/carbonitride/nitride compounds. In 2011, the Gogotsi used HF acid to selectively etch the Al atomic layer of ternary-layered carbide material Ti3AlC2 to obtain Ti3C2Tx (Tx stands for the surface terminations, for example, hydroxyl, oxygen or fluorine) [10]. Ti3AlC2 is a MAX phase material, namely a typical ternary-layered ceramic. Generally, they may be shown as Mn+1AXn, M meaning the early transition metal, such as Sc, Ti, V, Zr, Hf, Nb, Ta, Cr and Mo, A meaning the main group 13–14 elements in the periodic table, such as Al, Si, P, S, Ga, As, In and Sn and X meaning C or N. n is generally 1, 2 or 3 [11]. Ti3C2Tx has the precursor MAX structure and its properties are similar to the graphene. Thus, it was named MXene. The graphene-like MXene nanosheet may be shown as Mn+1XnTx, where Tx is the functional group attached to the surface of MXene, such as -O, -OH and -F. M2XTx, M3X2Tx and M4X3Tx structures for n = 1, 2 and 3, respectively, had been created [12]. Recently, the (M′M′)n+1XnTx structure was found, meaning that M may also be composed of two transition metal elements [13]. Currently, more than 70 precursors of MAX phase have been reported, and an increasing number of graphene-like MXene nanosheets have been experimentally fabricated, including Ti3C2, Ti2C, Nb2C, V2C, (Ti0.5,Nb0.5)2C, (V0.5, Cr0.5)3C2, Ti3CN, Ta4C3, Ti4N3, etc. [14]. Ti4N3 nanosheet is one of the first nitrogen series of MXene obtained experimentally [15]. The graphene-like MXene nanosheet family with the unique hexagonal lattice and symmetry group P63/mmc structure have metallicity, but they have many advantages of a ceramic material. A covalent bond exists between M-X ion atoms-mixed valence metallic bonding in MXene, whereas only a C–C bond exists in graphene. The graphene-like MXene nanosheet had been predicted to have more adjustable performances than the graphene [16]. Therefore, the graphene-like MXene nanosheet has a broad application prospect in transparent conductive film, supercapacitors, polymer reinforcement phase, purifying agent, field effect tube, hybrid nanocomposite and electromagnetic shielding [17]. They may be also used widely in many areas such as electronic devices [18], optical devices [19], magnetic materials [20,21,22,23,24], thermoelectric materials [25,26,27,28] and biosensors [29].
The miniaturization and portability of modern electronic devices has put forward higher requirements about the magnetism of electronic materials. As emerging materials at present, 2D materials have become the focus of experimental and theoretical research [30,31,32]. However, most 2D materials themselves are non-magnetic. How to induce and regulate magnetism in 2D non-magnetic materials is increasingly becoming the focus of research [33]. On the other hand, prepared materials always have defects such as atomic disorder, swap, vacancy and impurity. They all cause important influences on the electronic structure, and then magnetic and optical properties of 2D materials [34,35]. The doping of elements B and V on different positions of the Ti2C MXene nanosheet had resulted in great changes in the electronic structure, and then magnetic properties of this nanosheet so that some novel semiconductor properties were added [36]. Similar magnetic behavior had been also observed in different MXene decorated by some functional groups. For examples, Cr2C is a half-metallic ferromagnetic. However, with F, Cl, OH or H functionalization, Cr2C is transformed as the antiferromagnetic semiconductor [37]. The antiferromagnetic metal Cr2N becomes a stable ferromagnetic semi-metal under the action of O functional groups [38]. Cr2TiC2O2 is nonmagnetic, whereas Cr2TiC2F2 and Cr2TiC2(OH)2 are antiferromagnetic, but Cr2VC2(OH)2, Cr2VC2F2 and Cr2VC2O2 are ferromagnetic [39]. Few research had been carried on the surface doping and defects. The influence of point defects on the electronic structure, formation energy and magnetism of Ti2XT2 (X = C/N, T = OH, F, O) had been studied. Results showed that small quantities of point defects might cause much variation of magnetic and electronic properties in the above material [40]. Therefore, although the defect has not become the research focus of new materials, it is still urgent to carry on the defect research for ensuring the practical application of 2D MXene materials in spintronic devices.
M4X3 (M meaning the transition metal element and X meaning C/N) MXene nanosheet is an ordinary 2D material in the MXene family. It has a large atomic layer thickness (seven layers, with a thickness greater than 7 Å), and a complex structure comprising overlapping and staggered layers. Furthermore, the Ti4N3 nanosheet is the first prepared N-based MXene and it has an intrinsic magnetic moment, which is weak, and then may be eliminated by surface functional groups [15]. In this paper, to understand influences of the atomic defect, swap disordering and vacancy on the structural, magnetic and electronic properties of 2D MXene material, the Ti4N3 MXene nanosheet was investigated. The structure, electronic properties, and magnetism of Ti4N3 nanosheet without functional groups were analyzed firstly. Subsequently the Ti or N vacancy defect was investigated for the surface or subsurface layer of the Ti4N3 nanosheet. Secondly, a swap defect (named as Frenkel-type defect) between the N atom on the subsurface layer and Ti atom on the surface layer was studied. The structure change, electronic properties and magnetism of atoms around the defect atom were calculated and analyzed. In the end, the surface Ti atom of Ti4N3 nanosheet was replaced by Sc, V and Zr atoms, respectively. The effects of doping on the structure, electronic properties and magnetism of the atoms, and then the Ti4N3 nanosheet were discussed. We hope our results are useful to elucidating the various electronic and magnetic behaviors of 2D materials and the application research of new 2D Ti-based MXene nanosheet in spintronics.

2. Calculation Method

All calculations were performed using the Vienna ab initio simulation package (VASP) based on the density functional theory (DFT). The Perdew–Burke–Ernzerhof (PBE) exchange correlation function under the generalized gradient approximation (GGA) is used in calculations [41,42,43]. To treat the electron-ion properly, the interaction between the core electron and the valence electron is described by plane wave super-soft pseudopotential. Ti: 3d24s2, N: 2s22p3, Sc: 3d14s2, Zr: 4p64d25s2 and V: 3d34s2 valence electron configurations were specifically considered. In this work, a 3 × 3 × 1 supercell was used and spin polarization was selected for structural optimization and single point energy calculation.
In the self-consistent field calculation, a global convergence standard of 1 × 10−6 eV, cutoff energy of 500 eV, force per each atom of no more than 0.02 eV/Å, and 9 × 9 × 1 k-point grid precision and integral Brillouin zone were used. For structural optimization, the experimental lattice constant 2.991 Å of single Ti4N3 [44] was set as the initial value of Ti4N3 nanosheet. Then for defect and doping calculation, the optimized lattice constant of Ti4N3 nanosheet was selected as the initial value.

3. Results and Discussion

3.1. Structure, Electronic Properties and Magnetism of Ti4N3 Nanosheet

Ti4N3 nanosheet is experimentally prepared as the first N-based series MXene nanosheet [15] by melting fluoride salt in argon gas environment and the temperature was 550 °C. The nanosheet was etched away from Ti4AlN3 precursor powder layer. Figure 1 shows the construction processing of the Ti4N3 MXene nanosheet by etching off the Al atomic layer from the Ti4AlN3 bulk. The Ti4N3 nanosheet had a hexagonal structure with sandwich layers. The N atomic layer was sandwiched between the upper and lower Ti atomic layers. Each N atom was bonded with six nearest Ti atoms. Three Ti atoms were located on the upper layer and the other three Ti atoms were on the lower layer. The whole Ti4N3 nanosheet was composed of seven alternating layers of Ti and N layers. The structure was more complex than those of M3X2 and M2X. Therefore, we deduced that M4X3 had better physical and chemical properties than M3X2 and M2X.
In our work, the spin polarization was set for the structure optimization of Ti4N3 nanosheet. The optimized lattice constants a and c, bond length (dTix−Nx) and atomic layer thickness L are listed in Table 1 for comparing them with the structural parameters of the precursor Ti4AlN3 [44]. The structure parameters difference between Ti4N3 and Ti4AlN3 was relatively small. For the lattice constants, the error did not exceed 2%. This indicates that the Ti4N3 nanosheet was stable. There was no significant change between bonds due to etching, which also proves that the bond length of M-X is stronger than that of M-A [45].
Table 2 shows some structural parameters of Ti4N3 nanosheet. For simplicity, the surface Ti atom, the subsurface N atom, the next subsurface Ti atom and the central layer N atom are marked as Ti1, N2, Ti3 and N4, respectively. In Table 1, the bond lengths dTi1-N2 and dN2-Ti3 were different, which shows that N atoms were located in a distorted octahedron. This structure was similar to the Ti2NTx calculated by Arkamita Bandyopadhyay et al. [40], but it is different from the single-layer Ti4C3 nanosheet, which is a regular octahedral structure [46].
In order to discuss electronic and magnetic properties of the Ti4N3 nanosheet, the total magnetic moment of Ti4N3 nanosheet is calculated as 1.173 µB, which may be weakened, even eliminated by the action of the functional groups. This result accords with the conclusion that the magnetism may be removed by functionalization [47]. The atomic magnetic moment of Ti atoms on the surface and the next subsurface was 0.924 and 0.212 µB, respectively, whereas the atomic magnetic moment of the N atom on the subsurface and central layers were 0.030 and 0.010 µB, respectively. Therefore, the total magnetic moment was mainly contributed by the spin-polarized d-electrons of Ti atoms in the surface layer, which was similar to results in Reference [47], in which MXenes are magnetic and the magnetism is primarily due to surface Ti atoms.
In Figure 2, the total density of states (TDOS) and partial density of states (PDOS) are shown. From Figure 2, near the Fermi surface the spin-up channel had a large valley and the Fermi level was located at the valley bottom. However, for the spin-down band a relatively large peak crossed over the Fermi level. This results in a great spin-polarization (more than 80%) in the Ti4N3 nanosheet from the spin-polarizability Equation (1), where N↑ and N↓ were spin-up and spin-down TDOS at the Fermi level, respectively. Therefore, the Ti4N3 nanosheet might be a kind of candidate material in 2D spintronics because of its high spin polarizability [48].
P = N ↑ − N ↓ N ↑ + N ↓ × 100 % ,
From Figure 2, TDOS near the Fermi level mainly originated from the surface Ti atoms, meaning that localization of d-electrons of surface Ti atoms played an important role in magnetism. The main reason was that the strong direct exchange magnetic coupling caused a remarkable spin split of energy bands near the Fermi level. This finding is in agreement with the above mentioned discussion on the total magnetic moment. Furthermore, the subsurface N2 atom was also spin polarized, which was induced by the neighbor magnetic atoms. This means that the indirect magnetic exchange between Ti1 atoms on the surface and the next subsurface Ti2 atoms might be bridged by the N2 atoms on the subsurface. Such a layer interaction could help stabilizing the whole structure of the Ti4N3 nanosheet.

3.2. Atomic Vacancy Effect of Ti4N3 Nanosheet

The atomic vacancy defect is an ordinary phenomenon in 2D materials. In general, high proportion vacancy may destruct properties of materials. We focused on the atomic vacancy defect of the Ti4N3 nanosheet. In Figure 3, the structure of the surface Ti-vacancy (a) and subsurface N-vacancy (b), which are the two types of vacancy effects that possibly have a relatively great impact on Ti4N3 nanosheet, were described dramatically. Moreover, in Ti-vacancy and N-vacancy system (labeled as Ti4N3-Ti and Ti4N3-N, respectively) in Table 2, the lattice constants a, the atomic layer thickness L, the bond length d between the vacancy and its neighbor atoms, the binding energy Eb and the forming energy Eform, and the total magnetic moment Mtot of the Ti4N3-Ti, Ti4N3-N and Ti4N3 system are listed. As far as Ti-vacancy is concerned, a surface Ti atom had 3 neighbor N atoms and 4 neighbor Ti atoms in the Ti4N3 system respectively, as shown in Figure 3a. When a surface Ti atom was lost, the bond length between Ti-vacancy and its neighbor surface Ti or subsurface N atom (labeled as dv−Ti or dv−N) shrank compared with the Ti4N3 system. Therefore, the atomic layer thickness L decreased slightly. Atomic vacancy could cause the surrounding space to collapse in the same way as the atom vacancy in other materials. The magnetic moment of surface Ti atom near the vacancy increased, owing to the enhancement of localization of d-electrons of the Ti atom. Four coordination numbers between Ti-vacancy and its neighbor Ti atoms were lost. Thus, in the Ti4N3-Ti system, the total magnetic moment increased from 1.173 to 1.817 µB.
In the Ti4N3 system, a subsurface N atom had four neighboring N atoms and six neighboring Ti atoms. In Table 2, we could see that in the N-vacancy (Ti4N3-N) system, the bond length dv−N between the vacancy and its neighbor subsurface N atom in the subsurface layer shrank in comparison with the Ti4N3 system. The atomic layer thickness L was stretched slightly due to the fact that the bridging interaction between two Ti-atomic layers supplied by N atoms was weakened. The system looks fluffy. Moreover, when a subsurface N atom was replaced by vacancy, six coordination numbers between N-vacancy and its neighbor Ti atoms at surface or the next subsurface might be lost. These atoms near the N-vacancy were far from each other. In the Ti4N3 -N system, the total magnetic moment increased sharply to 2.373 µB.
In Table 2, the binding energies of Ti4N3, Ti4N3-Ti and Ti4N3-N systems are listed. The binding energy can be defined as follows [49]:
Eb = (Etot − nTiuTi − nNuN)/ntot,
where Etot is the total energy of the defective and ideal system, nTi, nN and ntot indicate the number of Ti, N and total atoms, respectively. uTi and uN are the chemical potential of Ti and N atoms, respectively. All the binding energies of Ti4N3, Ti4N3-Ti and Ti4N3-N systems have a negative value. This finding can indicate that all systems were stable in structure. The binding energy of the Ti4N3-N system was the largest, which implies that the system had lost N atoms and might become unstable. Moreover, in Table 2 the formation energy Eform [48] was calculated by the following formula:
Eform = Edef − Eid − Σniui
where Edef and Eid were the total energy of the defective and “ideal” system, ni is the number of removed or added atoms and ui is the chemical potential of the corresponding atoms. The positive formation energies imply that the “ideal” Ti4N3 system is more stable than the defective systems. A relatively small value in Ti4N3-Ti system indicates that eliminating a surface Ti atom is easier than losing a subsurface N atom.
In Figure 4, the total TDOS in a unit cell and PDOS of the neighbor Ti or N atom for Ti-vacancy and N-vacancy were plotted dramatically in Ti4N3-Ti and Ti4N3-N nanosheets. From Figure 4a, a relatively large spin-up peak appeared near the Fermi level in the Ti-vacancy system. The peak was mainly derived from spin-up d-orbitals of surface Ti neighboring vacancy. The high spin polarizability in Ti4N3 was damaged. The subsurface N atom and the next subsurface Ti atom underwent a little change owing to the missing surface Ti atom. For the N-vacancy system, as shown in Figure 4b, the TDOS near Fermi level was contributed by the surface or the next subsurface Ti. A spin polarizability of more than 50% was still detected. In the two atomic vacancy systems, the middle layer N atom was not polarized visibly.

3.3. Frenkel-Type Defects in Ti4N3 Nanosheet

Besides single atomic vacancy effects, atomic swap disordering effect, namely a potential atomic disordering phenomenon in 2D MXene materials, is also studied in this work. In Figure 5a, the surface Ti atom and its neighboring N atom at the subsurface layer were swapped. Unfortunately, such a Ti-N swapped structure was unstable, and then it would evolve into the configuration shown in Figure 5b after structure optimization. In Figure 5b, one of the N atoms at the subsurface moved to the hole-site of three surface Ti atoms in that the Ti-N bond moved from swapped atoms slides along the original crystalline direction to the surface of the 2D material. The disordering configuration shown in Figure 5b was called as a Frenkel-type defect. In the optimized Frenkel-type defect structure, the bond length of Ti-N was 1.896 Å, the lattice constant was 2.995 Å and the atomic layer thickness was 7.329 Å. Compared with the “ideal” Ti4N3 structure, the outer Ti-N bond was evidently decreased owing to surface effect. The whole system looked more relaxed.
Compared with the “ideal” Ti4N3 system, the outside N atom was shown to stick to the surface and exhibited a slightly inward contraction. However, for the whole system, the interlayer spacing increased, which was similar to the behavior of the N-vacancy system discussed above, which led to a decrease of the vacuum layer thickness. To focus on the structure stability of the disordering Ti4N3 nanosheet, the binding energy Eb and the forming energy Eform were calculated by the above mentioned formula. Results show that the Eb and Eform were equal to −1.300 and −0.347 eV, respectively. The negative value indicates that these Frenkel-type defects were more stable than the “ideal” Ti4N3 system. This result is not surprising, because most MXenes decorated by some functional groups are more stable [50]. The atomic magnetic moment in the Frenkel-type disordering structure was also calculated. The total magnetic moment decreased from 1.173 to 1.084 µB due to the enhancement of indirect magnetic exchange between surface Ti atoms bridged by the outside N atom.
More information on the electronic properties of Frenkel-type defective Ti4N3 nanosheet is needed. In Figure 6, the TDOS and the PDOS of the outside N and its neighbor Ti atom in Frenkel-type defect structure are given and are compared with the Ti4N3 configuration. The outer N was located at the hole-site of three surface Ti atoms, the surface Ti atom neighbor of the N atom would increase, and the spin split near the Fermi level in the defective structure would decrease. As a result, the high spin polarization in Ti4N3 nanosheet was reduced sharply. The contribution of surface Ti atoms to TDOS was most significant from surface Ti atomic PDOS. The outside N and subsurface N provided little support. In this Frenkel-type defective Ti4N3 nanosheet, we detected a relatively high spin polarization (approximately 70% can be retained). The spin-polarization ratio is described by the formula [48].

3.4. Doping Effects of Transition Metal Z (Z = Sc, V, Zr) on the Ti4N3 Nanosheet

Impurities in materials are unavoidable in the preparation process and can easily affect physical and chemical properties. We implemented a theoretical calculation to reveal the doping properties of transition metal Z (Z = Sc, V, Zr) on the Ti4N3 nanosheet. In Figure 7, a surface Ti atom was replaced by Sc, V and Zr, atoms in a Ti4N3 supercell to simulate possible doping behavior. Impurity atom concentration can be close to 2% in this 3 × 3 × 1 supercell. After geometrical optimization, the lattice constant a, bond length d, binding energy Eb, forming energy Eform, the neighbor Ti atomic magnetic moment of the doped atom MTi, atomic magnetic moment of Z atom MZ and total magnetic moment Mtot are listed in Table 3. The binding energy Eb is defined using the above formula. The formation energy Eform is defined as follows [51]:
E form = E T i 4 N 3 − Z − E T i 4 N 3 + n T i μ T i − n Z μ Z
where E T i 4 N 3 − Z are E T i 4 N 3 are total energies of doped Ti4N3-Z system and “ideal” Ti4N3 system, respectively. nZ or nTi is the number of Z or Ti atom. µTi or µZ is the chemical potential of Z or Ti atoms.
For the doped systems of Ti4N3-Z (Z = Sc, V, Zr), the calculated lattice barely changed, as shown by the comparison with the Ti4N3 nanosheet. In the Ti4N3-V system, the thickness of layer L tended to extend, whereas the bond length of dV-Ti or dV-N tended to shrink. Moreover, to focus on structure stability, we show that all of the binding energies were negative in Table 3. This finding implies that this structure was stable. We predicted that Ti4N3-V was the most stable, due to the fact that the binding value of Ti4N3-V was the smallest among all structures. By comparing with the “ideal” Ti4N3 system, the doping of V element on Ti4N3 emitted energy because of the negative Eform. For Zr-doping, a relatively large forming energy indicates the difficulty of fabrication.
In Table 3, both Ti4N3-Sc and Ti4N3-V systems, which have one less electron and one more electron by comparing with the Ti4N3 system separately, show high magnetism. Localization of the surface transition metal atoms was increased due to the relatively large bond length between surface impurity atoms and surface Ti atom or subsurface N atom. Although Ti4N3-Sc was a one-less-electron system, it can present high magnetism. For the same reason, the total magnetic moment was enhanced in the Ti4N3-Zr system.
Finally, for the Ti4N3-V system, the added electron entered the spin-up channel and resulted in a magnetic moment increment of 1 µB. In Table 3, the total magnetic moment derived from the surface V atom. However, the bond length of dV-Ti or dV-N in the Ti4N3-V system was smaller than that in the Ti4N3 system. More direct magnetic hybridization partly weakened the total magnetism. On the whole, surface doping of transition metal on a Ti4N3 nanosheet can mediate magnetism. This result provides a controlled way for us to design 2D MXene materials with high magnetic properties.
In Figure 8, the TDOS of the doped system Ti4N3-Z (Z = Sc, V, Zr) and the PDOS of surface Z atom and its neighbor surface Ti and subsurface N atom are presented. In Figure 8a, because Sc is one electron less than the Ti atom, the TDOS near the Fermi level decreased and presented a large spin valley. The PDOS of surface Ti atom neighboring the Sc atom shifted toward low-energy orientation due to the fact that the whole system was one electron less. For subsurface N atom, the contribution to TDOS was extremely small. As a result, in the doped system Ti4N3-Sc system, a high spin polarization ratio was reserved, and the spin-polarization ratio was described by Formula [48]. For the Ti4N3-V system, as shown in Figure 8b, we can see that near the Fermi level, some spin-peaks appeared in the spin-up channel because of one more electron. Similar behaviors were detected in the PDOS of surface Ti atoms owing to rehybridization. However, for the doped Ti4N3-Zr system, as shown in Figure 8c, the strong Zr-Ti interaction could widen the spin split near the Fermi level owing to the short bond length of Zr-Ti. In the PDOS of surface Ti and V atoms, some peaks appeared near the Fermi level. This system presented a relatively low spin polarization but a large magnetism.

4. Conclusions

The atomic vacancy defect, Frenkel-type defect and transition metal Z (Z = Sc, V, Zr) doping in Ti4N3 MXene nanosheet were investigated comprehensively by the first-principles calculation based on density functional theory. The “ideal” Ti4N3 had a magnetic moment of 1.173 µB and a high spin polarization ration of more than 80%. Firstly, atomic vacancy in the Ti4N3 MXene was studied. Although the system was stable even with the absence of a surface Ti or subsurface N atom, the Ti-vacancy appeared easier than the N-vacancy in the Ti4N3 MXene nanosheet. Both atomic vacancies in Ti4N3 could increase magnetism. Secondly, detection from swapped atom disordering indicates that the surface Ti-N swapped disordering was unstable and evolved into a Frenkel-type defect. In the Frenkel-type defect system, the total magnetic moment was decreased due to the enhancement of indirect magnetic exchange between surface Ti atoms bridged by the outside N atom and presented a relatively high spin polarization of approximately 70%. Finally, the doping effects of transition metal Z (Z = Sc, V, Zr) on the Ti4N3 nanosheet were systematically investigated. The results revealed that all of the doped systems were structurally stable and had relatively large magnetism, which was derived from the directed magnetic exchange between surface Z and Ti atoms. Surface atomic relaxation also played an important role in magnetism and electronic properties. Especially in the doped system Ti4N3-Sc system, a high spin polarization ratio was reserved. The Ti4N3 MXene nanosheet doped by Sc atom could be a potential candidate for application to spintronics. Studies on atomic defects and doping from transition metals (Sc, V, Zr) in MXene nanosheet Ti4N3 can help elucidate the various electronic and magnetic behaviors of real 2D materials and contribute to the development of new 2D Ti-based MXene.

Author Contributions

Methodology, J.L. and B.W.; software, T.Z. and K.Y.; data curation, Y.L. and Q.Y.; writing-original draft preparation, T.Z. and W.Z.; writing-review and editing, J.L.; B.W. and T.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Natural Science Foundation of China (Grant No. 11304410), Key Laboratory and Scientific Research Foundation of Guizhou Province (QJHKY[2019]055), Outstanding Youth Science and Technological Innovation Talents Training of Zunyi City (ZYQK[2018]7), Key Laboratory and Scientific Research Foundation of Zunyi City (SSKH[2015]55), Natural Science Foundation of Technology Department (QKHJZ-LKZS[2014]10, QJHJZ-LKZS[2012]03, and KHJZ[2014]2170), Youth Science Foundation of Education Ministry (QJHKZ[2012]084) and the Key Support Discipline ([2011]275) of Guizhou Province of China.

Conflicts of Interest

The authors declare no conflict of interest. The authors claim that none of the material in our manuscript has been published or is under consideration for publication elsewhere. This manuscipt is our original work.

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Applsci 10 02450 g001 550
Figure 1. Schematic of construction processing of the Ti4N3 MXene nanosheet by etching off the Al atomic layer from the Ti4AlN3 bulk. (a) Ti4AlN3 bulk, (b) Ti4N3 bulk and (c) front, (d) side and (e) top view of the Ti4N3 MXene nanosheet.
Figure 1. Schematic of construction processing of the Ti4N3 MXene nanosheet by etching off the Al atomic layer from the Ti4AlN3 bulk. (a) Ti4AlN3 bulk, (b) Ti4N3 bulk and (c) front, (d) side and (e) top view of the Ti4N3 MXene nanosheet.
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Applsci 10 02450 g002 550
Figure 2. Total density of states (TDOS) and partial density of states (PDOS) Ti4N3 nanosheet. ↑ and ↓ indicate the spin-up and spin-down orbitals, respectively. The Fermi level (dashed vertical line) is set to zero. The TDOS is transited to a primitive cell.
Figure 2. Total density of states (TDOS) and partial density of states (PDOS) Ti4N3 nanosheet. ↑ and ↓ indicate the spin-up and spin-down orbitals, respectively. The Fermi level (dashed vertical line) is set to zero. The TDOS is transited to a primitive cell.
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Figure 3. Schematic of a vacancy defect: (a) surface Ti-vacancy and (b) subsurface N-vacancy on a Ti4N3 nanosheet.
Figure 3. Schematic of a vacancy defect: (a) surface Ti-vacancy and (b) subsurface N-vacancy on a Ti4N3 nanosheet.
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Figure 4. TDOS and PDOS of vacancy defected Ti4N3 nanosheet: (a) Ti4N3-Ti and (b)Ti4N3-N. ↑ and ↓ indicate the spin-up and spin-down orbitals, respectively. The Fermi level (dashed vertical line) is set to zero. The TDOS is transited to a primitive cell.
Figure 4. TDOS and PDOS of vacancy defected Ti4N3 nanosheet: (a) Ti4N3-Ti and (b)Ti4N3-N. ↑ and ↓ indicate the spin-up and spin-down orbitals, respectively. The Fermi level (dashed vertical line) is set to zero. The TDOS is transited to a primitive cell.
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Figure 5. Schematic of the Ti-N swapped (a) before and (b) after geometric optimization on the Ti4N3 nanosheet.
Figure 5. Schematic of the Ti-N swapped (a) before and (b) after geometric optimization on the Ti4N3 nanosheet.
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Figure 6. TDOS and PDOS of the Frenkel-type defected Ti4N3 nanosheet. ↑ and ↓ indicate the spin-up and spin-down orbitals, respectively. The Fermi level (dashed vertical line) is set to zero. The TDOS is transited to a primitive cell.
Figure 6. TDOS and PDOS of the Frenkel-type defected Ti4N3 nanosheet. ↑ and ↓ indicate the spin-up and spin-down orbitals, respectively. The Fermi level (dashed vertical line) is set to zero. The TDOS is transited to a primitive cell.
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Figure 7. Schematic of doping transition metal Z (Z = Sc, V, Zr) on the Ti4N3 nanosheet.
Figure 7. Schematic of doping transition metal Z (Z = Sc, V, Zr) on the Ti4N3 nanosheet.
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Figure 8. The TDOS and PDOS of transition metal (a) Sc, (b) V and (c) Zr doped Ti4N3 nanosheet. ↑ and ↓ indicate the spin-up and spin-down orbitals, respectively. The Fermi level (dashed vertical line) is set to zero. The TDOS is transited to a primitive cell.
Figure 8. The TDOS and PDOS of transition metal (a) Sc, (b) V and (c) Zr doped Ti4N3 nanosheet. ↑ and ↓ indicate the spin-up and spin-down orbitals, respectively. The Fermi level (dashed vertical line) is set to zero. The TDOS is transited to a primitive cell.
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Table
Table 1. Calculated lattice constants a and c, atomic layer thickness L, bond lengths between the N2 atom at subsurface and its neighbor Ti1 atom (dTi1-N2) or Ti3 atom (dN2-Ti3) at the surface or the next subsurface, respectively.
Table 1. Calculated lattice constants a and c, atomic layer thickness L, bond lengths between the N2 atom at subsurface and its neighbor Ti1 atom (dTi1-N2) or Ti3 atom (dN2-Ti3) at the surface or the next subsurface, respectively.
Systema (Å)c (Å)L (Å)dTi1−N2 (Å)dN2−Ti3 (Å)
Ti4AlN3[44]2.99123.3967.2392.0822.096
Ti4N32.99323.4397.2352.0622.119
Table
Table 2. Calculated lattice constants a, atomic layer thickness L, binding energy Eb and formation energy Eform and total magnetic moment Mtot, where bond lengths between the vacancy atom at surface (or subsurface) and its neighbor Ti1, N2 or Ti3 atom at surface, subsurface or next subsurface, respectively.
Table 2. Calculated lattice constants a, atomic layer thickness L, binding energy Eb and formation energy Eform and total magnetic moment Mtot, where bond lengths between the vacancy atom at surface (or subsurface) and its neighbor Ti1, N2 or Ti3 atom at surface, subsurface or next subsurface, respectively.
Systema (Å)L(Å)dv−Ti1 (Å)dv−N2 (Å)dv−Ti3 (Å)Eb (eV)Eform (eV)Mtot (µB)
Ti4N32.9937.2352.993(2.062)2.062(2.993)2.918(2.119)−1.295-1.173
Ti4N3-Ti2.9957.1762.9862.0452.841−1.2812.1671.817
Ti4N3-N2.9887.3682.0632.9882.161−1.2017.1182.373
Table
Table 3. Calculated lattice constants a, atomic layer thickness L, binding energy Eb, forming energy Eform, total magnetic moment Mtot, magnetic moment of Z atom or its neighbor Ti atom at the surface, bond length between the doping Z atom at surface and its neighbor Ti1 or N2 atom at the surface or subsurface, respectively.
Table 3. Calculated lattice constants a, atomic layer thickness L, binding energy Eb, forming energy Eform, total magnetic moment Mtot, magnetic moment of Z atom or its neighbor Ti atom at the surface, bond length between the doping Z atom at surface and its neighbor Ti1 or N2 atom at the surface or subsurface, respectively.
Atoma (Å)L (Å)dZ-Ti1 (Å)dZ-N2(Å)Eb (eV)Eform (eV)MTi(µB)MZ (µB)Mtot (µB)
Ti4N32.9937.2352.9192.062−1.295−0.4900.3891.173
Ti4N3-Sc2.9997.2173.0292.217−1.2800.9300.5940.3561.649
Ti4N3-Zr2.9997.2113.0902.220−1.2204.7150.5220.2941.772
Ti4N3-V2.9917.2412.8021.985−1.335−2.5050.6681.3152.365

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MDPI and ACS Style

Zhou, T.; Zhao, W.; Yang, K.; Yao, Q.; Li, Y.; Wu, B.; Liu, J. Atomic Vacancy Defect, Frenkel Defect and Transition Metals (Sc, V, Zr) Doping in Ti4N3 MXene Nanosheet: A First-Principles Investigation. Appl. Sci. 2020, 10, 2450. https://doi.org/10.3390/app10072450

AMA Style

Zhou T, Zhao W, Yang K, Yao Q, Li Y, Wu B, Liu J. Atomic Vacancy Defect, Frenkel Defect and Transition Metals (Sc, V, Zr) Doping in Ti4N3 MXene Nanosheet: A First-Principles Investigation. Applied Sciences. 2020; 10(7):2450. https://doi.org/10.3390/app10072450

Chicago/Turabian Style

Zhou, Tingyan, Wan Zhao, Kun Yang, Qian Yao, Yangjun Li, Bo Wu, and Jun Liu. 2020. "Atomic Vacancy Defect, Frenkel Defect and Transition Metals (Sc, V, Zr) Doping in Ti4N3 MXene Nanosheet: A First-Principles Investigation" Applied Sciences 10, no. 7: 2450. https://doi.org/10.3390/app10072450

APA Style

Zhou, T., Zhao, W., Yang, K., Yao, Q., Li, Y., Wu, B., & Liu, J. (2020). Atomic Vacancy Defect, Frenkel Defect and Transition Metals (Sc, V, Zr) Doping in Ti4N3 MXene Nanosheet: A First-Principles Investigation. Applied Sciences, 10(7), 2450. https://doi.org/10.3390/app10072450

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