Covalency-Dependent Vibrational Dynamics in Two-Dimensional

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Covalency-Dependent Vibrational Dynamics in Two-Dimensional Titanium Carbides Tao Hu, Minmin Hu, Zhaojin Li, Hui Zhang, Chao Zhang, Jiemin Wang, and Xiaohui Wang J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b08626 • Publication Date (Web): 11 Dec 2015 Downloaded from http://pubs.acs.org on December 13, 2015

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The Journal of Physical Chemistry

Covalency-Dependent Vibrational Dynamics in Two-Dimensional Titanium Carbides Tao Hu,†,‡ Minmin Hu,†,‡ Zhaojin Li,†,‡ Hui Zhang,†,‡ Chao Zhang,† Jiemin Wang,† and Xiaohui Wang∗,†

†

Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang 110016, China ‡

University of Chinese Academy of Sciences, Beijing 100049, China

ABSTRACT: Structure and vibrational dynamics of T-terminated titanium carbide monosheets Ti2CT2 (T = O, F, OH) are studied by means of first-principles calculations to understand their inherent relation. Terminations modulate the crystal structures through the redistribution of valence electron density among the atoms in the monosheets, particularly Ti atoms. Phonon partial density of states analysis shows a clear feature of collaborative vibration, which reflects the covalent nature of bonds in the monosheets. Two metrics of covalency and cophonicity proposed very recently are adopted to quantitatively correlate the vibrational properties with the electro-structural characteristics of the system. A remarkable positive correlation between the covalency and vibrational dynamics specified as Raman shifts and IR wavenumbers is found. The bond-specific covalency metrics depend on not only the identity of terminations but also the thickness of the two-dimensional titanium carbides. For example, in the case of Ti3C2T2 with increased thickness, red shift in Raman shifts and IR wavenumbers occurs as a result of the decrease in covalency.

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1. INTRODUCTION Due to the fact that their thickness is significantly smaller than those in the other two dimensions, atomically thin materials such as graphene1 and inorganic graphene analogues (IGAs) exhibit remarkable physical properties. Since the pioneering work on graphene1, world-wide enthusiasm for 2D materials including IGAs has rapidly grown. These IGAs include hexagonal boron nitride (h-BN)2, transition metal oxides and hydroxides3, transition metal dichalcogenides (TMDs, like WS2, and MoS2, etc.)4−6, clays7, zeolite8, stanese9, as well as phosphorene10. Very recently, a new family of IGAs, called MXenes11 have emerged. The MXenes were synthesized by chemical exfoliation12,13 from layered ternary carbides/nitrides referred to as MAX phases14 with strong in-plane bonds and weak coupling between layers15. Unlike graphene, BN monosheet, TMDs and many other 2D materials, MXenes have not only versatile chemical compositions but also tunable thickness of the atomic layer since MAX phases possess 211, 312, 413, and 523 phases where M stands for early transition metals and X for C or N16. Moreover, they have already shown promising performance in electrochemical energy storage systems, lead and dye adsorption16−37. As a typical MXene, Ti2CT2 (T = O, F, OH), derived from Ti2AlC by chemical exfoliation13,36,38−40, is believed to have superior gravimetric capacity over Ti3C2T2 as the former has the least number of atomic layers per MXene sheet.16 To date, MXenes have been investigated both experimentally and theoretically. The experimental works were focused on synthesis and characterization11−13,16,20−22,27−29,31−34,41−49, while the theoretical calculations were concentrated on the electronic and electrochemical properties11,16,23−26,37,50−55. For instance, electronic structure investigations of Ti2CT2 (T = O, F, OH) monosheets indicated that it is narrow band gap semiconducting (Ti2CO2)11,55,56 or metallic (Ti2C, Ti2CF2 and Ti2C(OH)2)50,53−57 depending on the identity of terminations. 2


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Playing a major role in many of the physical properties such as thermal and electronic conductivity for condensed matters, phonons could offer fundamental understanding of newly-emerging 2D materials like MXenes.58−60 However, it is still a conundrum to perfectively exfoliate MXene monosheets in experiments to investigate their phonon properties. Therefore, the limited papers addressing this issue are all from theoretical perspectives (Ti3C2T261, Ti2CO256,62 and Sc2CF263). Considering the fact that several kinds of terminations (O, OH and F) usually coexist in the exfoliated MXenes16,64, it is somewhat frustrating that there have been no systematic reports on phonon properties of Ti2CT2 monosheets in the literature. Here, we aim to figure out how the identity of terminations influences the lattice dynamics and vibrational properties of the emerging 2D material. In this paper, we present a systematic study on the static and dynamical properties of bare Ti2C monosheet and T-terminated Ti2CT2 monosheets using density functional theory (DFT) calculations. Bearing termination groups, the crystal structure is modulated through the redistribution of valence electron density among the atoms in the monosheets, particularly the Ti atoms. Phonon dispersions and partial density of states (PDOS) show obvious differences. Raman and infrared (IR) active modes significantly depend on the identity of terminations. More importantly, it is found that the Raman shifts and IR wavenumbers are related to the covalency of relevant bonds. For example, as the atomic layers increase from Ti2CT2 to Ti3C2T2, the covalency of the [Tin+1Cn] nanosheet decreases and corresponding vibration modes have red shifts.

2. COMPUTATIONAL METHODS In this study, bare Ti2C monosheet was constructed by removing Al layers from Ti2AlC, in which Ti, Al and C reside in the P63/mmc space group at 4f (1/3, 2/3, u), 2d (1/3, 2/3, 3/4) and 2a (0, 0, 3



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1/2), respectively. After Tang et al.23 and Enyashin et al.52,53, one bare and three fully T-terminated monosheets (Ti2CT2, Figure 1) were constructed. To avoid inter-block interactions, a vacuum region of about 15 Å was intercalated between the adjacent [Ti2C] blocks.

Figure 1. Crystal structure of Ti2C(OH)2 monosheet. (a) Side view of a 6 × 6 × 1 supercell; (b) top view of a 2 × 2 × 1 supercell. Terminations (OH, O, F) are located at the hollow sites of Ti and C atoms. (c) Illustration of the first

Brillouin zone.

The DFT calculations were performed using the Cambridge Sequential Total Energy Package (CASTEP)65,66. The electron-ion interaction was represented by using plane-wave pseudo potential. The electronic exchange correlation energy was treated as GGA-PBE67. Ultra-soft potentials66 were utilized for the calculations. Configurations of H−1s1, C−2s22p2, O−2s22p4, Ti−3s23p63d24s2 were treated as valence electrons. The Monkhorst-Pack scheme68 with 9 × 9 × 1 k points meshes were used for the integration in the irreducible Brillouin zone so that the individual spacing was less than 0.05 Å−1. The cutoff energy was set at 380 eV. The Broyden– Fletcher–Goldfarb–Shanno minimization scheme69 was used to minimize the total energy and interatomic forces. Fermi level was smeared by 0.1 eV. The convergence for energy was chosen as 1.0 × 10−9 eV/atom, and the structures were relaxed until the maximum force exerted on the

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atoms became less than 0.001 eV/Å. After then, phonon calculations were performed on these optimized structures. For the calculation of dynamical matrix, we used a supercell method70 implemented in the CASTEP code. In this method, a specific atom was displaced by 0.005 Å in both positive and negative direction to introduce forces acting on surrounding atoms. In order to avoid interactions among image atoms due to the periodical boundary condition, a large 4 × 4 × 1 supercell with more than 40 atoms was used in the present work. Using the present first-principles calculation scheme, we also calculated Raman active frequencies of Ti2AlC and Ti3AlC2 (Table S1 and S2 in the Supporting Information). The calculated frequencies agree well with the experimental data available, indicating that the calculation scheme was reliable. Details are included in the Supporting Information.

3. RESULTS AND DISCUSSION 3.1. Structural features. Ground-state structures of Ti2C and Ti2CT2 (T = O, F, OH) monosheets with fully relaxed geometry optimization were first investigated. The four types of monosheets _

are all crystallized in the space group of P3m1 (No. 164). The other structural data including lattice parameters, monosheet thickness d (vertical distance from top-most atomic layer to bottom-most atomic layer) and bond lengths are summarized in Table 1. Phonon band structures along a linear path joining the high-symmetry points of the irreducible Brillouin zone are investigated in the following section. We do not find any unstable displacements, indicating that the considered geometries represent stable configurations. This is consistent with previous work by Khazaei et al.56 and Guo et al.62 The stability of a free-standing Ti2CT2 monosheet was also confirmed by molecular dynamics calculations at elevated temperatures (Figure S1), as presented in the Supporting Information. 5



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Table 1. Optimized structural data for Ti2C and Ti2CT2 (T = O, F, OH) monosheets Formula Ti2C

Ti2CO2

Ti2CF2

Ti2C(OH)2

Lattice parameters (Å) a 3.035 c 17.608 d 2.299 a 3.031 c 19.222 d 4.425 a 3.057 c 19.973 d 4.777 a 3.074 c 21.656 d 6.786

Bond lengths (Å) Ti−C 2.096

Atoms Ti C

Wyckoff position 2d 1b

Internal coordinates (1/3, 2/3, 0.4347) (0, 0, 0.5)

Ti−C Ti−O

2.184 1.971

Ti C O Ti C F Ti C O H

2d 1b 2d 2d 1b 2d 2d 1b 2d 2d

(1/3, 2/3,0.4321) (0, 0, 0.5) (2/3, 1/3, 0.3849) (1/3, 2/3, 0.4431) (0, 0, 0.5) (0, 0, 0.3804) (1/3, 2/3, 0.4474) (0, 0, 0.5) (2/3, 1/3, 0.3885) (2/3, 1/3, 0.3433)

Ti−C Ti−F

2.099 2.164

Ti−C Ti−O O−H

2.109 2.185 0.980

Compared with bare Ti2C monosheet, T-terminated monosheets have larger thickness d because of the increased atomic layers while the Ti and C atoms remain the same Wyckoff positions. With the terminations, the Ti−C bond length are all elongated more or less (quantitatively, corresponding to the decrease in covalency metric of Ti−C as discussed in Section 3.3), implying that the terminations strongly interact with the [Ti2C] block. These changes in the Ti−C bond length originate from the redistribution of valence electrons of the involved atoms. As shown in Figure 2, the electron-depleted zone around Ti atoms is obvious while the valence electrons are enriched around the electronegative atoms like C, O and F. The strong localization of electrons between Ti atoms and the terminations weakens the attraction between Ti and C atoms. As a result, Ti atoms are pushed out somewhat from the basal plane, leading to the increase in Ti−C bond length and the thickness of [Ti2C] block in the T-terminated monosheets. Similar termination effect on the structural modulation has also been found in Ti3C2T2.61 The terminations play dual roles in the system. On one hand, the terminations interact with the Ti atoms in a strong manner, stabilizing the [Ti2C] slab. On the other hand, the valence electrons from Ti are localized around the terminations. Consequently, a transition from a conductor56 to 6


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semiconducting55 happens once the O terminations are introduced on Ti2C surface. In the absence of conductive Ti atomic layer, it can be expected that the electronic conduction of Ti2CT2 is not as good as Ti3C2T2.55

_

Figure 2. Charge density difference on (1120) atomic plane of (a) Ti2C, (b) Ti2CO2, (c) Ti2CF2 and (d) Ti2C(OH)2 with

respect to atoms.

3.2. Phonon dispersions and PDOS. Figure 3 presents phonon dispersions and PDOS for Ti2C, Ti2CO2, Ti2CF2 and Ti2C(OH)2 monosheets. As shown therein, for each monosheet there are three acoustic branches (the three lower energy cures) while the rest corresponds to optical branches. Band gaps centered around 500 cm−1 exist in Ti2C and Ti2CF2 monosheets. The vibration frequencies of the main body of the monosheet, [Ti2C] block, are all below 800 cm−1.

The PDOS of the optical branches in Figure 3 shows a clear feature of collaborative vibration, as evidenced by the overlap of the projected bands. In Ti2C and Ti2CF2, the vibrations around 600 cm−1 are collaborative vibration of Ti and C. In oxygen-containing Ti2CO2 and Ti2C(OH)2, the 7



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collaborative vibration of Ti and O (or OH) are also around 600 cm−1. These high-frequency phonons need higher energy to excite, signifying the strong nature of the related bonds like Ti−C and Ti−O. As shown in Figure 3, the terminations of O and OH contribute to most of the phonon states around 500 cm−1, bridging the band gaps centered around 500 cm−1 in Ti2C and Ti2CF2 monosheets. The band gaps thus disappear in Ti2CO2 and Ti2C(OH)2. Lower-frequency (< 500 cm−1) phonons are overall motion of all atoms in the monosheets. In the case of Ti2C(OH)2 monosheet, the highest band at about 3700 cm−1 corresponds to the internal stretching mode of the OH termination.

Figure 3. Calculated phonon dispersions along high-symmetry directions of the Brillouin zone and the phonon

PDOS of (a) Ti2C, (b) Ti2CO2, (c) Ti2CF2 and (d) Ti2C(OH)2 monosheets. The slope of the black dash lines along the longitudinal acoustic branches near Γ corresponds to the speed of sound and the in-plane stiffness. The

highlighted band gaps in (a) and (c) disappear after terminated with O and OH.

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In order to better understand the collaborative vibration, we calculated cophonicity metrics (Cph), which has been successfully applied to investigate lattice dynamics of TMDs71. The value of Cph quantifies the contribution of atoms to the PDOS in a certain frequency range. The smaller the Cph, A‒B is, the higher is the mixing of the A and B atom contributions to the frequency band, and the two atoms have the same weight in the determination of the modes specific of the considered energy range71. The results are presented in Table S3 and Figure S2 in the Supporting Information. Among the values of Cphs for all atomic pairs in the investigated system, the value of Cph, Ti‒F is the smallest, as the collaborative vibrations of Ti and F in Ti2CF2 are the most obvious in Figure 3c.

We next compare the slopes of the longitudinal acoustic branches near Γ, which correspond to the speed of sound and reveal the in-plane stiffness10. Our results in Table S4 indicate that the in-plane elastic response of four MXenes is nearly isotropic, with nearly the same value for the speed of sound along the Γ‒M and the Γ‒K directions, v = v, agreeing with elastic calculations62 that Ti2CT2 are elastically isotropic 2D materials. In-plane speeds of sound in Ti2CT2 with terminations are in this order: v (Ti2CO2) > v (Ti2CF2) > v (Ti2C(OH)2) >

v (Ti2C). Strongly bonding with the [Ti2C] block, the terminations increase the in-plane stiffness of the monosheets among which Ti2CO2 is the stiffest.

3.3. Raman shifts and IR wavenumbers. According to the crystal information of the Ti2C and Ti2CT2 in Table 1, the optical phonons in the center of the Brillouin zone can be classified as the following irreducible representations: Γoptical (Ti2C) = Eg (Raman) + A1g (Raman) + Eu (IR) + A2u (IR) Γoptical (Ti2CO2) = 2Eg (Raman) + 2A1g (Raman) + 2Eu (IR) + 2A2u (IR) 9



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Γoptical (Ti2CF2) = 2Eg (Raman) + 2A1g (Raman) + 2Eu (IR) + 2A2u (IR) Γoptical (Ti2C(OH)2) = 3Eg (Raman) + 3A1g (Raman) + 3Eu (IR) + 3A2u (IR) The phonon dispersion also provides fundamental information regarding Raman and IR spectra. The results of vibration modes are listed in Table 2. The active modes are classified according to their vibrational directions and main contributing atom species. Schematic illustrations of the vibrations are presented in Table S5 and S6 in the Supporting Information.

Table 2. Calculated wavenumbers for the Raman and IR active modes of Ti2C and Ti2CT2 monosheets (in cm−1). Raman mode

IR mode

Modes Ti2C

ω1 (Eg) 236

ω2 (A1g) 333

ω3 (Eg)

ω4 (A1g)

Ti2CO2

128

293

409

596

Ti2CF2

192

283

254

505

Ti2C(OH)2

192

288

283

528

’

’

Modes

ω1 (Eu)

ω2 (A2u)

Ti2C

637

520

Ti2CO2

240

Ti2CF2 Ti2C(OH)2

’

’

ω3 (Eu)

ω4 (A2u)

578

505

741

257

451

669

666

286

489

657

633

ω5 (Eg)

ω6 (A1g)

445

3707

’

ω5 (Eu)

ω6’ (A2u)

444

3701

To further understand the role that the terminations play in the vibrational properties of the monosheets, the Raman and IR frequencies of the four monosheets are compared in detail. First of all, the frequencies of both Raman and IR active modes are deeply dependent on the identity of terminations. For Raman active modes, the frequency at 236 cm−1 (Eg mode) in bare Ti2C monosheet shifts to lower wavenumbers of 128, 192 and 192 cm−1 upon terminating with O, F and OH, respectively. Since the mode is mainly contributed by the in-plane vibrations of Ti and C atoms (Figure 4), the red shift demonstrates that the terminations weaken the in-plane vibration of the two atoms. In Ti2C monosheet, the frequency at 333 cm−1 (A1g mode) corresponds to the 10


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out-of-plane stretching vibrations of Ti and C. With the termination of O, F and OH, the mode at 333 cm−1 is softened to 293, 283 and 288 cm−1, respectively. This indicates that the terminations on the surfaces weaken the out-of-plane motion of Ti atoms. Such modulations in frequency are attributed to the elongation of the Ti−C bond, as discussed in Section 3.1. Notably, the modes at 445 and 3707 cm−1 in Ti2C(OH)2 are assigned to the in-plane and the out-of-plane vibrations of OH, respectively. In contrast to the above-mentioned modes, these two OH-related modes have negligible contribution from the [Ti2C] block. The remaining Raman active modes in T-terminated Ti2CT2 are introduced by comprising more atoms in a unit cell. The roles terminations play in IR active modes generally follow the trend as those in Raman active modes. The Raman and IR vibration modes of Ti2C(OH)2 are predicted in Figure 4. For the other three monosheets of Ti2C, Ti2CO2 and Ti2CF2, their vibration modes are demonstrated in Figure S3−S5 (Supporting Information), respectively.

Figure 4. Raman and IR active vibration modes of Ti2C(OH)2 monosheet. Ti, C, O and H atoms are denoted by

orange, green, blue, and brown spheres, respectively.

3.4. Experimental vibrational spectra. We also carried out Raman measurements of experimentally achieved lamellae which have been examined by X-ray diffraction (XRD) and 11



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scanning electron microscope (SEM) in Figure S6 in the Supporting Information. Micro Raman spectra were collected at various temperatures from 83 to 283 K. The Raman bands are generally independent on temperature, as shown in Figure S7 (Supporting Information). All the bands are in a broad manner. In order to separate the bands, we tentatively conducted peaks fitting (Figure S8 in the Supporting Information). The calculated Raman active frequencies roughly match the bands in the spectrum. For the sake of simplicity, only the Raman spectrum recorded at 83 K is presented in Figure S8. Strictly, there are some deviations between the calculated active modes and the collected Raman spectrum. The deviations are most likely caused by the following factors61. The calculations are based on Ti2CT2 with homogenous terminations while the exfoliated lamellae are always terminated with several species16,64. Second, our calculation is carried on non-strained monosheet models while the lamellae are constrained with residual stress (corrugated, as shown in Figure S6b). Deviation between theoretical results and experimental results here is also partly due to high concentration of terminations in our calculations. Experimentally, due to the poor wavenumber resolution (cannot reach several wavenumbers), the experimental IR spectra aren’t presented here.

3.5 Correlation between vibrational properties and covalency. In order to check the influence of [Tin+1Cn] blocks on Raman shifts and IR wavenumbers, the vibration modes in Ti2CT2 and Ti3C2T2 monosheet are thoroughly compared. The Raman shifts of Ti2CT2 are higher than the corresponding vibrational modes in Ti3C2T2, with the exception of ω6 in OH-containing MXenes. In other words, as the atomic layer increases from Ti2CT2 to Ti3C2T2, the vibrational modes involved in the [Tin+1Cn] nanosheet experience somewhat red shifts (See Figure 5). This interesting feature makes it possible to readily distinguish these two materials with the same composition elements 12


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by means of Raman spectroscopy.

Figure 5. (a) Raman and (b) IR active modes and calculated frequencies of Ti2CT2 (T = O, F, OH) monosheet (red

line). For comparison, corresponding vibrational frequencies of Ti3C2T2 monosheet (blue dot line) are also included. Note that the Raman shifts of Ti2CT2 are higher than the corresponding vibrational modes in Ti3C2T2, with the exception of ω6 in OH-containing MXenes.

As shown in Figure 5, the Raman shifts and IR wavenumbers in Ti2CT2 are greater than those corresponding modes in Ti3C2T2. To understand the bond-specific features, we calculated the covalency metric (C), which has been successfully applied to understand nanoscale friction and structural distortion at the atomic scale71,72. According to Cammarata et al. 71,72, a larger value of C means higher covalency of the bond. Figure 6 presents the calculated Cs of Ti2CT2 and Ti3C2T2 monosheets. By comparing Figure 5 and Figure 6, a remarkable positive correlation is found between the covalency and the vibrational properties (Raman shifts and IR wavenumbers). 13



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Specifically, the values of Cs for all the Ti−C and Ti−T bonds in Ti2CT2 are higher than those in Ti3C2T2 except those of O−H bond. Then we check the exceptional one in Raman active modes, ω6 in Ti2C(OH)2 and Ti3C2(OH)2 (ω6 is the stretching modes of OH). Interestingly, it is noteworthy that the C of O−H bond in Ti2C(OH)2 is smaller than that in Ti3C2(OH)2. The correlation between Raman shifts and C is perfectly evidenced by the coherent trend of Raman shifts and C in Ti2C(OH)2 and Ti3C2(OH)2. The calculation results of C are presented in Table S7 in the Supporting Information. Last but not the least, the general correlation between C and Cph is also quite good (see Figure S9 in the Supporting Information). The C−Cph plot generally shows a positive correlation between covalency and cophonicity in the studied system except the Ti−F atomic pair in Tin+1CnF2 monosheets.

Figure 6. Calculated covalency metrics of Ti2CT2 and Ti3C2T2 monosheets. Note that the covalency metrics (a) Ti−C,

(b) Ti−T of Ti2CT2 are larger than those of Ti3C2T2 except (c) O−H. There are two nonequivalent Ti atoms in Ti3C2T2, 61

namely, central Ti (Ti1) and surface Ti (Ti2), in line with our previous work .

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4. CONCLUSIONS

A detailed comparative study of static and lattice dynamical properties of Ti2CT2 and Ti3C2T2 monosheets, has been comprehensively done. It is established that there is a remarkable correlation between bond covalency and vibrational dynamics as specifically demonstrated by Raman shifts and IR wavenumbers in the two representatives of the emerging two-dimensional materials of MXenes. The covalency and cophonicity positively correlate in the Tin+1CnT2 system. Such covalency-dependent vibrational properties shed light on better understanding Raman and IR active modes from an electronic-structure perspective in the future study of the big family of MXenes and other related low-dimensional materials.

ASSOCIATED CONTENT

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Additional experimental details and information on ab initio molecular dynamics, results of benchmark calculation, data fitting and vibrational mode analysis.

AUTHOR INFORMATION

Corresponding Author

∗E-mail: [email protected]. Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS

This work was supported by the Chinese Academy of Sciences (CAS) and Shenyang National Laboratory for Materials Science, Institute of Metal Research, CAS. The authors would like to thank Long Chen for Raman experiments. 15



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Table of Contents

A remarkable positive correlation between vibrational properties and covalency of Ti2CT2 and Ti3C2T2 (T = O, F, OH) monosheets is found by means of density functional theory calculations.

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Covalency-Dependent Vibrational Dynamics in Two-Dimensional

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