Comparative analysis of frictional behavior and mechanism of molybdenum ditelluride with different structures

Two-dimensional (2D) transition metal dichalcogenides (TMDCs) have layered structures with excellent tribological properties. Since the energy difference between hexagonal-molybdenum ditelluride (2H-MoTe2) and distorted octahedral-molybdenum ditelluride (1T’-MoTe2) is very small among the transition metal dichalcogenides (TMDCs), MoTe2 becomes one of the most promising candidates for phase engineering. In our experiment, we found that the friction force and friction coefficient (COF) of 2H-MoTe2 were an order of magnitude smaller than those of 1T’-MoTe2 by the atomic force microscope (AFM) experiments. The friction difference between 1T’-MoTe2 and 2H-MoTe2 was further verified in molecular dynamics (MD) simulations. The density functional theory (DFT) calculations suggest that the friction contrast is related to the difference in sliding energy barrier of the potential energy surface (PES) for a tip sliding across the surface. The PES obtained from the DFT calculation indicates that the maximum energy barrier and the minimum energy path (MEP) energy barrier of 2H-MoTe2 are both smaller than those of 1T’-MoTe2, which means that less energy needs to be dissipated during the sliding process. The difference in energy barrier of the PES could be ascribed to its larger interlayer spacing and weaker Mo–Te interatomic interactions within the layers of 2H-MoTe2 than those of 1T’-MoTe2. The obvious friction difference between 1T’-MoTe2 and 2H-MoTe2 not only provides a new non-destructive means to detect the phase transition by the AFM, but also provides a possibility to tune friction by controlling the phase transition, which has the potential to be applied in extreme environments such as space lubrication.


Introduction
Two-dimensional (2D) materials have layered structures with weak van der waals forces between the adjacent atomic layers, which makes it easy to slide [1].Among various 2D materials, transition metal dichalcogenides (TMDCs) have attracted considerable attention for their excellent tribological performance under extreme conditions such as space environment [2].Although the frictional properties of MoS 2 have been extensively studied [3,4], the frictional properties of other members of the TMDC family remain relatively unexplored.
It has been shown that the friction force of molybdenum ditelluride (MoTe 2 ) is lower than those of MoS 2 and MoSe 2 under identical conditions [5].Therefore, MoTe 2 has the potential to become one of the most promising materials for excellent frictional properties.
As the chalcogen elements (S, Se, and Te) in TMDCs have relatively small electronegativity, either covalent or ionic bonds may be formed, leading to the generation of structural polymorphs with different bonding configurations and close energy [6].According to the density functional theory (DFT) calculations, semiconductor hexagonal (2H) and metallic distorted www.Springer.com/journal/40544| Friction octahedral (1T′) phases of MoTe 2 can be stable at room temperature, and the energy difference between these two phases is about 38 meV for per formula MoTe 2 [7], which is very small among the TMDC family.It has been shown that weak non-chemical external stimuli, such as temperature [8], tensile strain [7,9], laser irradiation [10,11], plasma treatment [12], electrostatic doping [13], and electric fields [14], can drive the semiconductor-to-metal transition of the MoTe 2 .It has been confirmed that inducing the transition from 2H-molybdenum ditelluride (2H-MoTe 2 ) to 1T′-molybdenum ditelluride (1T′-MoTe 2 ) can improve the contact quality of transistors [15] and promote the catalytic activity of hydrogen evolution reaction [16].Consequently, MoTe 2 is considered as one of the most promising candidates for phase engineering.
The layered structure and diverse structural polymorphs of MoTe 2 imply abundant and even excellent frictional properties to some extent.However, the frictional behavior of MoTe 2 with different structures is not clear, especially for 1T′-MoTe 2 .In fact, it has been the goal of scholars to effectively reduce friction, explain frictional behavior and mechanism, and achieve active regulation of friction.Among the mainstream friction regulation methods, strain-regulated friction [17] is limited by the magnitude of the load, and electric field-regulated friction [18] also has the limitation in the conductivity of materials, so new regulation methods need to be studied.Potentially, since the properties of different phases vary greatly, the use of phase transitions is an ideal method to achieve the modulation of friction properties.Therefore, the study of the frictional properties of MoTe 2 with different structures is particularly urgent.
Here, the frictional behavior of 1T′-MoTe 2 and 2H-MoTe 2 was investigated experimentally and theoretically, and the reasons for the lower friction force and friction coefficient (COF) of 2H-MoTe 2 than those of 1T′-MoTe 2 were explained in depth from the perspective of energy.The frictional contrast existing between these two phases illustrates that the 1T′-MoTe 2 and 2H-MoTe 2 can be distinguished nondestructively by measuring the atomic friction.The study of the frictional behavior of MoTe 2 with different structures shows that the frictional behavior of different phases varies greatly due to the different atomic arrangements, indicating that the friction can be modified by changing the atomic arrangements, such as controlling the semiconductor-metal transition of MoTe 2 .

Sample preparation and characterization
The substrate was a die cut from a Si(100) wafer with about 300 nm of thermally grown SiO 2 .Both 1T′-MoTe 2 and 2H-MoTe 2 crystals (HQ Graphene, the Netherlands) were transferred to a silicon wafer by mechanical exfoliation assisted by polydimethylsiloxane [19].The optical images (acquired by Olympus BX60 microscope with Canon DS126431 camera) of the samples are shown in Figs.1(a) and 1(b).The thickness of the sample was measured using a commercial atomic force microscope (AFM; Cypher S, Asylum Research, Oxford Instruments) in contact mode.The thicknesses of friction regions of the 1T′-MoTe 2 and 2H-MoTe 2 were 39 and 32 nm, respectively.To further confirm the compositions of these two materials, the Raman spectra (LabRAM HR evolution, HORIBA; 514 nm) were applied to characterize the MoTe 2 flakes.As shown in Fig. 1(c), characteristic peaks of 1T′-MoTe 2 (A g at 111 cm −1 , B g at 164 cm −1 , and A g at 259 cm −1 ) can be clearly seen.Besides, the Raman characteristic peaks (A ′ 1 at 173 cm −1 and E' at 234 cm −1 ) are attributed to the 2H-MoTe 2 [20], as shown in Fig. 1(d).The characteristic peaks are in good agreement with their theoretical values, which proves the purity of the material.

Friction force measurements
Friction measurements were carried out using the AFM under ambient conditions.The normal and lateral force constants of the silicon probe (PPP-LFMR, Nanosensors) were calibrated using the thermal noise method and improved wedge calibration method [21], respectively.The spring constant of the probe is about 0.26 N/m, and the lateral force constant is nearly 341 nN/V.In the lateral force mode, friction maps were measured with gradient loading applied to a square region of 200 nm × 200 nm with a scanning frequency of 2 Hz, as shown in Figs.2(a In contrast, the friction map of 2H-MoTe 2 varies slightly with gradient loading.In order to understand the relationship between the friction force and the friction direction, the relative angles of the sample and the probe were changed by rotating the sample.In addition, three different locations were selected for friction measurements under each condition, and the variations of friction force with load were obtained, as shown in Fig. 2(c).For 2H-MoTe 2 , the difference of  friction force with angles at 0°, 43°, 80°, and 110° of sample rotation was small, and the friction force can be considered isotropic.When the angles of the 1T′-MoTe 2 sample were varied to 0°, 32°, 70°, and 100°, the difference in adhesion had some degree of influence on the magnitude of the friction force, but the overall trend of friction was not very different.Since the friction difference between 1T′-MoTe 2 and 2H-MoTe 2 was concerned, the anisotropy of frictional force was no longer considered.It can be found that the frictional force of the 2H phase was one order of magnitude smaller than that of the 1T′ phase.The COF of 1T′-MoTe 2 was 0.311, while that of 2H-MoTe 2 was only 0.013, which can be obtained by performing a linear fit to the data.
By further reducing the scan range to 20 nm × 20 nm and increasing the scanning frequency to 20 Hz, the friction maps including atomic-scale stick-slip motion information were obtained, as shown in Figs.3(a) and 3(f).The reciprocal lattice information (Figs.3(b) and 3(g)) is obtained by the two-dimensional fast Fourier transform (2D FFT) analysis of Figs.3(a) and 3(f).However, the lattice in the magnitude/modulus maps obtained by the 2D FFT is a reciprocal lattice, which should be transferred to real space.Lattice vectors as well as the angles between the two vectors of the real lattice were obtained after the transformation following the formula [22].
The measured lattice basis vectors and angles in the real lattice of 1T′-MoTe 2 were 6.0 Å, 3.5 Å and 83°, which were similar to the theoretical values of 6.4 Å, 3.5 Å, and 90°.Similarly, as for 2H-MoTe 2 , the measured  | https://mc03.manuscriptcentral.com/frictionvalues of 3.6 Å, 3.6 Å, and 118° matched well with the theoretical values of 3.5 Å, 3.5 Å, and 120°.The difference between measured and theoretical values was most likely due to lattice distortion caused by the presence of the load.Moreover, high-resolution atomic-scale stick-slip maps can be achieved after filtering from friction maps, as shown in Figs.3(c) and 3(h).The atomic-scale stick-slip map of 1T′-MoTe 2 showed the characteristics of a square structure, which was very similar to the unit-cell structure (Fig. 3(d)).A six-membered ring structure is observed in Fig. 3(h), which was consistent with the unit-cell parameters of 2H-MoTe 2 , as shown in Fig. 3(i).The friction profiles (Figs.3(e) and 3(j)) are extracted from Figs. 3(c) and 3(h), respectively, corresponding to the blue dashed lines.The period of atomic stick-slip was 6.3 Å for 1T′-MoTe 2 and 3.55 Å for 2H-MoTe 2 , which were in good agreement with their lengths of the lattice basis vectors.Obviously, 1T′-MoTe 2 exhibited larger atomic scale friction than 2H-MoTe 2 in atomic-scale stick-slip.In general, the 2D FFT and filtering of atomic-scale stick-slip friction maps can reveal the friction process and distinguish the two materials with no damage.

Molecular dynamics (MD) simulation
In order to ensure the reliability of the experimental results, MD simulations were carried out.The MD model consisted of four layers of MoTe 2 , which was obtained from the optimized structure.The atoms of bottom layer were fixed as the boundary, while the rest atoms were set as the thermostatic atomic layer with a Langevin thermostat maintained at a temperature of 300 K.The periodic boundary condition was used in x and y directions, and the fixed boundary condition was adopted in the z direction.To compare the frictional behavior of these two materials, the reactive force filed (ReaxFF) potential function [23] was chosen to describe the interaction between Mo and Te atoms for both materials.In order to be compatible with the ReaxFF potential function, the fix indent command was used to realize the simulation of the friction process.The indenter with a radius of 2 nm acted as virtual spherical probes and slid at a constant speed of 10 m/s in the x direction in 0.25 ns, as shown in the inset of Fig. 4(c).The magnitude of the applied load was adjusted by the press-in depth of indenter, and the forces on the indenter in x and z directions were recorded as friction and load, respectively.All MD simulations were performed using the Large-Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [24], and the visualization was displayed and analyzed using the OVITO (version 3.3.5,OVITO GmbH) and VESTA (version3, JP-Minerals) softwares [26].
As shown in Figs.www.Springer.com/journal/40544| Friction the friction force of the 2H phase was always smaller than that of the 1T′ phase, and the COFs obtained from the fitting curves were 0.039 and 0.158, respectively.Although the simulation conditions could not match the experiments precisely due to computational limitations, the results obtained from the simulation were congruent with the experimental results in trend.In summary, the results of the MD simulations further confirmed the reliability of the experimental results.

Discussion
During the friction measurement, materials were measured under the same environment and condition, so the temperature, humidity, and velocity of the experiment were not the main reasons of the friction difference between 1T′-MoTe 2 and 2H-MoTe 2 .In addition, the friction force did not change significantly with tip wear in the experiment, and the MD simulation did not include the influence of the tip wear, so both the wear and elastic deformation of the tip were not the dominant mechanism as well.Furthermore, since the friction force was closely related to the surface roughness of the material, the difference of the surface roughness in the friction areas of these two materials was measured to be within 0.25 nm (root-mean-square roughness), which was not sufficient to produce such a significant friction contrast.
To further analyze the reason for the friction contrast between 1T′-MoTe 2 and 2H-MoTe 2 , the DFT calculations were carried out using the Vienna ab initio Simulation Package (VASP; version 5.4.4,Hafner) [27].For all the DFT calculations, the exchange correlation terms were treated by the Perdew-Berke-Ernzerhof (PBE) [28] form of the generalized gradient approximation (GGA).Standard VASP projector augmented-wave (PAW) [29] potentials were used to describe Mo, Te, C, and H.Among van der Waals corrections, the optB88-vdW function [30] was further used for calculating the sliding energy.A single methane (CH 4 ) molecule was used, acting as the probe in the AFM experiment, to simulate the friction process [31].A model containing a supercell of 288 atoms and a CH 4 molecule was constructed to avoid interactions between neighboring CH 4 molecules.Moreover, a vacuum region of 15 Å was set up in the z direction to avoid the interaction between adjacent supercells in the z direction.After convergence test calculations, the plane-wave basis kinetic energy cutoff was set to be 500 eV, and the Brillouin zone was sampled by a Monkhorst-Pack [32] k-point mesh of 1 × 1 × 1.The electronic self-consistent calculations were converged within 10 −5 eV.The internal structure relaxations stopped when the residual force on each atom was less than 0.01 eV/Å.The bilayer MoTe 2 and CH 4 molecules were first optimized separately, and then combined for structural optimization.For calculating the sliding energy, the atoms of the MoTe 2 were fixed for VASP selective dynamics, while the CH 4 molecule was displaced at different positions, restricting the degree of freedom of the in-plane positions [33][34][35].
The potential energy surfaces (PESs) (Figs.5(a) and 5(b)) display different patterns corresponding to their lattice structures.The maximum energy barrier of 1T′-MoTe 2 is 53.80 meV, which is more than twice as large as that of 2H-MoTe 2 (22.20 meV).Therefore, in a random sliding process, the maxmium potential barrier that 2H-MoTe 2 needed to overcome was smaller than that of 1T′-MoTe 2 , implying less energy dissipation and smaller friction force [36].For the case of a specific friction path, the process of sliding along the minimum energy path (MEP) was analyzed.The MEP of 1T′-MoTe 2 was corresponding to the arrow (Fig. 5(a)), starting from A1, passing through A2, and ending at A3. Corresponding to the atomic structure, as shown in the inset of Fig. 5(c), CH 4 molecule moved from the initial molecular structure position, and then moved along the arrow to end at the CH 4 structure.For 2H-MoTe 2 , the MEP moved from B1 (Fig. 5(b)) in the direction of the arrow, passed B2, and ended at point B3.The corresponding path in the atomic structure is shown in the inset of Fig. 5(d).The potential energy profiles along the MEP are shown in Figs.5(c) and 5(d).The minimum energy barrier of 1T′-MoTe 2 (9.3 meV) was nearly twice as large as that of 2H-MoTe 2 (5.7 meV), which showed good consistency with the maximum energy barrier.The differences that exist on the maximum energy barrier and MEP energy barrier were an intuitive explanation for the friction difference between these two phases of MoTe 2 .To investigate the effect of charge distribution on the PES, the charge distributions of the bilayer MoTe 2 with optimized geometries were calculated, as shown in Figs.6(a) and 6(b).In the three-dimensional (3D) charge distribution plots, more charges distributed around atoms, especially Mo atoms.The 2D charge analysis was performed on the (010) crystal plane of the 1T′ phase and the (100) crystal plane of the 2H phase.The charge density around Mo atoms was higher than that of Te atoms, and the isoelectric surface around the Mo atoms of 2H-MoTe 2 was closer to a sphere in appearance.The comparison of the two systems indicated that the charge density in the 2D plane showed relatively small differences.Moreover, the influence of electrons was not considered in the MD simulation, so the difference in charge densities was not the main reason for the difference of friction characteristics of the two phases.By analyzing the optimized crystal structures of both phases after the DFT simulations, as shown in Figs.6(c) and 6(d), it was found that the atomic arrangement of the 1T′ phase was relatively disordered compared to that of the 2H phase, which indicated that both the bond lengths and the bond angles were different.The DFT simulations showed that the cohesion energy [37] of the 2H-MoTe 2 was 20.06 meV, smaller than that of the 1T′-MoTe 2 per MoTe 2 formula unit, which means that the energy required to break the chemical bond between Mo and Te atoms was lower, and the intra-layer interaction was weaker.Besides, the interlayer distance (d = 7.002 Å, the minimum distance between Mo atoms of adjacent layers [33]) of 2H-MoTe 2 was larger than that of the 1T′ phase (d = 6.679Å).The larger d indicates weaker interlayer interactions, which contributes to the decrease of friction [33,38].The DFT simulations showed that the interlayer binding energy of the 2H phase was 4.77 meV, smaller than that of the 1T′ phase per MoTe 2 formula unit.In summary, the weaker interactions between Mo and Te atoms and the larger layer spacing of 2H-MoTe 2 lead to a smaller PES barrier for 1T′-MoTe 2 , causing a smaller friction force than that of the 1T′-MoTe 2 .
Some differences can be found between experiments and simulations.When simulations were performed based on experimental conditions, there were some reasonable simplifications between the model and the actual conditions due to the limitations of computational power and computational cost, such as neglecting the influence of tip materials when performing MD simulations and replacing the AFM probe by a CH 4 molecule when performing the DFT simulations.These reasonable simplifications were unavoidable, which leads to differences between experiments and simulations.In general, although the specific numerical relationships do not match perfectly, the simulation and experimental results are in good agreement in terms of trends and can explain the experimental friction behavior intuitively based on simplifying certain conditions.

Conclusions
In summary, it was found that the friction of 2H-MoTe 2 was an order of magnitude smaller than that of 1T′-MoTe 2 , and the COFs were 0.013 and 0.311, respectively.The DFT calculations revealed that the difference between the PES barriers of these two materials was found to be the intuitive explanation for the friction difference.The larger d and weaker interactions between Mo and Te atoms of the 2H-MoTe 2 were the deeper reasons for the smaller friction force than that of the 1T′-MoTe 2 .The differences in friction between different structural phases of MoTe 2 indicate a close relationship between friction and atomic arrangement, which suggests that friction can be actively regulated by controlling the phase transition.

Fig. 1
Fig. 1 Characterizations of MoTe 2 .Optical microscope images of (a) 1T′-MoTe 2 and (b) 2H-MoTe 2 on SiO 2 /Si substrates.The insets of (a) and (b) show the height profiles along the yellow dashed lines measured by the AFM.Raman spectra of (c) 1T′-MoTe 2 and (d) 2H-MoTe 2 obtained from the areas shown in the red dashed circles in (a) and (b), respectively.Friction experiments were carried out in the area shown in the orange boxes of (a) and (b).

Fig. 2
Fig. 2 Friction force measurements using the AFM.Mappings of friction forces at different loads for (a) 1T′-MoTe 2 and (b) 2H-MoTe 2 .(c) Variations of friction force with load at different rotation angles of samples.The error bars show the standard errors over three sliding cycles.The dashed lines show the linear fits to the data, and the marked slopes are the COFs.

Fig. 3
Fig. 3 Atomic-scale friction maps of MoTe 2 .(a) Mapping of friction signal of 1T′-MoTe 2 .(b) Reciprocal lattice obtained by 2D FFT on (a).(c) Atomic-level stick-slip map obtained by FFT filtering of (a).(d) Unit cell structure of 1T′-MoTe 2 .(e) Friction profile extracted along the blue dashed line in (c).(f) Mapping of friction signal of 2H-MoTe 2 .(g) Reciprocal lattice obtained by 2D FFT on (f).(h) Atomic-level stick-slip map obtained by FFT filtering of (f).(i) Unit cell structure of 2H-MoTe 2. (j) Friction profile extracted along the blue dashed line in (h).

Fig. 4
Fig. 4 MD simulations of friction process.Top view of atom arrangement of uppermost layers of MoTe 2 : (a) 1T′-MoTe 2 and (b) 2H-MoTe 2 MD models.(c) Variations of friction force with load obtained from MD simulation.The inset in the upper left corner is the schematic diagram of the simulation.The dashed lines show the linear fits to the data, and the marked slopes are the COFs.

Fig. 5 Fig. 6
Fig. 5 DFT simulations of PES distribution of MoTe 2 .PESs of bilayer (a) 1T′-MoTe 2 and (b) 2H-MoTe 2 with CH 4 molecule at the top.The arrows and letters marked in (a) and (b) indicate the routes of MEPs.Relative energy barriers calculated for translation of CH 4 along the path indicated by the arrows for (c) 1T′-MoTe 2 and (d) 2H-MoTe 2 .The insets (in (c) and (d)) represent the sliding paths of CH 4 along the MEP, where the positions at the beginning of the arrows are the initial positions of the CH 4 molecule and the structures at the termination of the arrows are the final positions of the CH 4 molecule.