Chen
Qian
and
Jiugen
Wang
*
Department of mechanical engineering, Zhejiang University, 866 Yuhangtang Rd, Hangzhou 310058, P. R. China. E-mail: me_jg@zju.edu.cn
First published on 18th November 2019
In this study, we obtained dodecagonal monolayer silicene with three-fold and four-fold coordination by melt quenching via molecular dynamics (MD) simulations. Stretching simulation of the pre-strained dodecagonal silicene showed lower critical stress than the honeycomb silicene and resulted in an increase in six-fold rings during the plastic deformation since the four-coordinated atom sites are less mechanically favoured than the three-coordinated sites. The friction behaviours with an AFM tip sliding on the dodecagonal and honeycomb surfaces under different loads and tip sizes were simulated and compared. For all the investigated cases, the dodecagonal surface always showed a lower mean friction force than the honeycomb surface. The lower friction of the quasicrystal was observed, and the mechanism was illuminated successfully for the first time by MD simulations. The reduced friction of dodecagonal silicene can be explained by the morphology of the one-dimensional potential energy surface (PES). The 1D PES of dodecagonal silicene has longer potential corrugation lengths than honeycomb silicene, which induce mild motion of the tip in the stick process and lower friction force. Considering the close density of the employed dodecagonal and honeycomb structure, the longer potential corrugation length is a consequence of the quasiperiodic morphology rather than the interspace between atoms. Besides, with a larger tip size, the 1D PES on the dodecagonal surface has a flatter area, which contributes further to the reduced friction force on the dodecagonal surface.
Most bulk quasicrystals exhibit desirable properties including high brittleness, low friction, low surface energy, high hardness, wear resistance, anti-corrosion, high thermal resistance, high resistance, excellent dispersion strengthening property and hydrogen storage.15–20,24 Furthermore, the micro-pillar experiment on an Al–Pd–Mn icosahedral quasicrystal and Al–Co–Ni exhibited the highest specific strength among reported materials to our knowledge with excellent ductility.25,26 Moreover, the properties of quasicrystals in the nanoscale remain to be explored.
With the prosperity of 2D materials, silicene has garnered widespread interest due to its compatibility with bulk silicon in micro-electro mechanical systems (MEMS) and the semiconductor industry. Silicene nanosheets with different superstructures have been epitaxially deposited on the surfaces of Ag(111),27 Ag(110),28 Ir(111),29 ZrB2(0001),30 ZrC(111)31 and MoS2.32 The scalable fabrication of high-quality silicene has been successfully achieved with mild oxidation and exfoliation of Ca2Si.33 Free-standing monolayer silicene has a low buckled honeycomb structure with a lattice constant of 3.84 Å and buckling length of 0.40 Å due to pseudo-Jahn–Teller distortion (PJT).34 Its band structure shows massless Dirac fermion-like charge carrier, while its π and π* bands cross linearly through the Fermi level.35 Also, its bandgap is tunable with electrical field,36 making it a potential candidate for electrical field transistors.37 First principle calculation predicted that silicene doped by transition metal elements (Cu, Ag, Au, Pt, and Ir) will induce a sizeable direct bandgap at specific coverage and enables a p–i–n junction with three types of doping at different regions.38 The oxidation of the silicene superstructure surface on the Ag(111) substrate can open a tunable bandgap ranging from 0.11 to 0.30 eV.39 When the stacking mode of bilayer silicene was investigated, the indirect bandgaps of 0.29 eV and 1.16 eV were observed for the AA′ and slide-2AA morphologies, respectively.40,41 The in-plane stiffness of monolayer silicene obtained by DFTB is 62.7 N m−1 in the zigzag direction and 63.4 N m−1 in the armchair direction, which are merely 10% of that of graphene.42 Furthermore, recent studies showed its potential application for the absorption of toxic gases (NO2 and SO2),43 hydrogen storage44 and as an anode material for lithium-ion batteries.45
In this context, we employed massive parallel molecular dynamics simulation to obtain monolayer dodecagonal silicene with procedures analogous to that used for bilayer silicon quasicrystals. The obtained monolayer dodecagonal conformation was mechanically unstable at room temperature, and thus further steps were adopted to stabilise the dodecagonal structure at 10 K. Simulation of the quasicrystal silicene in tension was performed to study its mechanical property and fracture dynamics. Considering the low friction coefficient property of bulk quasicrystals, friction tests of the quasicrystal silicene were performed in contact mode using an atomic force microscope (AFM).
(1) |
(2) |
(3) |
Silicon was firstly melted into a liquid and confined between two Lennard-Jones 9-3 potential walls,
(4) |
Tensile simulation of dodecagonal silicene was performed under periodic boundary condition with ample vacuum space in the vertical direction to eliminate periodic image. The quasicrystal silicene size used for tension was 110.8 Å × 196.9 Å in the x- and y-direction, respectively, while a quasicrystal of a specific size could not be constructed with simple replication of a unit cell, and the size of prepared dodecagonal silicene is only relevant to the initial state of liquid silicon and quenching process. The Velocity-Verlet integrator was used to update the velocity and position every 1 fs. Dodecagonal silicene was stretched with a strain rate of 108 s−1 in the y-direction and the length of the simulation box in the x-direction was kept constant. Therefore, silicene was subject to a biaxial stress state during the tensile process. The Nose–Hoover thermostat was coupled to control the temperature at 10 K with a temperature damping parameter of 100 fs. To obtain the stress–strain relationship, the virial tensor52 was calculated as follows:
(5) |
(6) |
To probe the friction on the incommensurate surface, the simulation was performed as a diamond tip sliding across the dodecagonal silicene, which is illustrated in Fig. 1. During the stick-slip process, the tip can have a high instantaneous speed and excessive oscillation, which interfere with observation. The kinetic energy is typically dissipated through the materials in contact by a thermostat. However, for the hemispherical tip and rigid silicene, the limited contact area will aggravate the oscillation. Therefore, a diamond block was adopted to increase the contact area and eliminate the excessive oscillation. The tip movement perpendicular to the sliding direction was confined to the original position. The size of the tip was 20 Å × 20 Å × 10 Å, while the topmost 3 Å slab of the silicon atoms was rigid. The load was imposed directly on the rigid part of the tip. In the lateral direction, the rigid layer was coupled to a virtual atom with the spring, while the virtual atom moved with constant velocity and pulled the tip forward during the sliding process. The stiffness of the spring k = 10 N m−1 was used to mimic the compliance of the AFM system cantilever, which has been employed in previous studies,53 and that k is larger than the effective stiffness of the contact. Unlike graphene, which is chemically inert, silicene (especially dodecagonal silicene) presents higher chemical activities. Consequently, the friction with the diamond tip would easily lead to the damage of the silicene. Thus, to preserve the structures, the silicene was set as rigid during the friction process. In previous literature, rigid phosphorene54 and rigid crystalline surfaces55,56 were successfully used to explore the effects of lattice commensurability on friction with MD simulations. A small time step of 1 fs was adopted to capture the motion of the diamond tip. The Lennard-Jones potential was used for interaction between silicon and carbon atoms, where ε and σ were 0.092 eV and 3.0 Å with a cutoff radius equal to 10 Å, respectively. These LJ parameters were successfully used to describe the van der Waals force between graphene and a silicon tip.57 The covalent bond of C–C in the diamond tip was described with widely used Tersoff potential. The system was initially relaxed for 100 ps with a load of 40 nN. Then the virtual atom was moved with a constant velocity of v = 2 nm ns−1 for 3 ns (6 nm in the sliding direction). The force coupled to the virtual atom was recorded as the friction force of the diamond tip. The temperature was 10 K to exclude thermal fluctuation and controlled with the Nose–Hoover thermostat under an NVT ensemble. Furthermore, friction on the zigzag direction of monolayer silicene was simulated under the same condition for comparison.
Fig. 2b shows the radial distribution function (RDF) of the system at different temperatures. The smooth attenuation of RDF after the first peak at 1800 K shows a typical feature for the liquid phase. As the temperature approaches the value of 1200 K, the third, fourth and fifth peaks emerge, indicating a phase transition from liquid to a solid structure. Besides, the value of 1200 K is close to the phase transition temperature of 1226 K derived from Fig. 2a. At the temperature of 300 K, more distinct RDF peaks can be found. The local atomic structure of dodecagonal silicene at 300 K is illustrated in Fig. 3a. For the coordination number (CN) of the dodecagonal structure at 300 K, 54.1% is equal to 3 and 45.9% is equal to 4, indicating an sp2 and sp3 hybridization mode, respectively. The cutoff radius used for CN is 3 Å, which is the first minimum of the RDF. In Fig. 3a, a dodecagonal cluster is mapped into a 12-fold tiling with some distortion since the SW potential favors the tetrahedral angles of bulk silicon. For comparison, a perfect dodecagonal tiling59 is illustrated in Fig. 3b. The selected area electron diffraction (SAED)60 was simulated for the structure at 300 K, as shown in Fig. 3c. The diffraction pattern in Fig. 3c shows a symmetry of 12-fold, indicating the dodecagonal conformation. To quantify the disorder of the dodecagonal silicene, we performed additional SAED calculations for a perfect dodecagonal quasi-lattice and the low bucked honeycomb silicene. The perfect dodecagonal quasi-lattice was obtained by the projection method.61 The percentages of the frames in the SAED patterns with an intensity higher than 50 (10) are 1.13% (6.03%), 1.10% (3.64%) and 0.59% (1.72%) for the dodecagonal silicene, the perfect dodecagonal quasi-lattice and the low buckled honeycomb silicene, respectively. The degree of localization in the k-space for the dodecagonal silicene is slightly lower than that of the perfect dodecagonal quasi-lattice and lower than that of the low buckled honeycomb silicene. Note that the preparation of the dodecagonal silicene still conforms to the Mermin–Wagner theorem due to the presence of the potential walls in the third direction.
Fig. 5 shows the friction force versus sliding distance relationship for the low buckled honeycomb and dodecagonal silicene. The typical stick-slip pattern of the atomic force microscope is observed. For the honeycomb structure, the curve of the frictional force indicates some multiple-slip mechanism with a sliding length of around either 3.9 Å or 7.7 Å, which is almost equal to the lattice constant of 3.84 Å or twice that. In contrast, the stick-slip friction for dodecagonal silicene is aperiodic with a varying peak force in the studied sliding length scale as a result of the quasiperiodic morphology. Both the mean friction force and peak force of the honeycomb structure are significantly larger than that of the dodecagonal silicene. However, it is not convincing to conclude that the dodecagonal structure will induce a lower friction force since the low buckled honeycomb structure has a larger buckling length. Further simulations were performed with all the silicon atoms in the same atomic plan for both the honeycomb and dodecagonal silicene.
Fig. 5 Stick-slip friction pattern of low buckled honeycomb and dodecagonal silicene with a tip side length of 20 Å under a load of 40 nN. |
To study the load dependency of friction force, loads of 20 nN, 40 nN, 60 nN and 80 nN were applied to the diamond tip. Fig. 6a shows the mean friction as a function of the load on the planar honeycomb and dodecagonal silicene. The mean friction forces of the planar structures (0.68 nN for the dodecagonal silicene and 1.13 nN for the honeycomb silicene) under the load of 40 nN were lower than that for their buckled counterparts (0.90 nN for the dodecagonal silicene and 2.95 nN for the honeycomb silicene), which was expected due to the larger atomic asperities of the buckled structures. For both planar structures, the mean force increased monotonically with load, and the difference between the honeycomb and dodecagonal structures widened for a larger load. For each load investigated, dodecagonal silicene always showed a lower mean friction force than the honeycomb silicene. It seems that the lower friction force of dodecagonal silicene is an intrinsic property instead of a result of specific loads.
Fig. 6 Mean friction force of planar honeycomb and dodecagonal silicene: (a) under loads of 20 nN, 40 nN, 60 nN and 80 nN and (b) with tip side lengths of 20 Å, 30 Å and 40 Å. |
To exclude the effect of tip size, we simulated the sliding process with the tip of side lengths equal to 20 Å, 30 Å and 40 Å under a load of 40 nN. The height of the tip for both cases was 10 Å. The mean friction with different tip sizes is illustrated in Fig. 6b. For each tip size, the mean friction on the planar dodecagonal silicene was always lower than the planar honeycomb silicene. The mean friction of the dodecagonal structure decreased monotonically with an increase in the size of the tip. Differently from the monotonic decreasing tendency of dodecagonal silicene, the mean force of the honeycomb structure firstly decreased as the tip size changed from 20 Å to 30 Å and then increased as tip size increased to 40 Å. For the diamond tip with a side length of 40 Å, the mean force of the dodecagonal silicene was even 4 times lower than that of the honeycomb silicene. Fig. 7 illustrates the top view of the last layer of atoms of the tip with a side length of 40 Å and the silicene layer with a dodecagonal or honeycomb structure. Unfortunately, the friction with a larger size tip could not be simulated since the oscillation of a larger tip is difficult to control.
Fig. 7 Top view of the last layer of atoms of the tip with a side length of 40 Å and the silicene with (a) dodecagonal structure and (b) honeycomb structure. |
To analyse the origin of the lower friction force on dodecagonal silicene, the stick-slip process and one-dimensional potential energy surface (PES) are discussed. Fig. 8 shows the friction force versus sliding distance (upper panel), the position of the diamond tip (middle panel) and one-dimensional PES (lower panel) on planar dodecagonal silicene and planar honeycomb silicene with the tip side lengths of 20 Å (Fig. 8a), 30 Å (Fig. 8b) and 40 Å (Fig. 8c). It should be noted that the one-dimensional PES was obtained with a uniformly moving tip and its abscissa is the position of the tip instead of the x-coordinate value of the virtual atom. The stick-slip friction curve of the honeycomb structure is almost periodic with a constant peak force. Whereas, the friction force of dodecagonal is aperiodic with changing peak forces, which is expected due to its quasiperiodic structure. From Fig. 8a and b, it is not easy to directly tell which structure has a lower friction force since some of the peak forces of dodecagonal silicene are lower than the honeycomb structure and some are higher. In Fig. 8a, the one-dimensional PES for honeycomb silicene is periodic with two energy minima in each period, while the PES on the dodecagonal surface is aperiodic with varying amplitudes of potential corrugation. Generally, the depth of the potential barrier for dodecagonal silicene is larger than that of honeycomb silicene in Fig. 8a. This is opposite to our expectation about the relationship between friction and the potential corrugation, indicating that there are more dominant mechanisms such as lattice mismatch.62 As we looked further into the morphology of PES in Fig. 8a, the PES of the honeycomb structure is more compact with smaller lengths of potential corrugation. Moreover, the compact morphology of PES of the honeycomb structure made the tip stick firmly to the potential corrugation before the slip. On the contrary, the longer length of the potential corrugation and mild slope of PES for dodecagonal silicene allowed the tip to move forward slowly in the stick process and resulted in a lower mean friction force despite the higher potential barrier. The typical mild motion of the tip during the stick process on the dodecagonal surface is marked and magnified in the middle panel of Fig. 8a. Therefore, a higher potential barrier does not necessarily lead to higher friction force with different lengths of potential corrugation. Note that the density of dodecagonal silicene is quite close to that of honeycomb silicene (with a difference about 2.96%), where the longer length of potential corrugation is not a consequence of the distance between atoms but is attributed to the quasiperiodic morphology.
Filippov et al.22 (in the framework of the Tomlinson model with parameters chosen to fit the experimental results) assumed that the potential corrugation lengths differing in the periodic and quasiperiodic directions was the reason for the reduced friction, and the quasiperiodicity itself was not relevant. Although further studies23 found that Filippov's parameters did not correspond to the STM images of the experimental surface, our calculations show that the quasiperiodicity itself will cause longer potential corrugation lengths. Besides, our simulation result is in accordance with the widely reported experiments about the reduced friction of quasicrystals.15–20
Moreover, the difference between friction behaviours with varying tip sizes in Fig. 8 should be analysed for both dodecagonal and honeycomb silicene. For the honeycomb structure, the morphologies of the one-dimensional PES for various tip sizes are all featured with the same periodic length while each period has two different potential corrugations. As side length of the tip increases to 30 Å, one of the amplitudes of potential corrugation increases slightly from 0.37 eV to 0.47 eV and the other decreases from 0.33 eV to 0.20 eV; thus, the mean force decreases from 1.12 nN to 0.61 nN in Fig. 8b. The amplitude of both potential corrugations increases remarkably for the tip with a side length of 40 Å, which accounts for higher the mean friction force in Fig. 8c. In contrast, the general potential corrugations on dodecagonal silicene for different tip sizes have similar magnitude, which is different from that on the honeycomb surface.
With an increase in tip size, more relatively flat areas can be identified on the 1D PES of the dodecagonal surface in Fig. 8c. The flatter morphology of potential corrugation further contributes to the reduced friction force on the dodecagonal silicene, in addition to the mechanism of longer potential corrugation length.
This journal is © the Owner Societies 2020 |