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Numerical study of three-body diamond abrasive polishing single crystal Si under graphene lubrication by molecular dynamics simulation
Computational Materials Science 171 (2020) 109214
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Numerical study of three-body diamond abrasive polishing single crystal Si under graphene lubrication by molecular dynamics simulation
T
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Houfu Daia,b, , Fa Zhanga, Yuqi Zhoua a b
College of Mechanical Engineering, Guizhou University, Guiyang 550025, China State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Molecular dynamics Three-body diamond abrasive Mechanical polishing Graphene lubrication Subsurface damage
In this study, molecular dynamics (MD) simulation was used to investigate a new mechanical polishing method for three-body polishing of single crystal Si under the lubrication of graphene. The polishing depth and polishing speed were adjusted under the same processing parameters to compare the results. The development of polishing force, atomic displacement, coordination number, temperature, potential energy, friction coefficient, and polishing surface morphology was studied during nano-polishing. The analysis shows that the polishing depth in silicon polishing plays a crucial role in the change of coordination number of silicon. The deeper the polishing depth, the higher the polishing force, the more obvious the subsurface damage layer, the higher the potential energy. High defect atomic number and high normal stress. Moreover, the material removal rate is proportional to the polishing depth; a larger polishing speed significantly increases temperatures and potential energy. However, a smaller polishing rate does not result in fewer defective atoms and Bct5-SI/SI-II type atoms, as well as lower material removal efficiency. Finally, graphene-lubricated three-body polished single crystal silicon can improve the surface quality and reduce material removal efficiency.
1. Introduction With the development of science and technology, the application prospect of hard and brittle materials is very broad. These materials are used in new energy, aerospace, automotive, general machinery and other industries owing to their high hardness, high strength, anti-wear, high-temperature resistance, corrosion resistance, oxidation resistance, and other excellent physical and mechanical properties. In addition to being used for making tools and coating on a tough substrate for wear parts, they can also be used as a key component for bearings, seal rings, and aero engines [1–4]. Ultra-precision polishing is an effective processing method to obtain an ultra-smooth surface [5]. However, due to the high brittleness, high hardness, low plasticity, microcracks, and other shortcomings of hard and brittle materials, many types of damages such as metamorphic layers, surface/subsurface cracks, residual stresses, phase change regions often occur during ordinary polishing [6–8]. These damages will seriously affect the processing quality and surface characteristics of hard and brittle materials and will significantly reduce the fatigue/ breaking strength, corrosion resistance, wear resistance and other performance of the workpiece, and even catastrophic failure. Therefore, it is important to thoroughly investigate and reveal the polishing
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mechanism of hard and brittle materials, research advanced polishing process, predict and control the polishing damage introduced by hard and brittle materials during polishing to improve polishing efficiency, improve surface quality and improve the reliability of processed parts. It has become an urgent problem to be solved in the application of hard and brittle materials. The ultra-precision polishing process of tools through molecular dynamics simulation has been extensively investigated, but most scholars regard the tool as a rigid body with no rotation speed, and this is inconsistent with the tool movement during the actual polishing process. Jain et al. [9] proposed a mathematical model based on twinbody machining in 1999; however, the theoretical results did not match the experimental data of surface roughness changes well. In the same year, they proposed neural network methods to construct a learning model to predict the problem of material removal in limited experimental data. Trezona et al. [10] established a theoretical model to derive a correlation wear trend plot to determine the proportion of twobody wear and three-body wear dominated in the microscale abrasive wear test. Xie et al. [11] experimentally studied the mechanism of material removal during free grinding and polishing and. A theoretical model was developed to predict the relationship between polishing parameters and the wear rate of hard abrasive particles (softer than
Corresponding author at: College of Mechanical Engineering, Guizhou University, Guiyang 550025, China. E-mail address: [email protected] (H. Dai).
https://doi.org/10.1016/j.commatsci.2019.109214 Received 2 June 2019; Received in revised form 20 August 2019; Accepted 20 August 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.
Computational Materials Science 171 (2020) 109214
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processing is necessary. When the shear stress is too low to maintain dislocation emission in the chip formation region, crack propagation becomes dominant. Goel et al. [27] pointed out that in the processing of hard and brittle materials in nanometers, the temperature analysis of the processing region is very important. The temperature change is determined by the number of atoms, the energy released by the environment, and the release rate. Dai et al. [28] shows that potential energy is the internal energy of the system and it changes with the position or arrangement of atoms in the object. The change in potential energy is one of the important factors to be considered in the nanoprocessing. The following physical quantities were calculated: the temperature of the graphene layer/polishing region, the graphene layer/workpiece internal coordination number, the polishing region stress, the graphene layer friction coefficient, and the internal potential energy of the workpiece. In this study, the diamond polishing particles in the ultra-precision three-body polishing of single crystal silicon under graphene, different polishing speed/temperature on the internal silicon atom coordination number of the workpiece, the surface morphology of the process, the damage degree of the subsurface layer, friction. The coefficient and the stress, and temperature and potential energy in the polished area vary with polishing distance. Ultimately, deeper polishing depth has a decisive effect on the phase transition of the silicon atoms, resulting in a more severe subsurface damage layer, thereby increasing the coefficient of friction, stress, potential energy, and temperature inside the workpiece. We found that the phase change atom, temperature, potential energy, subsurface damage layer, surface topography and friction coefficient of the workpiece did not change significantly when the speed of the triamma polishing of the diamond abrasive grains was low, proving that the graphene was in the form of diamond. The three-body polishing of single crystal silicon has an ultra-lubricating effect.
abrasive particles) sandwiched between the cushion and the workpiece. Fang et al. [12] indicates that the motion pattern of the abrasive grains in the three-body wear is very important for the wear of the material. They observed the movement of individual abrasive particles in detail using a device for three-body wear. In the two-body contact sliding (the tool has no rotation speed), the hard and brittle material is deformed into a way of no wear, adhesion, pear cultivation, and cutting [13,14]. However, in the three-body contact sliding (the knife rotates), the deformation of the hard and brittle material has no wear, condensation, adhesion, and pear cultivation. Zhang et al. [15] first studied the ultraprecision polishing wear mechanism of single crystal silicon by molecular dynamics (MD) simulation and found that amorphous phase transformation is the main deformation of single crystal silicon. Zarudi et al. [16] used molecular dynamics (MD) simulation and experimental methods to study the atomic structure changes of single crystal silicon during ultra-precision polishing, indicating that the MD simulation results were almost consistent with the experimental results. Zhao et al. [17] used three-dimensional MD simulation to study the material removal mechanism of mechanical polishing of single crystal silicon by using diamond as the tools. They also studied the effects of diamond abrasive particle autotransmission speed and direction [18], indicating that with increasing rotation speed of diamond abrasive grains, the deformation mechanism changes from cutting to plowing; the rotation speed and direction of abrasive grains affect the surface topography and quality of the workpiece and the distribution and evolution of defects under the surface of the workpiece. In the actual production process, due to the adverse effects of friction on the processing efficiency, durability and environmental compatibility, reducing the mechanical friction associated with friction and wear in mobile mechanical systems has attracted increasing attention. This problem can be addressed by searching new materials that reduce friction and wear. Coatings and lubricants (liquid or solid) are especially important. In 2008, Lee et al. [19] proposed that graphene is one of the materials with the highest strength known. They measured the elasticity and intrinsic fracture strength of the freestanding single-layer graphene film by nanoindentation under atomic force microscopy. The atomically perfect nanoscale material was mechanically tested. The results show that the ocene has good toughness and good mechanical properties. Berman et al. [20] provided a tribological investigation based on nanoscale to macroscopic grapheme. Graphene can be used not only as a lubricant, but also as an additive for lubricating oils, composites and solvents and has a significant effect on the friction and wear generated during processing. Bai et al. [21] studied the lubrication behavior of graphene-like diamond-like carbon (DLC) film scratched at the tip of diamond by MD simulation, indicating that graphene can effectively lubricate the DLC film. The wear condition in the lubrication process mainly depends on the normal force. The smaller normal force can obtain ultra-low friction force, which is expressed as the super-lubrication phenomenon of graphene. Zhang et al. [22] used MD simulation to study the friction behavior of diamond tip nano-scratches on multilayer graphene. It is considered that when the scratch depth is less than 5.3 Å, the graphene layer has ultra-low friction performance. At scratch depth greater than 5.3 Å, the graphene undergoes a phase change, and the friction coefficient increases by at least 10 times. These literature studies show that graphene has sufficient mechanical properties and superlubricity during processing to be used as a solid lubricant for ultra-precision three-body abrasive polishing of single crystal silicon. Wang et al. [23] and Zhang et al. [24] considered that the change in the atomic coordination number (CN) of the workpiece during statistical processing has a guiding significance for the phase transition of the research workpiece. However, Gilman et al. [25] pointed out that the CN of Si-II cannot be fully expressed as 6, and other measures are needed to confirm the HPPT state of the workpiece. Cai et al. [26] proposed that in order to better understand the brittle-ductile transition mechanism, studying the distribution and variation of stress during
2. Simulation method Fig. 1 shows a three-dimensional model of ultra-precision threebody polishing of single crystal Si in a single layer of graphene. The dimensions of the workpiece in the x, y, and z directions are 55a × 25a × 25a(a = 5.43Å ; the size of graphene in the x, y direction is120b × 60b(b = 2.47Å) ; the abrasive radius is 4 nm. The workpiece is divided into three areas: Newtonian, thermostat, and boundary atoms. Among them, the boundary atoms do not participate in the motion during the simulation and remain fixed in the space to reduce the boundary effect and maintain the lattice symmetry. The atomic motion in the constant temperature region and the Newton region follows Newton's second law of motion. The model uses the Velocity Verlet algorithm to integrate in 1 fs time steps. The thermostat atoms use a speed scaling approach to ensure reasonable outward heat transfer. In order to obtain more accurate observation data, a cutting area of 4nm × 7.5nm × 1nm was set at the rubbing passage. The rest of the model is shown in Table 1. During the three-body abrasive polishing process, the rotational speed, cutting speed, and indentation depth of the abrasive particles are not negligible, and different variables have different effects on the physical factors inside the workpiece. In this study, the effect of a variable on the physical factors operating inside the workpiece in the case of determining two of these variables was investigated. In microscopic atomic simulation calculations, choosing the appropriate potential energy function is a necessary condition for obtaining accurate results. In this study, there are six different interaction potentials for two types of atoms in the polishing process of this study: Si–Si (internal potential of the workpiece), C–Si (potential between the abrasive particles and the workpiece), C–C (internal potential of the diamond), C–Si (potential between the graphene and the workpiece), C–C (graphene) Interaction potential with abrasive grains), C–C (graphene internal potential). Because diamond hardness is much larger than single crystal silicon and graphene, it is considered to be a rigid 2
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Fig. 1. Schematic diagram of the MD simulation model.
body, and its deformation and wear are not considered during the indentation process [29]. Based on the past work experience and experimental data [30,31], the Tersoff potential function is a three-body potential function suitable for describing the interaction between silicon atoms (Si–Si) in a workpiece [32]. The Airebo potential function is based on the Rebo potential function improved by the Tersoff potential, considering the interaction between the particles, increasing the repulsion between the particles and accounting the effects of the fourbody torsion. Therefore, the Airebo potential function can well simulate the interaction between graphene internal (C–C) atoms [33]. Tersoff/ zbl three-body potential function has been used to describe the atomic potential between workpiece and graphene (Si–C) [34]. The Morse potential function is faster and less expensive than the Tersoff potential function; therefore, it was used to describe the interaction between the workpiece and the abrasive atom (C–Si) [22,35]. Since the diamond indenter and graphene do not form a bond, the L–J potential function is used, the specific parameters are: εc − c = 2.86meV , σc − c = 0.347nm , the cutoff radius is 2.5 Å [36]. We will list the different polishing information in Table 2 to make the reader more convenient in the next reading.
Table 2 Polishing parameters.
3. Results and discussion
the surrounding environment, and the cutoff radius is 2.6 Å. After adjusting different variables, a partial cross-sectional view of the workpiece is shown in Fig. 2(a)–(c). It was found that greater the depth of the abrasive under the polishing process, greater the depth of the damaged layer under the surface; the polishing depth of the abrasive particles has a decisive effect on the depth of the underlying damaged layer. Next, the change in the polishing depth, CN = 3, Bct5-Si (CN = 5), Si-II (CN = 6) in the workpiece with the polishing distance was measured. The deeper the indentation depth of the abrasive grains, the more obvious the changes in the three atoms of CN = 3, Bct5-Si (CN = 5) and Si-II (CN = 6). The number of bct5-Si and Si-II increases with increasing polishing distance, and the increase in bct5-Si is much faster than that of Si-II. Because Si-II is unstable at pressures below 4
Polishing scheme
Polishing speed (m/s)
Polishing depth (nm)
Abrasive rotation speed (m/s)
Case I Case II Case III
100 100 100
0. 5 1 2
100 100 100
Case IV Case V Case VI
50 100 200
1 1 1
100 100 100
Table 3 Various high-pressure phases of silicon.
With increasing polishing distance, other phases such as Si-II, Si-XI, and Si-V appear in the workpiece [37]. As reported in the literature, [33] the phase transition in silicon is inextricably linked to the change in the distance between the atoms. The distance between four adjacent silicon atoms in the unprocessed process is between 2.35 Å and 2.43 Å. The neighboring atoms are distributed in the range 2.58 Å. The change in the distance between the atoms is related to the change in the coordination number of silicon from 4 to 6 [38]. Table 3 lists Si-I (brittle), Si-II (Metallic), Si-XII (R8), Si-III, Bct-5, the distance and number of five silicon-phase atoms from neighboring atoms [30,39–41]. In this study, in order to identify the different phases formed by the workpiece atoms, the radius was chosen to be larger than the maximum bond length in
Phase of silicon
Lattice structure
Interatomic distance (Å)/Quantity
Si-I(brittle) Si-II(Metallic) Si-III Si-XII(R8) Bct-5
Diamond cubic Beta-tin bc8(BCC) Rhombohedral Crystalline
2.42/4 2.42/4 2.37/4 2.39/4 2.31/1
and and and and and
2.585/2 2.585/2 3.41/1 3.23/1 or 3.36/1 2.44/4
Table 1 Simulation parameters. Materials
Workpiece:silicon
Lubricant:graphene
Tool:diamond
Number of atoms Workpiece dimension Abrasive dimension Graphene dimension Workpiece surface Time step Initial temperature Polished area
281,856 55a × 25a × 25a (a = 5.43 Å) Radius 4 nm 120b × 60b (b = 2.47 Å) [0 0 –1] on (0 0 1) surface 1 fs 300 K 4nm × 7.5nm × 1nm
2805
11,544
3
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Fig. 2. The atomic phase change statistics of the three-body polished workpiece after adjusting for different variables: (a) Case I; (b) Case II; (c) Case III. Coloring the atom according to the coordination number (CN). In the workpiece, Si-I (CN = 4), the boundary layer and the atoms of the constant temperature layer are invisible, and the abrasive grains are indicated by broken lines. (d) The amount of CN = 3 atoms in the workpiece varies according to the polishing distance; (e) the number of Bct5-Si (CN = 5) atoms in the workpiece according to the polishing distance; (f) Si-II in the workpiece (CN = 6) The number of atoms varies according to the polishing distance.
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Fig. 3. Atomic phase change statistics of three-body polished workpieces after adjusting different variables: (a) Case IV; (b) Case V; (c) Case VI. Coloring the atom according to the coordination number (CN). In the workpiece, Si-I (CN = 4), the boundary layer, and the atoms of the constant temperature layer are invisible, and the abrasive grains are indicated by broken lines. (d) The amount of CN = 3 atoms in the workpiece varies according to the polishing distance; (e) the number of Bct5-Si (CN = 5) atoms in the workpiece according to the polishing distance; (f) Si-II in the workpiece (CN = 6) the number of atoms varies according to the polishing distance; (g) the average number of Si-II atoms.
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Fig. 4. Adjusting the cross-sectional view of a transient defect structure formed by three-body polishing of an abrasive with a single variable: (a) Case I; (b) Case II; (c) Case III; (d) number of defective atoms at different polishing depths.
Fig. 5. Adjusting a cross-sectional view of a transient defect structure formed by three-body polishing of abrasives: (a) Case IV; (b) Case V; (c) Case VI; (d) Number of defective atoms at different polishing speeds.
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Fig. 6. Shows the distribution of stress in the polishing zone with the polishing distance when changing the polishing depth: (a) σxx, (b) σyy, (c) σxy.
Among them, Si-I is represented by blue atom, and Si-II, a dislocation atom and a defective atom of a surface atom, is represented by gray. Obviously, with increasing polishing depth, the number of damaged atoms in the workpiece increases. Fig. 4(c) and (d) show that when the polishing layer and the boundary layer of the workpiece with a polishing depth of 2 nm are destroyed and the number of damaged atoms are significantly higher than that in the other two cases, this again proves that the polishing depth damages the subsurface and thus the polishing layer has a decisive effect. Fig. 5(a)–(c) show the distribution of diamond structure atoms in the workpiece when the polishing speed is adjusted. The polishing depth is always maintained at 1 nm during the adjustment of the polishing speed. With increasing polishing speed, the difference in damaged atoms in the workpiece is not significant, because during processing, a single layer of graphene is applied to the surface of the workpiece as a lubricant to reduce the effect of polishing rate of the abrasive particles on the defective atoms in the workpiece. This better illustrates the super-lubricating effect of graphene, allowing diamond abrasive grains to produce a better polished surface in nano-scale mechanical tri-body polishing. When the shear stress is greater than the flow stress of the workpiece material, dislocations are more likely to occur inside the material, resulting in cracks [30]. Fig. 6 shows a comparison between the stress components in the polished area. σxx represents the normal stress in the x direction, σyy represents the normal stress in the y direction, and σxy represents the shear stress. Fig. 6(a)–(c) show the change in stress in the
GPa when polished [42], metal Si-II loses its crystal structure and transforms into amorphous silicon and other phases, such as R8 (Si-XII, Rhombohedral) and bc8 (Si-III, BCC) [43]. This leads to the rebound phenomenon of Si-II (CN = 6) shown in Fig. 2(f), i.e., the Si-II (CN = 6) will exhibit unstable fluctuations with increasing pressure. As shown from the graph in Fig. 2(f), the change in Si-II (CN = 6) was not remarkable, when the polishing depth was 0. 5 nm and 1 nm. As the polishing rate increases, more and more Si-II atoms appear under the abrasive grains, but the change in the number of Si-II atoms is not obvious as a whole. Fig. 2(d) and (e) show that when the polishing speed is 100 m/s, the number of CN = 3 and Bct5-Si (CN = 5) generated inside the workpiece is less than that at 50 m/s and 200 m/s, proving that faster polishing speed in the three-body polishing does not produce more CN = 3 and Bct5-Si (CN = 5) atoms. Fig. 3(f) and (g) show the variation in Si-II atoms with polishing distance at different polishing speeds, and the average number of Si-II atoms decreases with increasing polishing speed. The CNA method is usually used to distinguish between FCC, HCP, and BCC structures, but it is not suitable for identifying diamond structures. Therefore, in the study, the neighbor particle structure identification method is used. This method first identifies the first-level neighboring atoms of the central atom and then identifies the neighbors of these neighboring atoms. Finally, the central atom and the CNA map of the two atoms are calculated. If the map is arranged according to FCC, the central atom is labeled as a cubic diamond atom. If the HCP structure is met, the central atom is labeled as hexagonal diamond [40]. 7
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Fig. 7. Shows the distribution of stress in the polishing zone with the polishing distance when changing the polishing speed: (a) σxx, (b)σyy, (c)σxy.
Fig. 8. Temperature distribution in the polished area: (a) changing the polishing depth; (b) changing the polishing speed.
pressure of the silicon atoms in the workpiece, greater the stress component produced. Fig. 7(a)–(c) show the tendency of the individual stress components to change is generally uniform with changing polishing speed. When the three-body abrasive grains reach the 8 nm position, the respective stress components are maximized, and the larger the polishing speed, the larger the stress component, and the faster the stress recovery rate. In the graphene-lubricated three-body abrasive-polished single crystal
polishing zone with changing abrasive grain polishing depth. It can be noticed that the trends of the three stresses adjusted for different polishing depths are generally similar. Obviously, as the depth of polishing of Case I–III increases, the magnitudes of the three stress curves increase in turn. In addition, the polishing area is 8–12 nm, and as the polishing depth increases, the maximum value of each decomposition stress is larger and the recovery speed of stress is faster. This can be attributed to the deeper the polishing depth, the greater the hydrostatic 8
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Fig. 9. Distribution of potential energy in the polishing zone with changing polishing depth: (a) potential energy varies with polishing distance; (b) average potential energy.
Fig. 10. Distribution of potential energy in the polishing zone with changing polishing speed: (a) potential energy varies with polishing distance; (b) average potential energy.
Fig. 11. Variation of friction coefficient during polishing: (a) changing the polishing depth; (b) changing the polishing speed. 1 2
3
∑i mi vi2 = 2 Nkb T,where N is the number of atoms in the measurement area, vi is the velocity of the ith atom, mi is the mass of the ith atom, and kb is the Boltzmann constant. The five polishing methods in this study are relatively stationary; therefore, the kinetic energy changes caused by the motion of the workpiece during the analysis are not accounted. Fig. 8(a) and (b) show that as the polishing depth deepens and the polishing speed increases, the polishing zone temperature rises sharply, proving that both the polishing depth and the velocity
silicon, both the polishing depth and the polishing speed have significant effects on the normal stress (σxx, σyy) and the tangential force (σxy), requires attention. The effect of polishing depth and polishing speed on temperature during three-body abrasive polishing under graphene lubrication is shown in Fig. 6(a) and (b) for a better understanding. Based on literature data [44–47], the temperature is the overall property of the workpiece calculated by indirect measurement. The formula: 9
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Fig. 12. Surface topography of the workpiece after adjusting the polishing speed: (a) Case IV; (b) Case V; (c) Case VI.
Fig. 13. Surface topography of the workpiece after adjusting the polishing depth: (a) Case I; (b) Case II; (c) Case III.
Fig. 10(c) and (d) show that the average potential energy is significantly lower at the polishing rates of 0.5 m/s and 1 m/s compared to that at 2 m/s. When the polishing rate is 0. 5 m/s or 1 m/s, there is no obvious change in the potential energy change trend, and the average potential energy is close to the same. This proves that the smaller the polishing speed of the three bodies under graphene lubrication, the smaller the potential energy. The coefficient of friction is defined as the tangential force Fy divided by the normal force Fx, expressing the ability of the diamond
have a significant effect on the temperature change of the polishing zone. Potential energy is the transformation of the internal energy of the system due to changes in the position or arrangement of atoms within the object [48]. Fig. 9(a) shows that with increasing polishing depth, more atoms in the workpiece participate in the motion, increasing the potential energy in advance. In addition, the deeper the polishing depth, the larger the peak potential energy. This can be seen more clearly from the average potential energy map Fig. 9(b). 10
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two atomic numbers are produced at a polishing rate of 1 m/s; however, the polishing rate slightly affects the Si-II atoms. 3) The polishing depth is increased and the speed is increased. σxx, σyy, and σxy are more compressible. The easier the atomic dislocation, the more prone it is to brittle-ductile transition. 4) Temperature and potential energy increase with increasing abrasive depth and speed. However, when the speed is small, the difference between potential energy and temperature is not large.
abrasive particles to remove material in nanopolishing and is an important factor in the polishing process. In the process of polishing monocrystalline silicon by graphene-lubricated three-body abrasive grains, Fig. 11(a) shows that the friction coefficient becomes larger with increasing polishing depth, and according to Fig. 11(b), the polishing rate is too fast and too slow is not conducive to reducing the coefficient of friction. Based on literature [49], the friction coefficient of diamond polished single crystal silicon without graphene reaches 0.797. This study confirms that graphene is superlubricated when tri-crystal polishing single crystal silicon. Fig. 12(a)–(c) show the adjustment of the polishing rate of the surface morphology of the workpiece after polishing and the contour of the cross-section, indicating that the change in the polishing speed strongly influences the surface morphology and contour after polishing. It is well known that as the abrasive particles move forward, more and more silicon atoms will accumulate on both sides and the front end of the abrasive particles. However, in the case of graphene lubrication, Fig. 12(a) shows that the two sides of the abrasive grains and the front end did not accumulate a lot of debris, but instead left the residual silicon atoms under the abrasive grains sliding down probably because the abrasive grains rotate too fast and the polishing speed is slow. Fig. 12(b) shows that the polishing speed is 100 m/s under graphene lubrication. At a rotation speed of 100 m/s, no residual silicon atoms are left under the abrasive grains. At the same time, it will not produce more debris. Comparing Fig. 12(a) and (b), it is proved that when the rotation speed of the abrasive grains is greater than the polishing speed, residual atoms appear below the abrasive grains. When the polishing speed is 200 m/s and the abrasive grain rotation speed is 100 m/s, the surface topography of the workpiece is shown in Fig. 12(c). Comparing it with Fig. 12(a) and (b) shows that the faster the polishing speed, more cutting accumulates. In these three images, the surface morphology and cross-sectional profile of the workpiece with a z-direction difference of 1.5 nm were observed. Compared to the previous study, it can be proved that the addition of graphene-lubricated three-body polished single crystal silicon improves the surface quality and reduces the material removal efficiency. The effect of different polishing depths on the surface of the polished workpiece is shown in Fig. 13. Obviously, the deeper the polishing depth, the more obvious the indentation and swarf left by the workpiece, and the higher the amount of material removed, resulting in a higher coefficient of friction. In addition, we believe that the polishing depth has a decisive effect on the amount of material removed, and therefore the lubrication effect of graphene cannot be judged by Fig. 13.
CRediT authorship contribution statement Houfu Dai: Writing - original draft, Visualization. Fa Zhang: Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation. Yuqi Zhou: Writing - review & editing. Acknowledgements The authors would like to appreciate the fund project for the introduction of talents in Guizhou University (No. [2017]24), Guizhou Province Education Department Youth Science and technology talent growth project (No. [2018]110), and National Natural Science Foundation cultivation project for young teachers of Guizhou University (No. [2017]5788). References [1] M. Ge, H. Zhu, C. Huang, et al., Investigation on critical crack-free cutting depth for single-crystal silicon slicing with fixed abrasive wire saw based on the scratching machining experiments, Mater. Sci. Semicond. Process. 74 (2018) 261–266. [2] J. Ruckman, H. Pollicove, D. Golini, Advanced manufacturing generates conformal optics: optoelectronics world: optics, Laser Focus World 35 (7) (1999) S13–S15. [3] T. Saga, Advances in crystalline silicon solar cell technology for industrial mass production, NPG Asia Mater. 2 (2010) 96–102. [4] B. Guo, Q. Zhao, X. Fang, Precision grinding of optical glass with laser microstructured coarse-grained diamond wheels, J. Mater. Process. Technol. 214 (5) (2014) 1045–1051. [5] X.S. Han, Y.Z. Hu, S.Y. Yu, Appl. Phys. A 95 (2009) 899. [6] I. Zarudi, T. Nguyen, L.C. Zhang, Effect of temperature and stress on plastic deformation in monocrystalline silicon induced by scratching, Appl. Phys. Lett. 86 (2005) 011922. [7] Y. Gogotsi, G. Zhou, S.S. Ku, et al., Raman microspectroscopy analysis of pressureinduced metallization in scratching of silicon, Semicond. Sci. Technol. 16 (2001) 345. [8] Y.Q. Wu, H. Huang, J. Zou, et al., Nanoscratch-induced deformation of single crystal silicon, J. Vac. Sci. Technol. B 27 (2009) 1374–1377. [9] R.K. Jain, V.K. Jain, Simulation of surface generated in abrasive flow machiningprocess, Robot. Comput. Integr. Manuf. 15 (1999) 403–412. [10] K. Adachi, I.M. Hutchings, Wear-mode mapping for the micro-scale abrasion test, Wear 255 (1) (2003) 23–29. [11] Y. Xie, B. Bhushan, Effects of particle size, polishing pad and contact pressure in free abrasive polishing, Wear 200 (1–2) (1996) 281–295. [12] Kong X.L. Fang, et al., Movement pattern of abrasive particles in three-body abrasion, Wear (1993) 782–789. [13] T. Inamura, S. Shimada, N. Takezawa, N. Ikawa, CIRP Ann-Manuf. Technol. 48 (1999) 81. [14] W.J. Zong, D. Li, K. Cheng, T. Sun, H.X. Wang, Y.C. Liang, Int. J. Mach. Tools Manuf. 45 (2005) 783. [15] L. Zhang, H. Tanaka, Atomic scale deformation in silicon monocrystalline silicon in surface nano-modification, Nanotechnology 15 (1) (2003) 104. [16] L. Zhang, H. Zhao, Z. Ma, et al., A study on phase transformation of monocrystalline silicon due to ultra-precision polishing by molecular dynamics simulation, AIP Adv. 2 (4) (2012) 899. [17] Y. Yang, H. Zhao, L. Zhang, et al., Molecular dynamics simulation of self-rotation effects on ultra-precision polishing single-silicon copper, AIP Adv. 3 (10) (2013) 899. [18] J. Guo, H. Suzuki, S. Morita, et al., A real-time polishing force control system for ultraprecision finishing of micro-optics, Precis. Eng. 37 (4) (2013) 787–792. [19] C. Lee, X. Wei, J.W. Kysar, et al., Measurement of the elastic properties and intrinsic strength of monolayer graphene, Science 321 (5887) (2008) 385–388. [20] D. Berman, A. Erdemir, A.V. Sumant, Graphene: a new emerging lubricant, Mater. Today 17 (1) (2014) 31–42. [21] L. Bai, N. Srikanth, B. Zhao, et al., Lubrication mechanisms of graphene for DLC films scratched by a diamond tip, J. Phys. D Appl. Phys. 49 (48) (2016) 485302. [22] Q. Zhang, D. Diao, M. Kubo, Nanoscratching of multi-layer graphene by molecular dynamics simulations, Tribol. Int. 88 (2015) 85–88. [23] Y. Wang, S. Ruffell, K. Sears, A.P. Knights, J.E. Bradby, J.S. Williams, Electrical
4. Conclusions In this study, MD simulation was successfully used to study the polishing of diamond abrasive grains in three-body polished single crystal silicon under graphene lubrication. Based on the results of this study, the main conclusions can be summarized as follows: 1) Graphene has an ultra-lubricating effect when diamond tri-crystal polishing single crystal silicon. The results show that the number of subsurface defective atoms caused by the difference in polishing speed is low at constant polishing depth. Moreover, at lower polishing speeds, the surface topography of the workpiece is perfect and there is no excessive chipping. In addition, the three-body polishing process of adding graphene has a smaller coefficient of friction. These results indicate that graphene can reduce the atomic removal rate during the diamond tri-body polishing of graphene with a remarkable lubrication effect. 2) At higher depth of the abrasive grains, the changes in the three atoms of CN = 3, Bct5-Si, and Si-II are more obvious. It can be observed that the number of bct5-Si and Si-II increases with the polishing distance, and the increase in bct5-Si is much faster than that of Si-II. In addition, a minimum of CN = 3, Bct5-Si (CN = 5) and 11
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properties of Si-XII and Si-III formed by nanoindentation, Optoelectronic and icroelectronic Materials and Devices (COMMAD), 2010 Conference on, (2010). L. Zhang, H. Zhao, Y. Yang, et al., Evaluation of repeated single-point diamond turning on the deformation behavior of monocrystalline silicon via molecular dynamic simulations, Appl. Phys. A 116 (1) (2014) 141–150. J.J. Gilman, Mechanism of shear-induced metallization, Czech J. Phys. 45 (11) (1995) 913–919. M.B. Cai, X.P. Li, M. Rahman, Study of the temperature and stress in nanoscale ductile mode cutting of silicon using molecular dynamics simulation, J. Mater. Process. Technol. 192 (2007) 607–612. S. Goel, X. Luo, R.L. Reuben, Wear mechanism of diamond tools against singlecrystal silicon in single point diamond turning process, Tribol. Int. 57 (2013) 272–281. H. Dai, G. Chen, C. Zhou, et al., A numerical study of ultraprecision machining of mono-crystalline silicon with laser nano-structured diamond tools by atomistic simulation, Appl. Surf. Sci. 393 (2017) 405–416. H. Dai, S. Li, G. Chen, Molecular dynamics simulation of subsurface damage mechanism during nanoscratching of single crystal silicon, Proc. Inst. Mech. Eng. J: J. Eng Tribol. (2018) 1350650118765351. C.S. Moura, L. Amaral, Molecular dynamics simulation of silicon nanostructures, Nucl. Instrum. Meth. Phys. Res., Sect. B 228 (1–4) (2005) 37–40. J. Tersoff, New empirical model for the structural properties of silicon, Phys. Rev. Lett. 56 (6) (1986) 632. F.H. Stillinger, T.A. Weber, Computer simulation of local order in condensed phases of silicon, Phys. Rev. B 31 (8) (1985) 5262. W.C.D. Cheong, L.C. Zhang, Molecular dynamics simulation of phase transformations in silicon monocrystals due to nano-indentation, Nanotechnology 11 (3) (2000) 173. J. Tersoff, New empirical approach for the structure and energy of covalent systems, Phys. Rev. B 37 (12) (1988) 6991. L.V. Sang, Affect of the graphene layers on the melting temperature of silicon by molecular dynamics simulations, Comput. Mater. Sci. 111 (2016) 252–256. Y.Y. Zhang, C.M. Wang, Y. Cheng, et al., Mechanical properties of bilayer graphene sheets coupled by sp3 bonding, Carbon 49 (13) (2011) 4511–4517. D.E. Kim, S.I. Oh, Atomistic simulation of structural phase transformations in monocrystalline silicon induced by nanoindentation, Nanotechnology 17 (9) (2006)
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Numerical study of three-body diamond abrasive polishing single crystal Si under graphene lubrication by molecular dynamics simulation
T
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Houfu Daia,b, , Fa Zhanga, Yuqi Zhoua a b
College of Mechanical Engineering, Guizhou University, Guiyang 550025, China State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Molecular dynamics Three-body diamond abrasive Mechanical polishing Graphene lubrication Subsurface damage
In this study, molecular dynamics (MD) simulation was used to investigate a new mechanical polishing method for three-body polishing of single crystal Si under the lubrication of graphene. The polishing depth and polishing speed were adjusted under the same processing parameters to compare the results. The development of polishing force, atomic displacement, coordination number, temperature, potential energy, friction coefficient, and polishing surface morphology was studied during nano-polishing. The analysis shows that the polishing depth in silicon polishing plays a crucial role in the change of coordination number of silicon. The deeper the polishing depth, the higher the polishing force, the more obvious the subsurface damage layer, the higher the potential energy. High defect atomic number and high normal stress. Moreover, the material removal rate is proportional to the polishing depth; a larger polishing speed significantly increases temperatures and potential energy. However, a smaller polishing rate does not result in fewer defective atoms and Bct5-SI/SI-II type atoms, as well as lower material removal efficiency. Finally, graphene-lubricated three-body polished single crystal silicon can improve the surface quality and reduce material removal efficiency.
1. Introduction With the development of science and technology, the application prospect of hard and brittle materials is very broad. These materials are used in new energy, aerospace, automotive, general machinery and other industries owing to their high hardness, high strength, anti-wear, high-temperature resistance, corrosion resistance, oxidation resistance, and other excellent physical and mechanical properties. In addition to being used for making tools and coating on a tough substrate for wear parts, they can also be used as a key component for bearings, seal rings, and aero engines [1–4]. Ultra-precision polishing is an effective processing method to obtain an ultra-smooth surface [5]. However, due to the high brittleness, high hardness, low plasticity, microcracks, and other shortcomings of hard and brittle materials, many types of damages such as metamorphic layers, surface/subsurface cracks, residual stresses, phase change regions often occur during ordinary polishing [6–8]. These damages will seriously affect the processing quality and surface characteristics of hard and brittle materials and will significantly reduce the fatigue/ breaking strength, corrosion resistance, wear resistance and other performance of the workpiece, and even catastrophic failure. Therefore, it is important to thoroughly investigate and reveal the polishing
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mechanism of hard and brittle materials, research advanced polishing process, predict and control the polishing damage introduced by hard and brittle materials during polishing to improve polishing efficiency, improve surface quality and improve the reliability of processed parts. It has become an urgent problem to be solved in the application of hard and brittle materials. The ultra-precision polishing process of tools through molecular dynamics simulation has been extensively investigated, but most scholars regard the tool as a rigid body with no rotation speed, and this is inconsistent with the tool movement during the actual polishing process. Jain et al. [9] proposed a mathematical model based on twinbody machining in 1999; however, the theoretical results did not match the experimental data of surface roughness changes well. In the same year, they proposed neural network methods to construct a learning model to predict the problem of material removal in limited experimental data. Trezona et al. [10] established a theoretical model to derive a correlation wear trend plot to determine the proportion of twobody wear and three-body wear dominated in the microscale abrasive wear test. Xie et al. [11] experimentally studied the mechanism of material removal during free grinding and polishing and. A theoretical model was developed to predict the relationship between polishing parameters and the wear rate of hard abrasive particles (softer than
Corresponding author at: College of Mechanical Engineering, Guizhou University, Guiyang 550025, China. E-mail address: [email protected] (H. Dai).
https://doi.org/10.1016/j.commatsci.2019.109214 Received 2 June 2019; Received in revised form 20 August 2019; Accepted 20 August 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.
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processing is necessary. When the shear stress is too low to maintain dislocation emission in the chip formation region, crack propagation becomes dominant. Goel et al. [27] pointed out that in the processing of hard and brittle materials in nanometers, the temperature analysis of the processing region is very important. The temperature change is determined by the number of atoms, the energy released by the environment, and the release rate. Dai et al. [28] shows that potential energy is the internal energy of the system and it changes with the position or arrangement of atoms in the object. The change in potential energy is one of the important factors to be considered in the nanoprocessing. The following physical quantities were calculated: the temperature of the graphene layer/polishing region, the graphene layer/workpiece internal coordination number, the polishing region stress, the graphene layer friction coefficient, and the internal potential energy of the workpiece. In this study, the diamond polishing particles in the ultra-precision three-body polishing of single crystal silicon under graphene, different polishing speed/temperature on the internal silicon atom coordination number of the workpiece, the surface morphology of the process, the damage degree of the subsurface layer, friction. The coefficient and the stress, and temperature and potential energy in the polished area vary with polishing distance. Ultimately, deeper polishing depth has a decisive effect on the phase transition of the silicon atoms, resulting in a more severe subsurface damage layer, thereby increasing the coefficient of friction, stress, potential energy, and temperature inside the workpiece. We found that the phase change atom, temperature, potential energy, subsurface damage layer, surface topography and friction coefficient of the workpiece did not change significantly when the speed of the triamma polishing of the diamond abrasive grains was low, proving that the graphene was in the form of diamond. The three-body polishing of single crystal silicon has an ultra-lubricating effect.
abrasive particles) sandwiched between the cushion and the workpiece. Fang et al. [12] indicates that the motion pattern of the abrasive grains in the three-body wear is very important for the wear of the material. They observed the movement of individual abrasive particles in detail using a device for three-body wear. In the two-body contact sliding (the tool has no rotation speed), the hard and brittle material is deformed into a way of no wear, adhesion, pear cultivation, and cutting [13,14]. However, in the three-body contact sliding (the knife rotates), the deformation of the hard and brittle material has no wear, condensation, adhesion, and pear cultivation. Zhang et al. [15] first studied the ultraprecision polishing wear mechanism of single crystal silicon by molecular dynamics (MD) simulation and found that amorphous phase transformation is the main deformation of single crystal silicon. Zarudi et al. [16] used molecular dynamics (MD) simulation and experimental methods to study the atomic structure changes of single crystal silicon during ultra-precision polishing, indicating that the MD simulation results were almost consistent with the experimental results. Zhao et al. [17] used three-dimensional MD simulation to study the material removal mechanism of mechanical polishing of single crystal silicon by using diamond as the tools. They also studied the effects of diamond abrasive particle autotransmission speed and direction [18], indicating that with increasing rotation speed of diamond abrasive grains, the deformation mechanism changes from cutting to plowing; the rotation speed and direction of abrasive grains affect the surface topography and quality of the workpiece and the distribution and evolution of defects under the surface of the workpiece. In the actual production process, due to the adverse effects of friction on the processing efficiency, durability and environmental compatibility, reducing the mechanical friction associated with friction and wear in mobile mechanical systems has attracted increasing attention. This problem can be addressed by searching new materials that reduce friction and wear. Coatings and lubricants (liquid or solid) are especially important. In 2008, Lee et al. [19] proposed that graphene is one of the materials with the highest strength known. They measured the elasticity and intrinsic fracture strength of the freestanding single-layer graphene film by nanoindentation under atomic force microscopy. The atomically perfect nanoscale material was mechanically tested. The results show that the ocene has good toughness and good mechanical properties. Berman et al. [20] provided a tribological investigation based on nanoscale to macroscopic grapheme. Graphene can be used not only as a lubricant, but also as an additive for lubricating oils, composites and solvents and has a significant effect on the friction and wear generated during processing. Bai et al. [21] studied the lubrication behavior of graphene-like diamond-like carbon (DLC) film scratched at the tip of diamond by MD simulation, indicating that graphene can effectively lubricate the DLC film. The wear condition in the lubrication process mainly depends on the normal force. The smaller normal force can obtain ultra-low friction force, which is expressed as the super-lubrication phenomenon of graphene. Zhang et al. [22] used MD simulation to study the friction behavior of diamond tip nano-scratches on multilayer graphene. It is considered that when the scratch depth is less than 5.3 Å, the graphene layer has ultra-low friction performance. At scratch depth greater than 5.3 Å, the graphene undergoes a phase change, and the friction coefficient increases by at least 10 times. These literature studies show that graphene has sufficient mechanical properties and superlubricity during processing to be used as a solid lubricant for ultra-precision three-body abrasive polishing of single crystal silicon. Wang et al. [23] and Zhang et al. [24] considered that the change in the atomic coordination number (CN) of the workpiece during statistical processing has a guiding significance for the phase transition of the research workpiece. However, Gilman et al. [25] pointed out that the CN of Si-II cannot be fully expressed as 6, and other measures are needed to confirm the HPPT state of the workpiece. Cai et al. [26] proposed that in order to better understand the brittle-ductile transition mechanism, studying the distribution and variation of stress during
2. Simulation method Fig. 1 shows a three-dimensional model of ultra-precision threebody polishing of single crystal Si in a single layer of graphene. The dimensions of the workpiece in the x, y, and z directions are 55a × 25a × 25a(a = 5.43Å ; the size of graphene in the x, y direction is120b × 60b(b = 2.47Å) ; the abrasive radius is 4 nm. The workpiece is divided into three areas: Newtonian, thermostat, and boundary atoms. Among them, the boundary atoms do not participate in the motion during the simulation and remain fixed in the space to reduce the boundary effect and maintain the lattice symmetry. The atomic motion in the constant temperature region and the Newton region follows Newton's second law of motion. The model uses the Velocity Verlet algorithm to integrate in 1 fs time steps. The thermostat atoms use a speed scaling approach to ensure reasonable outward heat transfer. In order to obtain more accurate observation data, a cutting area of 4nm × 7.5nm × 1nm was set at the rubbing passage. The rest of the model is shown in Table 1. During the three-body abrasive polishing process, the rotational speed, cutting speed, and indentation depth of the abrasive particles are not negligible, and different variables have different effects on the physical factors inside the workpiece. In this study, the effect of a variable on the physical factors operating inside the workpiece in the case of determining two of these variables was investigated. In microscopic atomic simulation calculations, choosing the appropriate potential energy function is a necessary condition for obtaining accurate results. In this study, there are six different interaction potentials for two types of atoms in the polishing process of this study: Si–Si (internal potential of the workpiece), C–Si (potential between the abrasive particles and the workpiece), C–C (internal potential of the diamond), C–Si (potential between the graphene and the workpiece), C–C (graphene) Interaction potential with abrasive grains), C–C (graphene internal potential). Because diamond hardness is much larger than single crystal silicon and graphene, it is considered to be a rigid 2
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Fig. 1. Schematic diagram of the MD simulation model.
body, and its deformation and wear are not considered during the indentation process [29]. Based on the past work experience and experimental data [30,31], the Tersoff potential function is a three-body potential function suitable for describing the interaction between silicon atoms (Si–Si) in a workpiece [32]. The Airebo potential function is based on the Rebo potential function improved by the Tersoff potential, considering the interaction between the particles, increasing the repulsion between the particles and accounting the effects of the fourbody torsion. Therefore, the Airebo potential function can well simulate the interaction between graphene internal (C–C) atoms [33]. Tersoff/ zbl three-body potential function has been used to describe the atomic potential between workpiece and graphene (Si–C) [34]. The Morse potential function is faster and less expensive than the Tersoff potential function; therefore, it was used to describe the interaction between the workpiece and the abrasive atom (C–Si) [22,35]. Since the diamond indenter and graphene do not form a bond, the L–J potential function is used, the specific parameters are: εc − c = 2.86meV , σc − c = 0.347nm , the cutoff radius is 2.5 Å [36]. We will list the different polishing information in Table 2 to make the reader more convenient in the next reading.
Table 2 Polishing parameters.
3. Results and discussion
the surrounding environment, and the cutoff radius is 2.6 Å. After adjusting different variables, a partial cross-sectional view of the workpiece is shown in Fig. 2(a)–(c). It was found that greater the depth of the abrasive under the polishing process, greater the depth of the damaged layer under the surface; the polishing depth of the abrasive particles has a decisive effect on the depth of the underlying damaged layer. Next, the change in the polishing depth, CN = 3, Bct5-Si (CN = 5), Si-II (CN = 6) in the workpiece with the polishing distance was measured. The deeper the indentation depth of the abrasive grains, the more obvious the changes in the three atoms of CN = 3, Bct5-Si (CN = 5) and Si-II (CN = 6). The number of bct5-Si and Si-II increases with increasing polishing distance, and the increase in bct5-Si is much faster than that of Si-II. Because Si-II is unstable at pressures below 4
Polishing scheme
Polishing speed (m/s)
Polishing depth (nm)
Abrasive rotation speed (m/s)
Case I Case II Case III
100 100 100
0. 5 1 2
100 100 100
Case IV Case V Case VI
50 100 200
1 1 1
100 100 100
Table 3 Various high-pressure phases of silicon.
With increasing polishing distance, other phases such as Si-II, Si-XI, and Si-V appear in the workpiece [37]. As reported in the literature, [33] the phase transition in silicon is inextricably linked to the change in the distance between the atoms. The distance between four adjacent silicon atoms in the unprocessed process is between 2.35 Å and 2.43 Å. The neighboring atoms are distributed in the range 2.58 Å. The change in the distance between the atoms is related to the change in the coordination number of silicon from 4 to 6 [38]. Table 3 lists Si-I (brittle), Si-II (Metallic), Si-XII (R8), Si-III, Bct-5, the distance and number of five silicon-phase atoms from neighboring atoms [30,39–41]. In this study, in order to identify the different phases formed by the workpiece atoms, the radius was chosen to be larger than the maximum bond length in
Phase of silicon
Lattice structure
Interatomic distance (Å)/Quantity
Si-I(brittle) Si-II(Metallic) Si-III Si-XII(R8) Bct-5
Diamond cubic Beta-tin bc8(BCC) Rhombohedral Crystalline
2.42/4 2.42/4 2.37/4 2.39/4 2.31/1
and and and and and
2.585/2 2.585/2 3.41/1 3.23/1 or 3.36/1 2.44/4
Table 1 Simulation parameters. Materials
Workpiece:silicon
Lubricant:graphene
Tool:diamond
Number of atoms Workpiece dimension Abrasive dimension Graphene dimension Workpiece surface Time step Initial temperature Polished area
281,856 55a × 25a × 25a (a = 5.43 Å) Radius 4 nm 120b × 60b (b = 2.47 Å) [0 0 –1] on (0 0 1) surface 1 fs 300 K 4nm × 7.5nm × 1nm
2805
11,544
3
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Fig. 2. The atomic phase change statistics of the three-body polished workpiece after adjusting for different variables: (a) Case I; (b) Case II; (c) Case III. Coloring the atom according to the coordination number (CN). In the workpiece, Si-I (CN = 4), the boundary layer and the atoms of the constant temperature layer are invisible, and the abrasive grains are indicated by broken lines. (d) The amount of CN = 3 atoms in the workpiece varies according to the polishing distance; (e) the number of Bct5-Si (CN = 5) atoms in the workpiece according to the polishing distance; (f) Si-II in the workpiece (CN = 6) The number of atoms varies according to the polishing distance.
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Fig. 3. Atomic phase change statistics of three-body polished workpieces after adjusting different variables: (a) Case IV; (b) Case V; (c) Case VI. Coloring the atom according to the coordination number (CN). In the workpiece, Si-I (CN = 4), the boundary layer, and the atoms of the constant temperature layer are invisible, and the abrasive grains are indicated by broken lines. (d) The amount of CN = 3 atoms in the workpiece varies according to the polishing distance; (e) the number of Bct5-Si (CN = 5) atoms in the workpiece according to the polishing distance; (f) Si-II in the workpiece (CN = 6) the number of atoms varies according to the polishing distance; (g) the average number of Si-II atoms.
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Fig. 4. Adjusting the cross-sectional view of a transient defect structure formed by three-body polishing of an abrasive with a single variable: (a) Case I; (b) Case II; (c) Case III; (d) number of defective atoms at different polishing depths.
Fig. 5. Adjusting a cross-sectional view of a transient defect structure formed by three-body polishing of abrasives: (a) Case IV; (b) Case V; (c) Case VI; (d) Number of defective atoms at different polishing speeds.
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Fig. 6. Shows the distribution of stress in the polishing zone with the polishing distance when changing the polishing depth: (a) σxx, (b) σyy, (c) σxy.
Among them, Si-I is represented by blue atom, and Si-II, a dislocation atom and a defective atom of a surface atom, is represented by gray. Obviously, with increasing polishing depth, the number of damaged atoms in the workpiece increases. Fig. 4(c) and (d) show that when the polishing layer and the boundary layer of the workpiece with a polishing depth of 2 nm are destroyed and the number of damaged atoms are significantly higher than that in the other two cases, this again proves that the polishing depth damages the subsurface and thus the polishing layer has a decisive effect. Fig. 5(a)–(c) show the distribution of diamond structure atoms in the workpiece when the polishing speed is adjusted. The polishing depth is always maintained at 1 nm during the adjustment of the polishing speed. With increasing polishing speed, the difference in damaged atoms in the workpiece is not significant, because during processing, a single layer of graphene is applied to the surface of the workpiece as a lubricant to reduce the effect of polishing rate of the abrasive particles on the defective atoms in the workpiece. This better illustrates the super-lubricating effect of graphene, allowing diamond abrasive grains to produce a better polished surface in nano-scale mechanical tri-body polishing. When the shear stress is greater than the flow stress of the workpiece material, dislocations are more likely to occur inside the material, resulting in cracks [30]. Fig. 6 shows a comparison between the stress components in the polished area. σxx represents the normal stress in the x direction, σyy represents the normal stress in the y direction, and σxy represents the shear stress. Fig. 6(a)–(c) show the change in stress in the
GPa when polished [42], metal Si-II loses its crystal structure and transforms into amorphous silicon and other phases, such as R8 (Si-XII, Rhombohedral) and bc8 (Si-III, BCC) [43]. This leads to the rebound phenomenon of Si-II (CN = 6) shown in Fig. 2(f), i.e., the Si-II (CN = 6) will exhibit unstable fluctuations with increasing pressure. As shown from the graph in Fig. 2(f), the change in Si-II (CN = 6) was not remarkable, when the polishing depth was 0. 5 nm and 1 nm. As the polishing rate increases, more and more Si-II atoms appear under the abrasive grains, but the change in the number of Si-II atoms is not obvious as a whole. Fig. 2(d) and (e) show that when the polishing speed is 100 m/s, the number of CN = 3 and Bct5-Si (CN = 5) generated inside the workpiece is less than that at 50 m/s and 200 m/s, proving that faster polishing speed in the three-body polishing does not produce more CN = 3 and Bct5-Si (CN = 5) atoms. Fig. 3(f) and (g) show the variation in Si-II atoms with polishing distance at different polishing speeds, and the average number of Si-II atoms decreases with increasing polishing speed. The CNA method is usually used to distinguish between FCC, HCP, and BCC structures, but it is not suitable for identifying diamond structures. Therefore, in the study, the neighbor particle structure identification method is used. This method first identifies the first-level neighboring atoms of the central atom and then identifies the neighbors of these neighboring atoms. Finally, the central atom and the CNA map of the two atoms are calculated. If the map is arranged according to FCC, the central atom is labeled as a cubic diamond atom. If the HCP structure is met, the central atom is labeled as hexagonal diamond [40]. 7
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Fig. 7. Shows the distribution of stress in the polishing zone with the polishing distance when changing the polishing speed: (a) σxx, (b)σyy, (c)σxy.
Fig. 8. Temperature distribution in the polished area: (a) changing the polishing depth; (b) changing the polishing speed.
pressure of the silicon atoms in the workpiece, greater the stress component produced. Fig. 7(a)–(c) show the tendency of the individual stress components to change is generally uniform with changing polishing speed. When the three-body abrasive grains reach the 8 nm position, the respective stress components are maximized, and the larger the polishing speed, the larger the stress component, and the faster the stress recovery rate. In the graphene-lubricated three-body abrasive-polished single crystal
polishing zone with changing abrasive grain polishing depth. It can be noticed that the trends of the three stresses adjusted for different polishing depths are generally similar. Obviously, as the depth of polishing of Case I–III increases, the magnitudes of the three stress curves increase in turn. In addition, the polishing area is 8–12 nm, and as the polishing depth increases, the maximum value of each decomposition stress is larger and the recovery speed of stress is faster. This can be attributed to the deeper the polishing depth, the greater the hydrostatic 8
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Fig. 9. Distribution of potential energy in the polishing zone with changing polishing depth: (a) potential energy varies with polishing distance; (b) average potential energy.
Fig. 10. Distribution of potential energy in the polishing zone with changing polishing speed: (a) potential energy varies with polishing distance; (b) average potential energy.
Fig. 11. Variation of friction coefficient during polishing: (a) changing the polishing depth; (b) changing the polishing speed. 1 2
3
∑i mi vi2 = 2 Nkb T,where N is the number of atoms in the measurement area, vi is the velocity of the ith atom, mi is the mass of the ith atom, and kb is the Boltzmann constant. The five polishing methods in this study are relatively stationary; therefore, the kinetic energy changes caused by the motion of the workpiece during the analysis are not accounted. Fig. 8(a) and (b) show that as the polishing depth deepens and the polishing speed increases, the polishing zone temperature rises sharply, proving that both the polishing depth and the velocity
silicon, both the polishing depth and the polishing speed have significant effects on the normal stress (σxx, σyy) and the tangential force (σxy), requires attention. The effect of polishing depth and polishing speed on temperature during three-body abrasive polishing under graphene lubrication is shown in Fig. 6(a) and (b) for a better understanding. Based on literature data [44–47], the temperature is the overall property of the workpiece calculated by indirect measurement. The formula: 9
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Fig. 12. Surface topography of the workpiece after adjusting the polishing speed: (a) Case IV; (b) Case V; (c) Case VI.
Fig. 13. Surface topography of the workpiece after adjusting the polishing depth: (a) Case I; (b) Case II; (c) Case III.
Fig. 10(c) and (d) show that the average potential energy is significantly lower at the polishing rates of 0.5 m/s and 1 m/s compared to that at 2 m/s. When the polishing rate is 0. 5 m/s or 1 m/s, there is no obvious change in the potential energy change trend, and the average potential energy is close to the same. This proves that the smaller the polishing speed of the three bodies under graphene lubrication, the smaller the potential energy. The coefficient of friction is defined as the tangential force Fy divided by the normal force Fx, expressing the ability of the diamond
have a significant effect on the temperature change of the polishing zone. Potential energy is the transformation of the internal energy of the system due to changes in the position or arrangement of atoms within the object [48]. Fig. 9(a) shows that with increasing polishing depth, more atoms in the workpiece participate in the motion, increasing the potential energy in advance. In addition, the deeper the polishing depth, the larger the peak potential energy. This can be seen more clearly from the average potential energy map Fig. 9(b). 10
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two atomic numbers are produced at a polishing rate of 1 m/s; however, the polishing rate slightly affects the Si-II atoms. 3) The polishing depth is increased and the speed is increased. σxx, σyy, and σxy are more compressible. The easier the atomic dislocation, the more prone it is to brittle-ductile transition. 4) Temperature and potential energy increase with increasing abrasive depth and speed. However, when the speed is small, the difference between potential energy and temperature is not large.
abrasive particles to remove material in nanopolishing and is an important factor in the polishing process. In the process of polishing monocrystalline silicon by graphene-lubricated three-body abrasive grains, Fig. 11(a) shows that the friction coefficient becomes larger with increasing polishing depth, and according to Fig. 11(b), the polishing rate is too fast and too slow is not conducive to reducing the coefficient of friction. Based on literature [49], the friction coefficient of diamond polished single crystal silicon without graphene reaches 0.797. This study confirms that graphene is superlubricated when tri-crystal polishing single crystal silicon. Fig. 12(a)–(c) show the adjustment of the polishing rate of the surface morphology of the workpiece after polishing and the contour of the cross-section, indicating that the change in the polishing speed strongly influences the surface morphology and contour after polishing. It is well known that as the abrasive particles move forward, more and more silicon atoms will accumulate on both sides and the front end of the abrasive particles. However, in the case of graphene lubrication, Fig. 12(a) shows that the two sides of the abrasive grains and the front end did not accumulate a lot of debris, but instead left the residual silicon atoms under the abrasive grains sliding down probably because the abrasive grains rotate too fast and the polishing speed is slow. Fig. 12(b) shows that the polishing speed is 100 m/s under graphene lubrication. At a rotation speed of 100 m/s, no residual silicon atoms are left under the abrasive grains. At the same time, it will not produce more debris. Comparing Fig. 12(a) and (b), it is proved that when the rotation speed of the abrasive grains is greater than the polishing speed, residual atoms appear below the abrasive grains. When the polishing speed is 200 m/s and the abrasive grain rotation speed is 100 m/s, the surface topography of the workpiece is shown in Fig. 12(c). Comparing it with Fig. 12(a) and (b) shows that the faster the polishing speed, more cutting accumulates. In these three images, the surface morphology and cross-sectional profile of the workpiece with a z-direction difference of 1.5 nm were observed. Compared to the previous study, it can be proved that the addition of graphene-lubricated three-body polished single crystal silicon improves the surface quality and reduces the material removal efficiency. The effect of different polishing depths on the surface of the polished workpiece is shown in Fig. 13. Obviously, the deeper the polishing depth, the more obvious the indentation and swarf left by the workpiece, and the higher the amount of material removed, resulting in a higher coefficient of friction. In addition, we believe that the polishing depth has a decisive effect on the amount of material removed, and therefore the lubrication effect of graphene cannot be judged by Fig. 13.
CRediT authorship contribution statement Houfu Dai: Writing - original draft, Visualization. Fa Zhang: Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation. Yuqi Zhou: Writing - review & editing. Acknowledgements The authors would like to appreciate the fund project for the introduction of talents in Guizhou University (No. [2017]24), Guizhou Province Education Department Youth Science and technology talent growth project (No. [2018]110), and National Natural Science Foundation cultivation project for young teachers of Guizhou University (No. [2017]5788). References [1] M. Ge, H. Zhu, C. Huang, et al., Investigation on critical crack-free cutting depth for single-crystal silicon slicing with fixed abrasive wire saw based on the scratching machining experiments, Mater. Sci. Semicond. Process. 74 (2018) 261–266. [2] J. Ruckman, H. Pollicove, D. Golini, Advanced manufacturing generates conformal optics: optoelectronics world: optics, Laser Focus World 35 (7) (1999) S13–S15. [3] T. Saga, Advances in crystalline silicon solar cell technology for industrial mass production, NPG Asia Mater. 2 (2010) 96–102. [4] B. Guo, Q. Zhao, X. Fang, Precision grinding of optical glass with laser microstructured coarse-grained diamond wheels, J. Mater. Process. Technol. 214 (5) (2014) 1045–1051. [5] X.S. Han, Y.Z. Hu, S.Y. Yu, Appl. Phys. A 95 (2009) 899. [6] I. Zarudi, T. Nguyen, L.C. Zhang, Effect of temperature and stress on plastic deformation in monocrystalline silicon induced by scratching, Appl. Phys. Lett. 86 (2005) 011922. [7] Y. Gogotsi, G. Zhou, S.S. Ku, et al., Raman microspectroscopy analysis of pressureinduced metallization in scratching of silicon, Semicond. Sci. Technol. 16 (2001) 345. [8] Y.Q. Wu, H. Huang, J. Zou, et al., Nanoscratch-induced deformation of single crystal silicon, J. Vac. Sci. Technol. B 27 (2009) 1374–1377. [9] R.K. Jain, V.K. Jain, Simulation of surface generated in abrasive flow machiningprocess, Robot. Comput. Integr. Manuf. 15 (1999) 403–412. [10] K. Adachi, I.M. Hutchings, Wear-mode mapping for the micro-scale abrasion test, Wear 255 (1) (2003) 23–29. [11] Y. Xie, B. Bhushan, Effects of particle size, polishing pad and contact pressure in free abrasive polishing, Wear 200 (1–2) (1996) 281–295. [12] Kong X.L. Fang, et al., Movement pattern of abrasive particles in three-body abrasion, Wear (1993) 782–789. [13] T. Inamura, S. Shimada, N. Takezawa, N. Ikawa, CIRP Ann-Manuf. Technol. 48 (1999) 81. [14] W.J. Zong, D. Li, K. Cheng, T. Sun, H.X. Wang, Y.C. Liang, Int. J. Mach. Tools Manuf. 45 (2005) 783. [15] L. Zhang, H. Tanaka, Atomic scale deformation in silicon monocrystalline silicon in surface nano-modification, Nanotechnology 15 (1) (2003) 104. [16] L. Zhang, H. Zhao, Z. Ma, et al., A study on phase transformation of monocrystalline silicon due to ultra-precision polishing by molecular dynamics simulation, AIP Adv. 2 (4) (2012) 899. [17] Y. Yang, H. Zhao, L. Zhang, et al., Molecular dynamics simulation of self-rotation effects on ultra-precision polishing single-silicon copper, AIP Adv. 3 (10) (2013) 899. [18] J. Guo, H. Suzuki, S. Morita, et al., A real-time polishing force control system for ultraprecision finishing of micro-optics, Precis. Eng. 37 (4) (2013) 787–792. [19] C. Lee, X. Wei, J.W. Kysar, et al., Measurement of the elastic properties and intrinsic strength of monolayer graphene, Science 321 (5887) (2008) 385–388. [20] D. Berman, A. Erdemir, A.V. Sumant, Graphene: a new emerging lubricant, Mater. Today 17 (1) (2014) 31–42. [21] L. Bai, N. Srikanth, B. Zhao, et al., Lubrication mechanisms of graphene for DLC films scratched by a diamond tip, J. Phys. D Appl. Phys. 49 (48) (2016) 485302. [22] Q. Zhang, D. Diao, M. Kubo, Nanoscratching of multi-layer graphene by molecular dynamics simulations, Tribol. Int. 88 (2015) 85–88. [23] Y. Wang, S. Ruffell, K. Sears, A.P. Knights, J.E. Bradby, J.S. Williams, Electrical
4. Conclusions In this study, MD simulation was successfully used to study the polishing of diamond abrasive grains in three-body polished single crystal silicon under graphene lubrication. Based on the results of this study, the main conclusions can be summarized as follows: 1) Graphene has an ultra-lubricating effect when diamond tri-crystal polishing single crystal silicon. The results show that the number of subsurface defective atoms caused by the difference in polishing speed is low at constant polishing depth. Moreover, at lower polishing speeds, the surface topography of the workpiece is perfect and there is no excessive chipping. In addition, the three-body polishing process of adding graphene has a smaller coefficient of friction. These results indicate that graphene can reduce the atomic removal rate during the diamond tri-body polishing of graphene with a remarkable lubrication effect. 2) At higher depth of the abrasive grains, the changes in the three atoms of CN = 3, Bct5-Si, and Si-II are more obvious. It can be observed that the number of bct5-Si and Si-II increases with the polishing distance, and the increase in bct5-Si is much faster than that of Si-II. In addition, a minimum of CN = 3, Bct5-Si (CN = 5) and 11
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