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Amorphization anisotropy and the internal of amorphous layer in diamond nanoscale friction
Computational Materials Science 95 (2014) 551–556
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Amorphization anisotropy and the internal of amorphous layer in diamond nanoscale friction Ning Yang, WenJun Zong ⇑, ZengQiang Li, Tao Sun Center for Precision Engineering, Harbin Institute of Technology, 150001 Harbin, PR China
a r t i c l e
i n f o
Article history: Received 12 March 2014 Received in revised form 9 July 2014 Accepted 21 August 2014 Available online 15 September 2014 Keywords: Diamond crystal Frictional sliding MD simulation Amorphization
a b s t r a c t In this work, molecular dynamic (MD) simulation is employed to investigate the formation and evolution of amorphous carbons in the surface layer of diamond crystal as the frictional sliding is performed on diamond (1 0 0) plane. Simulation results reveal that the formation of amorphous carbons at the sliding interface is inevitable due to the friction. In this case, transformation from diamond sp3 hybridized carbons to sp2 hybridization structures is dominant. More interestingly, most of the sp hybridized carbons appear on the topmost surface of the amorphous layer. Amorphization rate in sliding along the [1 0 0] direction is greater than that along the [1 1 0] direction due to the smaller resistance forces. In the light of the velocity variation of carbon atoms, the amorphous layer is divided into two layers, i.e. the coherent layer and transition layer. Moreover, a density transition region appears with the formation of amorphous carbons, and the thickness of transition region can be used to characterize the amorphization degree. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Diamond crystal has the superior hardness and Young’s modulus, and it is difficult to be deformed under the external load. So the force-induced deformation mechanism of diamond crystal is always the focus subject in the frontier discussions. Recently, diamond carbons amorphization due to the mechanical stress has been paid attention increasingly. In 1999, Gogotsi et al. employed micro-Raman spectroscopy to observe what happens to diamond crystal as it suffers from the high contact compression as a result of pressing a sharp diamond indenter against its surface. And they found that diamond carbons under indenter will transform into the graphite [1]. Gogotsi’s work clearly indicates that in the abrasive-based polishing or frictional sliding on diamond, an amorphous layer will come into being on its surface. In order to find the factors causing diamond carbons amorphization or remove the unwanted amorphous layer, some interesting works had also been carried out. In 1991, Wang applied reflection electron microscopy (REM) to image the surface structures of the polished diamond (0 0 1) faces before and after the frictional sliding [2]. He suggested that in this case the plastic deformation happens in the contact region of ⇑ Corresponding author. Address: P.O. Box 413, Harbin Institute of Technology, 150001 Harbin, PR China. Fax: +86 0451 86415244. E-mail address: [email protected] (W. Zong). http://dx.doi.org/10.1016/j.commatsci.2014.08.040 0927-0256/Ó 2014 Elsevier B.V. All rights reserved.
diamond surface due to the high contact pressure. In 1994, Couto et al. compared the surface morphologies of the mechanically polished diamond crystal and the chemical vapor deposition (CVD) diamond film with scanning tunneling microscopy (STM) and atomic force microscopy (AFM). They found that the mechanical polishing will result in the formation of nanometer grooves on diamond surface [3]. In 2000, van Bouwelen reported that on a microstructural level diamond crystal will degrade if the mechanical polishing is performed on its surface [4]. In 2002, with high-resolution electron microscopy and electron-energy-loss spectroscopy, van Bouwelen et al. analyzed the density, percentage of sp2 hybridized carbons, and oxygen content of the debris produced in mechanical polishing diamond crystal. The results revealed that the chemical structures of the debris are amorphous carbons [5]. In 2007, Grierson pointed out that the amorphous carbons are composed of sp2 and sp3 hybridized structures [6]. In addition to the experimental observations, computer-aided simulations have also been carried out to understand the frictional behavior of diamond crystal at nanometer scale. In 1992, Harrison et al. employed molecular dynamics (MD) simulation to study the friction occurred between two hydrogenterminated diamond (1 1 1) surfaces in different crystallographic directions. They claimed that the frictional force is dependent on the external load, temperature, and sliding velocity [7]. In 1993, Harrison et al. utilized MD simulations to represent the effects of chemically-bound flexible hydrocarbon species on the friction
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properties of diamond (1 1 1) surfaces [8]. In 1994, Harrison and Brenner adopted MD simulations to explore the atomic-scale chemistry and associated wear that occurs when diamond surfaces are placed in sliding contact, which provides insight into the tribochemistry that occurs at diamond and related covalently bonded interfaces [9]. In 1995, Harrison et al. investigated the atomic-scale friction and energy dissipation in diamond by using MD method [10]. In 2007, Gao et al. employed AFM and MD to examine the dependence of single asperity friction on the load, sliding direction and surface orientation of diamond. They pointed out that the nanoscale tribology behavior of diamond is dramatically different from the established macroscopic behavior, and it is linearly dependent on the load [11]. In 2008, Bródka et al. calculated the structure and graphization of nanodiamond particles with MD simulation [12]. In 2009, Ma et al. simulated the formation of graphene-like carbons layer due to the shear-induced graphitization of amorphous carbon films [13]. In 2010, Lin et al. studied the nanotribological behavior of diamond surfaces by using MD and experiments, and finally they evaluated the microstructural behavior with fractal theory and statistic parameters [14]. In 2011, Moseler et al. illustrated the amorphization of diamond carbons with a ‘pilot’ atom concept, and resultantly they formulated the time dependent thickness of amorphous layer. Moreover, they declared that for diamond crystal the wear anisotropy is caused by the amorphization of diamond carbons [15]. In 2012, Fairchild et al. investigated the tensile strength of diamond by exploiting the ion beam induced swelling of lattice to cause amorphization of diamond, and subsequently they performed MD simulations to reveal the diamond amorphization mechanism. Their modeling suggested that the diamond amorphization is strain driven [16]. Although the interesting works outlined above demonstrate that the diamond amorphization is the dominant deformation mechanism for the sliding friction on diamond surfaces, the microstructural behavior happened in the amorphous layer have not been revealed satisfactorily. Therefore in this work, MD simulation is employed to represent the nanoscale friction on diamond surfaces. The formation of amorphous layer is simulated, and the amorphization anisotropy of diamond is explained according to the resistance force of carbon atoms that escaping from diamond surface. Finally, the nanoscale behavior within the amorphous layer is analyzed.
simulation, the micro-canonical (NVE) ensemble is used, and the target external stress in y direction is set as 10 Gpa, i.e. the normal pressure of the simulation system. And then the Nose–Hoover barostat is used to regulate and control the system pressure. At the beginning of friction simulation, the regions corresponding to the abrasive particle, adatoms layer, Newton layer, thermostat layer and fixed layer are set up respectively, as shown in Fig. 1. During the friction simulation, the system is free in y direction, and the periodic boundary condition is used in z and x directions. The polished diamond crystal, i.e. the lower part shown in Fig. 1, is oriented with (1 0 0) crystal plane, which is composed of the fixed layer, thermostat layer and Newton layer. The upper diamond is defined as the abrasive. In mechanical smoothing diamond crystal, the friction marks or nanoscale grooves always come into being on the polished diamond surface [21], so it is reasonable to consider the diamond abrasive as a rigid body. The diamond abrasive moves at a constant velocity of 50 m/s, and a constant force is applied to maintain an external pressure of 10 Gpa, as shown in Fig. 1. The bulk diamond is built in terms of the diamond lattice, and the carbon atoms arrange regularly the same as the ideal diamond crystal. The topmost surface of the bulk diamond is formed by randomly deleting the carbon atoms in the region adjacent to the diamond abrasive, which forms the adatoms layer to avoid the cold welding. As shown in Fig. 1, the initial atomic configuration consists of two bulk diamonds, and they are separated by the adatoms. The carbon atoms in the fixed layer are restricted and have no freedoms in any direction. Considering that a constant environment temperature should be maintained for the simulation system, the temperature of carbon atoms in the thermostat layer is explicitly reset by rescaling the velocity of atoms. For the atoms in the Newton layer, a standard velocity-Verlet integrator is adopted [22].
3. Result and discussion 3.1. Amorphization anisotropy in typical crystal directions During simulation, the upper diamond abrasive was set to move along the crystal orientation [1 0 0] and [1 1 0] of the lower
2. Molecular dynamic modeling In order to well understand the tribological behavior of diamond crystal surfaces in lapping, MD simulation is performed with the open source software LAMMPS [17] and VMD [18] in this work. The time step used for integration is 0.5 femtosecond. And the second-generation reactive empirical bond-order potential is used to describe the interaction of carbon atoms, which allows for the phase transformation [11,19]. The expression for the potential function and the related potential parameters can be found in [19].The chemical binding energy E can be written as
E¼
XX R ½V ðr ij Þ bij V A ðrij Þ i jð>iÞ
where the V R ðrÞ and V A ðrÞ are the pair-additive interaction that representing all the interatomic repulsions and attraction from valence electrons respectively; bij is the bond order between atoms i and j. Before calculation, the simulation system should be equilibrated under the isothermal-isobaric (npt) ensemble firstly. The overall dimension of MD model is 4a 4a 25a, where a is the diamond lattice constant of 0.356683 nm [20]. Under this ensemble, the bulk diamond was created to fill the simulation box. Room temperature is specified as the target system temperature. In the sliding
Fig. 1. MD simulation model of the diamond nanoscale friction system.
N. Yang et al. / Computational Materials Science 95 (2014) 551–556
diamond surface respectively. The snapshots of sliding simulation in the [1 0 0] direction at 0.1 ns, 0.25 ns, 0.75 ns, 1.75 ns and 2.5 ns are presented in Fig. 2. It can be clearly seen that the thickness of amorphous layer increases with the increment of simulation time, and the diamond carbons in the topmost surface layer of crystal diamond successively transform to the amorphous phases. A similar process can also been observed in sliding along the [1 1 0] direction. After a simulation time of 2.5 ns, a distinct amorphization layer appears, as shown in Fig. 3. Comparing the 3D close-ups of crystal layer and amorphous layer in Fig. 4, the atoms in crystal layer arrange in an ordered form, but the atoms in amorphous layer are disordered. By observing the cross section, the thickness variations of amorphous layer at different sliding time are captured, as plotted in Fig. 5. From this figure, it can be seen that along the [1 0 0] sliding direction the thickness of the amorphization layer is larger than that along the [1 1 0] sliding direction, which demonstrates that the increasing rate of the amorphous layer thickness in the [1 0 0] direction is slightly faster. This result agrees with the experimental observations, i.e. that the material removal rate in the [1 0 0] direction is greater than that in the [1 1 0] direction for the (1 0 0) or (1 1 0) plane [23,24]. Previous work reported that the amorphization probability of diamond carbons is responsible for the wear rate anisotropy of diamond surface [15]. To be different, the wear rate anisotropy is explained from a new viewpoint in this work. In our work, the second-generation reactive empirical bond-order potential field is employed to compute the forces [19]. The results show that carbon atoms subject to different resistance forces when they attempt to separate themselves from the crystal diamond surface along different directions. Fig. 6 presents the MD simulation of single carbon atom (marked in green color) escaping from the diamond crystal surface. As shown in Fig. 6, the escaping movement of carbon atom can be defined with two direction angles of h and u. Here h is set as the included angle between the projection of escaping vector and the orientation [1 0 0] of diamond (1 0 0) plane, and u denotes the included angle between the escaping vector and diamond (1 0 0) plane. Moreover, all the carbon atoms of diamond crystal are fixed. The resistance forces calculated in different escaping directions are presented in Fig. 7. In Fig. 7, the positive force denotes that the force vector is identical to the escaping direction of carbon atom, whereas the negative force means the force vector is opposite to the carbon atom motion. From the figures above, it can be clearly seen that the
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Fig. 3. 2D close-ups of the carbon atoms at the friction interface before (a) and after (b) sliding friction.
Fig. 4. 3D close-ups of the carbon atoms in crystal bulk (a) and amorphous layer (b).
resistance forces of carbon atom that moves along the [1 1 0] direction, i.e. having an escaping angle of 45° for h, are generally larger than that along the [1 0 0] direction. Such difference is more visible at a smaller escaping angle u, such as u = 15°, is applied. When the single carbon atom escapes along the [1 1 0] direction, the larger resistance force means the carbon atoms on the topmost diamond surface are more difficult to separate themselves from the diamond bulk. As pictorially shown in Fig. 5, the larger resistance force or the greater difficulty in separating carbons from the diamond bulk leads to a smaller increasing rate of amorphous layer thickness. 3.2. Microstructural behavior of the amorphous layer As discussed above, diamond carbons amorphization results in a deteriorated layer on the crystal surface. In order to investigate
Fig. 2. Snapshots of sliding simulation in the [1 0 0] direction at a simulation time of (a) 0.1 ns, (b) 0.25 ns, (c) 0.75 ns, (d) 1.75 ns and (e) 2.5 ns.
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Fig. 8. Logarithm to base 10 of the mean velocity magnitude of carbon atoms versus the height at a simulation time of 2.5 ns: (a) sliding in the [1 0 0] direction; (b) sliding in the [1 1 0] direction.
Fig. 5. Thickness variations of amorphous layer versus sliding time.
Fig. 6. MD simulation for single carbon atom moving near diamond (1 0 0) plane.
Fig. 9. Displacement of a selected atom in the middle of the bulk diamond under the abrasive sliding: (a) along the [1 0 0] direction; (b) along the [1 1 0] direction.
the microstructural behavior occurred in the amorphous layer, the velocity and relative density of carbon atoms, as well as the ratio of different carbon structures along the height direction (as shown in Fig. 1), are analyzed in this section. Fig. 8 plots the logarithm to base 10 of the mean velocity magnitude of carbon atoms versus the height as the abrasive slides along the [1 0 0] and [1 1 0] directions on the (1 0 0) plane. In this figure, part 1 denotes the diamond bulk, and part 2 and part 3 represent different regions of the amorphous layer. For part 2 and part 3, it can be seen that the variation trends of the atom velocity have
changed considerably. Especially for part 2, the magnitude of mean velocity presents an exponential growth along the height direction. According to the velocity difference of part 2 and part 3, the amorphous layer can be divided into two sub-layers. For the sub-layer corresponding to part 3, carbons contact with the abrasive particle directly. Therefore, this sub-layer is defined as the coherent layer. In the coherent layer, carbon atoms move in stick-slip mode, and the shearing happens frequently. Fig. 9 shows the displacement of a selected carbon atom in the middle of the bulk diamond under the abrasive sliding along the [1 0 0] and [1 1 0] directions.
Fig. 7. Resistance forces simulated in different escaping directions. Blue line indicates the angle h = 0° (along the [1 0 0] direction), green line angle h = 45° (along the [1 1 0] direction): (a) u = 15°, (b) u = 30°, (c) = 45, (d) u = 60°, (e) u = 75° and (f) u = 90°. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
N. Yang et al. / Computational Materials Science 95 (2014) 551–556
Fig. 10. Variation of the relative density under the abrasive sliding on the (1 0 0) plane and along the [1 0 0] direction at a simulation time of 2 ns.
Table 1 Variation of L (Angstrom) calculated in different sliding directions. Simulation time (ns) Sliding direction
1
1.25
1.5
1.75
2
2.25
2.5
[1 0 0] [1 1 0]
6.2 3.8
6.4 3.8
6.3 3.7
6.6 3.8
6.6 3.7
6.7 3.7
6.6 3.7
Regardless of the abrasive sliding direction, the visible fluctuation of the selected carbon atom can be easily found in Fig. 9, which indicates that the stick-slip motion appears on the top part of the bulk diamond. It is noticed that the stick-slip behavior is also observed in confined liquid films [25,26], which indicates that the diamond amorphous layer has the same lubricant effect in friction as the confined liquid films. Moreover, the sub-layer corresponding to part 2 shown in Fig. 8 can be considered as the transition layer. This amorphous sub-layer covers on the bulk diamond and lies beneath the coherent layer.
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In this work, the diamond crystal density is employed as the reference density, and the ratio of the density of amorphous layer calculated from MD simulation to the reference one is defined as the relative density. Variation of the relative density with the height increasing is plotted in Fig. 10. As shown in this figure, point A denotes the peak value of the relative density with the largest height value, and point B denotes the average value of the diamond bulk with the largest height value. L is the horizontal distance between point A and point B, which characterizes the thickness of the density transition region. The values of L calculated at different simulation time are listed in Table 1. It can be seen in Fig. 10 that the peak value of the relative density has no variation in the bulk. The peak value begins to decrease at a certain height corresponding to point A. In this case, the larger the height is, the littler the relative density does. At point B, the relative density approaches to the average value. As listed in Table 1, it can be found that the values of L generated under the abrasive sliding along the [1 0 0] or [1 1 0] direction change slightly. However, the ones generated along the [1 0 0] direction are clearly bigger than that generated along the [1 1 0] direction. As exhibited in Fig. 9, the movement of carbon atoms within the diamond bulk, i.e. the distortion induced by the sliding of diamond abrasive particle, will change the spatial distribution of carbon atoms. Because of the different resistance forces under the abrasive sliding along the [1 0 0] and [1 1 0] directions as discussed above, the sliding-induced distortion along the height direction is also different. Resistance force in the [1 1 0] direction is larger than that in the [1 0 0] direction. Such difference means that the distortion generated in sliding along the [1 1 0] direction will be smaller than that generated along the [1 0 0] direction. That is to say, the smaller distortion leads to the less value of L, which has a good consistency with the calculated results as listed in Table 1. Therefore, the value of L or the thickness of density transition region can be employed to characterize the amorphization degree for the diamond crystal when its surface suffers from the sliding friction. As discussed above, the amorphization of carbon atoms is inevitable when the abrasive slides on the diamond surface, which
Fig. 11. Ratios of different hybridization carbons in the amorphous layer when the abrasive slides on the diamond (1 0 0) plane along the [1 0 0] direction: (a) sp3, (b) sp2 and (c) sp.
Fig. 12. Ratios of different hybridization carbons in the amorphous layer when the abrasive slides on the diamond (1 0 0) plane along the [1 1 0] direction: (a) sp3, (b) sp2 and (c) sp.
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means that the transformation of sp3 hybridized carbons to sp2 or sp ones takes place on the diamond surface. Phase transformation contains bonds breakage and generates new hybridization, i.e. that the chemical property of diamond surface will change [27]. Different hybridization of carbon atoms has different number of chemical bonds. A sp3 hybridized carbon atom has 4 bonds, 3 bonds for the sp2 type, and 2 bonds for the sp type. Therefore in the MD simulations, the hybridization of a carbon atom can be identified in terms of its coordinate number, i.e. the number of neighbor atoms within a specified cutoff distance from itself. In this work, the cutoff distance is configured as 0.2 nm according to the second-generation reactive empirical bond-order potential force field [19]. When the abrasive slides on the diamond (1 0 0) plane along the [1 0 0] and [1 1 0] directions, the variations of carbon atoms with different hybridization along the height direction are shown in Figs. 11 and 12 respectively. From Figs. 11 and 12, it can be clearly seen that the sp hybridized carbons mainly distribute in the topmost amorphous layer, i.e. the coherent layer as defined above, regardless of the sliding direction of the abrasive. And the content of the sp carbons reaches up to the highest at the sliding contact interface. These observations agree well with the fact that the sp structures on the diamond surface wear as they are exposed to air [28]. Moreover, the ratio of the sp2 structures increases with the increment of height, which is far greater than the one of the sp phases at the same height. To be different for the sp3 phases, however, a decreasing trend appears. These observations indicate that in the topmost surface layer of diamond crystal the transformation of diamond sp3 phases to the sp2 phases dominates in the diamond amorphization induced by the abrasive sliding. 4. Conclusions In this work, MD simulations are employed to investigate the amorphous layer formation of diamond crystal when the diamond abrasive slides on the (1 0 0) plane along the [1 0 0] and [1 1 0] directions. According to the simulation results and the related analyses above, some important conclusions can be drawn as follows. (1) Due to the mechanical effect of the abrasive, the amorphization of carbon atoms inevitably takes place to form an amorphous layer on the topmost surface of diamond crystal. According to the velocity difference of carbon atoms, the amorphous layer can be divided into two sub-layers, i.e. the coherent layer and the transition layer. Stick-slip behavior is found in the coherent layer, which indicates that the amorphous layer has the lubricant effect in sliding friction. (2) In phase transformation, diamond sp3 hybridization carbons primarily translate to the sp2 ones. The sp phases mainly appear in the coherent layer.
(3) The amorphization rate of diamond carbons is related to the resistance force of the sliding abrasive. There is a smaller resistance force as the abrasive slides along the [1 0 0] direction. So the amorphization rate generated by the abrasive sliding along the [1 0 0] direction is bigger than that generated along the [1 1 0] direction. (4) The relative atom density of the amorphous layer is smaller than that in the bulk, and a density transition region appears in the amorphous layer. The thickness of the density transition region can be used to qualitatively characterize the degree of the diamond amorphization.
Acknowledgements This work was supported by the Natural Science Foundation of China (No. 51175127), the Fundamental Research Funds for the Central Universities (Nos. HIT.BRETIII.201412 and HIT.NSRIF.2014050) and the Major Special Subject of High-end CNC Machine Tools and Basic Manufacturing Equipment Science and Technology of China (No. 2011ZX04004-031). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]
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Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Amorphization anisotropy and the internal of amorphous layer in diamond nanoscale friction Ning Yang, WenJun Zong ⇑, ZengQiang Li, Tao Sun Center for Precision Engineering, Harbin Institute of Technology, 150001 Harbin, PR China
a r t i c l e
i n f o
Article history: Received 12 March 2014 Received in revised form 9 July 2014 Accepted 21 August 2014 Available online 15 September 2014 Keywords: Diamond crystal Frictional sliding MD simulation Amorphization
a b s t r a c t In this work, molecular dynamic (MD) simulation is employed to investigate the formation and evolution of amorphous carbons in the surface layer of diamond crystal as the frictional sliding is performed on diamond (1 0 0) plane. Simulation results reveal that the formation of amorphous carbons at the sliding interface is inevitable due to the friction. In this case, transformation from diamond sp3 hybridized carbons to sp2 hybridization structures is dominant. More interestingly, most of the sp hybridized carbons appear on the topmost surface of the amorphous layer. Amorphization rate in sliding along the [1 0 0] direction is greater than that along the [1 1 0] direction due to the smaller resistance forces. In the light of the velocity variation of carbon atoms, the amorphous layer is divided into two layers, i.e. the coherent layer and transition layer. Moreover, a density transition region appears with the formation of amorphous carbons, and the thickness of transition region can be used to characterize the amorphization degree. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Diamond crystal has the superior hardness and Young’s modulus, and it is difficult to be deformed under the external load. So the force-induced deformation mechanism of diamond crystal is always the focus subject in the frontier discussions. Recently, diamond carbons amorphization due to the mechanical stress has been paid attention increasingly. In 1999, Gogotsi et al. employed micro-Raman spectroscopy to observe what happens to diamond crystal as it suffers from the high contact compression as a result of pressing a sharp diamond indenter against its surface. And they found that diamond carbons under indenter will transform into the graphite [1]. Gogotsi’s work clearly indicates that in the abrasive-based polishing or frictional sliding on diamond, an amorphous layer will come into being on its surface. In order to find the factors causing diamond carbons amorphization or remove the unwanted amorphous layer, some interesting works had also been carried out. In 1991, Wang applied reflection electron microscopy (REM) to image the surface structures of the polished diamond (0 0 1) faces before and after the frictional sliding [2]. He suggested that in this case the plastic deformation happens in the contact region of ⇑ Corresponding author. Address: P.O. Box 413, Harbin Institute of Technology, 150001 Harbin, PR China. Fax: +86 0451 86415244. E-mail address: [email protected] (W. Zong). http://dx.doi.org/10.1016/j.commatsci.2014.08.040 0927-0256/Ó 2014 Elsevier B.V. All rights reserved.
diamond surface due to the high contact pressure. In 1994, Couto et al. compared the surface morphologies of the mechanically polished diamond crystal and the chemical vapor deposition (CVD) diamond film with scanning tunneling microscopy (STM) and atomic force microscopy (AFM). They found that the mechanical polishing will result in the formation of nanometer grooves on diamond surface [3]. In 2000, van Bouwelen reported that on a microstructural level diamond crystal will degrade if the mechanical polishing is performed on its surface [4]. In 2002, with high-resolution electron microscopy and electron-energy-loss spectroscopy, van Bouwelen et al. analyzed the density, percentage of sp2 hybridized carbons, and oxygen content of the debris produced in mechanical polishing diamond crystal. The results revealed that the chemical structures of the debris are amorphous carbons [5]. In 2007, Grierson pointed out that the amorphous carbons are composed of sp2 and sp3 hybridized structures [6]. In addition to the experimental observations, computer-aided simulations have also been carried out to understand the frictional behavior of diamond crystal at nanometer scale. In 1992, Harrison et al. employed molecular dynamics (MD) simulation to study the friction occurred between two hydrogenterminated diamond (1 1 1) surfaces in different crystallographic directions. They claimed that the frictional force is dependent on the external load, temperature, and sliding velocity [7]. In 1993, Harrison et al. utilized MD simulations to represent the effects of chemically-bound flexible hydrocarbon species on the friction
552
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properties of diamond (1 1 1) surfaces [8]. In 1994, Harrison and Brenner adopted MD simulations to explore the atomic-scale chemistry and associated wear that occurs when diamond surfaces are placed in sliding contact, which provides insight into the tribochemistry that occurs at diamond and related covalently bonded interfaces [9]. In 1995, Harrison et al. investigated the atomic-scale friction and energy dissipation in diamond by using MD method [10]. In 2007, Gao et al. employed AFM and MD to examine the dependence of single asperity friction on the load, sliding direction and surface orientation of diamond. They pointed out that the nanoscale tribology behavior of diamond is dramatically different from the established macroscopic behavior, and it is linearly dependent on the load [11]. In 2008, Bródka et al. calculated the structure and graphization of nanodiamond particles with MD simulation [12]. In 2009, Ma et al. simulated the formation of graphene-like carbons layer due to the shear-induced graphitization of amorphous carbon films [13]. In 2010, Lin et al. studied the nanotribological behavior of diamond surfaces by using MD and experiments, and finally they evaluated the microstructural behavior with fractal theory and statistic parameters [14]. In 2011, Moseler et al. illustrated the amorphization of diamond carbons with a ‘pilot’ atom concept, and resultantly they formulated the time dependent thickness of amorphous layer. Moreover, they declared that for diamond crystal the wear anisotropy is caused by the amorphization of diamond carbons [15]. In 2012, Fairchild et al. investigated the tensile strength of diamond by exploiting the ion beam induced swelling of lattice to cause amorphization of diamond, and subsequently they performed MD simulations to reveal the diamond amorphization mechanism. Their modeling suggested that the diamond amorphization is strain driven [16]. Although the interesting works outlined above demonstrate that the diamond amorphization is the dominant deformation mechanism for the sliding friction on diamond surfaces, the microstructural behavior happened in the amorphous layer have not been revealed satisfactorily. Therefore in this work, MD simulation is employed to represent the nanoscale friction on diamond surfaces. The formation of amorphous layer is simulated, and the amorphization anisotropy of diamond is explained according to the resistance force of carbon atoms that escaping from diamond surface. Finally, the nanoscale behavior within the amorphous layer is analyzed.
simulation, the micro-canonical (NVE) ensemble is used, and the target external stress in y direction is set as 10 Gpa, i.e. the normal pressure of the simulation system. And then the Nose–Hoover barostat is used to regulate and control the system pressure. At the beginning of friction simulation, the regions corresponding to the abrasive particle, adatoms layer, Newton layer, thermostat layer and fixed layer are set up respectively, as shown in Fig. 1. During the friction simulation, the system is free in y direction, and the periodic boundary condition is used in z and x directions. The polished diamond crystal, i.e. the lower part shown in Fig. 1, is oriented with (1 0 0) crystal plane, which is composed of the fixed layer, thermostat layer and Newton layer. The upper diamond is defined as the abrasive. In mechanical smoothing diamond crystal, the friction marks or nanoscale grooves always come into being on the polished diamond surface [21], so it is reasonable to consider the diamond abrasive as a rigid body. The diamond abrasive moves at a constant velocity of 50 m/s, and a constant force is applied to maintain an external pressure of 10 Gpa, as shown in Fig. 1. The bulk diamond is built in terms of the diamond lattice, and the carbon atoms arrange regularly the same as the ideal diamond crystal. The topmost surface of the bulk diamond is formed by randomly deleting the carbon atoms in the region adjacent to the diamond abrasive, which forms the adatoms layer to avoid the cold welding. As shown in Fig. 1, the initial atomic configuration consists of two bulk diamonds, and they are separated by the adatoms. The carbon atoms in the fixed layer are restricted and have no freedoms in any direction. Considering that a constant environment temperature should be maintained for the simulation system, the temperature of carbon atoms in the thermostat layer is explicitly reset by rescaling the velocity of atoms. For the atoms in the Newton layer, a standard velocity-Verlet integrator is adopted [22].
3. Result and discussion 3.1. Amorphization anisotropy in typical crystal directions During simulation, the upper diamond abrasive was set to move along the crystal orientation [1 0 0] and [1 1 0] of the lower
2. Molecular dynamic modeling In order to well understand the tribological behavior of diamond crystal surfaces in lapping, MD simulation is performed with the open source software LAMMPS [17] and VMD [18] in this work. The time step used for integration is 0.5 femtosecond. And the second-generation reactive empirical bond-order potential is used to describe the interaction of carbon atoms, which allows for the phase transformation [11,19]. The expression for the potential function and the related potential parameters can be found in [19].The chemical binding energy E can be written as
E¼
XX R ½V ðr ij Þ bij V A ðrij Þ i jð>iÞ
where the V R ðrÞ and V A ðrÞ are the pair-additive interaction that representing all the interatomic repulsions and attraction from valence electrons respectively; bij is the bond order between atoms i and j. Before calculation, the simulation system should be equilibrated under the isothermal-isobaric (npt) ensemble firstly. The overall dimension of MD model is 4a 4a 25a, where a is the diamond lattice constant of 0.356683 nm [20]. Under this ensemble, the bulk diamond was created to fill the simulation box. Room temperature is specified as the target system temperature. In the sliding
Fig. 1. MD simulation model of the diamond nanoscale friction system.
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diamond surface respectively. The snapshots of sliding simulation in the [1 0 0] direction at 0.1 ns, 0.25 ns, 0.75 ns, 1.75 ns and 2.5 ns are presented in Fig. 2. It can be clearly seen that the thickness of amorphous layer increases with the increment of simulation time, and the diamond carbons in the topmost surface layer of crystal diamond successively transform to the amorphous phases. A similar process can also been observed in sliding along the [1 1 0] direction. After a simulation time of 2.5 ns, a distinct amorphization layer appears, as shown in Fig. 3. Comparing the 3D close-ups of crystal layer and amorphous layer in Fig. 4, the atoms in crystal layer arrange in an ordered form, but the atoms in amorphous layer are disordered. By observing the cross section, the thickness variations of amorphous layer at different sliding time are captured, as plotted in Fig. 5. From this figure, it can be seen that along the [1 0 0] sliding direction the thickness of the amorphization layer is larger than that along the [1 1 0] sliding direction, which demonstrates that the increasing rate of the amorphous layer thickness in the [1 0 0] direction is slightly faster. This result agrees with the experimental observations, i.e. that the material removal rate in the [1 0 0] direction is greater than that in the [1 1 0] direction for the (1 0 0) or (1 1 0) plane [23,24]. Previous work reported that the amorphization probability of diamond carbons is responsible for the wear rate anisotropy of diamond surface [15]. To be different, the wear rate anisotropy is explained from a new viewpoint in this work. In our work, the second-generation reactive empirical bond-order potential field is employed to compute the forces [19]. The results show that carbon atoms subject to different resistance forces when they attempt to separate themselves from the crystal diamond surface along different directions. Fig. 6 presents the MD simulation of single carbon atom (marked in green color) escaping from the diamond crystal surface. As shown in Fig. 6, the escaping movement of carbon atom can be defined with two direction angles of h and u. Here h is set as the included angle between the projection of escaping vector and the orientation [1 0 0] of diamond (1 0 0) plane, and u denotes the included angle between the escaping vector and diamond (1 0 0) plane. Moreover, all the carbon atoms of diamond crystal are fixed. The resistance forces calculated in different escaping directions are presented in Fig. 7. In Fig. 7, the positive force denotes that the force vector is identical to the escaping direction of carbon atom, whereas the negative force means the force vector is opposite to the carbon atom motion. From the figures above, it can be clearly seen that the
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Fig. 3. 2D close-ups of the carbon atoms at the friction interface before (a) and after (b) sliding friction.
Fig. 4. 3D close-ups of the carbon atoms in crystal bulk (a) and amorphous layer (b).
resistance forces of carbon atom that moves along the [1 1 0] direction, i.e. having an escaping angle of 45° for h, are generally larger than that along the [1 0 0] direction. Such difference is more visible at a smaller escaping angle u, such as u = 15°, is applied. When the single carbon atom escapes along the [1 1 0] direction, the larger resistance force means the carbon atoms on the topmost diamond surface are more difficult to separate themselves from the diamond bulk. As pictorially shown in Fig. 5, the larger resistance force or the greater difficulty in separating carbons from the diamond bulk leads to a smaller increasing rate of amorphous layer thickness. 3.2. Microstructural behavior of the amorphous layer As discussed above, diamond carbons amorphization results in a deteriorated layer on the crystal surface. In order to investigate
Fig. 2. Snapshots of sliding simulation in the [1 0 0] direction at a simulation time of (a) 0.1 ns, (b) 0.25 ns, (c) 0.75 ns, (d) 1.75 ns and (e) 2.5 ns.
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Fig. 8. Logarithm to base 10 of the mean velocity magnitude of carbon atoms versus the height at a simulation time of 2.5 ns: (a) sliding in the [1 0 0] direction; (b) sliding in the [1 1 0] direction.
Fig. 5. Thickness variations of amorphous layer versus sliding time.
Fig. 6. MD simulation for single carbon atom moving near diamond (1 0 0) plane.
Fig. 9. Displacement of a selected atom in the middle of the bulk diamond under the abrasive sliding: (a) along the [1 0 0] direction; (b) along the [1 1 0] direction.
the microstructural behavior occurred in the amorphous layer, the velocity and relative density of carbon atoms, as well as the ratio of different carbon structures along the height direction (as shown in Fig. 1), are analyzed in this section. Fig. 8 plots the logarithm to base 10 of the mean velocity magnitude of carbon atoms versus the height as the abrasive slides along the [1 0 0] and [1 1 0] directions on the (1 0 0) plane. In this figure, part 1 denotes the diamond bulk, and part 2 and part 3 represent different regions of the amorphous layer. For part 2 and part 3, it can be seen that the variation trends of the atom velocity have
changed considerably. Especially for part 2, the magnitude of mean velocity presents an exponential growth along the height direction. According to the velocity difference of part 2 and part 3, the amorphous layer can be divided into two sub-layers. For the sub-layer corresponding to part 3, carbons contact with the abrasive particle directly. Therefore, this sub-layer is defined as the coherent layer. In the coherent layer, carbon atoms move in stick-slip mode, and the shearing happens frequently. Fig. 9 shows the displacement of a selected carbon atom in the middle of the bulk diamond under the abrasive sliding along the [1 0 0] and [1 1 0] directions.
Fig. 7. Resistance forces simulated in different escaping directions. Blue line indicates the angle h = 0° (along the [1 0 0] direction), green line angle h = 45° (along the [1 1 0] direction): (a) u = 15°, (b) u = 30°, (c) = 45, (d) u = 60°, (e) u = 75° and (f) u = 90°. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 10. Variation of the relative density under the abrasive sliding on the (1 0 0) plane and along the [1 0 0] direction at a simulation time of 2 ns.
Table 1 Variation of L (Angstrom) calculated in different sliding directions. Simulation time (ns) Sliding direction
1
1.25
1.5
1.75
2
2.25
2.5
[1 0 0] [1 1 0]
6.2 3.8
6.4 3.8
6.3 3.7
6.6 3.8
6.6 3.7
6.7 3.7
6.6 3.7
Regardless of the abrasive sliding direction, the visible fluctuation of the selected carbon atom can be easily found in Fig. 9, which indicates that the stick-slip motion appears on the top part of the bulk diamond. It is noticed that the stick-slip behavior is also observed in confined liquid films [25,26], which indicates that the diamond amorphous layer has the same lubricant effect in friction as the confined liquid films. Moreover, the sub-layer corresponding to part 2 shown in Fig. 8 can be considered as the transition layer. This amorphous sub-layer covers on the bulk diamond and lies beneath the coherent layer.
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In this work, the diamond crystal density is employed as the reference density, and the ratio of the density of amorphous layer calculated from MD simulation to the reference one is defined as the relative density. Variation of the relative density with the height increasing is plotted in Fig. 10. As shown in this figure, point A denotes the peak value of the relative density with the largest height value, and point B denotes the average value of the diamond bulk with the largest height value. L is the horizontal distance between point A and point B, which characterizes the thickness of the density transition region. The values of L calculated at different simulation time are listed in Table 1. It can be seen in Fig. 10 that the peak value of the relative density has no variation in the bulk. The peak value begins to decrease at a certain height corresponding to point A. In this case, the larger the height is, the littler the relative density does. At point B, the relative density approaches to the average value. As listed in Table 1, it can be found that the values of L generated under the abrasive sliding along the [1 0 0] or [1 1 0] direction change slightly. However, the ones generated along the [1 0 0] direction are clearly bigger than that generated along the [1 1 0] direction. As exhibited in Fig. 9, the movement of carbon atoms within the diamond bulk, i.e. the distortion induced by the sliding of diamond abrasive particle, will change the spatial distribution of carbon atoms. Because of the different resistance forces under the abrasive sliding along the [1 0 0] and [1 1 0] directions as discussed above, the sliding-induced distortion along the height direction is also different. Resistance force in the [1 1 0] direction is larger than that in the [1 0 0] direction. Such difference means that the distortion generated in sliding along the [1 1 0] direction will be smaller than that generated along the [1 0 0] direction. That is to say, the smaller distortion leads to the less value of L, which has a good consistency with the calculated results as listed in Table 1. Therefore, the value of L or the thickness of density transition region can be employed to characterize the amorphization degree for the diamond crystal when its surface suffers from the sliding friction. As discussed above, the amorphization of carbon atoms is inevitable when the abrasive slides on the diamond surface, which
Fig. 11. Ratios of different hybridization carbons in the amorphous layer when the abrasive slides on the diamond (1 0 0) plane along the [1 0 0] direction: (a) sp3, (b) sp2 and (c) sp.
Fig. 12. Ratios of different hybridization carbons in the amorphous layer when the abrasive slides on the diamond (1 0 0) plane along the [1 1 0] direction: (a) sp3, (b) sp2 and (c) sp.
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means that the transformation of sp3 hybridized carbons to sp2 or sp ones takes place on the diamond surface. Phase transformation contains bonds breakage and generates new hybridization, i.e. that the chemical property of diamond surface will change [27]. Different hybridization of carbon atoms has different number of chemical bonds. A sp3 hybridized carbon atom has 4 bonds, 3 bonds for the sp2 type, and 2 bonds for the sp type. Therefore in the MD simulations, the hybridization of a carbon atom can be identified in terms of its coordinate number, i.e. the number of neighbor atoms within a specified cutoff distance from itself. In this work, the cutoff distance is configured as 0.2 nm according to the second-generation reactive empirical bond-order potential force field [19]. When the abrasive slides on the diamond (1 0 0) plane along the [1 0 0] and [1 1 0] directions, the variations of carbon atoms with different hybridization along the height direction are shown in Figs. 11 and 12 respectively. From Figs. 11 and 12, it can be clearly seen that the sp hybridized carbons mainly distribute in the topmost amorphous layer, i.e. the coherent layer as defined above, regardless of the sliding direction of the abrasive. And the content of the sp carbons reaches up to the highest at the sliding contact interface. These observations agree well with the fact that the sp structures on the diamond surface wear as they are exposed to air [28]. Moreover, the ratio of the sp2 structures increases with the increment of height, which is far greater than the one of the sp phases at the same height. To be different for the sp3 phases, however, a decreasing trend appears. These observations indicate that in the topmost surface layer of diamond crystal the transformation of diamond sp3 phases to the sp2 phases dominates in the diamond amorphization induced by the abrasive sliding. 4. Conclusions In this work, MD simulations are employed to investigate the amorphous layer formation of diamond crystal when the diamond abrasive slides on the (1 0 0) plane along the [1 0 0] and [1 1 0] directions. According to the simulation results and the related analyses above, some important conclusions can be drawn as follows. (1) Due to the mechanical effect of the abrasive, the amorphization of carbon atoms inevitably takes place to form an amorphous layer on the topmost surface of diamond crystal. According to the velocity difference of carbon atoms, the amorphous layer can be divided into two sub-layers, i.e. the coherent layer and the transition layer. Stick-slip behavior is found in the coherent layer, which indicates that the amorphous layer has the lubricant effect in sliding friction. (2) In phase transformation, diamond sp3 hybridization carbons primarily translate to the sp2 ones. The sp phases mainly appear in the coherent layer.
(3) The amorphization rate of diamond carbons is related to the resistance force of the sliding abrasive. There is a smaller resistance force as the abrasive slides along the [1 0 0] direction. So the amorphization rate generated by the abrasive sliding along the [1 0 0] direction is bigger than that generated along the [1 1 0] direction. (4) The relative atom density of the amorphous layer is smaller than that in the bulk, and a density transition region appears in the amorphous layer. The thickness of the density transition region can be used to qualitatively characterize the degree of the diamond amorphization.
Acknowledgements This work was supported by the Natural Science Foundation of China (No. 51175127), the Fundamental Research Funds for the Central Universities (Nos. HIT.BRETIII.201412 and HIT.NSRIF.2014050) and the Major Special Subject of High-end CNC Machine Tools and Basic Manufacturing Equipment Science and Technology of China (No. 2011ZX04004-031). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]
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