Revealing the deformation mechanisms of 6H-silicon carbide under nano-cutting

Computational Materials Science 137 (2017) 282–288

Contents lists available at ScienceDirect

Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci

Revealing the deformation mechanisms of 6H-silicon carbide under nano-cutting Zhonghuai Wu, Weidong Liu, Liangchi Zhang ⇑ Laboratory for Precision and Nano Processing Technologies, School of Mechanical and Manufacturing Engineering, University of New South Wales, NSW 2052, Australia

a r t i c l e

i n f o

Article history: Received 27 April 2017 Received in revised form 31 May 2017 Accepted 31 May 2017 Available online xxxx Keywords: Silicon carbide Nano-cutting Molecular dynamics Dislocation activation Phase transformation Ductile regime machining

a b s t r a c t 6H silicon carbide (6H-SiC) is one of the most commonly used polytypes in commercial SiCs, such as its applications in high-temperature electronic devices, ultra-precision micro/nano dies and highperformance mirrors. However, the deformation mechanisms of 6H-SiC under nano-machining are unclear. This has significantly hindered the development of the material’s ductile-regime and damagefree machining for micro/nano and miniaturized surfaces. This paper aims to explore such deformation mechanisms with the aid of large-scale molecular dynamics analysis. The results showed that with increasing the depth of cut 6H-SiC undergoes transition from elastic deformation to continuous plastic deformation and then to intermittent cleavage. A dislocation and structural analysis revealed that the plastic deformation of 6H-SiC can be realised via phase transformation from the Wurtzite structure to an amorphous structure, and/or through dislocations on the basal plane and/or pyramidal plane. Ó 2017 Elsevier B.V. All rights reserved.

1. Introduction Single crystal silicon carbide (SiC) is one of the most important ceramics and has been widely used in the applications that require high endurance [1]. Because of its excellent mechanical, thermal and chemical stabilities [2], for example, SiC is an ideal die material for precision micro/nano molding, is very suitable for fabricating semiconductor electronic devices that operate at high temperatures or high voltages [3], and has been used in high performance mirrors of infrared universe imaging systems [4]. However, the intrinsic brittleness and high hardness of SiC [5] have caused tremendous difficulties in the fabrication of ultra-precision micro/nano components, such as in producing miniaturized functional surfaces. The brittleness and ultra-hardness of SiC are associated with the strong covalent bonding, particularly the short sp3 bonding and closely packed diamond lattice structure [4]. At the nanoscale, however, it was reported that SiC could achieve uniform plastic deformation [6–9], which has led to further studies for achieving the ductile-regime machining of SiC [9–14]. For example, in the grinding of a single crystal 6H-SiC, Yin et al. [9] found a brittleductile transition with decreasing the diamond grit size. Patten et al. [14] also demonstrated a ductile material removal on single crystal 6H-SiC by single-point diamond turning. ⇑ Corresponding author. E-mail address: [email protected] (L. Zhang). http://dx.doi.org/10.1016/j.commatsci.2017.05.048 0927-0256/Ó 2017 Elsevier B.V. All rights reserved.

Some studies have tried to clarify the underlying mechanisms of the nanoscale plasticity and brittle-ductile transition in SiC, both experimentally and numerically. Plasticity induced by amorphization was observed on 3C-SiC by using molecular dynamics (MD) simulations of nano-indentation and nano-scratching [15,16]. A phase transformation of sp3-to-sp2 order-disorder transition was also proposed based on some MD nano-cutting simulations on 3C-SiC [17–19]. With the aid of the MD nano-indentation simulations, Szlufarska et al. [20,21] found that the dislocations in 3CSiC were first activated to initiate plastic deformation, and amorphization was due to the coalescence of the dislocation loops. Chen et al. [22] reported that dislocation activity should be the only plastic deformation mechanism of 3C-SiC. With increasing the depth of cut, Mishra and Szlufarska [23] found a transition of deformation regime of 3C-SiC from plowing to cutting with different categories of dislocations activated. Compared with 3C-SiC, 6H-SiC has been more widely used in industry because it is easier to be produced [24]. However, there are only a few studies on 6H-SiC. Patten et al. [14,25] reported that they observed amorphous microstructure on a machined surface, and that the chips of 6H-SiC could be obtained under singlepoint diamond turning. They proposed a high-pressure phase transformation (HPPT) mechanism. Grim et al. [26] experimentally confirmed that basal dislocation could also be activated in the subsurface of 6H-SiC after mechanical polishing. It should be noted that 6H-SiC has a complicated Wurtzite structure, of which the dislocation/slip system is very different from that of 3C–SiC (a Zinc

Z. Wu et al. / Computational Materials Science 137 (2017) 282–288

blende structure). Thus the deformation mechanisms and ductileregime machining strategies developed for 3C-SiC cannot be simply applied to 6H-SiC. To understand the possible mechanisms of plasticity of SiC, it is helpful to revisit the mechanics of plastic deformation. It is known [27] that to achieve a macroscopic homogeneous threedimensional plastic deformation, five independent strain tensor components are required. This is because an arbitrary threedimensional strain tensor has six independent components. However, when a material is incompressible during plastic deformation, one of the strain tensor components becomes redundant and only five of them are independent. Similarly, for a two-dimensional problem (plane-stress/strain), two independent strain tensor components are required. The minimum number of strain tensor components for the plastic deformation in ceramics and silicon can be through sufficient independent dislocation and twinning systems [28–31] or phase transformations [32–41]. In polycrystalline alumina, three independent slip systems (two basal and one prism) and two twin systems have been found to make the ductile regime machining possible. In single crystalline silicon, it has been clarified that the homogeneous plastic deformation in ductile-regime machining of the material is through structural transformations rather than dislocation glides [32–34,36–41]. Moreover, for materials of the Wurtzite structures such as BeO [42] and GaN [43], the plastic deformation mechanism is also via phase transformation. To date, however, it is still unclear whether sufficient slip systems or phase transformations can be initiated in 6H-SiC to produce at least five independent strain components, such that ductileregime machining of the material is possible or not. This paper aims to study the deformation mechanisms of 6HSiC under noncutting. Particularly, the study tends to understand which deformation mechanism dominates the nanoscale ductility in the machining of 6H-SiC, and how possible mechanisms evolve with the depth of cut. A series of nano-cutting simulations with the aid of large-scale molecular dynamics (MD) technique will be car1  2 0i ried out on the (0 0 0 1) basal plane of 6H-SiC along the h1 direction, with different depths of cut from 0.5 nm to 3 nm.

2. Methodology All MD simulations of nano-cutting in this study were conducted by the large-scale atomic/molecular massively parallel simulator (LAMMPS) [44]. Fig. 1a shows the established model consisting of a workpiece of 6H-SiC and a diamond cutting tool. The workpiece was divided into three different parts: a Newtonian atoms zone, a thermostatic atomic layer and a boundary atomic layer. The motions of the Newtonian atoms were controlled by the second Newton’s law (NVE ensemble). The thermostatic atoms (NVT ensemble) were applied to maintain the equilibrium temperature of the whole model. The boundary atoms were fixed during the simulation processes to eliminate the rigid body motion of the system [33,34,45]. Considering that the modulus and hardness of diamond are much higher than those of 6H-SiC, the diamond cutting tool was assumed to be rigid. The Tersoff potential was used for modelling the atomic interaction in the SiC workpiece [46,47]. The interaction between the silicon carbide atoms and the diamond indenter atoms are described by the Morse potential [33,34]. The cutting processes were conducted on the (0 0 0 1) basal  0i (the x axis) as plane (vertical to z axis) along direction h1 1 2  1 0 0i crysshown in Fig. 1a. The y axis of the workpiece is in the h1 tallographic direction (see Fig. 1b). To reduce the computation time, periodic boundary condition was applied in the y-direction while fixed boundary conditions were used in x- and z-direction. The MD simulation model was first relaxed at 300 K. After

283

relaxation, the cutting tool advanced with a speed of 100 m/s, which is in the range of a typical cutting speed in MD simulations [18,48,49]. The detailed simulation parameters and model dimensions are listed in Table 1. To study the changes of deformation mechanism of 6H-SiC, four different depths of cut were selected, i.e., 0.3 nm, 0.5 nm, 2 nm and 3 nm. The MD results were visualized and analyzed by using OVITO [50]. The dislocations were analyzed by the dislocation extraction algorithm (DXA) [51]. Phase transformations were identified by the radial distribution function and bond angle distribution analysis. 3. Results and discussion 3.1. Deformation and chip formation Fig. 2a to d shows the deformation and chip formation of 6H-SiC workpieces under nano-cutting at four different depths of cut. For the convenience of comparison, a uniform cutting length of 18 nm was used in all the cases. In the figures, red1 and green atoms correspond to carbon and silicon atoms in the 6H-SiC workpiece, respectively. The carbon atoms of the diamond cutting tool, however, are indicated by yellow. The cyan atoms are those that have lost their positions in their initial diamond structure during nanocutting, which have become ‘non-diamond structural atoms’. Those colored in black represent the surface atoms of the SiC workpiece. It is clear that the deformation and chip formation of 6H-SiC workpiece vary with the depth of cut, d. At d = 0.3 nm (Fig. 2a), no chip was formed. The subsurface was deformed by the cutting tool, but after the tool passed over, the workpiece material returned to their original diamond structure, except a small zone at the first tool-workpiece engagement. This indicates that the deformation of 6H-SiC was purely elastic when the nano-cutting entered its steady stage. At d = 0.5 nm (Fig. 2b), ploughing (without material removal) occurred first, but it transferred to cutting with a chip formed. During the cutting, the atomic bonds of several layers of machined surface atoms had lost their originally diamond crystalline lattice structure. Moreover, a long and narrow deformation/structural transformation regime was formed in the subsurface. Unlike the above cases at a small depth of cut, when d was increased to 2 nm and 3 nm (as shown in Fig. 2c and d), the cutting processes were with steady chipping and subsurface structural transformation. Moreover, crystalline clusters (highlighted by the arrows in Fig. 2c and d) and a small deformation/structural transformation zone ahead of the cutting tool (circled in Fig. 2c and d) emerged. It is also interesting to notice that at the cutting of d = 3 nm, a small atomic cluster within the chip could retain their original diamond crystalline lattice structure (see the enlarged part in Fig. 2d). The presence of such crystalline atoms within the chip could be due to the severe plastic deformation of surrounding material, which could be taken as a precursor of nano-cleavage [52]. As stated above, the cyan atoms in Fig. 2 are those that had lost their initial positions in the diamond structure. However, the new structures they formed are unclear. This will be elaborated in Sections 3.2 and 3.3 below. 3.2. Dislocation analysis The resultant defect surfaces and dislocations are shown in Fig. 3a to d, corresponding to Fig. 2a to d, respectively. Fig. 3e is 1 For interpretation of color in Fig. 2, the reader is referred to the web version of this article.

284

Z. Wu et al. / Computational Materials Science 137 (2017) 282–288

Fig. 1. (a) MD simulation model of nano-cutting, and (b) schematic diagram of the nano-cutting direction corresponding to the crystal structural orientations of 6H-SiC.

Table 1 Parameters used in the MD simulation. Dimensions of the SiC workpiece (x  y  z) Total number of 6H-SiC atoms in the workpiece Total number of carbon atoms in the workpiece Tool edge radius Tool rake angle Tool clearance angle Depth of cut Equilibration temperature Time step

45.14 nm  2.58 nm  11.89 nm 138,768 24,016 2 nm 15° 10° 0.3, 0.5, 2, 3 nm 300 K 0.5 fs

a schematic diagram of the dislocation systems. At d = 0.3 nm, no dislocation was observed and the machined surface is very smooth, showing that only elastic deformation occurred during the steady cutting process. At d = 0.5 nm, a partial dislocation with Burgers  0 0i in the basal plane formed underneath the vectors of 1=3 h1 1 cutting tool, corresponding to the tip of the subsurface deformation region in Fig. 2b. With the migration of this partial dislocation, a stacking fault zone was left behind [53], corresponding to the long and narrow band in the subsurface region in Fig. 2b. Similar partial dislocations were also found in the cases of d = 2 nm (Fig. 3c) and 3 nm (Fig. 3d). Moreover, in the latter two cases, per 0i were additionfect dislocations with Burgers vector of 1=3 h1 1 2 ally activated on the same basal plane in the un-machined region, corresponding to the circled regions in Fig. 2c and d. As the stacking fault energy does not play any role in the migration of a perfect dislocation [54,55], no sub-surface defects were left behind with

the proceeding of the cutting tool (see Fig. 2c and d). It should be noted that Fig. 3 only shows the activating dislocations at the specific cutting lengths and another pyramidal dislocation has also been identified during the cutting process (see Section 3.4). To further understand the nucleation of dislocations, stress analysis was conducted to explore the mechanisms behind DXA results. Fig. 4a and c shows the von-Mises shear stress distributions before and after the dislocation nucleation (time interval 0.5 ps) in the workpiece at d = 0.5 nm. The corresponding DXA results are shown in Fig. 4b and d, respectively. It can be seen that the maximum shear stress in the region ahead of the cutting tool was approximate 14.9 GPa before dislocation nucleation (see Fig. 4a). After the dislocation nucleation, there was a considerable stress release as shown in Fig. 4c. Fig. 4e shows the corresponding local temperature distribution of the workpiece before the dislocation nucleation, indicating that the temperature in the primary shear zone approached 750 K. Fig. 5a and c shows the stress distribution changes due to dislocation nucleation at d = 2 nm, and Fig. 5b and d gives the corresponding DXA results. It can be seen that before nucleation the maximum stress was 13.7 GPa, but after nucleation the value reduced to 12.9 GPa. Fig. 5e shows that the temperature in the primary shear zone at d = 2 nm was approximate 1200 K. To quantitatively reveal the temperature effect on the critical stress of the dislocation nucleation, let us develop an analytical model based on the transition state theory [56]. The dislocation nucleation rate m in a unit volume of material is generally written as an Arrhenius-type equation [57]:



m ¼ Nm0  exp 

DG kT



ð1Þ

Fig. 2. Deformation evolution in 6H-SiC due to the variation of the depth of cut d of the diamond cutting tool (total cutting length = 18 nm). (a) d = 0.3 nm, (b) d = 0.5 nm, (c) d = 2 nm, and (d) d = 3 nm.

Z. Wu et al. / Computational Materials Science 137 (2017) 282–288

285

Fig. 3. Variation of dislocation development with depth of cut d. (a) d = 0.3 nm, (b) d = 0.5 nm, (c) d = 2 nm, (d) d = 3 nm, and (e) a schematic diagram of the dislocation systems.

Fig. 4. The stress and temperature distributions in the workpiece during the nucleation of the leading dislocation at d = 0.5 nm. (a) and (c) Stress distribution before and after the dislocation nucleation, (b) and (d) DXA results before and after the dislocation nucleation, and (e) temperature distribution before the dislocation nucleation.

where the Gibbs free energy

DG ¼ H  s  V;

ð2Þ

N is the number of nucleation sites, m0 is the constant preexponential factor, H is the activation enthalpy or activation energy, s is the applied shear stress, V is the activation volume, k is the Boltzmann constant and T is the absolute temperature. DG can be further expressed as a linear function of temperature [58]:

DG ¼ akT

ð3Þ

where a is the scaling coefficient. Combining Eqs. (2) with (3), the relationship between s and T could be expressed as:

H V

s¼ 

akT V

ð4Þ

At absolute zero (T = 0 K), dislocation nucleation is fully determined by athermal stress threshold and thus s equals to its theoretical value stheo; at the melting point temperature (T = Tm),

6H-SiC becomes liquid and could not resist any shear stress if its viscosity effect is ignored, thus s = 0. Substituting these conditions into Eq. (4) gives rise to:



s ¼ stheo 1 

T Tm

 ð5Þ

Considering that the melting temperature of 6H-SiC is 3130 K [59] and its theoretical athermal stress is 21 GPa [60–62], the above analytical model predicts that the critical stresses of dislocation nucleation at 750 K and 1200 K should be 15.97 GPa and 12.95 GPa, respectively, which are in excellent agreement with those predicted by the molecular dynamics simulations (14.9 GPa at 0.5 nm with cutting induced temperature of 750 K and 13.7 GPa at 2 nm with cutting-induced temperature of 1200 K). It can therefore be concluded that a larger depth of cut enhances the dislocation nucleation because it generates more heat. To further review the temperature effect on the critical stress, we have also changed the cutting speed to 50 m/s at the cutting depth of 2 nm. The calculated temperature in the primary shear zone is about 1000 K, and the

286

Z. Wu et al. / Computational Materials Science 137 (2017) 282–288

Fig. 5. The stress and temperature distributions in the workpiece during the leading dislocation nucleation at d = 2 nm. (a) and (c) Stress distributions before and after the dislocation nucleation, (b) and (d) DXA results before and after the dislocation nucleation, and (e) temperature distribution before the dislocation nucleation.

Fig. 6. (a) RDF radial distribution function analysis and (b) bond angle distribution analysis.

corresponding critical shear stress is 14.4 GPa, which agrees very well with the predicted values of 14.3 GPa by Eq. (5). Furthermore, we also carried out uniaxial compression simulations of 6H-SiC 5  1 0 3i at two difspecimens (5.5 nm  5.3 nm  16.7 nm) along h5 ferent temperatures, 1 K and 300 K. The resulted critical shear stresses are 21.2 GPa and 19.9 GPa, respectively, which also match very well the predicted values by Eq. (5). Eq. (5) can be used for predicting the critical stress of 6H-SiC at other different temperatures. 3.3. Phase transformation As shown in Figs. 2 and 3, several subsurface layers in the machined workpiece and in the chips are no longer in the material’s diamond structure. In these regions, no dislocation appeared. To determine their structures, radial distribution function (RDF) and bond angle analysis of the atoms were employed. For comparison, similar analyses were also conducted on an un-machined 6H-SiC workpiece and a melt-quenched amorphous SiC (a-SiC) system. As shown in Fig. 6a and b, both the bond angle distribution and radial distribution function of un-machined 6H-SiC workpiece are quite different with the corresponding distributions of the machined 6H-SiC workpiece and the melting-quenched amorphous

SiC system, while the latter two are quite similar to each other. This clearly suggests that the 6H-SiC workpiece have transformed from its originally crystalline structure to amorphous structure after machining. 3.4. Ductile deformation analysis For the case at the depth of cut d = 2 or 3 nm, the deformation of 6H-SiC can be regarded as a two-dimensional problem because a periodic boundary condition was applied along the y-direction. As such, two independent strain tensor components are required to achieve homogeneous plastic deformation. Fig. 7 shows that there are indeed two independent slip systems, basal and pyramidal dislocation systems, in the subsurface which could accommodate the plastic deformation of 6H-SiC under the cutting conditions. It was the interaction of these systems that led to the formation of the crystalline clusters observed in Fig. 2c and d. Macroscopic homogeneous plastic deformation has also been realized by the uniformly transformed amorphous layer induced by the nano-cutting as shown in Fig. 2. Thus this mechanism of ductile-regime machining of 6H-SiC is similar to that of monocrystalline silicon which has been clarified both theoretically and experimentally by [32–36].

Z. Wu et al. / Computational Materials Science 137 (2017) 282–288

287

Fig. 7. The slip systems at d = 2 nm. (a) Deformed surface morphology, (b) the result from the DXA analysis, and (c) the schematic diagram of the glide plane.

4. Conclusions This paper has revealed the possible deformation mechanisms of 6H-SiC subjected to nano-cutting. The study has concluded that the 6H-SiC can experience the transition from elastic to plastic deformation when the depth of cut d increases and then to an intermittent cleavage. The ductile-regime machining of 6H-SiC at the nano-scale can be achieved by either the structural transformation, or by the migration of dislocations (in the case of plan-strain deformation), or by a combination of them. The structural transformation took place in 6H-SiC has been confirmed to be an amorphous transformation. At a small d, partial basal dislocations would be activated and their migration would lead to a stacking fault in the basal plane of the material. At a larger d, two type of  0i and f0 0 0 1g h1 0 1  0i) dislocation systems, basal (f0 0 0 1g h1 1 2  2g h1 1 2  3i) dislocations could be activated and pyramidal (f1 1 2 simultaneously. The critical stress of dislocation nucleation decreases with increasing d because of cutting-induced temperature rise in the material. An analytical model has been developed, and has been used to predict the critical stress at different temperature. It shows that the critical stress is 15.97 GPa at 750 K and 12.95 GPa at 1200 K. Acknowledgement The authors appreciate the Australian Research Council for its financial support to this work under the Discovery-Project Grant DP140103476. Zhonghuai Wu has been supported by CSC and TFS of UNSW. This research was undertaken with the assistance of resources provided at the NCI National Facility systems through the National Computational Merit Allocation Scheme supported by the Australian Government. References [1] S. Goel, The current understanding on the diamond machining of silicon carbide, J. Phys. D Appl. Phys. 47 (2014) 243001. [2] C. Hall, M. Tricard, H. Murakoshi, Y. Yamamoto, K. Kuriyama, H. Yoko, New mold manufacturing techniques, Optics & Photonics 2005: International Society for Optics and Photonics, 2005, p. 58680V. [3] C.E. Weitzel, J.W. Palmour, C.H. Carter, K. Moore, K. Nordquist, S. Allen, C. Thero, M. Bhatnagar, Silicon carbide high-power devices, IEEE Trans. Electron. Dev. 43 (1996) 1732–1741. [4] S. Suyama, Y. Itoh, High-strength reaction-sintered silicon carbide for largescale mirrors-effect of surface oxide layer on bending strength, in: Advances in Science and Technology, vol. 63, Trans Tech Publ, 2011, pp. 374–382. [5] P. Mélinon, B. Masenelli, F. Tournus, A. Perez, Playing with carbon and silicon at the nanoscale, Nat. Mater. 6 (2007) 479–490. [6] C.A. Schuh, A.C. Lund, Application of nucleation theory to the rate dependence of incipient plasticity during nanoindentation, J. Mater. Res. 19 (2004) 2152– 2158.

[7] X. Zhao, R.M. Langford, I.P. Shapiro, P. Xiao, Onset plastic deformation and cracking behavior of silicon carbide under contact load at room temperature, J. Am. Ceram. Soc. 94 (2011) 3509–3514. [8] S. Shim, J.-I. Jang, G.M. Pharr, Extraction of flow properties of single-crystal silicon carbide by nanoindentation and finite-element simulation, Acta Mater. 56 (2008) 3824–3832. [9] L. Yin, E.Y. Vancoille, K. Ramesh, H. Huang, Surface characterization of 6H-SiC (0 0 0 1) substrates in indentation and abrasive machining, Int. J. Mach. Tools Manuf. 44 (2004) 607–615. [10] T.G. Bifano, T.A. Dow, R.O. Scattergood, Ductile-regime grinding: a new technology for machining brittle materials, J. Eng. Ind. 113 (1991) 184–189. [11] S. Agarwal, P.V. Rao, Experimental investigation of surface/subsurface damage formation and material removal mechanisms in SiC grinding, Int. J. Mach. Tools Manuf. 48 (2008) 698–710. [12] J. Yan, Z. Zhang, T. Kuriyagawa, Mechanism for material removal in diamond turning of reaction-bonded silicon carbide, Int. J. Mach. Tools Manuf. 49 (2009) 366–374. [13] D. Ravindra, J. Patten, Improving the surface roughness of a CVD coated silicon carbide disk by performing ductile regime single point diamond turning, in: ASME 2008 International Manufacturing Science and Engineering Conference collocated with the 3rd JSME/ASME International Conference on Materials and Processing, American Society of Mechanical Engineers, 2008, pp. 155–161. [14] J. Patten, W. Gao, K. Yasuto, Ductile regime nanomachining of single-crystal silicon carbide, J. Manuf. Sci. Eng. 127 (2005) 522–532. [15] A. Noreyan, J. Amar, I. Marinescu, Molecular dynamics simulations of nanoindentation of-SiC with diamond indenter, Mater. Sci. Eng., B 117 (2005) 235–240. [16] A. Noreyan, J. Amar, Molecular dynamics simulations of nanoscratching of 3C SiC, Wear 265 (2008) 956–962. [17] S. Goel, X. Luo, R. Reuben, W. Rashid, Atomistic aspects of ductile responses of cubic silicon carbide during nanometric cutting, Nanoscale Res. Lett. 6 (2011) 589. [18] S. Goel, X. Luo, R.L. Reuben, Molecular dynamics simulation model for the quantitative assessment of tool wear during single point diamond turning of cubic silicon carbide, Comput. Mater. Sci. 51 (2012) 402–408. [19] S. Goel, X.C. Luo, R. Reuben, W. Bin Rashid, J.N. Sun, Single point diamond turning of single crystal silicon carbide: molecular dynamic simulation study, in: Key Engineering Materials, vol. 496, Trans Tech Publ, 2012, pp. 150–155. [20] I. Szlufarska, R.K. Kalia, A. Nakano, P. Vashishta, Atomistic mechanisms of amorphization during nanoindentation of SiC: a molecular dynamics study, Phys. Rev. B 71 (2005) 174113. [21] I. Szlufarska, R.K. Kalia, A. Nakano, P. Vashishta, Nanoindentation-induced amorphization in silicon carbide, Appl. Phys. Lett. 85 (2004) 378–380. [22] H.-P. Chen, R.K. Kalia, A. Nakano, P. Vashishta, I. Szlufarska, Multimillion-atom nanoindentation simulation of crystalline silicon carbide: orientation dependence and anisotropic pileup, J. Appl. Phys. 102 (2007) 063514. [23] M. Mishra, I. Szlufarska, Dislocation controlled wear in single crystal silicon carbide, J. Mater. Sci. 48 (2013) 1593–1603. [24] M.B. Wijesundara, R.G. Azevedo, SiC materials and processing technology, in: Silicon Carbide Microsystems for Harsh Environments, Springer, 2011, pp. 33– 95. [25] B. Bhattacharya, J.A. Patten, J. Jacob, P.J. Blau, J. Howe, J.D. Braden, Ductile Regime Nano-Machining of Polycrystalline Silicon Carbide (6H), American Society of Precision Engineers, 2005. [26] J. Grim, M. Benamara, M. Skowronski, W. Everson, V. Heydemann, Transmission electron microscopy analysis of mechanical polishing-related damage in silicon carbide wafers, Semicond. Sci. Technol. 21 (2006) 1709. [27] R.v. Mises, Mechanik der plastischen Formänderung von Kristallen, ZAMM-J. Appl. Math. Mech./Z. Angew. Math. Mech. 8 (1928) 161–185. [28] I. Zarudi, L.C. Zhang, Y.-W. Mai, Subsurface damage in alumina induced by single-point scratching, J. Mater. Sci. 31 (1996) 905–914.

288

Z. Wu et al. / Computational Materials Science 137 (2017) 282–288

[29] I. Zarudi, L.C. Zhang, D. Cockayne, Subsurface structure of alumina associated with single-point scratching, J. Mater. Sci. 33 (1998) 1639–1645. [30] I. Zarudi, L.C. Zhang, Initiation of dislocation systems in alumina under singlepoint scratching, J. Mater. Res. 14 (1999) 1430–1436. [31] I. Zarudi, L.C. Zhang, On the limit of surface integrity of alumina by ductilemode grinding, J. Eng. Mater. Technol. 122 (2000) 129–134. [32] W.C.D. Cheong, L.C. Zhang, Molecular dynamics simulation of phase transformations in silicon monocrystals due to nano-indentation, Nanotechnology 11 (2000) 173–180. [33] L.C. Zhang, H. Tanaka, On the mechanics and physics in the nano-indentation of silicon monocrystals, JSME Int. J. A-Solid Mech. 42 (1999) 546–559. [34] L.C. Zhang, H. Tanaka, Atomic scale deformation in silicon monocrystals induced by two-body and three-body contact sliding, Tribol. Int. 31 (1998) 425–433. [35] Q. Fang, L. Zhang, Prediction of the threshold load of dislocation emission in silicon during nanoscratching, Acta Mater. 61 (2013) 5469–5476. [36] S.K. Deb, M. Wilding, M. Somayazulu, P.F. McMillan, Pressure-induced amorphization and an amorphous–amorphous transition in densified porous silicon, Nature 414 (2001) 528–530. [37] I. Zarudi, L.C. Zhang, Subsurface damage in single-crystal silicon due to grinding and polishing, J. Mater. Sci. Lett. 15 (1996) 586–587. [38] I. Zarudi, L.C. Zhang, Effect of ultraprecision grinding on the microstructural change in silicon monocrystals, J. Mater. Process. Technol. 84 (1998) 149–158. [39] I. Zarudi, L.C. Zhang, Structure changes in mono-crystalline silicon subjected to indentation—experimental findings, Tribol. Int. 32 (1999) 701–712. [40] L.C. Zhang, I. Zarudi, Towards a deeper understanding of plastic deformation in mono-crystalline silicon, Int. J. Mech. Sci. 43 (2001) 1985–1996. [41] I. Zarudi, L.C. Zhang, W.C.D. Cheong, T.X. Yu, The difference of phase distributions in silicon after indentation with Berkovich and spherical indenters, Acta Mater. 53 (2005) 4795–4800. [42] Y. Cai, S. Wu, R. Xu, J. Yu, Pressure-induced phase transition and its atomistic mechanism in BeO: a theoretical calculation, Phys. Rev. B 73 (2006) 184104. [43] S. Limpijumnong, W.R. Lambrecht, Homogeneous strain deformation path for the wurtzite to rocksalt high-pressure phase transition in GaN, Phys. Rev. Lett. 86 (2001) 91. [44] S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys. 117 (1995) 1–19. [45] L.C. Zhang, Solid Mechanics for Engineers, Palgrave Basingstoke, UK, 2001. [46] J. Tersoff, Modeling solid-state chemistry: interatomic potentials for multicomponent systems, Phys. Rev. B 39 (1989) 5566.

[47] K. Leung, Z. Pan, D. Warner, Atomistic-based predictions of crack tip behavior in silicon carbide across a range of temperatures and strain rates, Acta Mater. 77 (2014) 324–334. [48] D.D. Cui, K. Mylvaganam, L.C. Zhang, Nano-grooving on copper by nanomilling and nano-cutting, in: Advanced Materials Research, vol. 325, Trans Tech Publ, 2011, pp. 576–581. [49] D.D. Cui, K. Mylvaganam, L.C. Zhang, W.D. Liu, Some critical issues for a reliable molecular dynamics simulation of nano-machining, Comput. Mater. Sci. 90 (2014) 23–31. [50] A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO—the Open Visualization Tool, Modell. Simul. Mater. Sci. Eng. 18 (2009) 015012. [51] A. Stukowski, V.V. Bulatov, A. Arsenlis, Automated identification and indexing of dislocations in crystal interfaces, Modell. Simul. Mater. Sci. Eng. 20 (2012) 085007. [52] J. Wilks, E. Wilks, Properties and Applications of Diamond, ButterworthHeinemann, Oxford, 1991. [53] J.-L. Demenet, M. Hong, P. Pirouz, Plastic behavior of 4H-SiC single crystals deformed at low strain rates, Scr. Mater. 43 (2000) 865–870. [54] S. Kiani, K. Leung, V. Radmilovic, A. Minor, J.-M. Yang, D. Warner, S. Kodambaka, Dislocation glide-controlled room-temperature plasticity in 6HSiC single crystals, Acta Mater. 80 (2014) 400–406. [55] J.L. Demenet, M. Amer, C. Tromas, D. Eyidi, J. Rabier, Dislocations in 4H-and 3CSiC single crystals in the brittle regime, Physica Status Solidi (C) 10 (2013) 64– 67. [56] H.R. Pruppacher, J.D. Klett, P.K. Wang, Microphysics of Clouds and Precipitation, 1998. [57] C. Schuh, J. Mason, A. Lund, Quantitative insight into dislocation nucleation from high-temperature nanoindentation experiments, Nat. Mater. 4 (2005) 617–621. [58] D. Caillard, J.-L. Martin, Thermally Activated Mechanisms in Crystal Plasticity, Elsevier, 2003. [59] C.-M. Zetterling, Process Technology for Silicon Carbide Devices, IET, 2002. [60] D. Lorenz, A. Zeckzer, U. Hilpert, P. Grau, H. Johansen, H. Leipner, Pop-in effect as homogeneous nucleation of dislocations during nanoindentation, Phys. Rev. B 67 (2003) 172101. [61] S. Wang, H. Ye, Ab initio elastic constants for the lonsdaleite phases of C, Si and Ge, J. Phys.: Condens. Matter 15 (2003) 5307. [62] K.E. Petersen, Silicon as a mechanical material, Proc. IEEE 70 (1982) 420–457.