Atomistic aspects of ductile responses of cubic silicon carbide during nanometric cutting
© Goel et al; licensee Springer. 2011
Received: 2 August 2011
Accepted: 11 November 2011
Published: 11 November 2011
Cubic silicon carbide (SiC) is an extremely hard and brittle material having unique blend of material properties which makes it suitable candidate for microelectromechanical systems and nanoelectromechanical systems applications. Although, SiC can be machined in ductile regime at nanoscale through single-point diamond turning process, the root cause of the ductile response of SiC has not been understood yet which impedes significant exploitation of this ceramic material. In this paper, molecular dynamics simulation has been carried out to investigate the atomistic aspects of ductile response of SiC during nanometric cutting process. Simulation results show that cubic SiC undergoes sp 3 -sp 2 order-disorder transition resulting in the formation of SiC-graphene-like substance with a growth rate dependent on the cutting conditions. The disorder transition of SiC causes the ductile response during its nanometric cutting operations. It was further found out that the continuous abrasive action between the diamond tool and SiC causes simultaneous sp 3 -sp 2 order-disorder transition of diamond tool which results in graphitization of diamond and consequent tool wear.
Keywordsductile regime nanometric cutting silicon carbide diamond tool tool wear
Commercial applications of SiC 
Properties of SiC
High sublimation temperature
High temperature transducer elements
High temperature sensor diaphragms and resonators
Large band gap
High temperature electronics
Sensors for smart engines
On chip signal conditioning
Low wear and high hardness
Coated mechanical contacts
Stable in harsh environments
Valve/pumps for corrosives
Flow sensors for acids
Moreover, SiC is also capable of meeting the requirements of operation in hostile environments (up to 873 K) where conventional silicon-based electronics (limited to 623 K) cannot function. The National Aeronautics and Space Administration agency, NASA, has recently been making efforts to develop SiC as future material for advanced semiconductor electronic device applications .
Single-point diamond turning (SPDT) is now an established ultra-precision machining process to manufacture free-form shapes and mirror-finished machined surfaces [4, 5]. SPDT was established by exploiting a so called "brittle-ductile transition" phenomenon which has made various brittle materials, amenable to ultra-precision machining using a diamond cutting tool [6, 7]. Investigations on exploring silicon carbide as a diamond-turnable material are thus of scientific and technological interest.
Experimental investigation on the feasibility of ductile regime machining of SiC through SPDT was first reported in 2005 . Common believe on machining mechanism of SiC has been that a nanoscale undeformed chip thickness compounded with slow feed rate helps to achieve high-pressure phase transformations (HPPT) which causes ductile responses from this brittle material [9, 10]. However, no such evidence of HPPT during nanometric cutting of SiC has been reported yet and the root cause of ductile response of SiC is still unknown. Molecular dynamics (MD) simulation results have been successful in the past to address number of problems concerning the nanometric cutting processes of brittle materials like silicon [11–14].
In this paper, Tersoff potential energy function  was used in the MD simulation to elucidate the atomistic mechanism underlying the ductile responses from the cubic SiC during nanometric cutting. Resorting to the simulation results, a theory has been presented and discussed.
MD simulation model
where a ix represents the i th atom's acceleration in the x direction, m i is the mass of the i th atom, F ix is the interaction force acting on the i th atom by the j th atom in the x direction, x i indicates the i th atom's x-coordinate and V is the potential energy.
where N is the number of atoms, v i represents the velocity of i th atom, k b is the Boltzmann constant which is equal to 1.3806503 × 10−23 J/K and T represents the temperature on atoms. However, the instantaneous fluctuations in K.E. of atoms could be very high so K.E. should be averaged (time and/or spatial) over few timesteps to be converted into equivalent temperature. It shall be noted here that the movement of the tool will also be a contributor to the kinetic energy so the tool displacement was accordingly subtracted before equivalent temperature conversion.
Selection of potential energy function
Tersoff potential parameters 
1.1 × 10−6
4.1612 × 10−6
1.0039 × 105
Large-scale atomic/molecular massively parallel simulator software  was used to perform the simulation.
Calculation of equilibrium lattice parameter
Using inappropriate lattice parameter will affect the total energy content of the system which may lead to lots of thermal vibrations during equilibration process. Thus, the resulting fluctuations will alter the machining parameters like undeformed chip thickness, nose radius, etc. to a large extent during energy minimization which will produce erroneous simulation results. Goel et al. [17, 18] have recently suggested to use the equilibrium lattice parameters to represent realistic MD simulation.
MD simulation setup
Variables used in the MD simulation model
Dimensions of SiC workpiece
14.2624 × 4.6353 × 5.4845 nm
Numbers of β-SiC atoms in the workpiece
Numbers of carbon atoms in the cutting tool
Tool nose radius
Undeformed chip thickness
Tool rake and clearance angle
-25° and 10°
Workpiece machining surface
Tool orientation and cutting direction
Cubic and <100>
Results and discussions
Observations from MD simulation results
Figure 4 also represents the chip morphology of β-silicon carbide (cubic) during the nanometric cutting process against a deformable diamond tool. It can be seen from Figure 4 that the cutting chips are curly shaped, which suggests that material removal is occurring in ductile regime by deformation rather than fracture. During the machining process, a few carbon atoms from the diamond tool deformed and are separated from the tool which can be seen on the machined surface of SiC.
Temperature during the machining process
Angular distribution function of SiC during cutting
As shown in Figure 7, the sp 3 hybridisation has a tetrahedral geometry with a bond angle of 109.5°. However, when this tetrahedral geometry is distorted the bond angle changes to 120° and results in planarization and consequent sp 2 hybridisation. This sp 3 -sp 2 transition occurs due to the abrasive action between diamond cutting tool and SiC workpiece. Thus, a change in bond angle from 109.5° to 120° obtained through angular distribution function is an indication of sp 3 -sp 2 order-disorder transition and transformation of cubic silicon carbide to SiC-graphene-like substance.
Radial distribution function and relative tool wear
The radial distribution functions (RDF), g(r), also called pair distribution functions or pair correlation functions, are the primary linkage between macroscopic thermodynamic properties and intermolecular interactions.
It is widely known that the thermal stability of diamond gets adversely effected in the environment of severe temperature . This causes graphitization/sp 3 -sp 2 order-disorder transition of the diamond tool during nanometric cutting of SiC. It can be seen from Figure 10 that at timestep 0, the RDF of diamond tool shows its first peak at 1.54 Å which is the known bond length of diamond  while few bonds(dangling bonds) on the surface shows a small peak at 1.42 Å. During cutting, the small peak continued to grow at a bond length of 1.42 Å with corresponding decrease in the number of atoms at the bond length of 1.54 Å. The bond length of 1.42 Å is the known bond length of another stable allotrope of carbon known as graphite  which is much weaker than diamond due to the layered structure. Thus, g(r) confirms the graphitization of the diamond tool during SPDT operation of cubic SiC and consequent wear as earlier observed from Figure 4. The numbers of the SiC atoms in the cutting chips are more than those deformed carbon atoms from the diamond tool and this proves that the rate of sp 3 -sp 2 transition of diamond tool is relatively slower than SiC.
The phenomenon of sp 3 -sp 2 order-disorder transition during SPDT of SiC also appears to be similar in nature to what occurs during polishing of diamond, which has been explained in details by Pastweka et al.  using MD simulation studies.
The MD simulation has been used to gain extensive insights into the atomistic aspects of ductile responses of SiC during nanometric cutting operations. The following conclusions can be drawn accordingly:
During nanometric cutting, the tetrahedral bonding structure of β-SiC work material gets distorted accompanying the change of bond angle from 109.5° to 120° which represents sp 3 -sp 2 order-disorder transition of SiC.
This sp 3 -sp 2 disorder causes the formation of SiC-graphene-like substance which causes ductile response from cubic SiC.
The formation of SiC-graphene-like substance is attributed to the high temperature during the nanometric cutting which is consequent due to the abrasive action between these two ultra-hard materials.
Abrasive action also causes simultaneous sp 3 -sp 2 order-disorder transition of the diamond tool but at relatively slower rate which results in tool wear.
a Readers are requested to refer to the web-based version of this article for correct interpretation of the colour legends.
b Developed at the University of Illinois, USA
c Developed at LLNL, USA
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