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Available online at www.sciencedirect.com

Journal of the European Ceramic Society 32 (2012) 3423–3434

quantitative assessment of nanometric machinability of major polytypes ofsingle crystal silicon carbide

Xichun Luo a,b,∗, Saurav Goel a, Robert L. Reuben a

a School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EH144AS, Scotland, UKb School of Computing and Engineering, University of Huddersfield HD1 3DH, UK

Received 20 January 2012; received in revised form 3 April 2012; accepted 10 April 2012Available online 10 May 2012

bstract

he influence of polymorphism on nanometric machinability of single crystal silicon carbide (SiC) has been investigated through molecularynamics (MD) simulation. The simulation results are compared with silicon as a reference material.

Cutting hardness was adopted as a quantifier of the machinability of the polytypes of single crystal SiC. 3C-SiC offered highest cutting resistance∼2.9 times that of silicon) followed by the 4H-SiC (∼2.8 times that of silicon) whereas 6H-SiC (∼2.1 times that of silicon) showed the least.espite its high cutting resistance, 4H-SiC showed the minimum sub-surface crystal lattice deformed layer depth, in contrast to 6H-SiC. Further

nalysis of temperatures in the cutting zone and the percentage tool wear indicated that single point diamond turning (SPDT) of single crystaliC could be limited to either 6H-SiC or 4H-SiC depending upon quality and cost considerations as these were found to be more responsive andmenable to SPDT compared to single crystal 3C-SiC.

2012 Elsevier Ltd. All rights reserved.

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eywords: Nanometric cutting; Ductile regime machining; Tool wear; SiC; Sil

. Introduction

Silicon carbide (SiC) has been recognized as a potential can-idate for large-scale quantum computing applications, noseovers in Airborne laser (ABL) devices, laser radar systems, vac-um ultraviolet (VUV) telescopes and weather satellites.1 Theres also a growing interest in the use of SiC in the optics industryor space based laser mirrors as a replacement for beryllium.2

ue to its superior properties, such as high-temperature resis-ance and chemical inertness, SiC is being actively explored asfuture material for advanced semiconductor electronic device

pplications,3 leading to a potential demand for cost effectiveanufacturing of complex SiC components with mirror finish.avies et al.4 have quoted Fortune5 saying that “Ultraprecisionachining (UPM) is doing for light what integrated circuits did

or electronics”.Single point diamond turning (SPDT) is now an established

ltra precision manufacturing method to obtain mirror finish

∗ Corresponding author. Tel.: +44 0 1314513197; fax: +44 0 1314513129.E-mail address: x.luo@hud.ac.uk (X. Luo).

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955-2219/$ – see front matter © 2012 Elsevier Ltd. All rights reserved.ttp://dx.doi.org/10.1016/j.jeurceramsoc.2012.04.016

urfaces right up to the edge of the element6 on a variety of brittleaterials.4,7–10 In fact, the diamond turned optical surface has a

etter metallurgical structure than that obtained after machiningsing polishing and lapping processes.11 Therefore, significantost reduction can be achieved to produce optical quality andamage-free SiC surfaces through diamond turning as it willequire fewer manufacturing steps than grinding, polishing andapping methods.

SiC exhibits one-dimensional polymorphism, all polytypesaving the same planar arrangement of Si and C atoms butifferent stacking sequences. About 250 polytypes of sili-on carbide (SiC) have been recognized by their energeticquivalence demonstrated through theoretical thermodynamicalculations.12 The two major polymorphs are �-SiC and �-SiCith hexagonal and zinc-blende lattice structures, respectively.he main engineering properties of �-SiC (3C-SiC) and �-SiC

6H-SiC and 4H-SiC) are listed in Table 1, along with the corre-ponding values for single crystal silicon as a reference material.

It can be seen that the properties of the individual poly-

ypes differ significantly despite the fact that all share the sameetrahedral geometry of silicon and carbon atoms as shown inig. 1.

3424 X. Luo et al. / Journal of the European Ceramic Society 32 (2012) 3423–3434

Table 1Engineering properties of polytypes of SiC and silicon.

Parameter 3C-SiC 4H-SiC 6H-SiC Silicon

Experimental lattice parameter (Å) a = 4.35913 a = 3.07913 a = 3.081713 5.4314

c = 10.25413 c = 15.118313

Mechanical propertiesBulk modulus (K) (GPa) 22515 21516 21516 9817

Shear modulus (G) (GPa) 12418 131.418 131.418 79.918

Hardness (H) on (1 0 0) plane (GPa) 25–3016 2620 20–2621 9.819

Poisson’s ratio (υ) 0.26718 0.23118 0.23118 0.2718

Young’s modulus (E) (GPa) “E = 3K(1 − 2υ)” 314.55 347.01 347.01 135.24Fracture toughness (Kc) (MPa m1/2) 2.0222 1.923 1.923 0.924

3.23 for CVDElectronic properties 25–29

Band gap (eV) 2.3 3.2 3 1.1Hole mobility (cm2/V.s) 40 115 90 420Electron mobility (cm2/V.s) 750 //c-axis: 800 ⊥ c-axis: 800 //c-axis: 60 ⊥ c-axis: 800 1200Thermal conductivity (W/cm-K) 4.9 3–5 3–5 1.5Electron saturation velocity (cm/s × 107) 2.5 2Breakdown electric field strength (V/cm × 106) 1.8 //c-

Fig. 1. Tetrahedral geometry of SiC.

SiasS

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dSC

Fig. 2. Stacking sequence of bila

2 1axis: 3 ⊥ c-axis: 2.5 //c-axis: 3.2 ⊥ c-axis: >1 0.6

This difference in material properties of various polytypes ofiC is fundamentally attributable to the difference in the stack-

ng arrangement of SiC bilayers along the c-axis of �-SiC andlong the (0 0 1) direction of �-SiC.30 Fig. 2 shows the stackingequence of silicon and carbon atoms in various polytypes ofiC.

It can be seen from Fig. 2 that, if the first Si-C layer isabelled A, a close packed structure can be obtained placing theext layer at either of positions B or C. The various polytypesf SiC are simply permutations of three such positions. Thus

efined, the stacking sequence is ABC in 3C-SiC, ABCB in 4H-iC and ABCACB in 6H-SiC. Although, SPDT of 6H-SiC,31,32

VD(polycrystalline) 3C-SiC,1 RB-SiC10 and 4H-SiC33 has

yers in polytypes of SiC.28

X. Luo et al. / Journal of the European Ceramic Society 32 (2012) 3423–3434 3425

f MD

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een successfully demonstrated, a theoretical study at a funda-ental atomic level will answer some key questions which are

ifficult to observe on-line during experiments. For example, its important to know if it is possible to generate defect-free sur-aces in all the major polytypes of single crystal silicon carbide,nd, if so, under what machining conditions. Also, it is of interesto know if some polytypes are more amenable to SPDT. Hence,t is worthwhile to simulate the SPDT mechanism for all poly-ypes of SiC simultaneously, which is the key motivation forhe current work to characterize quantitatively the nanometricachinability and investigate the feasibility of SPDT for vari-

us polytypes of SiC in a way that is indexed to silicon, whichs comparatively well-studied.

This is an important precursor to experimental studies, whichould not only be expensive, but would also not permit directbservation of all the events occurring at the atomic level, whichormally take place over timescales in the femtosecond range.ot every simulation method is suitable for this application; for

xample, the classical theory of finite element method (FEM)ssumes the material to behave as a continuum whereas theelevant atomic level phenomena are discrete.

If, as suspected, the key to such processes lies in under-tanding the atomic level events, MD should be an appropriateimulation approach, as it is one which has already been suc-essful in addressing a number of key problems concerninganometric cutting processes.34–38 The relatively slow compu-ational speed can be overcome using the quasi-continuum (QC)

ulti-scale simulation method39 which harnesses the combineddvantages of both MD and FEM. However, QC software is yeto be developed to simulate silicon-like complex diamond cubicattices. Considering the above limitations, this paper adopts atate-of the-art MD simulation employing a suitable three-bodyotential energy function for describing the SPDT of variousolytypes of SiC alongside silicon as a reference material.

. MD simulation

A public-domain computer code, known as “Large-scaletomic/molecular massively parallel simulator” (LAMMPS)40

ttzi

simulation model.

as used to perform the MD simulation. The following para-raphs give details of the implementation of this code for theimulation in hand.

.1. MD simulation model

A schematic diagram of the nanometric cutting simulationodel is shown in Fig. 3. Both the single-crystal SiC workpiece

nd the diamond cutting tool have been modelled as deformableodies in order to study the tribological interactions between thewo. This is in contrast to previous simulations which have takenhe cutting tool to be a rigid body, a reasonable assumption if theocus of interest is the mechanism of nanometric cutting ratherhan the tool wear.41–43 The model developed in this work isased on the boundary condition of bottom and closed cut outide which was found more appropriate to study nanometricutting process.44 Also, the MD model incorporates a negativeool rake angle, as this is generally recommended for machiningrittle materials. 45 The atoms of both cutting tool and workpieceere allocated into one of the three different zones: Newton

toms, thermostatic atoms and boundary atoms.The essence of nanometric cutting simulation through MD is

imply a classical solver of Newton’s second law of motion,here the atoms in the Newton and thermostatic zones are

ssumed to follow Newton’s second law as follows:

ix = Fix

mi

= d2xi

dt2 , Fix = −dV

dxi

(1)

here aix represents the ith atom’s acceleration in the x directionnd mi is the mass of the ith atom. Fix is the interaction forcecting on the ith atom by the jth atom in the x direction, xi is ithtom’s x-coordinate and V is the potential energy function.

The boundary atoms are assumed to remain unaffected dur-ng the simulation and thus remain fixed in their initial latticeositions, serving to reduce the boundary effects and maintain

he symmetry of the lattice. In conventional machining opera-ions, the energy from plastic deformation in the primary shearone and friction at the tool–chip interface generate heat, whichs carried away by chips and lubricant and by conduction into the

3 n Ceramic Society 32 (2012) 3423–3434

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Table 2Tersoff potential parameters.46,47

Si–Si C–C

A (eV) 1830.8 1393.6B (eV) 471.18 346.74λ (Å−1) 2.4799 3.4879μ (Å−1) 1.7322 2.2119β 1.1 × 10−6 1.5724 × 10−7

n 0.78734 0.72751c 1.0039 × 105 3.8049 × 104

d 16.217 4.3484h −0.59825 −0.57058R (Å) 2.7 1.8S (Å) 3 2.1χ

f

f

b

TP

W

364SEaaaaCCCCUCECT

426 X. Luo et al. / Journal of the Europea

ool and workpiece. The nanometric cutting model is, however,xtremely small and is not capable of dissipating the cutting heattself. The motion of the thermostatic atoms is therefore re-scaledo a temperature of 300 K at every time step. The velocity of thetoms can be used to compute the local temperature of the atomssing the relationship between kinetic energy and temperature:

1

2

∑i

miv2i = 3

2NkbT (2)

here N is the number of atoms, vi represents the velocity ofth atom, kb is the Boltzmann constant (1.3806503 × 10−23 J/K)nd T represents the atomistic temperature. However, the instan-aneous fluctuations in kinetic energy per atom would be veryigh so these are averaged temporally and/or spatially over fewimesteps and reassigned to each atom at every N steps to be con-erted into equivalent temperature. It should be noted here thathe movement of the tool will also contribute to the kinetic energyo the component of tool displacement should accordingly beubtracted.

.2. Potential energy function

A potential energy function fundamentally governs the accu-acy and reliability of the results obtained from the MDimulation. Hence, an appropriate potential function for siliconnd carbon interactions must be chosen. The Tersoff potentialunction, being a three-body potential function, can provide aore realistic description of covalent bonded materials like sili-

on and carbon, so it was used to describe Si–Si, C–C and Si–Cnteractions as follows:

∑ ∑

=

i

Ei = 1

2i /= j

Vij

, Vij = fc(rij)[fR(rij) + bijfA(rij)] (3)g

able 3rocess variables used for MD simulation model.

orkpiece material Numberworkpiec

C–SiC (14.2624 nm × 4.6353 nm × 4.2787 nm) 28600H–SiC (14.2624 nm × 4.6353 nm × 5.1347 nm) 31999H–SiC (14.2624 nm × 4.6353 nm × 3.92216 nm) 27360ilicon (14.2624 nm × 4.6353 nm × 4.2787 nm) 14840quilibrium lattice parameters used for the workpiece (Å)= b = c = 4.321; α = β = γ = 90◦= b = 3.07; c = 14.26; α = β = 90◦; γ = 120◦= b = 3.07; c = 9.856; α = β = 90◦; γ = 120◦= b = c = 5.432; α = β = γ = 90◦rystal orientation of diamond toolrystal orientation of workpieceutting directionutting edge radius (nm)ncut chip thickness/in-feed (nm)utting tool rake and clearance anglequilibration temperatureutting velocityimestep

Si–C 0.9776

R(rij) = Aij exp(−λijrij) , fA(rij) = −Bij exp(−μijrij)

(4)

c(rij) =

⎧⎪⎪⎪⎨⎪⎪⎪⎩

1 rij < Rij

1

2+ 1

2cos

[π

(rij − Rij

Sij − Rij

)]Sij > rij > Rij

0 rij > Sij

(5)

ij = χij(1 + βnii ζni

ij )−1/2ni

, ζij =∑

k /= i,j

fc(rik)ωikg(θijk)

(6)

(θijk) = 1 + c2i

d2i

− c2i

[d2i + hi − cos θijk]

(7)

of atoms in thee

Number of atoms in the diamond cutting tool

21192256071942621192

3C–SiC6H–SiC4H–SiCSiliconCubic(010)<1 0 0>2.29741.3128−25◦ and 10◦300 K100 m/s0.5 fs

X. Luo et al. / Journal of the European Ceramic Society 32 (2012) 3423–3434 3427

Fig. 4. Unit cell of SiC. (a) Orthographic view, �-SiC, (b) view onto (0 0 1)p

wearotob

Fig. 5. Cutting forces during nanometric cutting (a) thrust forces and (b) cuttingforces.

Fig. 6. Comparison of thrust and cutting forces during nanometric cutting.

lane, �-SiC, (c) view onto (1 0 0) plane, �-SiC.

here Ei is the site energy, the sub-function, Vij describes thenergy between two atoms (i and j), (i, j and k) label the threetoms of the system, fR represents a repulsive pair potential, fAepresents an attractive pair potential, fC represents a smooth cut-ff function to limit the range of the potential, rij is the length ofhe i–j bond, bij is the bond order term, ζij counts the number of

ther bonds to atom i besides the i–j bond, θijk is the bond angleetween the bonds i–j and i–k and χSi–C is the mixing parameter.

3428 X. Luo et al. / Journal of the European Ceramic Society 32 (2012) 3423–3434

anometric cutting (a) 3C-SiC, (b) 6H-SiC, (c) 4H-SiC, (d) silicon.

wi

2

ubamadnakpt

Fig. 7. Comparison of forces on individual material during n

The potential function parameters and process variableshich were used in the current MD simulation model are listed

n Tables 2 and 3.

.3. MD simulation setup

The MD simulation model was developed by replicating thenit cell using periodic boundary conditions. This was followedy energy minimization to avoid overlaps in the positions of thetoms. The simulation model was equilibrated to 300 K under theicro canonical (NVE) ensemble and the initial velocities of the

toms were assigned in accordance with a Maxwell–Boltzmannistribution. During the equilibration process, the total energy isot conserved and so the trajectories must not be used to compute

ny properties while the potential energy continues to convert toinetic energy and vice-versa. This procedure causes the tem-erature to fluctuate until it becomes stationary. Once sufficientime has been given for equilibration, the velocity scaling is

Fig. 8. Cutting hardness of various polytypes of SiC compared with silicon.

X. Luo et al. / Journal of the European Ceramic Society 32 (2012) 3423–3434 3429

Fig. 9. (a) Sub-surface crystal lattice deformed layer depth and chip morphology of 4H-SiC. (b) Sub-surface crystal lattice deformed layer depth and chip morphologyo pholom

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f 3C-SiC. (c) Sub-surface crystal lattice deformed layer depth and chip mororphology of silicon.

emoved and the system then follows NVE dynamics. Differentiews of the unit cell of SiC are shown in Fig. 4 where the greennd red colours1 correspond to silicon and carbon atoms respec-ively. Visual Molecular Dynamics (VMD) software48 was usedor enhanced visualization of atomistic data.

. Results and discussions

This section covers observations and discussion of the sig-ificance of the MD simulations in terms of the cutting forces,utting hardness, chip morphology, workpiece deformation,emperature in the cutting zone and, finally, the tool wear.

.1. Cutting forces and cutting hardness

Fig. 5 shows schematically the orientation of the compo-ents of cutting force acting on the tool. The “cutting force”Fc) acts in the x direction, the “thrust force” (Ft) acts inhe y direction and Fz acts in the direction orthogonal tohe X and Y planes. A comparison of the main componentsthrust and cutting forces) for all the simulations is shown in

ig. 6.

It can be seen from Fig. 6 that the magnitudes of the forces areignificantly higher for all polytypes of SiC compared to silicon

1 Readers are referred to the web based version of this article to interpret theorrect colour legends.

hefaies

gy of 6H-SiC. (d) Sub-surface crystal lattice deformed layer depth and chip

nd, as with the thrust force (Fy), the highest in magnitude isor 3C-SiC, followed by 4H-SiC and 6H-SiC in that order. Theagnitudes of the cutting forces (Fx) were however, found to be

n a different order, the highest being for 3C-SiC, followed byH-SiC and 4H-SiC.

Fig. 7 shows an individual comparison of thrust and cuttingorce development for each material. It seems that the cuttingorces (Fc) are higher than the thrust forces (Ft) for machiningilicon, whereas the reverse is the case for SiC. In conventionalutting, the dominance of cutting forces over thrust forces isttributed to the larger shear plane area which results from aecrease in shear angle.

The magnitude and nature of the thrust and cutting forcesbserved in 3C-SiC here are in close agreement with anotherD simulation study which used the ABOP formalism based

otential energy function.49 Patten and Gao50 have demon-trated that increasing the negative tool rake angle will increasehe thrust force (Fy) compared to the cutting force (Fx) duringPDT. It is of further interest to note that higher cutting forcesere observed while cutting 6H-SiC with a tool having a neg-

tive rake angle of −45◦.31 However, the cutting tool deployedad a very large clearance angle (40◦) and hence it experi-nced lower thrust forces than cutting forces. Neither thrustorce nor cutting force in the current case is a clear criterion tossess the relative machinability of the material. The difficulty

n evaluation of the machinability of the material can, how-ver, be overcome using the “cutting hardness”, which has beenuggested51 as a quantitative indicator of the cutting resistance of

3 n Ceramic Society 32 (2012) 3423–3434

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430 X. Luo et al. / Journal of the Europea

material irrespective of the machining parameters, expressed asollows:

verage cutting hardness = resultant force

volume of material removed

=√

Ft2 + Fc2

bdl(8)

here Ft and Fc are the thrust and cutting forces, respectively,is the width or depth of cut, d is the uncut chip thickness and

is the length of cut. The evolutions of cutting hardness for 3C-iC, 4H-SiC, 6H-SiC are shown in Fig. 8, compared with theeference material, silicon.

The average values of cutting hardness over the 10 nm tooldvancement for silicon, 3C-SiC, 6H-SiC and 4H-SiC wereound as 9.1, 26.4, 19.2 and 25.5 respectively, so 3C-SiC offeredhe highest cutting resistance (∼2.9 times that of silicon) fol-owed by 4H-SiC (∼2.8 times silicon) and 6H-SiC (∼2.1 timesilicon).

The ratios of transition pressure and cutting hardness wereound to be 2.25, 2.15, 1.75 and 1.42 for 6H-SiC, 3C-SiC,H-SiC and silicon respectively. A study made during the970s reported this ratio in carborundum as 1.6952 and looksn reasonable agreement with the value of 1.75 obtained forH-SiC.

.2. Chip morphology and sub-surface crystal latticeeformed layer depth

The sub-surface damage thickness is critical informa-ion at each step of the manufacturing process. Monnoyet al.53 have indicated that different experimental methods.g. Normarski observation, transmission electron microscopy,utherford backscattering, photon backscattering, KOH etch-

ng, Raman scattering and even positron annihilation have beensed to identify the sub-surface deformation layer depth. Sincell the machining parameters in the current simulation wereept the same, the sub-surface deformation will give a usefulelative measure for the individual polytypes. Moreover, chiporphology and subsurface deformation are of critical inter-

st because they govern the obtainable surface finish and formccuracy. In the current simulation, although, both SiC andilicon show curly chip formation, the extent of this varies andhe finished surface and subsurface obtained after machining dif-ers significantly. Thus, severe plastic deformation, compoundedith high pressure underneath the tool, results in alteration of

he microstructure in the sub-surface of the machined compo-ent. Depending upon the characteristics of the sub-surface, thisay influence component life by its effect on residual stress,

atigue and creep. The chip shapes in Fig. 9 show that chipormation has taken place in all four materials by deformationather than fracture, i.e. that ductile-regime machining could bechieved.

Fig. 9 also shows an estimate of the sub-surface deformationepth below the uncut surface directly under the tool positionor all the polytypes of SiC and silicon. The quality of the fin-shed surface (indicated by the deformed layer depth) appears

os

t

ig. 10. Comparison of temperature evolutions during nanometric cutting.

o be the best obtained on 4H-SiC, followed by 3C-SiC, sili-on and, finally, 6H-SiC whose sub-surface is heavily distorted.his can be quantified by subtracting the uncut chip thickness

rom the estimate shown in Fig. 9, giving maximum sub-surfaceeformed layer depths from the finished surface of 0.32 nm,.42 nm, 1.54 nm and 1.15 nm accounting for about 1.24, 1.32,.18 and 1.87 times the uncut chip thickness for 4H-SiC, 3C-SiC,H-SiC and silicon, respectively.

Experimental measurement of sub-surface deformation depths time consuming and difficult. Whereas the nanometric cut-ing and nano-indentation processes differs 54, the sub-surfaceeformation measured experimentally during nano-indentationn 6H-SiC, found to be 2.5 times the maximum indentation depth5 provides further evidence that 6H-SiC is apt to undergo largeub-surface deformations during contact loading. To further con-rm these findings, the critical crack length, which is dependentn the fracture toughness and hardness has been calculated as

hown in Table 4.

Amongst the polytypes, 3C-SiC has the maximum frac-ure toughness and maximum hardness while 6H-SiC has the

X. Luo et al. / Journal of the European Ceramic Society 32 (2012) 3423–3434 3431

3.02.52.01.51.00.50.0

-20

0

20

40

60

80

100

120

140 g(r) before cutting

g(r

)

Bondlength (angstrom)

3.02.52.01.51.00.50.0

0

20

40

60

80

g(r) while cutting 3C-SiC

g(r

)

Bondlength (angstrom)

3.02.52.01.51.00.50.0

0

20

40

60

80

100 g(r) while cutting 4H-SiC

g(r

)

3.02.52.01.51.00.50.0

0

20

40

60

80

100

120

g(r) while cutting 6H-SiC

g(r

)

iamon

lSfscpM6t

tiw

(tpstripbr

TC

S

1234

Bondlength (angstrom)

Fig. 11. Radial distribution function of d

east hardness and shares the same fracture toughness as 4H-iC. The ductile regime machining model 58 assumes thatracture damage starts at a critical chip thickness so thatmaller critical crack lengths are desirable in order that arack free machined surface is obtained making 4H-SiC thereferred choice over other polytypes for SPDT. Thus, bothD and the ductile regime machining model suggest that

H-SiC give the poorest and 4H-SiC the best surface condi-ions.

It is interesting to note that, despite the differences between

he nano-indentation process and nanometric cutting processes,t’s a similar ductile response is found for silicon in both59–61,hich occurs by the virtue of high pressure phase transformation

ttT

able 4alculation of critical crack length.56,57

. no. Material Fracture toughness(MPa m1/2) (from Table 1)

3C-SiC 2.024H-SiC 1.96H-SiC 1.9Silicon 0.9

Bondlength (angstrom)

d tool against various polytypes of SiC.

HPPT). In contrast to silicon, silicon carbide has been reportedo give different responses some 62,63 suggesting, for exam-le that 3C-SiC undergoes amorphization and another groupuggesting that it transforms from its stable zinc-blende lat-ice structure to a rocksalt structure 15,64,65. Similarly, differentesponses have been reported, for 6H-SiC and 4H-SiC, includ-ng transformation to a polycrystalline phase,55 no high pressurehase transformation10,66 and dislocation nucleation followedy propagation within the zinc-blende phase.67 Since, nanomet-ic cutting involves high pressure and moderate temperature31 in

he cutting zone, an sp3–sp2 transition right under the wake of theool was suggested as a mechanism for the ductility of 3C-SiC.68

his is further consistent with the fact that SiC, in common with

Hardness (GPa) (obtainedfrom current simulation)

Critical crack length (�m)

c∗ = 120[

K2c

H2

]

26.4 0.702525.5 0.666719.2 1.1751

9.1 1.1737

3 n Ceramic Society 32 (2012) 3423–3434

dsS

3

ee

tspchisrtmt

3

btmhtfs

trmws

iidic1f(Dtbctstgtd

1086420

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

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0.35

0.40

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ea

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Tool advancement (nm)

3C-SiC

6H-SiC

Silicon

4H-SiC

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4

tt

1

2

3

432 X. Luo et al. / Journal of the Europea

iamond, requires a lower force for bond-bending than bondtretching, the opposite to other typical semi-conductors such asi, Ge, Si3N4 or GeAs.69,70

.3. Temperature during the machining process

Fig. 10 shows the average rise in temperature of the cuttingdge of the tool and on the workpiece as the tool moves throughach of the workpiece materials.

The 3C-SiC showed the highest temperatures both on the cut-ing edge and the workpiece followed by 4H-SiC, 6H-SiC andilicon, so that all polytypes of SiC result in higher cutting tem-eratures than single crystal silicon. A high temperature in theutting zone reduces the life of diamond tools37 as it reducesardness through graphitization of the diamond a process whichs accelerated further in the presence of properly directed sheartresses.71 This mechanism can be examined by analysis of theadial distribution function, as discussed in the next section. Highemperatures are, of course, known to compromise the life of dia-

ond tools, and an appropriate coolant may help to amelioratehis and provide improved surface roughness as well.72,73

.4. Tool wear

Wear of diamond tools is undesirable in SPDT not onlyecause of the replacement cost but also because of its effect onhe attainable surface finish. In-process degradation of the dia-

ond tool due to wear may alter the tool–workpiece contact andence the machining conditions which can cause a sudden transi-ion of material removal mechanism from ductile mode to brittleracture in the cutting region with consequent deterioration inurface finish.

A good understanding of the wear mechanism is an essen-ial step in identifying mitigation measures. Recently, it has beeneported that diamond tools undergo graphitization during nano-etric cutting of 3C-SiC.49 However, the root cause of toolear during nanometric cutting of other polytypes of SiC is

till unknown.It is widely accepted that measurement of the variation

n inter-atomic distance during machining simulations givesnsights into the wear mechanism. For this purpose, the radialistribution function for diamond tool is plotted before and dur-ng nanometric cutting in Fig. 11, which shows that, beforeutting, the radial distribution function −g(r) has a peak at.54 A which is the known bond length of diamond74 while aew bonds on the surface (dangling bonds) result in a small peakvisible as a slight asymmetry of the 1.54 A peak) at 1.42 A.uring machining, with the continued advancement of the tool,

his small peak continues to grow at the expense of the num-er of atoms with a bond length of 1.54 A. This observation isommon for all the polytypes of SiC but with varying magni-ude. The value of 1.42 A is the known bond length of anothertable allotrope of carbon, graphite75 which is much weaker

han diamond due to its chemical structure. Thus, g(r) confirmsraphitization of diamond tools during SPDT for all the poly-ypes of SiC. It is also now known that, while machining silicon,iamond undergoes graphitization in addition to the formation

Fig. 12. Percentage tool wear of diamond tool.

f silicon carbide, albeit via a combined process of chemicalnd abrasion wear.61. Based on this, a novel, generic method-logy to quantify tool wear from MD simulations using thehange in coordination number has been recently reported byhe authors.49 The evolution of the percentage tool wear for allhe cases using this approach is plotted in Fig. 12.

Fig. 12 suggest that the most rapid wear will occur whileutting 3C-SiC and 4H-SiC, interestingly, that 6H-SiC will showhe least wear among the polytypes of SiC, approaching that ofilicon. The increasing order of wear seems reasonably in lineith the fact that the cutting hardnesses of 3C-SiC and 4H-SiCere higher than 6H-SiC, although there is a significant drop to

each that of silicon.

. Conclusions

An MD simulation model has been used to develop a quanti-ative and qualitative understanding of the single point diamondurning of various polytypes of SiC with reference to silicon.

The following conclusions can be drawn accordingly:

. A relatively new parameter, “cutting hardness” indicates that3C-SiC (∼2.9 times that of silicon) offers the highest cuttingresistance followed by 4H-SiC (∼2.8 times silicon) and 6H-SiC (∼2.1 times silicon).

. The thrust forces observed while machining SiC were higherthan the cutting forces, whereas the opposite was the case forsilicon using the same cutting conditions.

. Deformed chips were generated in all cases which indicatethat ductile regime machining is possible on all polytypesof SiC as well as silicon. However, there was a significantvariation in the indicated quality of finished surfaces and sub-

surface crystal lattice deformed layer depths. The simulationsindicated that 4H-SiC would produce the best sub-surfaceintegrity followed by 3C-SiC, silicon and 6H-SiC. Thus,

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despite showing the lowest cutting resistance, 6H-SiC indi-cates the worst sub-surface integrity of the polytypes studied.

. Cutting temperatures on the tool and workpiece also indi-cated that 3C-SiC offered the most cutting resistancefollowed by 4H-SiC, 6H-SiC and silicon.

. The RDF and development of carbon co-ordination numberboth indicated that diamond cutting tools would graphitizedue to abrasion against all the polytypes studied. While 3C-SiC and 4H-SiC indicated a high volume of wear, 6H-SiCsuggests intermediate tool wear but still somewhat higherthan silicon.

. Considering all the above findings, it is reasonable to con-clude that two of the polytypes may be suitable for SPDT,4H-SiC offering the same cutting resistance as 3C-SiC butproviding a better surface with less tool wear. However, 6H-SiC offered about half the cutting resistance of 4H-SiC butgenerated a poorer surface. Thus, the choice between 6H-SiC and 4H-SiC would be dictated by the trade-off betweenmachined surface quality and cost considerations.

t must be noted here that the conclusions on the nanometricachinability of 3C-SiC are valid only for single crystal 3C-iC and not for polycrystalline SiC. In other work, it has beenhown that both chemically vapour deposited (CVD) 3C-SiCnd reaction bonded (RB-SiC) are easier to machine than singlerystal SiC.73 This is because of the difference in the mechanismf chip formation between single crystal and polycrystalline SiC.

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