article md simulation of eﬁect of crystal orientation and

CHINESE JOURNAL OF CHEMICAL PHYSICS VOLUME 20, NUMBER 6 DECEMBER 27, 2007

ARTICLE

MD Simulation of Effect of Crystal Orientation and Cutting Direction onNanometric Cutting Using AFM Pin Tool†

Jun-jie Zhang∗, Tao Sun, Yong-da Yan, Ying-chun Liang, Shen Dong

School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001, China

(Dated: Received on June 22, 2007; Accepted on October 10, 2007)

Three-dimensional molecular dynamics simulations of nanometric cutting monocrystalline copper usingatomic force microscopy pin tool are conducted to investigate the effect of crystal orientation and cor-responding cutting direction on the deformation characteristics. EAM potential and Morse potential areutilized respectively to compute the interactions between workpiece atoms, interactions between workpieceatoms and tool atoms. The results reveal that the nanometric cutting processes are significantly affected bycrystal orientation and cutting direction. Along the [110] cutting direction, better quality of chip patternand smaller workpiece material deformation region can be obtained than along the [100] cutting direction.Cutting the workpiece material (110) crystal orientation, samaller chip volume and smaller subsurface de-formed region can be obtained than cutting the workpiece material (100) crystal orientation. The variationsof workpiece atoms potential energy in different cutting processes are investigated.

Key words: Nanometric cutting, Atomic force microscopy, Molecular dynamics, Crystal orientation, Cut-ting direction

I. INTRODUCTION

Recently, the atomic force microscopy (AFM)-basednanometric cutting technique has been proposed to di-rectly machine material surfaces and fabricate micro-and nano-components in micro-electro-mechanical sys-tems (MEMS) and nano-electro-mechanical systems(NEMS) [1-6]. The main challenge of this novel tech-nique is to develop a fundamental understanding of thenanometric cutting mechanism and mechanics, such asthe chip formation, elastic deformation and plastic de-formation, and friction. Hence, theoretical analysis andinvestigation of the cutting mechanism at the atomic-scale greatly facilitate the development of high precisionmachining micro- and nano-components. However, asthe nanometric cutting involves only a few atomic lay-ers at the surface, it is inherently atomistic rather thancontinuous, so it is extremely difficult to observe thecutting process and to measure the process parametersthrough experiments, and the conventional continuummechanics theory can not be applied to the analysis ofthe nanometric cutting process due to the size limita-tion. An alternative approach is molecular dynamics(MD) simulation, which has been confirmed to be bestsuit for the analysis of the nanometric cutting process[7-10].

Single crystal materials are anisotropic in their phys-ical and mechanical properties, so workpiece materials

†Part of the special issue from “The 6th China International Con-ference on Nanoscience and Technology, Chengdu (2007)”.∗Author to whom correspondence should be addressed. E-mail: [email protected], Tel: +86-451-86412934, Fax: +86-451-86415244

elastic modulus are influenced during nanometric cut-ting process with different crystal orientations and cor-responding cutting directions, consequently the elasticrecovery degrees of machined surface vary, which sig-nificantly affects the finish, accuracy, and surface in-tegrity. In order to achieve high precision machining innanometric cutting, molecular dynamics studies of theeffect of crystal orientation and cutting direction on de-formation characteristics, such as chip formation andsubsurface deformed behaviors are necessary.

Some typical works that investigated the effect ofcrystal orientation and cutting direction on the cuttingprocess using MD simulation include that Komanduriet al. conducted MD simulation of nanometric cuttingon single crystal aluminum in specific combinations ofcrystal orientation and cutting direction using diamondtool [11,12]. They investigated the nature of deforma-tion and the extent of anisotropy of workpiece material.Kim et al. performed three-dimensional MD simulationof the nano-lithography process of monocrystalline cop-per using an AFM tip to evaluate the effect of crystal-lographic factors on the nano-deformation characteris-tics [13], and reported the crystal orientation and theploughing direction had a significant influence on vary-ing the force and surface quality of the machined ma-terial. Pei et al. performed a series of large scale MDsimulation with the model size of more than four-millionatoms to study the nanometric machining of copper,and the effect of crystal orientation and cutting direc-tion were investigated [14]. They reported that the crys-tal orientation and cutting direction have a strong ef-fect on material deformation, dislocation movement andcutting force.

However, previous studies mainly focused on the cut-ting force and nature of deformation, and haven’t inves-

DOI:10.1088/1674-0068/20/06/619-624 619 c©2007 Chinese Physical Society

620 Chin. J. Chem. Phys., Vol. 20, No. 6 Jun-jie Zhang et al.

tigate the effect of crystal orientation and correspondingcutting direction on the chip formation and workpiecematerial deformation region, which play a key role forfabricating fine surface quality nano-components.

Therefore, in this work three-dimensional MD simu-lations of nanometric cutting of monocrystalline copperusing an AFM pin tool are performed to investigatethe effect of specific combinations of crystal orientationand cutting direction ((010)[100], (010)[101], (101)[010],(101)[110]) on deformation characteristics, such as chipformation, subsurface deformed region, and variationsof workpiece atoms potential energy in each cutting pro-cess.

II. MD SIMULATION METHODOLOGY

As shown in Fig.1, a workpiece and a tool are as-sumed to consist respectively of monocrystalline cop-per and rigid diamond. The fixed integration step sizeis chosen as 0.5 fs.

Boundary atoms Thermostat atoms Tool atoms

Newtonian atoms

y

xz

FIG. 1 MD simulation model of nanometric cutting usingAFM pin tool.

The size of workpiece utilized in the current MD sim-ulations is 32a×12a×30a, where a is the lattice con-stant of copper (0.361 nm), and the number of work-piece atoms is corresponding to the workpiece crys-tal orientation. The workpiece includes three differ-ent kinds’ atoms, namely, boundary atoms, thermostatatoms, and Newtonian atoms, respectively. The mo-tion of thermostat atoms and Newtonian atoms obeythe Newton’s second law, and are determined by di-rect integration of the classical Hamiltonian equationsof motion using Velocity-Verlet method. The two layersof boundary atoms in the left side of the workpiece andthe bottom of the workpiece are kept fixed in space andserver to reduce the edge effects. The initial tempera-ture of the workpiece is 293 K, and in order to stabilizethe average temperature of the thermostat layers at 293K, heat dissipation is carried out through the thermo-stat atoms, whose velocities are adjusted by the pres-ence of velocity reset functions at every 5 time steps ofthe computation [15]. The periodic boundary condition

is used in z-direction to reduce the effects of simulationscale.

The AFM pin tool has the configuration of co-shapeof sphere and cylinder, and the radius of the sphereis 1.07 nm. The pin tool employed is configured from1762 atoms and is treated as a rigid body in the currentsimulations.

For the Cu–Cu interaction between the workpieceatoms, the established EAM potential is used, whichhas been used successfully in nanometric cutting study[16-18]. For EAM potential, the total atomic potentialenergy of a system Etot is expressed as:

Etot =12

∑

ij

φij (rij) +∑

i

F (ρi)i (1)

where φij is the pair-interaction energy between atomsi and j, and Fi is the embedded energy of atom i. ρi isthe host electron density at site i induced by all otheratoms in the system, which is given by:

ρi =∑

j 6=i

ρj (rij) (2)

for the Cu–C interaction between workpiece atoms andtool atoms, Morse potential is used, which is relativelysimple and computationally inexpensive compared tothe EAM potential [19-21]. The Morse potential is writ-ten as:

Etot =∑

ij

D0

[e−2α(r−r0) − 2e−α(r−r0)

](3)

where Etot is a pair potential energy function; D0 isthe cohesion energy; α is the elastic modulus; r and r0

are the instantaneous and equilibrium distance betweenatoms i and j, respectively. The cutoff radius of theMorse potential is chosen as 902.5 pm, which ensuresthat the calculations will not consume large amounts ofcomputational time.

In the current MD simulations, the cutting speed isselected as 200 m/s to keep the computational time to areasonable value, though this high cutting speed is unre-alistic. Previous studies have confirmed that there waslittle difference between the effects of a cutting speedof 20, 50, 100, 200, and 250 m/s on the surface quality[22,23].

Figure 2 shows the various crystal orientations andcutting directions for the monocrystalline copper in thecurrent simulations (Table I).

III. RESULTS AND DISCUSSION

Nanometric cutting monocrystalline copper using anAFM pin tool with different combinations of crystal ori-entation and cutting direction, (010)[100], (010)[101],(101)[010], (101)[110], are conducted in the currentsimulations. All the simulations are performed usingan AFM pin tool with radius of 1.07 nm, velocity of200 m/s, uncut chip thickness of 0.54 nm.

DOI:10.1088/1674-0068/20/06/619-624 c©2007 Chinese Physical Society

Chin. J. Chem. Phys., Vol. 20, No. 6 MD of Crystal Orientation and Cutting Direction 621

FIG. 2 Crystal orientation and cutting direction utilized inthe current simulations.

TABLE I summarizes the numbers of workpiece atoms ac-cording with the four combinations

Combination Number of workpiece atoms

(010)[100] 48750

(010)[110] 48394

(110)[010] 46971

(110)[110] 46410

A. On the nature of deformation behavior of nanometriccutting process

Figure 3 shows the representative nanometric cuttingprocess with a tool travel of 2, 4, and 6 nm for a com-bination of workpiece crystal orientation (100) and cut-ting direction [100]. It maybe noted that the discussionof the results presented here is based not only on theMD simulations plots but also on the detailed study ofthe animations of the cutting process. Both of the plotsand animations are created using VMD-VMD, an opensource and free molecular visualization program [24].

There are two deformation states between the work-piece and tool, as ploughing state, cutting state.The workpiece material deformation region is localizedaround the tool. Some workpiece material atoms accu-mulated ahead of the tool edge, consequently formedchip. Simultaneity, some workpiece material atomspiled up on the left and right sides of the V-groove,consequently formed remarkable side-flow.

The deformation mechanism could be explained: Innanometric cutting process, with the ploughing of tooledge, workpiece material atoms surround the pin toolundergo complicated plastic deformation and elastic de-

2 nm 4 nm 6 nm

FIG. 3 Deformation behaviors of cutting process with dif-ferent tool travel.

formation, lattice of workpiece atom is deformed asbuckled. When the strain energy stored in the deformedlattice exceeds a specific level, the atoms are re-arrangedsuccessively onto the lower lattice so as to relax the lat-tice strain, and a lot of dislocations are generated in theworkpiece near the tool-work interface. Some of themmove into the shear zone, and workpiece atoms accumu-late ahead of the tool and formed chip, some workpieceatoms pile up on both side of the groove simultaneity.And some dislocations move downward and penetrateinto the workpiece beneath the tool edge. After thepassing of tool edge, machined surface experiences elas-tic recovery, almost all of penetrated dislocations be-gin to move back and finally disappear from the work-piece surface. However, considerable distorted atomsinevitably existe in the subsurface deformation region[25].

B. Effect of crystal combination on chip formation

Figure 4 shows the effect of crystal orientation andcutting direction on chip formation during deformationprocess. Each figure shows cross-section views of the xyplane and with the same tool travel of 7 nm.

Figure 4(a) with a crystallographic combination of(010)[100] shows that there are clear workpiece materialaccumulation ahead of the AFM pin tool, and the chipvolume is similar to the Fig.4(b) with a crystallographiccombination of (010)[101]. However, there are smalldifference in chip pattern between the two crystallo-graphic combinations. Under the crystallographic com-bination of (010)[100] the atoms at the chip surface areloosely connected to each other, while under the crys-tallographic combination of (010)[101] the atoms at thechip surface are more closely connected to each other.Figure 4 (c) and (d) shows that the atoms at the chipsurface are more closely connected to each other un-der the crystallographic combination of (101)[110] thanthe crystallographic combination of (101)[001]. In boththese crystal combinations as shown in Fig.4 (a) and(c), the cutting direction corresponds to the [100] fam-ily, and the cutting direction corresponds to the [110]family for Fig.4 (b) and (d). It indicates that alongthe [110] cutting direction family better quality of chippattern can be obtained than along the [100] cuttingdirection family.

The chip volume is bigger under the crystallographiccombination of (010)[100] than the crystallographiccombination of (101)[001] as shown in Fig.4 (a) and(b), which with the same cutting direction but differentworkpiece material crystal orientation. It is the samecase for Fig.4 (b) and (d), the chip volume is bigger un-der the crystallographic combination of (010)[101] thanthe crystallographic combination of (101)[110]. In Fig.4(a) and (b), the crystal orientation corresponds to the(100) family, and the crystal orientation corresponds tothe (110) family for Fig.4 (c) and (d). It indicates that



(a) (110)[100] (b) (010)[101]

(c) (101)[001] (d) (101)[110]

FIG. 4 Variations of chip formation for various combinations of crystal orientation and cutting direction.

cutting the workpiece material crystal orientation fam-ily (110) samaller chip volume can be obtained morethan cutting the workpiece material crystal orientationfamily (100).

Therefore, it concludes that the crystal orientationand cutting direction have a significant effect on thechip formation, such as chip pattern and chip volume.

C. Effect of crystal combination on workpiece materialdeformation region

Figure 5 shows the effect of crystal orientation andcutting direction on workpiece material deformation re-gion during nanometric cutting process. Each figureshows the plane view of the xz plane as shown inFig.5(e) with the same tool travel of 7 nm. In the cur-rent study the area of workpiece material deformationregion is pointed out by the black line manually in orderto denote it efficiently, as shown in Fig.5 (a)-(d).

As shown in Fig.5(a) with a crystal combination of(010)[100], it is clear that tha range of workpiece mate-rial deformation is limited to the workpiece atoms sur-rounding the tool, and a remarkable side-flow on thetwo sides of the tool. It is the same case for Fig.5(b)with a crystal combination of (010)[101]. But there areslight difference for the two crystal combination, whichis with the same workpiece material crystal orientationbut different cutting direction. The workpiece mate-rial deformation region is smaller for Fig.5 (b) than(a). Furthermore, Figure 5 (c) and (d) show that theworkpiece material deformation region is smaller for thecrystal combination of (101)[110] than the crystal com-

bination of (101)[001]. It indicates that along the [110]cutting direction family results smaller workpiece ma-terial deformation region than along the [100] cuttingdirection family.

Figure 5 (a) and (c) show the workpiece material de-formation regions for crystal combination with the samecutting direction but different workpiece material crys-tal orientation. It is clear that both the workpiece ma-terial deformation region and side-flow volume are big-ger with the crystal combination of (010)[100] than thecrystal combination of (101)[001]. It is the same casefor Fig.5 (b) and (d), both the workpiece material de-formation region and side-flow volume are bigger withthe crystal combination of (010)[101] than the crystalcombination of (101)[110]. It indicates that cutting theworkpiece material crystal orientation family (110) re-sults smaller subsurface deformed region than cuttingthe crystal orientation family (100).

Figure 6 shows the variations of workpiece atoms po-tential energy obtained by MD simulation of nanomet-ric cutting process with different combinations of crys-tal orientation and cutting direction. The workpieceatoms potential energy increase with the tool advance-ment. It can be seen that potential energy-time stepdiagrams of nanometric cutting process with differentcombinations of crystal orientation and cutting direc-tion seem parallel to each other. However, the poten-tial energy is larger for the workpiece material crystalorientation family (1101) than the workpiece materialcrystal orientation family (100). It indicates that thenumber of workpiece deformation atoms is smaller withthe crystal orientation (101) than the crystal orienta-tion (010), which basically agrees with the result that


Chin. J. Chem. Phys., Vol. 20, No. 6 MD of Crystal Orientation and Cutting Direction 623

(a) (010)[100] (b) (010)[101]

(c) (101)[001] (d) (101)[110]

(e) Cross-section view of xz plane

View

FIG. 5 Variations of area of subsurface deformation regionfor various combinations of crystal orientation and cuttingdirection.

cutting the workpiece material crystal orientation (101)results smaller workpiece material deformation regionthan the workpiece material crystal orientation (010).

Komanduri [11-12] and Kim [13] both reported thatfor (100)[100] combination, dislocation generated atabout 45◦ to the cutting direction. In (100)[110] com-bination, dislocation generated parallel to the cuttingdirection. In (110)[100], dislocation generated normalto the cutting direction. In (110)[110], dislocation gen-erated parallel as well as perpendicular to the cuttingdirection. In the current study, this effect of crystalorientation and cutting direction on chip formation andworkpiece material deformation region can be explainedby the conclusions above, as in term of the different di-rections of the workpiece dislocation slip direction tothe cutting direction. For example, there is less work-piece deformation for the (110) crystal orientation fam-ily than the (100) crystal orientation family, as thedirection of slip direction to the cutting direction is

FIG. 6 Variations of potential energy for various combina-tions of crystal orientation and cutting direction.

smaller for the (110) crystal orientation family than the(100) crystal orientation family.

IV. CONCLUSION

Three-dimensional MD simulations of nanometriccutting using AFM pin tool are performed to investigatethe effect of crystal orientation and cutting directionon deformation characteristics, such as chip formation,workpiece material deformation region, and variationsof potential energy. Based on the study, conclusions aregiven as follows:

MD simulations of nanometric cutting monocrys-talline copper using an AFM pin tool reveal that work-piece material crystal orientation and cutting directionhave a significant effect on the chip formation and work-piece material deformation region during the deforma-tion process. Along the [110] cutting direction family,better quality of chip pattern and smaller workpiece ma-terial deformation region can be obtained than alongthe [100] cutting direction family. Cutting the work-piece material crystal orientation family (110), samallerchip volume and smaller subsurface deformed region canbe obtained than cutting the workpiece material crystalorientation family (100). The potential energy requiredfor removal of workpiece atoms was larger for the work-piece material crystal orientation family (110) than theworkpiece material crystal orientation family (100).

V. ACKNOWLEDGMENTS

This work was supported by the National Natu-ral Science Foundation of China (No.50575058 andNo.50605012).



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