A_Study_of_the_Subsurface_Damaged_Layers_in_Nanoscratching_Process.pdf

368 Int. J. Abrasive Technology, Vol. 2, No. 4, 2009

Copyright 2009 Inderscience Enterprises Ltd.

A study of the subsurface damaged layers in nanoscratching

Jiaxuan Chen*, Yingchun Liang, Mingjun Chen and Qingshun Bai Center for Precision Engineering, Harbin Institute of Technology, 413#, No. 92, West Da-Zhi Street, Harbin, Heilongjiang, China E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] *Corresponding author

Yulan Tang Municipal and Environment Engineering Institute, Shenyang Jianzhu University, Shenyang 110168, China E-mail: [email protected]

Abstract: Molecular dynamics (MD) simulations are carried out to study a three-pyramid tip nanoscratching single crystal copper. The surface integrity and subsurface damaged layers are investigated by the different scratching depths and crystal orientation. The effects show that nanoscratching process results in the extension of the high energy atoms in the subsurface from near the tool to the whole subsurface. The area of high energy atoms in subsurface is basically in consistence with that of the higher residual stress. The ordering degree of subsurface atoms decreases as the increase of scratching depths. The (100) plane body compared to the (111) plane body after scratching process, the numbers of defects in subsurface of the former are more than that of the latter, the surface integrity and the ordering degree of subsurface of the former is better than that of the latter, but the area of the subsurface damaged layers of the former is larger. It is noted that there exists the stack fault in subsurface for the (111) plane body.

Keywords: molecular dynamics; MD; embedded atom method; EAM; subsurface-damaged layers; scratching; energy; residual stress; defect; dislocation; ordering degree; crystal orientation; slip vector.

Reference to this paper should be made as follows: Chen, J., Liang, Y., Chen, M., Bai, Q. and Tang, Y. (2009) A study of the subsurface damaged layers in nanoscratching, Int. J. Abrasive Technology, Vol. 2, No. 4, pp.368381.

Biographical notes: Jiaxuan Chen works in the Center for Precision Engineering, Harbin Institute of Technology. His research interests include molecular dynamics, nanomachining, the subsurface deforming mechanism and mechanical properties of micro-nano structure, and the properties of nanostructure.

A study of the subsurface damaged layers in nanoscratching 369

Yingchun Liang joined Harbin Institute of Technology in 1988 and received his PhD from Harbin Institute of Technology, China in 1994, where he is currently a Professor, PhD Supervisor and Dean of the School of Mechatronics Engineering. He worked in Chiba University in Japan as a Visiting Professor from 1996 to 1997. He is a member of Asian Society for Precision Engineering and Nanotechnology (ASPEN) and European Society for Precision Engineering and Nanotechnology (EUSPEN). His current research interests include ultra-precision machining and diamond tool fabrication, nanomachining and nano-technology, non-standard precision equipment design and manufacture, modern design theory and methods.

Mingjun Chen received his PhD from Harbin Institute of Technology, Harbin in 2002. Currently, he is a Professor at the Center for Precision Engineering, Harbin Institute of Technology, Harbin, China. His research interests include ultra-precision cutting and grinding mechanism, ultra-precision optical components processing technology (non-ball surface, the complex surface parts) and non-linear optical material ultra-precision machining technology. He is a Reviewer for Journal of Mechanical Engineering.

Qingshun Bai graduated from Harbin Institute of Technology, Harbin in 2004. He received his ME and PhD from Harbin Institute of Technology, Harbin in 1998 and 2000 respectively. Currently, he is an Associate Professor at the Center for Precision Engineering, Harbin Institute of Technology, Harbin, China. His research interests include hard and brittle material and the mechanism of ultra-precision machining technology, the complexity of the optical surface of the ultra-precision processing technology, materials processing difficult to precise vibration of the diamond processing technology and micro-nano-cutting surface forming mechanism.

Yulan Tang received his PhD from Harbin Institute of Technology, Harbin in 2004. Currently, he is an Associate Professor at the Shenyang Jianzhu University. His research interests include water treatment technology, molecular dynamics and nano-cutting theory and technology.

1 Introduction

Nanomachining with machine tools and position-control techniques aim to produce high quality surfaces in terms of form accuracy, surface finish and surface integrity for optical, mechanical and electronic components, and are one of the developing tendencies for the modern manufacture. Nowadays, the atomic force microscopy (AFM) based nanoscratching technique has been an important method to investigate nanowear, nanofriction and nanomachining since Mate et al. (1987) discovered the atomic scale stick-slip phenomenon and used it for the first. Nanoscratching experiments using the AFM diamond tip are carried out to evaluate and validate the simulation results. Many researchers (Fujisawa et al., 1993, 1995; Morita et al., 1996) have attempted to analyse the atomic-scale friction and nanomachining mechanism using AFM and some worthwhile insight has been reported. However, AFM is expensive and is not easy for many people to utilise, and also has many limits in functions i.e. the tip of AFM is hard to realise curve motion accurately and keep constant depths stably, as a result of the flexibility of cantilever in nanoscratching process. The traditional finite-element method

370 J. Chen et al.

is not appropriate to analyse the mechanism of nanomachining because the nanomachining process involves only a few atomic layers at the surface. The molecular dynamics simulation (MDS) is verified by many researchers to be an efficient method to research the removal mechanism and phenomenon in nanomachining process. As pioneers, Hoover et al. (1990), Belak and Stowers (1990) made the two-dimensional nanoscratching and nanoindentation processes of the MDS for single crystal metal. Subsequently, Shimada et al. (1992, 1993, 1994) and Komanduri et al. (1999, 2000a, 2000b) have carried out MDS of nanometric cutting of single crystal copper and aluminium using the simple pair potential to model interatomic forces. They considered the effect of tool-edge radius, crystal orientation and depths of cut, cutting direction and tool geometry on the chip formation process, the removal mechanism and the nature of deformation of the materials. The MDS using the embedded atom method (EAM) to investigate the nanomachining process were reported in prevenient researches. For example, Fang and Weng (2000) conducted nanoscale cutting simulations to the relation of the tool angle and the frictional coefficient, and stick-slip behaviour was observed. Li et al. (2001) performed MDS of sliding friction showing that elastic deformation of the surface layers can also be a main cause of the atomic-scale stick-slip phenomenon. Ye et al. (2003) studied the effect of different scratching speed on the defects in workpiece during nanomachining process. Mulliah et al. (2004a, 2004b) used three-dimensional MD model to study the nanomachining process and the stick-slip behaviour of friction. Liang et al. (2007, 2008a, 2008b) considered the effects of tool rake angle on cutting forces and residual stress, in addition, they analysed the mechanical properties of scratched nanostructure. Cheong and Zhang (2000) indicated the transformation from diamond cubic structure to silicon in a small zone near the indenter tip using the MD simulation of nanoindentation of silicon. Since MDS can simulate the process of the AFM-based nanoscratching and single point diamond turning, and reveal the mechanism of nanomachining, Cheng et al. (2003) and Fang et al. (2007) using MDS also investigated the issue of critical chip thickness in the process of nanomachining. Cai et al. (2007) further investigated the brittle-ductile transition in cutting of brittle materials and demonstrated that ductile cutting process could be formed when the radial of the tool edge is small and smaller than that of the thickness of the undeformed chip. For macro specimen, the subsurface deformation of the specimen from the machining process had little effect on its mechanical properties. It is noted that the surface integrity and subsurface damaged layer resulting from nanomachining process have important effects on the properties of nanostructure. However, from the papers published, we found that previous studies focused on showing the surface finish, chip forming, the cutting forces and system potential energy during nanomachining. Little attention has been paid to investigate relationship of the subsurface potential energy and stress variation to this atom deformation behaviour.

Therefore, in the current work, 3D MDS using a three-pyramid tip to scratch the surface of single crystal copper are conducted to investigate the effects of subsurface potential energy and atomic stress changed on the subsurface damaged layer and surface integrity with different scratching depths, scratching direction and crystal orientations.


2 Simulation model and method

2.1 Nanomachining model

Our MDS system is composed of the monocrystalline copper and a three-pyramid tip of diamond, the tool scratches the (010) plane of the workpiece along [100] direction and the (111) plane of workpiece along [1-21] direction respectively as shown in Figure 1 below.

Figure 1 Nanomachining simulation model (a) (100) plane workpiece (b) (111) plane workpiece (see online version for colours)

(a) (b)

Note: The colour of atoms is shown for slip vector index

To simulate the nanomachining of the (010) plane and (111) plane of copper, we utilise the copper nanostructure of dimensions 12-12-20 a0, where a0 is the lattice constant of copper (3.62 ). The Figures 1(a) and 1(b) show the deformation behaviour of the workpiece atoms during the AFM-based nanolithography process. All the simulations were conducted using a three-pyramid diamond tip, tool angle of 60 degrees and ploughing depth of 1.08 nm. The figures were obtained using a special MD post program developed at the Center for Precision Engineering, Harbin Institute of Technology.

2.2 Potential energy function and analysis method

The force acting on an individual atom is obtained by summing the forces contributed by the surrounding atoms. The potential used in the simulations is the well established EAM by Johnson (1988, 1999) to model the interactions of atoms, which has been very successful in modelling the elastic properties, defect formation energies and fracture mechanisms of various close-packed bulk metals. The total potential energy E for an atomic system is the sum of the embedding energy F and a short-range repulsive pair potential energy:

[ ( ) ( )]>

= + N Ni iji j i

E F u r (1)

z [1-21]

x [10-1]

y [111]

Dislocation

[0-11]

z [001]

x [100]

y [010]

Dislocation

[-101]

372 J. Chen et al.

( ) =i ijj

r (2)

where E is the sum of energy, i corresponds to the embedding energy, (rij) is the electron density at atom i due to all other atoms, F(i) is the embedding function and it is the energy to embed an atom of type i into background electron density i at site i; i is the electron density at atom i due to all other atoms, f(rij) is the contribution to the electron density at atom i due to atom j at distance rij from atom i; F(i)can be given by

/ /( ) [1 ln( )]( ) ( ) = c ee e eF E (3)

where

12 =e ef (4) 6 =e e (5)

( ) exp[ ( 1)]= ijij ee

rf r f

r (6)

(rij) in equation (2) represents the two-body potential between atoms i and j, which can be expressed as:

( ) exp[ ( 1)] = ijij ee

rr

r (7)

The parameters of the EAM potential used for this study are shown in Table 1.

Table 1 Parameters in EAM potentials for copper

Ec (eV) 3.54 5.09 e (eV) 0.59 5.85 fe 0.30 8.0001

While the Morse potential (Komanduri et al., 1999, 2000a, 2000b) is utilised to model the interactions between atoms of workpiece and tool. The Morse potential is written as:

0 0( ) [exp( 2 ( ) 2exp( ( )))] = ij ij ijr D A r r A r r (8) where (rij) is a pair potential energy function, D, A and r0 correspond to the cohesion energy, the elastic modulus and the atomic distance at equilibrium respectively.

The half step frog leap algorithm was used for time integration of the atomic coordinates. The temperature of the entire system was maintained at 293 K with a Nose-Hoover thermostat (Nose, 1984; Hoover, 1985).

It is necessary to calculate stress of every atom in order to analyse the relations between the stress states of atoms and the onset of defects. The stress in the atomistic simulation mn on plane m and along direction n can be given by:


1 1[ ]2

= + m nm n ij iji i imn ijs i i iji j

r rm v vF

N v V r (9)

where mi is the mass of atom i, Vi is the volume assigned to atom i, the term Ns stands for the number of particles in region s, where s is defined as the region of atomic interaction, rij is the distance between atoms i and j, and mijr and

nijr are two components of the vector

from atom i to j. We used the visualisation technique of slip vector that has successfully been proven

to be effective for the studies of dislocation nucleation in FCC crystals by Zimmerman et al. (2001) to quantify and visualise the plastic deformation in process of simulation.

1 ( )

= nas

s x Xn

(10)

where n is the number of the nearest neighbours of atom a, the term ns stands for the number of slipped neighbours, and x and X are the position vector difference of atoms and in the current and reference positions. Details of the workspace are summarised in Table 2.

Table 2 Workspace and simulation parameters

Potential for substrate EAM Interaction potential Morse Substrate FCC copper Tool Diamond tip of triangular-based pyramid Workspace dimensions 12-12-20 a0 (010) surface 20-12-12 a0 (010) surface Rake angle 60 Cutting directions [100] on (010) surface [1-21] on (111) surface Cutting depth 1 a0 to 3 a0 Cutting speed 180 m s1 Substrate temperature 293 K

3 Results and discussions

3.1 The nanometric machining process

The workpiece is relaxed to minimum energy before scratching process. After that, the tool begins to scratch the surface of the workpiece, scratching direction is [100] direction for the (010) plane body and [1-21] direction for the (111) plane body. At the initial stage of scratching process, some atoms of workpiece leave workpiece to be absorbed on the surface of the tool under the cutting and attracting action of the tool as shown in Figure 2(a). With the passage of the tool, more and more atoms of the

374 J. Chen et al.

workpiece begin to climb along the frontier surface of the tool under the shearing and attracting force of the tool, and pile up on the frontier surface of the tool, which is the initial stage of chip forming. At the same time, atoms of workpiece ahead and beneath the cutting tool are applied forceful shear and normal stress from the tool during scratching. For diminishing the high shear and normal stress, those atoms of workpiece begin to deviate from their initial position, and dislocations occur ahead the tool as shown in Figures 1 and 2. It can be seen from Figures 1 and 2 that the propagation of dislocations in (010) plane body ahead the tool is along [101], and the propagation direction of dislocations in (111) plane body ahead the tool is along [0-11] and [1-10]. The effects of defects such as dislocation are consistent with the results from Pei et al. (2006, 2007). From Figure 2, it is clear that the range of plastic deformation is limited to the work material molecules around the tool. There is a clear accumulation and pileup of amorphous structural molecules ahead of the tool and a remarkable side flow on the left and right sides of the tool as the tool moves forward.

Figure 2 Nanoscratching the workpiece on (111) orientation (a) 4.5 ps (b) 7 ps (c) 9 ps (de) 25 ps (see online version for colours)

(a) (b)

(c) (d)

(e)

Note: The colour of atoms are shown for slip vector index, and only atoms in the top two layers and the slip vector index is up to 0.30 as shown in Figures 2(a), 2(b), 2(c) and 2(e).

Withdrawal of the tool from the workpiece will generate edge collapse, burr and atom packing. Especially for (111) orientation workpiece, the withdrawing tool results in the


stack fault as shown in Figures 2(d) and 2(e). Since exit defects and side flow of molecules in AFM-based nanolithography can deteriorate the surface quality, it should be removed by an additional operation such as surface cleaning process of chemical mechanical polishing, if the obtained pattern is assumed to be used as an MEMS device having smooth surface quality. Moreover, the crystal orientation and ploughing direction were found to have a significant effect on the nanopatterning deformation characteristic and machined surface quality. As such, the surface roughness, as a means of assessing the machined surface quality, plays a key role in determining whether nanocomponents fabricated by AFM-based nanolithography have a fine surface quality suitable for MEMS applications.

3.2 Surface integrity and subsurface damaged layer

In order to analyse nanoscratched surface integrity, the state and area of subsurface damaged layer, we do cross-section views of scratching (100) plane body process: one way is cross section of xy plane which is perpendicular to z axis and in middle of the workpiece along scratching direction as shown in Figures 3(a) and 3(c); another way is perpendicular to y axis and the second layer atoms beneath the tool as shown in Figures 3(b) and 3(d). For the (111) body case, we also do similar cross-section views as shown in Figures 4(a) to 4(d).

Figure 3 Cross-section view of scratching (010) plane process for scratching 44 ps with scratching depths at 3 a0 (a) xz plane (b) xy plane; for scratching 73 ps (c) xz plane (d) xy plane (see online version for colours)

(a) (b)

(c) (d)

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Figure 4 Cross-section view of scratching (111) plane process for scratching 44 ps with scratching depths at 3 a0 (a) xz plane (b) xy plane ; for scratching 73 ps (c) xz plane (d) xy plane (see online version for colours)

(a) (b)

(c) (d)

It can be seen from Figures 3(a) to 3(b) that there are many vacancies in subsurface ahead and beneath the tool when the tool scratches the (010) plane of the workpiece. After scratching process, there exist several atomic steps in machined surface, which is atom-scale roughness from nanomachining process and there still exist many vacancies in subsurface after scratching process as shown in Figures 3(c) to 3(d). For scratching the (111) plane of the workpiece case, there are also some vacancies in the subsurface as shown in Figures 4(a) to 4(d), however, vacancies only exit near the tool. It is noted that there are not only some vacancies but also stack fault in the subsurface after scratching process, stack fault is denoted by black rectangle. The damaged layers of subsurface both for the (100) body and the (111) body are denoted by black ellipse line in Figures 3(c) and 4(c) after scratching process. It can be seen from Figures 3(c) and 4(c) that the area of the damaged layers of subsurface for the latter is slightly larger than the former. However, the atomic roughness of scratched surface for the former is worse for the latter. Also, it can be seen from Figures 3(d) and 4(d) that the numbers of defects such as vacancies in the subsurface of the (111) plane body compared to that of the (010) plane body are smaller.

Stack fault


3.3 Ordering degree of subsurface

The radial distribution function (RDF) or the pair correlation function is important because it provides information about the solid structure. It is a measure to determine the correlation between particles within a system. Specifically, it is a measure of, on average, the probability of finding a particle at a distance of r away from a given reference atom, so the ordering degrees of the subsurface atoms are shown by RDF. The number of defect atoms and ordering degree of subsurface also can be shown by the RDF. Figure 5 shows the RDF of subsurface atoms under scratching depths at 3 a0 for the (100) plane body and the (111) plane body. It is obvious to be seen from Figure 5 that the ordering degree of subsurface atoms for the (111) plane body compared to that for the (100) plane body is well. The RDF of the subsurface atoms after scratching process is shown in Figure 6 under different scratching depths. It can be seen from Figure 6 that the ordering degree decreases as scratching depths increase, and the trend both for the (100) plane body and (111) plane body is the same.

Figure 5 RDF of the subsurface in (100) body and (111) body after scratching process (see online version for colours)

Figure 6 RDF of the subsurface at different scratching depths (a) (100) plane body (b) (111) body plane (see online version for colours)

(a) (b)

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3.4 Energy and residual stress of subsurface layers The atoms averaged energy of subsurface layers for the (100) plane body and (111) plane body is also different during scratching as shown in Figure 7.

Figure 7 Atom averaged energy of the subsurface in (010) body and (111) body during scratching (see online version for colours)

It is clear that the atoms averaged energy of subsurface both for the (100) plane body and (111) plane body increase linearly at the initial stage of the scratching process, and begin to decrease gradually when the tip of the tool goes out from the workpiece. It is denoted that the atoms averaged energy peak of the subsurface for the (100) plane body compared to the (111) plane body is a little higher, which is attributed to that, the subsurface atoms of the latter weaken its high stress easily by lattice slip and decrease its energy. The changing details of subsurface atoms energy are recorded which are shown in Figure 8 in the nanoscratching process.

Figure 8 Atoms snapshot of the subsurface for (111) body at different time during scratching process (a) 30 ps (b) 117 ps (see online version for colours)

(a) (b)

Note: Atoms colour shown depends on its energy, arrow denotes scratching direction

Figure 8(a) shows the snapshot of subsurface atoms at scratching 30 ps, it is clear that the energy of the external surface atoms is higher than the inner atoms, but the inner atoms beneath the tool show the high energy state, which is attributed to the scratching action of the tool. When the tool is going out from the workpiece, the energy states of subsurface atoms are shown in Figure 8(b). The energy states of the inner atoms in the subsurface of the latter are clearly higher than that of the former. It is notable that the high energy atoms exist in the tool withdrawal position. With the progress of the nanoscratching

6.56 eV

y [111]

x [10-1]z [1-21]

x [10-1]

y [111]

x [1-21]

1.39 eV


process, it also can be seen from Figures 8(a) to 8(b) that nanoscratching process results in the extension of the high energy atoms from the subsurface near the tool to the whole subsurface. The inner temperature of workpiece depends on the energy of atoms, which indicates the nanomachining process results in the increase of subsurface atoms energy and causes the increase of temperature. As the energy of the subsurface atoms in area that the tool goes out is higher than in other area, the temperature in there from nanoscratching process is also high naturally.

As a matter of fact, the nanoscratching process is accompanied by lots of defects and the residual defects result in residual stresses within the machined nanostructure. Residual stress can be achieved according to equation (9). Figure 9 shows the residual stress in subsurface of the (100) plane body and (111) plane body, respectively.

Figure 9 Residual stress of the subsurface after scratching process (a) (100) body (b) (111) body (see online version for colours)

(a) (b)

Note: The unit of stress (GPa)

The higher atoms energy generally corresponds to the higher atomic stress. It can be seen from Figures 8(b) and 9(b) that the area of the higher energy in subsurface is basically in consistence with that of the higher residual stress. It is also of interest to see that the residual stress of the subsurface in the (100) plane body is higher than that in the (111) plane, which is due to more defects of the subsurface, such as vacancy, in the (100) plane body. Meanwhile, the high residual stress in subsurface of the (111) plane body is released by the lattice slip.

4 Conclusions

The conclusions can be drawn as follows:

During nanoscratching, there is a clear accumulation and pileup of amorphous structural molecules ahead of the tool and a remarkable side flow on the left and right sides of the tool as the tool moves forward. Compared with the subsurface damaged layer of the (111) orientation, the number of defects such as vacancy for (100) orientation is larger than that for the (111) orientation, but the affected area for the latter is larger than that for the former and the atom-scale roughness for the latter is slightly well. It is noted that stack fault also exists in the subsurface for the latter

380 J. Chen et al.

case. The ordering degree decreases as the increase of scratching depths for both the former and the latter, but the latter is also better than that of the former after scratching process.

Nanoscratching process results in the increase of atoms averaged energy of the subsurface, but atoms averaged energy in the subsurface for the (100) plane body is higher than that for the (111) plane body and atoms averaged energy in the subsurface decreases in some extent after nanomachining process.

Nanoscratching process results in the extension of the high energy atoms from the subsurface near the tool to the whole subsurface. Withdrawal of the tool from the workpiece will generate edge collapse, burr and dislocation. Especially for (111) orientation workpiece, the withdrawing tool results in the stack fault. Meanwhile, tool withdrawal position exits the higher energy atoms in the subsurface of the workpiece, which is basically in consistence with the position of the higher residual stress. It is also noted that the residual stress in subsurface for the (100) plane body is higher than the case for the (111) plane body.

Acknowledgements

We would like to thank the National Natural Science Foundation of China under Contract No. 50675050, the Outstanding Youth Fund of Heilongjiang Province under Contract No. JC200614 and the Key Laboratory Open Foundation of Shenyang Jianzhu University under Contract No. JX200707 for their financial supports.

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