Supplementary Materials

Large-scale molecular dynamics simulation of

wear in diamond-like carbon at the nanoscale Zhen-Dong Sha1, Viacheslav Sorkin1, Paulo S. Branicio1, Qing-Xiang Pei1, Yong-Wei Zhang1,* ,

and David J. Srolovitz1, 2**

1Institute of High Performance Computing, A*STAR, 138632, Singapore2Departments of Materials Science & Engineering and Mechanical Engineering & Applied Mechan-

ics, University of Pennsylvania, Philadelphia, PA 19104, USA

Molecular dynamics (MD) simulations were performed using the large-scale

atomic/molecular massively parallel simulator (LAMMPS) code.1 The essential part of MD

simulations is a reliable force field (empirical interatomic potential function). In the present

work, we employed a Tersoff potential with an extended cutoff and van der Waals interactions to

model the non-hydrogenated diamond-like carbon (DLC).2 This potential together with three

other potentials for DLC, the second generation reactive empirical bond order (REBO), the

standard Tersoff, and the Tersoff/ZBL, were evaluated by comparison with experimental data

and first-principle calculations.2 It was shown that the Tersoff potential with the extended cutoff

most successfully reproduced the first-principles and experimental structural and mechanical

data for DLC.2 Hence, in the present work, we employed this potential to study wear

mechanisms and laws.

** E-mail address: zhangyw@ihpc.a-star.edu.sg*** E-mail address: srol@seas.upenn.edu

1

Although the Tersoff potential describes the formation and rupture of chemical bonds, it

does not consider the dispersive forces. In the present work, we integrate the modified Tersoff

potential with the van der Waals (vdW) potential:3,4

E=12∑i ∑

j ≠i[Eij

Tersoff+EijvdW¿¿] ,(1)¿¿

where

EijvdW=¿, (2)

and the cn , k are cubic spline coefficients and for C-C interactions ε = 2.84 meV and σ = 3.4 Å. 5,6

It should be noted that this composite potential allows for the formation and rupture of chemical

bonds and non-bonded interactions at the contact interface, making it suitable to study wear. One

should note that the present work is fundamentally different from “wearless” nanoscale contacts

studied in previous MD simulations focussed on friction.7,8

In the present MD simulations, the system consisted of a flat non-hydrogenated DLC

sample and a hemispherical non-hydrogenated DLC (asperity) tip at the density of 2.9 g/cm3.

The tip had a height of 3 nm and radius of 4 nm and contained 12,058 atoms. The tip was

prepared by cutting the hemisphere from a bulk DLC sample (Fig. S1). Note that this tip was

similar to that used in recent wear experiments.9 The tip was first relaxed at 0 K using molecular

statics simulations to minimize its total energy. Subsequently the tip was gradually heated to and

equilibrated at 300 K. A 0.5 nm thick layer near the base of the hemispherical tip was rigidly

held during the simulations in order to maintain the prescribed normal load and sliding rate.

Similarly, the contact pad (see Fig. S1) was prepared by cutting a slab from a bulk DLC sample,

statically relaxed at 0K, and gradually heating to and equilibrating at 300 K. The pad contained

2

1,568,360 atoms and dimensions 45 nm × 45 nm × 5 nm. The bottom 1 nm of the DLC contact

pad was held fixed during the simulations. Periodic boundary conditions were applied in the

directions perpendicular to the contact pad surface.

An indentation simulation was first performed at 300 K in order to determine the normal

load (Tn) vs. penetration depth (h) relation. To do so, the tip was driven towards the contact pad

at 1.0 m/s – slow enough to allow the decay of most transients.10 The normal load was calculated

as the sum of the normal forces on the atoms within the top 0.5nm layer of the tip. The indentation

depth was defined as the difference between the lowest point of the tip and the initial, highest

position of the contact pad surface. The obtained normal load (Tn) vs. penetration depth (h)

relation is shown in Fig. S2.

Simulations of the lateral sliding with an externally applied constant normal load were

performed at 300 K. The external normal load was applied to the top 0.5 nm thick rigid layer of the

tip in order to keep the overall force on this layer at zero. Prior to the lateral sliding, the normal load

was applied for 30 ps to allow for the decay of transients. Then a fixed lateral velocity of 20 m/s was

applied to the top 0.5 nm thick rigid layer of the tip, while its normal velocity and position (in the z-

direction) were not constrained to ensure a constant normal load. The sliding velocity is much larger

than the typical velocities in scanning force microscopy (SFM) experiments, but comparable to

the operating conditions in some micromechanical systems (MEMS).8 Previous studies 7 have

also demonstrated that the magnitude of the sliding force and the observed law and mechanisms

depend weakly on sliding velocity. In the sliding simulations, we recorded the instantaneous

lateral forces. The lateral forces were obtained by averaging the instantaneous lateral forces over

a sliding distance.

3

We have also performed MD simulations on the loading and unloading processes during

indentation to investigate the plastic (irreversible) deformation of the tip within the normal load

range. In our work, the final distance between the tip and the substrate is about 0.6 Å and -0.5 Å for

the normal load of 4 nN and 104 nN, respectively. When the distance between the tip and the

substrate is -0.5 Å (i.e., the penetration depth reaches around 0.5 Å), we unload the tip at a very slow

velocity, as shown in Fig. S3. We find that after the unloading, the tip is able to fully recover its

original shape, indicating that there is no plastic (irreversible) deformation in the tip.

REFERENCES

1 S. Plimpton, J. Comput. Phys. 117, 1-19 (1995).2 Z. D. Sha, P. S. Branicio, V. Sorkin, Q. X. Pei, and Y. W. Zhang, Comp. Mater. Sci. 67,

146-150 (2013).3 K. M. Liew, X. Q. He, and C. H. Wong, Acta Mater. 52, 2521-2527 (2004).4 Z. G. Mao, A. Garg, and S. B. Sinnott, Nanotechnology 10, 273-277 (1999).5 D. W. Brenner, Phys. Rev. B 42, 9458-9471 (1990).6 D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Ni, and S. B. Sinnott, J.

Phys-Condens. Mat. 14, 783-802 (2002).7 Y. F. Mo and I. Szlufarska, Phys. Rev. B 81, 035405 (2010).8 Y. F. Mo, K. T. Turner, and I. Szlufarska, Nature 457, 1116-1119 (2009).9 B. Gotsmann and M. A. Lantz, Phys. Rev. Lett. 101, 125501 (2008).10 I. Szlufarska, R. K. Kalia, A. Nakano, and P. Vashishta, J. Appl. Phys. 102, 023509

(2007).

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Fig. S1. Atomistic models of the hemispherical DLC tip and the flat DLC contact pad.

Temperature is held at 300K. The atoms in the top 0.5 nm thick layer of the tip (brown) are

rigidly held/moved and the bottom 1 nm thick layer of the contact pad (dark blue) are rigidly

held. The remaining atoms (yellow and light blue) displace dynamically according to the MD

equations of motion.

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Fig. S2. The normal load (Tn) vs. penetration depth (h) relation obtained in a typical indentation

simulation at 300 K.

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Fig. S3: The tip deformation at the normal loads range. The arrows indicate the motion of the tip. For

clarity, the substrate is represented by the dotted line. h is the penetration depth.

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