## Abstract

The tribological performance of hydrogenated diamond-like carbon (DLC) coatings is studied by molecular dynamics simulations employing a screened reactive bond-order potential that has been adjusted to reliably describe bond-breaking under shear. Two types of DLC films are grown by CH_{2} deposition on an amorphous substrate with 45 and 60 eV impact energy resulting in 45 and 30% H content as well as 50 and 30% sp^{3} hybridization of the final films, respectively. By combining two equivalent realizations for both impact energies, a hydrogen-depleted and a hydrogen-rich tribo-contact is formed and studied for a realistic sliding speed of 20 m s^{−1} and loads of 1 and 5 GPa. While the hydrogen-rich system shows a pronounced drop of the friction coefficient for both loads, the hydrogen-depleted system exhibits such kind of running-in for 1 GPa, only. Chemical passivation of the DLC/DLC interface explains this running-in behavior. Fluctuations in the friction coefficient occurring at the higher load can be traced back to a cold welding of the DLC/DLC tribo-surfaces, leading to the formation of a transfer film (transferred from one DLC partner to the other) and the establishment of a new tribo-interface with a low friction coefficient. The presence of a hexadecane lubricant leads to low friction coefficients without any running-in for low loads. At 10 GPa load, the lubricant starts to degenerate resulting in enhanced friction.

This is a preview of subscription content, log in to check access.

## References

- 1.
Robertson, J.: Diamond-like amorphous carbon. Mater. Sci. Eng. R

**37**, 129–281 (2002) - 2.
Erdemir, A., Donnet, C.: Tribology of diamond-like carbon films: recent progress and future prospects. J. Phys. D: Appl. Phys.

**39**, R311–R327 (2006) - 3.
Ferrari, A.C.: Diamond-like carbon for magnetic storage disks. Surf. Coat. Technol.

**180-181**, 190–206 (2004) - 4.
Brand, J., Beckmann, C., Blug, B., Konrath, G., Hollstein, T.: Diamond-like carbon coatings—a new design element for tribological applications. Ind. Lubr. Tribol.

**54**, 291–295 (2002) - 5.
Maboudian, R.: Adhesion and friction issues associated with reliable operation of MEMS. MRS Bullet.

**23**, 47–51 (1998) - 6.
Sullivan, J.P., Friedmann, T.A., Hjort, K.: Diamond and amorphous carbon MEMS. MRS Bull.

**26**, 309–311 (2001) - 7.
Fontaine, J., Le Mogne, T., Loubet, J. L., Belin, M.: Achieving superlow friction with hydrogenated amorphous carbon: some key requirements. Thin Solid Films

**482**, 99–108 (2005) - 8.
Erdemir, A., Eryilmaz, O. L., Fenske, G.: Synthesis of diamondlike carbon films with superlow friction and wear properties. J. Vac. Sci. Technol. A

**18**, 1987–1992 (2000) - 9.
Donnet, C., Belin, M., Augé, J.C., Martin, J.M., Grill, A., Patel, V.: Tribochemistry of diamond-like carbon coatings in various environments. Surf. Coat. Technol.

**68–69**, 626–631 (1994) - 10.
Moseler, M., Gumbsch, P., Casiraghi, C., Ferrari, A.C., Robertson, J.: The ultrasmoothness of diamond-like carbon surfaces. Science

**309**, 1545–1548 (2005) - 11.
Harrison, J.A., Schall, J.D., Knippenberg, M.T., Gao, G., Mikulski, P.T.: Elucidating atomic-scale friction using molecular dynamics and specialized analysis techniques. J. Phys. Condens. Matter.

**20**, 354009 (2008) - 12.
Harrison, J.A., Gao, G., Schall, J.D., Knippenberg, M.T., Mikulski, P.T.: Friction between solids. Philos. Trans. R. Soc. A

**366**, 1469–1495 (2008) - 13.
Knippenberg, M.T., Mikulski, P.T., Dunlap, B.I., Harrison, J.A.: Atomic contributions to friction and load for tip–self-assembled monolayers interactions. Phys. Rev. B

**78**, 235409 (2008) - 14.
Mikulski, P.T., Herman, L.A., Harrison, J.A.: Odd and even model self-assembled monolayers: links between friction and structure. Langmuir

**21**, 12197–12206 (2005) - 15.
Gao, G.T., Mikulski, P.T., Harrison, J.A.: Molecular-scale tribology of amorphous carbon coatings: effects of film thickness, adhesion, and long-range interactions. J. Am. Chem. Soc.

**124**, 7202–7209 (2002) - 16.
Pastewka, L., Moser, S., Moseler, M., Blug, B., Meier, S., Hollstein, T., Gumbsch, P.: The running-in of amorphous hydrocarbon tribocoatings: a comparison between experiment and molecular dynamics simulations. Int. J. Mater. Res.

**99**, 1136–1143 (2008) - 17.
Allen, M.P., Tildesley, D.J.: Computer Simulation of Liquids. Oxford University Press, Oxford (1989)

- 18.
Finnis, M.W.: Interatomic Forces in Condensed Matter. Oxford University Press, Oxford (2004)

- 19.
Kohn, W., Sham, L.J.; Self-consistent equations including exchange and correlation effects. Phys. Rev.

**140**, A1133–A1138 (1965) - 20.
Tersoff, J.: New empirical model for the structural properties of silicon. Phys. Rev. Lett.

**56**, 632–635 (1986) - 21.
Abell, G.C.: Empirical chemical pseudopotential theory of molecular and metallic bonding. Phys. Rev. B

**31**, 6184–6196 (1985) - 22.
Brenner, D.W.: Empirical potential for hydrocarbons for use in simulating chemical vapor deposition of diamond films. Phys. Rev. B

**42**, 9458–9471 (1990) - 23.
Brenner, D.W., Shenderova, O.A., Harrison, J.A., Stuart, S.J., Ni B., Sinnott, S.B.: A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys. Condens. Matter.

**14**, 783–802 (2002) - 24.
Marder M. Molecular dynamics of cracks. Comput. Sci. Eng.

**1**(5), 48–55 (1999) - 25.
Pastewka, L., Pou, P., Pérez, R., Gumbsch, P., Moseler, M.: Describing bond-breaking processes by reactive potentials: importance of an environment-dependent interaction range. Phys. Rev. B

**78**, 161402(R) (2008) - 26.
Mattoni, A., Ippolito, M., Colombo, L.: Atomistic modeling of brittleness in covalent materials. Phys. Rev. B

**76**, 224103 (2007) - 27.
Baskes, M.I., Angelo, J.E., Bisson, C.L.: Atomistic calculations of composite interfaces. Modell. Simul. Mater. Sci. Eng.

**2**, 505–518 (1994) - 28.
Jäger, H.U., Albe, K.: Molecular-dynamics simulations of steady-state growth of ion-deposited tetrahedral amorphous carbon films. J. Appl. Phys.

**88**, 1129–1135 (2000) - 29.
Kumagai, T., Hara, S., Choi, J., Izumi, S., Kato, T.: Development of empirical bond-order-type interatomic potential for amorphous carbon structures. J. Appl. Phys.

**105**, 064310 (2009) - 30.
Adelman, S.A., Doll, J.D.: Generalized langevin equation approach for atom/solid-surface scattering: general formulation for classical scattering of harmonic solids. J. Chem. Phys.

**64**, 2375–2388 (1976) - 31.
Franzblau, D.S.: Computation of ring statistics for network models of solids. Phys. Rev. B

**44**, 4925–4930 (1991) - 32.
Thompson, P.A., Robbins, M.O.: Shear flow near solids: epitaxial order and flow boundary conditions. Phys. Rev. A

**41**, 6830 (1990) - 33.
Persson, B.N.J. Sliding Friction. Springer, Berlin (2000)

- 34.
Stuart, S.J., Tutein, A.T., Harrison, J.A.: A reactive potential for hydrocarbons with intermolecular interactions. J. Chem. Phys.

**112**, 6472–6486 (2000) - 35.
Mortensen, J.J., Hansen, L.W., Jacobsen, K.W.: Real-space grid implementation of the projector augmented wave method. Phys. Rev. B

**71**, 035109 (2005) - 36.
Dienwiebel, M., Verhoeven, G.S., Pradeep, N., Frenken, J.W.M., Heimberg, J.A., Zandbergen, H.W.: Superlubricity of graphite. Phys. Rev. Lett.

**92**, 126101 (2004) - 37.
Gupta, B.K., Malshe, A., Bhushan, B., Subramaniam, V.V.: Friction and wear properties of chemomechanically polished diamond films. J. Tribol.

**116**, 445–453 (1994) - 38.
Lo, S.-W., Tsai, S.-D.: Real-time observation of the evolution of contact area under boundary lubrication in sliding contact. J. Tribol.

**124**, 229–238 (2002) - 39.
Öttinger, H.C.: Beyond Equilibrium Thermodynamics. Wiley, New York (2005)

- 40.
Zwanzig, R.: Nonequilibrium Statistical Mechanics. Oxford University Press, Oxford (2001)

- 41.
Grabert, H.; Projection Operator Techniques in Nonequilibrium Statistical Mechanics. Springer, Berlin (1982)

- 42.
Svahn, F., Kassman-Rudolphi, Å., Hogmark, S.: On the effect of surface topography and humidity on lubricated running-in of a carbon based coating. Wear

**261**, 1237–1246 (2006) - 43.
Kohlhoff, S., Gumbsch, P., Fischmeister, H.F.: Crack propagation in b.c.c. crystals studied with a combined finite-element and atomistic model. Philos. Mag. A

**64**, 851–878 (1991) - 44.
Campañá, C., Müser, M.H.: Practical green’s function approach to the simulation of elastic semi-infinite solids. Phys. Rev. B

**74**, 075420 (2006)

## Acknowledgment

We thank the BMBF for funding this study within project OTRISKO. Computations were carried out on the clusters Hercules (Fh-ITWM), O2 (Fh-EMI), and Joe1 (Fh-IWM) within the Fraunhofer Society.

## Author information

## Appendix

### Appendix

### Pressure Coupling Algorithm

MD simulations only probe short-wavelength behavior and thus only model a representative element of the whole tribo-system, in our case the contact of two asperities. Since such a system is always open, the choice of boundary conditions, both thermal and mechanical, is crucial. In order to provide a realistic mechanical boundary, the distance between the two sliding surfaces needs to adjust according to the local pressure. Inertia and elastic moduli of the *bulk* material, which is not explicitly included in our MD simulations, resist this adjustment. By simply imposing a normal pressure on the simulation cell, these inertial and elastic contributions to pressure fluctuation within the representative cell are ignored. Hence, fluctuations will be suppressed leading to improper conditions within the representative volume element. On the other hand, fixing the distance of the two sliding partners can also lead to improper conditions due to stress accumulation within the sample. Here, we assume that the process of adjusting the bulk separation is dominated by the inertia of the sliding partners. Fixing the 0.3 nm top- and bottommost atoms, and increasing these rigid layers’ total mass *M*, models inertia effects (see Fig. 2). The finite periodic cell introduces short-wavelength fluctuations with a characteristic time scale of *t*
_{c} = *l*
*v*
^{−1} into the system, where *v* is the sliding velocity and *l* is the repetition length. We thus damp the normal movement of the top rigid layer with total mass *M* by adding a normal force of *F*
_{
z
} = *F*
_{ext} − γ*v*
_{
z
}. Here, *v*
_{
z
} is the rigid layer’s normal velocity and *F*
_{ext} is given by *F*
_{ext} = *p*
*A*, where* A* is the cross section of the cell parallel to the sliding direction and *p* the target pressure.

A guide to choose the free parameters *M* and γ can be obtained by estimating the response of the bulk separation, i.e., the separation of the top and bottom rigid slab of atoms, during sliding. Let us approximately decompose the normal response of the molecular simulation cell into a linear elastic component with spring constant *k* and an additional fluctuating force *F*
_{int}. The force *F*
_{int}(*t*) fluctuates with zero mean and is due to the sliding contact’s local topography and chemistry—it includes all contributions which are not captured by the linear elastic component. The distance *h*
_{
z
}(*t*) of the two sliding partners then evolves according to the differential equation

which is identical to that of a damped harmonic oscillator. Fourier transformation immediately yields the transfer function in frequency space

which describes the response of the separation distance *h*
_{
z
} to the fluctuating force *F*
_{int} as a function of frequency ω. The high-frequency limit of *F*
_{int}(ω) is unknown a priori; however, we know that fluctuations with a characteristic time scale of *t*
_{c} are introduced due to the periodic boundary conditions. All frequencies above ω_{c} = 2π*t*
_{c}
^{−1}
should not lead to a change in bulk separation and thus a change in the system’s integral density. We expect phase-transformations in the sliding partners, which should be able to change the bulk separation, to occur at frequencies below ω_{c}.

Two conditions are imposed: The system should be driven in the anharmonic limit to avoid resonances without overdamping; all frequency above and including ω_{c} should be cut-off. The first condition leads to

We fix the second parameter by choosing *f*(ω_{c}) = *p*
_{c}
*f*(0) where the empirical cut-off parameter *p*
_{c} is set to *p*
_{c} = 1%. This gives a total mass of

The resulting transfer function with the appropriate parameters for our systems is shown in the inset of Fig. 2. Frequencies up to half the recurrence frequency ω_{c} are efficiently damped. A movement of the two sliding partners is however not hindered as we confirmed by checking the normal pressure in the system, which reaches the prescribed value after typically 5 ns.

The considerations which lead to the mass *M* and dissipation constant γ should be regarded as order-of-magnitude considerations only. When going to larger sample sizes more sophisticated schemes will be necessary which also include the elastic response of the bulk material [44]. However, we expect that the elastic response of the bulk material which is explicitly included in our MD simulations supplies sufficient elasticity when the aspect ratio of the cell size along the sliding direction to the cell size perpendicular to the sliding plane is smaller than unity.

## Rights and permissions

## About this article

### Cite this article

Pastewka, L., Moser, S. & Moseler, M. Atomistic Insights into the Running-in, Lubrication, and Failure of Hydrogenated Diamond-Like Carbon Coatings.
*Tribol Lett* **39, **49–61 (2010). https://doi.org/10.1007/s11249-009-9566-8

Received:

Accepted:

Published:

Issue Date:

### Keywords

- Running-in
- Coatings
- Friction-reducing
- Boundary lubrication
- Friction mechanisms
- Unlubricated friction
- Carbon